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Diffstat (limited to 'src/boost/libs/math/reporting')
119 files changed, 58811 insertions, 0 deletions
diff --git a/src/boost/libs/math/reporting/accuracy/Jamfile.v2 b/src/boost/libs/math/reporting/accuracy/Jamfile.v2 new file mode 100644 index 000000000..7227a2fed --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/Jamfile.v2 @@ -0,0 +1,161 @@ +# Copyright Daryle Walker, Hubert Holin, John Maddock 2006 - 2007 +# copyright Paul A. Bristow 2006 - 2010 +# Distributed under the Boost Software License, Version 1.0. +# (See accompanying file LICENSE_1_0.txt or copy at +# http://www.boost.org/LICENSE_1_0.txt. +# \math_toolkit\libs\math\test\jamfile.v2 +# Runs all math toolkit tests, functions & distributions, +# and build math examples. + +# bring in the rules for testing +import testing ; +import modules ; +import path ; +import pch ; +import ../../../config/checks/config : requires ; +using quickbook ; +using auto-index ; + +project + : requirements + <include>../../include_private + ; + +if $(is_unix) +{ + local osname = [ SHELL uname ] ; + + switch $(osname) + { + case "Sun*" : OTHERFLAGS = "-lpthread -lrt" ; + case "*BSD*" : OTHERFLAGS = "-lpthread" ; + } +} + +# +# Configuration first: +# +lib gsl ; +lib gslcblas ; +lib Rmath ; +obj has_cxx17_cmath : has_cxx17_cmath.cpp ; +explicit has_cxx17_cmath ; +obj has_c99_cmath : has_c99_cmath.cpp ; +explicit has_c99_cmath ; +exe has_gsl : has_gsl.cpp gsl gslcblas ; +explicit has_gsl ; +exe has_rmath : has_rmath.cpp Rmath ; +explicit has_rmath ; + +CEPHES_SOURCE = acosh.c airy.c asin.c asinh.c atan.c atanh.c bdtr.c beta.c +btdtr.c cbrt.c chbevl.c chdtr.c clog.c cmplx.c const.c +cosh.c dawsn.c drand.c ei.c ellie.c ellik.c ellpe.c ellpj.c ellpk.c +exp.c exp10.c exp2.c expn.c expx2.c fabs.c fac.c fdtr.c +fresnl.c gamma.c gdtr.c hyp2f1.c hyperg.c i0.c i1.c igami.c incbet.c +incbi.c igam.c isnan.c iv.c j0.c j1.c jn.c jv.c k0.c k1.c kn.c kolmogorov.c +log.c log2.c log10.c lrand.c nbdtr.c ndtr.c ndtri.c pdtr.c planck.c +polevl.c polmisc.c polylog.c polyn.c pow.c powi.c psi.c rgamma.c round.c +shichi.c sici.c sin.c sindg.c sinh.c spence.c stdtr.c struve.c +tan.c tandg.c tanh.c unity.c yn.c zeta.c zetac.c +sqrt.c floor.c setprec.c mtherr.c ; + +path-constant here : . ; +make $(here)/third_party/cephes_double/acosh.c : : @check_exists ; +actions check_exists +{ + stat $(<) +} +explicit $(here)/third_party/cephes_double/acosh.c ; + +lib cephes_double : $(here)/third_party/cephes_double/$(CEPHES_SOURCE) + : + release + <link>static + [ check-target-builds $(here)/third_party/cephes_double/acosh.c : : <build>no ] + ; + +explicit cephes_double ; + +rule all-tests { + local result ; + for local source in [ glob test*.cpp ] + { + result += [ run $(source) /boost/regex//boost_regex /boost/system /boost/filesystem /boost/test//boost_unit_test_framework + : : : + [ check-target-builds has_gsl : <define>ALWAYS_TEST_DOUBLE : ] + <target-os>linux:<linkflags>-lpthread + <target-os>linux:<linkflags>-lrt + <toolset>gcc:<linkflags>$(OTHERFLAGS) ] + ; + result += [ run $(source) /boost/regex//boost_regex /boost/system /boost/filesystem /boost/test//boost_unit_test_framework + : : : [ check-target-builds has_cxx17_cmath : <define>TEST_CXX17_CMATH : <build>no ] + <target-os>linux:<linkflags>-lpthread + <target-os>linux:<linkflags>-lrt + <toolset>gcc:<linkflags>$(OTHERFLAGS) + : $(source:B)_cxx17_cmath ] + ; + result += [ run $(source) /boost/regex//boost_regex /boost/system /boost/filesystem /boost/test//boost_unit_test_framework + : : : [ check-target-builds has_c99_cmath : <define>TEST_C99 : <build>no ] + <target-os>linux:<linkflags>-lpthread + <target-os>linux:<linkflags>-lrt + <toolset>gcc:<linkflags>$(OTHERFLAGS) + : $(source:B)_c99 ] + ; + result += [ run $(source) /boost/regex//boost_regex /boost/system /boost/filesystem /boost/test//boost_unit_test_framework gsl gslcblas + : : : [ check-target-builds has_gsl : <define>TEST_GSL : <build>no ] + <target-os>linux:<linkflags>-lpthread + <target-os>linux:<linkflags>-lrt + <toolset>gcc:<linkflags>$(OTHERFLAGS) + : $(source:B)_gsl ] + ; + result += [ run $(source) /boost/regex//boost_regex /boost/system /boost/filesystem /boost/test//boost_unit_test_framework Rmath + : : : [ check-target-builds has_rmath : <define>TEST_RMATH : <build>no ] + <target-os>linux:<linkflags>-lpthread + <target-os>linux:<linkflags>-lrt + <toolset>gcc:<linkflags>$(OTHERFLAGS) + : $(source:B)_rmath ] + ; + result += [ run $(source) /boost/regex//boost_regex /boost/system /boost/filesystem /boost/test//boost_unit_test_framework cephes_double + : : : [ check-target-builds $(here)/third_party/cephes_double/acosh.c : <define>TEST_CEPHES <source>cephes_double : <build>no ] + <target-os>linux:<linkflags>-lpthread + <target-os>linux:<linkflags>-lrt + <toolset>gcc:<linkflags>$(OTHERFLAGS) + : $(source:B)_cephes ] + ; + } + return $(result) ; +} + +test-suite report_gen : [ all-tests ] ; + +path-constant images_location : html ; +path-constant here : . ; + +xml report : doc/report.qbk : <dependency>report_gen ; +boostbook standalone + : + report + : + # Path for links to Boost: + <xsl:param>boost.root=../../../../.. + + # Some general style settings: + <xsl:param>table.footnote.number.format=1 + <xsl:param>footnote.number.format=1 + <xsl:param>html.stylesheet=http://www.boost.org/doc/libs/1_58_0/doc/src/boostbook.css + + # HTML options first: + # Use graphics not text for navigation: + <xsl:param>navig.graphics=1 + # How far down we chunk nested sections, basically all of them: + <xsl:param>chunk.section.depth=0 + # Don't put the first section on the same page as the TOC: + <xsl:param>chunk.first.sections=0 + # How far down sections get TOC's + <xsl:param>toc.section.depth=2 + # Max depth in each TOC: + <xsl:param>toc.max.depth=4 + # How far down we go with TOC's + <xsl:param>generate.section.toc.level=10 + ; + diff --git a/src/boost/libs/math/reporting/accuracy/bindings.hpp b/src/boost/libs/math/reporting/accuracy/bindings.hpp new file mode 100644 index 000000000..f2d49a034 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/bindings.hpp @@ -0,0 +1,765 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef BOOST_MATH_BINDINGS +#define BOOST_MATH_BINDINGS + +#define ERROR_REPORTING_MODE +#include <stdexcept> + +#if TEST_CXX17_CMATH + +#include <cmath> + +#define TEST_LIBRARY_NAME "<cmath>" + +#define LOG1P_FUNCTION_TO_TEST std::log1p +#define EXPM1_FUNCTION_TO_TEST std::expm1 + +#define CBRT_FUNCTION_TO_TEST std::cbrt +#define ERF_FUNCTION_TO_TEST std::erf +#define ERFC_FUNCTION_TO_TEST std::erfc + +#define LGAMMA_FUNCTION_TO_TEST std::lgamma +#define TGAMMA_FUNCTION_TO_TEST std::tgamma + +#define BESSEL_I_FUNCTION_TO_TEST std::cyl_bessel_i +#define BESSEL_IN_FUNCTION_TO_TEST std::cyl_bessel_i +#define BESSEL_J_FUNCTION_TO_TEST std::cyl_bessel_j +#define BESSEL_JN_FUNCTION_TO_TEST std::cyl_bessel_j +#define BESSEL_JS_FUNCTION_TO_TEST std::sph_bessel +#define BESSEL_K_FUNCTION_TO_TEST std::cyl_bessel_k +#define BESSEL_KN_FUNCTION_TO_TEST std::cyl_bessel_k +#define BESSEL_Y_FUNCTION_TO_TEST std::cyl_neumann +#define BESSEL_YN_FUNCTION_TO_TEST std::cyl_neumann +#define BESSEL_YS_FUNCTION_TO_TEST std::sph_neumann + +#define BETA_FUNCTION_TO_TEST std::beta + +#define ELLINT_1_FUNCTION_TO_TEST std::ellint_1 +#define ELLINT_1C_FUNCTION_TO_TEST std::comp_ellint_1 +#define ELLINT_2_FUNCTION_TO_TEST std::ellint_2 +#define ELLINT_2C_FUNCTION_TO_TEST std::comp_ellint_2 +#define ELLINT_3_FUNCTION_TO_TEST std::ellint_3 +#define ELLINT_3C_FUNCTION_TO_TEST std::comp_ellint_3 + +#define EI_FUNCTION_TO_TEST std::expint + +#define LAGUERRE_FUNCTION_TO_TEST std::laguerre +#define ASSOC_LAGUERRE_FUNCTION_TO_TEST std::assoc_laguerre + +inline long double legendre_p_binder(int i, long double d) +{ + if(i < 0) + throw std::domain_error("order parameters less than 0 not supported in TR1"); + return std::legendre(i, d); +} +inline long double assoc_legendre_p_binder(int i, int j, long double d) +{ + if((i < 0) || (j < 0)) + throw std::domain_error("order parameters less than 0 not supported in TR1"); + return std::assoc_legendre(i, j, d); +} + +#define LEGENDRE_P_FUNCTION_TO_TEST legendre_p_binder +#define LEGENDRE_PA_FUNCTION_TO_TEST assoc_legendre_p_binder +#define ZETA_FUNCTION_TO_TEST std::riemann_zeta + +#define TYPE_TO_TEST long double + +#elif defined(TEST_C99) + +#include <math.h> + +#define TEST_LIBRARY_NAME "<math.h>" + +#ifdef _MSC_VER + +#define LOG1P_FUNCTION_TO_TEST ::log1p +#define EXPM1_FUNCTION_TO_TEST ::expm1 + +#define CBRT_FUNCTION_TO_TEST ::cbrt +#define ERF_FUNCTION_TO_TEST ::erf +#define ERFC_FUNCTION_TO_TEST ::erfc + +#define LGAMMA_FUNCTION_TO_TEST ::lgamma +#define TGAMMA_FUNCTION_TO_TEST ::tgamma +#define BESSEL_JN_FUNCTION_TO_TEST ::jn +#define BESSEL_YN_FUNCTION_TO_TEST ::yn + +#define TYPE_TO_TEST double + +#else + +#define LOG1P_FUNCTION_TO_TEST ::log1pl +#define EXPM1_FUNCTION_TO_TEST ::expm1l + +#define CBRT_FUNCTION_TO_TEST ::cbrtl +#define ERF_FUNCTION_TO_TEST ::erfl +#define ERFC_FUNCTION_TO_TEST ::erfcl + +#define LGAMMA_FUNCTION_TO_TEST ::lgammal +#define TGAMMA_FUNCTION_TO_TEST ::tgammal +//#define BESSEL_JN_FUNCTION_TO_TEST ::jnl +//#define BESSEL_JN_FUNCTION_TO_TEST ::ynl + +#define TYPE_TO_TEST long double +#endif + +#elif defined(TEST_GSL) + +#include <stdexcept> + +#include <gsl/gsl_sf.h> +#include <gsl/gsl_errno.h> +#include <gsl/gsl_version.h> + +#define TEST_LIBRARY_NAME "GSL " GSL_VERSION + +void gsl_handler(const char * reason, const char * file, int line, int gsl_errno) +{ + if(gsl_errno == GSL_ERANGE) return; // handle zero or infinity in our test code. + throw std::domain_error(reason); +} + +struct gsl_error_handler_setter +{ + gsl_error_handler_t * old_handler; + gsl_error_handler_setter() + { + old_handler = gsl_set_error_handler(gsl_handler); + } + ~gsl_error_handler_setter() + { + gsl_set_error_handler(old_handler); + } +}; + +static const gsl_error_handler_setter handler; + +inline double gsl_bessel_ys(unsigned i, double d) +{ + return gsl_sf_bessel_yl(i, d); +} + +inline double gsl_bessel_js(unsigned i, double d) +{ + return gsl_sf_bessel_jl(i, d); +} + +//#define CBRT_FUNCTION_TO_TEST boost::cbrt +#define ERF_FUNCTION_TO_TEST gsl_sf_erf +#define ERFC_FUNCTION_TO_TEST gsl_sf_erfc +//#define ERF_INV_FUNCTION_TO_TEST boost::math::erf_inv +//#define ERFC_INV_FUNCTION_TO_TEST boost::math::erfc_inv + +#define LGAMMA_FUNCTION_TO_TEST gsl_sf_lngamma +#define TGAMMA_FUNCTION_TO_TEST gsl_sf_gamma +//#define TGAMMA1PM1_FUNCTION_TO_TEST boost::math::tgamma1pm1 + +#define BESSEL_I_FUNCTION_TO_TEST gsl_sf_bessel_Inu +#define BESSEL_IN_FUNCTION_TO_TEST gsl_sf_bessel_In +//#define BESSEL_IP_FUNCTION_TO_TEST boost::math::cyl_bessel_i_prime +//#define BESSEL_IPN_FUNCTION_TO_TEST boost::math::cyl_bessel_i_prime +#define BESSEL_J_FUNCTION_TO_TEST gsl_sf_bessel_Jnu +#define BESSEL_JN_FUNCTION_TO_TEST gsl_sf_bessel_Jn +#define BESSEL_JS_FUNCTION_TO_TEST gsl_bessel_js +//#define BESSEL_JP_FUNCTION_TO_TEST boost::math::cyl_bessel_j_prime +//#define BESSEL_JPN_FUNCTION_TO_TEST boost::math::cyl_bessel_j_prime +//#define BESSEL_JPS_FUNCTION_TO_TEST boost::math::sph_bessel_prime +#define BESSEL_K_FUNCTION_TO_TEST gsl_sf_bessel_Knu +#define BESSEL_KN_FUNCTION_TO_TEST gsl_sf_bessel_Kn +//#define BESSEL_KP_FUNCTION_TO_TEST boost::math::cyl_bessel_k_prime +//#define BESSEL_KPN_FUNCTION_TO_TEST boost::math::cyl_bessel_k_prime +#define BESSEL_Y_FUNCTION_TO_TEST gsl_sf_bessel_Ynu +#define BESSEL_YN_FUNCTION_TO_TEST gsl_sf_bessel_Yn +#define BESSEL_YS_FUNCTION_TO_TEST gsl_bessel_ys +//#define BESSEL_YP_FUNCTION_TO_TEST boost::math::cyl_neumann_prime +//#define BESSEL_YNP_FUNCTION_TO_TEST boost::math::cyl_neumann_prime +//#define BESSEL_YSP_FUNCTION_TO_TEST boost::math::sph_neumann_prime + +#define BETA_FUNCTION_TO_TEST gsl_sf_beta +//#define BINOMIAL_FUNCTION_TO_TEST boost::math::binomial_coefficient<T> + +inline double RC(double a, double b) +{ + return gsl_sf_ellint_RC(a, b, GSL_PREC_DOUBLE); +} +inline double RD(double a, double b, double c) +{ + return gsl_sf_ellint_RD(a, b, c, GSL_PREC_DOUBLE); +} +inline double RF(double a, double b, double c) +{ + return gsl_sf_ellint_RF(a, b, c, GSL_PREC_DOUBLE); +} +inline double RJ(double a, double b, double c, double d) +{ + return gsl_sf_ellint_RJ(a, b, c, d, GSL_PREC_DOUBLE); +} + + +#define ELLINT_RC_FUNCTION_TO_TEST RC +#define ELLINT_RD_FUNCTION_TO_TEST RD +#define ELLINT_RF_FUNCTION_TO_TEST RF +//#define ELLINT_RG_FUNCTION_TO_TEST boost::math::ellint_rg +#define ELLINT_RJ_FUNCTION_TO_TEST RJ + +#define DIGAMMA_FUNCTION_TO_TEST gsl_sf_psi + +inline double ellintK(double a) { return gsl_sf_ellint_Kcomp(a, GSL_PREC_DOUBLE); } +inline double ellintE(double a) { return gsl_sf_ellint_Ecomp(a, GSL_PREC_DOUBLE); } +inline double ellintP(double a, double b) { return gsl_sf_ellint_Pcomp(a, -b, GSL_PREC_DOUBLE); } + +inline double ellintF(double a, double b) { return gsl_sf_ellint_F(b, a, GSL_PREC_DOUBLE); } +inline double ellintE2(double a, double b) { return gsl_sf_ellint_E(b, a, GSL_PREC_DOUBLE); } +inline double ellintP3(double a, double b, double c) { return gsl_sf_ellint_P(c, a, -b, GSL_PREC_DOUBLE); } +inline double ellintD2(double a, double b) { return gsl_sf_ellint_D(b, a, GSL_PREC_DOUBLE); } + +#define ELLINT_1_FUNCTION_TO_TEST ellintF +#define ELLINT_1C_FUNCTION_TO_TEST ellintK +#define ELLINT_2_FUNCTION_TO_TEST ellintE2 +#define ELLINT_2C_FUNCTION_TO_TEST ellintE +#define ELLINT_3_FUNCTION_TO_TEST ellintP3 +#define ELLINT_3C_FUNCTION_TO_TEST ellintP +#define ELLINT_D2_FUNCTION_TO_TEST ellintD2 +//#define ELLINT_D1_FUNCTION_TO_TEST boost::math::ellint_d + +#define EI_FUNCTION_TO_TEST gsl_sf_expint_Ei +#define EN_FUNCTION_TO_TEST gsl_sf_expint_En + +//#define HERMITE_FUNCTION_TO_TEST boost::math::hermite +//#define HEUMAN_LAMBDA_FUNCTION_TO_TEST boost::math::heuman_lambda + +//#define BETA_INC_FUNCTION_TO_TEST boost::math::beta +//#define BETAC_INC_FUNCTION_TO_TEST boost::math::betac +#define IBETA_FUNCTION_TO_TEST gsl_sf_beta_inc +//#define IBETAC_FUNCTION_TO_TEST boost::math::ibetac +//#define IBETA_INV_FUNCTION_TO_TEST boost::math::ibeta_inv +//#define IBETAC_INV_FUNCTION_TO_TEST boost::math::ibetac_inv +//#define IBETA_INVA_FUNCTION_TO_TEST boost::math::ibeta_inva +//#define IBETAC_INVA_FUNCTION_TO_TEST boost::math::ibetac_inva +//#define IBETA_INVB_FUNCTION_TO_TEST boost::math::ibeta_invb +//#define IBETAC_INVB_FUNCTION_TO_TEST boost::math::ibetac_invb + +#define IGAMMA_FUNCTION_TO_TEST gsl_sf_gamma_inc +//#define IGAMMAL_FUNCTION_TO_TEST boost::math::tgamma_lower +#define GAMMAP_FUNCTION_TO_TEST gsl_sf_gamma_inc_P +#define GAMMAQ_FUNCTION_TO_TEST gsl_sf_gamma_inc_Q +//#define GAMMAP_INV_FUNCTION_TO_TEST boost::math::gamma_p_inv +//#define GAMMAQ_INV_FUNCTION_TO_TEST boost::math::gamma_q_inv +//#define GAMMAP_INVA_FUNCTION_TO_TEST boost::math::gamma_p_inva +//#define GAMMAQ_INVA_FUNCTION_TO_TEST boost::math::gamma_q_inva + +inline double sn(double k, double u) +{ + double s, c, d; + gsl_sf_elljac_e(u, k * k, &s, &c, &d); + return s; +} +inline double cn(double k, double u) +{ + double s, c, d; + gsl_sf_elljac_e(u, k * k, &s, &c, &d); + return c; +} +inline double dn(double k, double u) +{ + double s, c, d; + gsl_sf_elljac_e(u, k * k, &s, &c, &d); + return d; +} + +#define SN_FUNCTION_TO_TEST sn +#define CN_FUNCTION_TO_TEST cn +#define DN_FUNCTION_TO_TEST dn +//#define JACOBI_ZETA_FUNCTION_TO_TEST boost::math::jacobi_zeta + +inline double laguerre(unsigned n, unsigned m, double x){ return gsl_sf_laguerre_n(n, m, x); } +inline double laguerre_0(unsigned n, double x){ return gsl_sf_laguerre_n(n, 0, x); } + +#define LAGUERRE_FUNCTION_TO_TEST laguerre_0 +#define ASSOC_LAGUERRE_FUNCTION_TO_TEST laguerre + +inline double legendre_q(unsigned n, double x) { return gsl_sf_legendre_Ql(n, x); } + +#define LEGENDRE_P_FUNCTION_TO_TEST gsl_sf_legendre_Pl +#define LEGENDRE_Q_FUNCTION_TO_TEST legendre_q +#define LEGENDRE_PA_FUNCTION_TO_TEST gsl_sf_legendre_Plm + +#define POLYGAMMA_FUNCTION_TO_TEST gsl_sf_psi_n +//#define TGAMMA_RATIO_FUNCTION_TO_TEST boost::math::tgamma_ratio +//#define TGAMMA_DELTA_RATIO_FUNCTION_TO_TEST boost::math::tgamma_delta_ratio +//#define SIN_PI_RATIO_FUNCTION_TO_TEST boost::math::sin_pi +//#define COS_PI_RATIO_FUNCTION_TO_TEST boost::math::cos_pi +#define TRIGAMMA_RATIO_FUNCTION_TO_TEST gsl_sf_psi_1 +#define ZETA_FUNCTION_TO_TEST gsl_sf_zeta + +#define TYPE_TO_TEST double + +#elif defined(TEST_RMATH) + +#define MATHLIB_STANDALONE +#include <Rmath.h> + +#undef trunc + +#define TEST_LIBRARY_NAME "Rmath " R_VERSION_STRING + +#define LOG1P_FUNCTION_TO_TEST log1p +#define EXPM1_FUNCTION_TO_TEST expm1 + +//#define CBRT_FUNCTION_TO_TEST boost::math::cbrt +//#define ERF_FUNCTION_TO_TEST boost::math::erf +//#define ERFC_FUNCTION_TO_TEST boost::math::erfc +//#define ERF_INV_FUNCTION_TO_TEST boost::math::erf_inv +//#define ERFC_INV_FUNCTION_TO_TEST boost::math::erfc_inv + +#define LGAMMA_FUNCTION_TO_TEST lgammafn +#define TGAMMA_FUNCTION_TO_TEST gammafn +//#define TGAMMA1PM1_FUNCTION_TO_TEST boost::math::tgamma1pm1 + +inline double I(double n, double x) +{ + if (x < 0) + throw std::domain_error("Unsupported domain"); + return bessel_i(x, n, 1); +} +inline double K(double n, double x) { return bessel_k(x, n, 1); } +inline double J(double n, double x) +{ + if (x < 0) + throw std::domain_error("Unsupported domain"); + return bessel_j(x, n); +} +inline double Y(double n, double x) { return bessel_y(x, n); } + +#define BESSEL_I_FUNCTION_TO_TEST I +#define BESSEL_IN_FUNCTION_TO_TEST I +//#define BESSEL_IP_FUNCTION_TO_TEST boost::math::cyl_bessel_i_prime +//#define BESSEL_IPN_FUNCTION_TO_TEST boost::math::cyl_bessel_i_prime +#define BESSEL_J_FUNCTION_TO_TEST J +#define BESSEL_JN_FUNCTION_TO_TEST J +//#define BESSEL_JS_FUNCTION_TO_TEST boost::math::sph_bessel +//#define BESSEL_JP_FUNCTION_TO_TEST boost::math::cyl_bessel_j_prime +//#define BESSEL_JPN_FUNCTION_TO_TEST boost::math::cyl_bessel_j_prime +//#define BESSEL_JPS_FUNCTION_TO_TEST boost::math::sph_bessel_prime +#define BESSEL_K_FUNCTION_TO_TEST K +#define BESSEL_KN_FUNCTION_TO_TEST K +//#define BESSEL_KP_FUNCTION_TO_TEST boost::math::cyl_bessel_k_prime +//#define BESSEL_KPN_FUNCTION_TO_TEST boost::math::cyl_bessel_k_prime +#define BESSEL_Y_FUNCTION_TO_TEST Y +#define BESSEL_YN_FUNCTION_TO_TEST Y +//#define BESSEL_YS_FUNCTION_TO_TEST boost::math::sph_neumann +//#define BESSEL_YP_FUNCTION_TO_TEST boost::math::cyl_neumann_prime +//#define BESSEL_YNP_FUNCTION_TO_TEST boost::math::cyl_neumann_prime +//#define BESSEL_YSP_FUNCTION_TO_TEST boost::math::sph_neumann_prime + +#define BETA_FUNCTION_TO_TEST beta +//#define BINOMIAL_FUNCTION_TO_TEST boost::math::binomial_coefficient<T> + +//#define ELLINT_RC_FUNCTION_TO_TEST boost::math::ellint_rc +//#define ELLINT_RD_FUNCTION_TO_TEST boost::math::ellint_rd +//#define ELLINT_RF_FUNCTION_TO_TEST boost::math::ellint_rf +//#define ELLINT_RG_FUNCTION_TO_TEST boost::math::ellint_rg +//#define ELLINT_RJ_FUNCTION_TO_TEST boost::math::ellint_rj + +#define DIGAMMA_FUNCTION_TO_TEST digamma + +//#define ELLINT_1_FUNCTION_TO_TEST boost::math::ellint_1 +//#define ELLINT_1C_FUNCTION_TO_TEST boost::math::ellint_1 +//#define ELLINT_2_FUNCTION_TO_TEST boost::math::ellint_2 +//#define ELLINT_2C_FUNCTION_TO_TEST boost::math::ellint_2 +//#define ELLINT_3_FUNCTION_TO_TEST boost::math::ellint_3 +//#define ELLINT_3C_FUNCTION_TO_TEST boost::math::ellint_3 +//#define ELLINT_D2_FUNCTION_TO_TEST boost::math::ellint_d +//#define ELLINT_D1_FUNCTION_TO_TEST boost::math::ellint_d + +//#define EI_FUNCTION_TO_TEST boost::math::expint +//#define EN_FUNCTION_TO_TEST boost::math::expint + +//#define HERMITE_FUNCTION_TO_TEST boost::math::hermite +//#define HEUMAN_LAMBDA_FUNCTION_TO_TEST boost::math::heuman_lambda + +inline double ibeta(double a, double b, double x) { return pbeta(x, a, b, 1, 0); } +inline double ibetac(double a, double b, double x) { return pbeta(x, a, b, 0, 0); } +inline double ibeta_inv(double a, double b, double x) { return qbeta(x, a, b, 1, 0); } +inline double ibetac_inv(double a, double b, double x) { return qbeta(x, a, b, 0, 0); } + +//#define BETA_INC_FUNCTION_TO_TEST boost::math::beta +//#define BETAC_INC_FUNCTION_TO_TEST boost::math::betac +#define IBETA_FUNCTION_TO_TEST ibeta +#define IBETAC_FUNCTION_TO_TEST ibetac +#define IBETA_INV_FUNCTION_TO_TEST ibeta_inv +#define IBETAC_INV_FUNCTION_TO_TEST ibetac_inv +//#define IBETA_INVA_FUNCTION_TO_TEST boost::math::ibeta_inva +//#define IBETAC_INVA_FUNCTION_TO_TEST boost::math::ibetac_inva +//#define IBETA_INVB_FUNCTION_TO_TEST boost::math::ibeta_invb +//#define IBETAC_INVB_FUNCTION_TO_TEST boost::math::ibetac_invb + +inline double gamma_p(double a, double x) { return pgamma(x, a, 1.0, 1, 0); } +inline double gamma_q(double a, double x) { return pgamma(x, a, 1.0, 0, 0); } +inline double gamma_p_inv(double a, double x) { return qgamma(x, a, 1.0, 1, 0); } +inline double gamma_q_inv(double a, double x) { return qgamma(x, a, 1.0, 0, 0); } + +//#define IGAMMA_FUNCTION_TO_TEST boost::math::tgamma +//#define IGAMMAL_FUNCTION_TO_TEST boost::math::tgamma_lower +#define GAMMAP_FUNCTION_TO_TEST gamma_p +#define GAMMAQ_FUNCTION_TO_TEST gamma_q +#define GAMMAP_INV_FUNCTION_TO_TEST gamma_p_inv +#define GAMMAQ_INV_FUNCTION_TO_TEST gamma_q_inv +//#define GAMMAP_INVA_FUNCTION_TO_TEST boost::math::gamma_p_inva +//#define GAMMAQ_INVA_FUNCTION_TO_TEST boost::math::gamma_q_inva + +//#define SN_FUNCTION_TO_TEST boost::math::jacobi_sn +//#define CN_FUNCTION_TO_TEST boost::math::jacobi_cn +//#define DN_FUNCTION_TO_TEST boost::math::jacobi_dn +//#define JACOBI_ZETA_FUNCTION_TO_TEST boost::math::jacobi_zeta + +//#define LAGUERRE_FUNCTION_TO_TEST boost::math::laguerre +//#define ASSOC_LAGUERRE_FUNCTION_TO_TEST boost::math::laguerre + +//#define LEGENDRE_P_FUNCTION_TO_TEST boost::math::legendre_p +//#define LEGENDRE_Q_FUNCTION_TO_TEST boost::math::legendre_q +//#define LEGENDRE_PA_FUNCTION_TO_TEST boost::math::legendre_p + +inline double polygamma(int n, double x) +{ + if (x < 0) + throw std::domain_error("Outside supported domain"); + return psigamma(x, n); +} + +#define POLYGAMMA_FUNCTION_TO_TEST polygamma +//#define TGAMMA_RATIO_FUNCTION_TO_TEST boost::math::tgamma_ratio +//#define TGAMMA_DELTA_RATIO_FUNCTION_TO_TEST boost::math::tgamma_delta_ratio +//#define SIN_PI_RATIO_FUNCTION_TO_TEST sinpi +//#define COS_PI_RATIO_FUNCTION_TO_TEST cospi +#define TRIGAMMA_RATIO_FUNCTION_TO_TEST trigamma +//#define ZETA_FUNCTION_TO_TEST boost::math::zeta + +//#define SQRT1PM1_FUNCTION_TO_TEST boost::math::sqrt1pm1 +//#define POWM1_FUNCTION_TO_TEST boost::math::powm1 +//#define OWENS_T_FUNCTION_TO_TEST boost::math::owens_t +//#define SPHERICAL_HARMONIC_R_FUNCTION_TO_TEST boost::math::spherical_harmonic_r +//#define SPHERICAL_HARMONIC_I_FUNCTION_TO_TEST boost::math::spherical_harmonic_i + +template <class T> T do_nc_beta_cdf(T a, T b, T nc, T x){ return pnbeta(x, a, b, nc, 1, 0); } +template <class T> T do_nc_beta_ccdf(T a, T b, T nc, T x){ return pnbeta(x, a, b, nc, 0, 0); } +template <class T> T do_nc_chi_squared_cdf(T df, T nc, T x){ return pnchisq(x, df, nc, 1, 0); } +template <class T> T do_nc_chi_squared_ccdf(T df, T nc, T x){ return pnchisq(x, df, nc, 0, 0); } +template <class T> T do_nc_t_cdf(T df, T nc, T x){ return pnt(x, df, nc, 1, 0); } +template <class T> T do_nc_t_ccdf(T df, T nc, T x){ return pnt(x, df, nc, 0, 0); } + +#define NC_BETA_CDF_FUNCTION_TO_TEST do_nc_beta_cdf +#define NC_BETA_CCDF_FUNCTION_TO_TEST do_nc_beta_ccdf +#define NC_CHI_SQUARED_CDF_FUNCTION_TO_TEST do_nc_chi_squared_cdf +#define NC_CHI_SQUARED_CCDF_FUNCTION_TO_TEST do_nc_chi_squared_ccdf +#define NC_T_CDF_FUNCTION_TO_TEST do_nc_t_cdf +#define NC_T_CCDF_FUNCTION_TO_TEST do_nc_t_ccdf + +#define TYPE_TO_TEST double + +#elif defined(TEST_CEPHES) + +#define TEST_LIBRARY_NAME "Cephes" +#define TYPE_TO_TEST double + +extern "C" { + + double log1p(double) throw(); + double expm1(double) throw(); + double cbrt(double) throw(); + double erf(double) throw(); + double erfc(double) throw(); + double gamma(double) throw(); + double lgam(double) throw(); + + double iv(double, double) throw(); + double jv(double, double) throw(); + double jn(int, double) throw(); + double kn(int, double) throw(); + double yn(int, double) throw(); + + double beta(double, double)throw(); + double psi(double); + + double ellik(double, double); + double ellpk(double); + double ellie(double, double); + double ellpe(double); + + double ei(double); + // Can't get any sensible values from Cephes expn??? + //double expn(double, double); + + double incbet(double, double, double); + double incbi(double, double, double); + + double igam(double, double); + double igamc(double, double); + double igami(double, double); + + double ellpj(double u, double m, double *sn, double *cn, double *dn, double *phi); + + double zetac(double); + +} + +inline double ellint_1(double k, double phi) { return ellik(phi, k * k); } +inline double ellint_2(double k, double phi) { return ellie(phi, k * k); } +inline double ellint_1(double k) { return ellpk(k * k); } +inline double ellint_2(double k) { return ellpe(k * k); } + +inline double sn(double k, double u) +{ + double sn, cn, dn, phi; + ellpj(u, k * k, &sn, &cn, &dn, &phi); + return sn; +} +inline double cn(double k, double u) +{ + double sn, cn, dn, phi; + ellpj(u, k * k, &sn, &cn, &dn, &phi); + return cn; +} + +inline double dn(double k, double u) +{ + double sn, cn, dn, phi; + ellpj(u, k * k, &sn, &cn, &dn, &phi); + return dn; +} + +#define LOG1P_FUNCTION_TO_TEST log1p +#define EXPM1_FUNCTION_TO_TEST expm1 + +#define CBRT_FUNCTION_TO_TEST cbrt +#define ERF_FUNCTION_TO_TEST erf +#define ERFC_FUNCTION_TO_TEST erfc +//#define ERF_INV_FUNCTION_TO_TEST boost::math::erf_inv +//#define ERFC_INV_FUNCTION_TO_TEST boost::math::erfc_inv + +#define LGAMMA_FUNCTION_TO_TEST lgam +#define TGAMMA_FUNCTION_TO_TEST gamma +//#define TGAMMA1PM1_FUNCTION_TO_TEST boost::math::tgamma1pm1 + +#define BESSEL_I_FUNCTION_TO_TEST iv +#define BESSEL_IN_FUNCTION_TO_TEST iv +//#define BESSEL_IP_FUNCTION_TO_TEST boost::math::cyl_bessel_i_prime +//#define BESSEL_IPN_FUNCTION_TO_TEST boost::math::cyl_bessel_i_prime +#define BESSEL_J_FUNCTION_TO_TEST jv +#define BESSEL_JN_FUNCTION_TO_TEST jn +//#define BESSEL_JS_FUNCTION_TO_TEST boost::math::sph_bessel +//#define BESSEL_JP_FUNCTION_TO_TEST boost::math::cyl_bessel_j_prime +//#define BESSEL_JPN_FUNCTION_TO_TEST boost::math::cyl_bessel_j_prime +//#define BESSEL_JPS_FUNCTION_TO_TEST boost::math::sph_bessel_prime +//#define BESSEL_K_FUNCTION_TO_TEST boost::math::cyl_bessel_k +#define BESSEL_KN_FUNCTION_TO_TEST kn +//#define BESSEL_KP_FUNCTION_TO_TEST boost::math::cyl_bessel_k_prime +//#define BESSEL_KPN_FUNCTION_TO_TEST boost::math::cyl_bessel_k_prime +//#define BESSEL_Y_FUNCTION_TO_TEST boost::math::cyl_neumann +#define BESSEL_YN_FUNCTION_TO_TEST yn +//#define BESSEL_YS_FUNCTION_TO_TEST boost::math::sph_neumann +//#define BESSEL_YP_FUNCTION_TO_TEST boost::math::cyl_neumann_prime +//#define BESSEL_YNP_FUNCTION_TO_TEST boost::math::cyl_neumann_prime +//#define BESSEL_YSP_FUNCTION_TO_TEST boost::math::sph_neumann_prime + +#define BETA_FUNCTION_TO_TEST beta +//#define BINOMIAL_FUNCTION_TO_TEST boost::math::binomial_coefficient<T> + +//#define ELLINT_RC_FUNCTION_TO_TEST boost::math::ellint_rc +//#define ELLINT_RD_FUNCTION_TO_TEST boost::math::ellint_rd +//#define ELLINT_RF_FUNCTION_TO_TEST boost::math::ellint_rf +//#define ELLINT_RG_FUNCTION_TO_TEST boost::math::ellint_rg +//#define ELLINT_RJ_FUNCTION_TO_TEST boost::math::ellint_rj + +#define DIGAMMA_FUNCTION_TO_TEST psi + +#define ELLINT_1_FUNCTION_TO_TEST ellint_1 +// Can't seem to get sensible answers from Cephes complete elliptic integrals??? +//#define ELLINT_1C_FUNCTION_TO_TEST ellint_1 +#define ELLINT_2_FUNCTION_TO_TEST ellint_2 +//#define ELLINT_2C_FUNCTION_TO_TEST ellint_2 +//#define ELLINT_3_FUNCTION_TO_TEST boost::math::ellint_3 +//#define ELLINT_3C_FUNCTION_TO_TEST boost::math::ellint_3 +//#define ELLINT_D2_FUNCTION_TO_TEST boost::math::ellint_d +//#define ELLINT_D1_FUNCTION_TO_TEST boost::math::ellint_d + +#define EI_FUNCTION_TO_TEST ei +//#define EN_FUNCTION_TO_TEST expn + +//#define HERMITE_FUNCTION_TO_TEST boost::math::hermite +//#define HEUMAN_LAMBDA_FUNCTION_TO_TEST boost::math::heuman_lambda + +//#define BETA_INC_FUNCTION_TO_TEST incbet +//#define BETAC_INC_FUNCTION_TO_TEST boost::math::betac +#define IBETA_FUNCTION_TO_TEST incbet +//#define IBETAC_FUNCTION_TO_TEST boost::math::ibetac +#define IBETA_INV_FUNCTION_TO_TEST incbi +//#define IBETAC_INV_FUNCTION_TO_TEST boost::math::ibetac_inv +//#define IBETA_INVA_FUNCTION_TO_TEST boost::math::ibeta_inva +//#define IBETAC_INVA_FUNCTION_TO_TEST boost::math::ibetac_inva +//#define IBETA_INVB_FUNCTION_TO_TEST boost::math::ibeta_invb +//#define IBETAC_INVB_FUNCTION_TO_TEST boost::math::ibetac_invb + +//#define IGAMMA_FUNCTION_TO_TEST boost::math::tgamma +//#define IGAMMAL_FUNCTION_TO_TEST boost::math::tgamma_lower +#define GAMMAP_FUNCTION_TO_TEST igam +#define GAMMAQ_FUNCTION_TO_TEST igamc +//#define GAMMAP_INV_FUNCTION_TO_TEST boost::math::gamma_p_inv +#define GAMMAQ_INV_FUNCTION_TO_TEST igami +//#define GAMMAP_INVA_FUNCTION_TO_TEST boost::math::gamma_p_inva +//#define GAMMAQ_INVA_FUNCTION_TO_TEST boost::math::gamma_q_inva + +#define SN_FUNCTION_TO_TEST sn +#define CN_FUNCTION_TO_TEST cn +#define DN_FUNCTION_TO_TEST dn + +#define ZETA_FUNCTION_TO_TEST zetac + +#else + +#include <boost/math/distributions/non_central_beta.hpp> +#include <boost/math/distributions/non_central_chi_squared.hpp> +#include <boost/math/distributions/non_central_t.hpp> + +#define TEST_LIBRARY_NAME "boost" + +#define LOG1P_FUNCTION_TO_TEST boost::math::log1p +#define EXPM1_FUNCTION_TO_TEST boost::math::expm1 + +#define CBRT_FUNCTION_TO_TEST boost::math::cbrt +#define ERF_FUNCTION_TO_TEST boost::math::erf +#define ERFC_FUNCTION_TO_TEST boost::math::erfc +#define ERF_INV_FUNCTION_TO_TEST boost::math::erf_inv +#define ERFC_INV_FUNCTION_TO_TEST boost::math::erfc_inv + +#define LGAMMA_FUNCTION_TO_TEST boost::math::lgamma +#define TGAMMA_FUNCTION_TO_TEST boost::math::tgamma +#define TGAMMA1PM1_FUNCTION_TO_TEST boost::math::tgamma1pm1 + +#define BESSEL_I_FUNCTION_TO_TEST boost::math::cyl_bessel_i +#define BESSEL_IN_FUNCTION_TO_TEST boost::math::cyl_bessel_i +#define BESSEL_IP_FUNCTION_TO_TEST boost::math::cyl_bessel_i_prime +#define BESSEL_IPN_FUNCTION_TO_TEST boost::math::cyl_bessel_i_prime +#define BESSEL_J_FUNCTION_TO_TEST boost::math::cyl_bessel_j +#define BESSEL_JN_FUNCTION_TO_TEST boost::math::cyl_bessel_j +#define BESSEL_JS_FUNCTION_TO_TEST boost::math::sph_bessel +#define BESSEL_JP_FUNCTION_TO_TEST boost::math::cyl_bessel_j_prime +#define BESSEL_JPN_FUNCTION_TO_TEST boost::math::cyl_bessel_j_prime +#define BESSEL_JPS_FUNCTION_TO_TEST boost::math::sph_bessel_prime +#define BESSEL_K_FUNCTION_TO_TEST boost::math::cyl_bessel_k +#define BESSEL_KN_FUNCTION_TO_TEST boost::math::cyl_bessel_k +#define BESSEL_KP_FUNCTION_TO_TEST boost::math::cyl_bessel_k_prime +#define BESSEL_KPN_FUNCTION_TO_TEST boost::math::cyl_bessel_k_prime +#define BESSEL_Y_FUNCTION_TO_TEST boost::math::cyl_neumann +#define BESSEL_YN_FUNCTION_TO_TEST boost::math::cyl_neumann +#define BESSEL_YS_FUNCTION_TO_TEST boost::math::sph_neumann +#define BESSEL_YP_FUNCTION_TO_TEST boost::math::cyl_neumann_prime +#define BESSEL_YNP_FUNCTION_TO_TEST boost::math::cyl_neumann_prime +#define BESSEL_YSP_FUNCTION_TO_TEST boost::math::sph_neumann_prime + +#define BETA_FUNCTION_TO_TEST boost::math::beta +#define BINOMIAL_FUNCTION_TO_TEST boost::math::binomial_coefficient<T> + +#define ELLINT_RC_FUNCTION_TO_TEST boost::math::ellint_rc +#define ELLINT_RD_FUNCTION_TO_TEST boost::math::ellint_rd +#define ELLINT_RF_FUNCTION_TO_TEST boost::math::ellint_rf +#define ELLINT_RG_FUNCTION_TO_TEST boost::math::ellint_rg +#define ELLINT_RJ_FUNCTION_TO_TEST boost::math::ellint_rj + +#define DIGAMMA_FUNCTION_TO_TEST boost::math::digamma + +#define ELLINT_1_FUNCTION_TO_TEST boost::math::ellint_1 +#define ELLINT_1C_FUNCTION_TO_TEST boost::math::ellint_1 +#define ELLINT_2_FUNCTION_TO_TEST boost::math::ellint_2 +#define ELLINT_2C_FUNCTION_TO_TEST boost::math::ellint_2 +#define ELLINT_3_FUNCTION_TO_TEST boost::math::ellint_3 +#define ELLINT_3C_FUNCTION_TO_TEST boost::math::ellint_3 +#define ELLINT_D2_FUNCTION_TO_TEST boost::math::ellint_d +#define ELLINT_D1_FUNCTION_TO_TEST boost::math::ellint_d + +#define EI_FUNCTION_TO_TEST boost::math::expint +#define EN_FUNCTION_TO_TEST boost::math::expint + +#define HERMITE_FUNCTION_TO_TEST boost::math::hermite +#define HEUMAN_LAMBDA_FUNCTION_TO_TEST boost::math::heuman_lambda + +#define BETA_INC_FUNCTION_TO_TEST boost::math::beta +#define BETAC_INC_FUNCTION_TO_TEST boost::math::betac +#define IBETA_FUNCTION_TO_TEST boost::math::ibeta +#define IBETAC_FUNCTION_TO_TEST boost::math::ibetac +#define IBETA_INV_FUNCTION_TO_TEST boost::math::ibeta_inv +#define IBETAC_INV_FUNCTION_TO_TEST boost::math::ibetac_inv +#define IBETA_INVA_FUNCTION_TO_TEST boost::math::ibeta_inva +#define IBETAC_INVA_FUNCTION_TO_TEST boost::math::ibetac_inva +#define IBETA_INVB_FUNCTION_TO_TEST boost::math::ibeta_invb +#define IBETAC_INVB_FUNCTION_TO_TEST boost::math::ibetac_invb + +#define IGAMMA_FUNCTION_TO_TEST boost::math::tgamma +#define IGAMMAL_FUNCTION_TO_TEST boost::math::tgamma_lower +#define GAMMAP_FUNCTION_TO_TEST boost::math::gamma_p +#define GAMMAQ_FUNCTION_TO_TEST boost::math::gamma_q +#define GAMMAP_INV_FUNCTION_TO_TEST boost::math::gamma_p_inv +#define GAMMAQ_INV_FUNCTION_TO_TEST boost::math::gamma_q_inv +#define GAMMAP_INVA_FUNCTION_TO_TEST boost::math::gamma_p_inva +#define GAMMAQ_INVA_FUNCTION_TO_TEST boost::math::gamma_q_inva + +#define SN_FUNCTION_TO_TEST boost::math::jacobi_sn +#define CN_FUNCTION_TO_TEST boost::math::jacobi_cn +#define DN_FUNCTION_TO_TEST boost::math::jacobi_dn +#define JACOBI_ZETA_FUNCTION_TO_TEST boost::math::jacobi_zeta + +#define LAGUERRE_FUNCTION_TO_TEST boost::math::laguerre +#define ASSOC_LAGUERRE_FUNCTION_TO_TEST boost::math::laguerre + +#define LEGENDRE_P_FUNCTION_TO_TEST boost::math::legendre_p +#define LEGENDRE_Q_FUNCTION_TO_TEST boost::math::legendre_q +#define LEGENDRE_PA_FUNCTION_TO_TEST boost::math::legendre_p + +#define POLYGAMMA_FUNCTION_TO_TEST boost::math::polygamma +#define TGAMMA_RATIO_FUNCTION_TO_TEST boost::math::tgamma_ratio +#define TGAMMA_DELTA_RATIO_FUNCTION_TO_TEST boost::math::tgamma_delta_ratio +#define SIN_PI_RATIO_FUNCTION_TO_TEST boost::math::sin_pi +#define COS_PI_RATIO_FUNCTION_TO_TEST boost::math::cos_pi +#define TRIGAMMA_RATIO_FUNCTION_TO_TEST boost::math::trigamma +#define ZETA_FUNCTION_TO_TEST boost::math::zeta + +#define SQRT1PM1_FUNCTION_TO_TEST boost::math::sqrt1pm1 +#define POWM1_FUNCTION_TO_TEST boost::math::powm1 +#define OWENS_T_FUNCTION_TO_TEST boost::math::owens_t +#define SPHERICAL_HARMONIC_R_FUNCTION_TO_TEST boost::math::spherical_harmonic_r +#define SPHERICAL_HARMONIC_I_FUNCTION_TO_TEST boost::math::spherical_harmonic_i + +template <class T> T do_nc_beta_cdf(T a, T b, T nc, T x){ return cdf(boost::math::non_central_beta_distribution<T>(a, b, nc), x); } +template <class T> T do_nc_beta_ccdf(T a, T b, T nc, T x){ return cdf(complement(boost::math::non_central_beta_distribution<T>(a, b, nc), x)); } +template <class T> T do_nc_chi_squared_cdf(T df, T nc, T x){ return cdf(boost::math::non_central_chi_squared_distribution<T>(df, nc), x); } +template <class T> T do_nc_chi_squared_ccdf(T df, T nc, T x){ return cdf(complement(boost::math::non_central_chi_squared_distribution<T>(df, nc), x)); } +template <class T> T do_nc_t_cdf(T df, T nc, T x){ return cdf(boost::math::non_central_t_distribution<T>(df, nc), x); } +template <class T> T do_nc_t_ccdf(T df, T nc, T x){ return cdf(complement(boost::math::non_central_t_distribution<T>(df, nc), x)); } + +#define NC_BETA_CDF_FUNCTION_TO_TEST do_nc_beta_cdf +#define NC_BETA_CCDF_FUNCTION_TO_TEST do_nc_beta_ccdf +#define NC_CHI_SQUARED_CDF_FUNCTION_TO_TEST do_nc_chi_squared_cdf +#define NC_CHI_SQUARED_CCDF_FUNCTION_TO_TEST do_nc_chi_squared_ccdf +#define NC_T_CDF_FUNCTION_TO_TEST do_nc_t_cdf +#define NC_T_CCDF_FUNCTION_TO_TEST do_nc_t_ccdf + + +#endif + +#if defined(TYPE_TO_TEST) && !defined(NAME_OF_TYPE_TO_TEST) +#define NAME_OF_TYPE_TO_TEST BOOST_STRINGIZE(TYPE_TO_TEST) +#endif + +// +// This include has to come at the end after all the setup is done: +// +#include "handle_test_result.hpp" + + +#endif + diff --git a/src/boost/libs/math/reporting/accuracy/handle_test_result.hpp b/src/boost/libs/math/reporting/accuracy/handle_test_result.hpp new file mode 100644 index 000000000..3410bb150 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/handle_test_result.hpp @@ -0,0 +1,515 @@ +// (C) Copyright John Maddock 2006-7. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef BOOST_MATH_HANDLE_TEST_RESULT +#define BOOST_MATH_HANDLE_TEST_RESULT + +#include <boost/math/tools/stats.hpp> +#include <boost/math/tools/precision.hpp> +#include <boost/lexical_cast.hpp> +#include <boost/regex.hpp> +#include <boost/test/test_tools.hpp> +#include <boost/filesystem.hpp> +#include <boost/filesystem/fstream.hpp> +#include <boost/interprocess/sync/named_mutex.hpp> +#include <boost/interprocess/sync/scoped_lock.hpp> +#include <boost/math/special_functions/fpclassify.hpp> +#include <iostream> +#include <iomanip> +#include <vector> +#include <set> + +#include <boost/math/tools/test.hpp> + +inline std::string sanitize_string(const std::string& s) +{ + static const boost::regex e("[^a-zA-Z0-9]+"); + return boost::regex_replace(s, e, "_"); +} + +static std::string content; +boost::filesystem::path path_to_content; + +struct content_loader +{ + boost::interprocess::named_mutex mu; + boost::interprocess::scoped_lock<boost::interprocess::named_mutex> lock; + content_loader() : mu(boost::interprocess::open_or_create, "handle_test_result"), lock(mu) + { + boost::filesystem::path p(__FILE__); + p = p.parent_path(); + p /= "doc"; + p /= "accuracy_tables.qbk"; + path_to_content = p; + if(boost::filesystem::exists(p)) + { + boost::filesystem::ifstream is(p); + if(is.good()) + { + do + { + char c = static_cast<char>(is.get()); + if(c != EOF) + content.append(1, c); + } while(is.good()); + } + } + } + ~content_loader() + { + boost::filesystem::ofstream os(path_to_content); + os << content; + } + void instantiate()const + { + } +}; + +static const content_loader loader; + +void load_table(std::vector<std::vector<std::string> >& table, std::string::const_iterator begin, std::string::const_iterator end) +{ + static const boost::regex item_e( + "\\[" + "([^\\[\\]]*(?0)?)*" + "\\]" + ); + + boost::regex_token_iterator<std::string::const_iterator> i(begin, end, item_e), j; + + while(i != j) + { + // Add a row: + table.push_back(std::vector<std::string>()); + boost::regex_token_iterator<std::string::const_iterator> k(i->first + 1, i->second - 1, item_e); + while(k != j) + { + // Add a cell: + table.back().push_back(std::string(k->first + 1, k->second - 1)); + ++k; + } + ++i; + } +} + +std::string save_table(std::vector<std::vector<std::string> >& table) +{ + std::string result; + + for(std::vector<std::vector<std::string> >::const_iterator i = table.begin(), j = table.end(); i != j; ++i) + { + result += "["; + for(std::vector<std::string>::const_iterator k = i->begin(), l = i->end(); k != l; ++k) + { + result += "["; + result += *k; + result += "]"; + } + result += "]\n"; + } + return result; +} + +void add_to_all_sections(const std::string& id, std::string list_name = "all_sections") +{ + std::string::size_type pos = content.find("[template " + list_name + "[]"), end_pos; + if(pos == std::string::npos) + { + // + // Just append to the end: + // + content.append("\n[template ").append(list_name).append("[]\n[").append(id).append("]\n]\n"); + } + else + { + // + // Read in the all list of sections, add our new one (in alphabetical order), + // and then rewrite the whole thing: + // + static const boost::regex item_e( + "\\[" + "([^\\[\\]]*(?0)?)*" + "\\]|\\]" + ); + boost::regex_token_iterator<std::string::const_iterator> i(content.begin() + pos + 12 + list_name.size(), content.end(), item_e), j; + std::set<std::string> sections; + while(i != j) + { + if(i->length() == 1) + { + end_pos = i->first - content.begin(); + break; + } + sections.insert(std::string(i->first + 1, i->second - 1)); + ++i; + } + sections.insert(id); + std::string new_list = "\n"; + for(std::set<std::string>::const_iterator sec = sections.begin(); sec != sections.end(); ++sec) + { + new_list += "[" + *sec + "]\n"; + } + content.replace(pos + 12 + list_name.size(), end_pos - pos - 12 - list_name.size(), new_list); + } +} + +void add_cell(const std::string& cell_name, const std::string& table_name, const std::string& row_name, const std::string& type_name) +{ + // + // Load the table, add our data, and re-write: + // + std::string table_id = "table_" + sanitize_string(table_name); + std::string column_heading = BOOST_COMPILER; + column_heading += "[br]"; + column_heading += BOOST_PLATFORM; + column_heading += "[br]"; + column_heading += type_name; + boost::regex table_e("\\[table:" + table_id + + "\\s[^\\[]+" + "((\\[" + "([^\\[\\]]*(?2)?)*" + "\\]\\s*)*\\s*)" + "\\]" + ); + + boost::smatch table_location; + if(regex_search(content, table_location, table_e)) + { + std::vector<std::vector<std::string> > table_data; + load_table(table_data, table_location[1].first, table_location[1].second); + // + // Figure out which column we're on: + // + unsigned column_id = 1001u; + for(unsigned i = 0; i < table_data[0].size(); ++i) + { + if(table_data[0][i] == column_heading) + { + column_id = i; + break; + } + } + if(column_id > 1000) + { + // + // Need a new column, must be adding a new compiler to the table! + // + table_data[0].push_back(column_heading); + for(unsigned i = 1; i < table_data.size(); ++i) + table_data[i].push_back(std::string()); + column_id = table_data[0].size() - 1; + } + // + // Figure out the row: + // + unsigned row_id = 1001; + for(unsigned i = 1; i < table_data.size(); ++i) + { + if(table_data[i][0] == row_name) + { + row_id = i; + break; + } + } + if(row_id > 1000) + { + // + // Need a new row, add it now: + // + table_data.push_back(std::vector<std::string>()); + table_data.back().push_back(row_name); + for(unsigned i = 1; i < table_data[0].size(); ++i) + table_data.back().push_back(std::string()); + row_id = table_data.size() - 1; + } + // + // Update the entry: + // + std::string& s = table_data[row_id][column_id]; + if(s.empty()) + { + std::cout << "Adding " << cell_name << " to empty cell."; + s = "[" + cell_name + "]"; + } + else + { + if(cell_name.find("_boost_") != std::string::npos) + { + std::cout << "Adding " << cell_name << " to start of cell."; + s.insert(0, "[" + cell_name + "][br][br]"); + } + else + { + std::cout << "Adding " << cell_name << " to end of cell."; + if((s.find("_boost_") != std::string::npos) && (s.find("[br]") == std::string::npos)) + s += "[br]"; // extra break if we're adding directly after the boost results. + s += "[br][" + cell_name + "]"; + } + } + // + // Convert back to a string and insert into content: + std::string c = save_table(table_data); + content.replace(table_location.position(1), table_location.length(1), c); + } + else + { + // + // Create a new table and try again: + // + std::string new_table = "\n[template " + table_id; + new_table += "[]\n[table:" + table_id; + new_table += " Error rates for "; + new_table += table_name; + new_table += "\n[[]["; + new_table += column_heading; + new_table += "]]\n"; + new_table += "[["; + new_table += row_name; + new_table += "][["; + new_table += cell_name; + new_table += "]]]\n]\n]\n"; + + std::string::size_type pos = content.find("[/tables:]"); + if(pos != std::string::npos) + content.insert(pos + 10, new_table); + else + content += "\n\n[/tables:]\n" + new_table; + // + // Add a section for this table as well: + // + std::string section_id = "section_" + sanitize_string(table_name); + if(content.find(section_id + "[]") == std::string::npos) + { + std::string new_section = "\n[template " + section_id + "[]\n[section:" + section_id + " " + table_name + "]\n[" + table_id + "]\n[endsect]\n]\n"; + pos = content.find("[/sections:]"); + if(pos != std::string::npos) + content.insert(pos + 12, new_section); + else + content += "\n\n[/sections:]\n" + new_section; + add_to_all_sections(section_id); + } + // + // Add to list of all tables (not in sections): + // + add_to_all_sections(table_id, "all_tables"); + } +} + +void set_result(const std::string& cell_name, const std::string& cell_content, const std::string& table_name, const std::string& row_name, const std::string& type_name) +{ + loader.instantiate(); + const boost::regex e("\\[template\\s+" + cell_name + + "\\[\\]([^\\n]*)\\]$"); + + boost::smatch what; + if(regex_search(content, what, e)) + { + content.replace(what.position(1), what.length(1), cell_content); + } + else + { + // Need to add new content: + std::string::size_type pos = content.find("[/Cell Content:]"); + std::string t = "\n[template " + cell_name + "[] " + cell_content + "]"; + if(pos != std::string::npos) + content.insert(pos + 16, t); + else + { + content.insert(0, t); + content.insert(0, "[/Cell Content:]"); + } + } + // + // Check to verify that our content is actually used somewhere, + // if not we need to create a place for it: + // + if(content.find("[" + cell_name + "]") == std::string::npos) + add_cell(cell_name, table_name, row_name, type_name); +} + +void set_error_content(const std::string& id, const std::string& error_s) +{ + boost::regex content_e("\\[template\\s+" + id + + "\\[\\]\\s+" + "(" + "[^\\]\\[]*" + "(?:" + "\\[" + "([^\\[\\]]*(?2)?)*" + "\\]" + "[^\\]\\[]*" + ")*" + + ")" + "\\]"); + boost::smatch what; + if(regex_search(content, what, content_e)) + { + // replace existing content: + content.replace(what.position(1), what.length(1), error_s); + } + else + { + // add new content: + std::string::size_type pos = content.find("[/error_content:]"); + if(pos != std::string::npos) + { + content.insert(pos + 17, "\n[template " + id + "[]\n" + error_s + "\n]\n"); + } + else + content.append("\n[/error_content:]\n[template " + id + "[]\n" + error_s + "\n]\n"); + } + // + // Add to all_errors if not already there: + // + if(content.find("[" + id + "]") == std::string::npos) + { + // Find all_errors template: + std::string::size_type pos = content.find("[template all_errors[]\n"); + if(pos != std::string::npos) + { + content.insert(pos + 23, "[" + id + "]\n"); + } + else + { + content.append("\n[template all_errors[]\n[").append(id).append("]\n]\n"); + } + } +} + +void remove_error_content(const std::string& error_id) +{ + // remove use template first: + std::string::size_type pos = content.find("[" + error_id + "]"); + if(pos != std::string::npos) + { + content.erase(pos, 2 + error_id.size()); + } + // then the template define itself: + boost::regex content_e("\\[template\\s+" + error_id + + "\\[\\]\\s+" + "(" + "[^\\]\\[]*" + "(?:" + "\\[" + "([^\\[\\]]*(?2)?)*" + "\\]" + "[^\\]\\[]*" + ")*" + ")" + "\\]"); + boost::smatch what; + if(regex_search(content, what, content_e)) + { + content.erase(what.position(), what.length()); + } +} + +template <class T, class Seq> +void handle_test_result(const boost::math::tools::test_result<T>& result, + const Seq& worst, int row, + const char* type_name, + const char* test_name, + const char* group_name) +{ + T eps = boost::math::tools::epsilon<T>(); + T max_error_found = (result.max)() / eps; + T mean_error_found = result.rms() / eps; + + std::string cell_name = sanitize_string(BOOST_COMPILER) + "_" + sanitize_string(BOOST_PLATFORM) + "_" + sanitize_string(type_name) + + "_" + sanitize_string(test_name) + "_" + sanitize_string(TEST_LIBRARY_NAME) + "_" + sanitize_string(group_name); + + std::stringstream ss; + ss << std::setprecision(3); + if(std::string(TEST_LIBRARY_NAME) != "boost") + ss << "(['" << TEST_LIBRARY_NAME << ":] "; + else + ss << "[role blue "; + + if((result.max)() > std::sqrt(eps)) + ss << "[role red "; + + + ss << "Max = "; + if((boost::math::isfinite)(max_error_found)) + ss << max_error_found; + else + ss << "+INF"; + ss << "[epsilon] (Mean = "; + if((boost::math::isfinite)(mean_error_found)) + ss << mean_error_found; + else + ss << "+INF"; + ss << "[epsilon])"; + + // + // Now check for error output from gross errors or unexpected exceptions: + // + std::stringbuf* pbuf = dynamic_cast<std::stringbuf*>(std::cerr.rdbuf()); + bool have_errors = false; + std::string error_id = "errors_" + cell_name; + if(pbuf) + { + std::string err_s = pbuf->str(); + if(err_s.size()) + { + if(err_s.size() > 4096) + { + std::string::size_type pos = err_s.find("\n", 4096); + if(pos != std::string::npos) + { + err_s.erase(pos); + err_s += "\n*** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***\n"; + } + } + std::string::size_type pos = err_s.find("\n"); + while(pos != std::string::npos) + { + err_s.replace(pos, 1, "[br]"); + pos = err_s.find("\n"); + } + err_s = "[h4 Error Output For " + std::string(test_name) + std::string(" with compiler ") + std::string(BOOST_COMPILER) + + std::string(" and library ") + std::string(TEST_LIBRARY_NAME) + " and test data " + + std::string(group_name) + "]\n\n[#" + error_id + "]\n" + err_s + std::string("\n\n\n"); + ss << " [link " << error_id << " And other failures.]"; + pbuf->str(""); + set_error_content(error_id, err_s); + have_errors = true; + } + } + if(!have_errors) + remove_error_content(error_id); + + + if(std::string(TEST_LIBRARY_NAME) != "boost") + ss << ")"; + else + ss << "]"; + + if((result.max)() > std::sqrt(eps)) + ss << "]"; + + std::string cell_content = ss.str(); + + set_result(cell_name, cell_content, test_name, group_name, type_name); +} + +struct error_stream_replacer +{ + std::streambuf* old_buf; + std::stringstream ss; + error_stream_replacer() + { + old_buf = std::cerr.rdbuf(); + std::cerr.rdbuf(ss.rdbuf()); + } + ~error_stream_replacer() + { + std::cerr.rdbuf(old_buf); + } +}; + +#endif // BOOST_MATH_HANDLE_TEST_RESULT + diff --git a/src/boost/libs/math/reporting/accuracy/has_c99_cmath.cpp b/src/boost/libs/math/reporting/accuracy/has_c99_cmath.cpp new file mode 100644 index 000000000..876585920 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/has_c99_cmath.cpp @@ -0,0 +1,17 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <math.h> + +int main() +{ + long double d = 1; + + d = ::erf(d); + d = ::erfc(d); + d = ::tgamma(d); + d = ::lgamma(d); + return d != 0 ? 0 : 1; +} diff --git a/src/boost/libs/math/reporting/accuracy/has_cxx17_cmath.cpp b/src/boost/libs/math/reporting/accuracy/has_cxx17_cmath.cpp new file mode 100644 index 000000000..a73540b53 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/has_cxx17_cmath.cpp @@ -0,0 +1,18 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <cmath> + +int main() +{ + long double d = 1; + + d = std::erf(d); + d = std::erfc(d); + d = std::tgamma(d); + d = std::lgamma(d); + d = std::comp_ellint_1(d); + return d != 0 ? 0 : 1; +} diff --git a/src/boost/libs/math/reporting/accuracy/has_gsl.cpp b/src/boost/libs/math/reporting/accuracy/has_gsl.cpp new file mode 100644 index 000000000..f66794393 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/has_gsl.cpp @@ -0,0 +1,12 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <gsl/gsl_sf.h> + +int main() +{ + double d = gsl_sf_bessel_Jn(2, 1.0); + return d != 0 ? 0 : 1; +} diff --git a/src/boost/libs/math/reporting/accuracy/has_libstdcxx_tr1.cpp b/src/boost/libs/math/reporting/accuracy/has_libstdcxx_tr1.cpp new file mode 100644 index 000000000..e2cb94488 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/has_libstdcxx_tr1.cpp @@ -0,0 +1,17 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <tr1/cmath> + +int main() +{ + long double d = 1; + + d = std::tr1::erf(d); + d = std::tr1::erfc(d); + d = std::tr1::tgamma(d); + d = std::tr1::lgamma(d); + return d != 0 ? 0 : 1; +} diff --git a/src/boost/libs/math/reporting/accuracy/has_rmath.cpp b/src/boost/libs/math/reporting/accuracy/has_rmath.cpp new file mode 100644 index 000000000..df6cb315a --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/has_rmath.cpp @@ -0,0 +1,13 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#define MATHLIB_STANDALONE +#include <Rmath.h> + +int main() +{ + double d = psigamma(2.0, 4); + return d != 0 ? 0 : 1; +} diff --git a/src/boost/libs/math/reporting/accuracy/html/index.html b/src/boost/libs/math/reporting/accuracy/html/index.html new file mode 100644 index 000000000..f859e717a --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/html/index.html @@ -0,0 +1,27805 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Special Function Error Rates Report</title> +<link rel="stylesheet" href="http://www.boost.org/doc/libs/1_58_0/doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> +<link rel="home" href="index.html" title="Special Function Error Rates Report"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td> +<td align="center"><a href="../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"></div> +<div class="article"> +<div class="titlepage"> +<div> +<div><h2 class="title"> +<a name="special_function_error_rates_rep"></a>Special Function Error Rates Report</h2></div> +<div><div class="legalnotice"> +<a name="special_function_error_rates_rep.legal"></a><p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></div> +</div> +<hr> +</div> +<div class="toc"> +<p><b>Table of Contents</b></p> +<dl> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_beta">beta</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_beta_incomplete_">beta + (incomplete)</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_betac">betac</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_binomial_coefficient">binomial_coefficient</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_boost_math_powm1">boost::math::powm1</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cbrt">cbrt</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cos_pi">cos_pi</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_i">cyl_bessel_i</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_integer_orders_">cyl_bessel_i + (integer orders)</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_prime">cyl_bessel_i_prime</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_prime_integer_orders_">cyl_bessel_i_prime + (integer orders)</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_j">cyl_bessel_j</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_integer_orders_">cyl_bessel_j + (integer orders)</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_prime">cyl_bessel_j_prime</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_prime_integer_orders_">cyl_bessel_j_prime + (integer orders)</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_k">cyl_bessel_k</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_integer_orders_">cyl_bessel_k + (integer orders)</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_prime">cyl_bessel_k_prime</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_prime_integer_orders_">cyl_bessel_k_prime + (integer orders)</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_neumann">cyl_neumann</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_neumann_integer_orders_">cyl_neumann + (integer orders)</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_neumann_prime">cyl_neumann_prime</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_neumann_prime_integer_orders_">cyl_neumann_prime + (integer orders)</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_digamma">digamma</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_1">ellint_1</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_1_complete_">ellint_1 + (complete)</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_2">ellint_2</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_2_complete_">ellint_2 + (complete)</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_3">ellint_3</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_3_complete_">ellint_3 + (complete)</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_d">ellint_d</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_d_complete_">ellint_d + (complete)</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_rc">ellint_rc</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_rd">ellint_rd</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_rf">ellint_rf</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_rg">ellint_rg</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_rj">ellint_rj</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_erf">erf</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_erf_inv">erf_inv</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_erfc">erfc</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_erfc_inv">erfc_inv</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_expint_Ei_">expint + (Ei)</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_expint_En_">expint + (En)</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_expm1">expm1</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_p">gamma_p</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_p_inv">gamma_p_inv</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_p_inva">gamma_p_inva</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_q">gamma_q</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_q_inv">gamma_q_inv</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_q_inva">gamma_q_inva</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_hermite">hermite</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_heuman_lambda">heuman_lambda</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibeta">ibeta</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibeta_inv">ibeta_inv</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibeta_inva">ibeta_inva</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibeta_invb">ibeta_invb</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibetac">ibetac</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibetac_inv">ibetac_inv</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibetac_inva">ibetac_inva</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibetac_invb">ibetac_invb</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_jacobi_cn">jacobi_cn</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_jacobi_dn">jacobi_dn</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_jacobi_sn">jacobi_sn</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_jacobi_zeta">jacobi_zeta</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_laguerre_n_m_x_">laguerre(n, + m, x)</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_laguerre_n_x_">laguerre(n, + x)</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_legendre_p">legendre_p</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_legendre_p_associated_">legendre_p + (associated)</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_legendre_q">legendre_q</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_lgamma">lgamma</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_log1p">log1p</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_beta_CDF">non + central beta CDF</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_beta_CDF_complement">non + central beta CDF complement</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_chi_squared_CDF">non + central chi squared CDF</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_chi_squared_CDF_complement">non + central chi squared CDF complement</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_t_CDF">non + central t CDF</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_t_CDF_complement">non + central t CDF complement</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_owens_t">owens_t</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_polygamma">polygamma</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_powm1">powm1</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sin_pi">sin_pi</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sph_bessel">sph_bessel</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sph_bessel_prime">sph_bessel_prime</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sph_neumann">sph_neumann</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sph_neumann_prime">sph_neumann_prime</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_spherical_harmonic_i">spherical_harmonic_i</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_spherical_harmonic_r">spherical_harmonic_r</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sqrt1pm1">sqrt1pm1</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma">tgamma</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma1pm1">tgamma1pm1</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma_delta_ratio">tgamma_delta_ratio</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma_incomplete_">tgamma + (incomplete)</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma_lower">tgamma_lower</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma_ratio">tgamma_ratio</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_trigamma">trigamma</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_zeta">zeta</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.error_logs">Error Logs</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_error_rates_rep.all_the_tables">Tables</a></span></dt> +</dl> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_beta"></a><a class="link" href="index.html#special_function_error_rates_rep.section_beta" title="beta">beta</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_beta.table_beta"></a><p class="title"><b>Table 1. Error rates for beta</b></p> +<div class="table-contents"><table class="table" summary="Error rates for beta"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Beta Function: Small Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_beta_GSL_2_1_Beta_Function_Small_Values">And + other failures.</a>)</span><br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 1.14ε (Mean = 0.574ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.86ε (Mean = 1.22ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 364ε (Mean = 76.2ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.86ε (Mean = 1.22ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.23ε (Mean = 1.14ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Beta Function: Medium Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.978ε (Mean = 0.0595ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.18e+03ε (Mean = 238ε))<br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.09e+03ε (Mean = 265ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 61.4ε (Mean = 19.4ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.07e+03ε (Mean = 264ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 107ε (Mean = 24.5ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 96.5ε (Mean = 22.4ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Beta Function: Divergent Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 12.1ε (Mean = 1.99ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 176ε (Mean = 28ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.99ε (Mean = 2.44ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 128ε (Mean = 23.8ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 18.8ε (Mean = 2.71ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 11.4ε (Mean = 2.19ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_beta_incomplete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_beta_incomplete_" title="beta (incomplete)">beta + (incomplete)</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_beta_incomplete_.table_beta_incomplete_"></a><p class="title"><b>Table 2. Error rates for beta (incomplete)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for beta (incomplete)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Incomplete Beta Function: Small Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 11.1ε (Mean = 2.32ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 18.7ε (Mean = 3.19ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.94ε (Mean = 2.17ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Incomplete Beta Function: Medium Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.568ε (Mean = 0.0254ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 69.2ε (Mean = 13.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 174ε (Mean = 25ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 90ε (Mean = 12.7ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Incomplete Beta Function: Large and Diverse Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.999ε (Mean = 0.0325ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.84e+04ε (Mean = 2.76e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.86e+04ε (Mean = 2.79e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 633ε (Mean = 29.7ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Incomplete Beta Function: Small Integer Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.786ε (Mean = 0.0323ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 11.6ε (Mean = 3.6ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 51.8ε (Mean = 11ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 26ε (Mean = 6.28ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_betac"></a><a class="link" href="index.html#special_function_error_rates_rep.section_betac" title="betac">betac</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_betac.table_betac"></a><p class="title"><b>Table 3. Error rates for betac</b></p> +<div class="table-contents"><table class="table" summary="Error rates for betac"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Incomplete Beta Function: Small Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.676ε (Mean = 0.0302ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.92ε (Mean = 2.3ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 11.2ε (Mean = 2.94ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.94ε (Mean = 2.06ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Incomplete Beta Function: Medium Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.949ε (Mean = 0.098ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 63.5ε (Mean = 13.5ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 97.6ε (Mean = 24.3ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 90.6ε (Mean = 14.8ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Incomplete Beta Function: Large and Diverse Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.12ε (Mean = 0.0458ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.05e+05ε (Mean = 5.45e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.04e+05ε (Mean = 5.46e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.72e+03ε (Mean = 113ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Incomplete Beta Function: Small Integer Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.586ε (Mean = 0.0314ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 11.1ε (Mean = 3.65ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 103ε (Mean = 17.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 26.2ε (Mean = 6.36ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_binomial_coefficient"></a><a class="link" href="index.html#special_function_error_rates_rep.section_binomial_coefficient" title="binomial_coefficient">binomial_coefficient</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_binomial_coefficient.table_binomial_coefficient"></a><p class="title"><b>Table 4. Error rates for binomial_coefficient</b></p> +<div class="table-contents"><table class="table" summary="Error rates for binomial_coefficient"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Binomials: small arguments + </p> + </td> +<td> + <p> + <span class="blue">Max = 1ε (Mean = 0.369ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.5ε (Mean = 0.339ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.5ε (Mean = 0.339ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1ε (Mean = 0.369ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Binomials: large arguments + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.939ε (Mean = 0.314ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 26.6ε (Mean = 6.13ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 53.2ε (Mean = 10.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 37.2ε (Mean = 7.4ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_boost_math_powm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_boost_math_powm1" title="boost::math::powm1">boost::math::powm1</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_boost_math_powm1.table_boost_math_powm1"></a><p class="title"><b>Table 5. Error rates for boost::math::powm1</b></p> +<div class="table-contents"><table class="table" summary="Error rates for boost::math::powm1"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + powm1 + </p> + </td> +<td> + <p> + (<span class="emphasis"><em><math.h>:</em></span> Max = 2.04ε (Mean = 0.493ε))<br> + <br> <span class="blue">Max = 2.04ε (Mean = 0.493ε)</span><br> + <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 2.04ε (Mean = 0.493ε)) + </p> + </td> +<td> + <p> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.06ε (Mean = 0.425ε))<br> + <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.06ε (Mean = 0.425ε))<br> + <br> <span class="blue">Max = 1.06ε (Mean = 0.425ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.88ε (Mean = 0.49ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.88ε (Mean = 0.49ε)) + </p> + </td> +<td> + <p> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.84ε (Mean = 0.486ε))<br> + <br> <span class="blue">Max = 1.84ε (Mean = 0.486ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_cbrt"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cbrt" title="cbrt">cbrt</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_cbrt.table_cbrt"></a><p class="title"><b>Table 6. Error rates for cbrt</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cbrt"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + cbrt Function + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.34ε (Mean = 0.471ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.34ε (Mean = 0.471ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.34ε (Mean = 0.471ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.34ε (Mean = 0.471ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.34ε (Mean = 0.471ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.7ε (Mean = 0.565ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.7ε (Mean = 0.565ε)) + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_cos_pi"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cos_pi" title="cos_pi">cos_pi</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_cos_pi.table_cos_pi"></a><p class="title"><b>Table 7. Error rates for cos_pi</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cos_pi"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + sin_pi and cos_pi + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.991ε (Mean = 0.302ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.991ε (Mean = 0.302ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.996ε (Mean = 0.284ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + sin_pi and cos_pi near integers and half integers + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.976ε (Mean = 0.28ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.976ε (Mean = 0.28ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.996ε (Mean = 0.298ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_cyl_bessel_i"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_i" title="cyl_bessel_i">cyl_bessel_i</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_cyl_bessel_i.table_cyl_bessel_i"></a><p class="title"><b>Table 8. Error rates for cyl_bessel_i</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Bessel I0: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 270ε (Mean = 91.6ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I0_Mathworld_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 1.52ε (Mean = 0.622ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I0_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.95ε (Mean = 0.738ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 8.49ε (Mean = 3.46ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I0_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.95ε (Mean = 0.661ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.762ε (Mean = 0.329ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel I1: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 128ε (Mean = 41ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I1_Mathworld_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 1.53ε (Mean = 0.483ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I1_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 5ε (Mean = 2.15ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I1_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.767ε (Mean = 0.398ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel In: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2.31ε (Mean = 0.838ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Mathworld_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 1.73ε (Mean = 0.601ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_In_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.8ε (Mean = 1.33ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 430ε (Mean = 163ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_In_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 463ε (Mean = 140ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.46ε (Mean = 1.32ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel Iv: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 5.95ε (Mean = 2.08ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 3.53ε (Mean = 1.39ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.12ε (Mean = 1.85ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 616ε (Mean = 221ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.12ε (Mean = 1.95ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.97ε (Mean = 1.24ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel In: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 261ε (Mean = 53.2ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Random_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 7.37ε (Mean = 2.4ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.62ε (Mean = 1.06ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 645ε (Mean = 132ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 176ε (Mean = 39.1ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.67ε (Mean = 1.88ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel Iv: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.661ε (Mean = 0.0441ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 6.18e+03ε (Mean = 1.55e+03ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Random_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + <span class="red">Max = 4.28e+08ε (Mean = 2.85e+07ε))</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.35ε (Mean = 1.62ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.05e+03ε (Mean = 224ε) + <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Random_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 283ε (Mean = 88.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.46ε (Mean = 1.71ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel Iv: Mathworld Data (large values) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 37ε (Mean = 18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data_large_values_">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + <span class="red">Max = 3.77e+168ε (Mean = 2.39e+168ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_Iv_Mathworld_Data_large_values_">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 14.7ε (Mean = 6.66ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 118ε (Mean = 57.2ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data_large_values_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 14.7ε (Mean = 6.59ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.67ε (Mean = 1.64ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_cyl_bessel_i_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_integer_orders_" title="cyl_bessel_i (integer orders)">cyl_bessel_i + (integer orders)</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_cyl_bessel_i_integer_orders_.table_cyl_bessel_i_integer_orders_"></a><p class="title"><b>Table 9. Error rates for cyl_bessel_i (integer orders)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i (integer orders)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Bessel I0: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0.79ε (Mean = 0.482ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 1.52ε (Mean = 0.622ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I0_Mathworld_Data_Integer_Version_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.95ε (Mean = 0.738ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 8.49ε (Mean = 3.46ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I0_Mathworld_Data_Integer_Version_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.95ε (Mean = 0.661ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.762ε (Mean = 0.329ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel I1: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0.82ε (Mean = 0.456ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 1.53ε (Mean = 0.483ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I1_Mathworld_Data_Integer_Version_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 5ε (Mean = 2.15ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I1_Mathworld_Data_Integer_Version_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.767ε (Mean = 0.398ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel In: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 5.15ε (Mean = 2.13ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__GSL_2_1_Bessel_In_Mathworld_Data_Integer_Version_">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 1.73ε (Mean = 0.601ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_In_Mathworld_Data_Integer_Version_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.8ε (Mean = 1.33ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 430ε (Mean = 163ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_In_Mathworld_Data_Integer_Version_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 463ε (Mean = 140ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.46ε (Mean = 1.32ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_cyl_bessel_i_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_prime" title="cyl_bessel_i_prime">cyl_bessel_i_prime</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_cyl_bessel_i_prime.table_cyl_bessel_i_prime"></a><p class="title"><b>Table 10. Error rates for cyl_bessel_i_prime</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Bessel I'0: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.82ε (Mean = 0.354ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel I'1: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.36ε (Mean = 0.782ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel I'n: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.31ε (Mean = 1.41ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 701ε (Mean = 212ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.61ε (Mean = 1.22ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel I'v: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.62ε (Mean = 0.512ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.89e+03ε (Mean = 914ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.89e+03ε (Mean = 914ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.76e+03ε (Mean = 1.19e+03ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel I'n: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.95ε (Mean = 1.06ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 195ε (Mean = 37.1ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.85ε (Mean = 1.82ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel I'v: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 14.1ε (Mean = 2.93ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 336ε (Mean = 68.5ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 14ε (Mean = 2.5ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel I'v: Mathworld Data (large values) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 42.6ε (Mean = 20.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 42.6ε (Mean = 20.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 59.5ε (Mean = 26.6ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_cyl_bessel_i_prime_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_prime_integer_orders_" title="cyl_bessel_i_prime (integer orders)">cyl_bessel_i_prime + (integer orders)</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_cyl_bessel_i_prime_integer_orders_.table_cyl_bessel_i_prime_integer_orders_"></a><p class="title"><b>Table 11. Error rates for cyl_bessel_i_prime (integer orders)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime (integer orders)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Bessel I'0: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.82ε (Mean = 0.354ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel I'1: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.36ε (Mean = 0.782ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel I'n: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.31ε (Mean = 1.41ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 701ε (Mean = 212ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.61ε (Mean = 1.22ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_cyl_bessel_j"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_j" title="cyl_bessel_j">cyl_bessel_j</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_cyl_bessel_j.table_cyl_bessel_j"></a><p class="title"><b>Table 12. Error rates for cyl_bessel_j</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Bessel J0: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 5.04ε (Mean = 1.78ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J0_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0.629ε (Mean = 0.223ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J0_Mathworld_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 0.629ε (Mean = 0.223ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J0_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.52ε (Mean = 1.2ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J0: Mathworld Data (Tricky cases) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span><br> + <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 4.79e+08ε (Mean = + 1.96e+08ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 8e+04ε (Mean = 3.27e+04ε)</span><br> + <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 6.5e+07ε (Mean = 2.66e+07ε))<br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.04e+07ε (Mean = 4.29e+06ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1e+07ε (Mean = 4.09e+06ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J1: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.59ε (Mean = 1.33ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 6.1ε (Mean = 2.95ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J1_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 6.62ε (Mean = 2.35ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J1_Mathworld_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 0.946ε (Mean = 0.39ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J1_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.44ε (Mean = 0.637ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.73ε (Mean = 0.976ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J1: Mathworld Data (tricky cases) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span><br> + <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 2.15e+06ε (Mean = + 1.58e+06ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 106ε (Mean = 47.5ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.75e+05ε (Mean = 5.32e+05ε))<br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.93e+06ε (Mean = 1.7e+06ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.23e+04ε (Mean = 1.45e+04ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel JN: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.85ε (Mean = 3.35ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.13e+19ε (Mean + = 5.16e+18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_JN_Mathworld_Data">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 6.9e+05ε (Mean = 2.15e+05ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_JN_Mathworld_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_JN_Mathworld_Data">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 463ε (Mean = 112ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 14.7ε (Mean = 5.4ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 14.7ε (Mean = 4.11ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 3.49e+05ε (Mean = 8.09e+04ε) + <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 10ε (Mean = 2.24ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2.39e+05ε (Mean = 5.37e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J_Mathworld_Data">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 14.7ε (Mean = 4.22ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 14.9ε (Mean = 3.89ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J: Mathworld Data (large values) + </p> + </td> +<td> + <p> + <span class="blue">Max = 607ε (Mean = 305ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> + Max = 34.9ε (Mean = 17.4ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data_large_values_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.536ε (Mean = 0.268ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.91e+03ε (Mean = 2.46e+03ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data_large_values_">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 5.9ε (Mean = 3.76ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 607ε (Mean = 305ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.31ε (Mean = 5.52ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel JN: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 50.8ε (Mean = 3.69ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.12e+03ε (Mean = 88.7ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 75.7ε (Mean = 5.36ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 3.93ε (Mean = 1.22ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 99.6ε (Mean = 22ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 17.5ε (Mean = 1.46ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 11.4ε (Mean = 1.68ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 501ε (Mean = 52.3ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 15.5ε (Mean = 3.33ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Random_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 6.74ε (Mean = 1.3ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 260ε (Mean = 34ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.24ε (Mean = 1.17ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J: Random Data (Tricky large values) + </p> + </td> +<td> + <p> + <span class="blue">Max = 785ε (Mean = 94.2ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 5.01e+17ε (Mean + = 6.23e+16ε))</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2.48e+05ε (Mean = 5.11e+04ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 71.6ε (Mean = 11.7ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 785ε (Mean = 97.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 59.2ε (Mean = 8.67ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_cyl_bessel_j_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_integer_orders_" title="cyl_bessel_j (integer orders)">cyl_bessel_j + (integer orders)</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_cyl_bessel_j_integer_orders_.table_cyl_bessel_j_integer_orders_"></a><p class="title"><b>Table 13. Error rates for cyl_bessel_j (integer orders)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j (integer orders)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Bessel J0: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 5.04ε (Mean = 1.78ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J0_Mathworld_Data_Integer_Version_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.12ε (Mean = 0.488ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 0.629ε (Mean = 0.223ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J0_Mathworld_Data_Integer_Version_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.52ε (Mean = 1.2ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.89ε (Mean = 0.988ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J0: Mathworld Data (Tricky cases) (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span><br> + <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 4.79e+08ε (Mean = + 1.96e+08ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 8e+04ε (Mean = 3.27e+04ε)</span><br> + <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1e+07ε (Mean = 4.11e+06ε))<br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.04e+07ε (Mean = 4.29e+06ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1e+07ε (Mean = 4.09e+06ε)</span><br> + <br> (<span class="emphasis"><em><math.h>:</em></span> <span class="red">Max + = 2.54e+08ε (Mean = 1.04e+08ε))</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J1: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.59ε (Mean = 1.33ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 6.1ε (Mean = 2.95ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J1_Mathworld_Data_Integer_Version_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.89ε (Mean = 0.721ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 0.946ε (Mean = 0.39ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J1_Mathworld_Data_Integer_Version_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.44ε (Mean = 0.637ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.73ε (Mean = 0.976ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 11.4ε (Mean = 4.15ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J1: Mathworld Data (tricky cases) (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span><br> + <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 2.15e+06ε (Mean = + 1.58e+06ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 106ε (Mean = 47.5ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.26e+06ε (Mean = 6.28e+05ε))<br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.93e+06ε (Mean = 1.7e+06ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.23e+04ε (Mean = 1.45e+04ε)</span><br> + <br> (<span class="emphasis"><em><math.h>:</em></span> Max = 1.44e+07ε (Mean + = 6.5e+06ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel JN: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.85ε (Mean = 3.35ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.13e+19ε (Mean + = 5.16e+18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_JN_Mathworld_Data_Integer_Version_">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 6.9e+05ε (Mean = 2.53e+05ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__GSL_2_1_Bessel_JN_Mathworld_Data_Integer_Version_">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_JN_Mathworld_Data_Integer_Version_">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 463ε (Mean = 112ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 14.7ε (Mean = 5.4ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> <span class="red">Max = +INFε (Mean + = +INFε) <a class="link" href="index.html#errors_Microsoft_Visual_C_version_14_1_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_">And + other failures.</a>)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_cyl_bessel_j_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_prime" title="cyl_bessel_j_prime">cyl_bessel_j_prime</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_cyl_bessel_j_prime.table_cyl_bessel_j_prime"></a><p class="title"><b>Table 14. Error rates for cyl_bessel_j_prime</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Bessel J0': Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 18.9ε (Mean = 6.82ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 18.9ε (Mean = 6.72ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.62ε (Mean = 2.55ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J0': Mathworld Data (Tricky cases) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.44ε (Mean = 3.34ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.44ε (Mean = 3.31ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.67ε (Mean = 1.74ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J1': Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.999ε (Mean = 0.627ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J1': Mathworld Data (tricky cases) + </p> + </td> +<td> + <p> + <span class="blue">Max = 287ε (Mean = 129ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 288ε (Mean = 129ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel JN': Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.527ε (Mean = 0.128ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.29e+03ε (Mean = 312ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.29e+03ε (Mean = 355ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 14ε (Mean = 6.13ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J': Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 21.5ε (Mean = 4.7ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 42.5ε (Mean = 9.31ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 42.5ε (Mean = 9.32ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 23.7ε (Mean = 8ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J': Mathworld Data (large values) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 989ε (Mean = 495ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 989ε (Mean = 495ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.9ε (Mean = 1.61ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel JN': Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.593ε (Mean = 0.0396ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 11.3ε (Mean = 1.85ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 79.4ε (Mean = 16.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.34ε (Mean = 0.999ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J': Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.885ε (Mean = 0.033ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 139ε (Mean = 6.47ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 279ε (Mean = 27.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 176ε (Mean = 9.75ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J': Random Data (Tricky large values) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 474ε (Mean = 62.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 474ε (Mean = 64.5ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 379ε (Mean = 45.4ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_cyl_bessel_j_prime_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_prime_integer_orders_" title="cyl_bessel_j_prime (integer orders)">cyl_bessel_j_prime + (integer orders)</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_cyl_bessel_j_prime_integer_orders_.table_cyl_bessel_j_prime_integer_orders_"></a><p class="title"><b>Table 15. Error rates for cyl_bessel_j_prime (integer orders)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime (integer orders)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Bessel J0': Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 18.9ε (Mean = 6.82ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 18.9ε (Mean = 6.72ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.62ε (Mean = 2.55ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J0': Mathworld Data (Tricky cases) (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.44ε (Mean = 3.34ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.44ε (Mean = 3.31ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.67ε (Mean = 1.74ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J1': Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.999ε (Mean = 0.627ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J1': Mathworld Data (tricky cases) (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 287ε (Mean = 129ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 288ε (Mean = 129ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel JN': Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.527ε (Mean = 0.128ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.29e+03ε (Mean = 312ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.29e+03ε (Mean = 355ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 14ε (Mean = 6.13ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_cyl_bessel_k"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_k" title="cyl_bessel_k">cyl_bessel_k</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_cyl_bessel_k.table_cyl_bessel_k"></a><p class="title"><b>Table 16. Error rates for cyl_bessel_k</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Bessel K0: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 9.33ε (Mean = 3.25ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 6.04ε (Mean = 2.16ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 0.833ε (Mean = 0.601ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.833ε (Mean = 0.552ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel K1: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 8.94ε (Mean = 3.19ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 6.26ε (Mean = 2.21ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 0.894ε (Mean = 0.516ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel Kn: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 12.9ε (Mean = 4.91ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kn_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 3.36ε (Mean = 1.43ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Mathworld_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 8.48ε (Mean = 2.98ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.63ε (Mean = 1.46ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel Kv: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.58ε (Mean = 2.39ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 13ε (Mean = 4.81ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 5.47ε (Mean = 2.04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 3.15ε (Mean = 1.35ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.21ε (Mean = 2.53ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.78ε (Mean = 2.19ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel Kv: Mathworld Data (large values) + </p> + </td> +<td> + <p> + <span class="blue">Max = 42.3ε (Mean = 21ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> + Max = 42.3ε (Mean = 19.8ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data_large_values_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 308ε (Mean = 142ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data_large_values_">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 84.6ε (Mean = 37.8ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 42.3ε (Mean = 21ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 59.8ε (Mean = 26.9ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel Kn: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.55ε (Mean = 1.12ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 13.9ε (Mean = 2.91ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.764ε (Mean = 0.0348ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.71ε (Mean = 1.76ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Random_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 7.47ε (Mean = 1.34ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.55ε (Mean = 1.12ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.34ε (Mean = 1.7ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel Kv: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.88ε (Mean = 1.48ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 13.6ε (Mean = 2.68ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Random_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.507ε (Mean = 0.0313ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 9.71ε (Mean = 1.47ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Random_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 7.37ε (Mean = 1.49ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.88ε (Mean = 1.47ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.33ε (Mean = 1.62ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_cyl_bessel_k_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_integer_orders_" title="cyl_bessel_k (integer orders)">cyl_bessel_k + (integer orders)</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_cyl_bessel_k_integer_orders_.table_cyl_bessel_k_integer_orders_"></a><p class="title"><b>Table 17. Error rates for cyl_bessel_k (integer orders)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k (integer orders)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Bessel K0: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 9.33ε (Mean = 3.25ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.2ε (Mean = 0.733ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 0.833ε (Mean = 0.601ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.833ε (Mean = 0.552ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel K1: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 8.94ε (Mean = 3.19ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0.626ε (Mean = 0.333ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 0.894ε (Mean = 0.516ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel Kn: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 12.9ε (Mean = 4.91ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k_integer_orders___cmath__Bessel_Kn_Mathworld_Data_Integer_Version_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 168ε (Mean = 59.5ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 8.48ε (Mean = 2.98ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.63ε (Mean = 1.46ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_cyl_bessel_k_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_prime" title="cyl_bessel_k_prime">cyl_bessel_k_prime</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_cyl_bessel_k_prime.table_cyl_bessel_k_prime"></a><p class="title"><b>Table 18. Error rates for cyl_bessel_k_prime</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Bessel K'0: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel K'1: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.761ε (Mean = 0.444ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel K'n: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.17ε (Mean = 1.75ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel K'v: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.94ε (Mean = 2.44ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.94ε (Mean = 2.34ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.94ε (Mean = 1.47ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel K'v: Mathworld Data (large values) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 59.2ε (Mean = 42.9ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 58.7ε (Mean = 42.6ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 18.6ε (Mean = 11.8ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel K'n: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.45ε (Mean = 1.19ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.45ε (Mean = 1.19ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.67ε (Mean = 1.73ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel K'v: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.95ε (Mean = 1.53ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.95ε (Mean = 1.52ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.32ε (Mean = 1.65ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_cyl_bessel_k_prime_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_prime_integer_orders_" title="cyl_bessel_k_prime (integer orders)">cyl_bessel_k_prime + (integer orders)</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_cyl_bessel_k_prime_integer_orders_.table_cyl_bessel_k_prime_integer_orders_"></a><p class="title"><b>Table 19. Error rates for cyl_bessel_k_prime (integer orders)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime (integer orders)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Bessel K'0: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel K'1: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.761ε (Mean = 0.444ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel K'n: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.17ε (Mean = 1.75ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_cyl_neumann"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_neumann" title="cyl_neumann">cyl_neumann</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_cyl_neumann.table_cyl_neumann"></a><p class="title"><b>Table 20. Error rates for cyl_neumann</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Y0: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 2.05e+05ε (Mean = 6.87e+04ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 60.9ε (Mean = 20.4ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 167ε (Mean = 56.5ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.61ε (Mean = 2.29ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Y1: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.33ε (Mean = 2.25ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 9.71e+03ε (Mean = 4.08e+03ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 23.4ε (Mean = 8.1ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 193ε (Mean = 64.4ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.33ε (Mean = 2.29ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.75ε (Mean = 1.72ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Yn: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.2e+20ε (Mean + = 6.97e+19ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yn_Mathworld_Data">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.993ε (Mean = 0.314ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.41e+05ε (Mean = 7.62e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yn_Mathworld_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 1.24e+04ε (Mean = 4e+03ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 35ε (Mean = 11.9ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Yv: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 10.7ε (Mean = 4.93ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 3.49e+15ε (Mean + = 1.05e+15ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 10ε (Mean = 3.02ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.07e+05ε (Mean = 3.22e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 243ε (Mean = 73.9ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 10.7ε (Mean = 5.1ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.89ε (Mean = 3.27ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Yv: Mathworld Data (large values) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.7ε (Mean = 1.33ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 43.2ε (Mean = 16.3ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data_large_values_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 60.8ε (Mean = 23ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data_large_values_">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 0.682ε (Mean = 0.335ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.7ε (Mean = 1.33ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.682ε (Mean = 0.423ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Y0 and Y1: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 10.8ε (Mean = 3.04ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 2.59e+03ε (Mean = 500ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 34.4ε (Mean = 8.9ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 83ε (Mean = 14.2ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 10.8ε (Mean = 3.04ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.17ε (Mean = 1.24ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Yn: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 338ε (Mean = 27.5ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 4.01e+03ε (Mean = 348ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 500ε (Mean = 47.8ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 691ε (Mean = 67.9ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 338ε (Mean = 27.5ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 117ε (Mean = 10.2ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Yv: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.08e+03ε (Mean = 149ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean + = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Random_Data">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.53ε (Mean = 0.102ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.41e+06ε (Mean = 7.67e+04ε))<br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.79e+05ε (Mean = 9.64e+03ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.08e+03ε (Mean = 149ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.23e+03ε (Mean = 69.9ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_cyl_neumann_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_neumann_integer_orders_" title="cyl_neumann (integer orders)">cyl_neumann + (integer orders)</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_cyl_neumann_integer_orders_.table_cyl_neumann_integer_orders_"></a><p class="title"><b>Table 21. Error rates for cyl_neumann (integer orders)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann (integer orders)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Y0: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 2.05e+05ε (Mean = 6.87e+04ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 6.46ε (Mean = 2.38ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 167ε (Mean = 56.5ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.61ε (Mean = 2.29ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 5.37e+03ε (Mean = 1.81e+03ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + Y1: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.33ε (Mean = 2.25ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 9.71e+03ε (Mean = 4.08e+03ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.51ε (Mean = 0.839ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 193ε (Mean = 64.4ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.33ε (Mean = 2.29ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.75ε (Mean = 1.72ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.86e+04ε (Mean = 6.2e+03ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + Yn: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.2e+20ε (Mean + = 6.97e+19ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann_integer_orders___cmath__Yn_Mathworld_Data_Integer_Version_">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.993ε (Mean = 0.314ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.41e+05ε (Mean = 7.62e+04ε))<br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.24e+04ε (Mean = 4e+03ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 35ε (Mean = 11.9ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> + Max = 2.49e+05ε (Mean = 8.14e+04ε)) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_cyl_neumann_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_neumann_prime" title="cyl_neumann_prime">cyl_neumann_prime</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_cyl_neumann_prime.table_cyl_neumann_prime"></a><p class="title"><b>Table 22. Error rates for cyl_neumann_prime</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Y'0: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.33ε (Mean = 3.12ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.33ε (Mean = 3.14ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.75ε (Mean = 1.75ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Y'1: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.58ε (Mean = 0.193ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 37.1ε (Mean = 12.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 34ε (Mean = 11.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.08ε (Mean = 1.2ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Y'n: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.05ε (Mean = 0.677ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 56ε (Mean = 18.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 56ε (Mean = 21.3ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 563ε (Mean = 178ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Y'v: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 21.5ε (Mean = 6.49ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 42.5ε (Mean = 13.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 42.5ε (Mean = 13.6ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 23.7ε (Mean = 10.1ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Y'v: Mathworld Data (large values) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.57ε (Mean = 1.24ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.57ε (Mean = 1.24ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.627ε (Mean = 0.237ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Y'0 and Y'1: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 23.8ε (Mean = 3.69ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 23.8ε (Mean = 3.69ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.95ε (Mean = 1.36ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Y'n: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.53ε (Mean = 0.0885ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.35e+03ε (Mean = 136ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.35e+03ε (Mean = 136ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 621ε (Mean = 36ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Y'v: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 56.8ε (Mean = 2.59ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.16e+05ε (Mean = 5.28e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.16e+05ε (Mean = 5.28e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.23e+04ε (Mean = 1.13e+03ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_cyl_neumann_prime_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_neumann_prime_integer_orders_" title="cyl_neumann_prime (integer orders)">cyl_neumann_prime + (integer orders)</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_cyl_neumann_prime_integer_orders_.table_cyl_neumann_prime_integer_orders_"></a><p class="title"><b>Table 23. Error rates for cyl_neumann_prime (integer orders)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime (integer orders)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Y'0: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.33ε (Mean = 3.12ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.33ε (Mean = 3.14ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.75ε (Mean = 1.75ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Y'1: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.58ε (Mean = 0.193ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 37.1ε (Mean = 12.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 34ε (Mean = 11.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.08ε (Mean = 1.2ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Y'n: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.05ε (Mean = 0.677ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 56ε (Mean = 18.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 56ε (Mean = 21.3ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 563ε (Mean = 178ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_digamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_digamma" title="digamma">digamma</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_digamma.table_digamma"></a><p class="title"><b>Table 24. Error rates for digamma</b></p> +<div class="table-contents"><table class="table" summary="Error rates for digamma"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Digamma Function: Large Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.84ε (Mean = 0.71ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 1.18ε (Mean = 0.331ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.39ε (Mean = 0.413ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.39ε (Mean = 0.413ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.98ε (Mean = 0.369ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Digamma Function: Near the Positive Root + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.891ε (Mean = 0.0995ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 135ε (Mean = 11.9ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 2.02e+03ε (Mean = 256ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.37ε (Mean = 0.477ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.31ε (Mean = 0.471ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.997ε (Mean = 0.527ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Digamma Function: Near Zero + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0.953ε (Mean = 0.348ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 1.17ε (Mean = 0.564ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.984ε (Mean = 0.361ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.984ε (Mean = 0.361ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.953ε (Mean = 0.337ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Digamma Function: Negative Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 4.56e+04ε (Mean = 3.91e+03ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 4.6e+04ε (Mean = 3.94e+03ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 180ε (Mean = 13ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 180ε (Mean = 13ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 214ε (Mean = 16.1ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Digamma Function: Values near 0 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0.866ε (Mean = 0.387ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 3.58e+05ε (Mean = 1.6e+05ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1ε (Mean = 0.592ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1ε (Mean = 0.592ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Digamma Function: Integer arguments + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.992ε (Mean = 0.215ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.18ε (Mean = 0.607ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 4.33ε (Mean = 0.982ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.888ε (Mean = 0.403ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.888ε (Mean = 0.403ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.992ε (Mean = 0.452ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Digamma Function: Half integer arguments + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.09ε (Mean = 0.531ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 46.2ε (Mean = 7.24ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.906ε (Mean = 0.409ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.906ε (Mean = 0.409ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.78ε (Mean = 0.314ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_ellint_1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_1" title="ellint_1">ellint_1</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_ellint_1.table_ellint_1"></a><p class="title"><b>Table 25. Error rates for ellint_1</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ellint_1"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Elliptic Integral F: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.94ε (Mean = 0.509ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean + = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_1__cmath__Elliptic_Integral_F_Mathworld_Data">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0.919ε (Mean = 0.544ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.94ε (Mean = 0.509ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.919ε (Mean = 0.542ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Elliptic Integral F: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.57ε (Mean = 0.56ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 2.56ε (Mean = 0.816ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2.99ε (Mean = 0.797ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.57ε (Mean = 0.561ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.26ε (Mean = 0.631ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_ellint_1_complete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_1_complete_" title="ellint_1 (complete)">ellint_1 + (complete)</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_ellint_1_complete_.table_ellint_1_complete_"></a><p class="title"><b>Table 26. Error rates for ellint_1 (complete)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ellint_1 (complete)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Elliptic Integral K: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.887ε (Mean = 0.296ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.19ε (Mean = 0.765ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0.623ε (Mean = 0.393ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.887ε (Mean = 0.296ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.915ε (Mean = 0.547ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Elliptic Integral K: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.27ε (Mean = 0.473ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 2.19ε (Mean = 0.694ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.851ε (Mean = 0.0851ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.32ε (Mean = 0.688ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.27ε (Mean = 0.473ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.958ε (Mean = 0.408ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_ellint_2"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_2" title="ellint_2">ellint_2</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_ellint_2.table_ellint_2"></a><p class="title"><b>Table 27. Error rates for ellint_2</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ellint_2"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Elliptic Integral E: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0.63ε (Mean = 0.325ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.656ε (Mean = 0.317ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean + = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_2__cmath__Elliptic_Integral_E_Mathworld_Data">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.656ε (Mean = 0.317ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.31ε (Mean = 0.727ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Elliptic Integral E: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 4.4ε (Mean = 1.16ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.05ε (Mean = 0.632ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 3.08e+04ε (Mean = 3.84e+03ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.05ε (Mean = 0.632ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.23ε (Mean = 0.639ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Elliptic Integral E: Small Angles + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0.5ε (Mean = 0.118ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1ε (Mean = 0.283ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> + Max = 2ε (Mean = 0.333ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1ε (Mean = 0.283ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1ε (Mean = 0.421ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_ellint_2_complete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_2_complete_" title="ellint_2 (complete)">ellint_2 + (complete)</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_ellint_2_complete_.table_ellint_2_complete_"></a><p class="title"><b>Table 28. Error rates for ellint_2 (complete)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ellint_2 (complete)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Elliptic Integral E: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 3.09ε (Mean = 1.04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_2_complete__GSL_2_1_Elliptic_Integral_E_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.836ε (Mean = 0.469ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 170ε (Mean = 55.1ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.836ε (Mean = 0.469ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.3ε (Mean = 0.615ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Elliptic Integral E: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 4.34ε (Mean = 1.18ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.97ε (Mean = 0.629ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 2.49e+04ε (Mean = 3.39e+03ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.97ε (Mean = 0.629ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.71ε (Mean = 0.553ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_ellint_3"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_3" title="ellint_3">ellint_3</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_ellint_3.table_ellint_3"></a><p class="title"><b>Table 29. Error rates for ellint_3</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ellint_3"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Elliptic Integral PI: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 475ε (Mean = 86.3ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean + = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Mathworld_Data">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.48e+05ε (Mean = 2.54e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_3_GSL_2_1_Elliptic_Integral_PI_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 475ε (Mean = 86.3ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 565ε (Mean = 102ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Elliptic Integral PI: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.54ε (Mean = 0.895ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 3.37e+20ε (Mean + = 3.47e+19ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Random_Data">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 633ε (Mean = 50.1ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.49ε (Mean = 0.885ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.33ε (Mean = 0.971ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Elliptic Integral PI: Large Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.7ε (Mean = 0.893ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.52e+18ε (Mean + = 4.83e+17ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Large_Random_Data">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.557ε (Mean = 0.0389ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 40.1ε (Mean = 7.77ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.7ε (Mean = 0.892ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.86ε (Mean = 0.944ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_ellint_3_complete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_3_complete_" title="ellint_3 (complete)">ellint_3 + (complete)</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_ellint_3_complete_.table_ellint_3_complete_"></a><p class="title"><b>Table 30. Error rates for ellint_3 (complete)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ellint_3 (complete)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Complete Elliptic Integral PI: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.4ε (Mean = 0.575ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 6.31e+20ε (Mean + = 1.53e+20ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Mathworld_Data">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 6.33e+04ε (Mean = 1.54e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_3_complete__GSL_2_1_Complete_Elliptic_Integral_PI_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.4ε (Mean = 0.575ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.971ε (Mean = 0.464ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Complete Elliptic Integral PI: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.45ε (Mean = 0.696ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 8.78e+20ε (Mean + = 1.02e+20ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Random_Data">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 24ε (Mean = 2.99ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.4ε (Mean = 0.677ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.46ε (Mean = 0.657ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_ellint_d"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_d" title="ellint_d">ellint_d</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_ellint_d.table_ellint_d"></a><p class="title"><b>Table 31. Error rates for ellint_d</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ellint_d"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Elliptic Integral E: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0.862ε (Mean = 0.568ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.3ε (Mean = 0.813ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.3ε (Mean = 0.813ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.862ε (Mean = 0.457ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Elliptic Integral D: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 3.01ε (Mean = 0.928ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.51ε (Mean = 0.883ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.51ε (Mean = 0.883ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.87ε (Mean = 0.805ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_ellint_d_complete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_d_complete_" title="ellint_d (complete)">ellint_d + (complete)</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_ellint_d_complete_.table_ellint_d_complete_"></a><p class="title"><b>Table 32. Error rates for ellint_d (complete)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ellint_d (complete)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Elliptic Integral E: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.637ε (Mean = 0.368ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.27ε (Mean = 0.735ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.27ε (Mean = 0.735ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.637ε (Mean = 0.368ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Elliptic Integral D: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.27ε (Mean = 0.334ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.27ε (Mean = 0.334ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.27ε (Mean = 0.355ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_ellint_rc"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rc" title="ellint_rc">ellint_rc</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_ellint_rc.table_ellint_rc"></a><p class="title"><b>Table 33. Error rates for ellint_rc</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ellint_rc"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + RC: Random data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2.4ε (Mean = 0.624ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.995ε (Mean = 0.433ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.962ε (Mean = 0.407ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_ellint_rd"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rd" title="ellint_rd">ellint_rd</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_ellint_rd.table_ellint_rd"></a><p class="title"><b>Table 34. Error rates for ellint_rd</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ellint_rd"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + RD: Random data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2.59ε (Mean = 0.878ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.73ε (Mean = 0.831ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.16ε (Mean = 0.803ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RD: y = z + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.896ε (Mean = 0.022ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.88ε (Mean = 0.839ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.65ε (Mean = 0.82ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 16.5ε (Mean = 0.843ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RD: x = y + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.824ε (Mean = 0.0272ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.74ε (Mean = 0.84ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.85ε (Mean = 0.865ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.51ε (Mean = 0.816ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RD: x = 0, y = z + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2ε (Mean = 0.656ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.19ε (Mean = 0.522ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.16ε (Mean = 0.497ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RD: x = y = z + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.03ε (Mean = 0.418ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.998ε (Mean = 0.387ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.03ε (Mean = 0.418ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RD: x = 0 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2.85ε (Mean = 0.781ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.79ε (Mean = 0.883ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.64ε (Mean = 0.894ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_ellint_rf"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rf" title="ellint_rf">ellint_rf</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_ellint_rf.table_ellint_rf"></a><p class="title"><b>Table 35. Error rates for ellint_rf</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ellint_rf"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + RF: Random data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2.73ε (Mean = 0.804ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.54ε (Mean = 0.674ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.02ε (Mean = 0.677ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RF: x = y = z + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0.999ε (Mean = 0.34ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.991ε (Mean = 0.345ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.999ε (Mean = 0.34ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RF: x = y or y = z or x = z + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.536ε (Mean = 0.00658ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.89ε (Mean = 0.749ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.95ε (Mean = 0.418ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.21ε (Mean = 0.394ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RF: x = 0, y = z + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.29ε (Mean = 0.527ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.894ε (Mean = 0.338ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.999ε (Mean = 0.407ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RF: z = 0 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2.54ε (Mean = 0.781ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.7ε (Mean = 0.539ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.89ε (Mean = 0.587ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_ellint_rg"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rg" title="ellint_rg">ellint_rg</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_ellint_rg.table_ellint_rg"></a><p class="title"><b>Table 36. Error rates for ellint_rg</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ellint_rg"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + RG: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.983ε (Mean = 0.0172ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.983ε (Mean = 0.0172ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.95ε (Mean = 0.951ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.65ε (Mean = 0.929ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RG: two values 0 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RG: All values the same or zero + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.992ε (Mean = 0.288ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.06ε (Mean = 0.348ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RG: two values the same + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.594ε (Mean = 0.0103ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.594ε (Mean = 0.0103ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.51ε (Mean = 0.404ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.96ε (Mean = 0.374ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RG: one value zero + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.14ε (Mean = 0.722ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.96ε (Mean = 0.674ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_ellint_rj"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rj" title="ellint_rj">ellint_rj</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_ellint_rj.table_ellint_rj"></a><p class="title"><b>Table 37. Error rates for ellint_rj</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ellint_rj"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + RJ: Random data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.52ε (Mean = 0.0184ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.57ε (Mean = 0.704ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_rj_GSL_2_1_RJ_Random_data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 186ε (Mean = 6.67ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 215ε (Mean = 7.66ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RJ: 4 Equal Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.03ε (Mean = 0.418ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.998ε (Mean = 0.387ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.03ε (Mean = 0.418ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RJ: 3 Equal Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 3.96ε (Mean = 1.06ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 20.8ε (Mean = 0.986ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 39.9ε (Mean = 1.17ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RJ: 2 Equal Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.6ε (Mean = 0.0228ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.57ε (Mean = 0.754ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 220ε (Mean = 6.64ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 214ε (Mean = 5.28ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RJ: Equal z and p + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.742ε (Mean = 0.0166ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.62ε (Mean = 0.699ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 17.2ε (Mean = 1.16ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 16.1ε (Mean = 1.14ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_erf"></a><a class="link" href="index.html#special_function_error_rates_rep.section_erf" title="erf">erf</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_erf.table_erf"></a><p class="title"><b>Table 38. Error rates for erf</b></p> +<div class="table-contents"><table class="table" summary="Error rates for erf"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Erf Function: Small Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.925ε (Mean = 0.193ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 0.944ε (Mean = 0.191ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.944ε (Mean = 0.191ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.841ε (Mean = 0.0687ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.06ε (Mean = 0.319ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.925ε (Mean = 0.193ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.944ε (Mean = 0.194ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.996ε (Mean = 0.182ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.57ε (Mean = 0.317ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + Erf Function: Medium Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.5ε (Mean = 0.193ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 0.921ε (Mean = 0.0723ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.921ε (Mean = 0.0723ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1ε (Mean = 0.119ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2.31ε (Mean = 0.368ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.5ε (Mean = 0.197ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.921ε (Mean = 0.071ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1ε (Mean = 0.171ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> + Max = 1.19ε (Mean = 0.244ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + Erf Function: Large Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> + Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em><math.h>:</em></span> Max + = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> + Max = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> + Max = 0ε (Mean = 0ε)) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_erf_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_erf_inv" title="erf_inv">erf_inv</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_erf_inv.table_erf_inv"></a><p class="title"><b>Table 39. Error rates for erf_inv</b></p> +<div class="table-contents"><table class="table" summary="Error rates for erf_inv"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Inverse Erf Function + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.996ε (Mean = 0.389ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.08ε (Mean = 0.395ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.09ε (Mean = 0.502ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_erfc"></a><a class="link" href="index.html#special_function_error_rates_rep.section_erfc" title="erfc">erfc</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_erfc.table_erfc"></a><p class="title"><b>Table 40. Error rates for erfc</b></p> +<div class="table-contents"><table class="table" summary="Error rates for erfc"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Erf Function: Small Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> + Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em><math.h>:</em></span> Max + = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.658ε (Mean = 0.0537ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.01ε (Mean = 0.485ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> + Max = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> + Max = 0ε (Mean = 0ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + Erf Function: Medium Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.76ε (Mean = 0.365ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.35ε (Mean = 0.307ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.35ε (Mean = 0.307ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.983ε (Mean = 0.213ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.64ε (Mean = 0.662ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.76ε (Mean = 0.38ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 2.81ε (Mean = 0.739ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.65ε (Mean = 0.373ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 2.36ε (Mean = 0.539ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + Erf Function: Large Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.57ε (Mean = 0.542ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.26ε (Mean = 0.441ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.26ε (Mean = 0.441ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.868ε (Mean = 0.147ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.9ε (Mean = 0.472ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.57ε (Mean = 0.564ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 4.91ε (Mean = 1.54ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.14ε (Mean = 0.248ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.84ε (Mean = 0.331ε)) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_erfc_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_erfc_inv" title="erfc_inv">erfc_inv</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_erfc_inv.table_erfc_inv"></a><p class="title"><b>Table 41. Error rates for erfc_inv</b></p> +<div class="table-contents"><table class="table" summary="Error rates for erfc_inv"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Inverse Erfc Function + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.996ε (Mean = 0.397ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.08ε (Mean = 0.403ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1ε (Mean = 0.491ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Inverse Erfc Function: extreme values + </p> + </td> +<td> + </td> +<td> + <p> + <span class="blue">Max = 1.62ε (Mean = 0.383ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.62ε (Mean = 0.383ε)</span> + </p> + </td> +<td> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_expint_Ei_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_expint_Ei_" title="expint (Ei)">expint + (Ei)</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_expint_Ei_.table_expint_Ei_"></a><p class="title"><b>Table 42. Error rates for expint (Ei)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for expint (Ei)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Exponential Integral Ei + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.05ε (Mean = 0.821ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 14.1ε (Mean = 2.43ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_expint_Ei___cmath__Exponential_Integral_Ei">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.994ε (Mean = 0.142ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.96ε (Mean = 0.703ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.05ε (Mean = 0.835ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.43ε (Mean = 0.54ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Exponential Integral Ei: double exponent range + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.72ε (Mean = 0.593ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 3.11ε (Mean = 1.13ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.998ε (Mean = 0.156ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.5ε (Mean = 0.612ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.72ε (Mean = 0.607ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.7ε (Mean = 0.66ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Exponential Integral Ei: long exponent range + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.98ε (Mean = 0.595ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.93ε (Mean = 0.855ε)) + </p> + </td> +<td> + </td> +<td> + <p> + <span class="blue">Max = 1.98ε (Mean = 0.575ε)</span> + </p> + </td> +<td> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_expint_En_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_expint_En_" title="expint (En)">expint + (En)</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_expint_En_.table_expint_En_"></a><p class="title"><b>Table 43. Error rates for expint (En)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for expint (En)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Exponential Integral En + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.589ε (Mean = 0.0331ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 58.5ε (Mean = 17.1ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.97ε (Mean = 2.13ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.97ε (Mean = 2.13ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.16ε (Mean = 1.85ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Exponential Integral En: small z values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 115ε (Mean = 23.6ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.99ε (Mean = 0.559ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.99ε (Mean = 0.559ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.62ε (Mean = 0.531ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Exponential Integral E1 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.556ε (Mean = 0.0625ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.988ε (Mean = 0.469ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.965ε (Mean = 0.414ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.965ε (Mean = 0.408ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.988ε (Mean = 0.486ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_expm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_expm1" title="expm1">expm1</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_expm1.table_expm1"></a><p class="title"><b>Table 44. Error rates for expm1</b></p> +<div class="table-contents"><table class="table" summary="Error rates for expm1"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Random test data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.992ε (Mean = 0.402ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 0.992ε (Mean = 0.402ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.992ε (Mean = 0.402ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.793ε (Mean = 0.126ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.793ε (Mean = 0.126ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.31ε (Mean = 0.428ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.996ε (Mean = 0.426ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.31ε (Mean = 0.496ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.31ε (Mean = 0.496ε)) + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_gamma_p"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_p" title="gamma_p">gamma_p</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_gamma_p.table_gamma_p"></a><p class="title"><b>Table 45. Error rates for gamma_p</b></p> +<div class="table-contents"><table class="table" summary="Error rates for gamma_p"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + tgamma(a, z) medium values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.955ε (Mean = 0.05ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 342ε (Mean = 45.8ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 389ε (Mean = 44ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 41.6ε (Mean = 8.09ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 239ε (Mean = 30.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 35.1ε (Mean = 6.98ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma(a, z) small values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 4.82ε (Mean = 0.758ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 1.01ε (Mean = 0.306ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2ε (Mean = 0.464ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2ε (Mean = 0.461ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.54ε (Mean = 0.439ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma(a, z) large values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.02e+03ε (Mean = 105ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 1.11e+03ε (Mean = 67.5ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.08e+04ε (Mean = 1.86e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.02e+04ε (Mean = 1.91e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 243ε (Mean = 20.2ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma(a, z) integer and half integer values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 128ε (Mean = 22.6ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 66.2ε (Mean = 12.2ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 11.8ε (Mean = 2.66ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 71.6ε (Mean = 9.47ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 13ε (Mean = 2.97ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_gamma_p_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_p_inv" title="gamma_p_inv">gamma_p_inv</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_gamma_p_inv.table_gamma_p_inv"></a><p class="title"><b>Table 46. Error rates for gamma_p_inv</b></p> +<div class="table-contents"><table class="table" summary="Error rates for gamma_p_inv"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + incomplete gamma inverse(a, z) medium values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.993ε (Mean = 0.15ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.88ε (Mean = 0.868ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.8ε (Mean = 0.406ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.89ε (Mean = 0.466ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.71ε (Mean = 0.34ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + incomplete gamma inverse(a, z) large values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 0.816ε (Mean = 0.0874ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.509ε (Mean = 0.0447ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.509ε (Mean = 0.0447ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.924ε (Mean = 0.108ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + incomplete gamma inverse(a, z) small values + </p> + </td> +<td> + <p> + <span class="blue">Max = 441ε (Mean = 53.9ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 547ε (Mean = 61.6ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.17e+03ε (Mean = 1.45e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.09e+04ε (Mean = 1.3e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.1e+03ε (Mean = 131ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_gamma_p_inva"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_p_inva" title="gamma_p_inva">gamma_p_inva</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_gamma_p_inva.table_gamma_p_inva"></a><p class="title"><b>Table 47. Error rates for gamma_p_inva</b></p> +<div class="table-contents"><table class="table" summary="Error rates for gamma_p_inva"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Incomplete gamma inverses. + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.87ε (Mean = 1.15ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.08ε (Mean = 1.12ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.92ε (Mean = 1.03ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_gamma_q"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_q" title="gamma_q">gamma_q</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_gamma_q.table_gamma_q"></a><p class="title"><b>Table 48. Error rates for gamma_q</b></p> +<div class="table-contents"><table class="table" summary="Error rates for gamma_q"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + tgamma(a, z) medium values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.927ε (Mean = 0.035ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 201ε (Mean = 13.5ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 131ε (Mean = 12.7ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 32.3ε (Mean = 6.61ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 199ε (Mean = 26.6ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 23.7ε (Mean = 4ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma(a, z) small values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> <span class="red">Max = 1.38e+10ε (Mean = 1.05e+09ε))</span><br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 65.6ε (Mean = 11ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.45ε (Mean = 0.885ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.45ε (Mean = 0.819ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.26ε (Mean = 0.74ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma(a, z) large values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2.71e+04ε (Mean = 2.16e+03ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 1.02e+03ε (Mean = 62.7ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.82e+03ε (Mean = 414ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.15e+04ε (Mean = 733ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 469ε (Mean = 31.5ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma(a, z) integer and half integer values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 118ε (Mean = 12.5ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 138ε (Mean = 16.9ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 11.1ε (Mean = 2.07ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 54.7ε (Mean = 6.16ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.72ε (Mean = 1.48ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_gamma_q_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_q_inv" title="gamma_q_inv">gamma_q_inv</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_gamma_q_inv.table_gamma_q_inv"></a><p class="title"><b>Table 49. Error rates for gamma_q_inv</b></p> +<div class="table-contents"><table class="table" summary="Error rates for gamma_q_inv"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + incomplete gamma inverse(a, z) medium values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.912ε (Mean = 0.154ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.66ε (Mean = 0.792ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.2ε (Mean = 0.627ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.2ε (Mean = 0.683ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.88ε (Mean = 0.469ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + incomplete gamma inverse(a, z) large values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.894ε (Mean = 0.0915ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.894ε (Mean = 0.106ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.814ε (Mean = 0.0856ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + incomplete gamma inverse(a, z) small values + </p> + </td> +<td> + <p> + <span class="blue">Max = 292ε (Mean = 36.4ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 415ε (Mean = 48.7ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.28e+03ε (Mean = 1.09e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.98e+03ε (Mean = 877ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 451ε (Mean = 64.7ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_gamma_q_inva"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_q_inva" title="gamma_q_inva">gamma_q_inva</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_gamma_q_inva.table_gamma_q_inva"></a><p class="title"><b>Table 50. Error rates for gamma_q_inva</b></p> +<div class="table-contents"><table class="table" summary="Error rates for gamma_q_inva"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Incomplete gamma inverses. + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.42ε (Mean = 1.3ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.86ε (Mean = 1.24ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.05ε (Mean = 1.08ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_hermite"></a><a class="link" href="index.html#special_function_error_rates_rep.section_hermite" title="hermite">hermite</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_hermite.table_hermite"></a><p class="title"><b>Table 51. Error rates for hermite</b></p> +<div class="table-contents"><table class="table" summary="Error rates for hermite"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Hermite Polynomials + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.24ε (Mean = 2.07ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.24ε (Mean = 2.07ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.46ε (Mean = 1.41ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_heuman_lambda"></a><a class="link" href="index.html#special_function_error_rates_rep.section_heuman_lambda" title="heuman_lambda">heuman_lambda</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_heuman_lambda.table_heuman_lambda"></a><p class="title"><b>Table 52. Error rates for heuman_lambda</b></p> +<div class="table-contents"><table class="table" summary="Error rates for heuman_lambda"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Elliptic Integral Jacobi Zeta: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.89ε (Mean = 0.887ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.89ε (Mean = 0.887ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.08ε (Mean = 0.734ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Elliptic Integral Heuman Lambda: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.82ε (Mean = 0.609ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.82ε (Mean = 0.608ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.12ε (Mean = 0.588ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_ibeta"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibeta" title="ibeta">ibeta</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_ibeta.table_ibeta"></a><p class="title"><b>Table 53. Error rates for ibeta</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ibeta"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Incomplete Beta Function: Small Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 682ε (Mean = 32.6ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 22.9ε (Mean = 3.35ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.97ε (Mean = 2.09ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 21.3ε (Mean = 2.75ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.4ε (Mean = 1.93ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Incomplete Beta Function: Medium Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 690ε (Mean = 151ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 232ε (Mean = 27.9ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 50ε (Mean = 12.1ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 124ε (Mean = 18.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 106ε (Mean = 16.3ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Incomplete Beta Function: Large and Diverse Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.26ε (Mean = 0.063ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.9e+05ε (Mean = 1.82e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibeta_GSL_2_1_Incomplete_Beta_Function_Large_and_Diverse_Values">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 574ε (Mean = 49.4ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.96e+04ε (Mean = 997ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.98e+04ε (Mean = 2.07e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.32e+03ε (Mean = 68.5ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Incomplete Beta Function: Small Integer Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 254ε (Mean = 50.9ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 62.2ε (Mean = 8.95ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.45ε (Mean = 0.814ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 44.5ε (Mean = 10.1ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.85ε (Mean = 0.791ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_ibeta_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibeta_inv" title="ibeta_inv">ibeta_inv</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_ibeta_inv.table_ibeta_inv"></a><p class="title"><b>Table 54. Error rates for ibeta_inv</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ibeta_inv"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Inverse incomplete beta + </p> + </td> +<td> + <p> + <span class="blue">Max = 11ε (Mean = 0.345ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.14e+121ε (Mean + = 3.28e+119ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibeta_inv_Rmath_3_2_3_Inverse_incomplete_beta">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.8e+04ε (Mean = 2.66e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.07e+04ε (Mean = 2.86e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.59e+03ε (Mean = 277ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_ibeta_inva"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibeta_inva" title="ibeta_inva">ibeta_inva</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_ibeta_inva.table_ibeta_inva"></a><p class="title"><b>Table 55. Error rates for ibeta_inva</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ibeta_inva"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Inverse incomplete beta + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.602ε (Mean = 0.0239ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 377ε (Mean = 24.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 438ε (Mean = 31.3ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 242ε (Mean = 22.9ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_ibeta_invb"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibeta_invb" title="ibeta_invb">ibeta_invb</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_ibeta_invb.table_ibeta_invb"></a><p class="title"><b>Table 56. Error rates for ibeta_invb</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ibeta_invb"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Inverse incomplete beta + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.765ε (Mean = 0.0422ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 407ε (Mean = 27.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 407ε (Mean = 24.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 409ε (Mean = 19.3ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_ibetac"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibetac" title="ibetac">ibetac</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_ibetac.table_ibetac"></a><p class="title"><b>Table 57. Error rates for ibetac</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ibetac"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Incomplete Beta Function: Small Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 22.4ε (Mean = 3.67ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 10.6ε (Mean = 2.22ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 13.8ε (Mean = 2.68ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.94ε (Mean = 1.71ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Incomplete Beta Function: Medium Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 204ε (Mean = 25.8ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 73.9ε (Mean = 11.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 132ε (Mean = 19.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 56.7ε (Mean = 14.3ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Incomplete Beta Function: Large and Diverse Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.981ε (Mean = 0.0573ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 889ε (Mean = 68.4ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.45e+04ε (Mean = 1.32e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.31e+04ε (Mean = 2.04e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.88e+03ε (Mean = 82.7ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Incomplete Beta Function: Small Integer Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 84.6ε (Mean = 18ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.34ε (Mean = 1.11ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 107ε (Mean = 17.1ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.37ε (Mean = 1.03ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_ibetac_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibetac_inv" title="ibetac_inv">ibetac_inv</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_ibetac_inv.table_ibetac_inv"></a><p class="title"><b>Table 58. Error rates for ibetac_inv</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ibetac_inv"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Inverse incomplete beta + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.977ε (Mean = 0.0976ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 3.01e+132ε (Mean + = 8.65e+130ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibetac_inv_Rmath_3_2_3_Inverse_incomplete_beta">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.88e+04ε (Mean = 3.16e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.05e+04ε (Mean = 3.33e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.93e+03ε (Mean = 198ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_ibetac_inva"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibetac_inva" title="ibetac_inva">ibetac_inva</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_ibetac_inva.table_ibetac_inva"></a><p class="title"><b>Table 59. Error rates for ibetac_inva</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ibetac_inva"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Inverse incomplete beta + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.683ε (Mean = 0.0314ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 382ε (Mean = 22.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 315ε (Mean = 23.7ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 408ε (Mean = 26.7ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_ibetac_invb"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibetac_invb" title="ibetac_invb">ibetac_invb</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_ibetac_invb.table_ibetac_invb"></a><p class="title"><b>Table 60. Error rates for ibetac_invb</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ibetac_invb"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Inverse incomplete beta + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.724ε (Mean = 0.0303ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 317ε (Mean = 19.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 369ε (Mean = 22.6ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 271ε (Mean = 16.4ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_jacobi_cn"></a><a class="link" href="index.html#special_function_error_rates_rep.section_jacobi_cn" title="jacobi_cn">jacobi_cn</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_jacobi_cn.table_jacobi_cn"></a><p class="title"><b>Table 61. Error rates for jacobi_cn</b></p> +<div class="table-contents"><table class="table" summary="Error rates for jacobi_cn"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Jacobi Elliptic: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 17.3ε (Mean = 4.29ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 71.6ε (Mean = 19.3ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 71.6ε (Mean = 19.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 45.8ε (Mean = 11.4ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Jacobi Elliptic: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.816ε (Mean = 0.0563ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.43ε (Mean = 0.803ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.68ε (Mean = 0.443ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.68ε (Mean = 0.454ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.83ε (Mean = 0.455ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Jacobi Elliptic: Random Small Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 55.2ε (Mean = 1.64ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 10.4ε (Mean = 0.594ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 10.4ε (Mean = 0.602ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 26.2ε (Mean = 1.17ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Jacobi Elliptic: Modulus near 1 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.919ε (Mean = 0.127ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 675ε (Mean = 87.1ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 675ε (Mean = 86.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 513ε (Mean = 126ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Jacobi Elliptic: Large Phi + </p> + </td> +<td> + <p> + <span class="blue">Max = 14.2ε (Mean = 0.927ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 5.92e+03ε (Mean = 477ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.97e+04ε (Mean = 1.9e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.97e+04ε (Mean = 1.9e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.27e+04ε (Mean = 1.93e+03ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_jacobi_dn"></a><a class="link" href="index.html#special_function_error_rates_rep.section_jacobi_dn" title="jacobi_dn">jacobi_dn</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_jacobi_dn.table_jacobi_dn"></a><p class="title"><b>Table 62. Error rates for jacobi_dn</b></p> +<div class="table-contents"><table class="table" summary="Error rates for jacobi_dn"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Jacobi Elliptic: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2.82ε (Mean = 1.18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 49ε (Mean = 14ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 49ε (Mean = 14ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 34.3ε (Mean = 8.71ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Jacobi Elliptic: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 3ε (Mean = 0.61ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.53ε (Mean = 0.473ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.53ε (Mean = 0.481ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.52ε (Mean = 0.466ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Jacobi Elliptic: Random Small Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.5ε (Mean = 0.0122ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.5ε (Mean = 0.391ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 22.4ε (Mean = 0.777ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 22.4ε (Mean = 0.763ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 16.1ε (Mean = 0.685ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Jacobi Elliptic: Modulus near 1 + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.28ε (Mean = 0.194ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.75e+03ε (Mean = 293ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.75e+03ε (Mean = 293ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.24e+03ε (Mean = 482ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Jacobi Elliptic: Large Phi + </p> + </td> +<td> + <p> + <span class="blue">Max = 14.1ε (Mean = 0.897ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 121ε (Mean = 22ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.82e+04ε (Mean = 1.79e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.82e+04ε (Mean = 1.79e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.67e+04ε (Mean = 1e+03ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_jacobi_sn"></a><a class="link" href="index.html#special_function_error_rates_rep.section_jacobi_sn" title="jacobi_sn">jacobi_sn</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_jacobi_sn.table_jacobi_sn"></a><p class="title"><b>Table 63. Error rates for jacobi_sn</b></p> +<div class="table-contents"><table class="table" summary="Error rates for jacobi_sn"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Jacobi Elliptic: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 588ε (Mean = 146ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 341ε (Mean = 80.7ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 341ε (Mean = 80.7ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 481ε (Mean = 113ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Jacobi Elliptic: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 4.02ε (Mean = 1.07ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.01ε (Mean = 0.584ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.01ε (Mean = 0.593ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.92ε (Mean = 0.567ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Jacobi Elliptic: Random Small Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 11.7ε (Mean = 1.65ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.99ε (Mean = 0.347ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.99ε (Mean = 0.347ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.11ε (Mean = 0.385ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Jacobi Elliptic: Modulus near 1 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 109ε (Mean = 7.35ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 109ε (Mean = 7.38ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 23.2ε (Mean = 1.85ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Jacobi Elliptic: Large Phi + </p> + </td> +<td> + <p> + <span class="blue">Max = 12ε (Mean = 0.771ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.54e+04ε (Mean = 2.63e+03ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.45e+04ε (Mean = 1.51e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.45e+04ε (Mean = 1.51e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.36e+04ε (Mean = 2.54e+03ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_jacobi_zeta"></a><a class="link" href="index.html#special_function_error_rates_rep.section_jacobi_zeta" title="jacobi_zeta">jacobi_zeta</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_jacobi_zeta.table_jacobi_zeta"></a><p class="title"><b>Table 64. Error rates for jacobi_zeta</b></p> +<div class="table-contents"><table class="table" summary="Error rates for jacobi_zeta"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Elliptic Integral Jacobi Zeta: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.66ε (Mean = 0.48ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.66ε (Mean = 0.48ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.52ε (Mean = 0.357ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Elliptic Integral Jacobi Zeta: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.99ε (Mean = 0.824ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.96ε (Mean = 1.06ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.89ε (Mean = 0.824ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Elliptic Integral Jacobi Zeta: Large Phi Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.92ε (Mean = 0.951ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.05ε (Mean = 1.13ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.52ε (Mean = 0.977ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_laguerre_n_m_x_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_laguerre_n_m_x_" title="laguerre(n, m, x)">laguerre(n, + m, x)</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_laguerre_n_m_x_.table_laguerre_n_m_x_"></a><p class="title"><b>Table 65. Error rates for laguerre(n, m, x)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for laguerre(n, m, x)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Associated Laguerre Polynomials + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.84ε (Mean = 0.0358ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 434ε (Mean = 10.7ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 167ε (Mean = 6.38ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 206ε (Mean = 6.86ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 167ε (Mean = 6.38ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 434ε (Mean = 11.1ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_laguerre_n_x_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_laguerre_n_x_" title="laguerre(n, x)">laguerre(n, + x)</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_laguerre_n_x_.table_laguerre_n_x_"></a><p class="title"><b>Table 66. Error rates for laguerre(n, x)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for laguerre(n, x)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Laguerre Polynomials + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.82ε (Mean = 0.408ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.1e+03ε (Mean = 185ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.39e+04ε (Mean = 828ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 4.2e+03ε (Mean = 251ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.39e+04ε (Mean = 828ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.1e+03ε (Mean = 185ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_legendre_p"></a><a class="link" href="index.html#special_function_error_rates_rep.section_legendre_p" title="legendre_p">legendre_p</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_legendre_p.table_legendre_p"></a><p class="title"><b>Table 67. Error rates for legendre_p</b></p> +<div class="table-contents"><table class="table" summary="Error rates for legendre_p"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Legendre Polynomials: Small Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.732ε (Mean = 0.0619ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 211ε (Mean = 20.4ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 69.2ε (Mean = 9.58ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 124ε (Mean = 13.2ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 69.2ε (Mean = 9.58ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 211ε (Mean = 20.4ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Legendre Polynomials: Large Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.632ε (Mean = 0.0693ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 300ε (Mean = 33.2ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 699ε (Mean = 59.6ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 343ε (Mean = 32.1ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 699ε (Mean = 59.6ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 300ε (Mean = 33.2ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_legendre_p_associated_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_legendre_p_associated_" title="legendre_p (associated)">legendre_p + (associated)</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_legendre_p_associated_.table_legendre_p_associated_"></a><p class="title"><b>Table 68. Error rates for legendre_p (associated)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for legendre_p (associated)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Associated Legendre Polynomials: Small Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.999ε (Mean = 0.05ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 121ε (Mean = 6.75ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_legendre_p_associated__GSL_2_1_Associated_Legendre_Polynomials_Small_Values">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 175ε (Mean = 9.88ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 175ε (Mean = 9.36ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_legendre_p_associated___cmath__Associated_Legendre_Polynomials_Small_Values">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 77.7ε (Mean = 5.59ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 121ε (Mean = 7.14ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_legendre_q"></a><a class="link" href="index.html#special_function_error_rates_rep.section_legendre_q" title="legendre_q">legendre_q</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_legendre_q.table_legendre_q"></a><p class="title"><b>Table 69. Error rates for legendre_q</b></p> +<div class="table-contents"><table class="table" summary="Error rates for legendre_q"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Legendre Polynomials: Small Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.612ε (Mean = 0.0517ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 46.4ε (Mean = 7.46ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 50.9ε (Mean = 9ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 50.9ε (Mean = 8.98ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 46.4ε (Mean = 7.32ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Legendre Polynomials: Large Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.49ε (Mean = 0.202ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.6e+03ε (Mean = 366ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.98e+03ε (Mean = 478ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.98e+03ε (Mean = 478ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.6e+03ε (Mean = 366ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_lgamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_lgamma" title="lgamma">lgamma</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_lgamma.table_lgamma"></a><p class="title"><b>Table 70. Error rates for lgamma</b></p> +<div class="table-contents"><table class="table" summary="Error rates for lgamma"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + factorials + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 33.6ε (Mean = 2.78ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 1.55ε (Mean = 0.592ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.991ε (Mean = 0.308ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.67ε (Mean = 0.487ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.67ε (Mean = 0.487ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.991ε (Mean = 0.383ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.36ε (Mean = 0.476ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.914ε (Mean = 0.175ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.958ε (Mean = 0.38ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + near 0 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 5.21ε (Mean = 1.57ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.42ε (Mean = 0.566ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 0.964ε (Mean = 0.543ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.964ε (Mean = 0.543ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.42ε (Mean = 0.566ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.964ε (Mean = 0.543ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.964ε (Mean = 0.462ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.962ε (Mean = 0.372ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + near 1 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 442ε (Mean = 88.8ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 7.99e+04ε (Mean = 1.68e+04ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.948ε (Mean = 0.36ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 0.615ε (Mean = 0.096ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.615ε (Mean = 0.096ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.948ε (Mean = 0.36ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.71ε (Mean = 0.581ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.867ε (Mean = 0.468ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.906ε (Mean = 0.565ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + near 2 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.17e+03ε (Mean = 274ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 2.63e+05ε (Mean = 5.84e+04ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.878ε (Mean = 0.242ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 0.741ε (Mean = 0.263ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.741ε (Mean = 0.263ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.878ε (Mean = 0.242ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.598ε (Mean = 0.235ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.591ε (Mean = 0.159ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.741ε (Mean = 0.473ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + near -10 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 24.9ε (Mean = 4.6ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 4.22ε (Mean = 1.26ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.81ε (Mean = 1.01ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 0.997ε (Mean = 0.412ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.997ε (Mean = 0.412ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.81ε (Mean = 1.01ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 3.04ε (Mean = 1.01ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.22ε (Mean = 1.33ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.997ε (Mean = 0.444ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + near -55 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 7.02ε (Mean = 1.47ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 250ε (Mean = 60.9ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.821ε (Mean = 0.513ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.58ε (Mean = 0.672ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.58ε (Mean = 0.672ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.59ε (Mean = 0.587ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.821ε (Mean = 0.674ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.821ε (Mean = 0.419ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 249ε (Mean = 43.1ε)) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_log1p"></a><a class="link" href="index.html#special_function_error_rates_rep.section_log1p" title="log1p">log1p</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_log1p.table_log1p"></a><p class="title"><b>Table 71. Error rates for log1p</b></p> +<div class="table-contents"><table class="table" summary="Error rates for log1p"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Random test data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.818ε (Mean = 0.227ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 0.818ε (Mean = 0.227ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.818ε (Mean = 0.227ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.846ε (Mean = 0.153ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.846ε (Mean = 0.153ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.3ε (Mean = 0.66ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.818ε (Mean = 0.249ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.509ε (Mean = 0.057ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.509ε (Mean = 0.057ε)) + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_non_central_beta_CDF"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_beta_CDF" title="non central beta CDF">non + central beta CDF</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_non_central_beta_CDF.table_non_central_beta_CDF"></a><p class="title"><b>Table 72. Error rates for non central beta CDF</b></p> +<div class="table-contents"><table class="table" summary="Error rates for non central beta CDF"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Non Central Beta, medium parameters + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.998ε (Mean = 0.0649ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.46e+26ε (Mean + = 3.5e+24ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_medium_parameters">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 824ε (Mean = 27.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 832ε (Mean = 38.1ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 242ε (Mean = 31ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Non Central Beta, large parameters + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.18ε (Mean = 0.175ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.01e+36ε (Mean + = 1.19e+35ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_large_parameters">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.5e+04ε (Mean = 3.78e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.57e+04ε (Mean = 4.45e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.66e+03ε (Mean = 500ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_non_central_beta_CDF_complement"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_beta_CDF_complement" title="non central beta CDF complement">non + central beta CDF complement</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_non_central_beta_CDF_complement.table_non_central_beta_CDF_complement"></a><p class="title"><b>Table 73. Error rates for non central beta CDF complement</b></p> +<div class="table-contents"><table class="table" summary="Error rates for non central beta CDF complement"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Non Central Beta, medium parameters + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.998ε (Mean = 0.0936ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 7.5e+97ε (Mean + = 1.37e+96ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_medium_parameters">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 396ε (Mean = 50.7ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 554ε (Mean = 57.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 624ε (Mean = 62.7ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Non Central Beta, large parameters + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.986ε (Mean = 0.188ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INFε (Mean + = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_large_parameters">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.83e+03ε (Mean = 993ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.56e+03ε (Mean = 707ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.25e+04ε (Mean = 1.49e+03ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_non_central_chi_squared_CDF"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_chi_squared_CDF" title="non central chi squared CDF">non + central chi squared CDF</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_non_central_chi_squared_CDF.table_non_central_chi_squared_CDF"></a><p class="title"><b>Table 74. Error rates for non central chi squared CDF</b></p> +<div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Non Central Chi Squared, medium parameters + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.99ε (Mean = 0.0544ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 727ε (Mean = 121ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 46.5ε (Mean = 10.3ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 115ε (Mean = 13.9ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 48.9ε (Mean = 10ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Non Central Chi Squared, large parameters + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.07ε (Mean = 0.102ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 3.27e+08ε (Mean + = 2.23e+07ε))</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.07e+03ε (Mean = 336ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.17e+03ε (Mean = 677ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.79e+03ε (Mean = 723ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_non_central_chi_squared_CDF_complement"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_chi_squared_CDF_complement" title="non central chi squared CDF complement">non + central chi squared CDF complement</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_non_central_chi_squared_CDF_complement.table_non_central_chi_squared_CDF_complement"></a><p class="title"><b>Table 75. Error rates for non central chi squared CDF complement</b></p> +<div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF complement"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Non Central Chi Squared, medium parameters + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.96ε (Mean = 0.0635ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INFε (Mean + = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_medium_parameters">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 107ε (Mean = 17.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 171ε (Mean = 22.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 98.6ε (Mean = 15.8ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Non Central Chi Squared, large parameters + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.11ε (Mean = 0.278ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INFε (Mean + = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_large_parameters">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.02e+03ε (Mean = 630ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.1e+03ε (Mean = 577ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.43e+03ε (Mean = 705ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_non_central_t_CDF"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_t_CDF" title="non central t CDF">non + central t CDF</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_non_central_t_CDF.table_non_central_t_CDF"></a><p class="title"><b>Table 76. Error rates for non central t CDF</b></p> +<div class="table-contents"><table class="table" summary="Error rates for non central t CDF"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Non Central T + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.796ε (Mean = 0.0691ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 5.28e+15ε (Mean + = 8.49e+14ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_Rmath_3_2_3_Non_Central_T">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 139ε (Mean = 31ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 145ε (Mean = 30.9ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 135ε (Mean = 32.1ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Non Central T (small non-centrality) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 2.09e+03ε (Mean = 244ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.86ε (Mean = 1.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.15ε (Mean = 2.13ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.17ε (Mean = 1.45ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Non Central T (large parameters) + </p> + </td> +<td> + <p> + <span class="blue">Max = 257ε (Mean = 72.1ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.46ε (Mean = 0.657ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.26e+05ε (Mean = 1.48e+05ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.24e+05ε (Mean = 1.47e+05ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 286ε (Mean = 62.8ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_non_central_t_CDF_complement"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_t_CDF_complement" title="non central t CDF complement">non + central t CDF complement</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_non_central_t_CDF_complement.table_non_central_t_CDF_complement"></a><p class="title"><b>Table 77. Error rates for non central t CDF complement</b></p> +<div class="table-contents"><table class="table" summary="Error rates for non central t CDF complement"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Non Central T + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.707ε (Mean = 0.0497ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 6.19e+15ε (Mean + = 6.72e+14ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_complement_Rmath_3_2_3_Non_Central_T">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 201ε (Mean = 31.7ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 340ε (Mean = 43.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 154ε (Mean = 32.1ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Non Central T (small non-centrality) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 1.87e+03ε (Mean = 263ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 10.5ε (Mean = 2.13ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 10.5ε (Mean = 2.39ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.6ε (Mean = 1.63ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Non Central T (large parameters) + </p> + </td> +<td> + <p> + <span class="blue">Max = 478ε (Mean = 96.3ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.24ε (Mean = 0.945ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.79e+05ε (Mean = 1.97e+05ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.79e+05ε (Mean = 1.97e+05ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 227ε (Mean = 50.4ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_owens_t"></a><a class="link" href="index.html#special_function_error_rates_rep.section_owens_t" title="owens_t">owens_t</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_owens_t.table_owens_t"></a><p class="title"><b>Table 78. Error rates for owens_t</b></p> +<div class="table-contents"><table class="table" summary="Error rates for owens_t"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Owens T (medium small values) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.34ε (Mean = 0.944ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.34ε (Mean = 0.911ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.37ε (Mean = 0.98ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Owens T (large and diverse values) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 49ε (Mean = 2.16ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 24.5ε (Mean = 1.39ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.78ε (Mean = 0.621ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_polygamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_polygamma" title="polygamma">polygamma</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_polygamma.table_polygamma"></a><p class="title"><b>Table 79. Error rates for polygamma</b></p> +<div class="table-contents"><table class="table" summary="Error rates for polygamma"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Mathematica Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.824ε (Mean = 0.0574ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 62.9ε (Mean = 12.8ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 108ε (Mean = 15.2ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.38ε (Mean = 1.84ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 34.3ε (Mean = 7.65ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.32ε (Mean = 1.95ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Mathematica Data - large arguments + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.998ε (Mean = 0.0592ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 244ε (Mean = 32.8ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_arguments">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + <span class="red">Max = 1.71e+56ε (Mean = 1.01e+55ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_arguments">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.23ε (Mean = 0.323ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 11.1ε (Mean = 0.848ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 150ε (Mean = 13.9ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Mathematica Data - negative arguments + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.516ε (Mean = 0.022ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 36.6ε (Mean = 3.04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_negative_arguments">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_negative_arguments">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 269ε (Mean = 87.7ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 269ε (Mean = 88.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 497ε (Mean = 129ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Mathematica Data - large negative arguments + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.79ε (Mean = 0.197ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_negative_arguments">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_negative_arguments">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 155ε (Mean = 96.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 155ε (Mean = 96.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 162ε (Mean = 101ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Mathematica Data - small arguments + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 15.2ε (Mean = 5.03ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 106ε (Mean = 20ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.33ε (Mean = 0.75ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.33ε (Mean = 0.75ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3ε (Mean = 0.496ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Mathematica Data - Large orders and other bug cases + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 151ε (Mean = 39.3ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_Large_orders_and_other_bug_cases">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_Large_orders_and_other_bug_cases">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 54.5ε (Mean = 13.3ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 145ε (Mean = 55.9ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 200ε (Mean = 57.2ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_powm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_powm1" title="powm1">powm1</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_powm1.table_powm1"></a><p class="title"><b>Table 80. Error rates for powm1</b></p> +<div class="table-contents"><table class="table" summary="Error rates for powm1"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + powm1 + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.06ε (Mean = 0.425ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.04ε (Mean = 0.493ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.88ε (Mean = 0.49ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.84ε (Mean = 0.486ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_sin_pi"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sin_pi" title="sin_pi">sin_pi</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_sin_pi.table_sin_pi"></a><p class="title"><b>Table 81. Error rates for sin_pi</b></p> +<div class="table-contents"><table class="table" summary="Error rates for sin_pi"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + sin_pi and cos_pi + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.996ε (Mean = 0.335ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.996ε (Mean = 0.336ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.99ε (Mean = 0.328ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + sin_pi and cos_pi near integers and half integers + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.976ε (Mean = 0.293ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.976ε (Mean = 0.293ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.996ε (Mean = 0.343ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_sph_bessel"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sph_bessel" title="sph_bessel">sph_bessel</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_sph_bessel.table_sph_bessel"></a><p class="title"><b>Table 82. Error rates for sph_bessel</b></p> +<div class="table-contents"><table class="table" summary="Error rates for sph_bessel"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Bessel j: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 243ε (Mean = 13.3ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.91e+06ε (Mean = 1.09e+05ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.978ε (Mean = 0.0445ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.79e+03ε (Mean = 107ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 243ε (Mean = 33.7ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 245ε (Mean = 16.3ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_sph_bessel_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sph_bessel_prime" title="sph_bessel_prime">sph_bessel_prime</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_sph_bessel_prime.table_sph_bessel_prime"></a><p class="title"><b>Table 83. Error rates for sph_bessel_prime</b></p> +<div class="table-contents"><table class="table" summary="Error rates for sph_bessel_prime"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Bessel j': Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.753ε (Mean = 0.0343ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 167ε (Mean = 12ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 167ε (Mean = 33.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 307ε (Mean = 25.2ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_sph_neumann"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sph_neumann" title="sph_neumann">sph_neumann</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_sph_neumann.table_sph_neumann"></a><p class="title"><b>Table 84. Error rates for sph_neumann</b></p> +<div class="table-contents"><table class="table" summary="Error rates for sph_neumann"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + y: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 234ε (Mean = 19.5ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.6e+06ε (Mean = 1.4e+05ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.995ε (Mean = 0.0665ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.5e+04ε (Mean = 5.33e+03ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 234ε (Mean = 19.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 281ε (Mean = 31.1ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_sph_neumann_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sph_neumann_prime" title="sph_neumann_prime">sph_neumann_prime</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_sph_neumann_prime.table_sph_neumann_prime"></a><p class="title"><b>Table 85. Error rates for sph_neumann_prime</b></p> +<div class="table-contents"><table class="table" summary="Error rates for sph_neumann_prime"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + y': Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.988ε (Mean = 0.0869ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 158ε (Mean = 18.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 158ε (Mean = 20.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 296ε (Mean = 25.6ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_spherical_harmonic_i"></a><a class="link" href="index.html#special_function_error_rates_rep.section_spherical_harmonic_i" title="spherical_harmonic_i">spherical_harmonic_i</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_spherical_harmonic_i.table_spherical_harmonic_i"></a><p class="title"><b>Table 86. Error rates for spherical_harmonic_i</b></p> +<div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_i"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Spherical Harmonics + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.36ε (Mean = 0.0765ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.89e+03ε (Mean = 108ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.03e+04ε (Mean = 327ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.27e+04ε (Mean = 725ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_spherical_harmonic_r"></a><a class="link" href="index.html#special_function_error_rates_rep.section_spherical_harmonic_r" title="spherical_harmonic_r">spherical_harmonic_r</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_spherical_harmonic_r.table_spherical_harmonic_r"></a><p class="title"><b>Table 87. Error rates for spherical_harmonic_r</b></p> +<div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_r"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Spherical Harmonics + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.58ε (Mean = 0.0707ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.89e+03ε (Mean = 108ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.03e+04ε (Mean = 327ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.27e+04ε (Mean = 725ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_sqrt1pm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sqrt1pm1" title="sqrt1pm1">sqrt1pm1</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_sqrt1pm1.table_sqrt1pm1"></a><p class="title"><b>Table 88. Error rates for sqrt1pm1</b></p> +<div class="table-contents"><table class="table" summary="Error rates for sqrt1pm1"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + sqrt1pm1 + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.3ε (Mean = 0.404ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.33ε (Mean = 0.404ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.54ε (Mean = 0.563ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.35ε (Mean = 0.497ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_tgamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma" title="tgamma">tgamma</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_tgamma.table_tgamma"></a><p class="title"><b>Table 89. Error rates for tgamma</b></p> +<div class="table-contents"><table class="table" summary="Error rates for tgamma"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + factorials + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 3.95ε (Mean = 0.783ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 314ε (Mean = 93.4ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.67ε (Mean = 0.617ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.66ε (Mean = 0.584ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.66ε (Mean = 0.584ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 172ε (Mean = 41ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> + Max = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.85ε (Mean = 0.566ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 3.17ε (Mean = 0.928ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + near 0 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 4.51ε (Mean = 1.92ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 1ε (Mean = 0.335ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2ε (Mean = 0.608ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> + Max = 1ε (Mean = 0.376ε))<br> (<span class="emphasis"><em><math.h>:</em></span> + Max = 1ε (Mean = 0.376ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2ε (Mean = 0.647ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> + Max = 0.5ε (Mean = 0.0791ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.5ε (Mean = 0.635ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.405ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + near 1 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 4.41ε (Mean = 1.81ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 1ε (Mean = 0.32ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.51ε (Mean = 1.02ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 0.918ε (Mean = 0.203ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.918ε (Mean = 0.203ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.01ε (Mean = 1.06ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.175ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.1ε (Mean = 0.59ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.4ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + near 2 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 7.95ε (Mean = 3.12ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 1ε (Mean = 0.191ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.1ε (Mean = 1.55ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 0.558ε (Mean = 0.298ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.558ε (Mean = 0.298ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.01ε (Mean = 1.89ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2ε (Mean = 0.733ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> + Max = 0ε (Mean = 0ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + near -10 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2.6ε (Mean = 1.05ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 34.9ε (Mean = 9.2ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.75ε (Mean = 0.895ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 2.26ε (Mean = 1.08ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 2.26ε (Mean = 1.08ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.75ε (Mean = 0.819ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.86ε (Mean = 0.881ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.866ε (Mean = 0.445ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + near -55 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.8ε (Mean = 0.782ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 3.89e+04ε (Mean = 9.52e+03ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.69ε (Mean = 1.09ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.79ε (Mean = 0.75ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.79ε (Mean = 0.75ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 98.5ε (Mean = 53.4ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.7ε (Mean = 1.35ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 3.87e+04ε (Mean = 6.71e+03ε)) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_tgamma1pm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma1pm1" title="tgamma1pm1">tgamma1pm1</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_tgamma1pm1.table_tgamma1pm1"></a><p class="title"><b>Table 90. Error rates for tgamma1pm1</b></p> +<div class="table-contents"><table class="table" summary="Error rates for tgamma1pm1"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + tgamma1pm1(dz) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.12ε (Mean = 0.49ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.61ε (Mean = 0.84ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.31ε (Mean = 0.517ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_tgamma_delta_ratio"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma_delta_ratio" title="tgamma_delta_ratio">tgamma_delta_ratio</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_tgamma_delta_ratio.table_tgamma_delta_ratio"></a><p class="title"><b>Table 91. Error rates for tgamma_delta_ratio</b></p> +<div class="table-contents"><table class="table" summary="Error rates for tgamma_delta_ratio"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + tgamma + small delta ratios + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.83ε (Mean = 1.3ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 15.4ε (Mean = 2.09ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.56ε (Mean = 1.31ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma + small delta ratios (negative delta) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.94ε (Mean = 1.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 18.3ε (Mean = 2.03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.43ε (Mean = 1.42ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma + small integer ratios + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.96ε (Mean = 0.677ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.96ε (Mean = 0.677ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.74ε (Mean = 0.736ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma + small integer ratios (negative delta) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.62ε (Mean = 0.451ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.62ε (Mean = 0.451ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.15ε (Mean = 0.685ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + integer tgamma ratios + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.997ε (Mean = 0.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.997ε (Mean = 0.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.968ε (Mean = 0.386ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + integer tgamma ratios (negative delta) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.853ε (Mean = 0.176ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.853ε (Mean = 0.176ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.974ε (Mean = 0.175ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_tgamma_incomplete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma_incomplete_" title="tgamma (incomplete)">tgamma + (incomplete)</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_tgamma_incomplete_.table_tgamma_incomplete_"></a><p class="title"><b>Table 92. Error rates for tgamma (incomplete)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for tgamma (incomplete)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + tgamma(a, z) medium values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 200ε (Mean = 13.3ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.47ε (Mean = 1.9ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 412ε (Mean = 95.5ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.14ε (Mean = 1.76ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma(a, z) small values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.753ε (Mean = 0.0474ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> <span class="red">Max = 1.38e+10ε (Mean + = 1.05e+09ε))</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.31ε (Mean = 0.775ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.13ε (Mean = 0.717ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.53ε (Mean = 0.66ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma(a, z) integer and half integer values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 117ε (Mean = 12.5ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.52ε (Mean = 1.48ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 79.6ε (Mean = 20.9ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.16ε (Mean = 1.33ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_tgamma_lower"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma_lower" title="tgamma_lower">tgamma_lower</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_tgamma_lower.table_tgamma_lower"></a><p class="title"><b>Table 93. Error rates for tgamma_lower</b></p> +<div class="table-contents"><table class="table" summary="Error rates for tgamma_lower"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + tgamma(a, z) medium values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.833ε (Mean = 0.0315ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.833ε (Mean = 0.0315ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.79ε (Mean = 1.46ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 363ε (Mean = 63.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.62ε (Mean = 1.49ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma(a, z) small values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.97ε (Mean = 0.555ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.97ε (Mean = 0.558ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.57ε (Mean = 0.525ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma(a, z) integer and half integer values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.83ε (Mean = 1.15ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 84.7ε (Mean = 17.5ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.69ε (Mean = 0.849ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_tgamma_ratio"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma_ratio" title="tgamma_ratio">tgamma_ratio</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_tgamma_ratio.table_tgamma_ratio"></a><p class="title"><b>Table 94. Error rates for tgamma_ratio</b></p> +<div class="table-contents"><table class="table" summary="Error rates for tgamma_ratio"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + tgamma ratios + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.694ε (Mean = 0.0347ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.99ε (Mean = 1.15ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 174ε (Mean = 61.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.28ε (Mean = 1.12ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_trigamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_trigamma" title="trigamma">trigamma</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_trigamma.table_trigamma"></a><p class="title"><b>Table 95. Error rates for trigamma</b></p> +<div class="table-contents"><table class="table" summary="Error rates for trigamma"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Mathematica Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.998ε (Mean = 0.105ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.34e+04ε (Mean = 1.49e+03ε))<br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.34e+04ε (Mean = 1.51e+03ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.28ε (Mean = 0.449ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.28ε (Mean = 0.449ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1ε (Mean = 0.382ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.section_zeta"></a><a class="link" href="index.html#special_function_error_rates_rep.section_zeta" title="zeta">zeta</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.section_zeta.table_zeta"></a><p class="title"><b>Table 96. Error rates for zeta</b></p> +<div class="table-contents"><table class="table" summary="Error rates for zeta"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Zeta: Random values greater than 1 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.846ε (Mean = 0.0833ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 5.45ε (Mean = 1ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 8.69ε (Mean = 1.03ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.846ε (Mean = 0.0833ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.836ε (Mean = 0.093ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Zeta: Random values less than 1 + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.03ε (Mean = 2.93ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 538ε (Mean = 59.3ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 137ε (Mean = 13.8ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 70.1ε (Mean = 17.1ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.84ε (Mean = 3.12ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Zeta: Values close to and greater than 1 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.995ε (Mean = 0.5ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.9e+06ε (Mean = 5.11e+05ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 7.73ε (Mean = 4.07ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.995ε (Mean = 0.5ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.994ε (Mean = 0.421ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Zeta: Values close to and less than 1 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.998ε (Mean = 0.508ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 8.53e+06ε (Mean = 1.87e+06ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0.991ε (Mean = 0.28ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.998ε (Mean = 0.508ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.991ε (Mean = 0.375ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Zeta: Integer arguments + </p> + </td> +<td> + <p> + <span class="blue">Max = 9ε (Mean = 3.06ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> + Max = 70.3ε (Mean = 17.4ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 3.75ε (Mean = 1.1ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 28ε (Mean = 5.62ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9ε (Mean = 3ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.error_logs"></a><a class="link" href="index.html#special_function_error_rates_rep.error_logs" title="Error Logs">Error Logs</a> +</h2></div></div></div> +<h5> +<a name="special_function_error_rates_rep.error_logs.h0"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_in"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_in">Error + Output For cyl_bessel_j (integer orders) with compiler Microsoft Visual C++ + version 14.1 and library <math.h> and test data Bessel JN: Mathworld + Data (Integer Version)</a> + </h5> +<p> + <a name="errors_Microsoft_Visual_C_version_14_1_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_"></a>CAUTION: + Found non-finite result, when a finite value was expected at entry 16<br> + Found: -nan(ind) Expected 0 Error: 1.79769e+308<br> 10, 1e-100, 0<br> CAUTION: + Gross error found at entry 16.<br> Found: -nan(ind) Expected 0 Error: 1.79769e+308<br> + 10, 1e-100, 0<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h1"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_legendre_p_asso"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_legendre_p_asso">Error + Output For legendre_p (associated) with compiler GNU C++ version 7.1.0 and + library GSL 2.1 and test data Associated Legendre Polynomials: Small Values</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_legendre_p_associated__GSL_2_1_Associated_Legendre_Polynomials_Small_Values"></a>domain + error<br> 3.75573, -3, 0.264719, 0.0186823<br> domain error<br> 3.75573, + -3, 0.670017, 0.0085227<br> domain error<br> 3.75573, -3, 0.915014, 0.00136786<br> + domain error<br> 3.75573, -3, 0.93539, 0.000921218<br> domain error<br> + 3.75573, -2, -0.804919, -0.035427<br> domain error<br> 3.75573, -2, -0.623236, + -0.0476446<br> domain error<br> 3.75573, -2, 0.629447, 0.0475072<br> + domain error<br> 3.75573, -2, 0.929777, 0.0157498<br> domain error<br> + 3.75573, -2, 0.985763, 0.0034837<br> domain error<br> 3.75573, -1, 0.093763, + -0.118979<br> domain error<br> 4.28576, -4, 0.0944412, 0.00255792<br> + domain error<br> 4.28576, -4, 0.670017, 0.000790849<br> domain error<br> + 4.28576, -3, -0.746026, -0.00458957<br> domain error<br> 4.28576, -2, -0.623236, + 0.0219016<br> domain error<br> 4.28576, -2, 0.629447, 0.0223081<br> domain + error<br> 4.28576, -2, 0.93539, 0.0133504<br> domain error<br> 4.28576, + -1, 0.915014, 0.132001<br> domain error<br> 4.28576, -1, 0.985763, 0.0787743<br> + domain error<br> 4.43859, -4, 0.093763, 0.00255858<br> domain error<br> + 4.43859, -4, 0.811584, 0.000303404<br> domain error<br> 4.43859, -4, 0.826752, + 0.000260835<br> domain error<br> 4.43859, -4, 0.929777, 4.78235e-05<br> + domain error<br> 4.43859, -3, -0.804919, -0.00350364<br> domain error<br> + 4.43859, -3, -0.729046, -0.00487043<br> domain error<br> 4.43859, -3, -0.623236, + -0.00620995<br> domain error<br> 4.43859, -3, 0.93539, 0.000861698<br> + domain error<br> 4.43859, -2, -0.557932, 0.0169167<br> domain error<br> + 4.43859, -2, -0.443004, 0.0062586<br> domain error<br> 4.43859, -2, 0.915014, + 0.016481<br> domain error<br> 4.43859, -1, 0.629447, -0.0138523<br> domain + error<br> 5.39088, -5, 0.0944412, 0.000254649<br> domain error<br> 5.39088, + -5, 0.264719, 0.000217164<br> domain error<br> 5.39088, -5, 0.670017, 5.87083e-05<br> + domain error<br> 5.39088, -5, 0.915014, 2.78273e-06<br> domain error<br> + 5.39088, -3, 0.929777, 0.000880849<br> domain error<br> 5.39088, -2, 0.629447, + 0.00448021<br> domain error<br> 5.39088, -2, 0.826752, 0.01718<br> domain + error<br> 5.39088, -2, 0.937736, 0.011583<br> domain error<br> 5.39088, + -1, -0.804919, 0.0276144<br> domain error<br> 5.39088, -1, -0.746026, -0.0119425<br> + domain error<br> 5.39088, -1, -0.443004, -0.0525987<br> domain error<br> + 5.39088, -1, 0.811584, 0.032475<br> domain error<br> 5.39088, -1, 0.985763, + 0.0759289<br> domain error<br> 5.97861, -5, -0.729046, 3.91223e-05<br> + domain error<br> 5.97861, -5, -0.383666, 0.000174899<br> domain error<br> + 5.97861, -5, 0.93539, 1.43993e-06<br> domain error<br> 5.97861, -4, -0.623236, + -0.000607048<br> domain error<br> 5.97861, -4, 0.264719, 0.00059614<br> + domain error<br> 5.97861, -3, 0.629447, 0.00313497<br> domain error<br> + 5.97861, -3, 0.670017, 0.00323895<br> domain error<br> 5.97861, -2, 0.915014, + 0.0140705<br> domain error<br> 5.97861, -2, 0.992923, 0.00171356<br> + domain error<br> 5.97861, -1, -0.746026, -0.0119425<br> domain error<br> + 5.97861, -1, 0.937736, 0.106972<br> domain error<br> 7.01297, -6, -0.443004, + -4.99177e-06<br> domain error<br> 7.01297, -6, 0.629447, 3.00689e-06<br> + domain error<br> 7.01297, -6, 0.811584, 7.00407e-07<br> domain error<br> + 7.01297, -6, 0.985763, 4.83431e-10<br> domain error<br> 7.01297, -3, 0.670017, + 0.000233323<br> domain error<br> 7.01297, -2, -0.804919, -0.0027739<br> + domain error<br> 7.01297, -1, -0.383666, 0.0397866<br> domain error<br> + 7.01297, -1, 0.929777, 0.0544549<br> domain error<br> 7.54701, -7, 0.929777, + 1.42008e-09<br> domain error<br> 7.54701, -6, 0.992923, 6.04622e-11<br> + domain error<br> 7.54701, -5, -0.804919, 1.18502e-05<br> domain error<br> + 7.54701, -5, -0.623236, 2.57049e-05<br> domain error<br> 7.54701, -5, -0.557932, + 2.60266e-05<br> domain error<br> 7.54701, -5, 0.826752, 9.64276e-06<br> + domain error<br> 7.54701, -4, -0.746026, -0.0001618<br> domain error<br> + 7.54701, -3, 0.0944412, 0.000622493<br> domain error<br> 7.54701, -3, 0.985763, + 9.14782e-05<br> domain error<br> 7.54701, -1, 0.811584, -0.0376184<br> + domain error<br> 11.8439, -10, -0.557932, -2.32652e-11<br> domain error<br> + 11.8439, -10, 0.811584, 1.01194e-12<br> domain error<br> 11.8439, -8, -0.746026, + -1.34891e-09<br> domain error<br> 11.8439, -8, -0.729046, -1.5428e-09<br> + domain error<br> 11.8439, -8, 0.985763, 5.90035e-14<br> domain error<br> + 11.8439, -4, 0.629447, -1.44723e-05<br> domain error<br> 11.8439, -4, 0.929777, + 1.98812e-05<br> domain error<br> 11.8439, -3, 0.670017, -4.58296e-05<br> + domain error<br> 11.8439, -2, 0.826752, -0.00244759<br> domain error<br> + 11.8439, -2, 0.992923, 0.00151458<br> domain error<br> 11.8439, -1, -0.383666, + 0.00419108<br> domain error<br> 11.85, -11, 0.093763, 1.16526e-11<br> + domain error<br> 11.85, -11, 0.929777, 2.05797e-16<br> domain error<br> + 11.85, -11, 0.93539, 1.32249e-16<br> domain error<br> *** FURTHER CONTENT + HAS BEEN TRUNCATED FOR BREVITY ***<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h2"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_legendre_p_ass0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_legendre_p_ass0">Error + Output For legendre_p (associated) with compiler GNU C++ version 7.1.0 and + library <cmath> and test data Associated Legendre Polynomials: Small + Values</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_legendre_p_associated___cmath__Associated_Legendre_Polynomials_Small_Values"></a>order + parameters less than 0 not supported in TR1<br> 3.75573, -3, 0.264719, 0.0186823<br> + order parameters less than 0 not supported in TR1<br> 3.75573, -3, 0.670017, + 0.0085227<br> order parameters less than 0 not supported in TR1<br> 3.75573, + -3, 0.915014, 0.00136786<br> order parameters less than 0 not supported in + TR1<br> 3.75573, -3, 0.93539, 0.000921218<br> order parameters less than + 0 not supported in TR1<br> 3.75573, -2, -0.804919, -0.035427<br> order + parameters less than 0 not supported in TR1<br> 3.75573, -2, -0.623236, -0.0476446<br> + order parameters less than 0 not supported in TR1<br> 3.75573, -2, 0.629447, + 0.0475072<br> order parameters less than 0 not supported in TR1<br> 3.75573, + -2, 0.929777, 0.0157498<br> order parameters less than 0 not supported in + TR1<br> 3.75573, -2, 0.985763, 0.0034837<br> order parameters less than + 0 not supported in TR1<br> 3.75573, -1, 0.093763, -0.118979<br> order parameters + less than 0 not supported in TR1<br> 4.28576, -4, 0.0944412, 0.00255792<br> + order parameters less than 0 not supported in TR1<br> 4.28576, -4, 0.670017, + 0.000790849<br> order parameters less than 0 not supported in TR1<br> 4.28576, + -3, -0.746026, -0.00458957<br> order parameters less than 0 not supported + in TR1<br> 4.28576, -2, -0.623236, 0.0219016<br> order parameters less + than 0 not supported in TR1<br> 4.28576, -2, 0.629447, 0.0223081<br> order + parameters less than 0 not supported in TR1<br> 4.28576, -2, 0.93539, 0.0133504<br> + order parameters less than 0 not supported in TR1<br> 4.28576, -1, 0.915014, + 0.132001<br> order parameters less than 0 not supported in TR1<br> 4.28576, + -1, 0.985763, 0.0787743<br> order parameters less than 0 not supported in + TR1<br> 4.43859, -4, 0.093763, 0.00255858<br> order parameters less than + 0 not supported in TR1<br> 4.43859, -4, 0.811584, 0.000303404<br> order + parameters less than 0 not supported in TR1<br> 4.43859, -4, 0.826752, 0.000260835<br> + order parameters less than 0 not supported in TR1<br> 4.43859, -4, 0.929777, + 4.78235e-05<br> order parameters less than 0 not supported in TR1<br> 4.43859, + -3, -0.804919, -0.00350364<br> order parameters less than 0 not supported + in TR1<br> 4.43859, -3, -0.729046, -0.00487043<br> order parameters less + than 0 not supported in TR1<br> 4.43859, -3, -0.623236, -0.00620995<br> + order parameters less than 0 not supported in TR1<br> 4.43859, -3, 0.93539, + 0.000861698<br> order parameters less than 0 not supported in TR1<br> 4.43859, + -2, -0.557932, 0.0169167<br> order parameters less than 0 not supported in + TR1<br> 4.43859, -2, -0.443004, 0.0062586<br> order parameters less than + 0 not supported in TR1<br> 4.43859, -2, 0.915014, 0.016481<br> order parameters + less than 0 not supported in TR1<br> 4.43859, -1, 0.629447, -0.0138523<br> + order parameters less than 0 not supported in TR1<br> 5.39088, -5, 0.0944412, + 0.000254649<br> order parameters less than 0 not supported in TR1<br> 5.39088, + -5, 0.264719, 0.000217164<br> order parameters less than 0 not supported + in TR1<br> 5.39088, -5, 0.670017, 5.87083e-05<br> order parameters less + than 0 not supported in TR1<br> 5.39088, -5, 0.915014, 2.78273e-06<br> + order parameters less than 0 not supported in TR1<br> 5.39088, -3, 0.929777, + 0.000880849<br> order parameters less than 0 not supported in TR1<br> 5.39088, + -2, 0.629447, 0.00448021<br> order parameters less than 0 not supported in + TR1<br> 5.39088, -2, 0.826752, 0.01718<br> order parameters less than 0 + not supported in TR1<br> 5.39088, -2, 0.937736, 0.011583<br> order parameters + less than 0 not supported in TR1<br> 5.39088, -1, -0.804919, 0.0276144<br> + order parameters less than 0 not supported in TR1<br> 5.39088, -1, -0.746026, + -0.0119425<br> order parameters less than 0 not supported in TR1<br> 5.39088, + -1, -0.443004, -0.0525987<br> order parameters less than 0 not supported + in TR1<br> 5.39088, -1, 0.811584, 0.032475<br> order parameters less than + 0 not supported in TR1<br> 5.39088, -1, 0.985763, 0.0759289<br> order parameters + less than 0 not supported in TR1<br> 5.97861, -5, -0.729046, 3.91223e-05<br> + order parameters less than 0 not supported in TR1<br> 5.97861, -5, -0.383666, + 0.000174899<br> order parameters less than 0 not supported in TR1<br> 5.97861, + -5, 0.93539, 1.43993e-06<br> order parameters less than 0 not supported in + TR1<br> 5.97861, -4, -0.623236, -0.000607048<br> order parameters less + than 0 not supported in TR1<br> 5.97861, -4, 0.264719, 0.00059614<br> order + parameters less than 0 not supported in TR1<br> 5.97861, -3, 0.629447, 0.00313497<br> + *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h3"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_wi"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_wi">Error + Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library Rmath + 3.2.3 and test data Bessel Iv: Mathworld Data (large values)</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_Iv_Mathworld_Data_large_values_"></a>CAUTION: + Gross error found at entry 0.<br> Found: 0 Expected 1.86459e-155 Error: 8.37988e+152<br> + -1, 3.72917e-155, 1.86459e-155<br> CAUTION: Gross error found at entry 1.<br> + Found: 0 Expected 1.86459e-155 Error: 8.37988e+152<br> 1, 3.72917e-155, 1.86459e-155<br> + CAUTION: Gross error found at entry 3.<br> Found: 0 Expected 8.02269e-175 + Error: 3.60559e+133<br> 1.125, 3.72917e-155, 8.02269e-175<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h4"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_in"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_in">Error + Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0 + and library Rmath 3.2.3 and test data Bessel In: Mathworld Data (Integer Version)</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_In_Mathworld_Data_Integer_Version_"></a>Unsupported + domain<br> -5, -1, -0.000271463<br> Unsupported domain<br> 10, -5, 0.00458004<br> + Unsupported domain<br> -100, -200, 4.35275e+74<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h5"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i0">Error + Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0 + and library Rmath 3.2.3 and test data Bessel I1: Mathworld Data (Integer Version)</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I1_Mathworld_Data_Integer_Version_"></a>Unsupported + domain<br> 1, -2, -1.59064<br> Unsupported domain<br> 1, -8, -399.873<br> + Unsupported domain<br> 1, -10, -2670.99<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h6"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i1">Error + Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0 + and library Rmath 3.2.3 and test data Bessel I0: Mathworld Data (Integer Version)</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I0_Mathworld_Data_Integer_Version_"></a>Unsupported + domain<br> 0, -2, 2.27959<br> Unsupported domain<br> 0, -7, 168.594<br> + Unsupported domain<br> 0, -1, 1.26607<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h7"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w0">Error + Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library Rmath + 3.2.3 and test data Bessel In: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_In_Mathworld_Data"></a>Unsupported + domain<br> -5, -1, -0.000271463<br> Unsupported domain<br> 10, -5, 0.00458004<br> + Unsupported domain<br> -100, -200, 4.35275e+74<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h8"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w1">Error + Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library Rmath + 3.2.3 and test data Bessel I1: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I1_Mathworld_Data"></a>Unsupported + domain<br> 1, -2, -1.59064<br> Unsupported domain<br> 1, -8, -399.873<br> + Unsupported domain<br> 1, -10, -2670.99<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h9"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w2">Error + Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library Rmath + 3.2.3 and test data Bessel I0: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I0_Mathworld_Data"></a>Unsupported + domain<br> 0, -2, 2.27959<br> Unsupported domain<br> 0, -7, 168.594<br> + Unsupported domain<br> 0, -1, 1.26607<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h10"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_wi"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_wi">Error + Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library Rmath + 3.2.3 and test data Bessel J: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J_Mathworld_Data"></a>CAUTION: + Gross error found at entry 6.<br> Found: 0 Expected -0.000747424 Error: 3.3591e+304<br> + 5.5, 1e+06, -0.000747424<br> CAUTION: Gross error found at entry 7.<br> + Found: 0 Expected -0.0007766 Error: 3.49022e+304<br> 5.125, 1e+06, -0.0007766<br> + CAUTION: Gross error found at entry 8.<br> Found: 0 Expected -0.000466323 + Error: 2.09576e+304<br> 5.875, 1e+06, -0.000466323<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h11"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i0">Error + Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0 + and library Rmath 3.2.3 and test data Bessel JN: Mathworld Data (Integer Version)</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_JN_Mathworld_Data_Integer_Version_"></a>Unsupported + domain<br> 5, -10, 0.234062<br> CAUTION: Gross error found at entry 6.<br> + Found: 0 Expected 0.000725964 Error: 3.26265e+304<br> -5, 1e+06, 0.000725964<br> + CAUTION: Gross error found at entry 7.<br> Found: 0 Expected -0.000725964 + Error: 3.26265e+304<br> 5, 1e+06, -0.000725964<br> Unsupported domain<br> + -5, -1, 0.000249758<br> Unsupported domain<br> 10, -10, 0.207486<br> + Unsupported domain<br> 10, -5, 0.0014678<br> CAUTION: Gross error found + at entry 12.<br> Found: 0 Expected -0.000331079 Error: 1.48795e+304<br> + -10, 1e+06, -0.000331079<br> CAUTION: Gross error found at entry 13.<br> + Found: 0 Expected -0.000331079 Error: 1.48795e+304<br> 10, 1e+06, -0.000331079<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h12"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i1">Error + Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0 + and library Rmath 3.2.3 and test data Bessel J1: Mathworld Data (Integer Version)</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J1_Mathworld_Data_Integer_Version_"></a>Unsupported + domain<br> 1, -2, -0.576725<br> Unsupported domain<br> 1, -8, -0.234636<br> + Unsupported domain<br> 1, -10, -0.0434727<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h13"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i2">Error + Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0 + and library Rmath 3.2.3 and test data Bessel J0: Mathworld Data (Integer Version)</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J0_Mathworld_Data_Integer_Version_"></a>Unsupported + domain<br> 0, -2, 0.223891<br> Unsupported domain<br> 0, -8, 0.171651<br> + Unsupported domain<br> 0, -10, -0.245936<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h14"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w0">Error + Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library Rmath + 3.2.3 and test data Bessel JN: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_JN_Mathworld_Data"></a>Unsupported + domain<br> 5, -10, 0.234062<br> CAUTION: Gross error found at entry 6.<br> + Found: 0 Expected 0.000725964 Error: 3.26265e+304<br> -5, 1e+06, 0.000725964<br> + CAUTION: Gross error found at entry 7.<br> Found: 0 Expected -0.000725964 + Error: 3.26265e+304<br> 5, 1e+06, -0.000725964<br> Unsupported domain<br> + -5, -1, 0.000249758<br> Unsupported domain<br> 10, -10, 0.207486<br> + Unsupported domain<br> 10, -5, 0.0014678<br> CAUTION: Gross error found + at entry 12.<br> Found: 0 Expected -0.000331079 Error: 1.48795e+304<br> + -10, 1e+06, -0.000331079<br> CAUTION: Gross error found at entry 13.<br> + Found: 0 Expected -0.000331079 Error: 1.48795e+304<br> 10, 1e+06, -0.000331079<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h15"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w1">Error + Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library Rmath + 3.2.3 and test data Bessel J1: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J1_Mathworld_Data"></a>Unsupported + domain<br> 1, -2, -0.576725<br> Unsupported domain<br> 1, -8, -0.234636<br> + Unsupported domain<br> 1, -10, -0.0434727<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h16"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w2">Error + Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library Rmath + 3.2.3 and test data Bessel J0: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J0_Mathworld_Data"></a>Unsupported + domain<br> 0, -2, 0.223891<br> Unsupported domain<br> 0, -8, 0.171651<br> + Unsupported domain<br> 0, -10, -0.245936<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h17"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ibetac_inv_with"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ibetac_inv_with">Error + Output For ibetac_inv with compiler GNU C++ version 7.1.0 and library Rmath + 3.2.3 and test data Inverse incomplete beta</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_ibetac_inv_Rmath_3_2_3_Inverse_incomplete_beta"></a>CAUTION: + Gross error found at entry 7.<br> Found: 3.8247e-302 Expected 0 Error: 1.71891e+06<br> + 1.38853e-05, 0.0497627, 0.632396, 0, 0<br> CAUTION: Gross error found at + entry 71.<br> Found: 1.38362e-204 Expected 0 Error: 6.21832e+103<br> 3.77931e-05, + 0.0150073, 0.835025, 0, 0<br> CAUTION: Gross error found at entry 90.<br> + Found: 1.09275e-303 Expected 0 Error: 49109.6<br> 4.29383e-05, 0.0428761, + 0.814742, 0, 0<br> CAUTION: Gross error found at entry 102.<br> Found: + 3.8625e-304 Expected 0 Error: 17358<br> 4.80089e-05, 0.0296236, 0.913384, + 0, 0<br> CAUTION: Gross error found at entry 115.<br> Found: 1.51774e-303 + Expected 0 Error: 68209.8<br> 0.000130387, 0.0404969, 0.814742, 0, 0<br> + CAUTION: Gross error found at entry 123.<br> Found: 1.28036e-303 Expected + 0 Error: 57541.4<br> 0.000149328, 0.0201182, 0.905801, 5.70765e-267, 0<br> + CAUTION: Gross error found at entry 133.<br> Found: 1.96732e-302 Expected + 0 Error: 884160<br> 0.000173563, 0.0301908, 0.913384, 4.21662e-213, 0<br> + CAUTION: Gross error found at entry 159.<br> Found: 1.48697e-191 Expected + 0 Error: 6.68279e+116<br> 0.000260723, 0.0252933, 0.632396, 0, 0<br> CAUTION: + Gross error found at entry 256.<br> Found: 9.24166e-245 Expected 0 Error: + 4.15342e+63<br> 0.00246975, 0.016063, 0.913384, 1, 0<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h18"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ibeta_inv_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ibeta_inv_with_">Error + Output For ibeta_inv with compiler GNU C++ version 7.1.0 and library Rmath + 3.2.3 and test data Inverse incomplete beta</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_ibeta_inv_Rmath_3_2_3_Inverse_incomplete_beta"></a>CAUTION: + Gross error found at entry 1.<br> Found: 1.90197e-247 Expected 0 Error: 8.54789e+60<br> + 1.12733e-05, 0.022662, 0.135563, 0, 0<br> CAUTION: Gross error found at entry + 30.<br> Found: 1.36217e-301 Expected 0 Error: 6.12191e+06<br> 2.10769e-05, + 0.0448972, 0.221112, 0, 0<br> CAUTION: Gross error found at entry 152.<br> + Found: 2.92621e-285 Expected 0 Error: 1.31511e+23<br> 0.000240381, 0.017982, + 0.221112, 0, 0<br> CAUTION: Gross error found at entry 184.<br> Found: + 5.63355e-203 Expected 0 Error: 2.53185e+105<br> 0.000348822, 0.0275467, 0.135563, + 0, 1.88165e-166<br> CAUTION: Gross error found at entry 205.<br> Found: + 5.52731e-303 Expected 0 Error: 248409<br> 0.000441212, 0.0313573, 0.127074, + 0, 9.07221e-121<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h19"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_bet"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_bet">Error + Output For non central beta CDF complement with compiler GNU C++ version 7.1.0 + and library Rmath 3.2.3 and test data Non Central Beta, large parameters</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_large_parameters"></a>CAUTION: + Gross error found at entry 10.<br> Found: 9.76918e-10 Expected 1.61248e-15 + Error: 605846<br> 290.682, 72.6705, 20005.4, 0.997663, 1, 1.61248e-15<br> + CAUTION: Gross error found at entry 11.<br> Found: 9.94184e-10 Expected 3.0108e-42 + Error: 3.30205e+32<br> 290.682, 145.341, 53489.1, 0.998663, 1, 3.0108e-42<br> + CAUTION: Gross error found at entry 16.<br> Found: 8.45406e-10 Expected 4.46652e-22 + Error: 1.89276e+12<br> 290.682, 1162.73, 2308.07, 0.656921, 1, 4.46652e-22<br> + CAUTION: Gross error found at entry 17.<br> Found: 9.41971e-10 Expected 1.7241e-50 + Error: 5.46356e+40<br> 290.682, 1453.41, 8064.48, 0.832237, 1, 1.7241e-50<br> + CAUTION: Gross error found at entry 18.<br> Found: 9.30663e-10 Expected 2.09803e-305 + Error: 4.43589e+295<br> 975.766, 731.824, 232.285, 0.919742, 1, 2.09803e-305<br> + CAUTION: Gross error found at entry 27.<br> Found: 9.76918e-10 Expected 9.3474e-18 + Error: 1.04512e+08<br> 1879.05, 187.905, 20005.4, 0.992215, 1, 9.3474e-18<br> + CAUTION: Gross error found at entry 28.<br> Found: 9.94184e-10 Expected 1.8122e-90 + Error: 5.48607e+80<br> 1879.05, 469.762, 53489.1, 0.994618, 1, 1.8122e-90<br> + CAUTION: Gross error found at entry 32.<br> Found: 9.27224e-10 Expected 3.18255e-15 + Error: 291345<br> 1879.05, 3758.1, 1879.05, 0.480508, 1, 3.18255e-15<br> + CAUTION: Gross error found at entry 33.<br> Found: 8.45406e-10 Expected 1.10218e-77 + Error: 7.67029e+67<br> 1879.05, 5637.15, 2308.07, 0.458181, 1, 1.10218e-77<br> + CAUTION: Gross error found at entry 34.<br> Found: 9.30663e-10 Expected 0 + Error: 4.18262e+298<br> 2308.07, 1154.03, 232.285, 0.919371, 1, 0<br> CAUTION: + Gross error found at entry 35.<br> Found: 8.93617e-10 Expected 0 Error: 4.01612e+298<br> + 2308.07, 1731.05, 290.682, 0.917262, 1, 0<br> CAUTION: Gross error found + at entry 43.<br> Found: 9.94184e-10 Expected 3.57283e-70 Error: 2.78262e+60<br> + 8064.48, 806.448, 53489.1, 0.988678, 1, 3.57283e-70<br> CAUTION: Gross error + found at entry 48.<br> Found: 8.45406e-10 Expected 8.78057e-74 Error: 9.62814e+63<br> + 8064.48, 16129, 2308.07, 0.421531, 1, 8.78057e-74<br> CAUTION: Gross error + found at entry 49.<br> Found: 9.30663e-10 Expected 0 Error: 4.18262e+298<br> + 15674.4, 3918.59, 232.285, 0.933726, 1, 0<br> CAUTION: Gross error found + at entry 50.<br> Found: 8.93617e-10 Expected 0 Error: 4.01612e+298<br> + 15674.4, 7837.19, 290.682, 0.917179, 1, 0<br> CAUTION: Gross error found + at entry 51.<br> Found: 8.9318e-10 Expected 0 Error: 4.01416e+298<br> 15674.4, + 11755.8, 975.766, 0.915784, 1, 0<br> CAUTION: Gross error found at entry + 63.<br> Found: 9.41971e-10 Expected 2.31296e-171 Error: 4.07258e+161<br> + 20005.4, 40010.8, 8064.48, 0.432094, 1, 2.31296e-171<br> CAUTION: Gross error + found at entry 64.<br> Found: 9.30663e-10 Expected 0 Error: 4.18262e+298<br> + 53489.1, 5348.92, 232.285, 0.954635, 1, 0<br> CAUTION: Gross error found + at entry 65.<br> Found: 8.93617e-10 Expected 0 Error: 4.01612e+298<br> + 53489.1, 13372.3, 290.682, 0.933478, 1, 0<br> CAUTION: Gross error found + at entry 66.<br> Found: 8.9318e-10 Expected 0 Error: 4.01416e+298<br> 53489.1, + 26744.6, 975.766, 0.91717, 1, 0<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h20"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_be0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_be0">Error + Output For non central beta CDF with compiler GNU C++ version 7.1.0 and library + Rmath 3.2.3 and test data Non Central Beta, large parameters</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_large_parameters"></a>CAUTION: + Gross error found at entry 0.<br> Found: 9.1136e-209 Expected 5.82279e-200 + Error: 6.38913e+08<br> 232.285, 209.056, 232.285, 0.062486, 5.82279e-200, + 1<br> CAUTION: Gross error found at entry 1.<br> Found: 4.08108e-115 Expected + 2.37643e-112 Error: 581.304<br> 232.285, 229.962, 290.682, 0.155342, 2.37643e-112, + 1<br> CAUTION: Gross error found at entry 2.<br> Found: 1.07549e-93 Expected + 9.53431e-89 Error: 88650<br> 232.285, 232.052, 975.766, 0.378086, 9.53431e-89, + 1<br> CAUTION: Gross error found at entry 3.<br> Found: 2.58402e-54 Expected + 8.27353e-53 Error: 31.0181<br> 232.285, 232.285, 1879.05, 0.625865, 8.27353e-53, + 1<br> CAUTION: Gross error found at entry 4.<br> Found: 1.93718e-19 Expected + 6.64275e-16 Error: 3428.08<br> 232.285, 232.308, 2308.07, 0.770774, 6.64275e-16, + 1<br> CAUTION: Gross error found at entry 21.<br> Found: 8.12962e-240 Expected + 1.82294e-219 Error: 2.24234e+20<br> 975.766, 974.79, 1879.05, 0.331337, 1.82294e-219, + 1<br> CAUTION: Gross error found at entry 22.<br> Found: 3.47274e-69 Expected + 1.42183e-67 Error: 39.9426<br> 975.766, 975.766, 2308.07, 0.514323, 1.42183e-67, + 1<br> CAUTION: Gross error found at entry 23.<br> Found: 5.86885e-50 Expected + 1.27896e-47 Error: 216.923<br> 975.766, 975.863, 8064.48, 0.753209, 1.27896e-47, + 1<br> CAUTION: Gross error found at entry 39.<br> Found: 4.82785e-230 Expected + 1.25446e-213 Error: 2.59838e+16<br> 2308.07, 2308.07, 8064.48, 0.54983, 1.25446e-213, + 1<br> CAUTION: Gross error found at entry 40.<br> Found: 1.22971e-87 Expected + 1.82618e-85 Error: 147.505<br> 2308.07, 2308.3, 15674.4, 0.733174, 1.82618e-85, + 1<br> CAUTION: Gross error found at entry 56.<br> Found: 2.97337e-127 Expected + 2.56068e-124 Error: 860.205<br> 15674.4, 15675.9, 20005.4, 0.55883, 2.56068e-124, + 1<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h21"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_be1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_be1">Error + Output For non central beta CDF complement with compiler GNU C++ version 7.1.0 + and library Rmath 3.2.3 and test data Non Central Beta, medium parameters</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_medium_parameters"></a>CAUTION: + Gross error found at entry 296.<br> Found: 9.44166e-10 Expected 6.22975e-10 + Error: 0.515577<br> 22.9367, 114.683, 19.5081, 0.480981, 1, 6.22975e-10<br> + CAUTION: Gross error found at entry 369.<br> Found: 2.52234e-10 Expected + 1.40246e-10 Error: 0.79851<br> 27.5277, 20.6457, 0.956697, 0.915111, 1, 1.40246e-10<br> + CAUTION: Gross error found at entry 429.<br> Found: 1.18105e-09 Expected + 7.45745e-10 Error: 0.58372<br> 28.8063, 21.6047, 60.3826, 0.946143, 1, 7.45745e-10<br> + CAUTION: Gross error found at entry 430.<br> Found: 2.44435e-09 Expected + 1.60695e-09 Error: 0.521115<br> 28.8063, 21.6047, 148.129, 0.965121, 1, 1.60695e-09<br> + CAUTION: Gross error found at entry 477.<br> Found: 7.57435e-10 Expected + 7.14133e-11 Error: 9.60635<br> 28.8063, 144.032, 42.3849, 0.504845, 1, 7.14133e-11<br> + CAUTION: Gross error found at entry 489.<br> Found: 4.8561e-10 Expected 5.62991e-11 + Error: 7.62553<br> 31.9438, 23.9579, 44.2068, 0.93835, 1, 5.62991e-11<br> + CAUTION: Gross error found at entry 490.<br> Found: 8.35187e-10 Expected + 1.87483e-10 Error: 3.45473<br> 31.9438, 23.9579, 135.747, 0.961117, 1, 1.87483e-10<br> + CAUTION: Gross error found at entry 491.<br> Found: 1.00174e-09 Expected + 2.38491e-10 Error: 3.20032<br> 31.9438, 23.9579, 191.501, 0.968273, 1, 2.38491e-10<br> + CAUTION: Gross error found at entry 537.<br> Found: 7.29746e-10 Expected + 1.31223e-12 Error: 555.111<br> 31.9438, 159.719, 34.2373, 0.489796, 1, 1.31223e-12<br> + CAUTION: Gross error found at entry 538.<br> Found: 2.49663e-09 Expected + 1.54239e-09 Error: 0.618681<br> 31.9438, 159.719, 126.472, 0.581861, 1, 1.54239e-09<br> + CAUTION: Gross error found at entry 549.<br> Found: 4.16125e-10 Expected + 4.8536e-13 Error: 856.353<br> 38.0822, 28.5617, 34.773, 0.931853, 1, 4.8536e-13<br> + CAUTION: Gross error found at entry 550.<br> Found: 9.69907e-10 Expected + 2.87054e-12 Error: 336.883<br> 38.0822, 28.5617, 127.953, 0.956104, 1, 2.87054e-12<br> + CAUTION: Gross error found at entry 551.<br> Found: 5.90132e-10 Expected + 4.08361e-12 Error: 143.512<br> 38.0822, 28.5617, 183.147, 0.963764, 1, 4.08361e-12<br> + CAUTION: Gross error found at entry 597.<br> Found: 4.67033e-10 Expected + 9.82939e-16 Error: 475139<br> 38.0822, 190.411, 27.0954, 0.475419, 1, 9.82939e-16<br> + CAUTION: Gross error found at entry 598.<br> Found: 9.33207e-10 Expected + 4.03465e-12 Error: 230.298<br> 38.0822, 190.411, 100.733, 0.544491, 1, 4.03465e-12<br> + CAUTION: Gross error found at entry 599.<br> Found: 7.4092e-10 Expected 9.53942e-11 + Error: 6.76693<br> 38.0822, 190.411, 169.826, 0.594614, 1, 9.53942e-11<br> + CAUTION: Gross error found at entry 609.<br> Found: 5.71813e-10 Expected + 1.17207e-14 Error: 48785.7<br> 42.7789, 32.0842, 28.3773, 0.927814, 1, 1.17207e-14<br> + CAUTION: Gross error found at entry 610.<br> Found: 5.16834e-10 Expected + 9.62679e-14 Error: 5367.71<br> 42.7789, 32.0842, 109.376, 0.950307, 1, 9.62679e-14<br> + CAUTION: Gross error found at entry 611.<br> Found: 6.08012e-10 Expected + 1.7454e-13 Error: 3482.51<br> 42.7789, 32.0842, 175.686, 0.960431, 1, 1.7454e-13<br> + CAUTION: Gross error found at entry 657.<br> Found: 5.59489e-10 Expected + 2.86344e-18 Error: 1.95391e+08<br> 42.7789, 213.895, 21.9724, 0.467166, 1, + 2.86344e-18<br> CAUTION: Gross error found at entry 658.<br> Found: 5.14798e-10 + Expected 2.50972e-14 Error: 20511.2<br> 42.7789, 213.895, 84.4175, 0.522676, + 1, 2.50972e-14<br> CAUTION: Gross error found at entry 659.<br> Found: + 8.49991e-10 Expected 2.38005e-12 Error: 356.131<br> 42.7789, 213.895, 160.056, + 0.576191, 1, 2.38005e-12<br> CAUTION: Gross error found at entry 671.<br> + Found: 3.03281e-10 Expected 2.22036e-15 Error: 136590<br> 44.5963, 33.4472, + 22.4929, 0.924976, 1, 2.22036e-15<br> CAUTION: Gross error found at entry + 672.<br> Found: 8.40636e-10 Expected 2.22384e-14 Error: 37800.1<br> 44.5963, + 33.4472, 94.9517, 0.946545, 1, 2.22384e-14<br> CAUTION: Gross error found + at entry 673.<br> Found: 8.15021e-10 Expected 4.75974e-14 Error: 17122.2<br> + 44.5963, 33.4472, 162.945, 0.95793, 1, 4.75974e-14<br> CAUTION: Gross error + found at entry 716.<br> Found: 1.11988e-10 Expected 2.84965e-22 Error: 3.92989e+11<br> + 44.5963, 222.981, 0.956697, 0.445432, 1, 2.84965e-22<br> CAUTION: Gross error + found at entry 717.<br> Found: 7.99524e-10 Expected 3.04552e-15 Error: 262523<br> + 44.5963, 222.981, 78.4454, 0.515267, 1, 3.04552e-15<br> CAUTION: Gross error + found at entry 718.<br> Found: 8.0958e-10 Expected 5.89458e-13 Error: 1372.43<br> + 44.5963, 222.981, 158.441, 0.57107, 1, 5.89458e-13<br> *** FURTHER CONTENT + HAS BEEN TRUNCATED FOR BREVITY ***<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h22"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_be2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_be2">Error + Output For non central beta CDF with compiler GNU C++ version 7.1.0 and library + Rmath 3.2.3 and test data Non Central Beta, medium parameters</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_medium_parameters"></a>CAUTION: + Gross error found at entry 14.<br> Found: 4.64669e-35 Expected 7.14875e-33 + Error: 152.846<br> 1.45431, 1.30887, 158.441, 0.0983847, 7.14875e-33, 1<br> + CAUTION: Gross error found at entry 15.<br> Found: 4.66674e-46 Expected 3.13332e-40 + Error: 671416<br> 1.45431, 1.30887, 196.222, 0.09869, 3.13332e-40, 1<br> + CAUTION: Gross error found at entry 18.<br> Found: 5.84342e-28 Expected 3.61559e-27 + Error: 5.18745<br> 1.45431, 1.43976, 159.586, 0.245596, 3.61559e-27, 1<br> + CAUTION: Gross error found at entry 19.<br> Found: 1.72833e-34 Expected 1.76943e-33 + Error: 9.2378<br> 1.45431, 1.43976, 198.576, 0.246444, 1.76943e-33, 1<br> + CAUTION: Gross error found at entry 22.<br> Found: 1.76915e-19 Expected 3.69506e-18 + Error: 19.8861<br> 1.45431, 1.45285, 159.621, 0.491116, 3.69506e-18, 1<br> + CAUTION: Gross error found at entry 23.<br> Found: 2.52007e-25 Expected 2.00482e-22 + Error: 794.544<br> 1.45431, 1.45285, 199.292, 0.492849, 2.00482e-22, 1<br> + CAUTION: Gross error found at entry 73.<br> Found: 2.04477e-34 Expected 2.45287e-33 + Error: 10.9958<br> 7.62448, 6.86203, 148.129, 0.0921776, 2.45287e-33, 1<br> + CAUTION: Gross error found at entry 74.<br> Found: 2.36587e-46 Expected 7.32638e-42 + Error: 30966<br> 7.62448, 6.86203, 193.539, 0.093784, 7.32638e-42, 1<br> + CAUTION: Gross error found at entry 76.<br> Found: 3.29122e-26 Expected 7.418e-25 + Error: 21.5387<br> 7.62448, 7.54824, 148.626, 0.228717, 7.418e-25, 1<br> + CAUTION: Gross error found at entry 77.<br> Found: 1.70126e-32 Expected 1.07666e-31 + Error: 5.32864<br> 7.62448, 7.54824, 193.774, 0.23303, 1.07666e-31, 1<br> + CAUTION: Gross error found at entry 79.<br> Found: 1.3478e-15 Expected 4.21836e-15 + Error: 2.12982<br> 7.62448, 7.61686, 151.548, 0.457773, 4.21836e-15, 1<br> + CAUTION: Gross error found at entry 80.<br> Found: 8.78487e-21 Expected 3.41238e-19 + Error: 37.8438<br> 7.62448, 7.61686, 194.119, 0.465826, 3.41238e-19, 1<br> + CAUTION: Gross error found at entry 132.<br> Found: 3.85783e-23 Expected + 1.54142e-22 Error: 2.99555<br> 19.9593, 17.9634, 44.2068, 0.0698905, 1.54142e-22, + 1<br> CAUTION: Gross error found at entry 133.<br> Found: 8.6122e-39 Expected + 3.94361e-38 Error: 3.5791<br> 19.9593, 17.9634, 135.747, 0.0829178, 3.94361e-38, + 1<br> CAUTION: Gross error found at entry 134.<br> Found: 3.61781e-52 Expected + 3.98669e-48 Error: 11018.6<br> 19.9593, 17.9634, 191.501, 0.0864897, 3.98669e-48, + 1<br> CAUTION: Gross error found at entry 135.<br> Found: 2.07122e-15 Expected + 7.08614e-15 Error: 2.42124<br> 19.9593, 19.7597, 55.6996, 0.176444, 7.08614e-15, + 1<br> CAUTION: Gross error found at entry 136.<br> Found: 2.28223e-27 Expected + 2.16759e-25 Error: 93.977<br> 19.9593, 19.7597, 136.272, 0.20393, 2.16759e-25, + 1<br> CAUTION: Gross error found at entry 137.<br> Found: 6.4251e-34 Expected + 4.0064e-33 Error: 5.23554<br> 19.9593, 19.7597, 191.898, 0.213398, 4.0064e-33, + 1<br> CAUTION: Gross error found at entry 139.<br> Found: 2.1734e-14 Expected + 4.65637e-14 Error: 1.14243<br> 19.9593, 19.9394, 145.168, 0.410858, 4.65637e-14, + 1<br> CAUTION: Gross error found at entry 140.<br> Found: 2.18388e-19 Expected + 5.1677e-18 Error: 22.663<br> 19.9593, 19.9394, 192.978, 0.426523, 5.1677e-18, + 1<br> CAUTION: Gross error found at entry 192.<br> Found: 3.29537e-23 Expected + 8.29996e-23 Error: 1.51867<br> 22.4174, 20.1757, 34.773, 0.0661999, 8.29996e-23, + 1<br> CAUTION: Gross error found at entry 193.<br> Found: 7.86091e-39 Expected + 2.77686e-38 Error: 2.5325<br> 22.4174, 20.1757, 127.953, 0.0809614, 2.77686e-38, + 1<br> CAUTION: Gross error found at entry 194.<br> Found: 3.0161e-51 Expected + 4.5396e-48 Error: 1504.12<br> 22.4174, 20.1757, 183.147, 0.0848857, 4.5396e-48, + 1<br> CAUTION: Gross error found at entry 195.<br> Found: 3.08022e-14 Expected + 1.42713e-13 Error: 3.6332<br> 22.4174, 22.1932, 37.6764, 0.162145, 1.42713e-13, + 1<br> CAUTION: Gross error found at entry 196.<br> Found: 8.89935e-28 Expected + 2.56187e-25 Error: 286.871<br> 22.4174, 22.1932, 131.096, 0.199361, 2.56187e-25, + 1<br> CAUTION: Gross error found at entry 197.<br> Found: 9.34392e-34 Expected + 6.14831e-33 Error: 5.58001<br> 22.4174, 22.1932, 186.799, 0.209601, 6.14831e-33, + 1<br> CAUTION: Gross error found at entry 199.<br> Found: 2.79341e-13 Expected + 4.79277e-13 Error: 0.71574<br> 22.4174, 22.395, 131.148, 0.398015, 4.79277e-13, + 1<br> CAUTION: Gross error found at entry 200.<br> Found: 3.13989e-19 Expected + 7.01608e-18 Error: 21.345<br> 22.4174, 22.395, 191.433, 0.419933, 7.01608e-18, + 1<br> *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h23"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_chi"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_chi">Error + Output For non central chi squared CDF complement with compiler GNU C++ version + 7.1.0 and library Rmath 3.2.3 and test data Non Central Chi Squared, large + parameters</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_large_parameters"></a>CAUTION: + Gross error found at entry 12.<br> Found: 0 Expected 1.17655e-12 Error: 5.28771e+295<br> + 101.815, 5236.73, 6406.25, 1, 1.17655e-12<br> CAUTION: Gross error found + at entry 13.<br> Found: 0 Expected 1.79374e-44 Error: 8.06149e+263<br> + 101.815, 9735.22, 12788.2, 1, 1.79374e-44<br> CAUTION: Gross error found + at entry 35.<br> Found: 2.58682e-14 Expected 1.84404e-61 Error: 1.4028e+47<br> + 107.623, 122.456, 920.317, 1, 1.84404e-61<br> CAUTION: Gross error found + at entry 36.<br> Found: 0 Expected 2.30757e-102 Error: 1.03707e+206<br> + 107.623, 156.292, 1319.58, 1, 2.30757e-102<br> CAUTION: Gross error found + at entry 52.<br> Found: 0 Expected 6.40952e-24 Error: 2.88059e+284<br> + 114.68, 417.884, 1065.13, 1, 6.40952e-24<br> CAUTION: Gross error found at + entry 53.<br> Found: 0 Expected 1.02366e-98 Error: 4.60058e+209<br> 114.68, + 669.781, 2353.38, 1, 1.02366e-98<br> CAUTION: Gross error found at entry + 69.<br> Found: 0 Expected 6.55726e-39 Error: 2.94699e+269<br> 118.032, + 3168.71, 4930.11, 1, 6.55726e-39<br> CAUTION: Gross error found at entry + 85.<br> Found: 0 Expected 7.30688e-22 Error: 3.28388e+286<br> 163.004, + 9735.22, 11877.9, 1, 7.30688e-22<br> CAUTION: Gross error found at entry + 86.<br> Found: 0 Expected 1.17171e-111 Error: 5.26596e+196<br> 163.004, + 25344.1, 33159.2, 1, 1.17171e-111<br> CAUTION: Gross error found at entry + 108.<br> Found: 1.12355e-13 Expected 2.67349e-61 Error: 4.20255e+47<br> + 256.292, 122.456, 1136.25, 1, 2.67349e-61<br> CAUTION: Gross error found + at entry 109.<br> Found: 1.16462e-13 Expected 8.30595e-116 Error: 1.40216e+102<br> + 256.292, 156.292, 1650.34, 1, 8.30595e-116<br> CAUTION: Gross error found + at entry 124.<br> Found: 1.05804e-13 Expected 1.01672e-15 Error: 103.064<br> + 517.884, 417.884, 1403.65, 1, 1.01672e-15<br> CAUTION: Gross error found + at entry 125.<br> Found: 2.00728e-13 Expected 3.50192e-56 Error: 5.73194e+42<br> + 517.884, 669.781, 2375.33, 1, 3.50192e-56<br> CAUTION: Gross error found + at entry 141.<br> Found: 0 Expected 1.36924e-20 Error: 6.15368e+287<br> + 769.781, 3168.71, 5120.04, 1, 1.36924e-20<br> CAUTION: Gross error found + at entry 142.<br> Found: 0 Expected 3.19215e-72 Error: 1.43463e+236<br> + 769.781, 5236.73, 9009.76, 1, 3.19215e-72<br> CAUTION: Gross error found + at entry 157.<br> Found: 0 Expected 7.26231e-08 Error: 3.26385e+300<br> + 1223.88, 9735.22, 12055, 1, 7.26231e-08<br> CAUTION: Gross error found at + entry 158.<br> Found: 0 Expected 4.5906e-56 Error: 2.06312e+252<br> 1223.88, + 25344.1, 31881.6, 1, 4.5906e-56<br> CAUTION: Gross error found at entry 194.<br> + Found: 0 Expected 5.34714e-12 Error: 2.40313e+296<br> 9835.22, 122.456, 10953.4, + 1, 5.34714e-12<br> CAUTION: Gross error found at entry 195.<br> Found: + 0 Expected 4.84412e-40 Error: 2.17706e+268<br> 9835.22, 156.292, 11989.8, + 1, 4.84412e-40<br> CAUTION: Gross error found at entry 196.<br> Found: + 0 Expected 5.50199e-83 Error: 2.47272e+225<br> 9835.22, 417.884, 13329, 1, + 5.50199e-83<br> CAUTION: Gross error found at entry 197.<br> Found: 0 Expected + 1.28192e-205 Error: 5.76124e+102<br> 9835.22, 669.781, 15757.5, 1, 1.28192e-205<br> + CAUTION: Gross error found at entry 211.<br> Found: 0 Expected 3.83272e-28 + Error: 1.72251e+280<br> 25444.1, 1123.88, 29224.8, 1, 3.83272e-28<br> CAUTION: + Gross error found at entry 212.<br> Found: 0 Expected 1.69815e-101 Error: + 7.63188e+206<br> 25444.1, 3168.71, 34335.4, 1, 1.69815e-101<br> CAUTION: + Gross error found at entry 213.<br> Found: 0 Expected 1.09245e-217 Error: + 4.90974e+90<br> 25444.1, 5236.73, 39885.1, 1, 1.09245e-217<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h24"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_ch0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_ch0">Error + Output For non central chi squared CDF complement with compiler GNU C++ version + 7.1.0 and library Rmath 3.2.3 and test data Non Central Chi Squared, medium + parameters</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_medium_parameters"></a>CAUTION: + Gross error found at entry 36.<br> Found: 1.11022e-14 Expected 1.30043e-26 + Error: 8.53738e+11<br> 1.95191, 109.376, 445.313, 1, 1.30043e-26<br> CAUTION: + Gross error found at entry 37.<br> Found: 0 Expected 1.45478e-39 Error: 6.53812e+268<br> + 1.95191, 109.444, 556.98, 1, 1.45478e-39<br> CAUTION: Gross error found at + entry 54.<br> Found: 2.91989e-14 Expected 4.25949e-21 Error: 6.85501e+06<br> + 1.95191, 159.586, 484.613, 1, 4.25949e-21<br> CAUTION: Gross error found + at entry 55.<br> Found: 0 Expected 1.33424e-37 Error: 5.99639e+270<br> + 1.95191, 159.621, 646.292, 1, 1.33424e-37<br> CAUTION: Gross error found + at entry 56.<br> Found: 1.25455e-14 Expected 1.95903e-56 Error: 6.40393e+41<br> + 1.95191, 160.056, 810.04, 1, 1.95903e-56<br> CAUTION: Gross error found at + entry 73.<br> Found: 0 Expected 4.34735e-25 Error: 1.9538e+283<br> 1.95191, + 193.539, 586.473, 1, 4.34735e-25<br> CAUTION: Gross error found at entry + 74.<br> Found: 0 Expected 4.66119e-45 Error: 2.09485e+263<br> 1.95191, + 193.774, 782.902, 1, 4.66119e-45<br> CAUTION: Gross error found at entry + 75.<br> Found: 4.77396e-15 Expected 8.92248e-68 Error: 5.35048e+52<br> + 1.95191, 194.119, 980.352, 1, 8.92248e-68<br> CAUTION: Gross error found + at entry 111.<br> Found: 0 Expected 3.1064e-15 Error: 1.39609e+293<br> + 20.4105, 84.4175, 314.484, 1, 3.1064e-15<br> CAUTION: Gross error found at + entry 112.<br> Found: 0 Expected 7.50903e-29 Error: 3.37473e+279<br> 20.4105, + 94.9517, 461.449, 1, 7.50903e-29<br> CAUTION: Gross error found at entry + 113.<br> Found: 3.77476e-15 Expected 1.74225e-43 Error: 2.1666e+28<br> + 20.4105, 97.0751, 587.428, 1, 1.74225e-43<br> CAUTION: Gross error found + at entry 130.<br> Found: 8.88178e-16 Expected 4.13277e-23 Error: 2.14911e+07<br> + 20.4105, 151.548, 515.876, 1, 4.13277e-23<br> CAUTION: Gross error found + at entry 131.<br> Found: 1.75415e-14 Expected 1.92146e-41 Error: 9.12928e+26<br> + 20.4105, 152.75, 692.642, 1, 1.92146e-41<br> CAUTION: Gross error found at + entry 132.<br> Found: 1.38778e-14 Expected 7.09864e-64 Error: 1.95499e+49<br> + 20.4105, 158.441, 894.26, 1, 7.09864e-64<br> CAUTION: Gross error found at + entry 149.<br> Found: 2.22045e-16 Expected 8.74501e-28 Error: 2.5391e+11<br> + 20.4105, 191.433, 635.532, 1, 8.74501e-28<br> CAUTION: Gross error found + at entry 150.<br> Found: 0 Expected 6.94227e-50 Error: 3.12002e+258<br> + 20.4105, 191.501, 847.648, 1, 6.94227e-50<br> CAUTION: Gross error found + at entry 151.<br> Found: 3.40838e-14 Expected 5.3889e-75 Error: 6.32482e+60<br> + 20.4105, 191.898, 1061.55, 1, 5.3889e-75<br> CAUTION: Gross error found at + entry 206.<br> Found: 5.88418e-15 Expected 2.69136e-22 Error: 2.18632e+07<br> + 22.8625, 141.209, 492.215, 1, 2.69136e-22<br> CAUTION: Gross error found + at entry 207.<br> Found: 3.60822e-14 Expected 1.64941e-40 Error: 2.18759e+26<br> + 22.8625, 145.168, 672.121, 1, 1.64941e-40<br> CAUTION: Gross error found + at entry 208.<br> Found: 3.73035e-14 Expected 1.6094e-61 Error: 2.31784e+47<br> + 22.8625, 148.129, 854.96, 1, 1.6094e-61<br> CAUTION: Gross error found at + entry 225.<br> Found: 0 Expected 3.73672e-27 Error: 1.67937e+281<br> 22.8625, + 182.675, 616.613, 1, 3.73672e-27<br> CAUTION: Gross error found at entry + 226.<br> Found: 0 Expected 8.85688e-49 Error: 3.98049e+259<br> 22.8625, + 183.147, 824.038, 1, 8.85688e-49<br> CAUTION: Gross error found at entry + 227.<br> Found: 0 Expected 2.29176e-74 Error: 1.02997e+234<br> 22.8625, + 186.799, 1048.31, 1, 2.29176e-74<br> CAUTION: Gross error found at entry + 282.<br> Found: 0 Expected 2.18831e-21 Error: 9.8348e+286<br> 23.3804, + 132.721, 468.305, 1, 2.18831e-21<br> CAUTION: Gross error found at entry + 283.<br> Found: 0 Expected 1.3071e-38 Error: 5.87439e+269<br> 23.3804, + 135.747, 636.51, 1, 1.3071e-38<br> CAUTION: Gross error found at entry 284.<br> + Found: 1.84297e-14 Expected 8.27843e-58 Error: 2.22623e+43<br> 23.3804, 136.272, + 798.262, 1, 8.27843e-58<br> CAUTION: Gross error found at entry 301.<br> + Found: 0 Expected 9.85282e-26 Error: 4.42808e+282<br> 23.3804, 169.826, 579.619, + 1, 9.85282e-26<br> CAUTION: Gross error found at entry 302.<br> Found: + 0 Expected 4.8094e-47 Error: 2.16145e+261<br> 23.3804, 174.486, 791.465, + 1, 4.8094e-47<br> CAUTION: Gross error found at entry 303.<br> Found: 1.11022e-16 + Expected 6.70476e-71 Error: 1.65587e+54<br> 23.3804, 175.686, 995.333, 1, + 6.70476e-71<br> CAUTION: Gross error found at entry 358.<br> Found: 0 Expected + 3.9702e-21 Error: 1.7843e+287<br> 26.2704, 126.472, 458.227, 1, 3.9702e-21<br> + CAUTION: Gross error found at entry 359.<br> *** FURTHER CONTENT HAS BEEN + TRUNCATED FOR BREVITY ***<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h25"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_t_c"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_t_c">Error + Output For non central t CDF complement with compiler GNU C++ version 7.1.0 + and library Rmath 3.2.3 and test data Non Central T</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_complement_Rmath_3_2_3_Non_Central_T"></a>CAUTION: + Gross error found at entry 56.<br> Found: 0.000186411 Expected 7.85192e-05 + Error: 1.37408<br> 61.6335, 46.2251, 68.8608, 0.999921, 7.85192e-05<br> + CAUTION: Gross error found at entry 75.<br> Found: 0.00011439 Expected 5.05344e-05 + Error: 1.26361<br> 80.8418, 60.6313, 86.1278, 0.999949, 5.05344e-05<br> + CAUTION: Gross error found at entry 93.<br> Found: 0.000655162 Expected 0.000423927 + Error: 0.545458<br> 100.733, 50.3663, 65.7619, 0.999576, 0.000423927<br> + CAUTION: Gross error found at entry 112.<br> Found: 0.000518249 Expected + 0.00034473 Error: 0.503348<br> 127.953, 63.9764, 81.0824, 0.999655, 0.00034473<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h26"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_t_0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_t_0">Error + Output For non central t CDF with compiler GNU C++ version 7.1.0 and library + Rmath 3.2.3 and test data Non Central T</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_Rmath_3_2_3_Non_Central_T"></a>CAUTION: + Gross error found at entry 74.<br> Found: 0.000830062 Expected 0.000522858 + Error: 0.587549<br> 79.7478, -39.8739, -53.8066, 0.000522858, 0.999477<br> + CAUTION: Gross error found at entry 94.<br> Found: 7.69292e-05 Expected 3.54024e-05 + Error: 1.17299<br> 101.191, -75.8936, -104.104, 3.54024e-05, 0.999965<br> + CAUTION: Gross error found at entry 113.<br> Found: 5.07713e-05 Expected + 2.4439e-05 Error: 1.07747<br> 128.792, -96.5942, -128.112, 2.4439e-05, 0.999976<br> + CAUTION: Gross error found at entry 132.<br> Found: 4.08612e-05 Expected + 2.01542e-05 Error: 1.02743<br> 146.56, -109.92, -143.392, 2.01542e-05, 0.99998<br> + CAUTION: Gross error found at entry 151.<br> Found: 3.55146e-05 Expected + 1.7803e-05 Error: 0.994869<br> 159.586, -119.689, -154.522, 1.7803e-05, 0.999982<br> + CAUTION: Gross error found at entry 170.<br> Found: 3.03671e-05 Expected + 1.55023e-05 Error: 0.958873<br> 175.686, -131.765, -168.211, 1.55023e-05, + 0.999984<br> CAUTION: Gross error found at entry 189.<br> Found: 2.61339e-05 + Expected 1.3581e-05 Error: 0.924298<br> 192.978, -144.733, -182.834, 1.3581e-05, + 0.999986<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h27"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with_">Error + Output For polygamma with compiler GNU C++ version 7.1.0 and library Rmath + 3.2.3 and test data Mathematica Data - Large orders and other bug cases</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_Large_orders_and_other_bug_cases"></a>CAUTION: + Found non-finite result, when a finite value was expected at entry 0<br> + Found: -nan Expected 2.07309e+257 Error: 1.79769e+308<br> 171, 2, 2.07309e+257<br> + CAUTION: Gross error found at entry 0.<br> Found: -nan Expected 2.07309e+257 + Error: 1.79769e+308<br> 171, 2, 2.07309e+257<br> CAUTION: Found non-finite + result, when a finite value was expected at entry 1<br> Found: -nan Expected + 7.42912e+188 Error: 1.79769e+308<br> 171, 5, 7.42912e+188<br> CAUTION: + Gross error found at entry 1.<br> Found: -nan Expected 7.42912e+188 Error: + 1.79769e+308<br> 171, 5, 7.42912e+188<br> CAUTION: Found non-finite result, + when a finite value was expected at entry 2<br> Found: -nan Expected -4.81295e+247 + Error: 1.79769e+308<br> 166, 2, -4.81295e+247<br> CAUTION: Gross error + found at entry 2.<br> Found: -nan Expected -4.81295e+247 Error: 1.79769e+308<br> + 166, 2, -4.81295e+247<br> CAUTION: Found non-finite result, when a finite + value was expected at entry 3<br> Found: -nan Expected -1.88439e+218 Error: + 1.79769e+308<br> 166, 3, -1.88439e+218<br> CAUTION: Gross error found at + entry 3.<br> Found: -nan Expected -1.88439e+218 Error: 1.79769e+308<br> + 166, 3, -1.88439e+218<br> CAUTION: Found non-finite result, when a finite + value was expected at entry 4<br> Found: -nan Expected 7.53144e+74 Error: + 1.79769e+308<br> 171, 23, 7.53144e+74<br> CAUTION: Gross error found at + entry 4.<br> Found: -nan Expected 7.53144e+74 Error: 1.79769e+308<br> 171, + 23, 7.53144e+74<br> CAUTION: Found non-finite result, when a finite value + was expected at entry 5<br> Found: -nan Expected -6.52661e-66 Error: 1.79769e+308<br> + 168, 150, -6.52661e-66<br> CAUTION: Gross error found at entry 5.<br> Found: + -nan Expected -6.52661e-66 Error: 1.79769e+308<br> 168, 150, -6.52661e-66<br> + CAUTION: Found non-finite result, when a finite value was expected at entry + 6<br> Found: -nan Expected 9.2734e-88 Error: 1.79769e+308<br> 169, 202, + 9.2734e-88<br> CAUTION: Gross error found at entry 6.<br> Found: -nan Expected + 9.2734e-88 Error: 1.79769e+308<br> 169, 202, 9.2734e-88<br> Outside supported + domain<br> 20, -9.5, -0.00103076<br> Outside supported domain<br> 21, + -9.5, 4.28582e+26<br> Outside supported domain<br> 22, -9.5, -0.00419144<br> + Outside supported domain<br> 23, -9.5, 8.6745e+29<br> Outside supported + domain<br> 24, -9.5, -0.0204825<br> Outside supported domain<br> 25, + -9.5, 2.08188e+33<br> Outside supported domain<br> 26, -9.5, -0.118403<br> + Outside supported domain<br> 27, -9.5, 5.84592e+36<br> Outside supported + domain<br> 28, -9.5, -0.798969<br> Outside supported domain<br> 29, -9.5, + 1.89875e+40<br> Outside supported domain<br> 30, -9.5, -6.22245<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h28"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with0">Error + Output For polygamma with compiler GNU C++ version 7.1.0 and library Rmath + 3.2.3 and test data Mathematica Data - large negative arguments</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_negative_arguments"></a>Outside + supported domain<br> 124, -1.5, 7.63705e+240<br> Outside supported domain<br> + 124, -2.5, 7.63705e+240<br> Outside supported domain<br> 124, -3.5, 7.63705e+240<br> + Outside supported domain<br> 124, -4.5, 7.63705e+240<br> Outside supported + domain<br> 124, -5.5, 7.63705e+240<br> Outside supported domain<br> 124, + -6.5, 7.63705e+240<br> Outside supported domain<br> 124, -7.5, 7.63705e+240<br> + Outside supported domain<br> 124, -8.5, 7.63705e+240<br> Outside supported + domain<br> 124, -9.5, 7.63705e+240<br> Outside supported domain<br> 124, + -10.5, 7.63705e+240<br> Outside supported domain<br> 124, -11.5, 7.63705e+240<br> + Outside supported domain<br> 124, -12.5, 7.63705e+240<br> Outside supported + domain<br> 124, -13.5, 7.63705e+240<br> Outside supported domain<br> + 124, -14.5, 7.63705e+240<br> Outside supported domain<br> 124, -15.5, 7.63705e+240<br> + Outside supported domain<br> 124, -16.5, 7.63705e+240<br> Outside supported + domain<br> 124, -17.5, 7.63705e+240<br> Outside supported domain<br> + 124, -18.5, 7.63705e+240<br> Outside supported domain<br> 124, -19.5, 7.63705e+240<br> + Outside supported domain<br> 124, -20.5, 7.63705e+240<br> Outside supported + domain<br> 124, -1.5, -7.63705e+240<br> Outside supported domain<br> + 124, -2.5, -7.63705e+240<br> Outside supported domain<br> 124, -3.5, -7.63705e+240<br> + Outside supported domain<br> 124, -4.5, -7.63705e+240<br> Outside supported + domain<br> 124, -5.5, -7.63705e+240<br> Outside supported domain<br> + 124, -6.5, -7.63705e+240<br> Outside supported domain<br> 124, -7.5, -7.63705e+240<br> + Outside supported domain<br> 124, -8.5, -7.63705e+240<br> Outside supported + domain<br> 124, -9.5, -7.63705e+240<br> Outside supported domain<br> + 124, -10.5, -7.63705e+240<br> Outside supported domain<br> 124, -11.5, + -7.63705e+240<br> Outside supported domain<br> 124, -12.5, -7.63705e+240<br> + Outside supported domain<br> 124, -13.5, -7.63705e+240<br> Outside supported + domain<br> 124, -14.5, -7.63705e+240<br> Outside supported domain<br> + 124, -15.5, -7.63705e+240<br> Outside supported domain<br> 124, -16.5, + -7.63705e+240<br> Outside supported domain<br> 124, -17.5, -7.63705e+240<br> + Outside supported domain<br> 124, -18.5, -7.63705e+240<br> Outside supported + domain<br> 124, -19.5, -7.63705e+240<br> Outside supported domain<br> + 124, -20.5, -7.63705e+240<br> Outside supported domain<br> 1, -0.5, 8.9348<br> + Outside supported domain<br> 2, -0.5, -0.828797<br> Outside supported domain<br> + 3, -0.5, 193.409<br> Outside supported domain<br> 4, -0.5, -3.47425<br> + Outside supported domain<br> 5, -0.5, 15371.1<br> Outside supported domain<br> + 6, -0.5, -43.4579<br> Outside supported domain<br> 7, -0.5, 2.58068e+06<br> + Outside supported domain<br> 8, -0.5, -1059.96<br> Outside supported domain<br> + 9, -0.5, 7.43185e+08<br> Outside supported domain<br> 10, -0.5, -42108.9<br> + Outside supported domain<br> 11, -0.5, 3.26999e+11<br> Outside supported + domain<br> 12, -0.5, -2.46448e+06<br> Outside supported domain<br> 13, + -0.5, 2.04047e+14<br> Outside supported domain<br> 14, -0.5, -1.9918e+08<br> + Outside supported domain<br> 15, -0.5, 1.71399e+17<br> Outside supported + domain<br> 16, -0.5, -2.12394e+10<br> Outside supported domain<br> 17, + -0.5, 1.86483e+20<br> Outside supported domain<br> 18, -0.5, -2.88824e+12<br> + Outside supported domain<br> 19, -0.5, 2.55108e+23<br> Outside supported + domain<br> 20, -0.5, -4.87773e+14<br> Outside supported domain<br> 21, + -0.5, 4.28582e+26<br> Outside supported domain<br> 1, -0.5, 8.9348<br> + Outside supported domain<br> 2, -0.5, -0.828843<br> Outside supported domain<br> + 3, -0.5, 193.409<br> Outside supported domain<br> 4, -0.5, -3.47791<br> + Outside supported domain<br> 5, -0.5, 15371.1<br> Outside supported domain<br> + 6, -0.5, -44.0732<br> Outside supported domain<br> 7, -0.5, 2.58068e+06<br> + Outside supported domain<br> 8, -0.5, -1237.15<br> Outside supported domain<br> + 9, -0.5, 7.43185e+08<br> Outside supported domain<br> 10, -0.5, -120071<br> + Outside supported domain<br> 11, -0.5, 3.26999e+11<br> Outside supported + domain<br> 12, -0.5, -5.11131e+07<br> Outside supported domain<br> 13, + -0.5, 2.04047e+14<br> Outside supported domain<br> 14, -0.5, -4.1064e+10<br> + Outside supported domain<br> 15, -0.5, 1.71399e+17<br> Outside supported + domain<br> 16, -0.5, -4.44822e+13<br> Outside supported domain<br> 17, + -0.5, 1.86483e+20<br> Outside supported domain<br> 18, -0.5, -6.08254e+16<br> + Outside supported domain<br> 19, -0.5, 2.55108e+23<br> Outside supported + domain<br> 20, -0.5, -1.02182e+20<br> Outside supported domain<br> 21, + -0.5, 4.28582e+26<br> Outside supported domain<br> 1, -0.5, 8.9348<br> + Outside supported domain<br> 2, -0.5, -0.828751<br> Outside supported domain<br> + 3, -0.5, 193.409<br> Outside supported domain<br> 4, -0.5, -3.47059<br> + Outside supported domain<br> *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY + ***<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h29"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with1">Error + Output For polygamma with compiler GNU C++ version 7.1.0 and library Rmath + 3.2.3 and test data Mathematica Data - negative arguments</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_negative_arguments"></a>Outside + supported domain<br> 1, -12.75, 19.6638<br> Outside supported domain<br> + 1, -12.25, 19.6608<br> Outside supported domain<br> 1, -11.75, 19.6576<br> + Outside supported domain<br> 1, -11.25, 19.6542<br> Outside supported domain<br> + 1, -10.75, 19.6504<br> Outside supported domain<br> 1, -10.25, 19.6463<br> + Outside supported domain<br> 1, -9.75, 19.6417<br> Outside supported domain<br> + 1, -9.25, 19.6367<br> Outside supported domain<br> 1, -8.75, 19.6312<br> + Outside supported domain<br> 1, -8.25, 19.625<br> Outside supported domain<br> + 1, -7.75, 19.6181<br> Outside supported domain<br> 1, -7.25, 19.6104<br> + Outside supported domain<br> 1, -6.75, 19.6015<br> Outside supported domain<br> + 1, -6.25, 19.5913<br> Outside supported domain<br> 1, -5.75, 19.5795<br> + Outside supported domain<br> 1, -5.25, 19.5657<br> Outside supported domain<br> + 1, -4.75, 19.5493<br> Outside supported domain<br> 1, -4.25, 19.5294<br> + Outside supported domain<br> 1, -3.75, 19.505<br> Outside supported domain<br> + 1, -3.25, 19.4741<br> Outside supported domain<br> 1, -2.75, 19.4339<br> + Outside supported domain<br> 1, -2.25, 19.3794<br> Outside supported domain<br> + 1, -1.75, 19.3016<br> Outside supported domain<br> 1, -1.25, 19.1819<br> + Outside supported domain<br> 1, -0.75, 18.9751<br> Outside supported domain<br> + 1, -0.25, 18.5419<br> Outside supported domain<br> 2, -12.75, -124.031<br> + Outside supported domain<br> 2, -12.25, 124.019<br> Outside supported domain<br> + 2, -11.75, -124.032<br> Outside supported domain<br> 2, -11.25, 124.018<br> + Outside supported domain<br> 2, -10.75, -124.033<br> Outside supported + domain<br> 2, -10.25, 124.016<br> Outside supported domain<br> 2, -9.75, + -124.035<br> Outside supported domain<br> 2, -9.25, 124.015<br> Outside + supported domain<br> 2, -8.75, -124.037<br> Outside supported domain<br> + 2, -8.25, 124.012<br> Outside supported domain<br> 2, -7.75, -124.04<br> + Outside supported domain<br> 2, -7.25, 124.009<br> Outside supported domain<br> + 2, -6.75, -124.044<br> Outside supported domain<br> 2, -6.25, 124.003<br> + Outside supported domain<br> 2, -5.75, -124.051<br> Outside supported domain<br> + 2, -5.25, 123.995<br> Outside supported domain<br> 2, -4.75, -124.061<br> + Outside supported domain<br> 2, -4.25, 123.981<br> Outside supported domain<br> + 2, -3.75, -124.08<br> Outside supported domain<br> 2, -3.25, 123.955<br> + Outside supported domain<br> 2, -2.75, -124.118<br> Outside supported domain<br> + 2, -2.25, 123.897<br> Outside supported domain<br> 2, -1.75, -124.214<br> + Outside supported domain<br> 2, -1.25, 123.721<br> Outside supported domain<br> + 2, -0.75, -124.587<br> Outside supported domain<br> 2, -0.25, 122.697<br> + Outside supported domain<br> 3, -12.75, 1558.54<br> Outside supported domain<br> + 3, -12.25, 1558.54<br> Outside supported domain<br> 3, -11.75, 1558.54<br> + Outside supported domain<br> 3, -11.25, 1558.54<br> Outside supported domain<br> + 3, -10.75, 1558.54<br> Outside supported domain<br> 3, -10.25, 1558.54<br> + Outside supported domain<br> 3, -9.75, 1558.54<br> Outside supported domain<br> + 3, -9.25, 1558.54<br> Outside supported domain<br> 3, -8.75, 1558.54<br> + Outside supported domain<br> 3, -8.25, 1558.54<br> Outside supported domain<br> + 3, -7.75, 1558.54<br> Outside supported domain<br> 3, -7.25, 1558.54<br> + Outside supported domain<br> 3, -6.75, 1558.54<br> Outside supported domain<br> + 3, -6.25, 1558.54<br> Outside supported domain<br> 3, -5.75, 1558.54<br> + Outside supported domain<br> 3, -5.25, 1558.54<br> Outside supported domain<br> + 3, -4.75, 1558.53<br> Outside supported domain<br> 3, -4.25, 1558.53<br> + Outside supported domain<br> 3, -3.75, 1558.52<br> Outside supported domain<br> + 3, -3.25, 1558.51<br> Outside supported domain<br> 3, -2.75, 1558.49<br> + Outside supported domain<br> 3, -2.25, 1558.46<br> Outside supported domain<br> + 3, -1.75, 1558.38<br> Outside supported domain<br> 3, -1.25, 1558.22<br> + Outside supported domain<br> 3, -0.75, 1557.75<br> Outside supported domain<br> + 3, -0.25, 1555.76<br> Outside supported domain<br> 4, -12.75, -24481.6<br> + Outside supported domain<br> 4, -12.25, 24481.6<br> Outside supported domain<br> + 4, -11.75, -24481.6<br> Outside supported domain<br> 4, -11.25, 24481.6<br> + Outside supported domain<br> 4, -10.75, -24481.6<br> Outside supported + domain<br> 4, -10.25, 24481.6<br> Outside supported domain<br> 4, -9.75, + -24481.6<br> Outside supported domain<br> 4, -9.25, 24481.6<br> Outside + supported domain<br> 4, -8.75, -24481.6<br> Outside supported domain<br> + 4, -8.25, 24481.6<br> Outside supported domain<br> 4, -7.75, -24481.6<br> + Outside supported domain<br> 4, -7.25, 24481.6<br> Outside supported domain<br> + 4, -6.75, -24481.6<br> Outside supported domain<br> 4, -6.25, 24481.6<br> + Outside supported domain<br> 4, -5.75, -24481.6<br> Outside supported domain<br> + 4, -5.25, 24481.6<br> Outside supported domain<br> *** FURTHER CONTENT + HAS BEEN TRUNCATED FOR BREVITY ***<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h30"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with2">Error + Output For polygamma with compiler GNU C++ version 7.1.0 and library Rmath + 3.2.3 and test data Mathematica Data - large arguments</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_arguments"></a>CAUTION: + Gross error found at entry 211.<br> Found: -0 Expected -8.44974e-268 Error: + 3.79751e+40<br> 30, 8.58993e+09, -8.44974e-268<br> CAUTION: Gross error + found at entry 212.<br> Found: -0 Expected -7.86943e-277 Error: 3.5367e+31<br> + 30, 1.71799e+10, -7.86943e-277<br> CAUTION: Gross error found at entry 213.<br> + Found: -0 Expected -7.32898e-286 Error: 3.29381e+22<br> 30, 3.43597e+10, + -7.32898e-286<br> CAUTION: Gross error found at entry 214.<br> Found: -0 + Expected -6.82564e-295 Error: 3.0676e+13<br> 30, 6.87195e+10, -6.82564e-295<br> + CAUTION: Gross error found at entry 215.<br> Found: -0 Expected -6.35687e-304 + Error: 28568.3<br> 30, 1.37439e+11, -6.35687e-304<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h31"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w3">Error + Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL + 2.1 and test data Bessel Iv: Mathworld Data (large values)</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data_large_values_"></a>domain + error<br> -1, 3.72917e-155, 1.86459e-155<br> domain error<br> -1.125, + 3.72917e-155, -1.34964e+173<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h32"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w4">Error + Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL + 2.1 and test data Bessel Iv: Random Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Random_Data"></a>domain + error<br> -80.4919, 24.7501, 4.18698e+28<br> domain error<br> -80.4919, + 63.7722, 2.03248e+06<br> domain error<br> -74.6026, 24.7501, 7.20977e+23<br> + domain error<br> -74.6026, 63.7722, 8.7549e+08<br> domain error<br> -72.9046, + 24.7501, 1.04535e+22<br> domain error<br> -72.9046, 63.7722, 4.7162e+09<br> + domain error<br> -62.3236, 24.7501, 3.65147e+14<br> domain error<br> + -62.3236, 63.7722, 8.56683e+13<br> domain error<br> -55.7932, 24.7501, + -7.70364e+09<br> domain error<br> -55.7932, 63.7722, 1.95969e+16<br> + domain error<br> -44.3004, 9.50706, 2.93478e+22<br> domain error<br> + -44.3004, 24.7501, 640.568<br> domain error<br> -44.3004, 63.7722, 8.05557e+19<br> + domain error<br> -38.3666, 5.11399, 2.89105e+27<br> domain error<br> + -38.3666, 9.50706, 8.80632e+16<br> domain error<br> -38.3666, 24.7501, + 0.389004<br> domain error<br> -38.3666, 63.7722, 3.06303e+21<br> underflow<br> + 81.1584, 0.00177219, 0<br> underflow<br> 81.1584, 0.00221773, 0<br> underflow<br> + 81.1584, 0.0074445, 6.08857e-319<br> underflow<br> 82.6752, 0.00177219, + 0<br> underflow<br> 82.6752, 0.00221773, 0<br> underflow<br> 82.6752, + 0.0074445, 0<br> underflow<br> 91.5014, 0.00177219, 0<br> underflow<br> + 91.5014, 0.00221773, 0<br> underflow<br> 91.5014, 0.0074445, 0<br> underflow<br> + 91.5014, 0.014336, 0<br> underflow<br> 91.5014, 0.0176092, 0<br> underflow<br> + 92.9777, 0.00177219, 0<br> underflow<br> 92.9777, 0.00221773, 0<br> underflow<br> + 92.9777, 0.0074445, 0<br> underflow<br> 92.9777, 0.014336, 0<br> underflow<br> + 92.9777, 0.0176092, 0<br> underflow<br> 93.539, 0.00177219, 0<br> underflow<br> + 93.539, 0.00221773, 0<br> underflow<br> 93.539, 0.0074445, 0<br> underflow<br> + 93.539, 0.014336, 0<br> underflow<br> 93.539, 0.0176092, 0<br> underflow<br> + 93.7736, 0.00177219, 0<br> underflow<br> 93.7736, 0.00221773, 0<br> underflow<br> + 93.7736, 0.0074445, 0<br> underflow<br> 93.7736, 0.014336, 0<br> underflow<br> + 93.7736, 0.0176092, 0<br> underflow<br> 98.5763, 0.00177219, 0<br> underflow<br> + 98.5763, 0.00221773, 0<br> underflow<br> 98.5763, 0.0074445, 0<br> underflow<br> + 98.5763, 0.014336, 0<br> underflow<br> 98.5763, 0.0176092, 0<br> underflow<br> + 99.2923, 0.00177219, 0<br> underflow<br> 99.2923, 0.00221773, 0<br> underflow<br> + 99.2923, 0.0074445, 0<br> underflow<br> 99.2923, 0.014336, 0<br> underflow<br> + 99.2923, 0.0176092, 0<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h33"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w5">Error + Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL + 2.1 and test data Bessel In: Random Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Random_Data"></a>underflow<br> + 70, 0.00177219, 1.75887e-314<br> underflow<br> 73, 0.00177219, 0<br> + underflow<br> 73, 0.00221773, 4.24896e-322<br> underflow<br> 76, 0.00177219, + 0<br> underflow<br> 76, 0.00221773, 0<br> underflow<br> 79, 0.00177219, + 0<br> underflow<br> 79, 0.00221773, 0<br> underflow<br> 79, 0.0074445, + 1.38676e-309<br> underflow<br> 82, 0.00177219, 0<br> underflow<br> + 82, 0.00221773, 0<br> underflow<br> 82, 0.0074445, 1.33398e-322<br> underflow<br> + 85, 0.00177219, 0<br> underflow<br> 85, 0.00221773, 0<br> underflow<br> + 85, 0.0074445, 0<br> underflow<br> 85, 0.014336, 1.81568e-311<br> underflow<br> + 88, 0.00177219, 0<br> underflow<br> 88, 0.00221773, 0<br> underflow<br> + 88, 0.0074445, 0<br> underflow<br> 88, 0.014336, 9.88131e-324<br> underflow<br> + 88, 0.0176092, 7.34647e-316<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h34"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w6"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w6">Error + Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL + 2.1 and test data Bessel Iv: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data"></a>domain + error<br> -4.99902, 2.125, 0.0267921<br> domain error<br> -5.5, 10, 597.578<br> + domain error<br> -5.5, 100, 9.22363e+41<br> domain error<br> -10.0003, + 0.000976562, 1.41474e+35<br> domain error<br> -10.0003, 50, 1.07153e+20<br> + domain error<br> -141.4, 100, 2066.28<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h35"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i2">Error + Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0 + and library GSL 2.1 and test data Bessel In: Mathworld Data (Integer Version)</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__GSL_2_1_Bessel_In_Mathworld_Data_Integer_Version_"></a>underflow<br> + 10, 1e-100, 0<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h36"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w7"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w7">Error + Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL + 2.1 and test data Bessel In: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Mathworld_Data"></a>domain + error<br> -2, 0, 0<br> domain error<br> -5, 100, 9.47009e+41<br> domain + error<br> -5, -1, -0.000271463<br> domain error<br> 10, -5, 0.00458004<br> + domain error<br> -100, -200, 4.35275e+74<br> underflow<br> 10, 1e-100, + 0<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h37"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w8"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w8">Error + Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL + 2.1 and test data Bessel I1: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I1_Mathworld_Data"></a>domain + error<br> 1, -2, -1.59064<br> domain error<br> 1, -8, -399.873<br> + domain error<br> 1, -10, -2670.99<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h38"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w9"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w9">Error + Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL + 2.1 and test data Bessel I0: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I0_Mathworld_Data"></a>domain + error<br> 0, -2, 2.27959<br> domain error<br> 0, -7, 168.594<br> domain + error<br> 0, -1, 1.26607<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h39"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_0">Error + Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath> + and test data Bessel Iv: Mathworld Data (large values)</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data_large_values_"></a>Bad + argument in __cyl_bessel_i.<br> -1, 3.72917e-155, 1.86459e-155<br> Bad + argument in __cyl_bessel_i.<br> -1.125, 3.72917e-155, -1.34964e+173<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h40"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_1">Error + Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath> + and test data Bessel Iv: Random Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Random_Data"></a>Bad + argument in __cyl_bessel_i.<br> -80.4919, 24.7501, 4.18698e+28<br> Bad + argument in __cyl_bessel_i.<br> -80.4919, 63.7722, 2.03248e+06<br> Bad + argument in __cyl_bessel_i.<br> -74.6026, 24.7501, 7.20977e+23<br> Bad + argument in __cyl_bessel_i.<br> -74.6026, 63.7722, 8.7549e+08<br> Bad argument + in __cyl_bessel_i.<br> -72.9046, 24.7501, 1.04535e+22<br> Bad argument + in __cyl_bessel_i.<br> -72.9046, 63.7722, 4.7162e+09<br> Bad argument in + __cyl_bessel_i.<br> -62.3236, 24.7501, 3.65147e+14<br> Bad argument in + __cyl_bessel_i.<br> -62.3236, 63.7722, 8.56683e+13<br> Bad argument in + __cyl_bessel_i.<br> -55.7932, 24.7501, -7.70364e+09<br> Bad argument in + __cyl_bessel_i.<br> -55.7932, 63.7722, 1.95969e+16<br> Bad argument in + __cyl_bessel_i.<br> -44.3004, 9.50706, 2.93478e+22<br> Bad argument in + __cyl_bessel_i.<br> -44.3004, 24.7501, 640.568<br> Bad argument in __cyl_bessel_i.<br> + -44.3004, 63.7722, 8.05557e+19<br> Bad argument in __cyl_bessel_i.<br> + -38.3666, 5.11399, 2.89105e+27<br> Bad argument in __cyl_bessel_i.<br> + -38.3666, 9.50706, 8.80632e+16<br> Bad argument in __cyl_bessel_i.<br> + -38.3666, 24.7501, 0.389004<br> Bad argument in __cyl_bessel_i.<br> -38.3666, + 63.7722, 3.06303e+21<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h41"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_2">Error + Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath> + and test data Bessel Iv: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data"></a>Bad + argument in __cyl_bessel_i.<br> -4.99902, 2.125, 0.0267921<br> Bad argument + in __cyl_bessel_i.<br> -5.5, 10, 597.578<br> Bad argument in __cyl_bessel_i.<br> + -5.5, 100, 9.22363e+41<br> Bad argument in __cyl_bessel_i.<br> -10.0003, + 0.000976562, 1.41474e+35<br> Bad argument in __cyl_bessel_i.<br> -10.0003, + 50, 1.07153e+20<br> Bad argument in __cyl_bessel_i.<br> -141.4, 100, 2066.28<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h42"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i3">Error + Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0 + and library <cmath> and test data Bessel In: Mathworld Data (Integer + Version)</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_In_Mathworld_Data_Integer_Version_"></a>Bad + argument in __cyl_bessel_i.<br> -2, 0, 0<br> Bad argument in __cyl_bessel_i.<br> + -5, 100, 9.47009e+41<br> Bad argument in __cyl_bessel_i.<br> -5, -1, -0.000271463<br> + Bad argument in __cyl_bessel_i.<br> 10, -5, 0.00458004<br> Bad argument + in __cyl_bessel_i.<br> -100, -200, 4.35275e+74<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h43"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i4">Error + Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0 + and library <cmath> and test data Bessel I1: Mathworld Data (Integer + Version)</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I1_Mathworld_Data_Integer_Version_"></a>Bad + argument in __cyl_bessel_i.<br> 1, -2, -1.59064<br> Bad argument in __cyl_bessel_i.<br> + 1, -8, -399.873<br> Bad argument in __cyl_bessel_i.<br> 1, -10, -2670.99<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h44"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i5">Error + Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0 + and library <cmath> and test data Bessel I0: Mathworld Data (Integer + Version)</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I0_Mathworld_Data_Integer_Version_"></a>Bad + argument in __cyl_bessel_i.<br> 0, -2, 2.27959<br> Bad argument in __cyl_bessel_i.<br> + 0, -7, 168.594<br> Bad argument in __cyl_bessel_i.<br> 0, -1, 1.26607<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h45"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_3">Error + Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath> + and test data Bessel In: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_In_Mathworld_Data"></a>Bad + argument in __cyl_bessel_i.<br> -2, 0, 0<br> Bad argument in __cyl_bessel_i.<br> + -5, 100, 9.47009e+41<br> Bad argument in __cyl_bessel_i.<br> -5, -1, -0.000271463<br> + Bad argument in __cyl_bessel_i.<br> 10, -5, 0.00458004<br> Bad argument + in __cyl_bessel_i.<br> -100, -200, 4.35275e+74<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h46"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_4">Error + Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath> + and test data Bessel I1: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I1_Mathworld_Data"></a>Bad + argument in __cyl_bessel_i.<br> 1, -2, -1.59064<br> Bad argument in __cyl_bessel_i.<br> + 1, -8, -399.873<br> Bad argument in __cyl_bessel_i.<br> 1, -10, -2670.99<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h47"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_5">Error + Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath> + and test data Bessel I0: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I0_Mathworld_Data"></a>Bad + argument in __cyl_bessel_i.<br> 0, -2, 2.27959<br> Bad argument in __cyl_bessel_i.<br> + 0, -7, 168.594<br> Bad argument in __cyl_bessel_i.<br> 0, -1, 1.26607<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h48"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w3">Error + Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL + 2.1 and test data Bessel J: Random Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Random_Data"></a>underflow<br> + 63.8868, 5.5381e-05, 0<br> underflow<br> 63.8868, 6.9304e-05, 0<br> underflow<br> + 63.8868, 0.000232641, 0<br> underflow<br> 63.8868, 0.000448, 8.39912e-323<br> + underflow<br> 63.8868, 0.000550287, 4.32897e-317<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h49"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w4">Error + Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL + 2.1 and test data Bessel J: Mathworld Data (large values)</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data_large_values_"></a>domain + error<br> -0.5, 1.2459e-206, 7.14823e+102<br> domain error<br> -256, + 8, 0<br> domain error<br> -2.5, 4, -0.0145679<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h50"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w5">Error + Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL + 2.1 and test data Bessel J: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data"></a>domain + error<br> -5.5, 3.1416, -2.5582<br> domain error<br> -5.5, 10000, 0.00244984<br> + domain error<br> -5.5, 10000, 0.00244984<br> domain error<br> -5.5, 1e+06, + 0.000279243<br> domain error<br> -0.5, 101, 0.0708185<br> domain error<br> + -10.0003, 0.000976562, 1.41474e+35<br> domain error<br> -10.0003, 15, -0.0902239<br> + domain error<br> -10.0003, 100, -0.0547614<br> domain error<br> -10.0003, + 20000, -0.00556869<br> domain error<br> -8.5, 12.5664, -0.257087<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h51"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i3">Error + Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0 + and library GSL 2.1 and test data Bessel JN: Mathworld Data (Integer Version)</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__GSL_2_1_Bessel_JN_Mathworld_Data_Integer_Version_"></a>underflow<br> + 10, 1e-100, 0<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h52"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w6"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w6">Error + Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL + 2.1 and test data Bessel JN: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_JN_Mathworld_Data"></a>domain + error<br> -1, 1.25, -0.510623<br> domain error<br> -2, 0, 0<br> domain + error<br> 5, -10, 0.234062<br> domain error<br> -5, 1e+06, 0.000725964<br> + domain error<br> -5, -1, 0.000249758<br> domain error<br> 10, -10, 0.207486<br> + domain error<br> 10, -5, 0.0014678<br> domain error<br> -10, 1e+06, -0.000331079<br> + underflow<br> 10, 1e-100, 0<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h53"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w7"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w7">Error + Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL + 2.1 and test data Bessel J1: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J1_Mathworld_Data"></a>domain + error<br> 1, -2, -0.576725<br> domain error<br> 1, -8, -0.234636<br> + domain error<br> 1, -10, -0.0434727<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h54"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w8"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w8">Error + Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL + 2.1 and test data Bessel J0: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J0_Mathworld_Data"></a>domain + error<br> 0, -2, 0.223891<br> domain error<br> 0, -8, 0.171651<br> + domain error<br> 0, -10, -0.245936<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h55"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w9"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w9">Error + Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library <cmath> + and test data Bessel J: Mathworld Data (large values)</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data_large_values_"></a>Bad + argument in __cyl_bessel_j.<br> -0.5, 1.2459e-206, 7.14823e+102<br> Bad + argument in __cyl_bessel_j.<br> -256, 8, 1.46866e-353<br> Bad argument + in __cyl_bessel_j.<br> -2.5, 4, -0.0145679<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h56"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_0">Error + Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library <cmath> + and test data Bessel J: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data"></a>Bad + argument in __cyl_bessel_j.<br> -5.5, 3.1416, -2.5582<br> Bad argument + in __cyl_bessel_j.<br> -5.5, 10000, 0.00244984<br> Bad argument in __cyl_bessel_j.<br> + -5.5, 10000, 0.00244984<br> Bad argument in __cyl_bessel_j.<br> -5.5, 1e+06, + 0.000279243<br> Bad argument in __cyl_bessel_j.<br> -0.5, 101, 0.0708185<br> + Bad argument in __cyl_bessel_j.<br> -10.0003, 0.000976562, 1.41474e+35<br> + Bad argument in __cyl_bessel_j.<br> -10.0003, 15, -0.0902239<br> Bad argument + in __cyl_bessel_j.<br> -10.0003, 100, -0.0547614<br> Bad argument in __cyl_bessel_j.<br> + -10.0003, 20000, -0.00556869<br> Bad argument in __cyl_bessel_j.<br> -8.5, + 12.5664, -0.257087<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h57"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i4">Error + Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0 + and library <cmath> and test data Bessel JN: Mathworld Data (Integer + Version)</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_JN_Mathworld_Data_Integer_Version_"></a>Bad + argument in __cyl_bessel_j.<br> -1, 1.25, -0.510623<br> Bad argument in + __cyl_bessel_j.<br> -2, 0, 0<br> Bad argument in __cyl_bessel_j.<br> + 5, -10, 0.234062<br> Bad argument in __cyl_bessel_j.<br> -5, 1e+06, 0.000725964<br> + Bad argument in __cyl_bessel_j.<br> -5, -1, 0.000249758<br> Bad argument + in __cyl_bessel_j.<br> 10, -10, 0.207486<br> Bad argument in __cyl_bessel_j.<br> + 10, -5, 0.0014678<br> Bad argument in __cyl_bessel_j.<br> -10, 1e+06, -0.000331079<br> + CAUTION: Gross error found at entry 15.<br> Found: 0.0042409 Expected 0.00128318 + Error: 2.305<br> 1000, 100000, 0.00128318<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h58"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i5">Error + Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0 + and library <cmath> and test data Bessel J1: Mathworld Data (Integer + Version)</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J1_Mathworld_Data_Integer_Version_"></a>Bad + argument in __cyl_bessel_j.<br> 1, -2, -0.576725<br> Bad argument in __cyl_bessel_j.<br> + 1, -8, -0.234636<br> Bad argument in __cyl_bessel_j.<br> 1, -10, -0.0434727<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h59"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i6"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i6">Error + Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0 + and library <cmath> and test data Bessel J0: Mathworld Data (Integer + Version)</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J0_Mathworld_Data_Integer_Version_"></a>Bad + argument in __cyl_bessel_j.<br> 0, -2, 0.223891<br> Bad argument in __cyl_bessel_j.<br> + 0, -8, 0.171651<br> Bad argument in __cyl_bessel_j.<br> 0, -10, -0.245936<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h60"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_1">Error + Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library <cmath> + and test data Bessel JN: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_JN_Mathworld_Data"></a>Bad + argument in __cyl_bessel_j.<br> -1, 1.25, -0.510623<br> Bad argument in + __cyl_bessel_j.<br> -2, 0, 0<br> Bad argument in __cyl_bessel_j.<br> + 5, -10, 0.234062<br> Bad argument in __cyl_bessel_j.<br> -5, 1e+06, 0.000725964<br> + Bad argument in __cyl_bessel_j.<br> -5, -1, 0.000249758<br> Bad argument + in __cyl_bessel_j.<br> 10, -10, 0.207486<br> Bad argument in __cyl_bessel_j.<br> + 10, -5, 0.0014678<br> Bad argument in __cyl_bessel_j.<br> -10, 1e+06, -0.000331079<br> + CAUTION: Gross error found at entry 15.<br> Found: 0.0042409 Expected 0.00128318 + Error: 2.305<br> 1000, 100000, 0.00128318<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h61"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_2">Error + Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library <cmath> + and test data Bessel J1: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J1_Mathworld_Data"></a>Bad + argument in __cyl_bessel_j.<br> 1, -2, -0.576725<br> Bad argument in __cyl_bessel_j.<br> + 1, -8, -0.234636<br> Bad argument in __cyl_bessel_j.<br> 1, -10, -0.0434727<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h62"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_3">Error + Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library <cmath> + and test data Bessel J0: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J0_Mathworld_Data"></a>Bad + argument in __cyl_bessel_j.<br> 0, -2, 0.223891<br> Bad argument in __cyl_bessel_j.<br> + 0, -8, 0.171651<br> Bad argument in __cyl_bessel_j.<br> 0, -10, -0.245936<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h63"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_wi"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_wi">Error + Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL + 2.1 and test data Bessel Kv: Random Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Random_Data"></a>domain + error<br> -80.4919, 24.7501, 6.57902e+28<br> domain error<br> -80.4919, + 63.7722, 2.39552e-09<br> domain error<br> -80.4919, 125.28, 3.06904e-45<br> + domain error<br> -80.4919, 255.547, 2.30343e-107<br> domain error<br> + -80.4919, 503.011, 1.20315e-217<br> domain error<br> -80.4919, 1007.46, + 0<br> domain error<br> -80.4919, 1185.4, 0<br> domain error<br> -80.4919, + 3534.52, 0<br> domain error<br> -80.4919, 8071.55, 0<br> domain error<br> + -80.4919, 16229.2, 0<br> domain error<br> -80.4919, 32066.2, 0<br> domain + error<br> -80.4919, 36367.9, 0<br> domain error<br> -74.6026, 24.7501, + 1.19405e+24<br> domain error<br> -74.6026, 63.7722, 5.81897e-12<br> domain + error<br> -74.6026, 125.28, 9.89214e-47<br> domain error<br> -74.6026, + 255.547, 3.9726e-108<br> domain error<br> -74.6026, 503.011, 4.87462e-218<br> + domain error<br> -74.6026, 1007.46, 0<br> domain error<br> -74.6026, + 1185.4, 0<br> domain error<br> -74.6026, 3534.52, 0<br> domain error<br> + -74.6026, 8071.55, 0<br> domain error<br> -74.6026, 16229.2, 0<br> domain + error<br> -74.6026, 32066.2, 0<br> domain error<br> -74.6026, 36367.9, + 0<br> domain error<br> -72.9046, 24.7501, 5.5618e+22<br> domain error<br> + -72.9046, 63.7722, 1.09452e-12<br> domain error<br> -72.9046, 125.28, 3.8393e-47<br> + domain error<br> -72.9046, 255.547, 2.45173e-108<br> domain error<br> + -72.9046, 503.011, 3.80454e-218<br> domain error<br> -72.9046, 1007.46, + 0<br> domain error<br> -72.9046, 1185.4, 0<br> domain error<br> -72.9046, + 3534.52, 0<br> domain error<br> -72.9046, 8071.55, 0<br> domain error<br> + -72.9046, 16229.2, 0<br> domain error<br> -72.9046, 32066.2, 0<br> domain + error<br> -72.9046, 36367.9, 0<br> domain error<br> -62.3236, 24.7501, + 6.74518e+14<br> domain error<br> -62.3236, 63.7722, 6.54531e-17<br> domain + error<br> -62.3236, 125.28, 1.65653e-49<br> domain error<br> -62.3236, + 255.547, 1.54767e-109<br> domain error<br> -62.3236, 503.011, 9.22721e-219<br> + domain error<br> -62.3236, 1007.46, 0<br> domain error<br> -62.3236, + 1185.4, 0<br> domain error<br> -62.3236, 3534.52, 0<br> domain error<br> + -62.3236, 8071.55, 0<br> domain error<br> -62.3236, 16229.2, 0<br> domain + error<br> -62.3236, 32066.2, 0<br> domain error<br> -62.3236, 36367.9, + 0<br> domain error<br> -55.7932, 24.7501, 2.00028e+10<br> domain error<br> + -55.7932, 63.7722, 3.01107e-19<br> domain error<br> -55.7932, 125.28, 8.54693e-51<br> + domain error<br> -55.7932, 255.547, 3.47666e-110<br> domain error<br> + -55.7932, 503.011, 4.29705e-219<br> domain error<br> -55.7932, 1007.46, + 0<br> domain error<br> -55.7932, 1185.4, 0<br> domain error<br> -55.7932, + 3534.52, 0<br> domain error<br> -55.7932, 8071.55, 0<br> domain error<br> + -55.7932, 16229.2, 0<br> domain error<br> -55.7932, 32066.2, 0<br> domain + error<br> -55.7932, 36367.9, 0<br> domain error<br> -44.3004, 9.50706, + 5.6936e+22<br> domain error<br> -44.3004, 24.7501, 1242.73<br> domain + error<br> -44.3004, 63.7722, 7.99341e-23<br> domain error<br> -44.3004, + 125.28, 9.88149e-53<br> domain error<br> -44.3004, 255.547, 3.73007e-111<br> + domain error<br> -44.3004, 503.011, 1.37367e-219<br> domain error<br> + -44.3004, 1007.46, 0<br> domain error<br> -44.3004, 1185.4, 0<br> domain + error<br> -44.3004, 3534.52, 0<br> domain error<br> -44.3004, 8071.55, + 0<br> domain error<br> -44.3004, 16229.2, 0<br> domain error<br> -44.3004, + 32066.2, 0<br> domain error<br> -44.3004, 36367.9, 0<br> domain error<br> + -38.3666, 5.11399, 4.97154e+27<br> domain error<br> -38.3666, 9.50706, + 1.51436e+17<br> domain error<br> -38.3666, 24.7501, 0.639495<br> domain + error<br> -38.3666, 63.7722, 2.19334e-24<br> domain error<br> -38.3666, + 125.28, 1.45351e-53<br> domain error<br> -38.3666, 255.547, 1.43713e-111<br> + domain error<br> -38.3666, 503.011, 8.44445e-220<br> domain error<br> + -38.3666, 1007.46, 0<br> domain error<br> -38.3666, 1185.4, 0<br> domain + error<br> -38.3666, 3534.52, 0<br> domain error<br> -38.3666, 8071.55, + 0<br> domain error<br> -38.3666, 16229.2, 0<br> domain error<br> -38.3666, + 32066.2, 0<br> domain error<br> -38.3666, 36367.9, 0<br> underflow<br> + 9.3763, 1007.46, 0<br> underflow<br> 9.3763, 1185.4, 0<br> underflow<br> + 9.3763, 3534.52, 0<br> underflow<br> 9.3763, 8071.55, 0<br> underflow<br> + 9.3763, 16229.2, 0<br> underflow<br> 9.3763, 32066.2, 0<br> underflow<br> + 9.3763, 36367.9, 0<br> underflow<br> 9.44412, 1007.46, 0<br> underflow<br> + 9.44412, 1185.4, 0<br> underflow<br> 9.44412, 3534.52, 0<br> underflow<br> + 9.44412, 8071.55, 0<br> underflow<br> 9.44412, 16229.2, 0<br> underflow<br> + 9.44412, 32066.2, 0<br> underflow<br> 9.44412, 36367.9, 0<br> underflow<br> + 26.4719, 1007.46, 0<br> underflow<br> 26.4719, 1185.4, 0<br> underflow<br> + 26.4719, 3534.52, 0<br> underflow<br> 26.4719, 8071.55, 0<br> underflow<br> + 26.4719, 16229.2, 0<br> underflow<br> 26.4719, 32066.2, 0<br> underflow<br> + 26.4719, 36367.9, 0<br> underflow<br> 62.9447, 1007.46, 0<br> underflow<br> + 62.9447, 1185.4, 0<br> underflow<br> 62.9447, 3534.52, 0<br> underflow<br> + 62.9447, 8071.55, 0<br> underflow<br> 62.9447, 16229.2, 0<br> underflow<br> + *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h64"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w0">Error + Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL + 2.1 and test data Bessel Kn: Random Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Random_Data"></a>underflow<br> + 0, 1007.46, 0<br> underflow<br> 0, 1185.4, 0<br> underflow<br> 0, 3534.52, + 0<br> underflow<br> 0, 8071.55, 0<br> underflow<br> 0, 16229.2, 0<br> + underflow<br> 0, 32066.2, 0<br> underflow<br> 0, 36367.9, 0<br> underflow<br> + 1, 1007.46, 0<br> underflow<br> 1, 1185.4, 0<br> underflow<br> 1, 3534.52, + 0<br> underflow<br> 1, 8071.55, 0<br> underflow<br> 1, 16229.2, 0<br> + underflow<br> 1, 32066.2, 0<br> underflow<br> 1, 36367.9, 0<br> underflow<br> + 4, 1007.46, 0<br> underflow<br> 4, 1185.4, 0<br> underflow<br> 4, 3534.52, + 0<br> underflow<br> 4, 8071.55, 0<br> underflow<br> 4, 16229.2, 0<br> + underflow<br> 4, 32066.2, 0<br> underflow<br> 4, 36367.9, 0<br> underflow<br> + 7, 1007.46, 0<br> underflow<br> 7, 1185.4, 0<br> underflow<br> 7, 3534.52, + 0<br> underflow<br> 7, 8071.55, 0<br> underflow<br> 7, 16229.2, 0<br> + underflow<br> 7, 32066.2, 0<br> underflow<br> 7, 36367.9, 0<br> underflow<br> + 10, 1007.46, 0<br> underflow<br> 10, 1185.4, 0<br> underflow<br> 10, + 3534.52, 0<br> underflow<br> 10, 8071.55, 0<br> underflow<br> 10, 16229.2, + 0<br> underflow<br> 10, 32066.2, 0<br> underflow<br> 10, 36367.9, 0<br> + underflow<br> 13, 1007.46, 0<br> underflow<br> 13, 1185.4, 0<br> underflow<br> + 13, 3534.52, 0<br> underflow<br> 13, 8071.55, 0<br> underflow<br> 13, + 16229.2, 0<br> underflow<br> 13, 32066.2, 0<br> underflow<br> 13, 36367.9, + 0<br> underflow<br> 16, 1007.46, 0<br> underflow<br> 16, 1185.4, 0<br> + underflow<br> 16, 3534.52, 0<br> underflow<br> 16, 8071.55, 0<br> underflow<br> + 16, 16229.2, 0<br> underflow<br> 16, 32066.2, 0<br> underflow<br> 16, + 36367.9, 0<br> underflow<br> 19, 1007.46, 0<br> underflow<br> 19, 1185.4, + 0<br> underflow<br> 19, 3534.52, 0<br> underflow<br> 19, 8071.55, 0<br> + underflow<br> 19, 16229.2, 0<br> underflow<br> 19, 32066.2, 0<br> underflow<br> + 19, 36367.9, 0<br> underflow<br> 22, 1007.46, 0<br> underflow<br> 22, + 1185.4, 0<br> underflow<br> 22, 3534.52, 0<br> underflow<br> 22, 8071.55, + 0<br> underflow<br> 22, 16229.2, 0<br> underflow<br> 22, 32066.2, 0<br> + underflow<br> 22, 36367.9, 0<br> underflow<br> 25, 1007.46, 0<br> underflow<br> + 25, 1185.4, 0<br> underflow<br> 25, 3534.52, 0<br> underflow<br> 25, + 8071.55, 0<br> underflow<br> 25, 16229.2, 0<br> underflow<br> 25, 32066.2, + 0<br> underflow<br> 25, 36367.9, 0<br> underflow<br> 28, 1007.46, 0<br> + underflow<br> 28, 1185.4, 0<br> underflow<br> 28, 3534.52, 0<br> underflow<br> + 28, 8071.55, 0<br> underflow<br> 28, 16229.2, 0<br> underflow<br> 28, + 32066.2, 0<br> underflow<br> 28, 36367.9, 0<br> underflow<br> 31, 1007.46, + 0<br> underflow<br> 31, 1185.4, 0<br> underflow<br> 31, 3534.52, 0<br> + underflow<br> 31, 8071.55, 0<br> underflow<br> 31, 16229.2, 0<br> underflow<br> + 31, 32066.2, 0<br> underflow<br> 31, 36367.9, 0<br> underflow<br> 34, + 1007.46, 0<br> underflow<br> 34, 1185.4, 0<br> underflow<br> 34, 3534.52, + 0<br> underflow<br> 34, 8071.55, 0<br> underflow<br> 34, 16229.2, 0<br> + underflow<br> 34, 32066.2, 0<br> underflow<br> 34, 36367.9, 0<br> underflow<br> + 37, 1007.46, 0<br> underflow<br> 37, 1185.4, 0<br> underflow<br> 37, + 3534.52, 0<br> underflow<br> 37, 8071.55, 0<br> underflow<br> 37, 16229.2, + 0<br> underflow<br> 37, 32066.2, 0<br> underflow<br> 37, 36367.9, 0<br> + underflow<br> 40, 1007.46, 0<br> underflow<br> 40, 1185.4, 0<br> underflow<br> + 40, 3534.52, 0<br> underflow<br> 40, 8071.55, 0<br> underflow<br> 40, + 16229.2, 0<br> underflow<br> 40, 32066.2, 0<br> underflow<br> 40, 36367.9, + 0<br> underflow<br> 43, 1007.46, 0<br> underflow<br> 43, 1185.4, 0<br> + underflow<br> 43, 3534.52, 0<br> underflow<br> 43, 8071.55, 0<br> underflow<br> + 43, 16229.2, 0<br> underflow<br> 43, 32066.2, 0<br> underflow<br> 43, + 36367.9, 0<br> underflow<br> 46, 1007.46, 0<br> underflow<br> 46, 1185.4, + 0<br> underflow<br> 46, 3534.52, 0<br> underflow<br> 46, 8071.55, 0<br> + underflow<br> 46, 16229.2, 0<br> underflow<br> 46, 32066.2, 0<br> underflow<br> + 46, 36367.9, 0<br> underflow<br> 49, 1007.46, 0<br> underflow<br> 49, + 1185.4, 0<br> underflow<br> 49, 3534.52, 0<br> underflow<br> 49, 8071.55, + 0<br> underflow<br> 49, 16229.2, 0<br> underflow<br> 49, 32066.2, 0<br> + underflow<br> 49, 36367.9, 0<br> underflow<br> 52, 1007.46, 0<br> underflow<br> + 52, 1185.4, 0<br> underflow<br> 52, 3534.52, 0<br> underflow<br> 52, + 8071.55, 0<br> underflow<br> 52, 16229.2, 0<br> underflow<br> 52, 32066.2, + 0<br> underflow<br> 52, 36367.9, 0<br> underflow<br> 55, 1007.46, 0<br> + underflow<br> 55, 1185.4, 0<br> underflow<br> 55, 3534.52, 0<br> underflow<br> + 55, 8071.55, 0<br> underflow<br> 55, 16229.2, 0<br> underflow<br> 55, + 32066.2, 0<br> underflow<br> 55, 36367.9, 0<br> underflow<br> 58, 1007.46, + 0<br> underflow<br> 58, 1185.4, 0<br> underflow<br> 58, 3534.52, 0<br> + underflow<br> 58, 8071.55, 0<br> underflow<br> 58, 16229.2, 0<br> underflow<br> + 58, 32066.2, 0<br> underflow<br> 58, 36367.9, 0<br> underflow<br> 61, + 1007.46, 0<br> underflow<br> 61, 1185.4, 0<br> underflow<br> 61, 3534.52, + 0<br> underflow<br> 61, 8071.55, 0<br> underflow<br> 61, 16229.2, 0<br> + underflow<br> 61, 32066.2, 0<br> underflow<br> 61, 36367.9, 0<br> underflow<br> + 64, 1007.46, 0<br> underflow<br> 64, 1185.4, 0<br> underflow<br> 64, + 3534.52, 0<br> underflow<br> 64, 8071.55, 0<br> underflow<br> 64, 16229.2, + 0<br> underflow<br> 64, 32066.2, 0<br> underflow<br> 64, 36367.9, 0<br> + underflow<br> 67, 1007.46, 0<br> underflow<br> 67, 1185.4, 0<br> underflow<br> + 67, 3534.52, 0<br> underflow<br> 67, 8071.55, 0<br> underflow<br> 67, + 16229.2, 0<br> *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h65"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w1">Error + Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL + 2.1 and test data Bessel Kv: Mathworld Data (large values)</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data_large_values_"></a>domain + error<br> -1, 3.72917e-155, 2.68156e+154<br> domain error<br> -1.125, + 3.72917e-155, 5.53984e+173<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h66"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w2">Error + Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL + 2.1 and test data Bessel Kv: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data"></a>domain + error<br> -5.5, 10, 7.33045e-05<br> domain error<br> -5.5, 100, 5.41275e-45<br> + domain error<br> -141.399, 50, 1.30185e+42<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h67"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w3">Error + Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL + 2.1 and test data Bessel Kn: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Mathworld_Data"></a>domain + error<br> -5, 100, 5.27326e-45<br> domain error<br> -10, 1, 1.80713e+08<br> + domain error<br> -1000, 700, 6.51562e-31<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h68"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w4">Error + Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library <cmath> + and test data Bessel Kv: Random Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Random_Data"></a>Bad + argument in __cyl_bessel_k.<br> -80.4919, 24.7501, 6.57902e+28<br> Bad + argument in __cyl_bessel_k.<br> -80.4919, 63.7722, 2.39552e-09<br> Bad + argument in __cyl_bessel_k.<br> -80.4919, 125.28, 3.06904e-45<br> Bad argument + in __cyl_bessel_k.<br> -80.4919, 255.547, 2.30343e-107<br> Bad argument + in __cyl_bessel_k.<br> -80.4919, 503.011, 1.20315e-217<br> Bad argument + in __cyl_bessel_k.<br> -80.4919, 1007.46, 2.86537e-438<br> Bad argument + in __cyl_bessel_k.<br> -80.4919, 1185.4, 8.63263e-516<br> Bad argument + in __cyl_bessel_k.<br> -80.4919, 3534.52, 5.01367e-1537<br> Bad argument + in __cyl_bessel_k.<br> -80.4919, 8071.55, 7.76555e-3508<br> Bad argument + in __cyl_bessel_k.<br> -80.4919, 16229.2, 0<br> Bad argument in __cyl_bessel_k.<br> + -80.4919, 32066.2, 0<br> Bad argument in __cyl_bessel_k.<br> -80.4919, + 36367.9, 0<br> Bad argument in __cyl_bessel_k.<br> -74.6026, 24.7501, 1.19405e+24<br> + Bad argument in __cyl_bessel_k.<br> -74.6026, 63.7722, 5.81897e-12<br> + Bad argument in __cyl_bessel_k.<br> -74.6026, 125.28, 9.89214e-47<br> Bad + argument in __cyl_bessel_k.<br> -74.6026, 255.547, 3.9726e-108<br> Bad + argument in __cyl_bessel_k.<br> -74.6026, 503.011, 4.87462e-218<br> Bad + argument in __cyl_bessel_k.<br> -74.6026, 1007.46, 1.82221e-438<br> Bad + argument in __cyl_bessel_k.<br> -74.6026, 1185.4, 5.87506e-516<br> Bad + argument in __cyl_bessel_k.<br> -74.6026, 3534.52, 4.40608e-1537<br> Bad + argument in __cyl_bessel_k.<br> -74.6026, 8071.55, 7.3384e-3508<br> Bad + argument in __cyl_bessel_k.<br> -74.6026, 16229.2, 0<br> Bad argument in + __cyl_bessel_k.<br> -74.6026, 32066.2, 0<br> Bad argument in __cyl_bessel_k.<br> + -74.6026, 36367.9, 0<br> Bad argument in __cyl_bessel_k.<br> -72.9046, + 24.7501, 5.5618e+22<br> Bad argument in __cyl_bessel_k.<br> -72.9046, 63.7722, + 1.09452e-12<br> Bad argument in __cyl_bessel_k.<br> -72.9046, 125.28, 3.8393e-47<br> + Bad argument in __cyl_bessel_k.<br> -72.9046, 255.547, 2.45173e-108<br> + Bad argument in __cyl_bessel_k.<br> -72.9046, 503.011, 3.80454e-218<br> + Bad argument in __cyl_bessel_k.<br> -72.9046, 1007.46, 1.60949e-438<br> + Bad argument in __cyl_bessel_k.<br> -72.9046, 1185.4, 5.28662e-516<br> + Bad argument in __cyl_bessel_k.<br> -72.9046, 3534.52, 4.25273e-1537<br> + Bad argument in __cyl_bessel_k.<br> -72.9046, 8071.55, 7.22542e-3508<br> + Bad argument in __cyl_bessel_k.<br> -72.9046, 16229.2, 0<br> Bad argument + in __cyl_bessel_k.<br> -72.9046, 32066.2, 0<br> Bad argument in __cyl_bessel_k.<br> + -72.9046, 36367.9, 0<br> Bad argument in __cyl_bessel_k.<br> -62.3236, + 24.7501, 6.74518e+14<br> Bad argument in __cyl_bessel_k.<br> -62.3236, + 63.7722, 6.54531e-17<br> Bad argument in __cyl_bessel_k.<br> -62.3236, + 125.28, 1.65653e-49<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 255.547, + 1.54767e-109<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 503.011, + 9.22721e-219<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 1007.46, + 7.91894e-439<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 1185.4, + 2.89281e-516<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 3534.52, + 3.4736e-1537<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 8071.55, + 6.6126e-3508<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 16229.2, + 0<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 32066.2, 0<br> Bad + argument in __cyl_bessel_k.<br> -62.3236, 36367.9, 0<br> Bad argument in + __cyl_bessel_k.<br> -55.7932, 24.7501, 2.00028e+10<br> Bad argument in + __cyl_bessel_k.<br> -55.7932, 63.7722, 3.01107e-19<br> Bad argument in + __cyl_bessel_k.<br> -55.7932, 125.28, 8.54693e-51<br> Bad argument in __cyl_bessel_k.<br> + -55.7932, 255.547, 3.47666e-110<br> Bad argument in __cyl_bessel_k.<br> + -55.7932, 503.011, 4.29705e-219<br> Bad argument in __cyl_bessel_k.<br> + -55.7932, 1007.46, 5.40242e-439<br> Bad argument in __cyl_bessel_k.<br> + -55.7932, 1185.4, 2.08996e-516<br> Bad argument in __cyl_bessel_k.<br> + -55.7932, 3534.52, 3.11458e-1537<br> Bad argument in __cyl_bessel_k.<br> + -55.7932, 8071.55, 6.30409e-3508<br> Bad argument in __cyl_bessel_k.<br> + -55.7932, 16229.2, 0<br> Bad argument in __cyl_bessel_k.<br> -55.7932, + 32066.2, 0<br> Bad argument in __cyl_bessel_k.<br> -55.7932, 36367.9, 0<br> + Bad argument in __cyl_bessel_k.<br> -44.3004, 9.50706, 5.6936e+22<br> Bad + argument in __cyl_bessel_k.<br> -44.3004, 24.7501, 1242.73<br> Bad argument + in __cyl_bessel_k.<br> -44.3004, 63.7722, 7.99341e-23<br> Bad argument + in __cyl_bessel_k.<br> -44.3004, 125.28, 9.88149e-53<br> Bad argument in + __cyl_bessel_k.<br> -44.3004, 255.547, 3.73007e-111<br> Bad argument in + __cyl_bessel_k.<br> -44.3004, 503.011, 1.37367e-219<br> Bad argument in + __cyl_bessel_k.<br> -44.3004, 1007.46, 3.05398e-439<br> Bad argument in + __cyl_bessel_k.<br> *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h69"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w5">Error + Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library <cmath> + and test data Bessel Kv: Mathworld Data (large values)</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data_large_values_"></a>Bad + argument in __cyl_bessel_k.<br> -1, 3.72917e-155, 2.68156e+154<br> Bad + argument in __cyl_bessel_k.<br> -1.125, 3.72917e-155, 5.53984e+173<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h70"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w6"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w6">Error + Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library <cmath> + and test data Bessel Kv: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data"></a>Bad + argument in __cyl_bessel_k.<br> -5.5, 10, 7.33045e-05<br> Bad argument + in __cyl_bessel_k.<br> -5.5, 100, 5.41275e-45<br> Bad argument in __cyl_bessel_k.<br> + -141.399, 50, 1.30185e+42<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h71"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_in"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_in">Error + Output For cyl_bessel_k (integer orders) with compiler GNU C++ version 7.1.0 + and library <cmath> and test data Bessel Kn: Mathworld Data (Integer + Version)</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k_integer_orders___cmath__Bessel_Kn_Mathworld_Data_Integer_Version_"></a>Bad + argument in __cyl_bessel_k.<br> -5, 100, 5.27326e-45<br> Bad argument in + __cyl_bessel_k.<br> -10, 1, 1.80713e+08<br> Bad argument in __cyl_bessel_k.<br> + -1000, 700, 6.51562e-31<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h72"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w7"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w7">Error + Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library <cmath> + and test data Bessel Kn: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kn_Mathworld_Data"></a>Bad + argument in __cyl_bessel_k.<br> -5, 100, 5.27326e-45<br> Bad argument in + __cyl_bessel_k.<br> -10, 1, 1.80713e+08<br> Bad argument in __cyl_bessel_k.<br> + -1000, 700, 6.51562e-31<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h73"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wit"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wit">Error + Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library GSL + 2.1 and test data Yv: Mathworld Data (large values)</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data_large_values_"></a>domain + error<br> -0.5, 1.2459e-206, 8.90598e-104<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h74"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi0">Error + Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library GSL + 2.1 and test data Yv: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data"></a>domain + error<br> -5.5, 3.125, -0.0274994<br> domain error<br> -5.5, 10000, -0.00759344<br> + domain error<br> -10.0003, 0.000976562, -1.50382e+38<br> domain error<br> + -10.0003, 100, 0.0583042<br> domain error<br> -141.75, 100, -3.8101e+09<br> + domain error<br> -8.5, 12.5664, 0.0436808<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h75"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi1">Error + Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library GSL + 2.1 and test data Yn: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yn_Mathworld_Data"></a>domain + error<br> -5, 1e+06, 0.000331052<br> domain error<br> -10, 1e+06, 0.000725952<br> + domain error<br> -1000, 700, -1.88753e+77<br> domain error<br> -25, 8, + 3.45114e+08<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h76"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi2">Error + Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library <cmath> + and test data Yv: Random Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Random_Data"></a>CAUTION: + Gross error found at entry 394.<br> Found: -3.29903 Expected 0.0192842 Error: + 1.18973e+4932<br> 125.28, 1007.46, 0.0192842<br> CAUTION: Gross error found + at entry 395.<br> Found: 1.13543 Expected 0.0230358 Error: 48.2897<br> + 125.28, 1185.4, 0.0230358<br> CAUTION: Gross error found at entry 396.<br> + Found: 0.00119445 Expected 0.00460223 Error: 2.85302<br> 125.28, 3534.52, + 0.00460223<br> CAUTION: Gross error found at entry 403.<br> Found: 1068 + Expected -0.00270959 Error: 1.18973e+4932<br> 255.547, 1007.46, -0.00270959<br> + CAUTION: Gross error found at entry 404.<br> Found: -395.006 Expected 0.00738845 + Error: 1.18973e+4932<br> 255.547, 1185.4, 0.00738845<br> CAUTION: Gross + error found at entry 405.<br> Found: 1.08701 Expected -0.000407036 Error: + 1.18973e+4932<br> 255.547, 3534.52, -0.000407036<br> CAUTION: Gross error + found at entry 406.<br> Found: 0.0232211 Expected 0.00886946 Error: 1.61809<br> + 255.547, 8071.55, 0.00886946<br> CAUTION: Gross error found at entry 411.<br> + Found: 65895.7 Expected -0.0158467 Error: 1.18973e+4932<br> 503.011, 1007.46, + -0.0158467<br> CAUTION: Gross error found at entry 412.<br> Found: -123316 + Expected 0.00594357 Error: 1.18973e+4932<br> 503.011, 1185.4, 0.00594357<br> + CAUTION: Gross error found at entry 413.<br> Found: -706.209 Expected 0.010151 + Error: 1.18973e+4932<br> 503.011, 3534.52, 0.010151<br> CAUTION: Gross + error found at entry 414.<br> Found: -21.2081 Expected 0.00888375 Error: + 1.18973e+4932<br> 503.011, 8071.55, 0.00888375<br> CAUTION: Gross error + found at entry 415.<br> Found: 0.0272835 Expected 0.00552287 Error: 3.94008<br> + 503.011, 16229.2, 0.00552287<br> CAUTION: Gross error found at entry 416.<br> + Found: 0.0103324 Expected 0.00445559 Error: 1.31898<br> 503.011, 32066.2, + 0.00445559<br> CAUTION: Gross error found at entry 417.<br> Found: 0.00540788 + Expected -0.00384344 Error: 1.18973e+4932<br> 503.011, 36367.9, -0.00384344<br> + CAUTION: Gross error found at entry 418.<br> Found: 5.43091e+07 Expected + -0.0772843 Error: 1.18973e+4932<br> 1007.46, 1007.46, -0.0772843<br> CAUTION: + Gross error found at entry 419.<br> Found: -2.84383e+07 Expected 0.0304312 + Error: 1.18973e+4932<br> 1007.46, 1185.4, 0.0304312<br> CAUTION: Gross + error found at entry 420.<br> Found: -61440.2 Expected -0.00474217 Error: + 1.29562e+07<br> 1007.46, 3534.52, -0.00474217<br> CAUTION: Gross error + found at entry 421.<br> Found: -4126.89 Expected -0.0074205 Error: 556146<br> + 1007.46, 8071.55, -0.0074205<br> CAUTION: Gross error found at entry 422.<br> + Found: -69.2831 Expected -0.00179572 Error: 38581.4<br> 1007.46, 16229.2, + -0.00179572<br> CAUTION: Gross error found at entry 423.<br> Found: 2.32048 + Expected 0.000750053 Error: 3092.76<br> 1007.46, 32066.2, 0.000750053<br> + CAUTION: Gross error found at entry 424.<br> Found: 3.90724 Expected 0.00305125 + Error: 1279.54<br> 1007.46, 36367.9, 0.00305125<br> CAUTION: Gross error + found at entry 425.<br> Found: -1.83374e+08 Expected -7.25176e+28 Error: + 3.95463e+20<br> 1185.4, 1007.46, -7.25176e+28<br> CAUTION: Gross error + found at entry 426.<br> Found: 1.09822e+08 Expected -0.0732059 Error: 1.18973e+4932<br> + 1185.4, 1185.4, -0.0732059<br> CAUTION: Gross error found at entry 427.<br> + Found: 315632 Expected 0.000479585 Error: 6.58136e+08<br> 1185.4, 3534.52, + 0.000479585<br> CAUTION: Gross error found at entry 428.<br> Found: 16815.6 + Expected 0.00174909 Error: 9.61391e+06<br> 1185.4, 8071.55, 0.00174909<br> + CAUTION: Gross error found at entry 429.<br> Found: 133.356 Expected 0.00416288 + Error: 32033.6<br> 1185.4, 16229.2, 0.00416288<br> CAUTION: Gross error + found at entry 430.<br> Found: -1.38401 Expected -0.000320056 Error: 4323.27<br> + 1185.4, 32066.2, -0.000320056<br> CAUTION: Gross error found at entry 431.<br> + Found: -17.7085 Expected -0.00417656 Error: 4238.96<br> 1185.4, 36367.9, + -0.00417656<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h77"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi3">Error + Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library <cmath> + and test data Yv: Mathworld Data (large values)</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data_large_values_"></a>Bad + argument in __cyl_neumann_n.<br> -0.5, 1.2459e-206, 8.90598e-104<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h78"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi4">Error + Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library <cmath> + and test data Yv: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data"></a>Bad + argument in __cyl_neumann_n.<br> -5.5, 3.125, -0.0274994<br> Bad argument + in __cyl_neumann_n.<br> -5.5, 10000, -0.00759344<br> Bad argument in __cyl_neumann_n.<br> + -10.0003, 0.000976562, -1.50382e+38<br> Bad argument in __cyl_neumann_n.<br> + -10.0003, 100, 0.0583042<br> Bad argument in __cyl_neumann_n.<br> -141.75, + 100, -3.8101e+09<br> Bad argument in __cyl_neumann_n.<br> -8.5, 12.5664, + 0.0436808<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h79"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_int"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_int">Error + Output For cyl_neumann (integer orders) with compiler GNU C++ version 7.1.0 + and library <cmath> and test data Yn: Mathworld Data (Integer Version)</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann_integer_orders___cmath__Yn_Mathworld_Data_Integer_Version_"></a>Bad + argument in __cyl_neumann_n.<br> -5, 1e+06, 0.000331052<br> Bad argument + in __cyl_neumann_n.<br> -10, 1e+06, 0.000725952<br> CAUTION: Gross error + found at entry 7.<br> Found: 0.0540745 Expected 0.00217255 Error: 23.8899<br> + 1000, 100000, 0.00217255<br> Bad argument in __cyl_neumann_n.<br> -1000, + 700, -1.88753e+77<br> Bad argument in __cyl_neumann_n.<br> -25, 8, 3.45114e+08<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h80"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi5">Error + Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library <cmath> + and test data Yn: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yn_Mathworld_Data"></a>Bad + argument in __cyl_neumann_n.<br> -5, 1e+06, 0.000331052<br> Bad argument + in __cyl_neumann_n.<br> -10, 1e+06, 0.000725952<br> CAUTION: Gross error + found at entry 7.<br> Found: 0.0540745 Expected 0.00217255 Error: 23.8899<br> + 1000, 100000, 0.00217255<br> Bad argument in __cyl_neumann_n.<br> -1000, + 700, -1.88753e+77<br> Bad argument in __cyl_neumann_n.<br> -25, 8, 3.45114e+08<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h81"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_beta_with_compi"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_beta_with_compi">Error + Output For beta with compiler GNU C++ version 7.1.0 and library GSL 2.1 and + test data Beta Function: Small Values</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_beta_GSL_2_1_Beta_Function_Small_Values"></a>CAUTION: + Found non-finite result, when a finite value was expected at entry 22<br> + Found: inf Expected 5.69832e+154 Error: 1.79769e+308<br> 2.98334e-154, 1.86459e-155, + 5.69832e+154<br> CAUTION: Gross error found at entry 22.<br> Found: inf + Expected 5.69832e+154 Error: 1.79769e+308<br> 2.98334e-154, 1.86459e-155, + 5.69832e+154<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h82"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_rj_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_rj_with_">Error + Output For ellint_rj with compiler GNU C++ version 7.1.0 and library GSL 2.1 + and test data RJ: Random data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_ellint_rj_GSL_2_1_RJ_Random_data"></a>domain + error<br> 1.77787e-31, 1.40657e+18, 10.046, -4.8298e-10, -2.51795e-10<br> + domain error<br> 3.37448e-31, 4.65772e+22, 0.469831, -4.33756e-09, -2.95865e-11<br> + domain error<br> 5.25297e-31, 5.85483e+25, 2.02482e-15, -1.87347e-28, 3.36445e+07<br> + domain error<br> 6.22216e-31, 3.43401e+23, 0.673005, -2.7626e-13, -7.58898e-12<br> + domain error<br> 6.26875e-31, 2.62568e-13, 1.06394e+24, -1.36451e+14, -6.70372e-25<br> + domain error<br> 6.84599e-31, 3.57666e-29, 1.82191e+11, -3.63292e+08, -8.35235e-13<br> + domain error<br> 8.90482e-31, 1.97093e-28, 1.14939e-31, -1.26424e-12, -6.39454e+26<br> + domain error<br> 1.07374e-30, 1.70005e-12, 1.88773e-25, -1.16558e-29, 4.31668e+32<br> + domain error<br> 1.17141e-30, 24.2523, 3.67522e+21, -4.79065e-22, 2.2702e-05<br> + domain error<br> 1.64143e-30, 2.01978e-22, 2.58942e+12, -8.52649e-12, -2.82629e+06<br> + domain error<br> 1.85141e-30, 0.0386712, 2.37846e-13, -1.57357e+15, -1.38574e-13<br> + domain error<br> 2.70034e-30, 4.43896e-24, 7.54576e+16, -1.1436e-14, -1.10082e+07<br> + domain error<br> 4.01162e-30, 2.73343e+23, 1.32333e+13, -1.86032e-07, -4.16626e-25<br> + domain error<br> 4.13665e-30, 1.08034e-30, 3.13547e-16, -5.58099e-08, -5.14643e+16<br> + domain error<br> 4.3728e-30, 7.79812e+12, 8.58894e+21, -4.58312e-24, 5.28901e-09<br> + domain error<br> 5.6397e-30, 1.64768e+23, 9.64423e-15, -1.82207e+20, -1.62886e-30<br> + domain error<br> 9.89841e-30, 9.69731e+10, 1.03263e+21, -0.00343967, -9.62714e-22<br> + domain error<br> 1.3797e-29, 6.03357e+08, 5.62497e-15, -5.87235e+16, -5.80287e-20<br> + domain error<br> 1.96963e-29, 3.22384e-25, 2.92187e+23, -3.80643e+27, -8.2513e-38<br> + domain error<br> 2.00927e-29, 5.6976e-05, 1.16219e+25, -1.64129e-22, 0.00318397<br> + domain error<br> 7.29506e-29, 5904.94, 9.93922e+10, -19.528, -1.60795e-09<br> + domain error<br> 1.19698e-28, 1.66816e-22, 28472, -1.21137e-19, -5.84699e+17<br> + domain error<br> 1.64095e-28, 2.13421e-21, 7.8914e-15, -1.77584e-07, -1.70156e+15<br> + domain error<br> 2.03475e-28, 4.40987e+15, 28739.1, -9624.5, -1.29418e-12<br> + domain error<br> 2.73113e-28, 1.08457e+19, 4.00674e+08, -5.70043e-11, 1.092e-17<br> + domain error<br> 5.52633e-28, 1.45707e-17, 1.29411e-27, -1.67255e-15, -5.84881e+24<br> + domain error<br> 5.61278e-28, 9.22881e-12, 8.64222e-13, -5.6282e+23, -4.57782e-18<br> + domain error<br> 6.08465e-28, 1.32249e+26, 1.25536e-30, -1.89097e-14, -223.246<br> + domain error<br> 9.50943e-28, 2.49682e-18, 0.000904584, -3.1419e-12, -2.44954e+14<br> + domain error<br> 1.20779e-27, 35383.2, 1.35533e-15, -4.67834e-24, 3.20581e+15<br> + domain error<br> 2.29822e-27, 3.35258e-16, 2.60689e+08, -9.99161e-20, -5.4924e+11<br> + domain error<br> 3.0926e-27, 3.11839e-13, 3.37883e-23, -1.94349e+26, -3.55191e-19<br> + domain error<br> 3.12803e-27, 1.15118e+16, 1.52495e+10, -4.2399e+13, -3.07515e-21<br> + domain error<br> 4.49747e-27, 716.685, 1.69018e-23, -1.32558e-14, -9.2291e+13<br> + domain error<br> 4.84575e-27, 3.44028e-27, 3.42665e+09, -812.399, -2.12767e-06<br> + domain error<br> 5.81424e-27, 3.70845e-15, 3.69338e+11, -4.15794e+06, -2.95944e-11<br> + domain error<br> 6.08654e-27, 1.23742e+08, 1.09124e-26, -2.19946e+16, -4.90896e-19<br> + domain error<br> 7.71967e-27, 9.46115e-26, 1.24324e+25, -522800, -5.83203e-17<br> + domain error<br> 9.20037e-27, 207550, 2.45782e-17, -6.06901e+29, -2.88945e-31<br> + domain error<br> 1.75502e-26, 5.81507e+16, 8.83063e+21, -1.11214e-21, 1.57697e-11<br> + domain error<br> 2.29965e-26, 2.9716e-21, 1.81059e-25, -5.23972e-08, -6.23302e+18<br> + domain error<br> 2.32628e-26, 0.0655133, 1.62901e-21, -7.15441e-17, -9.88586e+17<br> + domain error<br> 3.49194e-26, 2.53343e+14, 756.217, -1.3359e+10, -1.275e-16<br> + domain error<br> 1.009e-25, 0.0694304, 1.20267e-14, -1.55746e-22, 2.10701e+17<br> + domain error<br> 3.54771e-25, 1.67999e-27, 2.3917e+24, -9.98754e+25, -1.11704e-36<br> + domain error<br> 6.31714e-25, 3.4594e-28, 6.37951e-24, -1.25529e-24, -9.56292e+35<br> + domain error<br> 6.74086e-25, 2.47169e+12, 1.32962e+23, -6.78845e+06, -3.32861e-24<br> + domain error<br> 1.8099e-24, 4.5215e-06, 8.66937e-11, -3.70795e-08, -1.41893e+11<br> + domain error<br> 2.29798e-24, 9.30454e-30, 6.56584e-17, -9890.38, -373149<br> + domain error<br> 2.88161e-24, 8.82377e-05, 1.57747e+21, -4.25068e-24, 2260.61<br> + domain error<br> 3.25991e-24, 1.92923e+29, 3.09752e-05, -1.00986e+11, -1.25485e-24<br> + domain error<br> 6.36705e-24, 2.8074e+22, 1.75569e-13, -1.53152e+24, -4.89823e-34<br> + domain error<br> 7.90772e-24, 2.11611e-30, 1.42682e-07, -0.00296297, -5.38814e+07<br> + domain error<br> 1.05302e-23, 4.83473e+26, 4.43149e-30, -1.56818e+13, -3.6836e-25<br> + *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h83"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_1_with_c"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_1_with_c">Error + Output For ellint_1 with compiler GNU C++ version 7.1.0 and library <cmath> + and test data Elliptic Integral F: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_1__cmath__Elliptic_Integral_F_Mathworld_Data"></a>CAUTION: + Gross error found at entry 9.<br> Found: -7.02862e+09 Expected 1.04181e+20 + Error: 1.18973e+4932<br> 1e+20, 0.390625, 1.04181e+20<br> CAUTION: Gross + error found at entry 10.<br> Found: -9.3866e+09 Expected 1.39133e+50 Error: + 1.18973e+4932<br> 1e+50, 0.875, 1.39133e+50<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h84"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_2_comple"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_2_comple">Error + Output For ellint_2 (complete) with compiler GNU C++ version 7.1.0 and library + GSL 2.1 and test data Elliptic Integral E: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_ellint_2_complete__GSL_2_1_Elliptic_Integral_E_Mathworld_Data"></a>domain + error<br> -1, 1<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h85"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_2_with_c"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_2_with_c">Error + Output For ellint_2 with compiler GNU C++ version 7.1.0 and library <cmath> + and test data Elliptic Integral E: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_2__cmath__Elliptic_Integral_E_Mathworld_Data"></a>CAUTION: + Gross error found at entry 7.<br> Found: -6.3027e+09 Expected 9.34215e+09 + Error: 1.18973e+4932<br> 1e+10, -0.5, 9.34215e+09<br> CAUTION: Gross error + found at entry 8.<br> Found: -6.48129e+09 Expected 7.08861e+19 Error: 1.18973e+4932<br> + 7.3787e+19, 0.390625, 7.08861e+19<br> CAUTION: Gross error found at entry + 9.<br> Found: -5.13973e+09 Expected 7.1259e+49 Error: 1.18973e+4932<br> + 9.35361e+49, 0.878906, 7.1259e+49<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h86"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_comple"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_comple">Error + Output For ellint_3 (complete) with compiler GNU C++ version 7.1.0 and library + GSL 2.1 and test data Complete Elliptic Integral PI: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_ellint_3_complete__GSL_2_1_Complete_Elliptic_Integral_PI_Mathworld_Data"></a>domain + error<br> -4.14952e+180, 0.5, 7.71119e-91<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h87"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_c"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_c">Error + Output For ellint_3 with compiler GNU C++ version 7.1.0 and library GSL 2.1 + and test data Elliptic Integral PI: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_ellint_3_GSL_2_1_Elliptic_Integral_PI_Mathworld_Data"></a>domain + error<br> 1.125, 10, 0.25, 0.662468<br> domain error<br> 1.125, 3, 0.25, + -0.142697<br> domain error<br> 1.00391, 21.5, 0.125, -0.535406<br> domain + error<br> 1, 2, 0.5, -2.87535<br> domain error<br> 1, -2, 0.5, 2.87535<br> + domain error<br> 1, 2, 6.22302e-61, -2.18504<br> domain error<br> 1, + -2, 6.22302e-61, 2.18504<br> domain error<br> 20, 3.14257, 0.5, 0.000975941<br> + domain error<br> 20, -3.14257, 0.5, -0.000975941<br> domain error<br> + 1.01562, 1.6958, 0.5, -27.1647<br> domain error<br> 1.01562, -1.6958, 0.5, + 27.1647<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h88"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_compl0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_compl0">Error + Output For ellint_3 (complete) with compiler GNU C++ version 7.1.0 and library + <cmath> and test data Complete Elliptic Integral PI: Random Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Random_Data"></a>Argument + too small in __ellint_rj<br> -87.1743, 0.126987, 0.167413<br> Argument + too small in __ellint_rj<br> -87.1743, 0.135477, 0.167431<br> Argument + too small in __ellint_rj<br> -87.1743, 0.221034, 0.167683<br> Argument + too small in __ellint_rj<br> -87.1743, 0.308167, 0.168078<br> Argument + too small in __ellint_rj<br> -87.1743, 0.632359, 0.17122<br> Argument too + small in __ellint_rj<br> -87.1743, 0.814724, 0.175341<br> Argument too + small in __ellint_rj<br> -87.1743, 0.835009, 0.176056<br> Argument too + small in __ellint_rj<br> -87.1743, 0.905792, 0.179501<br> Argument too + small in __ellint_rj<br> -87.1743, 0.913376, 0.180014<br> Argument too + small in __ellint_rj<br> -87.1743, 0.968868, 0.186162<br> Argument too + small in __ellint_rj<br> -86.3168, 0.126987, 0.168233<br> Argument too + small in __ellint_rj<br> -86.3168, 0.135477, 0.168252<br> Argument too + small in __ellint_rj<br> -86.3168, 0.221034, 0.168506<br> Argument too + small in __ellint_rj<br> -86.3168, 0.308167, 0.168905<br> Argument too + small in __ellint_rj<br> -86.3168, 0.632359, 0.172077<br> Argument too + small in __ellint_rj<br> -86.3168, 0.814724, 0.176237<br> Argument too + small in __ellint_rj<br> -86.3168, 0.835009, 0.176958<br> Argument too + small in __ellint_rj<br> -86.3168, 0.905792, 0.180437<br> Argument too + small in __ellint_rj<br> -86.3168, 0.913376, 0.180955<br> Argument too + small in __ellint_rj<br> -86.3168, 0.968868, 0.187163<br> Argument too + small in __ellint_rj<br> -77.6756, 0.126987, 0.177238<br> Argument too + small in __ellint_rj<br> -77.6756, 0.135477, 0.177258<br> Argument too + small in __ellint_rj<br> -77.6756, 0.221034, 0.17754<br> Argument too small + in __ellint_rj<br> -77.6756, 0.308167, 0.17798<br> Argument too small in + __ellint_rj<br> -77.6756, 0.632359, 0.181485<br> Argument too small in + __ellint_rj<br> -77.6756, 0.814724, 0.186089<br> Argument too small in + __ellint_rj<br> -77.6756, 0.835009, 0.186888<br> Argument too small in + __ellint_rj<br> -77.6756, 0.905792, 0.190742<br> Argument too small in + __ellint_rj<br> -77.6756, 0.913376, 0.191315<br> Argument too small in + __ellint_rj<br> -77.6756, 0.968868, 0.1982<br> Argument too small in __ellint_rj<br> + -68.8751, 0.126987, 0.188077<br> Argument too small in __ellint_rj<br> + -68.8751, 0.135477, 0.188099<br> Argument too small in __ellint_rj<br> + -68.8751, 0.221034, 0.188414<br> Argument too small in __ellint_rj<br> + -68.8751, 0.308167, 0.188907<br> Argument too small in __ellint_rj<br> + -68.8751, 0.632359, 0.192834<br> Argument too small in __ellint_rj<br> + -68.8751, 0.814724, 0.198<br> Argument too small in __ellint_rj<br> -68.8751, + 0.835009, 0.198896<br> Argument too small in __ellint_rj<br> -68.8751, + 0.905792, 0.203226<br> Argument too small in __ellint_rj<br> -68.8751, + 0.913376, 0.203871<br> Argument too small in __ellint_rj<br> -68.8751, + 0.968868, 0.211615<br> Argument too small in __ellint_rj<br> -36.1317, + 0.126987, 0.258074<br> Argument too small in __ellint_rj<br> -36.1317, + 0.135477, 0.258115<br> Argument too small in __ellint_rj<br> -36.1317, + 0.221034, 0.258686<br> Argument too small in __ellint_rj<br> -36.1317, + 0.308167, 0.259579<br> Argument too small in __ellint_rj<br> -36.1317, + 0.632359, 0.266738<br> Argument too small in __ellint_rj<br> -36.1317, + 0.814724, 0.276242<br> Argument too small in __ellint_rj<br> -36.1317, + 0.835009, 0.2779<br> Argument too small in __ellint_rj<br> -36.1317, 0.905792, + 0.285938<br> Argument too small in __ellint_rj<br> -36.1317, 0.913376, + 0.287139<br> Argument too small in __ellint_rj<br> -36.1317, 0.968868, + 0.301608<br> Argument too small in __ellint_rj<br> -17.7129, 0.126987, + 0.363673<br> Argument too small in __ellint_rj<br> -17.7129, 0.135477, + 0.36375<br> Argument too small in __ellint_rj<br> -17.7129, 0.221034, 0.364822<br> + Argument too small in __ellint_rj<br> -17.7129, 0.308167, 0.366503<br> + Argument too small in __ellint_rj<br> -17.7129, 0.632359, 0.380066<br> + Argument too small in __ellint_rj<br> -17.7129, 0.814724, 0.398311<br> + Argument too small in __ellint_rj<br> -17.7129, 0.835009, 0.401518<br> + Argument too small in __ellint_rj<br> -17.7129, 0.905792, 0.417145<br> + Argument too small in __ellint_rj<br> -17.7129, 0.913376, 0.41949<br> Argument + too small in __ellint_rj<br> -17.7129, 0.968868, 0.447893<br> Argument + too small in __ellint_rj<br> -15.6641, 0.126987, 0.385409<br> Argument + too small in __ellint_rj<br> -15.6641, 0.135477, 0.385495<br> Argument + too small in __ellint_rj<br> -15.6641, 0.221034, 0.386686<br> Argument + too small in __ellint_rj<br> -15.6641, 0.308167, 0.388553<br> Argument + too small in __ellint_rj<br> -15.6641, 0.632359, 0.403643<br> Argument + too small in __ellint_rj<br> *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY + ***<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h89"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_compl1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_compl1">Error + Output For ellint_3 (complete) with compiler GNU C++ version 7.1.0 and library + <cmath> and test data Complete Elliptic Integral PI: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Mathworld_Data"></a>CAUTION: + Gross error found at entry 3.<br> Found: 1.28255 Expected 2.22144 Error: + 0.732051<br> 0.5, 0, 2.22144<br> Argument too small in __ellint_rj<br> + -4, 0.3, 0.712709<br> Argument too small in __ellint_rj<br> -100000, -0.5, + 0.00496945<br> Argument too small in __ellint_rj<br> -1e+10, -0.75, 1.5708e-05<br> + CAUTION: Gross error found at entry 8.<br> Found: 1.45615 Expected 101.045 + Error: 68.3919<br> 0.999023, -0.875, 101.045<br> Argument too small in + __ellint_rj<br> -4.14952e+180, 0.5, 7.71119e-91<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h90"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_0">Error + Output For ellint_3 with compiler GNU C++ version 7.1.0 and library <cmath> + and test data Elliptic Integral PI: Large Random Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Large_Random_Data"></a>Argument + too small in __ellint_rj<br> -88.2952, -8.04919, 0.814724, -0.874724<br> + Argument too small in __ellint_rj<br> -88.2952, -7.46026, 0.135477, -0.827189<br> + Argument too small in __ellint_rj<br> -88.2952, -7.29046, 0.905792, -0.877476<br> + Argument too small in __ellint_rj<br> -88.2952, -6.23236, 0.835009, -0.652152<br> + Argument too small in __ellint_rj<br> -88.2952, -5.57932, 0.126987, -0.512276<br> + Argument too small in __ellint_rj<br> -88.2952, -4.43004, 0.968868, -0.543324<br> + Argument too small in __ellint_rj<br> -88.2952, -3.83666, 0.913376, -0.513389<br> + Argument too small in __ellint_rj<br> -88.2952, 0.93763, 0.221034, 0.158243<br> + Argument too small in __ellint_rj<br> -88.2952, 0.944412, 0.632359, 0.160101<br> + Argument too small in __ellint_rj<br> -88.2952, 2.64719, 0.308167, 0.188127<br> + Argument too small in __ellint_rj<br> -88.2952, 6.29447, 0.0975404, 0.676465<br> + Argument too small in __ellint_rj<br> -88.2952, 6.70017, 0.547221, 0.817785<br> + Argument too small in __ellint_rj<br> -88.2952, 8.11584, 0.278498, 0.837452<br> + Argument too small in __ellint_rj<br> -88.2952, 8.26752, 0.188382, 0.837571<br> + Argument too small in __ellint_rj<br> -88.2952, 9.15014, 0.546881, 0.885365<br> + Argument too small in __ellint_rj<br> -88.2952, 9.29777, 0.992881, 1.06701<br> + Argument too small in __ellint_rj<br> -88.2952, 9.3539, 0.957507, 1.03573<br> + Argument too small in __ellint_rj<br> -88.2952, 9.37736, 0.996461, 1.13933<br> + Argument too small in __ellint_rj<br> -88.2952, 9.85763, 0.964889, 1.24906<br> + Argument too small in __ellint_rj<br> -88.2952, 9.92923, 0.967695, 1.25621<br> + Argument too small in __ellint_rj<br> -86.8166, -8.04919, 0.157613, -0.841405<br> + Argument too small in __ellint_rj<br> -86.8166, -7.46026, 0.725839, -0.859877<br> + Argument too small in __ellint_rj<br> -86.8166, -7.29046, 0.970593, -0.914439<br> + Argument too small in __ellint_rj<br> -86.8166, -6.23236, 0.98111, -0.710627<br> + Argument too small in __ellint_rj<br> -86.8166, -5.57932, 0.957167, -0.58106<br> + Argument too small in __ellint_rj<br> -86.8166, -4.43004, 0.109862, -0.499839<br> + Argument too small in __ellint_rj<br> -86.8166, -3.83666, 0.485376, -0.494286<br> + Argument too small in __ellint_rj<br> -86.8166, 0.93763, 0.798106, 0.162644<br> + Argument too small in __ellint_rj<br> -86.8166, 0.944412, 0.80028, 0.16282<br> + Argument too small in __ellint_rj<br> -86.8166, 2.64719, 0.297029, 0.18978<br> + Argument too small in __ellint_rj<br> -86.8166, 6.29447, 0.141886, 0.682392<br> + Argument too small in __ellint_rj<br> -86.8166, 6.70017, 0.00478348, 0.812885<br> + Argument too small in __ellint_rj<br> -86.8166, 8.11584, 0.421761, 0.849249<br> + Argument too small in __ellint_rj<br> -86.8166, 8.26752, 0.112465, 0.843648<br> + Argument too small in __ellint_rj<br> -86.8166, 9.15014, 0.915736, 0.953733<br> + Argument too small in __ellint_rj<br> -86.8166, 9.29777, 0.639763, 0.936743<br> + Argument too small in __ellint_rj<br> -86.8166, 9.3539, 0.792207, 0.987359<br> + Argument too small in __ellint_rj<br> -86.8166, 9.37736, 0.878431, 1.02525<br> + Argument too small in __ellint_rj<br> -86.8166, 9.85763, 0.959492, 1.25508<br> + Argument too small in __ellint_rj<br> -86.8166, 9.92923, 0.503663, 1.16735<br> + Argument too small in __ellint_rj<br> -84.7616, -8.04919, 0.655741, -0.873305<br> + Argument too small in __ellint_rj<br> -84.7616, -7.46026, 0.797929, -0.879044<br> + Argument too small in __ellint_rj<br> -84.7616, -7.29046, 0.0357117, -0.840785<br> + Argument too small in __ellint_rj<br> -84.7616, -6.23236, 0.361294, -0.635502<br> + Argument too small in __ellint_rj<br> -84.7616, -5.57932, 0.849129, -0.558231<br> + Argument too small in __ellint_rj<br> -84.7616, -4.43004, 0.211924, -0.506533<br> + Argument too small in __ellint_rj<br> -84.7616, -3.83666, 0.933993, -0.527681<br> + Argument too small in __ellint_rj<br> -84.7616, 0.93763, 0.68136, 0.163458<br> + Argument too small in __ellint_rj<br> -84.7616, 0.944412, 0.678735, 0.163582<br> + Argument too small in __ellint_rj<br> -84.7616, 2.64719, 0.398739, 0.193458<br> + Argument too small in __ellint_rj<br> -84.7616, 6.29447, 0.75774, 0.716086<br> + Argument too small in __ellint_rj<br> -84.7616, 6.70017, 0.740647, 0.847849<br> + Argument too small in __ellint_rj<br> -84.7616, 8.11584, 0.743132, 0.883827<br> + Argument too small in __ellint_rj<br> -84.7616, 8.26752, 0.474759, 0.864181<br> + Argument too small in __ellint_rj<br> -84.7616, 9.15014, 0.392227, 0.895646<br> + Argument too small in __ellint_rj<br> -84.7616, 9.29777, 0.422088, 0.933423<br> + Argument too small in __ellint_rj<br> *** FURTHER CONTENT HAS BEEN TRUNCATED + FOR BREVITY ***<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h91"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_1">Error + Output For ellint_3 with compiler GNU C++ version 7.1.0 and library <cmath> + and test data Elliptic Integral PI: Random Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Random_Data"></a>CAUTION: + Gross error found at entry 150.<br> Found: 1.09748 Expected 1.76311 Error: + 0.606506<br> 0.546881, 1.27977, 0.349984, 1.76311<br> CAUTION: Gross error + found at entry 151.<br> Found: 1.39529 Expected 2.4686 Error: 0.769232<br> + 0.546881, 1.31163, 0.907365, 2.4686<br> CAUTION: Gross error found at entry + 152.<br> Found: 1.17627 Expected 2.03097 Error: 0.726615<br> 0.546881, + 1.42281, 0.196595, 2.03097<br> CAUTION: Gross error found at entry 153.<br> + Found: 1.47192 Expected 2.76894 Error: 0.881179<br> 0.546881, 1.43473, 0.848468, + 2.76894<br> CAUTION: Gross error found at entry 154.<br> Found: 1.23674 + Expected 2.22733 Error: 0.800966<br> 0.546881, 1.50405, 0.251084, 2.22733<br> + CAUTION: Gross error found at entry 155.<br> Found: 1.87704 Expected 3.98415 + Error: 1.12257<br> 0.546881, 1.51564, 0.955018, 3.98415<br> CAUTION: Gross + error found at entry 156.<br> Found: 1.35817 Expected 2.53989 Error: 0.870091<br> + 0.546881, 1.52005, 0.616045, 2.53989<br> CAUTION: Gross error found at entry + 157.<br> Found: 1.48427 Expected 2.87082 Error: 0.934166<br> 0.546881, + 1.52189, 0.778898, 2.87082<br> CAUTION: Gross error found at entry 158.<br> + Found: 1.32687 Expected 2.48679 Error: 0.874176<br> 0.546881, 1.55961, 0.473289, + 2.48679<br> CAUTION: Gross error found at entry 159.<br> Found: 2.37485 + Expected 5.58805 Error: 1.35301<br> 0.546881, 1.56524, 0.98746, 5.58805<br> + CAUTION: Gross error found at entry 170.<br> Found: 1.08889 Expected 1.74565 + Error: 0.603142<br> 0.547221, 1.27977, 0.285839, 1.74565<br> CAUTION: Gross + error found at entry 171.<br> Found: 1.21346 Expected 2.03956 Error: 0.680778<br> + 0.547221, 1.31163, 0.67982, 2.03956<br> CAUTION: Gross error found at entry + 172.<br> Found: 1.36407 Expected 2.48392 Error: 0.820965<br> 0.547221, + 1.42281, 0.7572, 2.48392<br> CAUTION: Gross error found at entry 173.<br> + Found: 1.21442 Expected 2.12881 Error: 0.752947<br> 0.547221, 1.43473, 0.39232, + 2.12881<br> CAUTION: Gross error found at entry 174.<br> Found: 1.4409 + Expected 2.74399 Error: 0.904352<br> 0.547221, 1.50405, 0.753729, 2.74399<br> + CAUTION: Gross error found at entry 175.<br> Found: 1.32796 Expected 2.46156 + Error: 0.853642<br> 0.547221, 1.51564, 0.561557, 2.46156<br> CAUTION: Gross + error found at entry 176.<br> Found: 1.27163 Expected 2.32413 Error: 0.82767<br> + 0.547221, 1.52005, 0.380446, 2.32413<br> CAUTION: Gross error found at entry + 177.<br> Found: 1.24298 Expected 2.25511 Error: 0.814274<br> 0.547221, + 1.52189, 0.208068, 2.25511<br> CAUTION: Gross error found at entry 178.<br> + Found: 1.36528 Expected 2.58635 Error: 0.894379<br> 0.547221, 1.55961, 0.567822, + 2.58635<br> CAUTION: Gross error found at entry 179.<br> Found: 1.35151 + Expected 2.55463 Error: 0.890206<br> 0.547221, 1.56524, 0.527371, 2.55463<br> + CAUTION: Gross error found at entry 189.<br> Found: 1.01047 Expected 1.52344 + Error: 0.507658<br> 0.632359, 0.993308, 0.964966, 1.52344<br> CAUTION: + Gross error found at entry 190.<br> Found: 1.05231 Expected 1.84135 Error: + 0.749817<br> 0.632359, 1.27977, 0.129906, 1.84135<br> CAUTION: Gross error + found at entry 191.<br> Found: 1.07393 Expected 1.92224 Error: 0.789918<br> + 0.632359, 1.31163, 0.154438, 1.92224<br> CAUTION: Gross error found at entry + 192.<br> Found: 1.22616 Expected 2.43657 Error: 0.987156<br> 0.632359, + 1.42281, 0.568824, 2.43657<br> CAUTION: Gross error found at entry 193.<br> + Found: 1.18462 Expected 2.33142 Error: 0.968083<br> 0.632359, 1.43473, 0.394908, + 2.33142<br> CAUTION: Gross error found at entry 194.<br> Found: 1.25094 + Expected 2.59169 Error: 1.0718<br> 0.632359, 1.50405, 0.469391, 2.59169<br> + CAUTION: Gross error found at entry 195.<br> Found: 1.23693 Expected 2.56158 + Error: 1.07091<br> 0.632359, 1.51564, 0.387296, 2.56158<br> CAUTION: Gross + error found at entry 196.<br> Found: 1.19839 Expected 2.45293 Error: 1.04685<br> + 0.632359, 1.52005, 0.0119021, 2.45293<br> CAUTION: Gross error found at entry + 197.<br> Found: 1.39415 Expected 3.05228 Error: 1.18935<br> 0.632359, 1.52189, + 0.726955, 3.05228<br> CAUTION: Gross error found at entry 198.<br> Found: + 1.25489 Expected 2.6569 Error: 1.11723<br> 0.632359, 1.55961, 0.337123, 2.6569<br> + CAUTION: Gross error found at entry 199.<br> Found: 1.27021 Expected 2.70857 + Error: 1.13237<br> 0.632359, 1.56524, 0.38857, 2.70857<br> CAUTION: Gross + error found at entry 209.<br> Found: 0.83304 Expected 1.35947 Error: 0.631944<br> + 0.814724, 0.993308, 0.119547, 1.35947<br> CAUTION: Gross error found at entry + 210.<br> Found: 1.07764 Expected 2.50291 Error: 1.32258<br> *** FURTHER + CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h92"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_2">Error + Output For ellint_3 with compiler GNU C++ version 7.1.0 and library <cmath> + and test data Elliptic Integral PI: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Mathworld_Data"></a>CAUTION: + Gross error found at entry 0.<br> Found: -0.809353 Expected -1.55741 Error: + 0.924263<br> 1, -1, 0, -1.55741<br> CAUTION: Gross error found at entry + 11.<br> Found: 1.07555 Expected 13.2822 Error: 11.3492<br> 0.999023, 1.5, + 0, 13.2822<br> CAUTION: Gross error found at entry 13.<br> Found: -5.86896e+09 + Expected 1.53659e+10 Error: 1.18973e+4932<br> 0.5, 1e+10, 0.5, 1.53659e+10<br> + Argument too small in __ellint_rj<br> -100000, 10, 0.75, 0.0347926<br> + Argument too small in __ellint_rj<br> -1e+10, 10, 0.875, 0.000109956<br> + Argument too small in __ellint_rj<br> -1e+10, 1e+20, 0.875, 1.00001e+15<br> + Argument too small in __ellint_rj<br> -1e+10, 1.57031, 0.875, 1.57081e-05<br> + CAUTION: Gross error found at entry 18.<br> Found: -6.25413e+09 Expected + 6.43274e+21 Error: 1.18973e+4932<br> 0.999023, 1e+20, 0.875, 6.43274e+21<br> + CAUTION: Gross error found at entry 19.<br> Found: 0.102424 Expected 0.196321 + Error: 0.916748<br> 50, 0.125, 0.25, 0.196321<br> CAUTION: Gross error + found at entry 20.<br> Found: 0.798807 Expected 1.773 Error: 1.21956<br> + 1.125, 1, 0.25, 1.773<br> CAUTION: Gross error found at entry 21.<br> Found: + 7.07138 Expected 0.662468 Error: 9.6743<br> 1.125, 10, 0.25, 0.662468<br> + CAUTION: Gross error found at entry 22.<br> Found: 2.04288 Expected -0.142697 + Error: 1.18973e+4932<br> 1.125, 3, 0.25, -0.142697<br> CAUTION: Gross error + found at entry 23.<br> Found: 1.07762 Expected 22.2699 Error: 19.6659<br> + 1.00391, 1.5, 0.125, 22.2699<br> CAUTION: Gross error found at entry 24.<br> + Found: 15.1275 Expected -0.535406 Error: 1.18973e+4932<br> 1.00391, 21.5, + 0.125, -0.535406<br> CAUTION: Gross error found at entry 41.<br> Found: + 1.57454 Expected 3.0338 Error: 0.926787<br> 0.5, 2, 0, 3.0338<br> CAUTION: + Gross error found at entry 42.<br> Found: 3.0338 Expected 1.57454 Error: + 0.926787<br> -0.5, 2, 0, 1.57454<br> CAUTION: Gross error found at entry + 43.<br> Found: -1.57454 Expected -3.0338 Error: 0.926787<br> 0.5, -2, 0, + -3.0338<br> CAUTION: Gross error found at entry 44.<br> Found: -3.0338 + Expected -1.57454 Error: 0.926787<br> -0.5, -2, 0, -1.57454<br> CAUTION: + Found non-finite result, when a finite value was expected at entry 51<br> + Found: inf Expected -2.87535 Error: 1.18973e+4932<br> 1, 2, 0.5, -2.87535<br> + CAUTION: Gross error found at entry 51.<br> Found: inf Expected -2.87535 + Error: 1.18973e+4932<br> 1, 2, 0.5, -2.87535<br> CAUTION: Found non-finite + result, when a finite value was expected at entry 52<br> Found: -inf Expected + 2.87535 Error: 1.18973e+4932<br> 1, -2, 0.5, 2.87535<br> CAUTION: Gross + error found at entry 52.<br> Found: -inf Expected 2.87535 Error: 1.18973e+4932<br> + 1, -2, 0.5, 2.87535<br> CAUTION: Found non-finite result, when a finite value + was expected at entry 53<br> Found: inf Expected -2.18504 Error: 1.18973e+4932<br> + 1, 2, 6.22302e-61, -2.18504<br> CAUTION: Gross error found at entry 53.<br> + Found: inf Expected -2.18504 Error: 1.18973e+4932<br> 1, 2, 6.22302e-61, + -2.18504<br> CAUTION: Found non-finite result, when a finite value was expected + at entry 54<br> Found: -inf Expected 2.18504 Error: 1.18973e+4932<br> 1, + -2, 6.22302e-61, 2.18504<br> CAUTION: Gross error found at entry 54.<br> + Found: -inf Expected 2.18504 Error: 1.18973e+4932<br> 1, -2, 6.22302e-61, + 2.18504<br> CAUTION: Gross error found at entry 57.<br> Found: 0.703907 + Expected 0.000975941 Error: 720.259<br> 20, 3.14257, 0.5, 0.000975941<br> + CAUTION: Gross error found at entry 58.<br> Found: -0.703907 Expected -0.000975941 + Error: 720.259<br> 20, -3.14257, 0.5, -0.000975941<br> CAUTION: Gross error + found at entry 59.<br> Found: 1.24445 Expected -27.1647 Error: 1.18973e+4932<br> + 1.01562, 1.6958, 0.5, -27.1647<br> CAUTION: Gross error found at entry 60.<br> + Found: -1.24445 Expected 27.1647 Error: 1.18973e+4932<br> 1.01562, -1.6958, + 0.5, 27.1647<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h93"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_expint_ei_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_expint_ei_with_">Error + Output For expint (Ei) with compiler GNU C++ version 7.1.0 and library <cmath> + and test data Exponential Integral Ei</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_long_double_expint_Ei___cmath__Exponential_Integral_Ei"></a>Continued + fraction failed in __expint_En_cont_frac.<br> -1.30539, -0.134326<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h94"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ibeta_with_comp"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ibeta_with_comp">Error + Output For ibeta with compiler GNU C++ version 7.1.0 and library GSL 2.1 and + test data Incomplete Beta Function: Large and Diverse Values</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_ibeta_GSL_2_1_Incomplete_Beta_Function_Large_and_Diverse_Values"></a>underflow<br> + 1.04761e-05, 39078.2, 0.913384, 95444.4, 0, 1, 0<br> underflow<br> 1.2158e-05, + 24110.5, 0.135563, 82239.7, 0, 1, 0<br> underflow<br> 1.30342e-05, 26168.3, + 0.127074, 76710.7, 0, 1, 0<br> underflow<br> 1.51962e-05, 16177.5, 0.814742, + 65795.4, 0, 1, 0<br> underflow<br> 1.64873e-05, 470997, 0.127074, 60639.1, + 0, 1, 0<br> underflow<br> 1.66259e-05, 147819, 0.632396, 60134.5, 0, 1, + 0<br> underflow<br> 1.78638e-05, 439.387, 0.835025, 55972.4, 0, 1, 0<br> + underflow<br> 2.00434e-05, 482.007, 0.905801, 49885.1, 0, 1, 0<br> underflow<br> + 2.05189e-05, 236088, 0.835025, 48722.7, 0, 1, 0<br> underflow<br> 2.14336e-05, + 3719.28, 0.814742, 46647, 0, 1, 0<br> underflow<br> 2.24486e-05, 445071, + 0.221112, 44532.6, 0, 1, 0<br> underflow<br> 2.34849e-05, 25542.8, 0.968871, + 42569.8, 0, 1, 0<br> underflow<br> 2.39993e-05, 462.946, 0.814742, 41661.1, + 0, 1, 0<br> underflow<br> 2.52178e-05, 1832.27, 0.913384, 39646.4, 0, 1, + 0<br> underflow<br> 2.87756e-05, 25491.8, 0.905801, 34740.9, 0, 1, 0<br> + underflow<br> 2.89316e-05, 494.984, 0.968871, 34557.6, 0, 1, 0<br> underflow<br> + 3.11413e-05, 348144, 0.308236, 32098.3, 0, 1, 0<br> underflow<br> 3.12319e-05, + 33713, 0.221112, 32007.5, 0, 1, 0<br> underflow<br> 3.19889e-05, 3931.19, + 0.308236, 31251.9, 0, 1, 0<br> underflow<br> 3.27129e-05, 3109.49, 0.968871, + 30560.4, 0, 1, 0<br> underflow<br> 3.27529e-05, 25796.3, 0.835025, 30520.9, + 0, 1, 0<br> underflow<br> 3.34106e-05, 3378.01, 0.221112, 29922, 0, 1, + 0<br> underflow<br> 3.40793e-05, 288783, 0.814742, 29330.2, 0, 1, 0<br> + underflow<br> 3.46418e-05, 411.559, 0.913384, 28860.3, 0, 1, 0<br> underflow<br> + 3.61632e-05, 311937, 0.905801, 27639.2, 0, 1, 0<br> underflow<br> 3.75686e-05, + 386440, 0.913384, 26604.5, 0, 1, 0<br> underflow<br> 3.99261e-05, 495352, + 0.968871, 25032.6, 0, 1, 0<br> underflow<br> 4.01492e-05, 3246.23, 0.905801, + 24898.5, 0, 1, 0<br> underflow<br> 4.0288e-05, 2569.28, 0.835025, 24812.9, + 0, 1, 0<br> underflow<br> 4.11667e-05, 24253.8, 0.308236, 24280.8, 0, 1, + 0<br> underflow<br> 4.17714e-05, 274447, 0.135563, 23926.7, 0, 1, 0<br> + underflow<br> 4.66877e-05, 3780.93, 0.632396, 21410.1, 0, 1, 0<br> underflow<br> + 4.73604e-05, 48598.7, 0.632396, 21103.3, 0, 1, 0<br> underflow<br> 0.00013245, + 251.768, 0.968871, 7543.9, 0, 1, 0<br> underflow<br> 0.000168283, 195801, + 0.905801, 5929.61, 0, 1, 0<br> underflow<br> 0.000177906, 276489, 0.814742, + 5607.86, 0, 1, 0<br> underflow<br> 0.000183097, 316055, 0.127074, 5448.36, + 0, 1, 0<br> underflow<br> 0.000190369, 159132, 0.835025, 5240.42, 0, 1, + 0<br> underflow<br> 0.000191066, 419861, 0.913384, 5220.29, 0, 1, 0<br> + underflow<br> 0.000192195, 177798, 0.308236, 5190.39, 0, 1, 0<br> underflow<br> + 0.000220499, 107380, 0.135563, 4523.03, 0, 1, 0<br> underflow<br> 0.00022254, + 1432.25, 0.814742, 4485.74, 0, 1, 0<br> underflow<br> 0.000240291, 49604.4, + 0.632396, 4150.25, 0, 1, 0<br> underflow<br> 0.000251444, 15605.8, 0.135563, + 3966.81, 0, 1, 0<br> underflow<br> 0.000274279, 289206, 0.968871, 3632.79, + 0, 1, 0<br> underflow<br> 0.000274343, 2954.47, 0.308236, 3636.51, 0, 1, + 0<br> underflow<br> 0.000278714, 4023.16, 0.632396, 3579.05, 0, 1, 0<br> + underflow<br> 0.000288369, 460073, 0.221112, 3454.19, 0, 1, 0<br> underflow<br> + 0.000294717, 4642.26, 0.221112, 3384.08, 0, 1, 0<br> underflow<br> 0.000303403, + 2574.36, 0.835025, 3287.52, 0, 1, 0<br> underflow<br> 0.000304309, 4480.75, + 0.905801, 3277.17, 0, 1, 0<br> underflow<br> 0.00031313, 47957, 0.308236, + 3182.22, 0, 1, 0<br> underflow<br> 0.000320063, 25544.6, 0.905801, 3113.68, + 0, 1, 0<br> underflow<br> 0.000334818, 29065.5, 0.968871, 2975.86, 0, 1, + 0<br> underflow<br> 0.00034899, 41187.6, 0.913384, 2854.23, 0, 1, 0<br> + underflow<br> 0.000350247, 426.308, 0.905801, 2848.5, 0, 1, 0<br> underflow<br> + 0.000357727, 31752.2, 0.127074, 2784.5, 0, 1, 0<br> underflow<br> 0.000412091, + 367.714, 0.913384, 2420.17, 0, 1, 0<br> underflow<br> 0.000417933, 4668.47, + 0.968871, 2383.72, 0, 1, 0<br> underflow<br> 0.000424632, 17994.9, 0.221112, + 2344.63, 0, 1, 0<br> underflow<br> 0.000427051, 2443.44, 0.913384, 2333.28, + 0, 1, 0<br> underflow<br> 0.000437724, 454399, 0.632396, 2270.98, 0, 1, + 0<br> underflow<br> 0.000450377, 10660.8, 0.835025, 2210.53, 0, 1, 0<br> + underflow<br> 0.000475601, 19603, 0.814742, 2092.17, 0, 1, 0<br> underflow<br> + 0.00116972, 4487.22, 0.221112, 845.964, 0, 1, 0<br> underflow<br> 0.00124188, + 211066, 0.632396, 792.493, 0, 1, 0<br> underflow<br> 0.00128578, 4738.41, + 0.308236, 768.75, 0, 1, 0<br> underflow<br> 0.00133388, 46277.8, 0.913384, + 738.46, 0, 1, 0<br> underflow<br> 0.00138692, 2158.76, 0.814742, 712.816, + 0, 1, 0<br> underflow<br> 0.00153268, 13060.2, 0.968871, 642.474, 0, 1, + 0<br> underflow<br> 0.00159946, 1780.43, 0.968871, 617.202, 0, 1, 0<br> + *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h95"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with_">Error + Output For jacobi_dn with compiler GNU C++ version 7.1.0 and library GSL 2.1 + and test data Jacobi Elliptic: Modulus near 1</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1"></a>|m| + > 1.0<br> -4.0246, 1, -0.999361, 0.0357365, 0.0357231<br> |m| > 1.0<br> + -4.0246, 1, -0.999361, 0.0357497, 0.0357097<br> |m| > 1.0<br> -4.0246, + 1, -0.99936, 0.0357762, 0.0356829<br> |m| > 1.0<br> -4.0246, 1, -0.999359, + 0.0357895, 0.0356695<br> |m| > 1.0<br> -4.0246, 1.00001, -0.999354, + 0.0359354, 0.0355222<br> |m| > 1.0<br> -4.0246, 1.00003, -0.999347, + 0.0361343, 0.0353212<br> |m| > 1.0<br> -4.0246, 1.00004, -0.999343, + 0.036247, 0.0352073<br> |m| > 1.0<br> -4.0246, 1.0001, -0.999311, 0.0371157, + 0.0343296<br> |m| > 1.0<br> -4.0246, 1.00016, -0.99928, 0.0379513, 0.0334851<br> + |m| > 1.0<br> -4.0246, 1.00027, -0.999221, 0.0394571, 0.0319634<br> + |m| > 1.0<br> -4.0246, 1.00076, -0.99893, 0.0462407, 0.0251046<br> |m| + > 1.0<br> -4.0246, 1.00125, -0.998589, 0.0531109, 0.0181532<br> |m| + > 1.0<br> -4.0246, 1.00232, -0.99768, 0.0680761, 0.0029944<br> |m| > + 1.0<br> -4.0246, 1.00604, -0.992752, 0.120179, -0.049966<br> |m| > 1.0<br> + -4.0246, 1.01557, -0.967356, 0.25342, -0.186698<br> |m| > 1.0<br> -4.0246, + 1.03059, -0.890373, 0.455232, -0.397492<br> |m| > 1.0<br> -4.0246, 1.06239, + -0.607191, 0.794556, -0.76412<br> |m| > 1.0<br> -3.73013, 1, -0.998849, + 0.0479567, 0.0479467<br> |m| > 1.0<br> -3.73013, 1, -0.998849, 0.0479665, + 0.0479367<br> |m| > 1.0<br> -3.73013, 1, -0.998848, 0.0479862, 0.0479167<br> + |m| > 1.0<br> -3.73013, 1, -0.998848, 0.047996, 0.0479067<br> |m| > + 1.0<br> -3.73013, 1.00001, -0.998842, 0.0481042, 0.0477966<br> |m| > + 1.0<br> -3.73013, 1.00003, -0.998835, 0.0482517, 0.0476465<br> |m| > + 1.0<br> -3.73013, 1.00004, -0.998831, 0.0483354, 0.0475615<br> |m| > + 1.0<br> -3.73013, 1.0001, -0.9988, 0.0489797, 0.0469059<br> |m| > 1.0<br> + -3.73013, 1.00016, -0.998769, 0.0495995, 0.0462752<br> |m| > 1.0<br> + -3.73013, 1.00027, -0.998713, 0.0507164, 0.0451386<br> |m| > 1.0<br> + -3.73013, 1.00076, -0.998445, 0.0557477, 0.0400164<br> |m| > 1.0<br> + -3.73013, 1.00125, -0.998147, 0.0608429, 0.0348257<br> |m| > 1.0<br> + -3.73013, 1.00232, -0.997409, 0.0719406, 0.0235071<br> |m| > 1.0<br> + -3.73013, 1.00604, -0.993866, 0.110593, -0.016048<br> |m| > 1.0<br> + -3.73013, 1.01557, -0.977708, 0.209971, -0.118704<br> |m| > 1.0<br> + -3.73013, 1.03059, -0.931162, 0.364606, -0.281224<br> |m| > 1.0<br> + -3.73013, 1.06239, -0.753495, 0.657453, -0.599326<br> |m| > 1.0<br> + -3.64523, 1, -0.998637, 0.0521997, 0.0521906<br> |m| > 1.0<br> -3.64523, + 1, -0.998636, 0.0522087, 0.0521814<br> |m| > 1.0<br> -3.64523, 1, -0.998635, + 0.0522268, 0.052163<br> |m| > 1.0<br> -3.64523, 1, -0.998635, 0.0522358, + 0.0521538<br> |m| > 1.0<br> -3.64523, 1.00001, -0.99863, 0.052335, 0.0520526<br> + |m| > 1.0<br> -3.64523, 1.00003, -0.998622, 0.0524703, 0.0519145<br> + |m| > 1.0<br> -3.64523, 1.00004, -0.998618, 0.052547, 0.0518363<br> + |m| > 1.0<br> -3.64523, 1.0001, -0.998587, 0.0531379, 0.0512335<br> + |m| > 1.0<br> -3.64523, 1.00016, -0.998557, 0.0537063, 0.0506536<br> + |m| > 1.0<br> -3.64523, 1.00027, -0.998501, 0.0547305, 0.0496084<br> + |m| > 1.0<br> -3.64523, 1.00076, -0.998238, 0.0593443, 0.0448986<br> + |m| > 1.0<br> -3.64523, 1.00125, -0.997949, 0.0640165, 0.0401258<br> + |m| > 1.0<br> -3.64523, 1.00232, -0.997244, 0.0741927, 0.0297191<br> + |m| > 1.0<br> -3.64523, 1.00604, -0.993972, 0.109636, -0.00664888<br> + |m| > 1.0<br> -3.64523, 1.01557, -0.979623, 0.200844, -0.101111<br> + |m| > 1.0<br> -3.64523, 1.03059, -0.939163, 0.343472, -0.251382<br> + |m| > 1.0<br> -3.64523, 1.06239, -0.784719, 0.619852, -0.552253<br> + |m| > 1.0<br> -3.11618, 1, -0.996078, 0.0884811, 0.0884757<br> |m| > + 1.0<br> -3.11618, 1, -0.996077, 0.0884863, 0.0884702<br> |m| > 1.0<br> + -3.11618, 1, -0.996076, 0.0884967, 0.0884593<br> |m| > 1.0<br> -3.11618, + 1, -0.996076, 0.0885019, 0.0884538<br> |m| > 1.0<br> -3.11618, 1.00001, + -0.996071, 0.0885593, 0.0883936<br> |m| > 1.0<br> -3.11618, 1.00003, + -0.996064, 0.0886376, 0.0883114<br> |m| > 1.0<br> -3.11618, 1.00004, + -0.99606, 0.0886819, 0.0882648<br> |m| > 1.0<br> -3.11618, 1.0001, -0.99603, + 0.0890236, 0.0879059<br> |m| > 1.0<br> -3.11618, 1.00016, -0.996, 0.0893523, + 0.0875607<br> |m| > 1.0<br> -3.11618, 1.00027, -0.995947, 0.0899445, + 0.0869386<br> |m| > 1.0<br> -3.11618, 1.00076, -0.995702, 0.092612, + 0.0841353<br> |m| > 1.0<br> -3.11618, 1.00125, -0.995447, 0.0953126, + 0.0812953<br> |m| > 1.0<br> -3.11618, 1.00232, -0.994867, 0.101193, + 0.0751049<br> |m| > 1.0<br> -3.11618, 1.00604, -0.992571, 0.121667, + 0.0534858<br> |m| > 1.0<br> -3.11618, 1.01557, -0.984666, 0.174451, + -0.00273723<br> |m| > 1.0<br> -3.11618, 1.03059, -0.966077, 0.258253, + -0.0934336<br> |m| > 1.0<br> -3.11618, 1.06239, -0.901067, 0.433681, + -0.289151<br> |m| > 1.0<br> -2.78966, 1, -0.992478, 0.122424, 0.12242<br> + |m| > 1.0<br> -2.78966, 1, -0.992477, 0.122428, 0.122416<br> *** FURTHER + CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h96"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with_">Error + Output For jacobi_cn with compiler GNU C++ version 7.1.0 and library GSL 2.1 + and test data Jacobi Elliptic: Modulus near 1</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1"></a>|m| + > 1.0<br> -4.0246, 1, -0.999361, 0.0357365, 0.0357231<br> |m| > 1.0<br> + -4.0246, 1, -0.999361, 0.0357497, 0.0357097<br> |m| > 1.0<br> -4.0246, + 1, -0.99936, 0.0357762, 0.0356829<br> |m| > 1.0<br> -4.0246, 1, -0.999359, + 0.0357895, 0.0356695<br> |m| > 1.0<br> -4.0246, 1.00001, -0.999354, + 0.0359354, 0.0355222<br> |m| > 1.0<br> -4.0246, 1.00003, -0.999347, + 0.0361343, 0.0353212<br> |m| > 1.0<br> -4.0246, 1.00004, -0.999343, + 0.036247, 0.0352073<br> |m| > 1.0<br> -4.0246, 1.0001, -0.999311, 0.0371157, + 0.0343296<br> |m| > 1.0<br> -4.0246, 1.00016, -0.99928, 0.0379513, 0.0334851<br> + |m| > 1.0<br> -4.0246, 1.00027, -0.999221, 0.0394571, 0.0319634<br> + |m| > 1.0<br> -4.0246, 1.00076, -0.99893, 0.0462407, 0.0251046<br> |m| + > 1.0<br> -4.0246, 1.00125, -0.998589, 0.0531109, 0.0181532<br> |m| + > 1.0<br> -4.0246, 1.00232, -0.99768, 0.0680761, 0.0029944<br> |m| > + 1.0<br> -4.0246, 1.00604, -0.992752, 0.120179, -0.049966<br> |m| > 1.0<br> + -4.0246, 1.01557, -0.967356, 0.25342, -0.186698<br> |m| > 1.0<br> -4.0246, + 1.03059, -0.890373, 0.455232, -0.397492<br> |m| > 1.0<br> -4.0246, 1.06239, + -0.607191, 0.794556, -0.76412<br> |m| > 1.0<br> -3.73013, 1, -0.998849, + 0.0479567, 0.0479467<br> |m| > 1.0<br> -3.73013, 1, -0.998849, 0.0479665, + 0.0479367<br> |m| > 1.0<br> -3.73013, 1, -0.998848, 0.0479862, 0.0479167<br> + |m| > 1.0<br> -3.73013, 1, -0.998848, 0.047996, 0.0479067<br> |m| > + 1.0<br> -3.73013, 1.00001, -0.998842, 0.0481042, 0.0477966<br> |m| > + 1.0<br> -3.73013, 1.00003, -0.998835, 0.0482517, 0.0476465<br> |m| > + 1.0<br> -3.73013, 1.00004, -0.998831, 0.0483354, 0.0475615<br> |m| > + 1.0<br> -3.73013, 1.0001, -0.9988, 0.0489797, 0.0469059<br> |m| > 1.0<br> + -3.73013, 1.00016, -0.998769, 0.0495995, 0.0462752<br> |m| > 1.0<br> + -3.73013, 1.00027, -0.998713, 0.0507164, 0.0451386<br> |m| > 1.0<br> + -3.73013, 1.00076, -0.998445, 0.0557477, 0.0400164<br> |m| > 1.0<br> + -3.73013, 1.00125, -0.998147, 0.0608429, 0.0348257<br> |m| > 1.0<br> + -3.73013, 1.00232, -0.997409, 0.0719406, 0.0235071<br> |m| > 1.0<br> + -3.73013, 1.00604, -0.993866, 0.110593, -0.016048<br> |m| > 1.0<br> + -3.73013, 1.01557, -0.977708, 0.209971, -0.118704<br> |m| > 1.0<br> + -3.73013, 1.03059, -0.931162, 0.364606, -0.281224<br> |m| > 1.0<br> + -3.73013, 1.06239, -0.753495, 0.657453, -0.599326<br> |m| > 1.0<br> + -3.64523, 1, -0.998637, 0.0521997, 0.0521906<br> |m| > 1.0<br> -3.64523, + 1, -0.998636, 0.0522087, 0.0521814<br> |m| > 1.0<br> -3.64523, 1, -0.998635, + 0.0522268, 0.052163<br> |m| > 1.0<br> -3.64523, 1, -0.998635, 0.0522358, + 0.0521538<br> |m| > 1.0<br> -3.64523, 1.00001, -0.99863, 0.052335, 0.0520526<br> + |m| > 1.0<br> -3.64523, 1.00003, -0.998622, 0.0524703, 0.0519145<br> + |m| > 1.0<br> -3.64523, 1.00004, -0.998618, 0.052547, 0.0518363<br> + |m| > 1.0<br> -3.64523, 1.0001, -0.998587, 0.0531379, 0.0512335<br> + |m| > 1.0<br> -3.64523, 1.00016, -0.998557, 0.0537063, 0.0506536<br> + |m| > 1.0<br> -3.64523, 1.00027, -0.998501, 0.0547305, 0.0496084<br> + |m| > 1.0<br> -3.64523, 1.00076, -0.998238, 0.0593443, 0.0448986<br> + |m| > 1.0<br> -3.64523, 1.00125, -0.997949, 0.0640165, 0.0401258<br> + |m| > 1.0<br> -3.64523, 1.00232, -0.997244, 0.0741927, 0.0297191<br> + |m| > 1.0<br> -3.64523, 1.00604, -0.993972, 0.109636, -0.00664888<br> + |m| > 1.0<br> -3.64523, 1.01557, -0.979623, 0.200844, -0.101111<br> + |m| > 1.0<br> -3.64523, 1.03059, -0.939163, 0.343472, -0.251382<br> + |m| > 1.0<br> -3.64523, 1.06239, -0.784719, 0.619852, -0.552253<br> + |m| > 1.0<br> -3.11618, 1, -0.996078, 0.0884811, 0.0884757<br> |m| > + 1.0<br> -3.11618, 1, -0.996077, 0.0884863, 0.0884702<br> |m| > 1.0<br> + -3.11618, 1, -0.996076, 0.0884967, 0.0884593<br> |m| > 1.0<br> -3.11618, + 1, -0.996076, 0.0885019, 0.0884538<br> |m| > 1.0<br> -3.11618, 1.00001, + -0.996071, 0.0885593, 0.0883936<br> |m| > 1.0<br> -3.11618, 1.00003, + -0.996064, 0.0886376, 0.0883114<br> |m| > 1.0<br> -3.11618, 1.00004, + -0.99606, 0.0886819, 0.0882648<br> |m| > 1.0<br> -3.11618, 1.0001, -0.99603, + 0.0890236, 0.0879059<br> |m| > 1.0<br> -3.11618, 1.00016, -0.996, 0.0893523, + 0.0875607<br> |m| > 1.0<br> -3.11618, 1.00027, -0.995947, 0.0899445, + 0.0869386<br> |m| > 1.0<br> -3.11618, 1.00076, -0.995702, 0.092612, + 0.0841353<br> |m| > 1.0<br> -3.11618, 1.00125, -0.995447, 0.0953126, + 0.0812953<br> |m| > 1.0<br> -3.11618, 1.00232, -0.994867, 0.101193, + 0.0751049<br> |m| > 1.0<br> -3.11618, 1.00604, -0.992571, 0.121667, + 0.0534858<br> |m| > 1.0<br> -3.11618, 1.01557, -0.984666, 0.174451, + -0.00273723<br> |m| > 1.0<br> -3.11618, 1.03059, -0.966077, 0.258253, + -0.0934336<br> |m| > 1.0<br> -3.11618, 1.06239, -0.901067, 0.433681, + -0.289151<br> |m| > 1.0<br> -2.78966, 1, -0.992478, 0.122424, 0.12242<br> + |m| > 1.0<br> -2.78966, 1, -0.992477, 0.122428, 0.122416<br> *** FURTHER + CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h97"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with_">Error + Output For jacobi_sn with compiler GNU C++ version 7.1.0 and library GSL 2.1 + and test data Jacobi Elliptic: Modulus near 1</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1"></a>|m| + > 1.0<br> -4.0246, 1, -0.999361, 0.0357365, 0.0357231<br> |m| > 1.0<br> + -4.0246, 1, -0.999361, 0.0357497, 0.0357097<br> |m| > 1.0<br> -4.0246, + 1, -0.99936, 0.0357762, 0.0356829<br> |m| > 1.0<br> -4.0246, 1, -0.999359, + 0.0357895, 0.0356695<br> |m| > 1.0<br> -4.0246, 1.00001, -0.999354, + 0.0359354, 0.0355222<br> |m| > 1.0<br> -4.0246, 1.00003, -0.999347, + 0.0361343, 0.0353212<br> |m| > 1.0<br> -4.0246, 1.00004, -0.999343, + 0.036247, 0.0352073<br> |m| > 1.0<br> -4.0246, 1.0001, -0.999311, 0.0371157, + 0.0343296<br> |m| > 1.0<br> -4.0246, 1.00016, -0.99928, 0.0379513, 0.0334851<br> + |m| > 1.0<br> -4.0246, 1.00027, -0.999221, 0.0394571, 0.0319634<br> + |m| > 1.0<br> -4.0246, 1.00076, -0.99893, 0.0462407, 0.0251046<br> |m| + > 1.0<br> -4.0246, 1.00125, -0.998589, 0.0531109, 0.0181532<br> |m| + > 1.0<br> -4.0246, 1.00232, -0.99768, 0.0680761, 0.0029944<br> |m| > + 1.0<br> -4.0246, 1.00604, -0.992752, 0.120179, -0.049966<br> |m| > 1.0<br> + -4.0246, 1.01557, -0.967356, 0.25342, -0.186698<br> |m| > 1.0<br> -4.0246, + 1.03059, -0.890373, 0.455232, -0.397492<br> |m| > 1.0<br> -4.0246, 1.06239, + -0.607191, 0.794556, -0.76412<br> |m| > 1.0<br> -3.73013, 1, -0.998849, + 0.0479567, 0.0479467<br> |m| > 1.0<br> -3.73013, 1, -0.998849, 0.0479665, + 0.0479367<br> |m| > 1.0<br> -3.73013, 1, -0.998848, 0.0479862, 0.0479167<br> + |m| > 1.0<br> -3.73013, 1, -0.998848, 0.047996, 0.0479067<br> |m| > + 1.0<br> -3.73013, 1.00001, -0.998842, 0.0481042, 0.0477966<br> |m| > + 1.0<br> -3.73013, 1.00003, -0.998835, 0.0482517, 0.0476465<br> |m| > + 1.0<br> -3.73013, 1.00004, -0.998831, 0.0483354, 0.0475615<br> |m| > + 1.0<br> -3.73013, 1.0001, -0.9988, 0.0489797, 0.0469059<br> |m| > 1.0<br> + -3.73013, 1.00016, -0.998769, 0.0495995, 0.0462752<br> |m| > 1.0<br> + -3.73013, 1.00027, -0.998713, 0.0507164, 0.0451386<br> |m| > 1.0<br> + -3.73013, 1.00076, -0.998445, 0.0557477, 0.0400164<br> |m| > 1.0<br> + -3.73013, 1.00125, -0.998147, 0.0608429, 0.0348257<br> |m| > 1.0<br> + -3.73013, 1.00232, -0.997409, 0.0719406, 0.0235071<br> |m| > 1.0<br> + -3.73013, 1.00604, -0.993866, 0.110593, -0.016048<br> |m| > 1.0<br> + -3.73013, 1.01557, -0.977708, 0.209971, -0.118704<br> |m| > 1.0<br> + -3.73013, 1.03059, -0.931162, 0.364606, -0.281224<br> |m| > 1.0<br> + -3.73013, 1.06239, -0.753495, 0.657453, -0.599326<br> |m| > 1.0<br> + -3.64523, 1, -0.998637, 0.0521997, 0.0521906<br> |m| > 1.0<br> -3.64523, + 1, -0.998636, 0.0522087, 0.0521814<br> |m| > 1.0<br> -3.64523, 1, -0.998635, + 0.0522268, 0.052163<br> |m| > 1.0<br> -3.64523, 1, -0.998635, 0.0522358, + 0.0521538<br> |m| > 1.0<br> -3.64523, 1.00001, -0.99863, 0.052335, 0.0520526<br> + |m| > 1.0<br> -3.64523, 1.00003, -0.998622, 0.0524703, 0.0519145<br> + |m| > 1.0<br> -3.64523, 1.00004, -0.998618, 0.052547, 0.0518363<br> + |m| > 1.0<br> -3.64523, 1.0001, -0.998587, 0.0531379, 0.0512335<br> + |m| > 1.0<br> -3.64523, 1.00016, -0.998557, 0.0537063, 0.0506536<br> + |m| > 1.0<br> -3.64523, 1.00027, -0.998501, 0.0547305, 0.0496084<br> + |m| > 1.0<br> -3.64523, 1.00076, -0.998238, 0.0593443, 0.0448986<br> + |m| > 1.0<br> -3.64523, 1.00125, -0.997949, 0.0640165, 0.0401258<br> + |m| > 1.0<br> -3.64523, 1.00232, -0.997244, 0.0741927, 0.0297191<br> + |m| > 1.0<br> -3.64523, 1.00604, -0.993972, 0.109636, -0.00664888<br> + |m| > 1.0<br> -3.64523, 1.01557, -0.979623, 0.200844, -0.101111<br> + |m| > 1.0<br> -3.64523, 1.03059, -0.939163, 0.343472, -0.251382<br> + |m| > 1.0<br> -3.64523, 1.06239, -0.784719, 0.619852, -0.552253<br> + |m| > 1.0<br> -3.11618, 1, -0.996078, 0.0884811, 0.0884757<br> |m| > + 1.0<br> -3.11618, 1, -0.996077, 0.0884863, 0.0884702<br> |m| > 1.0<br> + -3.11618, 1, -0.996076, 0.0884967, 0.0884593<br> |m| > 1.0<br> -3.11618, + 1, -0.996076, 0.0885019, 0.0884538<br> |m| > 1.0<br> -3.11618, 1.00001, + -0.996071, 0.0885593, 0.0883936<br> |m| > 1.0<br> -3.11618, 1.00003, + -0.996064, 0.0886376, 0.0883114<br> |m| > 1.0<br> -3.11618, 1.00004, + -0.99606, 0.0886819, 0.0882648<br> |m| > 1.0<br> -3.11618, 1.0001, -0.99603, + 0.0890236, 0.0879059<br> |m| > 1.0<br> -3.11618, 1.00016, -0.996, 0.0893523, + 0.0875607<br> |m| > 1.0<br> -3.11618, 1.00027, -0.995947, 0.0899445, + 0.0869386<br> |m| > 1.0<br> -3.11618, 1.00076, -0.995702, 0.092612, + 0.0841353<br> |m| > 1.0<br> -3.11618, 1.00125, -0.995447, 0.0953126, + 0.0812953<br> |m| > 1.0<br> -3.11618, 1.00232, -0.994867, 0.101193, + 0.0751049<br> |m| > 1.0<br> -3.11618, 1.00604, -0.992571, 0.121667, + 0.0534858<br> |m| > 1.0<br> -3.11618, 1.01557, -0.984666, 0.174451, + -0.00273723<br> |m| > 1.0<br> -3.11618, 1.03059, -0.966077, 0.258253, + -0.0934336<br> |m| > 1.0<br> -3.11618, 1.06239, -0.901067, 0.433681, + -0.289151<br> |m| > 1.0<br> -2.78966, 1, -0.992478, 0.122424, 0.12242<br> + |m| > 1.0<br> -2.78966, 1, -0.992477, 0.122428, 0.122416<br> *** FURTHER + CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h98"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with0">Error + Output For jacobi_dn with compiler GNU C++ version 7.1.0 and library GSL 2.1 + and test data Jacobi Elliptic: Random Small Values</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values"></a>|m| + > 1.0<br> 1.65048e-12, 1.65574, 1.65048e-12, 1, 1<br> |m| > 1.0<br> + 2.06542e-12, 1.65574, 2.06542e-12, 1, 1<br> |m| > 1.0<br> 6.93323e-12, + 1.65574, 6.93323e-12, 1, 1<br> |m| > 1.0<br> 1.33514e-11, 1.65574, 1.33514e-11, + 1, 1<br> |m| > 1.0<br> 1.63998e-11, 1.65574, 1.63998e-11, 1, 1<br> + |m| > 1.0<br> 5.73016e-11, 1.65574, 5.73016e-11, 1, 1<br> |m| > 1.0<br> + 1.11373e-10, 1.65574, 1.11373e-10, 1, 1<br> |m| > 1.0<br> 1.42147e-10, + 1.65574, 1.42147e-10, 1, 1<br> |m| > 1.0<br> 3.80063e-10, 1.65574, 3.80063e-10, + 1, 1<br> |m| > 1.0<br> 6.09163e-10, 1.65574, 6.09163e-10, 1, 1<br> + |m| > 1.0<br> 1.02216e-09, 1.65574, 1.02216e-09, 1, 1<br> |m| > 1.0<br> + 2.88192e-09, 1.65574, 2.88192e-09, 1, 1<br> |m| > 1.0<br> 4.76278e-09, + 1.65574, 4.76278e-09, 1, 1<br> |m| > 1.0<br> 8.85413e-09, 1.65574, 8.85413e-09, + 1, 1<br> |m| > 1.0<br> 2.30503e-08, 1.65574, 2.30503e-08, 1, 1<br> + |m| > 1.0<br> 5.93925e-08, 1.65574, 5.93925e-08, 1, 1<br> |m| > 1.0<br> + 1.16676e-07, 1.65574, 1.16676e-07, 1, 1<br> |m| > 1.0<br> 2.37997e-07, + 1.65574, 2.37997e-07, 1, 1<br> |m| > 1.0<br> 4.68466e-07, 1.65574, 4.68466e-07, + 1, 1<br> |m| > 1.0<br> 9.3827e-07, 1.65574, 9.3827e-07, 1, 1<br> |m| + > 1.0<br> 1.10399e-06, 1.65574, 1.10399e-06, 1, 1<br> |m| > 1.0<br> + 3.29178e-06, 1.65574, 3.29178e-06, 1, 1<br> |m| > 1.0<br> 7.51721e-06, + 1.65574, 7.51721e-06, 1, 1<br> |m| > 1.0<br> 1.51147e-05, 1.65574, 1.51147e-05, + 1, 1<br> |m| > 1.0<br> 2.9864e-05, 1.65574, 2.9864e-05, 1, 1<br> |m| + > 1.0<br> 3.38703e-05, 1.65574, 3.38703e-05, 1, 1<br> |m| > 1.0<br> + 9.06601e-05, 1.65574, 9.06601e-05, 1, 1<br> |m| > 1.0<br> 0.000219495, + 1.65574, 0.000219495, 1, 1<br> |m| > 1.0<br> 0.000439522, 1.65574, 0.000439521, + 1, 1<br> |m| > 1.0<br> 0.000633315, 1.65574, 0.000633315, 1, 0.999999<br> + |m| > 1.0<br> 0.00111512, 1.65574, 0.00111512, 0.999999, 0.999998<br> + |m| > 1.0<br> 0.00196247, 1.65574, 0.00196246, 0.999998, 0.999995<br> + |m| > 1.0<br> 0.00555375, 1.65574, 0.00555365, 0.999985, 0.999958<br> + |m| > 1.0<br> 0.00869113, 1.65574, 0.00869072, 0.999962, 0.999896<br> + |m| > 1.0<br> 0.0299334, 1.65574, 0.0299166, 0.999552, 0.998772<br> + |m| > 1.0<br> 0.0512426, 1.65574, 0.0511588, 0.998691, 0.996406<br> + |m| > 1.0<br> 0.112013, 1.65574, 0.111143, 0.993804, 0.982922<br> |m| + > 1.0<br> 0.234804, 1.65574, 0.227, 0.973895, 0.926679<br> |m| > + 1.0<br> 0.489873, 1.65574, 0.425971, 0.904737, 0.708912<br> |m| > 1.0<br> + 0.751831, 1.65574, 0.553446, 0.832885, 0.400346<br> |m| > 1.0<br> 1.65574, + 1.65574, 0.408154, 0.912913, -0.737088<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h99"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with0">Error + Output For jacobi_cn with compiler GNU C++ version 7.1.0 and library GSL 2.1 + and test data Jacobi Elliptic: Random Small Values</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values"></a>|m| + > 1.0<br> 1.65048e-12, 1.65574, 1.65048e-12, 1, 1<br> |m| > 1.0<br> + 2.06542e-12, 1.65574, 2.06542e-12, 1, 1<br> |m| > 1.0<br> 6.93323e-12, + 1.65574, 6.93323e-12, 1, 1<br> |m| > 1.0<br> 1.33514e-11, 1.65574, 1.33514e-11, + 1, 1<br> |m| > 1.0<br> 1.63998e-11, 1.65574, 1.63998e-11, 1, 1<br> + |m| > 1.0<br> 5.73016e-11, 1.65574, 5.73016e-11, 1, 1<br> |m| > 1.0<br> + 1.11373e-10, 1.65574, 1.11373e-10, 1, 1<br> |m| > 1.0<br> 1.42147e-10, + 1.65574, 1.42147e-10, 1, 1<br> |m| > 1.0<br> 3.80063e-10, 1.65574, 3.80063e-10, + 1, 1<br> |m| > 1.0<br> 6.09163e-10, 1.65574, 6.09163e-10, 1, 1<br> + |m| > 1.0<br> 1.02216e-09, 1.65574, 1.02216e-09, 1, 1<br> |m| > 1.0<br> + 2.88192e-09, 1.65574, 2.88192e-09, 1, 1<br> |m| > 1.0<br> 4.76278e-09, + 1.65574, 4.76278e-09, 1, 1<br> |m| > 1.0<br> 8.85413e-09, 1.65574, 8.85413e-09, + 1, 1<br> |m| > 1.0<br> 2.30503e-08, 1.65574, 2.30503e-08, 1, 1<br> + |m| > 1.0<br> 5.93925e-08, 1.65574, 5.93925e-08, 1, 1<br> |m| > 1.0<br> + 1.16676e-07, 1.65574, 1.16676e-07, 1, 1<br> |m| > 1.0<br> 2.37997e-07, + 1.65574, 2.37997e-07, 1, 1<br> |m| > 1.0<br> 4.68466e-07, 1.65574, 4.68466e-07, + 1, 1<br> |m| > 1.0<br> 9.3827e-07, 1.65574, 9.3827e-07, 1, 1<br> |m| + > 1.0<br> 1.10399e-06, 1.65574, 1.10399e-06, 1, 1<br> |m| > 1.0<br> + 3.29178e-06, 1.65574, 3.29178e-06, 1, 1<br> |m| > 1.0<br> 7.51721e-06, + 1.65574, 7.51721e-06, 1, 1<br> |m| > 1.0<br> 1.51147e-05, 1.65574, 1.51147e-05, + 1, 1<br> |m| > 1.0<br> 2.9864e-05, 1.65574, 2.9864e-05, 1, 1<br> |m| + > 1.0<br> 3.38703e-05, 1.65574, 3.38703e-05, 1, 1<br> |m| > 1.0<br> + 9.06601e-05, 1.65574, 9.06601e-05, 1, 1<br> |m| > 1.0<br> 0.000219495, + 1.65574, 0.000219495, 1, 1<br> |m| > 1.0<br> 0.000439522, 1.65574, 0.000439521, + 1, 1<br> |m| > 1.0<br> 0.000633315, 1.65574, 0.000633315, 1, 0.999999<br> + |m| > 1.0<br> 0.00111512, 1.65574, 0.00111512, 0.999999, 0.999998<br> + |m| > 1.0<br> 0.00196247, 1.65574, 0.00196246, 0.999998, 0.999995<br> + |m| > 1.0<br> 0.00555375, 1.65574, 0.00555365, 0.999985, 0.999958<br> + |m| > 1.0<br> 0.00869113, 1.65574, 0.00869072, 0.999962, 0.999896<br> + |m| > 1.0<br> 0.0299334, 1.65574, 0.0299166, 0.999552, 0.998772<br> + |m| > 1.0<br> 0.0512426, 1.65574, 0.0511588, 0.998691, 0.996406<br> + |m| > 1.0<br> 0.112013, 1.65574, 0.111143, 0.993804, 0.982922<br> |m| + > 1.0<br> 0.234804, 1.65574, 0.227, 0.973895, 0.926679<br> |m| > + 1.0<br> 0.489873, 1.65574, 0.425971, 0.904737, 0.708912<br> |m| > 1.0<br> + 0.751831, 1.65574, 0.553446, 0.832885, 0.400346<br> |m| > 1.0<br> 1.65574, + 1.65574, 0.408154, 0.912913, -0.737088<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h100"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with0">Error + Output For jacobi_sn with compiler GNU C++ version 7.1.0 and library GSL 2.1 + and test data Jacobi Elliptic: Random Small Values</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values"></a>|m| + > 1.0<br> 1.65048e-12, 1.65574, 1.65048e-12, 1, 1<br> |m| > 1.0<br> + 2.06542e-12, 1.65574, 2.06542e-12, 1, 1<br> |m| > 1.0<br> 6.93323e-12, + 1.65574, 6.93323e-12, 1, 1<br> |m| > 1.0<br> 1.33514e-11, 1.65574, 1.33514e-11, + 1, 1<br> |m| > 1.0<br> 1.63998e-11, 1.65574, 1.63998e-11, 1, 1<br> + |m| > 1.0<br> 5.73016e-11, 1.65574, 5.73016e-11, 1, 1<br> |m| > 1.0<br> + 1.11373e-10, 1.65574, 1.11373e-10, 1, 1<br> |m| > 1.0<br> 1.42147e-10, + 1.65574, 1.42147e-10, 1, 1<br> |m| > 1.0<br> 3.80063e-10, 1.65574, 3.80063e-10, + 1, 1<br> |m| > 1.0<br> 6.09163e-10, 1.65574, 6.09163e-10, 1, 1<br> + |m| > 1.0<br> 1.02216e-09, 1.65574, 1.02216e-09, 1, 1<br> |m| > 1.0<br> + 2.88192e-09, 1.65574, 2.88192e-09, 1, 1<br> |m| > 1.0<br> 4.76278e-09, + 1.65574, 4.76278e-09, 1, 1<br> |m| > 1.0<br> 8.85413e-09, 1.65574, 8.85413e-09, + 1, 1<br> |m| > 1.0<br> 2.30503e-08, 1.65574, 2.30503e-08, 1, 1<br> + |m| > 1.0<br> 5.93925e-08, 1.65574, 5.93925e-08, 1, 1<br> |m| > 1.0<br> + 1.16676e-07, 1.65574, 1.16676e-07, 1, 1<br> |m| > 1.0<br> 2.37997e-07, + 1.65574, 2.37997e-07, 1, 1<br> |m| > 1.0<br> 4.68466e-07, 1.65574, 4.68466e-07, + 1, 1<br> |m| > 1.0<br> 9.3827e-07, 1.65574, 9.3827e-07, 1, 1<br> |m| + > 1.0<br> 1.10399e-06, 1.65574, 1.10399e-06, 1, 1<br> |m| > 1.0<br> + 3.29178e-06, 1.65574, 3.29178e-06, 1, 1<br> |m| > 1.0<br> 7.51721e-06, + 1.65574, 7.51721e-06, 1, 1<br> |m| > 1.0<br> 1.51147e-05, 1.65574, 1.51147e-05, + 1, 1<br> |m| > 1.0<br> 2.9864e-05, 1.65574, 2.9864e-05, 1, 1<br> |m| + > 1.0<br> 3.38703e-05, 1.65574, 3.38703e-05, 1, 1<br> |m| > 1.0<br> + 9.06601e-05, 1.65574, 9.06601e-05, 1, 1<br> |m| > 1.0<br> 0.000219495, + 1.65574, 0.000219495, 1, 1<br> |m| > 1.0<br> 0.000439522, 1.65574, 0.000439521, + 1, 1<br> |m| > 1.0<br> 0.000633315, 1.65574, 0.000633315, 1, 0.999999<br> + |m| > 1.0<br> 0.00111512, 1.65574, 0.00111512, 0.999999, 0.999998<br> + |m| > 1.0<br> 0.00196247, 1.65574, 0.00196246, 0.999998, 0.999995<br> + |m| > 1.0<br> 0.00555375, 1.65574, 0.00555365, 0.999985, 0.999958<br> + |m| > 1.0<br> 0.00869113, 1.65574, 0.00869072, 0.999962, 0.999896<br> + |m| > 1.0<br> 0.0299334, 1.65574, 0.0299166, 0.999552, 0.998772<br> + |m| > 1.0<br> 0.0512426, 1.65574, 0.0511588, 0.998691, 0.996406<br> + |m| > 1.0<br> 0.112013, 1.65574, 0.111143, 0.993804, 0.982922<br> |m| + > 1.0<br> 0.234804, 1.65574, 0.227, 0.973895, 0.926679<br> |m| > + 1.0<br> 0.489873, 1.65574, 0.425971, 0.904737, 0.708912<br> |m| > 1.0<br> + 0.751831, 1.65574, 0.553446, 0.832885, 0.400346<br> |m| > 1.0<br> 1.65574, + 1.65574, 0.408154, 0.912913, -0.737088<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h101"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with1">Error + Output For jacobi_dn with compiler GNU C++ version 7.1.0 and library GSL 2.1 + and test data Jacobi Elliptic: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data"></a>|m| + > 1.0<br> 2.98023e-08, 1.5, 2.98023e-08, 1, 1<br> |m| > 1.0<br> + -2.98023e-08, 1.5, -2.98023e-08, 1, 1<br> |m| > 1.0<br> 0.25, 1.5, 0.24183, + 0.970319, 0.931888<br> |m| > 1.0<br> -0.25, 1.5, -0.24183, 0.970319, + 0.931888<br> |m| > 1.0<br> 1.25, 1.5, 0.665876, 0.746063, -0.0486921<br> + |m| > 1.0<br> -1.25, 1.5, -0.665876, 0.746063, -0.0486921<br> |m| > + 1.0<br> 25, 1.5, 0.618665, 0.785655, 0.372585<br> |m| > 1.0<br> -25, + 1.5, -0.618665, 0.785655, 0.372585<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h102"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with1">Error + Output For jacobi_cn with compiler GNU C++ version 7.1.0 and library GSL 2.1 + and test data Jacobi Elliptic: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data"></a>|m| + > 1.0<br> 2.98023e-08, 1.5, 2.98023e-08, 1, 1<br> |m| > 1.0<br> + -2.98023e-08, 1.5, -2.98023e-08, 1, 1<br> |m| > 1.0<br> 0.25, 1.5, 0.24183, + 0.970319, 0.931888<br> |m| > 1.0<br> -0.25, 1.5, -0.24183, 0.970319, + 0.931888<br> |m| > 1.0<br> 1.25, 1.5, 0.665876, 0.746063, -0.0486921<br> + |m| > 1.0<br> -1.25, 1.5, -0.665876, 0.746063, -0.0486921<br> |m| > + 1.0<br> 25, 1.5, 0.618665, 0.785655, 0.372585<br> |m| > 1.0<br> -25, + 1.5, -0.618665, 0.785655, 0.372585<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h103"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with1">Error + Output For jacobi_sn with compiler GNU C++ version 7.1.0 and library GSL 2.1 + and test data Jacobi Elliptic: Mathworld Data</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data"></a>|m| + > 1.0<br> 2.98023e-08, 1.5, 2.98023e-08, 1, 1<br> |m| > 1.0<br> + -2.98023e-08, 1.5, -2.98023e-08, 1, 1<br> |m| > 1.0<br> 0.25, 1.5, 0.24183, + 0.970319, 0.931888<br> |m| > 1.0<br> -0.25, 1.5, -0.24183, 0.970319, + 0.931888<br> |m| > 1.0<br> 1.25, 1.5, 0.665876, 0.746063, -0.0486921<br> + |m| > 1.0<br> -1.25, 1.5, -0.665876, 0.746063, -0.0486921<br> |m| > + 1.0<br> 25, 1.5, 0.618665, 0.785655, 0.372585<br> |m| > 1.0<br> -25, + 1.5, -0.618665, 0.785655, 0.372585<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h104"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with3">Error + Output For polygamma with compiler GNU C++ version 7.1.0 and library GSL 2.1 + and test data Mathematica Data - Large orders and other bug cases</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_Large_orders_and_other_bug_cases"></a>underflow<br> + 168, 150, -6.52661e-66<br> underflow<br> 169, 202, 9.2734e-88<br> domain + error<br> 20, -9.5, -0.00103076<br> domain error<br> 21, -9.5, 4.28582e+26<br> + domain error<br> 22, -9.5, -0.00419144<br> domain error<br> 23, -9.5, + 8.6745e+29<br> domain error<br> 24, -9.5, -0.0204825<br> domain error<br> + 25, -9.5, 2.08188e+33<br> domain error<br> 26, -9.5, -0.118403<br> domain + error<br> 27, -9.5, 5.84592e+36<br> domain error<br> 28, -9.5, -0.798969<br> + domain error<br> 29, -9.5, 1.89875e+40<br> domain error<br> 30, -9.5, + -6.22245<br> underflow<br> 10, 1.32923e+36, -0<br> underflow<br> 15, + 1.32923e+36, 0<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h105"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with4">Error + Output For polygamma with compiler GNU C++ version 7.1.0 and library GSL 2.1 + and test data Mathematica Data - large negative arguments</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_negative_arguments"></a>domain + error<br> 124, -1.5, 7.63705e+240<br> domain error<br> 124, -2.5, 7.63705e+240<br> + domain error<br> 124, -3.5, 7.63705e+240<br> domain error<br> 124, -4.5, + 7.63705e+240<br> domain error<br> 124, -5.5, 7.63705e+240<br> domain + error<br> 124, -6.5, 7.63705e+240<br> domain error<br> 124, -7.5, 7.63705e+240<br> + domain error<br> 124, -8.5, 7.63705e+240<br> domain error<br> 124, -9.5, + 7.63705e+240<br> domain error<br> 124, -10.5, 7.63705e+240<br> domain + error<br> 124, -11.5, 7.63705e+240<br> domain error<br> 124, -12.5, 7.63705e+240<br> + domain error<br> 124, -13.5, 7.63705e+240<br> domain error<br> 124, -14.5, + 7.63705e+240<br> domain error<br> 124, -15.5, 7.63705e+240<br> domain + error<br> 124, -16.5, 7.63705e+240<br> domain error<br> 124, -17.5, 7.63705e+240<br> + domain error<br> 124, -18.5, 7.63705e+240<br> domain error<br> 124, -19.5, + 7.63705e+240<br> domain error<br> 124, -20.5, 7.63705e+240<br> domain + error<br> 124, -1.5, -7.63705e+240<br> domain error<br> 124, -2.5, -7.63705e+240<br> + domain error<br> 124, -3.5, -7.63705e+240<br> domain error<br> 124, -4.5, + -7.63705e+240<br> domain error<br> 124, -5.5, -7.63705e+240<br> domain + error<br> 124, -6.5, -7.63705e+240<br> domain error<br> 124, -7.5, -7.63705e+240<br> + domain error<br> 124, -8.5, -7.63705e+240<br> domain error<br> 124, -9.5, + -7.63705e+240<br> domain error<br> 124, -10.5, -7.63705e+240<br> domain + error<br> 124, -11.5, -7.63705e+240<br> domain error<br> 124, -12.5, + -7.63705e+240<br> domain error<br> 124, -13.5, -7.63705e+240<br> domain + error<br> 124, -14.5, -7.63705e+240<br> domain error<br> 124, -15.5, + -7.63705e+240<br> domain error<br> 124, -16.5, -7.63705e+240<br> domain + error<br> 124, -17.5, -7.63705e+240<br> domain error<br> 124, -18.5, + -7.63705e+240<br> domain error<br> 124, -19.5, -7.63705e+240<br> domain + error<br> 124, -20.5, -7.63705e+240<br> domain error<br> 2, -0.5, -0.828797<br> + domain error<br> 3, -0.5, 193.409<br> domain error<br> 4, -0.5, -3.47425<br> + domain error<br> 5, -0.5, 15371.1<br> domain error<br> 6, -0.5, -43.4579<br> + domain error<br> 7, -0.5, 2.58068e+06<br> domain error<br> 8, -0.5, -1059.96<br> + domain error<br> 9, -0.5, 7.43185e+08<br> domain error<br> 10, -0.5, + -42108.9<br> domain error<br> 11, -0.5, 3.26999e+11<br> domain error<br> + 12, -0.5, -2.46448e+06<br> domain error<br> 13, -0.5, 2.04047e+14<br> + domain error<br> 14, -0.5, -1.9918e+08<br> domain error<br> 15, -0.5, + 1.71399e+17<br> domain error<br> 16, -0.5, -2.12394e+10<br> domain error<br> + 17, -0.5, 1.86483e+20<br> domain error<br> 18, -0.5, -2.88824e+12<br> + domain error<br> 19, -0.5, 2.55108e+23<br> domain error<br> 20, -0.5, + -4.87773e+14<br> domain error<br> 21, -0.5, 4.28582e+26<br> domain error<br> + 2, -0.5, -0.828843<br> domain error<br> 3, -0.5, 193.409<br> domain error<br> + 4, -0.5, -3.47791<br> domain error<br> 5, -0.5, 15371.1<br> domain error<br> + 6, -0.5, -44.0732<br> domain error<br> 7, -0.5, 2.58068e+06<br> domain + error<br> 8, -0.5, -1237.15<br> domain error<br> 9, -0.5, 7.43185e+08<br> + domain error<br> 10, -0.5, -120071<br> domain error<br> 11, -0.5, 3.26999e+11<br> + domain error<br> 12, -0.5, -5.11131e+07<br> domain error<br> 13, -0.5, + 2.04047e+14<br> domain error<br> 14, -0.5, -4.1064e+10<br> domain error<br> + 15, -0.5, 1.71399e+17<br> domain error<br> 16, -0.5, -4.44822e+13<br> + domain error<br> 17, -0.5, 1.86483e+20<br> domain error<br> 18, -0.5, + -6.08254e+16<br> domain error<br> 19, -0.5, 2.55108e+23<br> domain error<br> + 20, -0.5, -1.02182e+20<br> domain error<br> 21, -0.5, 4.28582e+26<br> + domain error<br> 2, -0.5, -0.828751<br> domain error<br> 3, -0.5, 193.409<br> + domain error<br> 4, -0.5, -3.47059<br> domain error<br> 5, -0.5, 15371.1<br> + domain error<br> 6, -0.5, -42.8426<br> domain error<br> 7, -0.5, 2.58068e+06<br> + domain error<br> 8, -0.5, -882.773<br> domain error<br> 9, -0.5, 7.43185e+08<br> + domain error<br> 10, -0.5, 35853.7<br> domain error<br> 11, -0.5, 3.26999e+11<br> + domain error<br> 12, -0.5, 4.61841e+07<br> domain error<br> 13, -0.5, + 2.04047e+14<br> domain error<br> 14, -0.5, 4.06656e+10<br> domain error<br> + 15, -0.5, 1.71399e+17<br> domain error<br> 16, -0.5, 4.44397e+13<br> + domain error<br> 17, -0.5, 1.86483e+20<br> domain error<br> 18, -0.5, + 6.08197e+16<br> domain error<br> 19, -0.5, 2.55108e+23<br> domain error<br> + 20, -0.5, 1.02181e+20<br> domain error<br> 21, -0.5, 4.28582e+26<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h106"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with5">Error + Output For polygamma with compiler GNU C++ version 7.1.0 and library GSL 2.1 + and test data Mathematica Data - negative arguments</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_negative_arguments"></a>domain + error<br> 2, -12.75, -124.031<br> domain error<br> 2, -12.25, 124.019<br> + domain error<br> 2, -11.75, -124.032<br> domain error<br> 2, -11.25, + 124.018<br> domain error<br> 2, -10.75, -124.033<br> domain error<br> + 2, -10.25, 124.016<br> domain error<br> 2, -9.75, -124.035<br> domain + error<br> 2, -9.25, 124.015<br> domain error<br> 2, -8.75, -124.037<br> + domain error<br> 2, -8.25, 124.012<br> domain error<br> 2, -7.75, -124.04<br> + domain error<br> 2, -7.25, 124.009<br> domain error<br> 2, -6.75, -124.044<br> + domain error<br> 2, -6.25, 124.003<br> domain error<br> 2, -5.75, -124.051<br> + domain error<br> 2, -5.25, 123.995<br> domain error<br> 2, -4.75, -124.061<br> + domain error<br> 2, -4.25, 123.981<br> domain error<br> 2, -3.75, -124.08<br> + domain error<br> 2, -3.25, 123.955<br> domain error<br> 2, -2.75, -124.118<br> + domain error<br> 2, -2.25, 123.897<br> domain error<br> 2, -1.75, -124.214<br> + domain error<br> 2, -1.25, 123.721<br> domain error<br> 2, -0.75, -124.587<br> + domain error<br> 2, -0.25, 122.697<br> domain error<br> 3, -12.75, 1558.54<br> + domain error<br> 3, -12.25, 1558.54<br> domain error<br> 3, -11.75, 1558.54<br> + domain error<br> 3, -11.25, 1558.54<br> domain error<br> 3, -10.75, 1558.54<br> + domain error<br> 3, -10.25, 1558.54<br> domain error<br> 3, -9.75, 1558.54<br> + domain error<br> 3, -9.25, 1558.54<br> domain error<br> 3, -8.75, 1558.54<br> + domain error<br> 3, -8.25, 1558.54<br> domain error<br> 3, -7.75, 1558.54<br> + domain error<br> 3, -7.25, 1558.54<br> domain error<br> 3, -6.75, 1558.54<br> + domain error<br> 3, -6.25, 1558.54<br> domain error<br> 3, -5.75, 1558.54<br> + domain error<br> 3, -5.25, 1558.54<br> domain error<br> 3, -4.75, 1558.53<br> + domain error<br> 3, -4.25, 1558.53<br> domain error<br> 3, -3.75, 1558.52<br> + domain error<br> 3, -3.25, 1558.51<br> domain error<br> 3, -2.75, 1558.49<br> + domain error<br> 3, -2.25, 1558.46<br> domain error<br> 3, -1.75, 1558.38<br> + domain error<br> 3, -1.25, 1558.22<br> domain error<br> 3, -0.75, 1557.75<br> + domain error<br> 3, -0.25, 1555.76<br> domain error<br> 4, -12.75, -24481.6<br> + domain error<br> 4, -12.25, 24481.6<br> domain error<br> 4, -11.75, -24481.6<br> + domain error<br> 4, -11.25, 24481.6<br> domain error<br> 4, -10.75, -24481.6<br> + domain error<br> 4, -10.25, 24481.6<br> domain error<br> 4, -9.75, -24481.6<br> + domain error<br> 4, -9.25, 24481.6<br> domain error<br> 4, -8.75, -24481.6<br> + domain error<br> 4, -8.25, 24481.6<br> domain error<br> 4, -7.75, -24481.6<br> + domain error<br> 4, -7.25, 24481.6<br> domain error<br> 4, -6.75, -24481.6<br> + domain error<br> 4, -6.25, 24481.6<br> domain error<br> 4, -5.75, -24481.6<br> + domain error<br> 4, -5.25, 24481.6<br> domain error<br> 4, -4.75, -24481.6<br> + domain error<br> 4, -4.25, 24481.6<br> domain error<br> 4, -3.75, -24481.6<br> + domain error<br> 4, -3.25, 24481.5<br> domain error<br> 4, -2.75, -24481.6<br> + domain error<br> 4, -2.25, 24481.5<br> domain error<br> 4, -1.75, -24481.8<br> + domain error<br> 4, -1.25, 24481.1<br> domain error<br> 4, -0.75, -24483.2<br> + domain error<br> 4, -0.25, 24473.2<br> domain error<br> 5, -12.75, 492231<br> + domain error<br> 5, -12.25, 492231<br> domain error<br> 5, -11.75, 492231<br> + domain error<br> 5, -11.25, 492231<br> domain error<br> 5, -10.75, 492231<br> + domain error<br> 5, -10.25, 492231<br> domain error<br> 5, -9.75, 492231<br> + domain error<br> 5, -9.25, 492231<br> domain error<br> 5, -8.75, 492231<br> + domain error<br> 5, -8.25, 492231<br> domain error<br> 5, -7.75, 492231<br> + domain error<br> 5, -7.25, 492231<br> domain error<br> 5, -6.75, 492231<br> + domain error<br> 5, -6.25, 492231<br> domain error<br> 5, -5.75, 492231<br> + domain error<br> 5, -5.25, 492231<br> domain error<br> 5, -4.75, 492231<br> + domain error<br> 5, -4.25, 492231<br> domain error<br> 5, -3.75, 492231<br> + domain error<br> 5, -3.25, 492231<br> domain error<br> 5, -2.75, 492231<br> + domain error<br> 5, -2.25, 492231<br> domain error<br> 5, -1.75, 492231<br> + domain error<br> 5, -1.25, 492230<br> domain error<br> 5, -0.75, 492227<br> + domain error<br> 5, -0.25, 492199<br> domain error<br> 6, -12.75, -1.17912e+07<br> + domain error<br> 6, -12.25, 1.17912e+07<br> domain error<br> 6, -11.75, + -1.17912e+07<br> domain error<br> 6, -11.25, 1.17912e+07<br> domain error<br> + 6, -10.75, -1.17912e+07<br> domain error<br> 6, -10.25, 1.17912e+07<br> + domain error<br> 6, -9.75, -1.17912e+07<br> domain error<br> 6, -9.25, + 1.17912e+07<br> domain error<br> 6, -8.75, -1.17912e+07<br> domain error<br> + 6, -8.25, 1.17912e+07<br> domain error<br> 6, -7.75, -1.17912e+07<br> + domain error<br> 6, -7.25, 1.17912e+07<br> domain error<br> 6, -6.75, + -1.17912e+07<br> domain error<br> 6, -6.25, 1.17912e+07<br> domain error<br> + 6, -5.75, -1.17912e+07<br> domain error<br> 6, -5.25, 1.17912e+07<br> + domain error<br> 6, -4.75, -1.17912e+07<br> domain error<br> 6, -4.25, + 1.17912e+07<br> domain error<br> 6, -3.75, -1.17912e+07<br> domain error<br> + 6, -3.25, 1.17912e+07<br> domain error<br> 6, -2.75, -1.17912e+07<br> + domain error<br> 6, -2.25, 1.17912e+07<br> domain error<br> 6, -1.75, + -1.17912e+07<br> domain error<br> 6, -1.25, 1.17912e+07<br> *** FURTHER + CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br> + </p> +<h5> +<a name="special_function_error_rates_rep.error_logs.h107"></a> + <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with6"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with6">Error + Output For polygamma with compiler GNU C++ version 7.1.0 and library GSL 2.1 + and test data Mathematica Data - large arguments</a> + </h5> +<p> + <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_arguments"></a>underflow<br> + 30, 8.58993e+09, -8.44974e-268<br> underflow<br> 30, 1.71799e+10, -7.86943e-277<br> + underflow<br> 30, 3.43597e+10, -7.32898e-286<br> underflow<br> 30, 6.87195e+10, + -6.82564e-295<br> underflow<br> 30, 1.37439e+11, -6.35687e-304<br> underflow<br> + 30, 2.74878e+11, -5.9203e-313<br> underflow<br> 30, 5.49756e+11, -5.53354e-322<br> + underflow<br> 30, 1.09951e+12, -0<br> underflow<br> 30, 2.19902e+12, + -0<br> underflow<br> 30, 4.39805e+12, -0<br> underflow<br> 30, 8.79609e+12, + -0<br> underflow<br> 30, 1.75922e+13, -0<br> underflow<br> 30, 3.51844e+13, + -0<br> underflow<br> 30, 7.03687e+13, -0<br> underflow<br> 30, 1.40737e+14, + -0<br> underflow<br> 30, 2.81475e+14, -0<br> underflow<br> 30, 5.6295e+14, + -0<br> underflow<br> 30, 1.1259e+15, -0<br> underflow<br> 30, 2.2518e+15, + -0<br> underflow<br> 30, 4.5036e+15, -0<br> underflow<br> 30, 9.0072e+15, + -0<br> underflow<br> 30, 1.80144e+16, -0<br> underflow<br> 30, 3.60288e+16, + -0<br> underflow<br> 30, 7.20576e+16, -0<br> underflow<br> 30, 1.44115e+17, + -0<br> underflow<br> 30, 2.8823e+17, -0<br> underflow<br> 30, 5.76461e+17, + -0<br> underflow<br> 30, 1.15292e+18, -0<br> underflow<br> 30, 2.30584e+18, + -0<br> underflow<br> 30, 4.61169e+18, -0<br> underflow<br> 30, 9.22337e+18, + -0<br> underflow<br> 30, 1.84467e+19, -0<br> underflow<br> 30, 3.68935e+19, + -0<br> underflow<br> 30, 7.3787e+19, -0<br> underflow<br> 30, 1.47574e+20, + -0<br> underflow<br> 30, 2.95148e+20, -0<br> underflow<br> 30, 5.90296e+20, + -0<br> underflow<br> 30, 1.18059e+21, -0<br> underflow<br> 30, 2.36118e+21, + -0<br> underflow<br> 30, 4.72237e+21, -0<br> underflow<br> 30, 9.44473e+21, + -0<br> underflow<br> 30, 1.88895e+22, -0<br> underflow<br> 30, 3.77789e+22, + -0<br> underflow<br> 30, 7.55579e+22, -0<br> underflow<br> 30, 1.51116e+23, + -0<br> underflow<br> 30, 3.02231e+23, -0<br> underflow<br> 30, 6.04463e+23, + -0<br> underflow<br> 30, 1.20893e+24, -0<br> underflow<br> 30, 2.41785e+24, + -0<br> underflow<br> 30, 4.8357e+24, -0<br> underflow<br> 30, 9.67141e+24, + -0<br> underflow<br> 30, 1.93428e+25, -0<br> underflow<br> 30, 3.86856e+25, + -0<br> underflow<br> 30, 7.73713e+25, -0<br> underflow<br> 30, 1.54743e+26, + -0<br> underflow<br> 30, 3.09485e+26, -0<br> underflow<br> 30, 6.1897e+26, + -0<br> underflow<br> 30, 1.23794e+27, -0<br> underflow<br> 30, 2.47588e+27, + -0<br> underflow<br> 30, 4.95176e+27, -0<br> underflow<br> 30, 9.90352e+27, + -0<br> underflow<br> 30, 1.9807e+28, -0<br> underflow<br> 30, 3.96141e+28, + -0<br> underflow<br> 30, 7.92282e+28, -0<br> underflow<br> 30, 1.58456e+29, + -0<br> underflow<br> 30, 3.16913e+29, -0<br> underflow<br> 30, 6.33825e+29, + -0<br> underflow<br> 30, 1.26765e+30, -0<br> + </p> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_error_rates_rep.all_the_tables"></a><a class="link" href="index.html#special_function_error_rates_rep.all_the_tables" title="Tables">Tables</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_beta"></a><p class="title"><b>Table 97. Error rates for beta</b></p> +<div class="table-contents"><table class="table" summary="Error rates for beta"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Beta Function: Small Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_beta_GSL_2_1_Beta_Function_Small_Values">And + other failures.</a>)</span><br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 1.14ε (Mean = 0.574ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.86ε (Mean = 1.22ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 364ε (Mean = 76.2ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.86ε (Mean = 1.22ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.23ε (Mean = 1.14ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Beta Function: Medium Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.978ε (Mean = 0.0595ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.18e+03ε (Mean = 238ε))<br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.09e+03ε (Mean = 265ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 61.4ε (Mean = 19.4ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.07e+03ε (Mean = 264ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 107ε (Mean = 24.5ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 96.5ε (Mean = 22.4ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Beta Function: Divergent Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 12.1ε (Mean = 1.99ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 176ε (Mean = 28ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.99ε (Mean = 2.44ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 128ε (Mean = 23.8ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 18.8ε (Mean = 2.71ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 11.4ε (Mean = 2.19ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_beta_incomplete_"></a><p class="title"><b>Table 98. Error rates for beta (incomplete)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for beta (incomplete)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Incomplete Beta Function: Small Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 11.1ε (Mean = 2.32ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 18.7ε (Mean = 3.19ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.94ε (Mean = 2.17ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Incomplete Beta Function: Medium Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.568ε (Mean = 0.0254ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 69.2ε (Mean = 13.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 174ε (Mean = 25ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 90ε (Mean = 12.7ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Incomplete Beta Function: Large and Diverse Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.999ε (Mean = 0.0325ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.84e+04ε (Mean = 2.76e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.86e+04ε (Mean = 2.79e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 633ε (Mean = 29.7ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Incomplete Beta Function: Small Integer Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.786ε (Mean = 0.0323ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 11.6ε (Mean = 3.6ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 51.8ε (Mean = 11ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 26ε (Mean = 6.28ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_betac"></a><p class="title"><b>Table 99. Error rates for betac</b></p> +<div class="table-contents"><table class="table" summary="Error rates for betac"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Incomplete Beta Function: Small Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.676ε (Mean = 0.0302ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.92ε (Mean = 2.3ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 11.2ε (Mean = 2.94ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.94ε (Mean = 2.06ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Incomplete Beta Function: Medium Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.949ε (Mean = 0.098ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 63.5ε (Mean = 13.5ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 97.6ε (Mean = 24.3ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 90.6ε (Mean = 14.8ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Incomplete Beta Function: Large and Diverse Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.12ε (Mean = 0.0458ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.05e+05ε (Mean = 5.45e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.04e+05ε (Mean = 5.46e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.72e+03ε (Mean = 113ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Incomplete Beta Function: Small Integer Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.586ε (Mean = 0.0314ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 11.1ε (Mean = 3.65ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 103ε (Mean = 17.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 26.2ε (Mean = 6.36ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_binomial_coefficient"></a><p class="title"><b>Table 100. Error rates for binomial_coefficient</b></p> +<div class="table-contents"><table class="table" summary="Error rates for binomial_coefficient"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Binomials: small arguments + </p> + </td> +<td> + <p> + <span class="blue">Max = 1ε (Mean = 0.369ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.5ε (Mean = 0.339ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.5ε (Mean = 0.339ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1ε (Mean = 0.369ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Binomials: large arguments + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.939ε (Mean = 0.314ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 26.6ε (Mean = 6.13ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 53.2ε (Mean = 10.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 37.2ε (Mean = 7.4ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_boost_math_powm1"></a><p class="title"><b>Table 101. Error rates for boost::math::powm1</b></p> +<div class="table-contents"><table class="table" summary="Error rates for boost::math::powm1"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + powm1 + </p> + </td> +<td> + <p> + (<span class="emphasis"><em><math.h>:</em></span> Max = 2.04ε (Mean = 0.493ε))<br> + <br> <span class="blue">Max = 2.04ε (Mean = 0.493ε)</span><br> + <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 2.04ε (Mean = 0.493ε)) + </p> + </td> +<td> + <p> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.06ε (Mean = 0.425ε))<br> + <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.06ε (Mean = 0.425ε))<br> + <br> <span class="blue">Max = 1.06ε (Mean = 0.425ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.88ε (Mean = 0.49ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.88ε (Mean = 0.49ε)) + </p> + </td> +<td> + <p> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.84ε (Mean = 0.486ε))<br> + <br> <span class="blue">Max = 1.84ε (Mean = 0.486ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_cbrt"></a><p class="title"><b>Table 102. Error rates for cbrt</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cbrt"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + cbrt Function + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.34ε (Mean = 0.471ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.34ε (Mean = 0.471ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.34ε (Mean = 0.471ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.34ε (Mean = 0.471ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.34ε (Mean = 0.471ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.7ε (Mean = 0.565ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.7ε (Mean = 0.565ε)) + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_cos_pi"></a><p class="title"><b>Table 103. Error rates for cos_pi</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cos_pi"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + sin_pi and cos_pi + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.991ε (Mean = 0.302ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.991ε (Mean = 0.302ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.996ε (Mean = 0.284ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + sin_pi and cos_pi near integers and half integers + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.976ε (Mean = 0.28ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.976ε (Mean = 0.28ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.996ε (Mean = 0.298ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_i"></a><p class="title"><b>Table 104. Error rates for cyl_bessel_i</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Bessel I0: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 270ε (Mean = 91.6ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I0_Mathworld_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 1.52ε (Mean = 0.622ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I0_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.95ε (Mean = 0.738ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 8.49ε (Mean = 3.46ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I0_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.95ε (Mean = 0.661ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.762ε (Mean = 0.329ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel I1: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 128ε (Mean = 41ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I1_Mathworld_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 1.53ε (Mean = 0.483ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I1_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 5ε (Mean = 2.15ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I1_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.767ε (Mean = 0.398ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel In: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2.31ε (Mean = 0.838ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Mathworld_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 1.73ε (Mean = 0.601ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_In_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.8ε (Mean = 1.33ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 430ε (Mean = 163ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_In_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 463ε (Mean = 140ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.46ε (Mean = 1.32ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel Iv: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 5.95ε (Mean = 2.08ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 3.53ε (Mean = 1.39ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.12ε (Mean = 1.85ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 616ε (Mean = 221ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.12ε (Mean = 1.95ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.97ε (Mean = 1.24ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel In: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 261ε (Mean = 53.2ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Random_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 7.37ε (Mean = 2.4ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.62ε (Mean = 1.06ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 645ε (Mean = 132ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 176ε (Mean = 39.1ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.67ε (Mean = 1.88ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel Iv: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.661ε (Mean = 0.0441ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 6.18e+03ε (Mean = 1.55e+03ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Random_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + <span class="red">Max = 4.28e+08ε (Mean = 2.85e+07ε))</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.35ε (Mean = 1.62ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.05e+03ε (Mean = 224ε) + <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Random_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 283ε (Mean = 88.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.46ε (Mean = 1.71ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel Iv: Mathworld Data (large values) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 37ε (Mean = 18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data_large_values_">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + <span class="red">Max = 3.77e+168ε (Mean = 2.39e+168ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_Iv_Mathworld_Data_large_values_">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 14.7ε (Mean = 6.66ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 118ε (Mean = 57.2ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data_large_values_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 14.7ε (Mean = 6.59ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.67ε (Mean = 1.64ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_i_integer_orders_"></a><p class="title"><b>Table 105. Error rates for cyl_bessel_i (integer orders)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i (integer orders)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Bessel I0: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0.79ε (Mean = 0.482ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 1.52ε (Mean = 0.622ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I0_Mathworld_Data_Integer_Version_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.95ε (Mean = 0.738ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 8.49ε (Mean = 3.46ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I0_Mathworld_Data_Integer_Version_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.95ε (Mean = 0.661ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.762ε (Mean = 0.329ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel I1: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0.82ε (Mean = 0.456ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 1.53ε (Mean = 0.483ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I1_Mathworld_Data_Integer_Version_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 5ε (Mean = 2.15ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I1_Mathworld_Data_Integer_Version_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.767ε (Mean = 0.398ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel In: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 5.15ε (Mean = 2.13ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__GSL_2_1_Bessel_In_Mathworld_Data_Integer_Version_">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 1.73ε (Mean = 0.601ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_In_Mathworld_Data_Integer_Version_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.8ε (Mean = 1.33ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 430ε (Mean = 163ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_In_Mathworld_Data_Integer_Version_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 463ε (Mean = 140ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.46ε (Mean = 1.32ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_i_prime"></a><p class="title"><b>Table 106. Error rates for cyl_bessel_i_prime</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Bessel I'0: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.82ε (Mean = 0.354ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel I'1: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.36ε (Mean = 0.782ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel I'n: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.31ε (Mean = 1.41ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 701ε (Mean = 212ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.61ε (Mean = 1.22ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel I'v: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.62ε (Mean = 0.512ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.89e+03ε (Mean = 914ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.89e+03ε (Mean = 914ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.76e+03ε (Mean = 1.19e+03ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel I'n: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.95ε (Mean = 1.06ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 195ε (Mean = 37.1ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.85ε (Mean = 1.82ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel I'v: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 14.1ε (Mean = 2.93ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 336ε (Mean = 68.5ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 14ε (Mean = 2.5ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel I'v: Mathworld Data (large values) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 42.6ε (Mean = 20.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 42.6ε (Mean = 20.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 59.5ε (Mean = 26.6ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_i_prime_integer_orders_"></a><p class="title"><b>Table 107. Error rates for cyl_bessel_i_prime (integer orders)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime (integer orders)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Bessel I'0: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.82ε (Mean = 0.354ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel I'1: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.36ε (Mean = 0.782ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel I'n: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.31ε (Mean = 1.41ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 701ε (Mean = 212ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.61ε (Mean = 1.22ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_j"></a><p class="title"><b>Table 108. Error rates for cyl_bessel_j</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Bessel J0: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 5.04ε (Mean = 1.78ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J0_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0.629ε (Mean = 0.223ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J0_Mathworld_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 0.629ε (Mean = 0.223ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J0_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.52ε (Mean = 1.2ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J0: Mathworld Data (Tricky cases) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span><br> + <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 4.79e+08ε (Mean = + 1.96e+08ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 8e+04ε (Mean = 3.27e+04ε)</span><br> + <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 6.5e+07ε (Mean = 2.66e+07ε))<br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.04e+07ε (Mean = 4.29e+06ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1e+07ε (Mean = 4.09e+06ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J1: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.59ε (Mean = 1.33ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 6.1ε (Mean = 2.95ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J1_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 6.62ε (Mean = 2.35ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J1_Mathworld_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 0.946ε (Mean = 0.39ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J1_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.44ε (Mean = 0.637ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.73ε (Mean = 0.976ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J1: Mathworld Data (tricky cases) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span><br> + <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 2.15e+06ε (Mean = + 1.58e+06ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 106ε (Mean = 47.5ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.75e+05ε (Mean = 5.32e+05ε))<br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.93e+06ε (Mean = 1.7e+06ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.23e+04ε (Mean = 1.45e+04ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel JN: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.85ε (Mean = 3.35ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.13e+19ε (Mean + = 5.16e+18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_JN_Mathworld_Data">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 6.9e+05ε (Mean = 2.15e+05ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_JN_Mathworld_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_JN_Mathworld_Data">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 463ε (Mean = 112ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 14.7ε (Mean = 5.4ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 14.7ε (Mean = 4.11ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 3.49e+05ε (Mean = 8.09e+04ε) + <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 10ε (Mean = 2.24ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2.39e+05ε (Mean = 5.37e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J_Mathworld_Data">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 14.7ε (Mean = 4.22ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 14.9ε (Mean = 3.89ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J: Mathworld Data (large values) + </p> + </td> +<td> + <p> + <span class="blue">Max = 607ε (Mean = 305ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> + Max = 34.9ε (Mean = 17.4ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data_large_values_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.536ε (Mean = 0.268ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.91e+03ε (Mean = 2.46e+03ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data_large_values_">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 5.9ε (Mean = 3.76ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 607ε (Mean = 305ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.31ε (Mean = 5.52ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel JN: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 50.8ε (Mean = 3.69ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.12e+03ε (Mean = 88.7ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 75.7ε (Mean = 5.36ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 3.93ε (Mean = 1.22ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 99.6ε (Mean = 22ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 17.5ε (Mean = 1.46ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 11.4ε (Mean = 1.68ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 501ε (Mean = 52.3ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 15.5ε (Mean = 3.33ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Random_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 6.74ε (Mean = 1.3ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 260ε (Mean = 34ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.24ε (Mean = 1.17ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J: Random Data (Tricky large values) + </p> + </td> +<td> + <p> + <span class="blue">Max = 785ε (Mean = 94.2ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 5.01e+17ε (Mean + = 6.23e+16ε))</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2.48e+05ε (Mean = 5.11e+04ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 71.6ε (Mean = 11.7ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 785ε (Mean = 97.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 59.2ε (Mean = 8.67ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_j_integer_orders_"></a><p class="title"><b>Table 109. Error rates for cyl_bessel_j (integer orders)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j (integer orders)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Bessel J0: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 5.04ε (Mean = 1.78ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J0_Mathworld_Data_Integer_Version_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.12ε (Mean = 0.488ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 0.629ε (Mean = 0.223ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J0_Mathworld_Data_Integer_Version_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.52ε (Mean = 1.2ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.89ε (Mean = 0.988ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J0: Mathworld Data (Tricky cases) (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span><br> + <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 4.79e+08ε (Mean = + 1.96e+08ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 8e+04ε (Mean = 3.27e+04ε)</span><br> + <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1e+07ε (Mean = 4.11e+06ε))<br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.04e+07ε (Mean = 4.29e+06ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1e+07ε (Mean = 4.09e+06ε)</span><br> + <br> (<span class="emphasis"><em><math.h>:</em></span> <span class="red">Max + = 2.54e+08ε (Mean = 1.04e+08ε))</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J1: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.59ε (Mean = 1.33ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 6.1ε (Mean = 2.95ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J1_Mathworld_Data_Integer_Version_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.89ε (Mean = 0.721ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 0.946ε (Mean = 0.39ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J1_Mathworld_Data_Integer_Version_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.44ε (Mean = 0.637ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.73ε (Mean = 0.976ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 11.4ε (Mean = 4.15ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J1: Mathworld Data (tricky cases) (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span><br> + <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 2.15e+06ε (Mean = + 1.58e+06ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 106ε (Mean = 47.5ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.26e+06ε (Mean = 6.28e+05ε))<br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.93e+06ε (Mean = 1.7e+06ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.23e+04ε (Mean = 1.45e+04ε)</span><br> + <br> (<span class="emphasis"><em><math.h>:</em></span> Max = 1.44e+07ε (Mean + = 6.5e+06ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel JN: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.85ε (Mean = 3.35ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.13e+19ε (Mean + = 5.16e+18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_JN_Mathworld_Data_Integer_Version_">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 6.9e+05ε (Mean = 2.53e+05ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__GSL_2_1_Bessel_JN_Mathworld_Data_Integer_Version_">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_JN_Mathworld_Data_Integer_Version_">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 463ε (Mean = 112ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 14.7ε (Mean = 5.4ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> <span class="red">Max = +INFε (Mean + = +INFε) <a class="link" href="index.html#errors_Microsoft_Visual_C_version_14_1_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_">And + other failures.</a>)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_j_prime"></a><p class="title"><b>Table 110. Error rates for cyl_bessel_j_prime</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Bessel J0': Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 18.9ε (Mean = 6.82ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 18.9ε (Mean = 6.72ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.62ε (Mean = 2.55ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J0': Mathworld Data (Tricky cases) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.44ε (Mean = 3.34ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.44ε (Mean = 3.31ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.67ε (Mean = 1.74ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J1': Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.999ε (Mean = 0.627ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J1': Mathworld Data (tricky cases) + </p> + </td> +<td> + <p> + <span class="blue">Max = 287ε (Mean = 129ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 288ε (Mean = 129ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel JN': Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.527ε (Mean = 0.128ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.29e+03ε (Mean = 312ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.29e+03ε (Mean = 355ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 14ε (Mean = 6.13ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J': Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 21.5ε (Mean = 4.7ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 42.5ε (Mean = 9.31ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 42.5ε (Mean = 9.32ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 23.7ε (Mean = 8ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J': Mathworld Data (large values) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 989ε (Mean = 495ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 989ε (Mean = 495ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.9ε (Mean = 1.61ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel JN': Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.593ε (Mean = 0.0396ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 11.3ε (Mean = 1.85ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 79.4ε (Mean = 16.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.34ε (Mean = 0.999ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J': Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.885ε (Mean = 0.033ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 139ε (Mean = 6.47ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 279ε (Mean = 27.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 176ε (Mean = 9.75ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J': Random Data (Tricky large values) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 474ε (Mean = 62.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 474ε (Mean = 64.5ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 379ε (Mean = 45.4ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_j_prime_integer_orders_"></a><p class="title"><b>Table 111. Error rates for cyl_bessel_j_prime (integer orders)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime (integer orders)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Bessel J0': Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 18.9ε (Mean = 6.82ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 18.9ε (Mean = 6.72ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.62ε (Mean = 2.55ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J0': Mathworld Data (Tricky cases) (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.44ε (Mean = 3.34ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.44ε (Mean = 3.31ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.67ε (Mean = 1.74ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J1': Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.999ε (Mean = 0.627ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel J1': Mathworld Data (tricky cases) (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 287ε (Mean = 129ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 288ε (Mean = 129ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel JN': Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.527ε (Mean = 0.128ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.29e+03ε (Mean = 312ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.29e+03ε (Mean = 355ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 14ε (Mean = 6.13ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_k"></a><p class="title"><b>Table 112. Error rates for cyl_bessel_k</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Bessel K0: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 9.33ε (Mean = 3.25ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 6.04ε (Mean = 2.16ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 0.833ε (Mean = 0.601ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.833ε (Mean = 0.552ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel K1: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 8.94ε (Mean = 3.19ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 6.26ε (Mean = 2.21ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 0.894ε (Mean = 0.516ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel Kn: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 12.9ε (Mean = 4.91ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kn_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 3.36ε (Mean = 1.43ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Mathworld_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 8.48ε (Mean = 2.98ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.63ε (Mean = 1.46ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel Kv: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.58ε (Mean = 2.39ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 13ε (Mean = 4.81ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 5.47ε (Mean = 2.04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 3.15ε (Mean = 1.35ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.21ε (Mean = 2.53ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.78ε (Mean = 2.19ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel Kv: Mathworld Data (large values) + </p> + </td> +<td> + <p> + <span class="blue">Max = 42.3ε (Mean = 21ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> + Max = 42.3ε (Mean = 19.8ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data_large_values_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 308ε (Mean = 142ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data_large_values_">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 84.6ε (Mean = 37.8ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 42.3ε (Mean = 21ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 59.8ε (Mean = 26.9ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel Kn: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.55ε (Mean = 1.12ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 13.9ε (Mean = 2.91ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.764ε (Mean = 0.0348ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.71ε (Mean = 1.76ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Random_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 7.47ε (Mean = 1.34ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.55ε (Mean = 1.12ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.34ε (Mean = 1.7ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel Kv: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.88ε (Mean = 1.48ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 13.6ε (Mean = 2.68ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Random_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.507ε (Mean = 0.0313ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 9.71ε (Mean = 1.47ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Random_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 7.37ε (Mean = 1.49ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.88ε (Mean = 1.47ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.33ε (Mean = 1.62ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_k_integer_orders_"></a><p class="title"><b>Table 113. Error rates for cyl_bessel_k (integer orders)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k (integer orders)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Bessel K0: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 9.33ε (Mean = 3.25ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.2ε (Mean = 0.733ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 0.833ε (Mean = 0.601ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.833ε (Mean = 0.552ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel K1: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 8.94ε (Mean = 3.19ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0.626ε (Mean = 0.333ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 0.894ε (Mean = 0.516ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel Kn: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 12.9ε (Mean = 4.91ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k_integer_orders___cmath__Bessel_Kn_Mathworld_Data_Integer_Version_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 168ε (Mean = 59.5ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 8.48ε (Mean = 2.98ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.63ε (Mean = 1.46ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_k_prime"></a><p class="title"><b>Table 114. Error rates for cyl_bessel_k_prime</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Bessel K'0: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel K'1: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.761ε (Mean = 0.444ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel K'n: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.17ε (Mean = 1.75ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel K'v: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.94ε (Mean = 2.44ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.94ε (Mean = 2.34ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.94ε (Mean = 1.47ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel K'v: Mathworld Data (large values) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 59.2ε (Mean = 42.9ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 58.7ε (Mean = 42.6ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 18.6ε (Mean = 11.8ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel K'n: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.45ε (Mean = 1.19ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.45ε (Mean = 1.19ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.67ε (Mean = 1.73ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel K'v: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.95ε (Mean = 1.53ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.95ε (Mean = 1.52ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.32ε (Mean = 1.65ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_k_prime_integer_orders_"></a><p class="title"><b>Table 115. Error rates for cyl_bessel_k_prime (integer orders)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime (integer orders)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Bessel K'0: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel K'1: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.761ε (Mean = 0.444ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Bessel K'n: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.17ε (Mean = 1.75ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_cyl_neumann"></a><p class="title"><b>Table 116. Error rates for cyl_neumann</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Y0: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 2.05e+05ε (Mean = 6.87e+04ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 60.9ε (Mean = 20.4ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 167ε (Mean = 56.5ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.61ε (Mean = 2.29ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Y1: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.33ε (Mean = 2.25ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 9.71e+03ε (Mean = 4.08e+03ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 23.4ε (Mean = 8.1ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 193ε (Mean = 64.4ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.33ε (Mean = 2.29ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.75ε (Mean = 1.72ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Yn: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.2e+20ε (Mean + = 6.97e+19ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yn_Mathworld_Data">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.993ε (Mean = 0.314ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.41e+05ε (Mean = 7.62e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yn_Mathworld_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 1.24e+04ε (Mean = 4e+03ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 35ε (Mean = 11.9ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Yv: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 10.7ε (Mean = 4.93ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 3.49e+15ε (Mean + = 1.05e+15ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 10ε (Mean = 3.02ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.07e+05ε (Mean = 3.22e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 243ε (Mean = 73.9ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 10.7ε (Mean = 5.1ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.89ε (Mean = 3.27ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Yv: Mathworld Data (large values) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.7ε (Mean = 1.33ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 43.2ε (Mean = 16.3ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data_large_values_">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 60.8ε (Mean = 23ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data_large_values_">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 0.682ε (Mean = 0.335ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.7ε (Mean = 1.33ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.682ε (Mean = 0.423ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Y0 and Y1: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 10.8ε (Mean = 3.04ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 2.59e+03ε (Mean = 500ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 34.4ε (Mean = 8.9ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 83ε (Mean = 14.2ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 10.8ε (Mean = 3.04ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.17ε (Mean = 1.24ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Yn: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 338ε (Mean = 27.5ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 4.01e+03ε (Mean = 348ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 500ε (Mean = 47.8ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 691ε (Mean = 67.9ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 338ε (Mean = 27.5ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 117ε (Mean = 10.2ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Yv: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.08e+03ε (Mean = 149ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean + = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Random_Data">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.53ε (Mean = 0.102ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.41e+06ε (Mean = 7.67e+04ε))<br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.79e+05ε (Mean = 9.64e+03ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.08e+03ε (Mean = 149ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.23e+03ε (Mean = 69.9ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_cyl_neumann_integer_orders_"></a><p class="title"><b>Table 117. Error rates for cyl_neumann (integer orders)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann (integer orders)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Y0: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 2.05e+05ε (Mean = 6.87e+04ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 6.46ε (Mean = 2.38ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 167ε (Mean = 56.5ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.61ε (Mean = 2.29ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 5.37e+03ε (Mean = 1.81e+03ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + Y1: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.33ε (Mean = 2.25ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 9.71e+03ε (Mean = 4.08e+03ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.51ε (Mean = 0.839ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 193ε (Mean = 64.4ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.33ε (Mean = 2.29ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.75ε (Mean = 1.72ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.86e+04ε (Mean = 6.2e+03ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + Yn: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.2e+20ε (Mean + = 6.97e+19ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann_integer_orders___cmath__Yn_Mathworld_Data_Integer_Version_">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.993ε (Mean = 0.314ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.41e+05ε (Mean = 7.62e+04ε))<br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.24e+04ε (Mean = 4e+03ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 35ε (Mean = 11.9ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> + Max = 2.49e+05ε (Mean = 8.14e+04ε)) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_cyl_neumann_prime"></a><p class="title"><b>Table 118. Error rates for cyl_neumann_prime</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Y'0: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.33ε (Mean = 3.12ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.33ε (Mean = 3.14ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.75ε (Mean = 1.75ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Y'1: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.58ε (Mean = 0.193ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 37.1ε (Mean = 12.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 34ε (Mean = 11.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.08ε (Mean = 1.2ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Y'n: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.05ε (Mean = 0.677ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 56ε (Mean = 18.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 56ε (Mean = 21.3ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 563ε (Mean = 178ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Y'v: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 21.5ε (Mean = 6.49ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 42.5ε (Mean = 13.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 42.5ε (Mean = 13.6ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 23.7ε (Mean = 10.1ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Y'v: Mathworld Data (large values) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.57ε (Mean = 1.24ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.57ε (Mean = 1.24ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.627ε (Mean = 0.237ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Y'0 and Y'1: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 23.8ε (Mean = 3.69ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 23.8ε (Mean = 3.69ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.95ε (Mean = 1.36ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Y'n: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.53ε (Mean = 0.0885ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.35e+03ε (Mean = 136ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.35e+03ε (Mean = 136ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 621ε (Mean = 36ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Y'v: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 56.8ε (Mean = 2.59ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.16e+05ε (Mean = 5.28e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.16e+05ε (Mean = 5.28e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.23e+04ε (Mean = 1.13e+03ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_cyl_neumann_prime_integer_orders_"></a><p class="title"><b>Table 119. Error rates for cyl_neumann_prime (integer orders)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime (integer orders)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Y'0: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.33ε (Mean = 3.12ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.33ε (Mean = 3.14ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.75ε (Mean = 1.75ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Y'1: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.58ε (Mean = 0.193ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 37.1ε (Mean = 12.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 34ε (Mean = 11.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.08ε (Mean = 1.2ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Y'n: Mathworld Data (Integer Version) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.05ε (Mean = 0.677ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 56ε (Mean = 18.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 56ε (Mean = 21.3ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 563ε (Mean = 178ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_digamma"></a><p class="title"><b>Table 120. Error rates for digamma</b></p> +<div class="table-contents"><table class="table" summary="Error rates for digamma"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Digamma Function: Large Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.84ε (Mean = 0.71ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 1.18ε (Mean = 0.331ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.39ε (Mean = 0.413ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.39ε (Mean = 0.413ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.98ε (Mean = 0.369ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Digamma Function: Near the Positive Root + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.891ε (Mean = 0.0995ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 135ε (Mean = 11.9ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 2.02e+03ε (Mean = 256ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.37ε (Mean = 0.477ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.31ε (Mean = 0.471ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.997ε (Mean = 0.527ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Digamma Function: Near Zero + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0.953ε (Mean = 0.348ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 1.17ε (Mean = 0.564ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.984ε (Mean = 0.361ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.984ε (Mean = 0.361ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.953ε (Mean = 0.337ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Digamma Function: Negative Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 4.56e+04ε (Mean = 3.91e+03ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 4.6e+04ε (Mean = 3.94e+03ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 180ε (Mean = 13ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 180ε (Mean = 13ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 214ε (Mean = 16.1ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Digamma Function: Values near 0 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0.866ε (Mean = 0.387ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 3.58e+05ε (Mean = 1.6e+05ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1ε (Mean = 0.592ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1ε (Mean = 0.592ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Digamma Function: Integer arguments + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.992ε (Mean = 0.215ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.18ε (Mean = 0.607ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 4.33ε (Mean = 0.982ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.888ε (Mean = 0.403ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.888ε (Mean = 0.403ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.992ε (Mean = 0.452ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Digamma Function: Half integer arguments + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.09ε (Mean = 0.531ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 46.2ε (Mean = 7.24ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.906ε (Mean = 0.409ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.906ε (Mean = 0.409ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.78ε (Mean = 0.314ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_ellint_1"></a><p class="title"><b>Table 121. Error rates for ellint_1</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ellint_1"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Elliptic Integral F: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.94ε (Mean = 0.509ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean + = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_1__cmath__Elliptic_Integral_F_Mathworld_Data">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0.919ε (Mean = 0.544ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.94ε (Mean = 0.509ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.919ε (Mean = 0.542ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Elliptic Integral F: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.57ε (Mean = 0.56ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 2.56ε (Mean = 0.816ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2.99ε (Mean = 0.797ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.57ε (Mean = 0.561ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.26ε (Mean = 0.631ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_ellint_1_complete_"></a><p class="title"><b>Table 122. Error rates for ellint_1 (complete)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ellint_1 (complete)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Elliptic Integral K: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.887ε (Mean = 0.296ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.19ε (Mean = 0.765ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0.623ε (Mean = 0.393ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.887ε (Mean = 0.296ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.915ε (Mean = 0.547ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Elliptic Integral K: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.27ε (Mean = 0.473ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 2.19ε (Mean = 0.694ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.851ε (Mean = 0.0851ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.32ε (Mean = 0.688ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.27ε (Mean = 0.473ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.958ε (Mean = 0.408ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_ellint_2"></a><p class="title"><b>Table 123. Error rates for ellint_2</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ellint_2"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Elliptic Integral E: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0.63ε (Mean = 0.325ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.656ε (Mean = 0.317ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean + = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_2__cmath__Elliptic_Integral_E_Mathworld_Data">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.656ε (Mean = 0.317ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.31ε (Mean = 0.727ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Elliptic Integral E: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 4.4ε (Mean = 1.16ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.05ε (Mean = 0.632ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 3.08e+04ε (Mean = 3.84e+03ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.05ε (Mean = 0.632ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.23ε (Mean = 0.639ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Elliptic Integral E: Small Angles + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0.5ε (Mean = 0.118ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1ε (Mean = 0.283ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> + Max = 2ε (Mean = 0.333ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1ε (Mean = 0.283ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1ε (Mean = 0.421ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_ellint_2_complete_"></a><p class="title"><b>Table 124. Error rates for ellint_2 (complete)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ellint_2 (complete)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Elliptic Integral E: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 3.09ε (Mean = 1.04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_2_complete__GSL_2_1_Elliptic_Integral_E_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.836ε (Mean = 0.469ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 170ε (Mean = 55.1ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.836ε (Mean = 0.469ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.3ε (Mean = 0.615ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Elliptic Integral E: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 4.34ε (Mean = 1.18ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.97ε (Mean = 0.629ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 2.49e+04ε (Mean = 3.39e+03ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.97ε (Mean = 0.629ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.71ε (Mean = 0.553ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_ellint_3"></a><p class="title"><b>Table 125. Error rates for ellint_3</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ellint_3"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Elliptic Integral PI: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 475ε (Mean = 86.3ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean + = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Mathworld_Data">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.48e+05ε (Mean = 2.54e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_3_GSL_2_1_Elliptic_Integral_PI_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 475ε (Mean = 86.3ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 565ε (Mean = 102ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Elliptic Integral PI: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.54ε (Mean = 0.895ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 3.37e+20ε (Mean + = 3.47e+19ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Random_Data">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 633ε (Mean = 50.1ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.49ε (Mean = 0.885ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.33ε (Mean = 0.971ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Elliptic Integral PI: Large Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.7ε (Mean = 0.893ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.52e+18ε (Mean + = 4.83e+17ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Large_Random_Data">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.557ε (Mean = 0.0389ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 40.1ε (Mean = 7.77ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.7ε (Mean = 0.892ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.86ε (Mean = 0.944ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_ellint_3_complete_"></a><p class="title"><b>Table 126. Error rates for ellint_3 (complete)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ellint_3 (complete)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Complete Elliptic Integral PI: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.4ε (Mean = 0.575ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 6.31e+20ε (Mean + = 1.53e+20ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Mathworld_Data">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 6.33e+04ε (Mean = 1.54e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_3_complete__GSL_2_1_Complete_Elliptic_Integral_PI_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.4ε (Mean = 0.575ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.971ε (Mean = 0.464ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Complete Elliptic Integral PI: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.45ε (Mean = 0.696ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 8.78e+20ε (Mean + = 1.02e+20ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Random_Data">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 24ε (Mean = 2.99ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.4ε (Mean = 0.677ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.46ε (Mean = 0.657ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_ellint_d"></a><p class="title"><b>Table 127. Error rates for ellint_d</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ellint_d"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Elliptic Integral E: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0.862ε (Mean = 0.568ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.3ε (Mean = 0.813ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.3ε (Mean = 0.813ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.862ε (Mean = 0.457ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Elliptic Integral D: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 3.01ε (Mean = 0.928ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.51ε (Mean = 0.883ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.51ε (Mean = 0.883ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.87ε (Mean = 0.805ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_ellint_d_complete_"></a><p class="title"><b>Table 128. Error rates for ellint_d (complete)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ellint_d (complete)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Elliptic Integral E: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.637ε (Mean = 0.368ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.27ε (Mean = 0.735ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.27ε (Mean = 0.735ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.637ε (Mean = 0.368ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Elliptic Integral D: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.27ε (Mean = 0.334ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.27ε (Mean = 0.334ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.27ε (Mean = 0.355ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_ellint_rc"></a><p class="title"><b>Table 129. Error rates for ellint_rc</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ellint_rc"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + RC: Random data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2.4ε (Mean = 0.624ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.995ε (Mean = 0.433ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.962ε (Mean = 0.407ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_ellint_rd"></a><p class="title"><b>Table 130. Error rates for ellint_rd</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ellint_rd"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + RD: Random data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2.59ε (Mean = 0.878ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.73ε (Mean = 0.831ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.16ε (Mean = 0.803ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RD: y = z + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.896ε (Mean = 0.022ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.88ε (Mean = 0.839ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.65ε (Mean = 0.82ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 16.5ε (Mean = 0.843ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RD: x = y + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.824ε (Mean = 0.0272ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.74ε (Mean = 0.84ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.85ε (Mean = 0.865ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.51ε (Mean = 0.816ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RD: x = 0, y = z + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2ε (Mean = 0.656ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.19ε (Mean = 0.522ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.16ε (Mean = 0.497ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RD: x = y = z + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.03ε (Mean = 0.418ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.998ε (Mean = 0.387ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.03ε (Mean = 0.418ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RD: x = 0 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2.85ε (Mean = 0.781ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.79ε (Mean = 0.883ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.64ε (Mean = 0.894ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_ellint_rf"></a><p class="title"><b>Table 131. Error rates for ellint_rf</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ellint_rf"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + RF: Random data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2.73ε (Mean = 0.804ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.54ε (Mean = 0.674ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.02ε (Mean = 0.677ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RF: x = y = z + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0.999ε (Mean = 0.34ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.991ε (Mean = 0.345ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.999ε (Mean = 0.34ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RF: x = y or y = z or x = z + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.536ε (Mean = 0.00658ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.89ε (Mean = 0.749ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.95ε (Mean = 0.418ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.21ε (Mean = 0.394ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RF: x = 0, y = z + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.29ε (Mean = 0.527ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.894ε (Mean = 0.338ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.999ε (Mean = 0.407ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RF: z = 0 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2.54ε (Mean = 0.781ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.7ε (Mean = 0.539ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.89ε (Mean = 0.587ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_ellint_rg"></a><p class="title"><b>Table 132. Error rates for ellint_rg</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ellint_rg"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + RG: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.983ε (Mean = 0.0172ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.983ε (Mean = 0.0172ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.95ε (Mean = 0.951ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.65ε (Mean = 0.929ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RG: two values 0 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RG: All values the same or zero + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.992ε (Mean = 0.288ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.06ε (Mean = 0.348ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RG: two values the same + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.594ε (Mean = 0.0103ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.594ε (Mean = 0.0103ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.51ε (Mean = 0.404ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.96ε (Mean = 0.374ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RG: one value zero + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.14ε (Mean = 0.722ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.96ε (Mean = 0.674ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_ellint_rj"></a><p class="title"><b>Table 133. Error rates for ellint_rj</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ellint_rj"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + RJ: Random data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.52ε (Mean = 0.0184ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.57ε (Mean = 0.704ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_rj_GSL_2_1_RJ_Random_data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 186ε (Mean = 6.67ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 215ε (Mean = 7.66ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RJ: 4 Equal Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.03ε (Mean = 0.418ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.998ε (Mean = 0.387ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.03ε (Mean = 0.418ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RJ: 3 Equal Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 3.96ε (Mean = 1.06ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 20.8ε (Mean = 0.986ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 39.9ε (Mean = 1.17ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RJ: 2 Equal Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.6ε (Mean = 0.0228ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.57ε (Mean = 0.754ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 220ε (Mean = 6.64ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 214ε (Mean = 5.28ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + RJ: Equal z and p + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.742ε (Mean = 0.0166ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.62ε (Mean = 0.699ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 17.2ε (Mean = 1.16ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 16.1ε (Mean = 1.14ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_erf"></a><p class="title"><b>Table 134. Error rates for erf</b></p> +<div class="table-contents"><table class="table" summary="Error rates for erf"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Erf Function: Small Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.925ε (Mean = 0.193ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 0.944ε (Mean = 0.191ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.944ε (Mean = 0.191ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.841ε (Mean = 0.0687ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.06ε (Mean = 0.319ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.925ε (Mean = 0.193ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.944ε (Mean = 0.194ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.996ε (Mean = 0.182ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.57ε (Mean = 0.317ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + Erf Function: Medium Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.5ε (Mean = 0.193ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 0.921ε (Mean = 0.0723ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.921ε (Mean = 0.0723ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1ε (Mean = 0.119ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2.31ε (Mean = 0.368ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.5ε (Mean = 0.197ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.921ε (Mean = 0.071ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1ε (Mean = 0.171ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> + Max = 1.19ε (Mean = 0.244ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + Erf Function: Large Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> + Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em><math.h>:</em></span> Max + = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> + Max = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> + Max = 0ε (Mean = 0ε)) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_erf_inv"></a><p class="title"><b>Table 135. Error rates for erf_inv</b></p> +<div class="table-contents"><table class="table" summary="Error rates for erf_inv"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Inverse Erf Function + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.996ε (Mean = 0.389ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.08ε (Mean = 0.395ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.09ε (Mean = 0.502ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_erfc"></a><p class="title"><b>Table 136. Error rates for erfc</b></p> +<div class="table-contents"><table class="table" summary="Error rates for erfc"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Erf Function: Small Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> + Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em><math.h>:</em></span> Max + = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.658ε (Mean = 0.0537ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.01ε (Mean = 0.485ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> + Max = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> + Max = 0ε (Mean = 0ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + Erf Function: Medium Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.76ε (Mean = 0.365ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.35ε (Mean = 0.307ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.35ε (Mean = 0.307ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.983ε (Mean = 0.213ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.64ε (Mean = 0.662ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.76ε (Mean = 0.38ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 2.81ε (Mean = 0.739ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.65ε (Mean = 0.373ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 2.36ε (Mean = 0.539ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + Erf Function: Large Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.57ε (Mean = 0.542ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.26ε (Mean = 0.441ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.26ε (Mean = 0.441ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.868ε (Mean = 0.147ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.9ε (Mean = 0.472ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.57ε (Mean = 0.564ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 4.91ε (Mean = 1.54ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.14ε (Mean = 0.248ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.84ε (Mean = 0.331ε)) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_erfc_inv"></a><p class="title"><b>Table 137. Error rates for erfc_inv</b></p> +<div class="table-contents"><table class="table" summary="Error rates for erfc_inv"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Inverse Erfc Function + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.996ε (Mean = 0.397ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.08ε (Mean = 0.403ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1ε (Mean = 0.491ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Inverse Erfc Function: extreme values + </p> + </td> +<td> + </td> +<td> + <p> + <span class="blue">Max = 1.62ε (Mean = 0.383ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.62ε (Mean = 0.383ε)</span> + </p> + </td> +<td> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_expint_Ei_"></a><p class="title"><b>Table 138. Error rates for expint (Ei)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for expint (Ei)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Exponential Integral Ei + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.05ε (Mean = 0.821ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 14.1ε (Mean = 2.43ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_expint_Ei___cmath__Exponential_Integral_Ei">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.994ε (Mean = 0.142ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.96ε (Mean = 0.703ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.05ε (Mean = 0.835ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.43ε (Mean = 0.54ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Exponential Integral Ei: double exponent range + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.72ε (Mean = 0.593ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 3.11ε (Mean = 1.13ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.998ε (Mean = 0.156ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.5ε (Mean = 0.612ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.72ε (Mean = 0.607ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.7ε (Mean = 0.66ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Exponential Integral Ei: long exponent range + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.98ε (Mean = 0.595ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.93ε (Mean = 0.855ε)) + </p> + </td> +<td> + </td> +<td> + <p> + <span class="blue">Max = 1.98ε (Mean = 0.575ε)</span> + </p> + </td> +<td> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_expint_En_"></a><p class="title"><b>Table 139. Error rates for expint (En)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for expint (En)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Exponential Integral En + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.589ε (Mean = 0.0331ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 58.5ε (Mean = 17.1ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.97ε (Mean = 2.13ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.97ε (Mean = 2.13ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.16ε (Mean = 1.85ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Exponential Integral En: small z values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 115ε (Mean = 23.6ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.99ε (Mean = 0.559ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.99ε (Mean = 0.559ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.62ε (Mean = 0.531ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Exponential Integral E1 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.556ε (Mean = 0.0625ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.988ε (Mean = 0.469ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.965ε (Mean = 0.414ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.965ε (Mean = 0.408ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.988ε (Mean = 0.486ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_expm1"></a><p class="title"><b>Table 140. Error rates for expm1</b></p> +<div class="table-contents"><table class="table" summary="Error rates for expm1"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Random test data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.992ε (Mean = 0.402ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 0.992ε (Mean = 0.402ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.992ε (Mean = 0.402ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.793ε (Mean = 0.126ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.793ε (Mean = 0.126ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.31ε (Mean = 0.428ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.996ε (Mean = 0.426ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.31ε (Mean = 0.496ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.31ε (Mean = 0.496ε)) + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_gamma_p"></a><p class="title"><b>Table 141. Error rates for gamma_p</b></p> +<div class="table-contents"><table class="table" summary="Error rates for gamma_p"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + tgamma(a, z) medium values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.955ε (Mean = 0.05ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 342ε (Mean = 45.8ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 389ε (Mean = 44ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 41.6ε (Mean = 8.09ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 239ε (Mean = 30.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 35.1ε (Mean = 6.98ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma(a, z) small values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 4.82ε (Mean = 0.758ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 1.01ε (Mean = 0.306ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2ε (Mean = 0.464ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2ε (Mean = 0.461ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.54ε (Mean = 0.439ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma(a, z) large values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.02e+03ε (Mean = 105ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 1.11e+03ε (Mean = 67.5ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.08e+04ε (Mean = 1.86e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.02e+04ε (Mean = 1.91e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 243ε (Mean = 20.2ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma(a, z) integer and half integer values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 128ε (Mean = 22.6ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 66.2ε (Mean = 12.2ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 11.8ε (Mean = 2.66ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 71.6ε (Mean = 9.47ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 13ε (Mean = 2.97ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_gamma_p_inv"></a><p class="title"><b>Table 142. Error rates for gamma_p_inv</b></p> +<div class="table-contents"><table class="table" summary="Error rates for gamma_p_inv"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + incomplete gamma inverse(a, z) medium values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.993ε (Mean = 0.15ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.88ε (Mean = 0.868ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.8ε (Mean = 0.406ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.89ε (Mean = 0.466ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.71ε (Mean = 0.34ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + incomplete gamma inverse(a, z) large values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 0.816ε (Mean = 0.0874ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.509ε (Mean = 0.0447ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.509ε (Mean = 0.0447ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.924ε (Mean = 0.108ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + incomplete gamma inverse(a, z) small values + </p> + </td> +<td> + <p> + <span class="blue">Max = 441ε (Mean = 53.9ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 547ε (Mean = 61.6ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.17e+03ε (Mean = 1.45e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.09e+04ε (Mean = 1.3e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.1e+03ε (Mean = 131ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_gamma_p_inva"></a><p class="title"><b>Table 143. Error rates for gamma_p_inva</b></p> +<div class="table-contents"><table class="table" summary="Error rates for gamma_p_inva"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Incomplete gamma inverses. + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.87ε (Mean = 1.15ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.08ε (Mean = 1.12ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.92ε (Mean = 1.03ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_gamma_q"></a><p class="title"><b>Table 144. Error rates for gamma_q</b></p> +<div class="table-contents"><table class="table" summary="Error rates for gamma_q"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + tgamma(a, z) medium values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.927ε (Mean = 0.035ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 201ε (Mean = 13.5ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 131ε (Mean = 12.7ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 32.3ε (Mean = 6.61ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 199ε (Mean = 26.6ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 23.7ε (Mean = 4ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma(a, z) small values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> <span class="red">Max = 1.38e+10ε (Mean = 1.05e+09ε))</span><br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 65.6ε (Mean = 11ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.45ε (Mean = 0.885ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.45ε (Mean = 0.819ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.26ε (Mean = 0.74ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma(a, z) large values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2.71e+04ε (Mean = 2.16e+03ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 1.02e+03ε (Mean = 62.7ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.82e+03ε (Mean = 414ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.15e+04ε (Mean = 733ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 469ε (Mean = 31.5ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma(a, z) integer and half integer values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 118ε (Mean = 12.5ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 138ε (Mean = 16.9ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 11.1ε (Mean = 2.07ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 54.7ε (Mean = 6.16ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.72ε (Mean = 1.48ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_gamma_q_inv"></a><p class="title"><b>Table 145. Error rates for gamma_q_inv</b></p> +<div class="table-contents"><table class="table" summary="Error rates for gamma_q_inv"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + incomplete gamma inverse(a, z) medium values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.912ε (Mean = 0.154ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.66ε (Mean = 0.792ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.2ε (Mean = 0.627ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.2ε (Mean = 0.683ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.88ε (Mean = 0.469ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + incomplete gamma inverse(a, z) large values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.894ε (Mean = 0.0915ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.894ε (Mean = 0.106ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.814ε (Mean = 0.0856ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + incomplete gamma inverse(a, z) small values + </p> + </td> +<td> + <p> + <span class="blue">Max = 292ε (Mean = 36.4ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 415ε (Mean = 48.7ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.28e+03ε (Mean = 1.09e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.98e+03ε (Mean = 877ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 451ε (Mean = 64.7ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_gamma_q_inva"></a><p class="title"><b>Table 146. Error rates for gamma_q_inva</b></p> +<div class="table-contents"><table class="table" summary="Error rates for gamma_q_inva"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Incomplete gamma inverses. + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.42ε (Mean = 1.3ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.86ε (Mean = 1.24ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.05ε (Mean = 1.08ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_hermite"></a><p class="title"><b>Table 147. Error rates for hermite</b></p> +<div class="table-contents"><table class="table" summary="Error rates for hermite"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Hermite Polynomials + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.24ε (Mean = 2.07ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.24ε (Mean = 2.07ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.46ε (Mean = 1.41ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_heuman_lambda"></a><p class="title"><b>Table 148. Error rates for heuman_lambda</b></p> +<div class="table-contents"><table class="table" summary="Error rates for heuman_lambda"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Elliptic Integral Jacobi Zeta: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.89ε (Mean = 0.887ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.89ε (Mean = 0.887ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.08ε (Mean = 0.734ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Elliptic Integral Heuman Lambda: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.82ε (Mean = 0.609ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.82ε (Mean = 0.608ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.12ε (Mean = 0.588ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_ibeta"></a><p class="title"><b>Table 149. Error rates for ibeta</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ibeta"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Incomplete Beta Function: Small Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 682ε (Mean = 32.6ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 22.9ε (Mean = 3.35ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.97ε (Mean = 2.09ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 21.3ε (Mean = 2.75ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.4ε (Mean = 1.93ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Incomplete Beta Function: Medium Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 690ε (Mean = 151ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 232ε (Mean = 27.9ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 50ε (Mean = 12.1ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 124ε (Mean = 18.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 106ε (Mean = 16.3ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Incomplete Beta Function: Large and Diverse Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.26ε (Mean = 0.063ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.9e+05ε (Mean = 1.82e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibeta_GSL_2_1_Incomplete_Beta_Function_Large_and_Diverse_Values">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 574ε (Mean = 49.4ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.96e+04ε (Mean = 997ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.98e+04ε (Mean = 2.07e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.32e+03ε (Mean = 68.5ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Incomplete Beta Function: Small Integer Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 254ε (Mean = 50.9ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 62.2ε (Mean = 8.95ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.45ε (Mean = 0.814ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 44.5ε (Mean = 10.1ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.85ε (Mean = 0.791ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_ibeta_inv"></a><p class="title"><b>Table 150. Error rates for ibeta_inv</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ibeta_inv"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Inverse incomplete beta + </p> + </td> +<td> + <p> + <span class="blue">Max = 11ε (Mean = 0.345ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.14e+121ε (Mean + = 3.28e+119ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibeta_inv_Rmath_3_2_3_Inverse_incomplete_beta">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.8e+04ε (Mean = 2.66e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.07e+04ε (Mean = 2.86e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.59e+03ε (Mean = 277ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_ibeta_inva"></a><p class="title"><b>Table 151. Error rates for ibeta_inva</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ibeta_inva"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Inverse incomplete beta + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.602ε (Mean = 0.0239ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 377ε (Mean = 24.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 438ε (Mean = 31.3ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 242ε (Mean = 22.9ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_ibeta_invb"></a><p class="title"><b>Table 152. Error rates for ibeta_invb</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ibeta_invb"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Inverse incomplete beta + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.765ε (Mean = 0.0422ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 407ε (Mean = 27.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 407ε (Mean = 24.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 409ε (Mean = 19.3ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_ibetac"></a><p class="title"><b>Table 153. Error rates for ibetac</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ibetac"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Incomplete Beta Function: Small Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 22.4ε (Mean = 3.67ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 10.6ε (Mean = 2.22ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 13.8ε (Mean = 2.68ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.94ε (Mean = 1.71ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Incomplete Beta Function: Medium Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 204ε (Mean = 25.8ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 73.9ε (Mean = 11.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 132ε (Mean = 19.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 56.7ε (Mean = 14.3ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Incomplete Beta Function: Large and Diverse Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.981ε (Mean = 0.0573ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 889ε (Mean = 68.4ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.45e+04ε (Mean = 1.32e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.31e+04ε (Mean = 2.04e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.88e+03ε (Mean = 82.7ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Incomplete Beta Function: Small Integer Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 84.6ε (Mean = 18ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.34ε (Mean = 1.11ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 107ε (Mean = 17.1ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.37ε (Mean = 1.03ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_ibetac_inv"></a><p class="title"><b>Table 154. Error rates for ibetac_inv</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ibetac_inv"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Inverse incomplete beta + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.977ε (Mean = 0.0976ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 3.01e+132ε (Mean + = 8.65e+130ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibetac_inv_Rmath_3_2_3_Inverse_incomplete_beta">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.88e+04ε (Mean = 3.16e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.05e+04ε (Mean = 3.33e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.93e+03ε (Mean = 198ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_ibetac_inva"></a><p class="title"><b>Table 155. Error rates for ibetac_inva</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ibetac_inva"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Inverse incomplete beta + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.683ε (Mean = 0.0314ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 382ε (Mean = 22.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 315ε (Mean = 23.7ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 408ε (Mean = 26.7ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_ibetac_invb"></a><p class="title"><b>Table 156. Error rates for ibetac_invb</b></p> +<div class="table-contents"><table class="table" summary="Error rates for ibetac_invb"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Inverse incomplete beta + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.724ε (Mean = 0.0303ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 317ε (Mean = 19.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 369ε (Mean = 22.6ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 271ε (Mean = 16.4ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_jacobi_cn"></a><p class="title"><b>Table 157. Error rates for jacobi_cn</b></p> +<div class="table-contents"><table class="table" summary="Error rates for jacobi_cn"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Jacobi Elliptic: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 17.3ε (Mean = 4.29ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 71.6ε (Mean = 19.3ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 71.6ε (Mean = 19.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 45.8ε (Mean = 11.4ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Jacobi Elliptic: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.816ε (Mean = 0.0563ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.43ε (Mean = 0.803ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.68ε (Mean = 0.443ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.68ε (Mean = 0.454ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.83ε (Mean = 0.455ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Jacobi Elliptic: Random Small Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 55.2ε (Mean = 1.64ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 10.4ε (Mean = 0.594ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 10.4ε (Mean = 0.602ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 26.2ε (Mean = 1.17ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Jacobi Elliptic: Modulus near 1 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.919ε (Mean = 0.127ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 675ε (Mean = 87.1ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 675ε (Mean = 86.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 513ε (Mean = 126ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Jacobi Elliptic: Large Phi + </p> + </td> +<td> + <p> + <span class="blue">Max = 14.2ε (Mean = 0.927ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 5.92e+03ε (Mean = 477ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.97e+04ε (Mean = 1.9e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.97e+04ε (Mean = 1.9e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.27e+04ε (Mean = 1.93e+03ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_jacobi_dn"></a><p class="title"><b>Table 158. Error rates for jacobi_dn</b></p> +<div class="table-contents"><table class="table" summary="Error rates for jacobi_dn"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Jacobi Elliptic: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2.82ε (Mean = 1.18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 49ε (Mean = 14ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 49ε (Mean = 14ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 34.3ε (Mean = 8.71ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Jacobi Elliptic: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 3ε (Mean = 0.61ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.53ε (Mean = 0.473ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.53ε (Mean = 0.481ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.52ε (Mean = 0.466ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Jacobi Elliptic: Random Small Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.5ε (Mean = 0.0122ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.5ε (Mean = 0.391ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 22.4ε (Mean = 0.777ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 22.4ε (Mean = 0.763ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 16.1ε (Mean = 0.685ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Jacobi Elliptic: Modulus near 1 + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.28ε (Mean = 0.194ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.75e+03ε (Mean = 293ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.75e+03ε (Mean = 293ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.24e+03ε (Mean = 482ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Jacobi Elliptic: Large Phi + </p> + </td> +<td> + <p> + <span class="blue">Max = 14.1ε (Mean = 0.897ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 121ε (Mean = 22ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.82e+04ε (Mean = 1.79e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.82e+04ε (Mean = 1.79e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.67e+04ε (Mean = 1e+03ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_jacobi_sn"></a><p class="title"><b>Table 159. Error rates for jacobi_sn</b></p> +<div class="table-contents"><table class="table" summary="Error rates for jacobi_sn"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Jacobi Elliptic: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 588ε (Mean = 146ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 341ε (Mean = 80.7ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 341ε (Mean = 80.7ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 481ε (Mean = 113ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Jacobi Elliptic: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 4.02ε (Mean = 1.07ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.01ε (Mean = 0.584ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.01ε (Mean = 0.593ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.92ε (Mean = 0.567ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Jacobi Elliptic: Random Small Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 11.7ε (Mean = 1.65ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.99ε (Mean = 0.347ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.99ε (Mean = 0.347ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.11ε (Mean = 0.385ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Jacobi Elliptic: Modulus near 1 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 109ε (Mean = 7.35ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 109ε (Mean = 7.38ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 23.2ε (Mean = 1.85ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Jacobi Elliptic: Large Phi + </p> + </td> +<td> + <p> + <span class="blue">Max = 12ε (Mean = 0.771ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.54e+04ε (Mean = 2.63e+03ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.45e+04ε (Mean = 1.51e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.45e+04ε (Mean = 1.51e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.36e+04ε (Mean = 2.54e+03ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_jacobi_zeta"></a><p class="title"><b>Table 160. Error rates for jacobi_zeta</b></p> +<div class="table-contents"><table class="table" summary="Error rates for jacobi_zeta"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Elliptic Integral Jacobi Zeta: Mathworld Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.66ε (Mean = 0.48ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.66ε (Mean = 0.48ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.52ε (Mean = 0.357ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Elliptic Integral Jacobi Zeta: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.99ε (Mean = 0.824ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.96ε (Mean = 1.06ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.89ε (Mean = 0.824ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Elliptic Integral Jacobi Zeta: Large Phi Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.92ε (Mean = 0.951ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.05ε (Mean = 1.13ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.52ε (Mean = 0.977ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_laguerre_n_m_x_"></a><p class="title"><b>Table 161. Error rates for laguerre(n, m, x)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for laguerre(n, m, x)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Associated Laguerre Polynomials + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.84ε (Mean = 0.0358ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 434ε (Mean = 10.7ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 167ε (Mean = 6.38ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 206ε (Mean = 6.86ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 167ε (Mean = 6.38ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 434ε (Mean = 11.1ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_laguerre_n_x_"></a><p class="title"><b>Table 162. Error rates for laguerre(n, x)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for laguerre(n, x)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Laguerre Polynomials + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.82ε (Mean = 0.408ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.1e+03ε (Mean = 185ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.39e+04ε (Mean = 828ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 4.2e+03ε (Mean = 251ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.39e+04ε (Mean = 828ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.1e+03ε (Mean = 185ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_legendre_p"></a><p class="title"><b>Table 163. Error rates for legendre_p</b></p> +<div class="table-contents"><table class="table" summary="Error rates for legendre_p"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Legendre Polynomials: Small Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.732ε (Mean = 0.0619ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 211ε (Mean = 20.4ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 69.2ε (Mean = 9.58ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 124ε (Mean = 13.2ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 69.2ε (Mean = 9.58ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 211ε (Mean = 20.4ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Legendre Polynomials: Large Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.632ε (Mean = 0.0693ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 300ε (Mean = 33.2ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 699ε (Mean = 59.6ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 343ε (Mean = 32.1ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 699ε (Mean = 59.6ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 300ε (Mean = 33.2ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_legendre_p_associated_"></a><p class="title"><b>Table 164. Error rates for legendre_p (associated)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for legendre_p (associated)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Associated Legendre Polynomials: Small Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.999ε (Mean = 0.05ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 121ε (Mean = 6.75ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_legendre_p_associated__GSL_2_1_Associated_Legendre_Polynomials_Small_Values">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 175ε (Mean = 9.88ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 175ε (Mean = 9.36ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_legendre_p_associated___cmath__Associated_Legendre_Polynomials_Small_Values">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 77.7ε (Mean = 5.59ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 121ε (Mean = 7.14ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_legendre_q"></a><p class="title"><b>Table 165. Error rates for legendre_q</b></p> +<div class="table-contents"><table class="table" summary="Error rates for legendre_q"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Legendre Polynomials: Small Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.612ε (Mean = 0.0517ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 46.4ε (Mean = 7.46ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 50.9ε (Mean = 9ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 50.9ε (Mean = 8.98ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 46.4ε (Mean = 7.32ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Legendre Polynomials: Large Values + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.49ε (Mean = 0.202ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.6e+03ε (Mean = 366ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.98e+03ε (Mean = 478ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.98e+03ε (Mean = 478ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.6e+03ε (Mean = 366ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_lgamma"></a><p class="title"><b>Table 166. Error rates for lgamma</b></p> +<div class="table-contents"><table class="table" summary="Error rates for lgamma"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + factorials + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 33.6ε (Mean = 2.78ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 1.55ε (Mean = 0.592ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.991ε (Mean = 0.308ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.67ε (Mean = 0.487ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.67ε (Mean = 0.487ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.991ε (Mean = 0.383ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.36ε (Mean = 0.476ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.914ε (Mean = 0.175ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.958ε (Mean = 0.38ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + near 0 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 5.21ε (Mean = 1.57ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.42ε (Mean = 0.566ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 0.964ε (Mean = 0.543ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.964ε (Mean = 0.543ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.42ε (Mean = 0.566ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.964ε (Mean = 0.543ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.964ε (Mean = 0.462ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.962ε (Mean = 0.372ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + near 1 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 442ε (Mean = 88.8ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 7.99e+04ε (Mean = 1.68e+04ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.948ε (Mean = 0.36ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 0.615ε (Mean = 0.096ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.615ε (Mean = 0.096ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.948ε (Mean = 0.36ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.71ε (Mean = 0.581ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.867ε (Mean = 0.468ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.906ε (Mean = 0.565ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + near 2 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.17e+03ε (Mean = 274ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 2.63e+05ε (Mean = 5.84e+04ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.878ε (Mean = 0.242ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 0.741ε (Mean = 0.263ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.741ε (Mean = 0.263ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.878ε (Mean = 0.242ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.598ε (Mean = 0.235ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.591ε (Mean = 0.159ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.741ε (Mean = 0.473ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + near -10 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 24.9ε (Mean = 4.6ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 4.22ε (Mean = 1.26ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.81ε (Mean = 1.01ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 0.997ε (Mean = 0.412ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.997ε (Mean = 0.412ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.81ε (Mean = 1.01ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 3.04ε (Mean = 1.01ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.22ε (Mean = 1.33ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.997ε (Mean = 0.444ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + near -55 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 7.02ε (Mean = 1.47ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 250ε (Mean = 60.9ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.821ε (Mean = 0.513ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.58ε (Mean = 0.672ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.58ε (Mean = 0.672ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.59ε (Mean = 0.587ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.821ε (Mean = 0.674ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.821ε (Mean = 0.419ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 249ε (Mean = 43.1ε)) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_log1p"></a><p class="title"><b>Table 167. Error rates for log1p</b></p> +<div class="table-contents"><table class="table" summary="Error rates for log1p"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Random test data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.818ε (Mean = 0.227ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 0.818ε (Mean = 0.227ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.818ε (Mean = 0.227ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.846ε (Mean = 0.153ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.846ε (Mean = 0.153ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.3ε (Mean = 0.66ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.818ε (Mean = 0.249ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.509ε (Mean = 0.057ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.509ε (Mean = 0.057ε)) + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_non_central_beta_CDF"></a><p class="title"><b>Table 168. Error rates for non central beta CDF</b></p> +<div class="table-contents"><table class="table" summary="Error rates for non central beta CDF"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Non Central Beta, medium parameters + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.998ε (Mean = 0.0649ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.46e+26ε (Mean + = 3.5e+24ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_medium_parameters">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 824ε (Mean = 27.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 832ε (Mean = 38.1ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 242ε (Mean = 31ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Non Central Beta, large parameters + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.18ε (Mean = 0.175ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.01e+36ε (Mean + = 1.19e+35ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_large_parameters">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.5e+04ε (Mean = 3.78e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.57e+04ε (Mean = 4.45e+03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.66e+03ε (Mean = 500ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_non_central_beta_CDF_complement"></a><p class="title"><b>Table 169. Error rates for non central beta CDF complement</b></p> +<div class="table-contents"><table class="table" summary="Error rates for non central beta CDF complement"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Non Central Beta, medium parameters + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.998ε (Mean = 0.0936ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 7.5e+97ε (Mean + = 1.37e+96ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_medium_parameters">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 396ε (Mean = 50.7ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 554ε (Mean = 57.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 624ε (Mean = 62.7ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Non Central Beta, large parameters + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.986ε (Mean = 0.188ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INFε (Mean + = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_large_parameters">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.83e+03ε (Mean = 993ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.56e+03ε (Mean = 707ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.25e+04ε (Mean = 1.49e+03ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_non_central_chi_squared_CDF"></a><p class="title"><b>Table 170. Error rates for non central chi squared CDF</b></p> +<div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Non Central Chi Squared, medium parameters + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.99ε (Mean = 0.0544ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 727ε (Mean = 121ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 46.5ε (Mean = 10.3ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 115ε (Mean = 13.9ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 48.9ε (Mean = 10ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Non Central Chi Squared, large parameters + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.07ε (Mean = 0.102ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 3.27e+08ε (Mean + = 2.23e+07ε))</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.07e+03ε (Mean = 336ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.17e+03ε (Mean = 677ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.79e+03ε (Mean = 723ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_non_central_chi_squared_CDF_complement"></a><p class="title"><b>Table 171. Error rates for non central chi squared CDF complement</b></p> +<div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF complement"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Non Central Chi Squared, medium parameters + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.96ε (Mean = 0.0635ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INFε (Mean + = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_medium_parameters">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 107ε (Mean = 17.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 171ε (Mean = 22.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 98.6ε (Mean = 15.8ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Non Central Chi Squared, large parameters + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.11ε (Mean = 0.278ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INFε (Mean + = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_large_parameters">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.02e+03ε (Mean = 630ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.1e+03ε (Mean = 577ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.43e+03ε (Mean = 705ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_non_central_t_CDF"></a><p class="title"><b>Table 172. Error rates for non central t CDF</b></p> +<div class="table-contents"><table class="table" summary="Error rates for non central t CDF"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Non Central T + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.796ε (Mean = 0.0691ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 5.28e+15ε (Mean + = 8.49e+14ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_Rmath_3_2_3_Non_Central_T">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 139ε (Mean = 31ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 145ε (Mean = 30.9ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 135ε (Mean = 32.1ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Non Central T (small non-centrality) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 2.09e+03ε (Mean = 244ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.86ε (Mean = 1.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.15ε (Mean = 2.13ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.17ε (Mean = 1.45ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Non Central T (large parameters) + </p> + </td> +<td> + <p> + <span class="blue">Max = 257ε (Mean = 72.1ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.46ε (Mean = 0.657ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.26e+05ε (Mean = 1.48e+05ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.24e+05ε (Mean = 1.47e+05ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 286ε (Mean = 62.8ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_non_central_t_CDF_complement"></a><p class="title"><b>Table 173. Error rates for non central t CDF complement</b></p> +<div class="table-contents"><table class="table" summary="Error rates for non central t CDF complement"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Non Central T + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.707ε (Mean = 0.0497ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 6.19e+15ε (Mean + = 6.72e+14ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_complement_Rmath_3_2_3_Non_Central_T">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 201ε (Mean = 31.7ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 340ε (Mean = 43.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 154ε (Mean = 32.1ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Non Central T (small non-centrality) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 1.87e+03ε (Mean = 263ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 10.5ε (Mean = 2.13ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 10.5ε (Mean = 2.39ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.6ε (Mean = 1.63ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Non Central T (large parameters) + </p> + </td> +<td> + <p> + <span class="blue">Max = 478ε (Mean = 96.3ε)</span><br> <br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.24ε (Mean = 0.945ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.79e+05ε (Mean = 1.97e+05ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.79e+05ε (Mean = 1.97e+05ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 227ε (Mean = 50.4ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_owens_t"></a><p class="title"><b>Table 174. Error rates for owens_t</b></p> +<div class="table-contents"><table class="table" summary="Error rates for owens_t"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Owens T (medium small values) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.34ε (Mean = 0.944ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.34ε (Mean = 0.911ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.37ε (Mean = 0.98ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Owens T (large and diverse values) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 49ε (Mean = 2.16ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 24.5ε (Mean = 1.39ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.78ε (Mean = 0.621ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_polygamma"></a><p class="title"><b>Table 175. Error rates for polygamma</b></p> +<div class="table-contents"><table class="table" summary="Error rates for polygamma"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Mathematica Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.824ε (Mean = 0.0574ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 62.9ε (Mean = 12.8ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 108ε (Mean = 15.2ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.38ε (Mean = 1.84ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 34.3ε (Mean = 7.65ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9.32ε (Mean = 1.95ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Mathematica Data - large arguments + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.998ε (Mean = 0.0592ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 244ε (Mean = 32.8ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_arguments">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + <span class="red">Max = 1.71e+56ε (Mean = 1.01e+55ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_arguments">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.23ε (Mean = 0.323ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 11.1ε (Mean = 0.848ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 150ε (Mean = 13.9ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Mathematica Data - negative arguments + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.516ε (Mean = 0.022ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 36.6ε (Mean = 3.04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_negative_arguments">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_negative_arguments">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 269ε (Mean = 87.7ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 269ε (Mean = 88.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 497ε (Mean = 129ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Mathematica Data - large negative arguments + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.79ε (Mean = 0.197ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_negative_arguments">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_negative_arguments">And + other failures.</a>) + </p> + </td> +<td> + <p> + <span class="blue">Max = 155ε (Mean = 96.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 155ε (Mean = 96.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 162ε (Mean = 101ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Mathematica Data - small arguments + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 15.2ε (Mean = 5.03ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 106ε (Mean = 20ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.33ε (Mean = 0.75ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.33ε (Mean = 0.75ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3ε (Mean = 0.496ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Mathematica Data - Large orders and other bug cases + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 151ε (Mean = 39.3ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_Large_orders_and_other_bug_cases">And + other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_Large_orders_and_other_bug_cases">And + other failures.</a>)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 54.5ε (Mean = 13.3ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 145ε (Mean = 55.9ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 200ε (Mean = 57.2ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_powm1"></a><p class="title"><b>Table 176. Error rates for powm1</b></p> +<div class="table-contents"><table class="table" summary="Error rates for powm1"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + powm1 + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.06ε (Mean = 0.425ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.04ε (Mean = 0.493ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.88ε (Mean = 0.49ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.84ε (Mean = 0.486ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_sin_pi"></a><p class="title"><b>Table 177. Error rates for sin_pi</b></p> +<div class="table-contents"><table class="table" summary="Error rates for sin_pi"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + sin_pi and cos_pi + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.996ε (Mean = 0.335ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.996ε (Mean = 0.336ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.99ε (Mean = 0.328ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + sin_pi and cos_pi near integers and half integers + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.976ε (Mean = 0.293ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.976ε (Mean = 0.293ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.996ε (Mean = 0.343ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_sph_bessel"></a><p class="title"><b>Table 178. Error rates for sph_bessel</b></p> +<div class="table-contents"><table class="table" summary="Error rates for sph_bessel"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Bessel j: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 243ε (Mean = 13.3ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.91e+06ε (Mean = 1.09e+05ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.978ε (Mean = 0.0445ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.79e+03ε (Mean = 107ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 243ε (Mean = 33.7ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 245ε (Mean = 16.3ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_sph_bessel_prime"></a><p class="title"><b>Table 179. Error rates for sph_bessel_prime</b></p> +<div class="table-contents"><table class="table" summary="Error rates for sph_bessel_prime"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Bessel j': Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.753ε (Mean = 0.0343ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 167ε (Mean = 12ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 167ε (Mean = 33.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 307ε (Mean = 25.2ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_sph_neumann"></a><p class="title"><b>Table 180. Error rates for sph_neumann</b></p> +<div class="table-contents"><table class="table" summary="Error rates for sph_neumann"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + y: Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 234ε (Mean = 19.5ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.6e+06ε (Mean = 1.4e+05ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.995ε (Mean = 0.0665ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.5e+04ε (Mean = 5.33e+03ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 234ε (Mean = 19.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 281ε (Mean = 31.1ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_sph_neumann_prime"></a><p class="title"><b>Table 181. Error rates for sph_neumann_prime</b></p> +<div class="table-contents"><table class="table" summary="Error rates for sph_neumann_prime"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + y': Random Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.988ε (Mean = 0.0869ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 158ε (Mean = 18.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 158ε (Mean = 20.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 296ε (Mean = 25.6ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_spherical_harmonic_i"></a><p class="title"><b>Table 182. Error rates for spherical_harmonic_i</b></p> +<div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_i"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Spherical Harmonics + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.36ε (Mean = 0.0765ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.89e+03ε (Mean = 108ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.03e+04ε (Mean = 327ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.27e+04ε (Mean = 725ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_spherical_harmonic_r"></a><p class="title"><b>Table 183. Error rates for spherical_harmonic_r</b></p> +<div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_r"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Spherical Harmonics + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.58ε (Mean = 0.0707ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.89e+03ε (Mean = 108ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.03e+04ε (Mean = 327ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.27e+04ε (Mean = 725ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_sqrt1pm1"></a><p class="title"><b>Table 184. Error rates for sqrt1pm1</b></p> +<div class="table-contents"><table class="table" summary="Error rates for sqrt1pm1"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + sqrt1pm1 + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.3ε (Mean = 0.404ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.33ε (Mean = 0.404ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.54ε (Mean = 0.563ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.35ε (Mean = 0.497ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_tgamma"></a><p class="title"><b>Table 185. Error rates for tgamma</b></p> +<div class="table-contents"><table class="table" summary="Error rates for tgamma"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + factorials + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 3.95ε (Mean = 0.783ε))<br> (<span class="emphasis"><em>Rmath + 3.2.3:</em></span> Max = 314ε (Mean = 93.4ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.67ε (Mean = 0.617ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.66ε (Mean = 0.584ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.66ε (Mean = 0.584ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 172ε (Mean = 41ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> + Max = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.85ε (Mean = 0.566ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 3.17ε (Mean = 0.928ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + near 0 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 4.51ε (Mean = 1.92ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 1ε (Mean = 0.335ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2ε (Mean = 0.608ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> + Max = 1ε (Mean = 0.376ε))<br> (<span class="emphasis"><em><math.h>:</em></span> + Max = 1ε (Mean = 0.376ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2ε (Mean = 0.647ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> + Max = 0.5ε (Mean = 0.0791ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.5ε (Mean = 0.635ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.405ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + near 1 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 4.41ε (Mean = 1.81ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 1ε (Mean = 0.32ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.51ε (Mean = 1.02ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 0.918ε (Mean = 0.203ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.918ε (Mean = 0.203ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.01ε (Mean = 1.06ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.175ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.1ε (Mean = 0.59ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.4ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + near 2 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 7.95ε (Mean = 3.12ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 1ε (Mean = 0.191ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.1ε (Mean = 1.55ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 0.558ε (Mean = 0.298ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.558ε (Mean = 0.298ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.01ε (Mean = 1.89ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2ε (Mean = 0.733ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> + Max = 0ε (Mean = 0ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + near -10 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 2.6ε (Mean = 1.05ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 34.9ε (Mean = 9.2ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.75ε (Mean = 0.895ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 2.26ε (Mean = 1.08ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 2.26ε (Mean = 1.08ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.75ε (Mean = 0.819ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.86ε (Mean = 0.881ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0.866ε (Mean = 0.445ε)) + </p> + </td> +</tr> +<tr> +<td> + <p> + near -55 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 1.8ε (Mean = 0.782ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> + Max = 3.89e+04ε (Mean = 9.52e+03ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.69ε (Mean = 1.09ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.79ε (Mean = 0.75ε))<br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 1.79ε (Mean = 0.75ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 98.5ε (Mean = 53.4ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.7ε (Mean = 1.35ε)</span><br> <br> + (<span class="emphasis"><em><math.h>:</em></span> Max = 3.87e+04ε (Mean = 6.71e+03ε)) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_tgamma1pm1"></a><p class="title"><b>Table 186. Error rates for tgamma1pm1</b></p> +<div class="table-contents"><table class="table" summary="Error rates for tgamma1pm1"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + tgamma1pm1(dz) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.12ε (Mean = 0.49ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.61ε (Mean = 0.84ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.31ε (Mean = 0.517ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_tgamma_delta_ratio"></a><p class="title"><b>Table 187. Error rates for tgamma_delta_ratio</b></p> +<div class="table-contents"><table class="table" summary="Error rates for tgamma_delta_ratio"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + tgamma + small delta ratios + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.83ε (Mean = 1.3ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 15.4ε (Mean = 2.09ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.56ε (Mean = 1.31ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma + small delta ratios (negative delta) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.94ε (Mean = 1.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 18.3ε (Mean = 2.03ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.43ε (Mean = 1.42ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma + small integer ratios + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.96ε (Mean = 0.677ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.96ε (Mean = 0.677ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.74ε (Mean = 0.736ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma + small integer ratios (negative delta) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.62ε (Mean = 0.451ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.62ε (Mean = 0.451ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.15ε (Mean = 0.685ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + integer tgamma ratios + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.997ε (Mean = 0.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.997ε (Mean = 0.4ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.968ε (Mean = 0.386ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + integer tgamma ratios (negative delta) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.853ε (Mean = 0.176ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.853ε (Mean = 0.176ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.974ε (Mean = 0.175ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_tgamma_incomplete_"></a><p class="title"><b>Table 188. Error rates for tgamma (incomplete)</b></p> +<div class="table-contents"><table class="table" summary="Error rates for tgamma (incomplete)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + tgamma(a, z) medium values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 200ε (Mean = 13.3ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.47ε (Mean = 1.9ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 412ε (Mean = 95.5ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 8.14ε (Mean = 1.76ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma(a, z) small values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.753ε (Mean = 0.0474ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> <span class="red">Max = 1.38e+10ε (Mean + = 1.05e+09ε))</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.31ε (Mean = 0.775ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.13ε (Mean = 0.717ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.53ε (Mean = 0.66ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma(a, z) integer and half integer values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 117ε (Mean = 12.5ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.52ε (Mean = 1.48ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 79.6ε (Mean = 20.9ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.16ε (Mean = 1.33ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_tgamma_lower"></a><p class="title"><b>Table 189. Error rates for tgamma_lower</b></p> +<div class="table-contents"><table class="table" summary="Error rates for tgamma_lower"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + tgamma(a, z) medium values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.833ε (Mean = 0.0315ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.833ε (Mean = 0.0315ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.79ε (Mean = 1.46ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 363ε (Mean = 63.8ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 5.62ε (Mean = 1.49ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma(a, z) small values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.97ε (Mean = 0.555ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.97ε (Mean = 0.558ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.57ε (Mean = 0.525ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma(a, z) integer and half integer values + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0ε (Mean = 0ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 4.83ε (Mean = 1.15ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 84.7ε (Mean = 17.5ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.69ε (Mean = 0.849ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_tgamma_ratio"></a><p class="title"><b>Table 190. Error rates for tgamma_ratio</b></p> +<div class="table-contents"><table class="table" summary="Error rates for tgamma_ratio"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + tgamma ratios + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.694ε (Mean = 0.0347ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 2.99ε (Mean = 1.15ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 174ε (Mean = 61.2ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 3.28ε (Mean = 1.12ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_trigamma"></a><p class="title"><b>Table 191. Error rates for trigamma</b></p> +<div class="table-contents"><table class="table" summary="Error rates for trigamma"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Mathematica Data + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.998ε (Mean = 0.105ε)</span><br> <br> + (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.34e+04ε (Mean = 1.49e+03ε))<br> + (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.34e+04ε (Mean = 1.51e+03ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.28ε (Mean = 0.449ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1.28ε (Mean = 0.449ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 1ε (Mean = 0.382ε)</span> + </p> + </td> +</tr></tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="special_function_error_rates_rep.all_the_tables.table_zeta"></a><p class="title"><b>Table 192. Error rates for zeta</b></p> +<div class="table-contents"><table class="table" summary="Error rates for zeta"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> long double + </p> + </th> +<th> + <p> + GNU C++ version 7.1.0<br> linux<br> double + </p> + </th> +<th> + <p> + Sun compiler version 0x5150<br> Sun Solaris<br> long double + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.1<br> Win32<br> double + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Zeta: Random values greater than 1 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.846ε (Mean = 0.0833ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 5.45ε (Mean = 1ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 8.69ε (Mean = 1.03ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.846ε (Mean = 0.0833ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.836ε (Mean = 0.093ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Zeta: Random values less than 1 + </p> + </td> +<td> + <p> + <span class="blue">Max = 7.03ε (Mean = 2.93ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 538ε (Mean = 59.3ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 137ε (Mean = 13.8ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 70.1ε (Mean = 17.1ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 6.84ε (Mean = 3.12ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Zeta: Values close to and greater than 1 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.995ε (Mean = 0.5ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 1.9e+06ε (Mean = 5.11e+05ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 7.73ε (Mean = 4.07ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.995ε (Mean = 0.5ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.994ε (Mean = 0.421ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Zeta: Values close to and less than 1 + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.998ε (Mean = 0.508ε)</span><br> <br> + (<span class="emphasis"><em><cmath>:</em></span> Max = 8.53e+06ε (Mean = 1.87e+06ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 0.991ε (Mean = 0.28ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.998ε (Mean = 0.508ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 0.991ε (Mean = 0.375ε)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Zeta: Integer arguments + </p> + </td> +<td> + <p> + <span class="blue">Max = 9ε (Mean = 3.06ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> + Max = 70.3ε (Mean = 17.4ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL + 2.1:</em></span> Max = 3.75ε (Mean = 1.1ε)) + </p> + </td> +<td> + <p> + <span class="blue">Max = 28ε (Mean = 5.62ε)</span> + </p> + </td> +<td> + <p> + <span class="blue">Max = 9ε (Mean = 3ε)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"><p><small>Last revised: March 09, 2018 at 13:43:44 GMT</small></p></td> +<td align="right"><div class="copyright-footer"></div></td> +</tr></table> +<hr> +<div class="spirit-nav"></div> +</body> +</html> diff --git a/src/boost/libs/math/reporting/accuracy/test_bessel_i.cpp b/src/boost/libs/math/reporting/accuracy/test_bessel_i.cpp new file mode 100644 index 000000000..877dc9772 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_bessel_i.cpp @@ -0,0 +1,63 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_bessel_i.hpp" +#include <boost/math/special_functions/bessel.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_bessel(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_bessel(0.0f, "float"); + if(test_double) + test_bessel(0.0, "double"); + if(test_long_double) + test_bessel(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_bessel(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_bessel_i_prime.cpp b/src/boost/libs/math/reporting/accuracy/test_bessel_i_prime.cpp new file mode 100644 index 000000000..70a454d46 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_bessel_i_prime.cpp @@ -0,0 +1,64 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error +#include "bindings.hpp" +#include "../../test/test_bessel_i_prime.hpp" +#include <boost/math/special_functions/bessel_prime.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_bessel(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_bessel(0.0f, "float"); + if(test_double) + test_bessel(0.0, "double"); + if(test_long_double) + test_bessel(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_bessel(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_bessel_j.cpp b/src/boost/libs/math/reporting/accuracy/test_bessel_j.cpp new file mode 100644 index 000000000..dd4cef2b5 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_bessel_j.cpp @@ -0,0 +1,63 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_bessel_j.hpp" +#include <boost/math/special_functions/bessel.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_bessel(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_bessel(0.0f, "float"); + if(test_double) + test_bessel(0.0, "double"); + if(test_long_double) + test_bessel(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_bessel(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_bessel_j_prime.cpp b/src/boost/libs/math/reporting/accuracy/test_bessel_j_prime.cpp new file mode 100644 index 000000000..b39020cbf --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_bessel_j_prime.cpp @@ -0,0 +1,64 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error +#include "bindings.hpp" +#include "../../test/test_bessel_j_prime.hpp" +#include <boost/math/special_functions/bessel_prime.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_bessel_prime(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_bessel_prime(0.0f, "float"); + if(test_double) + test_bessel_prime(0.0, "double"); + if(test_long_double) + test_bessel_prime(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_bessel_prime(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_bessel_k.cpp b/src/boost/libs/math/reporting/accuracy/test_bessel_k.cpp new file mode 100644 index 000000000..010555d67 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_bessel_k.cpp @@ -0,0 +1,63 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_bessel_k.hpp" +#include <boost/math/special_functions/bessel.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_bessel(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_bessel(0.0f, "float"); + if(test_double) + test_bessel(0.0, "double"); + if(test_long_double) + test_bessel(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_bessel(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_bessel_k_prime.cpp b/src/boost/libs/math/reporting/accuracy/test_bessel_k_prime.cpp new file mode 100644 index 000000000..7678b56a4 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_bessel_k_prime.cpp @@ -0,0 +1,64 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error +#include "bindings.hpp" +#include "../../test/test_bessel_k_prime.hpp" +#include <boost/math/special_functions/bessel_prime.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_bessel(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_bessel(0.0f, "float"); + if(test_double) + test_bessel(0.0, "double"); + if(test_long_double) + test_bessel(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_bessel(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_bessel_y.cpp b/src/boost/libs/math/reporting/accuracy/test_bessel_y.cpp new file mode 100644 index 000000000..684a1bb51 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_bessel_y.cpp @@ -0,0 +1,63 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_bessel_y.hpp" +#include <boost/math/special_functions/bessel.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_bessel(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_bessel(0.0f, "float"); + if(test_double) + test_bessel(0.0, "double"); + if(test_long_double) + test_bessel(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_bessel(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_bessel_y_prime.cpp b/src/boost/libs/math/reporting/accuracy/test_bessel_y_prime.cpp new file mode 100644 index 000000000..eff8b8bf7 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_bessel_y_prime.cpp @@ -0,0 +1,64 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error +#include "bindings.hpp" +#include "../../test/test_bessel_y_prime.hpp" +#include <boost/math/special_functions/bessel_prime.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_bessel_prime(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_bessel_prime(0.0f, "float"); + if(test_double) + test_bessel_prime(0.0, "double"); + if(test_long_double) + test_bessel_prime(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_bessel_prime(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_beta.cpp b/src/boost/libs/math/reporting/accuracy/test_beta.cpp new file mode 100644 index 000000000..7c9dbb1ad --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_beta.cpp @@ -0,0 +1,63 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_beta.hpp" +#include <boost/math/special_functions/beta.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_beta(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_beta(0.0f, "float"); + if(test_double) + test_beta(0.0, "double"); + if(test_long_double) + test_beta(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_beta(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_binomial_coeff.cpp b/src/boost/libs/math/reporting/accuracy/test_binomial_coeff.cpp new file mode 100644 index 000000000..cd79e9c8f --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_binomial_coeff.cpp @@ -0,0 +1,63 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_binomial_coeff.hpp" +#include <boost/math/special_functions/binomial.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_binomial(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_binomial(0.0f, "float"); + if(test_double) + test_binomial(0.0, "double"); + if(test_long_double) + test_binomial(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_binomial(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_carlson.cpp b/src/boost/libs/math/reporting/accuracy/test_carlson.cpp new file mode 100644 index 000000000..3a23a6fc6 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_carlson.cpp @@ -0,0 +1,67 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_carlson.hpp" +#include <boost/math/special_functions/ellint_rc.hpp> +#include <boost/math/special_functions/ellint_rg.hpp> +#include <boost/math/special_functions/ellint_rf.hpp> +#include <boost/math/special_functions/ellint_rd.hpp> +#include <boost/math/special_functions/ellint_rj.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_spots(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_spots(0.0f, "float"); + if(test_double) + test_spots(0.0, "double"); + if(test_long_double) + test_spots(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_spots(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_cbrt.cpp b/src/boost/libs/math/reporting/accuracy/test_cbrt.cpp new file mode 100644 index 000000000..35108c3e9 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_cbrt.cpp @@ -0,0 +1,66 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/cbrt.hpp> +#include "bindings.hpp" +#include "../../test/test_cbrt.hpp" + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_cbrt(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_cbrt(0.0f, "float"); + if(test_double) + test_cbrt(0.0, "double"); + if(test_long_double) + test_cbrt(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_cbrt(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_digamma.cpp b/src/boost/libs/math/reporting/accuracy/test_digamma.cpp new file mode 100644 index 000000000..a211bc66f --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_digamma.cpp @@ -0,0 +1,63 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_digamma.hpp" +#include <boost/math/special_functions/digamma.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_digamma(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_digamma(0.0f, "float"); + if(test_double) + test_digamma(0.0, "double"); + if(test_long_double) + test_digamma(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_digamma(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_ellint_1.cpp b/src/boost/libs/math/reporting/accuracy/test_ellint_1.cpp new file mode 100644 index 000000000..ab19f2725 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_ellint_1.cpp @@ -0,0 +1,63 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_ellint_1.hpp" +#include <boost/math/special_functions/ellint_1.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_spots(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_spots(0.0f, "float"); + if(test_double) + test_spots(0.0, "double"); + if(test_long_double) + test_spots(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_spots(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_ellint_2.cpp b/src/boost/libs/math/reporting/accuracy/test_ellint_2.cpp new file mode 100644 index 000000000..27b3f2177 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_ellint_2.cpp @@ -0,0 +1,63 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_ellint_2.hpp" +#include <boost/math/special_functions/ellint_2.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_spots(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_spots(0.0f, "float"); + if(test_double) + test_spots(0.0, "double"); + if(test_long_double) + test_spots(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_spots(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_ellint_3.cpp b/src/boost/libs/math/reporting/accuracy/test_ellint_3.cpp new file mode 100644 index 000000000..cfc5e98f9 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_ellint_3.cpp @@ -0,0 +1,63 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_ellint_3.hpp" +#include <boost/math/special_functions/ellint_3.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_spots(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_spots(0.0f, "float"); + if(test_double) + test_spots(0.0, "double"); + if(test_long_double) + test_spots(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_spots(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_ellint_d.cpp b/src/boost/libs/math/reporting/accuracy/test_ellint_d.cpp new file mode 100644 index 000000000..d06d0390d --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_ellint_d.cpp @@ -0,0 +1,63 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_ellint_d.hpp" +#include <boost/math/special_functions/ellint_d.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_spots(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_spots(0.0f, "float"); + if(test_double) + test_spots(0.0, "double"); + if(test_long_double) + test_spots(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_spots(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_erf.cpp b/src/boost/libs/math/reporting/accuracy/test_erf.cpp new file mode 100644 index 000000000..6edd6119c --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_erf.cpp @@ -0,0 +1,63 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/math/special_functions/erf.hpp> +#include "bindings.hpp" +#include "../../test/test_erf.hpp" + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_erf(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_erf(0.0f, "float"); + if(test_double) + test_erf(0.0, "double"); + if(test_long_double) + test_erf(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_erf(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_expint.cpp b/src/boost/libs/math/reporting/accuracy/test_expint.cpp new file mode 100644 index 000000000..adc3c406f --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_expint.cpp @@ -0,0 +1,63 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_expint.hpp" +#include <boost/math/special_functions/expint.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_expint(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_expint(0.0f, "float"); + if(test_double) + test_expint(0.0, "double"); + if(test_long_double) + test_expint(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_expint(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_gamma.cpp b/src/boost/libs/math/reporting/accuracy/test_gamma.cpp new file mode 100644 index 000000000..f7dbb3cb3 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_gamma.cpp @@ -0,0 +1,66 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/gamma.hpp> +#include "bindings.hpp" +#include "../../test/test_gamma.hpp" + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_gamma(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_gamma(0.0f, "float"); + if(test_double) + test_gamma(0.0, "double"); + if(test_long_double) + test_gamma(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_cbrt(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_hermite.cpp b/src/boost/libs/math/reporting/accuracy/test_hermite.cpp new file mode 100644 index 000000000..9c7c6d20b --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_hermite.cpp @@ -0,0 +1,63 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_hermite.hpp" +#include <boost/math/special_functions/hermite.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_hermite(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_hermite(0.0f, "float"); + if(test_double) + test_hermite(0.0, "double"); + if(test_long_double) + test_hermite(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_hermite(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_heuman_lambda.cpp b/src/boost/libs/math/reporting/accuracy/test_heuman_lambda.cpp new file mode 100644 index 000000000..64a61a7bd --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_heuman_lambda.cpp @@ -0,0 +1,63 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_heuman_lambda.hpp" +#include <boost/math/special_functions/heuman_lambda.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_spots(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_spots(0.0f, "float"); + if(test_double) + test_spots(0.0, "double"); + if(test_long_double) + test_spots(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_spots(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_ibeta.cpp b/src/boost/libs/math/reporting/accuracy/test_ibeta.cpp new file mode 100644 index 000000000..285049d4f --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_ibeta.cpp @@ -0,0 +1,63 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_ibeta.hpp" +#include <boost/math/special_functions/beta.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_beta(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_beta(0.0f, "float"); + if(test_double) + test_beta(0.0, "double"); + if(test_long_double) + test_beta(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_beta(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_ibeta_inv.cpp b/src/boost/libs/math/reporting/accuracy/test_ibeta_inv.cpp new file mode 100644 index 000000000..6abe55be4 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_ibeta_inv.cpp @@ -0,0 +1,63 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_ibeta_inv.hpp" +#include <boost/math/special_functions/beta.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_beta(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_beta(0.0f, "float"); + if(test_double) + test_beta(0.0, "double"); + if(test_long_double) + test_beta(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_beta(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_ibeta_inva.cpp b/src/boost/libs/math/reporting/accuracy/test_ibeta_inva.cpp new file mode 100644 index 000000000..ff2f290b1 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_ibeta_inva.cpp @@ -0,0 +1,63 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_ibeta_inv_ab.hpp" +#include <boost/math/special_functions/beta.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_beta(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_beta(0.0f, "float"); + if(test_double) + test_beta(0.0, "double"); + if(test_long_double) + test_beta(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_beta(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_igamma.cpp b/src/boost/libs/math/reporting/accuracy/test_igamma.cpp new file mode 100644 index 000000000..c4a4efccf --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_igamma.cpp @@ -0,0 +1,61 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_igamma.hpp" +#include <boost/math/special_functions/gamma.hpp> + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_gamma(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_gamma(0.0f, "float"); + if(test_double) + test_gamma(0.0, "double"); + if(test_long_double) + test_gamma(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_gamma(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_igamma_inv.cpp b/src/boost/libs/math/reporting/accuracy/test_igamma_inv.cpp new file mode 100644 index 000000000..aa96cd34b --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_igamma_inv.cpp @@ -0,0 +1,61 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_igamma_inv.hpp" +#include <boost/math/special_functions/gamma.hpp> + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_gamma(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_gamma(0.0f, "float"); + if(test_double) + test_gamma(0.0, "double"); + if(test_long_double) + test_gamma(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_gamma(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_igamma_inva.cpp b/src/boost/libs/math/reporting/accuracy/test_igamma_inva.cpp new file mode 100644 index 000000000..125b2141a --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_igamma_inva.cpp @@ -0,0 +1,63 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_igamma_inva.hpp" +#include <boost/math/special_functions/gamma.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_gamma(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_gamma(0.0f, "float"); + if(test_double) + test_gamma(0.0, "double"); + if(test_long_double) + test_gamma(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_gamma(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_jacobi.cpp b/src/boost/libs/math/reporting/accuracy/test_jacobi.cpp new file mode 100644 index 000000000..4c9650ae0 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_jacobi.cpp @@ -0,0 +1,63 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_jacobi.hpp" +#include <boost/math/special_functions/jacobi_elliptic.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_spots(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_spots(0.0f, "float"); + if(test_double) + test_spots(0.0, "double"); + if(test_long_double) + test_spots(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_spots(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_jacobi_zeta.cpp b/src/boost/libs/math/reporting/accuracy/test_jacobi_zeta.cpp new file mode 100644 index 000000000..7e31f1e5e --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_jacobi_zeta.cpp @@ -0,0 +1,63 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_jacobi_zeta.hpp" +#include <boost/math/special_functions/jacobi_zeta.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_spots(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_spots(0.0f, "float"); + if(test_double) + test_spots(0.0, "double"); + if(test_long_double) + test_spots(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_spots(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_laguerre.cpp b/src/boost/libs/math/reporting/accuracy/test_laguerre.cpp new file mode 100644 index 000000000..b59891bb3 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_laguerre.cpp @@ -0,0 +1,63 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_laguerre.hpp" +#include <boost/math/special_functions/laguerre.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_laguerre(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_laguerre(0.0f, "float"); + if(test_double) + test_laguerre(0.0, "double"); + if(test_long_double) + test_laguerre(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_laguerre(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_legendre.cpp b/src/boost/libs/math/reporting/accuracy/test_legendre.cpp new file mode 100644 index 000000000..4b080fb0a --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_legendre.cpp @@ -0,0 +1,63 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_legendre.hpp" +#include <boost/math/special_functions/legendre.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_legendre_p(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_legendre_p(0.0f, "float"); + if(test_double) + test_legendre_p(0.0, "double"); + if(test_long_double) + test_legendre_p(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_legendre_p(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_log1p_expm1.cpp b/src/boost/libs/math/reporting/accuracy/test_log1p_expm1.cpp new file mode 100644 index 000000000..24016e385 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_log1p_expm1.cpp @@ -0,0 +1,67 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error +#include "bindings.hpp" +#include "../../test/log1p_expm1_test.hpp" +#include <boost/math/special_functions/expm1.hpp> +#include <boost/math/special_functions/log1p.hpp> +#define BOOST_TEST_MAIN +#include <boost/test/unit_test.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test(0.0f, "float"); + if(test_double) + test(0.0, "double"); + if(test_long_double) + test(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_nc_beta.cpp b/src/boost/libs/math/reporting/accuracy/test_nc_beta.cpp new file mode 100644 index 000000000..6a23b923e --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_nc_beta.cpp @@ -0,0 +1,65 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#define BOOST_TEST_MAIN +#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error +#include "bindings.hpp" +#include "../../test/test_nc_beta.hpp" +#include <boost/test/unit_test.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_accuracy(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_accuracy(0.0f, "float"); + if(test_double) + test_accuracy(0.0, "double"); + if(test_long_double) + test_accuracy(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_accuracy(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_nc_chi_squared.cpp b/src/boost/libs/math/reporting/accuracy/test_nc_chi_squared.cpp new file mode 100644 index 000000000..03e226443 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_nc_chi_squared.cpp @@ -0,0 +1,65 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#define BOOST_TEST_MAIN +#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error +#include "bindings.hpp" +#include "../../test/test_nc_chi_squared.hpp" +#include <boost/test/unit_test.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_accuracy(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_accuracy(0.0f, "float"); + if(test_double) + test_accuracy(0.0, "double"); + if(test_long_double) + test_accuracy(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_accuracy(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_nc_t.cpp b/src/boost/libs/math/reporting/accuracy/test_nc_t.cpp new file mode 100644 index 000000000..cf6be89a5 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_nc_t.cpp @@ -0,0 +1,65 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#define BOOST_TEST_MAIN +#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error +#include "bindings.hpp" +#include "../../test/test_nc_t.hpp" +#include <boost/test/unit_test.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_accuracy(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_accuracy(0.0f, "float"); + if(test_double) + test_accuracy(0.0, "double"); + if(test_long_double) + test_accuracy(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_accuracy(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_owens_t.cpp b/src/boost/libs/math/reporting/accuracy/test_owens_t.cpp new file mode 100644 index 000000000..4aa790cab --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_owens_t.cpp @@ -0,0 +1,65 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#define BOOST_TEST_MAIN +#include "bindings.hpp" +#include "../../test/test_owens_t.hpp" +#include <boost/math/special_functions/owens_t.hpp> // for owens_t function. +#include <boost/test/unit_test.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_owens_t(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_owens_t(0.0f, "float"); + if(test_double) + test_owens_t(0.0, "double"); + if(test_long_double) + test_owens_t(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_owens_t(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_polygamma.cpp b/src/boost/libs/math/reporting/accuracy/test_polygamma.cpp new file mode 100644 index 000000000..e0447fe38 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_polygamma.cpp @@ -0,0 +1,63 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_polygamma.hpp" +#include <boost/math/special_functions/polygamma.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_polygamma(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_polygamma(0.0f, "float"); + if(test_double) + test_polygamma(0.0, "double"); + if(test_long_double) + test_polygamma(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_polygamma(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_powm1.cpp b/src/boost/libs/math/reporting/accuracy/test_powm1.cpp new file mode 100644 index 000000000..378a11d32 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_powm1.cpp @@ -0,0 +1,66 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#define BOOST_TEST_MAIN +#include "bindings.hpp" +#include "../../test/powm1_sqrtp1m1_test.hpp" +#include <boost/math/special_functions/powm1.hpp> +#include <boost/math/special_functions/sqrt1pm1.hpp> +#include <boost/test/unit_test.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_powm1_sqrtp1m1(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_powm1_sqrtp1m1(0.0f, "float"); + if(test_double) + test_powm1_sqrtp1m1(0.0, "double"); + if(test_long_double) + test_powm1_sqrtp1m1(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_powm1_sqrtp1m1(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_spherical_harmonic.cpp b/src/boost/libs/math/reporting/accuracy/test_spherical_harmonic.cpp new file mode 100644 index 000000000..fa1ebef4e --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_spherical_harmonic.cpp @@ -0,0 +1,65 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_spherical_harmonic.hpp" +#include <boost/math/special_functions/spherical_harmonic.hpp> +#define BOOST_TEST_MAIN +#include <boost/test/unit_test.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_spherical_harmonic(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_spherical_harmonic(0.0f, "float"); + if(test_double) + test_spherical_harmonic(0.0, "double"); + if(test_long_double) + test_spherical_harmonic(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_spherical_harmonic(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_tgamma_ratio.cpp b/src/boost/libs/math/reporting/accuracy/test_tgamma_ratio.cpp new file mode 100644 index 000000000..19673b374 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_tgamma_ratio.cpp @@ -0,0 +1,63 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_tgamma_ratio.hpp" +#include <boost/math/special_functions/gamma.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_tgamma_ratio(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_tgamma_ratio(0.0f, "float"); + if(test_double) + test_tgamma_ratio(0.0, "double"); + if(test_long_double) + test_tgamma_ratio(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_tgamma_ratio(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_trig.cpp b/src/boost/libs/math/reporting/accuracy/test_trig.cpp new file mode 100644 index 000000000..f5095179a --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_trig.cpp @@ -0,0 +1,64 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_trig.hpp" +#include <boost/math/special_functions/sin_pi.hpp> +#include <boost/math/special_functions/cos_pi.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_trig(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_trig(0.0f, "float"); + if(test_double) + test_trig(0.0, "double"); + if(test_long_double) + test_trig(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_trig(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_trigamma.cpp b/src/boost/libs/math/reporting/accuracy/test_trigamma.cpp new file mode 100644 index 000000000..33a2d063b --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_trigamma.cpp @@ -0,0 +1,63 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_trigamma.hpp" +#include <boost/math/special_functions/trigamma.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_trigamma(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_trigamma(0.0f, "float"); + if(test_double) + test_trigamma(0.0, "double"); + if(test_long_double) + test_trigamma(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_trigamma(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/test_zeta.cpp b/src/boost/libs/math/reporting/accuracy/test_zeta.cpp new file mode 100644 index 000000000..619d4350c --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/test_zeta.cpp @@ -0,0 +1,63 @@ +// Copyright John Maddock 2006-15. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "bindings.hpp" +#include "../../test/test_zeta.hpp" +#include <boost/math/special_functions/zeta.hpp> + +BOOST_AUTO_TEST_CASE_EXPECTED_FAILURES(test_main, 10000); + +BOOST_AUTO_TEST_CASE(test_main) +{ + BOOST_MATH_CONTROL_FP; + + error_stream_replacer rep; + +#ifdef TYPE_TO_TEST + + test_zeta(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST); + +#else + bool test_float = false; + bool test_double = false; + bool test_long_double = false; + + if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits) + { + // + // Don't bother with long double, it's the same as double: + // + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + test_double = true; + } + else + { + if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false) + test_float = true; + if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false) + test_double = true; + test_long_double = true; + } + +#ifdef ALWAYS_TEST_DOUBLE + test_double = true; +#endif + + if(test_float) + test_zeta(0.0f, "float"); + if(test_double) + test_zeta(0.0, "double"); + if(test_long_double) + test_zeta(0.0L, "long double"); +#ifdef BOOST_MATH_USE_FLOAT128 + //test_zeta(0.0Q, "__float128"); +#endif + + +#endif +} + diff --git a/src/boost/libs/math/reporting/accuracy/third_party/cephes_double/readme.txt b/src/boost/libs/math/reporting/accuracy/third_party/cephes_double/readme.txt new file mode 100644 index 000000000..f5f49d0b1 --- /dev/null +++ b/src/boost/libs/math/reporting/accuracy/third_party/cephes_double/readme.txt @@ -0,0 +1,7 @@ +Place the source for the Cephes double precision library here if you want bjam to +build and test it when reporting accuracy results. + +Copyright 2015 John Maddock and Paul A. Bristow. +Distributed under the Boost Software License, Version 1.0. +(See accompanying file LICENSE_1_0.txt or copy at +http://www.boost.org/LICENSE_1_0.txt). diff --git a/src/boost/libs/math/reporting/performance/Jamfile.v2 b/src/boost/libs/math/reporting/performance/Jamfile.v2 new file mode 100644 index 000000000..6ea5bc8a2 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/Jamfile.v2 @@ -0,0 +1,188 @@ +# Copyright Daryle Walker, Hubert Holin, John Maddock 2006 - 2007 +# copyright Paul A. Bristow 2006 - 2010 +# Distributed under the Boost Software License, Version 1.0. +# (See accompanying file LICENSE_1_0.txt or copy at +# http://www.boost.org/LICENSE_1_0.txt. +# \math_toolkit\libs\math\test\jamfile.v2 +# Runs all math toolkit tests, functions & distributions, +# and build math examples. + +# bring in the rules for testing +import testing ; +import modules ; +import path ; +import pch ; +import ../../../config/checks/config : requires ; +using quickbook ; +using auto-index ; + +import ../../../predef/check/predef + : check require + : predef-check predef-require ; + +project + : requirements + <include>../../include_private + ; + +if $(is_unix) +{ + local osname = [ SHELL uname ] ; + + switch $(osname) + { + case "Sun*" : OTHERFLAGS = "-lpthread -lrt" ; + case "*BSD*" : OTHERFLAGS = "-lpthread" ; + } +} + +# +# Configuration first: +# +lib gsl ; +lib gslcblas ; +lib Rmath ; +obj has_libstdcxx_tr1 : ../accuracy/has_libstdcxx_tr1.cpp ; +explicit has_libstdcxx_tr1 ; +obj has_c99_cmath : has_c99_cmath.cpp ; +explicit has_c99_cmath ; +exe has_gsl : has_gsl.cpp gsl gslcblas ; +explicit has_gsl ; +exe has_rmath : has_rmath.cpp Rmath ; +explicit has_rmath ; +obj is_intel_win : is_intel_win.cpp ; +explicit is_intel_win ; + +CEPHES_SOURCE = acosh.c airy.c asin.c asinh.c atan.c atanh.c bdtr.c beta.c +btdtr.c cbrt.c chbevl.c chdtr.c clog.c cmplx.c const.c +cosh.c dawsn.c drand.c ei.c ellie.c ellik.c ellpe.c ellpj.c ellpk.c +exp.c exp10.c exp2.c expn.c expx2.c fabs.c fac.c fdtr.c +fresnl.c gamma.c gdtr.c hyp2f1.c hyperg.c i0.c i1.c igami.c incbet.c +incbi.c igam.c isnan.c iv.c j0.c j1.c jn.c jv.c k0.c k1.c kn.c kolmogorov.c +log.c log2.c log10.c lrand.c nbdtr.c ndtr.c ndtri.c pdtr.c planck.c +polevl.c polmisc.c polylog.c polyn.c pow.c powi.c psi.c rgamma.c round.c +shichi.c sici.c sin.c sindg.c sinh.c spence.c stdtr.c struve.c +tan.c tandg.c tanh.c unity.c yn.c zeta.c zetac.c +sqrt.c floor.c setprec.c mtherr.c ; + +DCDFLIB_SOURCE = dcdflib.c ipmpar.c ; + +path-constant here : . ; +make $(here)/third_party/cephes_double/acosh.c : : @check_exists ; +make $(here)/third_party/dcdflib/dcdflib.c : : @check_exists ; +actions check_exists +{ + stat $(<) +} +explicit $(here)/third_party/cephes_double/acosh.c ; +explicit $(here)/third_party/dcdflib/dcdflib.c ; + +lib cephes_double : $(here)/third_party/cephes_double/$(CEPHES_SOURCE) + : + release + <link>static + [ check-target-builds $(here)/third_party/cephes_double/acosh.c : : <build>no ] + ; + +explicit cephes_double ; + +lib dcdflib : $(here)/third_party/dcdflib/$(DCDFLIB_SOURCE) + : + release + <link>static + [ check-target-builds $(here)/third_party/dcdflib/dcdflib.c : : <build>no ] + ; + +explicit dcdflib ; + +obj table_helper : table_helper.cpp ; + +rule all-tests { + local result ; + for local source in [ glob test*.cpp ] + { + result += [ run $(source) /boost/regex//boost_regex /boost/system /boost/chrono /boost/filesystem table_helper + : : : release <include>../../test + [ check-target-builds ../accuracy//has_c99_cmath : <define>TEST_C99 ] + [ check-target-builds has_libstdcxx_tr1 : <define>TEST_LIBSTDCXX ] + [ check-target-builds ../accuracy//has_gsl : <define>TEST_GSL <source>gsl <source>gslcblas ] + [ check-target-builds ../accuracy//has_rmath : <define>TEST_RMATH <source>Rmath ] + # [ check-target-builds is_intel_win : <build>no : ] + [ check-target-builds $(here)/third_party/dcdflib/dcdflib.c : <define>TEST_DCDFLIB <source>dcdflib ] + <target-os>linux:<linkflags>-lpthread <target-os>linux:<linkflags>-lrt + #<toolset>msvc:<address-model>64 + ] ; + } + return $(result) ; +} + +# +# Special cases to test different compiler options, +# cbrt first as an example of a trivial function: +# +run test_cbrt.cpp /boost/regex//boost_regex /boost/system /boost/chrono /boost/filesystem table_helper + : : : debug <define>COMPILER_COMPARISON_TABLES [ predef-require "BOOST_COMP_MSVC" ] <address-model>32 : test_cbrt_msvc_debug ; +run test_cbrt.cpp /boost/regex//boost_regex /boost/system /boost/chrono /boost/filesystem table_helper + : : : release <define>COMPILER_COMPARISON_TABLES [ predef-require "BOOST_COMP_MSVC" ] <cxxflags>-Ox <address-model>32 : test_cbrt_msvc_release_32 ; +run test_cbrt.cpp /boost/regex//boost_regex /boost/system /boost/chrono /boost/filesystem table_helper + : : : release <define>COMPILER_COMPARISON_TABLES [ predef-require "BOOST_COMP_MSVC" ] <cxxflags>-Ox <address-model>64 : test_cbrt_msvc_release_64 ; +run test_cbrt.cpp /boost/regex//boost_regex /boost/system /boost/chrono /boost/filesystem table_helper + : : : release <define>COMPILER_COMPARISON_TABLES [ check-target-builds is_intel_win : : <build>no ] <toolset>intel:<cxxflags>-Ox <address-model>64 : test_cbrt_intel_release ; +# +# Now jn as a little more complex: +# +run test_jn.cpp /boost/regex//boost_regex /boost/system /boost/chrono /boost/filesystem table_helper + : : : debug <define>COMPILER_COMPARISON_TABLES <include>../../test [ predef-require "BOOST_COMP_MSVC" ] <address-model>32 : test_jn_msvc_debug ; +run test_jn.cpp /boost/regex//boost_regex /boost/system /boost/chrono /boost/filesystem table_helper + : : : release <define>COMPILER_COMPARISON_TABLES <include>../../test [ predef-require "BOOST_COMP_MSVC" ] <cxxflags>-Ox <address-model>32 : test_jn_msvc_release_32 ; +run test_jn.cpp /boost/regex//boost_regex /boost/system /boost/chrono /boost/filesystem table_helper + : : : release <define>COMPILER_COMPARISON_TABLES <include>../../test [ predef-require "BOOST_COMP_MSVC" ] <cxxflags>-Ox <address-model>64 : test_jn_msvc_release_64 ; +run test_jn.cpp /boost/regex//boost_regex /boost/system /boost/chrono /boost/filesystem table_helper + : : : release <define>COMPILER_COMPARISON_TABLES <include>../../test [ check-target-builds is_intel_win : : <build>no ] <address-model>64 : test_jn_intel_release ; +# +# Then something really expensive, like the inverse-incomplete-beta: +# +run test_ibeta_inv.cpp /boost/regex//boost_regex /boost/system /boost/chrono /boost/filesystem table_helper + : : : debug <define>COMPILER_COMPARISON_TABLES <include>../../test [ predef-require "BOOST_COMP_MSVC" ] <address-model>32 : test_ibeta_inv_msvc_debug ; +run test_ibeta_inv.cpp /boost/regex//boost_regex /boost/system /boost/chrono /boost/filesystem table_helper + : : : release <define>COMPILER_COMPARISON_TABLES <include>../../test [ predef-require "BOOST_COMP_MSVC" ] <cxxflags>-Ox <address-model>32 : test_ibeta_inv_msvc_release_32 ; +run test_ibeta_inv.cpp /boost/regex//boost_regex /boost/system /boost/chrono /boost/filesystem table_helper + : : : release <define>COMPILER_COMPARISON_TABLES <include>../../test [ predef-require "BOOST_COMP_MSVC" ] <cxxflags>-Ox <address-model>64 : test_ibeta_inv_msvc_release_64 ; +run test_ibeta_inv.cpp /boost/regex//boost_regex /boost/system /boost/chrono /boost/filesystem table_helper + : : : release <define>COMPILER_COMPARISON_TABLES <include>../../test [ check-target-builds is_intel_win : : <build>no ] <toolset>intel:<cxxflags>-Ox <address-model>64 : test_ibeta_inv_intel_release ; + +test-suite report_gen : [ all-tests ] test_cbrt_msvc_debug test_cbrt_msvc_release_32 test_cbrt_msvc_release_64 test_cbrt_intel_release + test_jn_msvc_debug test_jn_msvc_release_32 test_jn_msvc_release_64 test_jn_intel_release test_ibeta_inv_msvc_debug + test_ibeta_inv_msvc_release_32 test_ibeta_inv_msvc_release_64 test_ibeta_inv_intel_release ; + +path-constant images_location : html ; +path-constant here : . ; + +xml report : doc/report.qbk : <dependency>report_gen ; +boostbook standalone + : + report + : + # Path for links to Boost: + <xsl:param>boost.root=../../../../.. + + # Some general style settings: + <xsl:param>table.footnote.number.format=1 + <xsl:param>footnote.number.format=1 + <xsl:param>html.stylesheet=boostbook.css + + # HTML options first: + # Use graphics not text for navigation: + <xsl:param>navig.graphics=1 + # How far down we chunk nested sections, basically all of them: + <xsl:param>chunk.section.depth=0 + # Don't put the first section on the same page as the TOC: + <xsl:param>chunk.first.sections=0 + # How far down sections get TOC's + <xsl:param>toc.section.depth=2 + # Max depth in each TOC: + <xsl:param>toc.max.depth=4 + # How far down we go with TOC's + <xsl:param>generate.section.toc.level=10 + ; + diff --git a/src/boost/libs/math/reporting/performance/fibonacci.hpp b/src/boost/libs/math/reporting/performance/fibonacci.hpp new file mode 100644 index 000000000..cc5895b8f --- /dev/null +++ b/src/boost/libs/math/reporting/performance/fibonacci.hpp @@ -0,0 +1,1245 @@ +// Copyright (c) 2015 John Maddock +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#pragma once + +#include <vector> +#include <boost/multiprecision/cpp_int.hpp> +#include <boost/lexical_cast.hpp> + +template <class T> +std::vector<T> const& fibonacci_numbers(const boost::integral_constant<int, 16>&) +{ + static const boost::uint16_t numbers[] = { + static_cast<boost::uint16_t>(21u), + static_cast<boost::uint16_t>(34u), + static_cast<boost::uint16_t>(55u), + static_cast<boost::uint16_t>(89u), + static_cast<boost::uint16_t>(144u), + static_cast<boost::uint16_t>(233u), + static_cast<boost::uint16_t>(377u), + static_cast<boost::uint16_t>(610u), + static_cast<boost::uint16_t>(987u), + static_cast<boost::uint16_t>(1597u), + static_cast<boost::uint16_t>(2584u), + static_cast<boost::uint16_t>(4181u), + static_cast<boost::uint16_t>(6765u), + static_cast<boost::uint16_t>(17711u), + static_cast<boost::uint16_t>(10946u), + static_cast<boost::uint16_t>(17711u), + static_cast<boost::uint16_t>(28657u), + static_cast<boost::uint16_t>(46368u) + }; + static const std::vector<T> data(numbers, numbers + sizeof(numbers) / sizeof(numbers[0])); + + return data; +} + +template <class T> +std::vector<T> const& fibonacci_numbers(const boost::integral_constant<int, 32>&) +{ + static const boost::uint32_t numbers[] = { + 21u, + 34u, + 55u, + 89u, + 144u, + 233u, + 377u, + 610u, + 987u, + 1597u, + 2584u, + 4181u, + 6765u, + 10946u, + 17711u, + 28657u, + 46368u, + 75025u, + 121393u, + 196418u, + 317811u, + 514229u, + 832040u, + 1346269u, + 2178309u, + 3524578u, + 5702887u, + 9227465u, + 14930352u, + 24157817u, + 39088169u, + 63245986u, + 102334155u, + 165580141u, + 267914296u, + 433494437u, + 701408733u, + 1134903170u, + 1836311903u, + 2971215073u + }; + static const std::vector<T> data(numbers, numbers + sizeof(numbers) / sizeof(numbers[0])); + + return data; +} + +template <class T> +std::vector<T> const& fibonacci_numbers(const boost::integral_constant<int, 64>&) +{ + static const boost::uint64_t numbers[] = { + 21uLL, + 34uLL, + 55uLL, + 89uLL, + 144uLL, + 233uLL, + 377uLL, + 610uLL, + 987uLL, + 1597uLL, + 2584uLL, + 4181uLL, + 6765uLL, + 10946uLL, + 17711uLL, + 28657uLL, + 46368uLL, + 75025uLL, + 121393uLL, + 196418uLL, + 317811uLL, + 514229uLL, + 832040uLL, + 1346269uLL, + 2178309uLL, + 3524578uLL, + 5702887uLL, + 9227465uLL, + 14930352uLL, + 24157817uLL, + 39088169uLL, + 63245986uLL, + 102334155uLL, + 165580141uLL, + 267914296uLL, + 433494437uLL, + 701408733uLL, + 1134903170uLL, + 1836311903uLL, + 2971215073uLL, + 4807526976uLL, + 7778742049uLL, + 12586269025uLL, + 20365011074uLL, + 32951280099uLL, + 53316291173uLL, + 86267571272uLL, + 139583862445uLL, + 225851433717uLL, + 365435296162uLL, + 591286729879uLL, + 956722026041uLL, + 1548008755920uLL, + 2504730781961uLL, + 4052739537881uLL, + 6557470319842uLL, + 10610209857723uLL, + 17167680177565uLL, + 27777890035288uLL, + 44945570212853uLL, + 72723460248141uLL, + 117669030460994uLL, + 190392490709135uLL, + 308061521170129uLL, + 498454011879264uLL, + 806515533049393uLL, + 1304969544928657uLL, + 2111485077978050uLL, + 3416454622906707uLL, + 5527939700884757uLL, + 8944394323791464uLL, + 14472334024676221uLL, + 23416728348467685uLL, + 37889062373143906uLL, + 61305790721611591uLL, + 99194853094755497uLL, + 160500643816367088uLL, + 259695496911122585uLL, + 420196140727489673uLL, + 679891637638612258uLL, + 1100087778366101931uLL, + 1779979416004714189uLL, + 2880067194370816120uLL, + 4660046610375530309uLL, + 7540113804746346429uLL, + 12200160415121876738uLL, + }; + static const std::vector<T> data(numbers, numbers + sizeof(numbers) / sizeof(numbers[0])); + + return data; +} + +template <class T> +std::vector<T> const& fibonacci_numbers(const boost::integral_constant<int, 0>&) +{ + static const T numbers[] = { + boost::lexical_cast<T>("21"), + boost::lexical_cast<T>("34"), + boost::lexical_cast<T>("55"), + boost::lexical_cast<T>("89"), + boost::lexical_cast<T>("144"), + boost::lexical_cast<T>("233"), + boost::lexical_cast<T>("377"), + boost::lexical_cast<T>("610"), + boost::lexical_cast<T>("987"), + boost::lexical_cast<T>("1597"), + boost::lexical_cast<T>("2584"), + boost::lexical_cast<T>("4181"), + boost::lexical_cast<T>("6765"), + boost::lexical_cast<T>("10946"), + boost::lexical_cast<T>("17711"), + boost::lexical_cast<T>("28657"), + boost::lexical_cast<T>("46368"), + boost::lexical_cast<T>("75025"), + boost::lexical_cast<T>("121393"), + boost::lexical_cast<T>("196418"), + boost::lexical_cast<T>("317811"), + boost::lexical_cast<T>("514229"), + boost::lexical_cast<T>("832040"), + boost::lexical_cast<T>("1346269"), + boost::lexical_cast<T>("2178309"), + boost::lexical_cast<T>("3524578"), + boost::lexical_cast<T>("5702887"), + boost::lexical_cast<T>("9227465"), + boost::lexical_cast<T>("14930352"), + boost::lexical_cast<T>("24157817"), + boost::lexical_cast<T>("39088169"), + boost::lexical_cast<T>("63245986"), + boost::lexical_cast<T>("102334155"), + boost::lexical_cast<T>("165580141"), + boost::lexical_cast<T>("267914296"), + boost::lexical_cast<T>("433494437"), + boost::lexical_cast<T>("701408733"), + boost::lexical_cast<T>("1134903170"), + boost::lexical_cast<T>("1836311903"), + boost::lexical_cast<T>("2971215073"), + // 64-bit: + boost::lexical_cast<T>("4807526976"), + boost::lexical_cast<T>("7778742049"), + boost::lexical_cast<T>("12586269025"), + boost::lexical_cast<T>("20365011074"), + boost::lexical_cast<T>("32951280099"), + boost::lexical_cast<T>("53316291173"), + boost::lexical_cast<T>("86267571272"), + boost::lexical_cast<T>("139583862445"), + boost::lexical_cast<T>("225851433717"), + boost::lexical_cast<T>("365435296162"), + boost::lexical_cast<T>("591286729879"), + boost::lexical_cast<T>("956722026041"), + boost::lexical_cast<T>("1548008755920"), + boost::lexical_cast<T>("2504730781961"), + boost::lexical_cast<T>("4052739537881"), + boost::lexical_cast<T>("6557470319842"), + boost::lexical_cast<T>("10610209857723"), + boost::lexical_cast<T>("17167680177565"), + boost::lexical_cast<T>("27777890035288"), + boost::lexical_cast<T>("44945570212853"), + boost::lexical_cast<T>("72723460248141"), + boost::lexical_cast<T>("117669030460994"), + boost::lexical_cast<T>("190392490709135"), + boost::lexical_cast<T>("308061521170129"), + boost::lexical_cast<T>("498454011879264"), + boost::lexical_cast<T>("806515533049393"), + boost::lexical_cast<T>("1304969544928657"), + boost::lexical_cast<T>("2111485077978050"), + boost::lexical_cast<T>("3416454622906707"), + boost::lexical_cast<T>("5527939700884757"), + boost::lexical_cast<T>("8944394323791464"), + boost::lexical_cast<T>("14472334024676221"), + boost::lexical_cast<T>("23416728348467685"), + boost::lexical_cast<T>("37889062373143906"), + boost::lexical_cast<T>("61305790721611591"), + boost::lexical_cast<T>("99194853094755497"), + boost::lexical_cast<T>("160500643816367088"), + boost::lexical_cast<T>("259695496911122585"), + boost::lexical_cast<T>("420196140727489673"), + boost::lexical_cast<T>("679891637638612258"), + boost::lexical_cast<T>("1100087778366101931"), + boost::lexical_cast<T>("1779979416004714189"), + boost::lexical_cast<T>("2880067194370816120"), + boost::lexical_cast<T>("4660046610375530309"), + boost::lexical_cast<T>("7540113804746346429"), + boost::lexical_cast<T>("12200160415121876738"), + // 128-bit: + boost::lexical_cast<T>("19740274219868223167"), + boost::lexical_cast<T>("31940434634990099905"), + boost::lexical_cast<T>("51680708854858323072"), + boost::lexical_cast<T>("83621143489848422977"), + boost::lexical_cast<T>("135301852344706746049"), + boost::lexical_cast<T>("218922995834555169026"), + boost::lexical_cast<T>("354224848179261915075"), + boost::lexical_cast<T>("573147844013817084101"), + boost::lexical_cast<T>("927372692193078999176"), + boost::lexical_cast<T>("1500520536206896083277"), + boost::lexical_cast<T>("2427893228399975082453"), + boost::lexical_cast<T>("3928413764606871165730"), + boost::lexical_cast<T>("6356306993006846248183"), + boost::lexical_cast<T>("10284720757613717413913"), + boost::lexical_cast<T>("16641027750620563662096"), + boost::lexical_cast<T>("26925748508234281076009"), + boost::lexical_cast<T>("43566776258854844738105"), + boost::lexical_cast<T>("70492524767089125814114"), + boost::lexical_cast<T>("114059301025943970552219"), + boost::lexical_cast<T>("184551825793033096366333"), + boost::lexical_cast<T>("298611126818977066918552"), + boost::lexical_cast<T>("483162952612010163284885"), + boost::lexical_cast<T>("781774079430987230203437"), + boost::lexical_cast<T>("1264937032042997393488322"), + boost::lexical_cast<T>("2046711111473984623691759"), + boost::lexical_cast<T>("3311648143516982017180081"), + boost::lexical_cast<T>("5358359254990966640871840"), + boost::lexical_cast<T>("8670007398507948658051921"), + boost::lexical_cast<T>("14028366653498915298923761"), + boost::lexical_cast<T>("22698374052006863956975682"), + boost::lexical_cast<T>("36726740705505779255899443"), + boost::lexical_cast<T>("59425114757512643212875125"), + boost::lexical_cast<T>("96151855463018422468774568"), + boost::lexical_cast<T>("155576970220531065681649693"), + boost::lexical_cast<T>("251728825683549488150424261"), + boost::lexical_cast<T>("407305795904080553832073954"), + boost::lexical_cast<T>("659034621587630041982498215"), + boost::lexical_cast<T>("1066340417491710595814572169"), + boost::lexical_cast<T>("1725375039079340637797070384"), + boost::lexical_cast<T>("2791715456571051233611642553"), + boost::lexical_cast<T>("4517090495650391871408712937"), + boost::lexical_cast<T>("7308805952221443105020355490"), + boost::lexical_cast<T>("11825896447871834976429068427"), + boost::lexical_cast<T>("19134702400093278081449423917"), + boost::lexical_cast<T>("30960598847965113057878492344"), + boost::lexical_cast<T>("50095301248058391139327916261"), + boost::lexical_cast<T>("81055900096023504197206408605"), + boost::lexical_cast<T>("131151201344081895336534324866"), + boost::lexical_cast<T>("212207101440105399533740733471"), + boost::lexical_cast<T>("343358302784187294870275058337"), + boost::lexical_cast<T>("555565404224292694404015791808"), + boost::lexical_cast<T>("898923707008479989274290850145"), + boost::lexical_cast<T>("1454489111232772683678306641953"), + boost::lexical_cast<T>("2353412818241252672952597492098"), + boost::lexical_cast<T>("3807901929474025356630904134051"), + boost::lexical_cast<T>("6161314747715278029583501626149"), + boost::lexical_cast<T>("9969216677189303386214405760200"), + boost::lexical_cast<T>("16130531424904581415797907386349"), + boost::lexical_cast<T>("26099748102093884802012313146549"), + boost::lexical_cast<T>("42230279526998466217810220532898"), + boost::lexical_cast<T>("68330027629092351019822533679447"), + boost::lexical_cast<T>("110560307156090817237632754212345"), + boost::lexical_cast<T>("178890334785183168257455287891792"), + boost::lexical_cast<T>("289450641941273985495088042104137"), + boost::lexical_cast<T>("468340976726457153752543329995929"), + boost::lexical_cast<T>("757791618667731139247631372100066"), + boost::lexical_cast<T>("1226132595394188293000174702095995"), + boost::lexical_cast<T>("1983924214061919432247806074196061"), + boost::lexical_cast<T>("3210056809456107725247980776292056"), + boost::lexical_cast<T>("5193981023518027157495786850488117"), + boost::lexical_cast<T>("8404037832974134882743767626780173"), + boost::lexical_cast<T>("13598018856492162040239554477268290"), + boost::lexical_cast<T>("22002056689466296922983322104048463"), + boost::lexical_cast<T>("35600075545958458963222876581316753"), + boost::lexical_cast<T>("57602132235424755886206198685365216"), + boost::lexical_cast<T>("93202207781383214849429075266681969"), + boost::lexical_cast<T>("150804340016807970735635273952047185"), + boost::lexical_cast<T>("244006547798191185585064349218729154"), + boost::lexical_cast<T>("394810887814999156320699623170776339"), + boost::lexical_cast<T>("638817435613190341905763972389505493"), + boost::lexical_cast<T>("1033628323428189498226463595560281832"), + boost::lexical_cast<T>("1672445759041379840132227567949787325"), + boost::lexical_cast<T>("2706074082469569338358691163510069157"), + boost::lexical_cast<T>("4378519841510949178490918731459856482"), + boost::lexical_cast<T>("7084593923980518516849609894969925639"), + boost::lexical_cast<T>("11463113765491467695340528626429782121"), + boost::lexical_cast<T>("18547707689471986212190138521399707760"), + boost::lexical_cast<T>("30010821454963453907530667147829489881"), + boost::lexical_cast<T>("48558529144435440119720805669229197641"), + boost::lexical_cast<T>("78569350599398894027251472817058687522"), + boost::lexical_cast<T>("127127879743834334146972278486287885163"), + boost::lexical_cast<T>("205697230343233228174223751303346572685"), + boost::lexical_cast<T>("332825110087067562321196029789634457848"), + boost::lexical_cast<T>("538522340430300790495419781092981030533"), + boost::lexical_cast<T>("871347450517368352816615810882615488381"), + boost::lexical_cast<T>("1409869790947669143312035591975596518914"), + boost::lexical_cast<T>("2281217241465037496128651402858212007295"), + boost::lexical_cast<T>("3691087032412706639440686994833808526209"), + boost::lexical_cast<T>("5972304273877744135569338397692020533504"), + boost::lexical_cast<T>("9663391306290450775010025392525829059713"), + boost::lexical_cast<T>("15635695580168194910579363790217849593217"), + boost::lexical_cast<T>("25299086886458645685589389182743678652930"), + boost::lexical_cast<T>("40934782466626840596168752972961528246147"), + boost::lexical_cast<T>("66233869353085486281758142155705206899077"), + boost::lexical_cast<T>("107168651819712326877926895128666735145224"), + boost::lexical_cast<T>("173402521172797813159685037284371942044301"), + boost::lexical_cast<T>("280571172992510140037611932413038677189525"), + boost::lexical_cast<T>("453973694165307953197296969697410619233826"), + boost::lexical_cast<T>("734544867157818093234908902110449296423351"), + boost::lexical_cast<T>("1188518561323126046432205871807859915657177"), + boost::lexical_cast<T>("1923063428480944139667114773918309212080528"), + boost::lexical_cast<T>("3111581989804070186099320645726169127737705"), + boost::lexical_cast<T>("5034645418285014325766435419644478339818233"), + boost::lexical_cast<T>("8146227408089084511865756065370647467555938"), + boost::lexical_cast<T>("13180872826374098837632191485015125807374171"), + boost::lexical_cast<T>("21327100234463183349497947550385773274930109"), + boost::lexical_cast<T>("34507973060837282187130139035400899082304280"), + boost::lexical_cast<T>("55835073295300465536628086585786672357234389"), + boost::lexical_cast<T>("90343046356137747723758225621187571439538669"), + boost::lexical_cast<T>("146178119651438213260386312206974243796773058"), + boost::lexical_cast<T>("236521166007575960984144537828161815236311727"), + boost::lexical_cast<T>("382699285659014174244530850035136059033084785"), + boost::lexical_cast<T>("619220451666590135228675387863297874269396512"), + boost::lexical_cast<T>("1001919737325604309473206237898433933302481297"), + boost::lexical_cast<T>("1621140188992194444701881625761731807571877809"), + boost::lexical_cast<T>("2623059926317798754175087863660165740874359106"), + boost::lexical_cast<T>("4244200115309993198876969489421897548446236915"), + boost::lexical_cast<T>("6867260041627791953052057353082063289320596021"), + boost::lexical_cast<T>("11111460156937785151929026842503960837766832936"), + boost::lexical_cast<T>("17978720198565577104981084195586024127087428957"), + boost::lexical_cast<T>("29090180355503362256910111038089984964854261893"), + boost::lexical_cast<T>("47068900554068939361891195233676009091941690850"), + boost::lexical_cast<T>("76159080909572301618801306271765994056795952743"), + boost::lexical_cast<T>("123227981463641240980692501505442003148737643593"), + boost::lexical_cast<T>("199387062373213542599493807777207997205533596336"), + boost::lexical_cast<T>("322615043836854783580186309282650000354271239929"), + boost::lexical_cast<T>("522002106210068326179680117059857997559804836265"), + boost::lexical_cast<T>("844617150046923109759866426342507997914076076194"), + boost::lexical_cast<T>("1366619256256991435939546543402365995473880912459"), + boost::lexical_cast<T>("2211236406303914545699412969744873993387956988653"), + boost::lexical_cast<T>("3577855662560905981638959513147239988861837901112"), + boost::lexical_cast<T>("5789092068864820527338372482892113982249794889765"), + boost::lexical_cast<T>("9366947731425726508977331996039353971111632790877"), + boost::lexical_cast<T>("15156039800290547036315704478931467953361427680642"), + boost::lexical_cast<T>("24522987531716273545293036474970821924473060471519"), + boost::lexical_cast<T>("39679027332006820581608740953902289877834488152161"), + boost::lexical_cast<T>("64202014863723094126901777428873111802307548623680"), + boost::lexical_cast<T>("103881042195729914708510518382775401680142036775841"), + boost::lexical_cast<T>("168083057059453008835412295811648513482449585399521"), + boost::lexical_cast<T>("271964099255182923543922814194423915162591622175362"), + boost::lexical_cast<T>("440047156314635932379335110006072428645041207574883"), + boost::lexical_cast<T>("712011255569818855923257924200496343807632829750245"), + boost::lexical_cast<T>("1152058411884454788302593034206568772452674037325128"), + boost::lexical_cast<T>("1864069667454273644225850958407065116260306867075373"), + boost::lexical_cast<T>("3016128079338728432528443992613633888712980904400501"), + boost::lexical_cast<T>("4880197746793002076754294951020699004973287771475874"), + boost::lexical_cast<T>("7896325826131730509282738943634332893686268675876375"), + boost::lexical_cast<T>("12776523572924732586037033894655031898659556447352249"), + boost::lexical_cast<T>("20672849399056463095319772838289364792345825123228624"), + boost::lexical_cast<T>("33449372971981195681356806732944396691005381570580873"), + boost::lexical_cast<T>("54122222371037658776676579571233761483351206693809497"), + boost::lexical_cast<T>("87571595343018854458033386304178158174356588264390370"), + boost::lexical_cast<T>("141693817714056513234709965875411919657707794958199867"), + boost::lexical_cast<T>("229265413057075367692743352179590077832064383222590237"), + boost::lexical_cast<T>("370959230771131880927453318055001997489772178180790104"), + boost::lexical_cast<T>("600224643828207248620196670234592075321836561403380341"), + boost::lexical_cast<T>("971183874599339129547649988289594072811608739584170445"), + boost::lexical_cast<T>("1571408518427546378167846658524186148133445300987550786"), + boost::lexical_cast<T>("2542592393026885507715496646813780220945054040571721231"), + boost::lexical_cast<T>("4114000911454431885883343305337966369078499341559272017"), + boost::lexical_cast<T>("6656593304481317393598839952151746590023553382130993248"), + boost::lexical_cast<T>("10770594215935749279482183257489712959102052723690265265"), + boost::lexical_cast<T>("17427187520417066673081023209641459549125606105821258513"), + boost::lexical_cast<T>("28197781736352815952563206467131172508227658829511523778"), + boost::lexical_cast<T>("45624969256769882625644229676772632057353264935332782291"), + boost::lexical_cast<T>("73822750993122698578207436143903804565580923764844306069"), + boost::lexical_cast<T>("119447720249892581203851665820676436622934188700177088360"), + boost::lexical_cast<T>("193270471243015279782059101964580241188515112465021394429"), + boost::lexical_cast<T>("312718191492907860985910767785256677811449301165198482789"), + boost::lexical_cast<T>("505988662735923140767969869749836918999964413630219877218"), + boost::lexical_cast<T>("818706854228831001753880637535093596811413714795418360007"), + boost::lexical_cast<T>("1324695516964754142521850507284930515811378128425638237225"), + boost::lexical_cast<T>("2143402371193585144275731144820024112622791843221056597232"), + boost::lexical_cast<T>("3468097888158339286797581652104954628434169971646694834457"), + boost::lexical_cast<T>("5611500259351924431073312796924978741056961814867751431689"), + boost::lexical_cast<T>("9079598147510263717870894449029933369491131786514446266146"), + boost::lexical_cast<T>("14691098406862188148944207245954912110548093601382197697835"), + boost::lexical_cast<T>("23770696554372451866815101694984845480039225387896643963981"), + boost::lexical_cast<T>("38461794961234640015759308940939757590587318989278841661816"), + 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boost::lexical_cast<T>("2743817889319451230635546056054009544681084712771464890161362822678707313593236053503308379376927808216125619202744438745782564531197937665192801118797972726433426749681736"), + boost::lexical_cast<T>("4439590603858869180288980079727269710383226601574882557289218773109235779343341990738294004603210334397661407832357095801092424716112702801064428066697907999685333994717357"), + boost::lexical_cast<T>("7183408493178320410924526135781279255064311314346347447450581595787943092936578044241602383980138142613787027035101534546874989247310640466257229185495880726118760744399093"), + boost::lexical_cast<T>("11622999097037189591213506215508548965447537915921230004739800368897178872279920034979896388583348477011448434867458630347967413963423343267321657252193788725804094739116450"), + 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boost::lexical_cast<T>("883500839105108321488176730469533687771801170063443463474008794546134903135239255428108782427408863084498422836903676843731957402396845655555436941177518324607263075960973912"), + boost::lexical_cast<T>("1429534386761117496218850990648231216953367996806038580031624220600185789744424675546498909702825612297777197190134402501047224251346762776435775100647520636533096272723314165"), + boost::lexical_cast<T>("2313035225866225817707027721117764904725169166869482043505633015146320692879663930974607692130234475382275620027038079344779181653743608431991212041825038961140359348684288077"), + boost::lexical_cast<T>("3742569612627343313925878711765996121678537163675520623537257235746506482624088606521106601833060087680052817217172481845826405905090371208426987142472559597673455621407602242"), + 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boost::lexical_cast<T>("102098751241605365210994276911130356942241829717669088641675843357036577144651151663139927014083462234470205844005526668054605134051542095639503314608767192463861424988401337986848977992102593240"), + boost::lexical_cast<T>("165199249717838008158743058245780420215766768590131298708272645987824841020293881889311405773866850429566420076904922158529659340892491762955827899358214010685748100753200453335055149114435266869"), + boost::lexical_cast<T>("267298000959443373369737335156910777158008598307800387349948489344861418164945033552451332787950312664036625920910448826584264474944033858595331213966981203149609525741601791321904127106537860109"), + boost::lexical_cast<T>("432497250677281381528480393402691197373775366897931686058221135332686259185238915441762738561817163093603045997815370985113923815836525621551159113325195213835357626494802244656959276220973126978"), + boost::lexical_cast<T>("699795251636724754898217728559601974531783965205732073408169624677547677350183948994214071349767475757639671918725819811698188290780559480146490327292176416984967152236404035978863403327510987087"), + boost::lexical_cast<T>("1132292502314006136426698121962293171905559332103663759466390760010233936535422864435976809911584638851242717916541190796812112106617085101697649440617371630820324778731206280635822679548484114065"), + boost::lexical_cast<T>("1832087753950730891324915850521895146437343297309395832874560384687781613885606813430190881261352114608882389835267010608510300397397644581844139767909548047805291930967610316614686082875995101152"), + boost::lexical_cast<T>("2964380256264737027751613972484188318342902629413059592340951144698015550421029677866167691172936753460125107751808201405322412504014729683541789208526919678625616709698816597250508762424479215217"), + boost::lexical_cast<T>("4796468010215467919076529823006083464780245926722455425215511529385797164306636491296358572434288868069007497587075212013832712901412374265385928976436467726430908640666426913865194845300474316369"), + boost::lexical_cast<T>("7760848266480204946828143795490271783123148556135515017556462674083812714727666169162526263607225621529132605338883413419155125405427103948927718184963387405056525350365243511115703607724953531586"), + boost::lexical_cast<T>("12557316276695672865904673618496355247903394482857970442771974203469609879034302660458884836041514489598140102925958625432987838306839478214313647161399855131487433991031670424980898453025427847955"), + boost::lexical_cast<T>("20318164543175877812732817413986627031026543038993485460328436877553422593761968829621411099648740111127272708264842038852142963712266582163241365346363242536543959341396913936096602060750381379541"), + boost::lexical_cast<T>("32875480819871550678637491032482982278929937521851455903100411081023032472796271490080295935690254600725412811190800664285130802019106060377555012507763097668031393332428584361077500513775809227496"), + boost::lexical_cast<T>("53193645363047428491370308446469609309956480560844941363428847958576455066558240319701707035338994711852685519455642703137273765731372642540796377854126340204575352673825498297174102574526190607037"), + boost::lexical_cast<T>("86069126182918979170007799478952591588886418082696397266529259039599487539354511809782002971029249312578098330646443367422404567750478702918351390361889437872606746006254082658251603088301999834533"), + boost::lexical_cast<T>("139262771545966407661378107925422200898842898643541338629958106998175942605912752129483710006368244024430783850102086070559678333481851345459147768216015778077182098680079580955425705662828190441570"), + boost::lexical_cast<T>("225331897728885386831385907404374792487729316726237735896487366037775430145267263939265712977397493337008882180748529437982082901232330048377499158577905215949788844686333663613677308751130190276103"), + boost::lexical_cast<T>("364594669274851794492764015329796993386572215369779074526445473035951372751180016068749422983765737361439666030850615508541761234714181393836646926793920994026970943366413244569103014413958380717673"), + boost::lexical_cast<T>("589926567003737181324149922734171785874301532096016810422932839073726802896447280008015135961163230698448548211599144946523844135946511442214146085371826209976759788052746908182780323165088570993776"), + boost::lexical_cast<T>("954521236278588975816913938063968779260873747465795884949378312109678175647627296076764558944928968059888214242449760455065605370660692836050793012165747204003730731419160152751883337579046951711449"), + boost::lexical_cast<T>("1544447803282326157141063860798140565135175279561812695372311151183404978544074576084779694906092198758336762454048905401589449506607204278264939097537573413980490519471907060934663660744135522705225"), + boost::lexical_cast<T>("2498969039560915132957977798862109344396049027027608580321689463293083154191701872161544253851021166818224976696498665856655054877267897114315732109703320617984221250891067213686546998323182474416674"), + boost::lexical_cast<T>("4043416842843241290099041659660249909531224306589421275694000614476488132735776448246323948757113365576561739150547571258244504383875101392580671207240894031964711770362974274621210659067317997121899"), + boost::lexical_cast<T>("6542385882404156423057019458522359253927273333617029856015690077769571286927478320407868202608134532394786715847046237114899559261142998506896403316944214649948933021254041488307757657390500471538573"), + boost::lexical_cast<T>("10585802725247397713156061118182609163458497640206451131709690692246059419663254768654192151365247897971348454997593808373144063645018099899477074524185108681913644791617015762928968316457818468660472"), + boost::lexical_cast<T>("17128188607651554136213080576704968417385770973823480987725380770015630706590733089062060353973382430366135170844640045488043622906161098406373477841129323331862577812871057251236725973848318940199045"), + boost::lexical_cast<T>("27713991332898951849369141694887577580844268614029932119435071462261690126253987857716252505338630328337483625842233853861187686551179198305850552365314432013776222604488073014165694290306137408859517"), + boost::lexical_cast<T>("44842179940550505985582222271592545998230039587853413107160452232277320832844720946778312859312012758703618796686873899349231309457340296712224030206443755345638800417359130265402420264154456349058562"), + boost::lexical_cast<T>("72556171273449457834951363966480123579074308201883345226595523694539010959098708804494565364650643087041102422529107753210418996008519495018074582571758187359415023021847203279568114554460593757918079"), + boost::lexical_cast<T>("117398351213999963820533586238072669577304347789736758333755975926816331791943429751272878223962655845744721219215981652559650305465859791730298612778201942705053823439206333544970534818615050106976641"), + boost::lexical_cast<T>("189954522487449421655484950204552793156378655991620103560351499621355342751042138555767443588613298932785823641745089405770069301474379286748373195349960130064468846461053536824538649373075643864894720"), + boost::lexical_cast<T>("307352873701449385476018536442625462733683003781356861894107475548171674542985568307040321812575954778530544860961071058329719606940239078478671808128162072769522669900259870369509184191690693971871361"), + boost::lexical_cast<T>("497307396188898807131503486647178255890061659772976965454458975169527017294027706862807765401189253711316368502706160464099788908414618365227045003478122202833991516361313407194047833564766337836766081"), + boost::lexical_cast<T>("804660269890348192607522023089803718623744663554333827348566450717698691837013275169848087213765208489846913363667231522429508515354857443705716811606284275603514186261573277563557017756457031808637442"), + boost::lexical_cast<T>("1301967666079246999739025509736981974513806323327310792803025425887225709131040982032655852614954462201163281866373391986529297423769475808932761815084406478437505702622886684757604851321223369645403523"), + boost::lexical_cast<T>("2106627935969595192346547532826785693137550986881644620151591876604924400968054257202503939828719670691010195230040623508958805939124333252638478626690690754041019888884459962321161869077680401454040965"), + boost::lexical_cast<T>("3408595602048842192085573042563767667651357310208955412954617302492150110099095239235159792443674132892173477096414015495488103362893809061571240441775097232478525591507346647078766720398903771099444488"), + boost::lexical_cast<T>("5515223538018437384432120575390553360788908297090600033106209179097074511067149496437663732272393803583183672326454639004446909302018142314209719068465787986519545480391806609399928589476584172553485453"), + boost::lexical_cast<T>("8923819140067279576517693617954321028440265607299555446060826481589224621166244735672823524716067936475357149422868654499935012664911951375780959510240885218998071071899153256478695309875487943652929941"), + boost::lexical_cast<T>("14439042678085716960949814193344874389229173904390155479167035660686299132233394232110487256988461740058540821749323293504381921966930093689990678578706673205517616552290959865878623899352072116206415394"), + boost::lexical_cast<T>("23362861818152996537467507811299195417669439511689710925227862142275523753399638967783310781704529676533897971172191948004316934631842045065771638088947558424515687624190113122357319209227560059859345335"), + boost::lexical_cast<T>("37801904496238713498417322004644069806898613416079866404394897802961822885633033199893798038692991416592438792921515241508698856598772138755762316667654231630033304176481072988235943108579632176065760729"), + boost::lexical_cast<T>("61164766314391710035884829815943265224568052927769577329622759945237346639032672167677108820397521093126336764093707189513015791230614183821533954756601790054548991800671186110593262317807192235925106064"), + boost::lexical_cast<T>("98966670810630423534302151820587335031466666343849443734017657748199169524665705367570906859090512509718775557015222431021714647829386322577296271424256021684582295977152259098829205426386824411990866793"), + boost::lexical_cast<T>("160131437125022133570186981636530600256034719271619021063640417693436516163698377535248015679488033602845112321108929620534730439060000506398830226180857811739131287777823445209422467744194016647915972857"), + boost::lexical_cast<T>("259098107935652557104489133457117935287501385615468464797658075441635685688364082902818922538578546112563887878124152051556445086889386828976126497605113833423713583754975704308251673170580841059906839650"), + boost::lexical_cast<T>("419229545060674690674676115093648535543536104887087485861298493135072201852062460438066938218066579715409000199233081672091175525949387335374956723785971645162844871532799149517674140914774857707822812507"), + boost::lexical_cast<T>("678327652996327247779165248550766470831037490502555950658956568576707887540426543340885860756645125827972888077357233723647620612838774164351083221391085478586558455287774853825925814085355698767729652157"), + boost::lexical_cast<T>("1097557198057001938453841363644415006374573595389643436520255061711780089392489003778952798974711705543381888276590315395738796138788161499726039945177057123749403326820574003343599955000130556475552464664"), + boost::lexical_cast<T>("1775884851053329186233006612195181477205611085892199387179211630288487976932915547119838659731356831371354776353947549119386416751626935664077123166568142602335961782108348857169525769085486255243282116821"), + boost::lexical_cast<T>("2873442049110331124686847975839596483580184681281842823699466692000268066325404550898791458706068536914736664630537864515125212890415097163803163111745199726085365108928922860513125724085616811718834581485"), + boost::lexical_cast<T>("4649326900163660310919854588034777960785795767174042210878678322288756043258320098018630118437425368286091440984485413634511629642042032827880286278313342328421326891037271717682651493171103066962116698306"), + boost::lexical_cast<T>("7522768949273991435606702563874374444365980448455885034578145014289024109583724648917421577143493905200828105615023278149636842532457129991683449390058542054506691999966194578195777217256719878680951279791"), + boost::lexical_cast<T>("12172095849437651746526557151909152405151776215629927245456823336577780152842044746936051695580919273486919546599508691784148472174499162819563735668371884382928018891003466295878428710427822945643067978097"), + boost::lexical_cast<T>("19694864798711643182133259715783526849517756664085812280034968350866804262425769395853473272724413178687747652214531969933785314706956292811247185058430426437434710890969660874074205927684542824324019257888"), + boost::lexical_cast<T>("31866960648149294928659816867692679254669532879715739525491791687444584415267814142789524968305332452174667198814040661717933786881455455630810920726802310820362729781973127169952634638112365769967087235985"), + boost::lexical_cast<T>("51561825446860938110793076583476206104187289543801551805526760038311388677693583538642998241029745630862414851028572631651719101588411748442058105785232737257797440672942788044026840565796908594291106493873"), + boost::lexical_cast<T>("83428786095010233039452893451168885358856822423517291331018551725755973092961397681432523209335078083037082049842613293369652888469867204072869026512035048078160170454915915213979475203909274364258193729858"), + boost::lexical_cast<T>("134990611541871171150245970034645091463044111967318843136545311764067361770654981220075521450364823713899496900871185925021371990058278952514927132297267785335957611127858703258006315769706182958549300223731"), + boost::lexical_cast<T>("218419397636881404189698863485813976821900934390836134467563863489823334863616378901508044659699901796936578950713799218391024878528146156587796158809302833414117781582774618471985790973615457322807493953589"), + boost::lexical_cast<T>("353410009178752575339944833520459068284945046358154977604109175253890696634271360121583566110064725510836075851584985143412396868586425109102723291106570618750075392710633321729992106743321640281356794177320"), + boost::lexical_cast<T>("571829406815633979529643697006273045106845980748991112071673038743714031497887739023091610769764627307772654802298784361803421747114571265690519449915873452164193174293407940201977897716937097604164288130909"), + boost::lexical_cast<T>("925239415994386554869588530526732113391791027107146089675782213997604728132159099144675176879829352818608730653883769505215818615700996374793242741022444070914268567004041261931970004460258737885521082308229"), + boost::lexical_cast<T>("1497068822810020534399232227533005158498637007856137201747455252741318759630046838167766787649593980126381385456182553867019240362815567640483762190938317523078461741297449202133947902177195835489685370439138"), + boost::lexical_cast<T>("2422308238804407089268820758059737271890428034963283291423237466738923487762205937312441964529423332944990116110066323372235058978516564015277004931960761593992730308301490464065917906637454573375206452747367"), + boost::lexical_cast<T>("3919377061614427623668052985592742430389065042819420493170692719480242247392252775480208752179017313071371501566248877239254299341332131655760767122899079117071192049598939666199865808814650408864891823186505"), + boost::lexical_cast<T>("6341685300418834712936873743652479702279493077782703784593930186219165735154458712792650716708440646016361617676315200611489358319848695671037772054859840711063922357900430130265783715452104982240098275933872"), + boost::lexical_cast<T>("10261062362033262336604926729245222132668558120602124277764622905699407982546711488272859468887457959087733119242564077850743657661180827326798539177758919828135114407499369796465649524266755391104990099120377"), + boost::lexical_cast<T>("16602747662452097049541800472897701834948051198384828062358553091918573717701170201065510185595898605104094736918879278462233015981029522997836311232618760539199036765399799926731433239718860373345088375054249"), + boost::lexical_cast<T>("26863810024485359386146727202142923967616609318986952340123175997617981700247881689338369654483356564191827856161443356312976673642210350324634850410377680367334151172899169723197082763985615764450078474174626"), + boost::lexical_cast<T>("43466557686937456435688527675040625802564660517371780402481729089536555417949051890403879840079255169295922593080322634775209689623239873322471161642996440906533187938298969649928516003704476137795166849228875"), + boost::lexical_cast<T>("70330367711422815821835254877183549770181269836358732742604905087154537118196933579742249494562611733487750449241765991088186363265450223647106012053374121273867339111198139373125598767690091902245245323403501") + }; + static const std::vector<T> data(numbers, numbers + sizeof(numbers) / sizeof(numbers[0])); + + return data; +} + +template <class T> +std::vector<std::pair<T, T> > const& fibonacci_numbers_permution_1() +{ + typedef boost::integral_constant<int, + ((std::numeric_limits<T>::digits <= 16) ? 16 : ((std::numeric_limits<T>::digits <= 32) ? 32 : (std::numeric_limits<T>::digits <= 64) ? 64 : 0)) + > tag_type; + + static std::vector<std::pair<T, T> > data; + static bool init = false; + if(!init) + { + init = true; + for(unsigned i = 0; i < fibonacci_numbers<T>(tag_type()).size() - 1; ++i) + data.push_back(std::make_pair(fibonacci_numbers<T>(tag_type())[i], fibonacci_numbers<T>(tag_type())[i + 1])); + } + return data; +} + +template <class T> +std::vector<std::pair<T, T> > const& fibonacci_numbers_permution_2() +{ + typedef boost::integral_constant<int, + ((std::numeric_limits<T>::digits <= 16) ? 16 : ((std::numeric_limits<T>::digits <= 32) ? 32 : (std::numeric_limits<T>::digits <= 64) ? 64 : 0)) + > tag_type; + + static std::vector<std::pair<T, T> > data; + static bool init = false; + if(!init) + { + init = true; + for(unsigned i = 0; i < fibonacci_numbers<T>(tag_type()).size(); ++i) + for(unsigned j = 0; j < fibonacci_numbers<T>(tag_type()).size(); ++j) + data.push_back(std::make_pair(fibonacci_numbers<T>(tag_type())[i], fibonacci_numbers<T>(tag_type())[j])); + } + return data; +} + +template <class T> +std::vector<std::pair<T, T> > const & trivial_gcd_test_cases() +{ + static const std::pair<T, T> a[] = { + std::pair<T, T>(0, 0), + std::pair<T, T>(0, 832040u), + std::pair<T, T>(832040u, 0), + std::pair<T, T>(1u << 15, 1u << 4), + std::pair<T, T>(1u << 3, 1u << 14), + std::pair<T, T>(832040u, 832040u), + std::pair<T, T>(991u * 3 * 7, 991u), + std::pair<T, T>(991u * 2, 991u), + }; + static const std::vector<std::pair<T, T> > data(a, a + sizeof(a) / sizeof(a[0])); + return data; +} + diff --git a/src/boost/libs/math/reporting/performance/html/boostbook.css b/src/boost/libs/math/reporting/performance/html/boostbook.css new file mode 100644 index 000000000..d42b3c022 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/html/boostbook.css @@ -0,0 +1,700 @@ + +/*============================================================================= +Copyright (c) 2004 Joel de Guzman +http://spirit.sourceforge.net/ + +Copyright 2013 Niall Douglas additions for colors and alignment. +Copyright 2013 Paul A. Bristow additions for more colors and alignments. + +Distributed under the Boost Software License, Version 1.0. 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width: 20%; text-align: justify; +} + +/* Text colors. +Names at http://www.w3.org/TR/2002/WD-css3-color-20020219/ 4.3. X11 color keywords. +Quickbook Usage: [role red Some red text] + +*/ +span.red { inline-block; color: red; } +span.green { color: green; } +span.lime { color: #00FF00; } +span.blue { color: blue; } +span.navy { color: navy; } +span.yellow { color: yellow; } +span.magenta { color: magenta; } +span.indigo { color: #4B0082; } +span.cyan { color: cyan; } +span.purple { color: purple; } +span.gold { color: gold; } +span.silver { color: silver; } /* lighter gray */ +span.gray { color: #808080; } /* light gray */ diff --git a/src/boost/libs/math/reporting/performance/html/index.html b/src/boost/libs/math/reporting/performance/html/index.html new file mode 100644 index 000000000..2b2954e32 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/html/index.html @@ -0,0 +1,16754 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Special Function and Distribution Performance Report</title> +<link rel="stylesheet" href="boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> +<link rel="home" href="index.html" title="Special Function and Distribution Performance Report"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td> +<td align="center"><a href="../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"></div> +<div class="article"> +<div class="titlepage"> +<div> +<div><h2 class="title"> +<a name="special_function_and_distributio"></a>Special Function and Distribution Performance Report</h2></div> +<div><div class="legalnotice"> +<a name="special_function_and_distributio.legal"></a><p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></div> +</div> +<hr> +</div> +<div class="toc"> +<p><b>Table of Contents</b></p> +<dl class="toc"> +<dt><span class="section"><a href="index.html#special_function_and_distributio.section_Compiler_Comparison_on_Windows_x64">Compiler + Comparison on Windows x64</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_and_distributio.section_Compiler_Option_Comparison_on_Windows_x64">Compiler + Option Comparison on Windows x64</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_and_distributio.section_Distribution_performance_comparison_for_different_performance_options_with_GNU_C_version_9_2_0_on_Windows_x64">Distribution + performance comparison for different performance options with GNU C++ version + 9.2.0 on Windows x64</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_and_distributio.section_Distribution_performance_comparison_for_different_performance_options_with_Microsoft_Visual_C_version_14_2_on_Windows_x64">Distribution + performance comparison for different performance options with Microsoft Visual + C++ version 14.2 on Windows x64</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_and_distributio.section_Distribution_performance_comparison_with_GNU_C_version_9_2_0_on_Windows_x64">Distribution + performance comparison with GNU C++ version 9.2.0 on Windows x64</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_and_distributio.section_Distribution_performance_comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64">Distribution + performance comparison with Microsoft Visual C++ version 14.2 on Windows x64</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_and_distributio.section_Library_Comparison_with_GNU_C_version_9_2_0_on_Windows_x64">Library + Comparison with GNU C++ version 9.2.0 on Windows x64</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_and_distributio.section_Library_Comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64">Library + Comparison with Microsoft Visual C++ version 14.2 on Windows x64</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_and_distributio.section_Polynomial_Arithmetic_GNU_C_version_9_2_0_Windows_x64_">Polynomial + Arithmetic (GNU C++ version 9.2.0, Windows x64)</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_and_distributio.section_Polynomial_Arithmetic_Microsoft_Visual_C_version_14_2_Windows_x64_">Polynomial + Arithmetic (Microsoft Visual C++ version 14.2, Windows x64)</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_and_distributio.section_Polynomial_Method_Comparison_with_GNU_C_version_9_2_0_on_Windows_x64">Polynomial + Method Comparison with GNU C++ version 9.2.0 on Windows x64</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_and_distributio.section_Polynomial_Method_Comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64">Polynomial + Method Comparison with Microsoft Visual C++ version 14.2 on Windows x64</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_and_distributio.section_Rational_Method_Comparison_with_GNU_C_version_9_2_0_on_Windows_x64">Rational + Method Comparison with GNU C++ version 9.2.0 on Windows x64</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_and_distributio.section_Rational_Method_Comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64">Rational + Method Comparison with Microsoft Visual C++ version 14.2 on Windows x64</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_and_distributio.section_gcd_method_comparison_with_GNU_C_version_9_2_0_on_Windows_x64">gcd + method comparison with GNU C++ version 9.2.0 on Windows x64</a></span></dt> +<dt><span class="section"><a href="index.html#special_function_and_distributio.section_gcd_method_comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64">gcd + method comparison with Microsoft Visual C++ version 14.2 on Windows x64</a></span></dt> +</dl> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_and_distributio.section_Compiler_Comparison_on_Windows_x64"></a><a class="link" href="index.html#special_function_and_distributio.section_Compiler_Comparison_on_Windows_x64" title="Compiler Comparison on Windows x64">Compiler + Comparison on Windows x64</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_and_distributio.section_Compiler_Comparison_on_Windows_x64.table_Compiler_Comparison_on_Windows_x64"></a><p class="title"><b>Table 1. Compiler Comparison on Windows x64</b></p> +<div class="table-contents"><table class="table" summary="Compiler Comparison on Windows x64"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Function + </p> + </th> +<th> + <p> + Microsoft Visual C++ version 14.2<br> boost 1.73 + </p> + </th> +<th> + <p> + GNU C++ version 9.2.0<br> boost 1.73 + </p> + </th> +<th> + <p> + GNU C++ version 9.2.0<br> boost 1.73<br> promote_double<false> + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + assoc_laguerre + </p> + </td> +<td> + <p> + <span class="blue">1.41<br> (179ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (137ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (127ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + assoc_legendre + </p> + </td> +<td> + <p> + <span class="blue">1.76<br> (248ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.36<br> (192ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (141ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + beta + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (123ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.62<br> (322ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.93<br> (237ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + beta (incomplete) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (470ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.95<br> (1385ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.58<br> (741ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + cbrt + </p> + </td> +<td> + <p> + <span class="red">3.40<br> (51ns)</span> + </p> + </td> +<td> + <p> + <span class="red">4.67<br> (70ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (15ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + cyl_bessel_i + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (281ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.38<br> (949ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.38<br> (387ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + cyl_bessel_i (integer order) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (195ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.06<br> (597ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (195ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + cyl_bessel_j + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (371ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.39<br> (886ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.35<br> (499ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + cyl_bessel_j (integer order) + </p> + </td> +<td> + <p> + <span class="blue">1.28<br> (123ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.92<br> (184ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (96ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + cyl_bessel_k + </p> + </td> +<td> + <p> + <span class="green">1.11<br> (385ns)</span> + </p> + </td> +<td> + <p> + <span class="red">19.68<br> (6847ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (348ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + cyl_bessel_k (integer order) + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (217ns)</span> + </p> + </td> +<td> + <p> + <span class="red">18.17<br> (3724ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (205ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + cyl_neumann + </p> + </td> +<td> + <p> + <span class="green">1.17<br> (6696ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.76<br> (10032ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (5715ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + cyl_neumann (integer order) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (158ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.20<br> (348ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.59<br> (252ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + digamma + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (20ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.45<br> (69ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.30<br> (46ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ellint_1 + </p> + </td> +<td> + <p> + <span class="blue">1.57<br> (390ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.41<br> (349ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (248ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ellint_1 (complete) + </p> + </td> +<td> + <p> + <span class="blue">1.64<br> (77ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.64<br> (77ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (47ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ellint_2 + </p> + </td> +<td> + <p> + <span class="blue">1.81<br> (702ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.50<br> (583ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (388ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ellint_2 (complete) + </p> + </td> +<td> + <p> + <span class="red">3.11<br> (84ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.11<br> (57ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (27ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ellint_3 + </p> + </td> +<td> + <p> + <span class="red">3.47<br> (1381ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.68<br> (670ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (398ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ellint_3 (complete) + </p> + </td> +<td> + <p> + <span class="red">inf<br> (802ns)</span> + </p> + </td> +<td> + <p> + <span class="green">-nan(ind)<br> (0ns)</span> + </p> + </td> +<td> + <p> + <span class="green">-nan(ind)<br> (0ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ellint_rc + </p> + </td> +<td> + <p> + <span class="blue">1.55<br> (59ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.21<br> (84ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (38ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ellint_rd + </p> + </td> +<td> + <p> + <span class="blue">1.32<br> (271ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.26<br> (260ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (206ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ellint_rf + </p> + </td> +<td> + <p> + <span class="blue">1.27<br> (62ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.94<br> (95ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (49ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ellint_rj + </p> + </td> +<td> + <p> + <span class="blue">1.46<br> (264ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.29<br> (414ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (181ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + erf + </p> + </td> +<td> + <p> + <span class="blue">1.30<br> (43ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.85<br> (61ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (33ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + erfc + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (54ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.76<br> (90ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (51ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + expint + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (27ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.41<br> (92ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.22<br> (60ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + expint (En) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (106ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.94<br> (206ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.29<br> (137ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + expm1 + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (11ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.00<br> (33ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.36<br> (26ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gamma_p + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (303ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">2.00<br> (605ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.17<br> (355ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gamma_p_inv + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1266ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.85<br> (2341ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.15<br> (1460ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gamma_q + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (294ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.10<br> (618ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.21<br> (356ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gamma_q_inv + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1194ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.66<br> (1987ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.14<br> (1357ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ibeta + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (512ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.63<br> (1344ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.31<br> (673ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ibeta_inv + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1910ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.49<br> (4751ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.48<br> (2822ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ibetac + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (525ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.60<br> (1365ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.27<br> (668ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ibetac_inv + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1676ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.85<br> (4778ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.74<br> (2910ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + jacobi_cn + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (181ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.10<br> (561ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">2.00<br> (362ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + jacobi_dn + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (203ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.03<br> (616ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.93<br> (392ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + jacobi_sn + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (202ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.81<br> (568ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.73<br> (350ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + laguerre + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (107ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.07<br> (112ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (105ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + legendre + </p> + </td> +<td> + <p> + <span class="green">1.11<br> (283ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.25<br> (320ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (255ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + legendre Q + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (309ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.51<br> (466ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.15<br> (354ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + lgamma + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (80ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.67<br> (214ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">2.00<br> (160ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + log1p + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (14ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.07<br> (29ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.21<br> (17ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + polygamma + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (4193ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.85<br> (7743ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.91<br> (8018ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + sph_bessel + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (668ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.48<br> (975ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (661ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + sph_neumann + </p> + </td> +<td> + <p> + <span class="green">1.07<br> (1138ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.96<br> (3153ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1064ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (74ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.50<br> (259ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.14<br> (158ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma (incomplete) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (208ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.30<br> (478ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.64<br> (342ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + trigamma + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (12ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.83<br> (34ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.17<br> (14ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + zeta + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (117ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.65<br> (310ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.89<br> (221ns)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_and_distributio.section_Compiler_Option_Comparison_on_Windows_x64"></a><a class="link" href="index.html#special_function_and_distributio.section_Compiler_Option_Comparison_on_Windows_x64" title="Compiler Option Comparison on Windows x64">Compiler + Option Comparison on Windows x64</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_and_distributio.section_Compiler_Option_Comparison_on_Windows_x64.table_Compiler_Option_Comparison_on_Windows_x64"></a><p class="title"><b>Table 2. Compiler Option Comparison on Windows x64</b></p> +<div class="table-contents"><table class="table" summary="Compiler Option Comparison on Windows x64"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Function + </p> + </th> +<th> + <p> + cl /Od (x86 build) + </p> + </th> +<th> + <p> + cl /arch:sse2 /Ox (x86 build) + </p> + </th> +<th> + <p> + cl /Ox (x64 build) + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + boost::math::cbrt + </p> + </td> +<td> + <p> + <span class="red">5.05<br> (202ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.20<br> (48ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (40ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + boost::math::cyl_bessel_j (integer orders) + </p> + </td> +<td> + <p> + <span class="red">4.38<br> (530ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (121ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (124ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + boost::math::ibeta_inv + </p> + </td> +<td> + <p> + <span class="red">4.52<br> (8277ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.11<br> (2042ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1833ns)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_and_distributio.section_Distribution_performance_comparison_for_different_performance_options_with_GNU_C_version_9_2_0_on_Windows_x64"></a><a class="link" href="index.html#special_function_and_distributio.section_Distribution_performance_comparison_for_different_performance_options_with_GNU_C_version_9_2_0_on_Windows_x64" title="Distribution performance comparison for different performance options with GNU C++ version 9.2.0 on Windows x64">Distribution + performance comparison for different performance options with GNU C++ version + 9.2.0 on Windows x64</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_and_distributio.section_Distribution_performance_comparison_for_different_performance_options_with_GNU_C_version_9_2_0_on_Windows_x64.table_Distribution_performance_comparison_for_different_performance_options_with_GNU_C_version_9_2_0_on_Windows_x64"></a><p class="title"><b>Table 3. Distribution performance comparison for different performance options + with GNU C++ version 9.2.0 on Windows x64</b></p> +<div class="table-contents"><table class="table" summary="Distribution performance comparison for different performance options + with GNU C++ version 9.2.0 on Windows x64"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Function + </p> + </th> +<th> + <p> + boost 1.73 + </p> + </th> +<th> + <p> + Boost<br> promote_double<false> + </p> + </th> +<th> + <p> + Boost<br> promote_double<false><br> digits10<10> + </p> + </th> +<th> + <p> + Boost<br> float<br> promote_float<false> + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + ArcSine (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.10<br> (22ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.30<br> (26ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (20ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.20<br> (64ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ArcSine (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (5ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (5ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (5ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.60<br> (8ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ArcSine (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (53ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (53ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (54ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (55ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Beta (CDF) + </p> + </td> +<td> + <p> + <span class="red">2.32<br> (362ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.31<br> (205ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.17<br> (183ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (156ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Beta (PDF) + </p> + </td> +<td> + <p> + <span class="red">2.44<br> (302ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.12<br> (139ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.13<br> (140ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (124ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Beta (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.76<br> (1968ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.24<br> (1383ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1118ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (1155ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Binomial (CDF) + </p> + </td> +<td> + <p> + <span class="red">3.57<br> (959ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.30<br> (350ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.27<br> (341ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (269ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Binomial (PDF) + </p> + </td> +<td> + <p> + <span class="red">2.39<br> (339ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (142ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.20<br> (171ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (148ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Binomial (quantile) + </p> + </td> +<td> + <p> + <span class="red">3.20<br> (4255ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.42<br> (1884ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.19<br> (1582ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1328ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Cauchy (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.12<br> (19ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.18<br> (20ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (17ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.18<br> (54ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Cauchy (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.33<br> (4ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.67<br> (5ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (3ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.33<br> (4ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Cauchy (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.32<br> (25ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.21<br> (23ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (19ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.21<br> (23ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ChiSquared (CDF) + </p> + </td> +<td> + <p> + <span class="red">2.79<br> (953ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.55<br> (529ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.27<br> (434ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (341ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ChiSquared (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.82<br> (189ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (104ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (105ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (106ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ChiSquared (quantile) + </p> + </td> +<td> + <p> + <span class="red">2.40<br> (1452ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.49<br> (901ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.19<br> (717ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (605ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Exponential (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.14<br> (33ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (29ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (30ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (29ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Exponential (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (54ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (51ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (50ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (52ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Exponential (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.89<br> (36ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (19ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (20ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.21<br> (23ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ExtremeValue (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (104ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (101ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (99ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (103ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ExtremeValue (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (144ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (144ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (138ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (142ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ExtremeValue (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.07<br> (64ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (61ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (60ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.13<br> (68ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + F (CDF) + </p> + </td> +<td> + <p> + <span class="red">3.55<br> (668ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.58<br> (297ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.23<br> (232ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (188ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + F (PDF) + </p> + </td> +<td> + <p> + <span class="red">2.29<br> (291ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (135ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (129ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (127ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + F (quantile) + </p> + </td> +<td> + <p> + <span class="red">2.17<br> (2215ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.14<br> (1163ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1023ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.07<br> (1090ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Gamma (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.94<br> (492ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.19<br> (301ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.10<br> (280ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (254ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Gamma (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.55<br> (236ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (152ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (152ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (153ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Gamma (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.95<br> (1204ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.35<br> (837ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (619ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (644ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Geometric (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.38<br> (40ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (29ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (29ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.07<br> (31ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Geometric (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (46ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (46ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (46ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (47ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Geometric (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.64<br> (36ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (22ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (22ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.09<br> (24ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Hypergeometric (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.11<br> (49938ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (45127ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (45445ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.12<br> (50682ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Hypergeometric (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.13<br> (53353ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (49364ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (47376ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.20<br> (57034ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Hypergeometric (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (105555ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.25<br> (132253ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.36<br> (143254ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.70<br> (179941ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseChiSquared (CDF) + </p> + </td> +<td> + <p> + <span class="red">3.48<br> (1326ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.70<br> (647ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.33<br> (508ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (381ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseChiSquared (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.87<br> (217ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.09<br> (126ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (116ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (117ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseChiSquared (quantile) + </p> + </td> +<td> + <p> + <span class="red">2.81<br> (1852ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.57<br> (1035ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.22<br> (800ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (658ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseGamma (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.95<br> (516ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.21<br> (320ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.09<br> (289ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (264ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseGamma (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.67<br> (256ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.09<br> (167ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (161ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (153ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseGamma (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.94<br> (1268ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.36<br> (884ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (652ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (666ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseGaussian (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.83<br> (172ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.83<br> (172ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.82<br> (171ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (94ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseGaussian (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (28ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.14<br> (32ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (28ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.07<br> (30ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseGaussian (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.94<br> (2657ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.93<br> (2635ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.72<br> (2359ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1368ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Laplace (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (50ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (49ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (49ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (53ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Laplace (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (49ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (50ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (49ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (51ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Laplace (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (33ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (33ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (32ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.16<br> (37ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + LogNormal (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.73<br> (176ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.25<br> (127ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.28<br> (131ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (102ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + LogNormal (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (87ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (86ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (84ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.07<br> (90ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + LogNormal (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.23<br> (116ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (94ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (95ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (100ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Logistic (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (46ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (47ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (46ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (47ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Logistic (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (46ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (47ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (47ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.07<br> (49ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Logistic (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (33ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (34ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (33ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.15<br> (38ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NegativeBinomial (CDF) + </p> + </td> +<td> + <p> + <span class="red">3.95<br> (1158ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.66<br> (485ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.32<br> (386ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (293ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NegativeBinomial (PDF) + </p> + </td> +<td> + <p> + <span class="red">2.29<br> (307ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (135ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (134ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (136ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NegativeBinomial (quantile) + </p> + </td> +<td> + <p> + <span class="red">2.81<br> (6154ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.19<br> (2608ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (2190ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.26<br> (2752ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralBeta (CDF) + </p> + </td> +<td> + <p> + <span class="red">2.62<br> (1450ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.46<br> (806ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.28<br> (708ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (553ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralBeta (PDF) + </p> + </td> +<td> + <p> + <span class="red">2.58<br> (969ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.31<br> (490ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.15<br> (433ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (375ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralBeta (quantile) + </p> + </td> +<td> + <p> + <span class="red">3.69<br> (37583ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">2.00<br> (20369ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.81<br> (18498ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (10193ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralChiSquared (CDF) + </p> + </td> +<td> + <p> + <span class="red">2.22<br> (4037ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.79<br> (3256ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.28<br> (2332ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1819ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralChiSquared (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.58<br> (630ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.29<br> (514ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (399ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (409ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralChiSquared (quantile) + </p> + </td> +<td> + <p> + <span class="red">3.14<br> (33255ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.94<br> (20620ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.26<br> (13388ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (10603ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralF (CDF) + </p> + </td> +<td> + <p> + <span class="red">2.48<br> (1426ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.32<br> (762ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.13<br> (652ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (576ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralF (PDF) + </p> + </td> +<td> + <p> + <span class="red">2.74<br> (1306ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.37<br> (652ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.15<br> (548ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (477ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralF (quantile) + </p> + </td> +<td> + <p> + <span class="red">2.64<br> (22025ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.38<br> (11560ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.12<br> (9319ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (8356ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralT (CDF) + </p> + </td> +<td> + <p> + <span class="red">3.75<br> (6473ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.83<br> (3155ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.63<br> (2819ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1727ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralT (PDF) + </p> + </td> +<td> + <p> + <span class="red">2.81<br> (4098ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.40<br> (2040ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.42<br> (2066ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1456ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralT (quantile) + </p> + </td> +<td> + <p> + <span class="red">3.80<br> (65926ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.87<br> (32431ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.37<br> (23756ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (17331ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Normal (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.78<br> (135ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.53<br> (116ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.22<br> (93ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (76ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Normal (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (48ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.23<br> (59ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.19<br> (57ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.33<br> (64ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Normal (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.45<br> (80ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (55ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (55ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (56ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Pareto (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.13<br> (59ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (52ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.15<br> (60ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (55ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Pareto (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.07<br> (96ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (92ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (97ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (90ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Pareto (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (82ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (84ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (82ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (85ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Poisson (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.97<br> (254ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (134ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.16<br> (150ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (129ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Poisson (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.61<br> (171ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (112ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (106ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (111ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Poisson (quantile) + </p> + </td> +<td> + <p> + <span class="red">2.16<br> (1128ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.23<br> (641ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.26<br> (657ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (523ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Rayleigh (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.24<br> (47ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (38ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (39ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (41ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Rayleigh (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (64ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.09<br> (70ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (66ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.09<br> (70ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Rayleigh (quantile) + </p> + </td> +<td> + <p> + <span class="blue">2.00<br> (48ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (24ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (26ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.29<br> (31ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + SkewNormal (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.40<br> (669ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.32<br> (632ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.15<br> (549ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (479ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + SkewNormal (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.27<br> (173ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.17<br> (159ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.15<br> (156ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (136ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + SkewNormal (quantile) + </p> + </td> +<td> + <p> + <span class="red">2.15<br> (6968ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.82<br> (5903ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.32<br> (4287ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (3237ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + StudentsT (CDF) + </p> + </td> +<td> + <p> + <span class="red">3.15<br> (1151ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.98<br> (721ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.03<br> (741ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (365ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + StudentsT (PDF) + </p> + </td> +<td> + <p> + <span class="red">2.12<br> (360ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.09<br> (186ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.11<br> (188ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (170ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + StudentsT (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.70<br> (1461ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.35<br> (1161ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.28<br> (1099ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (859ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Weibull (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.30<br> (96ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (77ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.15<br> (85ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (74ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Weibull (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.18<br> (164ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (139ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.15<br> (160ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (148ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Weibull (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.12<br> (133ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.13<br> (134ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (119ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (123ns)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_and_distributio.section_Distribution_performance_comparison_for_different_performance_options_with_Microsoft_Visual_C_version_14_2_on_Windows_x64"></a><a class="link" href="index.html#special_function_and_distributio.section_Distribution_performance_comparison_for_different_performance_options_with_Microsoft_Visual_C_version_14_2_on_Windows_x64" title="Distribution performance comparison for different performance options with Microsoft Visual C++ version 14.2 on Windows x64">Distribution + performance comparison for different performance options with Microsoft Visual + C++ version 14.2 on Windows x64</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_and_distributio.section_Distribution_performance_comparison_for_different_performance_options_with_Microsoft_Visual_C_version_14_2_on_Windows_x64.table_Distribution_performance_comparison_for_different_performance_options_with_Microsoft_Visual_C_version_14_2_on_Windows_x64"></a><p class="title"><b>Table 4. Distribution performance comparison for different performance options + with Microsoft Visual C++ version 14.2 on Windows x64</b></p> +<div class="table-contents"><table class="table" summary="Distribution performance comparison for different performance options + with Microsoft Visual C++ version 14.2 on Windows x64"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Function + </p> + </th> +<th> + <p> + boost 1.73 + </p> + </th> +<th> + <p> + Boost<br> promote_double<false><br> digits10<10> + </p> + </th> +<th> + <p> + Boost<br> float<br> promote_float<false> + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + ArcSine (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.30<br> (43ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (33ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (33ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ArcSine (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (17ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (18ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (17ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ArcSine (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.20<br> (30ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (25ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.20<br> (30ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Beta (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.37<br> (158ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.22<br> (140ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (115ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Beta (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (104ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.14<br> (109ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (96ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Beta (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.07<br> (806ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.11<br> (833ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (753ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Binomial (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.80<br> (413ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.50<br> (344ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (230ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Binomial (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (127ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.41<br> (178ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (126ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Binomial (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.38<br> (2024ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.18<br> (1727ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1466ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Cauchy (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (26ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (27ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.23<br> (32ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Cauchy (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (8ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.38<br> (11ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.13<br> (9ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Cauchy (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.37<br> (26ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (19ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.37<br> (26ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ChiSquared (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.35<br> (676ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.59<br> (798ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (501ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ChiSquared (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (93ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.27<br> (118ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.22<br> (113ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ChiSquared (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.62<br> (1073ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.83<br> (1211ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (662ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Exponential (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.70<br> (17ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.10<br> (11ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (10ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Exponential (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.50<br> (15ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.70<br> (17ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (10ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Exponential (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.18<br> (20ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (17ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (17ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ExtremeValue (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.18<br> (26ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.18<br> (26ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (22ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ExtremeValue (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (27ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (26ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (25ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ExtremeValue (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.48<br> (34ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.09<br> (25ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (23ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + F (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.56<br> (277ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.28<br> (228ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (178ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + F (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.07<br> (97ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.13<br> (103ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (91ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + F (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.17<br> (901ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (770ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (833ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Gamma (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.30<br> (234ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.29<br> (233ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (180ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Gamma (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.25<br> (85ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.25<br> (85ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (68ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Gamma (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.64<br> (640ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.28<br> (501ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (390ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Geometric (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.13<br> (18ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (16ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.19<br> (19ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Geometric (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.85<br> (24ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.54<br> (20ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (13ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Geometric (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.18<br> (20ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (17ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (17ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Hypergeometric (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (244196ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.07<br> (260490ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.11<br> (271879ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Hypergeometric (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (272497ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (282183ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.09<br> (296020ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Hypergeometric (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (308077ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (307365ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (326617ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseChiSquared (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.65<br> (584ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.30<br> (459ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (353ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseChiSquared (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.37<br> (78ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.32<br> (75ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (57ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseChiSquared (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.68<br> (884ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.30<br> (684ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (527ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseGamma (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.36<br> (244ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.17<br> (210ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (179ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseGamma (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.36<br> (91ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.39<br> (93ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (67ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseGamma (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.58<br> (638ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.12<br> (452ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (403ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseGaussian (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.28<br> (109ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.32<br> (112ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (85ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseGaussian (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.09<br> (12ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.18<br> (13ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (11ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseGaussian (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.58<br> (1651ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.15<br> (1209ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1048ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Laplace (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (13ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (13ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (13ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Laplace (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (14ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.46<br> (19ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (13ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Laplace (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (14ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (13ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (13ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + LogNormal (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (79ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (76ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (82ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + LogNormal (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.25<br> (35ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.07<br> (30ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (28ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + LogNormal (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.13<br> (61ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.09<br> (59ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (54ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Logistic (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (14ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.07<br> (15ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.36<br> (19ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Logistic (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (18ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (17ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.29<br> (22ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Logistic (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (15ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.33<br> (20ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.33<br> (20ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NegativeBinomial (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.69<br> (481ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.33<br> (378ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (285ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NegativeBinomial (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (114ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (113ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.09<br> (123ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NegativeBinomial (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.21<br> (2651ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (2186ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.17<br> (2554ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralBeta (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.90<br> (735ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.54<br> (597ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (387ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralBeta (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.62<br> (489ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.56<br> (471ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (302ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralBeta (quantile) + </p> + </td> +<td> + <p> + <span class="red">2.35<br> (14689ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.10<br> (13173ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (6263ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralChiSquared (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.84<br> (2643ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.45<br> (2087ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1438ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralChiSquared (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.36<br> (290ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.28<br> (272ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (213ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralChiSquared (quantile) + </p> + </td> +<td> + <p> + <span class="red">2.49<br> (16692ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.59<br> (10665ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (6699ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralF (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.54<br> (608ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.36<br> (538ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (396ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralF (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.44<br> (467ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.30<br> (420ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (324ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralF (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.73<br> (9122ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.44<br> (7572ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (5271ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralT (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.65<br> (2375ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.38<br> (1985ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1441ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralT (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.58<br> (1701ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.34<br> (1440ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1075ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralT (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.93<br> (23683ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.35<br> (16597ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (12284ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Normal (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.09<br> (89ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (82ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.29<br> (106ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Normal (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.33<br> (28ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.38<br> (29ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (21ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Normal (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (44ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (43ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (44ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Pareto (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.26<br> (34ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.30<br> (35ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (27ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Pareto (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.50<br> (102ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.56<br> (106ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (68ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Pareto (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.79<br> (50ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.36<br> (38ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (28ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Poisson (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.11<br> (84ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (76ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (77ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Poisson (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.40<br> (49ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.43<br> (50ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (35ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Poisson (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.10<br> (440ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (400ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.10<br> (441ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Rayleigh (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.25<br> (15ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (13ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (12ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Rayleigh (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (14ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (14ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (13ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Rayleigh (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.15<br> (23ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.15<br> (23ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (20ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + SkewNormal (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (259ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (256ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.13<br> (289ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + SkewNormal (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (94ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (91ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (98ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + SkewNormal (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.47<br> (2843ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1936ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.24<br> (2391ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + StudentsT (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.83<br> (429ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.85<br> (434ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (235ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + StudentsT (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.36<br> (146ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.26<br> (135ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (107ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + StudentsT (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.53<br> (729ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.57<br> (749ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (476ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Weibull (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.62<br> (63ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.51<br> (59ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (39ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Weibull (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.75<br> (89ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.76<br> (90ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (51ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Weibull (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.63<br> (62ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.55<br> (59ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (38ns)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_and_distributio.section_Distribution_performance_comparison_with_GNU_C_version_9_2_0_on_Windows_x64"></a><a class="link" href="index.html#special_function_and_distributio.section_Distribution_performance_comparison_with_GNU_C_version_9_2_0_on_Windows_x64" title="Distribution performance comparison with GNU C++ version 9.2.0 on Windows x64">Distribution + performance comparison with GNU C++ version 9.2.0 on Windows x64</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_and_distributio.section_Distribution_performance_comparison_with_GNU_C_version_9_2_0_on_Windows_x64.table_Distribution_performance_comparison_with_GNU_C_version_9_2_0_on_Windows_x64"></a><p class="title"><b>Table 5. Distribution performance comparison with GNU C++ version 9.2.0 on Windows + x64</b></p> +<div class="table-contents"><table class="table" summary="Distribution performance comparison with GNU C++ version 9.2.0 on Windows + x64"> +<colgroup> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Function + </p> + </th> +<th> + <p> + boost 1.73 + </p> + </th> +<th> + <p> + Boost<br> promote_double<false> + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + ArcSine (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (22ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.18<br> (26ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ArcSine (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (5ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (5ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ArcSine (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (53ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (53ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Beta (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.77<br> (362ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (205ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Beta (PDF) + </p> + </td> +<td> + <p> + <span class="red">2.17<br> (302ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (139ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Beta (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.42<br> (1968ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1383ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Binomial (CDF) + </p> + </td> +<td> + <p> + <span class="red">2.74<br> (959ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (350ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Binomial (PDF) + </p> + </td> +<td> + <p> + <span class="red">2.39<br> (339ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (142ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Binomial (quantile) + </p> + </td> +<td> + <p> + <span class="red">2.26<br> (4255ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1884ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Cauchy (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (19ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (20ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Cauchy (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (4ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.25<br> (5ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Cauchy (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.09<br> (25ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (23ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ChiSquared (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.80<br> (953ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (529ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ChiSquared (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.82<br> (189ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (104ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ChiSquared (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.61<br> (1452ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (901ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Exponential (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.14<br> (33ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (29ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Exponential (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (54ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (51ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Exponential (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.89<br> (36ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (19ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ExtremeValue (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (104ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (101ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ExtremeValue (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (144ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (144ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ExtremeValue (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (64ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (61ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + F (CDF) + </p> + </td> +<td> + <p> + <span class="red">2.25<br> (668ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (297ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + F (PDF) + </p> + </td> +<td> + <p> + <span class="red">2.16<br> (291ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (135ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + F (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.90<br> (2215ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1163ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Gamma (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.63<br> (492ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (301ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Gamma (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.55<br> (236ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (152ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Gamma (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.44<br> (1204ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (837ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Geometric (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.38<br> (40ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (29ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Geometric (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (46ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (46ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Geometric (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.64<br> (36ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (22ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Hypergeometric (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.11<br> (49938ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (45127ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Hypergeometric (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (53353ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (49364ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Hypergeometric (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (105555ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.25<br> (132253ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseChiSquared (CDF) + </p> + </td> +<td> + <p> + <span class="red">2.05<br> (1326ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (647ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseChiSquared (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.72<br> (217ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (126ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseChiSquared (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.79<br> (1852ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1035ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseGamma (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.61<br> (516ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (320ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseGamma (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.53<br> (256ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (167ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseGamma (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.43<br> (1268ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (884ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseGaussian (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (172ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (172ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseGaussian (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (28ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.14<br> (32ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseGaussian (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (2657ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (2635ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Laplace (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (50ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (49ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Laplace (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (49ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (50ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Laplace (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (33ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (33ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + LogNormal (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.39<br> (176ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (127ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + LogNormal (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (87ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (86ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + LogNormal (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.23<br> (116ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (94ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Logistic (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (46ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (47ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Logistic (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (46ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (47ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Logistic (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (33ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (34ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NegativeBinomial (CDF) + </p> + </td> +<td> + <p> + <span class="red">2.39<br> (1158ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (485ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NegativeBinomial (PDF) + </p> + </td> +<td> + <p> + <span class="red">2.27<br> (307ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (135ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NegativeBinomial (quantile) + </p> + </td> +<td> + <p> + <span class="red">2.36<br> (6154ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (2608ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralBeta (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.80<br> (1450ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (806ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralBeta (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.98<br> (969ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (490ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralBeta (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.85<br> (37583ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (20369ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralChiSquared (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.24<br> (4037ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (3256ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralChiSquared (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.23<br> (630ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (514ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralChiSquared (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.61<br> (33255ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (20620ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralF (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.87<br> (1426ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (762ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralF (PDF) + </p> + </td> +<td> + <p> + <span class="red">2.00<br> (1306ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (652ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralF (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.91<br> (22025ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (11560ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralT (CDF) + </p> + </td> +<td> + <p> + <span class="red">2.05<br> (6473ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (3155ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralT (PDF) + </p> + </td> +<td> + <p> + <span class="red">2.01<br> (4098ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (2040ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralT (quantile) + </p> + </td> +<td> + <p> + <span class="red">2.03<br> (65926ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (32431ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Normal (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.16<br> (135ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (116ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Normal (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (48ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.23<br> (59ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Normal (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.45<br> (80ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (55ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Pareto (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.13<br> (59ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (52ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Pareto (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (96ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (92ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Pareto (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (82ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (84ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Poisson (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.90<br> (254ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (134ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Poisson (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.53<br> (171ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (112ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Poisson (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.76<br> (1128ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (641ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Rayleigh (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.24<br> (47ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (38ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Rayleigh (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (64ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.09<br> (70ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Rayleigh (quantile) + </p> + </td> +<td> + <p> + <span class="blue">2.00<br> (48ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (24ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + SkewNormal (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (669ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (632ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + SkewNormal (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.09<br> (173ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (159ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + SkewNormal (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.18<br> (6968ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (5903ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + StudentsT (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.60<br> (1151ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (721ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + StudentsT (PDF) + </p> + </td> +<td> + <p> + <span class="blue">1.94<br> (360ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (186ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + StudentsT (quantile) + </p> + </td> +<td> + <p> + <span class="blue">1.26<br> (1461ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1161ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Weibull (CDF) + </p> + </td> +<td> + <p> + <span class="blue">1.25<br> (96ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (77ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Weibull (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.18<br> (164ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (139ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Weibull (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (133ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (134ns)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_and_distributio.section_Distribution_performance_comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64"></a><a class="link" href="index.html#special_function_and_distributio.section_Distribution_performance_comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64" title="Distribution performance comparison with Microsoft Visual C++ version 14.2 on Windows x64">Distribution + performance comparison with Microsoft Visual C++ version 14.2 on Windows x64</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_and_distributio.section_Distribution_performance_comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64.table_Distribution_performance_comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64"></a><p class="title"><b>Table 6. Distribution performance comparison with Microsoft Visual C++ version + 14.2 on Windows x64</b></p> +<div class="table-contents"><table class="table" summary="Distribution performance comparison with Microsoft Visual C++ version + 14.2 on Windows x64"> +<colgroup> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Function + </p> + </th> +<th> + <p> + boost 1.73 + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + ArcSine (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (43ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ArcSine (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (17ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ArcSine (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (30ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Beta (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (158ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Beta (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (104ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Beta (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (806ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Binomial (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (413ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Binomial (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (127ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Binomial (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (2024ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Cauchy (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (26ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Cauchy (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (8ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Cauchy (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (26ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ChiSquared (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (676ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ChiSquared (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (93ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ChiSquared (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1073ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Exponential (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (17ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Exponential (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (15ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Exponential (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (20ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ExtremeValue (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (26ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ExtremeValue (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (27ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ExtremeValue (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (34ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + F (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (277ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + F (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (97ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + F (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (901ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Gamma (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (234ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Gamma (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (85ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Gamma (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (640ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Geometric (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (18ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Geometric (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (24ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Geometric (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (20ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Hypergeometric (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (244196ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Hypergeometric (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (272497ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Hypergeometric (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (308077ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseChiSquared (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (584ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseChiSquared (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (78ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseChiSquared (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (884ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseGamma (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (244ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseGamma (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (91ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseGamma (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (638ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseGaussian (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (109ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseGaussian (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (12ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + InverseGaussian (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1651ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Laplace (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (13ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Laplace (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (14ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Laplace (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (14ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + LogNormal (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (79ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + LogNormal (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (35ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + LogNormal (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (61ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Logistic (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (14ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Logistic (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (18ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Logistic (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (15ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NegativeBinomial (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (481ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NegativeBinomial (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (114ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NegativeBinomial (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (2651ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralBeta (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (735ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralBeta (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (489ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralBeta (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (14689ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralChiSquared (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (2643ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralChiSquared (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (290ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralChiSquared (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (16692ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralF (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (608ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralF (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (467ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralF (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (9122ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralT (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (2375ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralT (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1701ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + NonCentralT (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (23683ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Normal (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (89ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Normal (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (28ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Normal (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (44ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Pareto (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (34ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Pareto (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (102ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Pareto (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (50ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Poisson (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (84ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Poisson (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (49ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Poisson (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (440ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Rayleigh (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (15ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Rayleigh (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (14ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Rayleigh (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (23ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + SkewNormal (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (259ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + SkewNormal (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (94ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + SkewNormal (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (2843ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + StudentsT (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (429ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + StudentsT (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (146ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + StudentsT (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (729ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Weibull (CDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (63ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Weibull (PDF) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (89ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Weibull (quantile) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (62ns)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_and_distributio.section_Library_Comparison_with_GNU_C_version_9_2_0_on_Windows_x64"></a><a class="link" href="index.html#special_function_and_distributio.section_Library_Comparison_with_GNU_C_version_9_2_0_on_Windows_x64" title="Library Comparison with GNU C++ version 9.2.0 on Windows x64">Library + Comparison with GNU C++ version 9.2.0 on Windows x64</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_and_distributio.section_Library_Comparison_with_GNU_C_version_9_2_0_on_Windows_x64.table_Library_Comparison_with_GNU_C_version_9_2_0_on_Windows_x64"></a><p class="title"><b>Table 7. Library Comparison with GNU C++ version 9.2.0 on Windows x64</b></p> +<div class="table-contents"><table class="table" summary="Library Comparison with GNU C++ version 9.2.0 on Windows x64"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Function + </p> + </th> +<th> + <p> + boost 1.73 + </p> + </th> +<th> + <p> + boost 1.73<br> promote_double<false> + </p> + </th> +<th> + <p> + tr1/cmath + </p> + </th> +<th> + <p> + math.h + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + assoc_laguerre<br> (2240/2240 tests selected) + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (137ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (127ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (137ns)</span> + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + assoc_legendre<br> (110/400 tests selected) + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (40ns)</span> + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + beta<br> (2204/2204 tests selected) + </p> + </td> +<td> + <p> + <span class="blue">1.60<br> (322ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.18<br> (237ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (201ns)</span> + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + cbrt<br> (85/85 tests selected) + </p> + </td> +<td> + <p> + <span class="red">4.67<br> (70ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (15ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">2.00<br> (30ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.13<br> (32ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + cyl_bessel_i (integer order)<br> (515/526 tests selected) + </p> + </td> +<td> + <p> + <span class="red">3.06<br> (597ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (195ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (196ns)</span> + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + cyl_bessel_i<br> (215/240 tests selected) + </p> + </td> +<td> + <p> + <span class="red">5.68<br> (949ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.32<br> (387ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (167ns)</span> + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + cyl_bessel_j (integer order)<br> (253/268 tests selected) + </p> + </td> +<td> + <p> + <span class="blue">1.92<br> (184ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (96ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.12<br> (300ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.94<br> (186ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + cyl_bessel_j<br> (442/451 tests selected) + </p> + </td> +<td> + <p> + <span class="red">2.15<br> (886ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.21<br> (499ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (412ns)</span> + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + cyl_bessel_k (integer order)<br> (505/508 tests selected) + </p> + </td> +<td> + <p> + <span class="red">18.17<br> (3724ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (205ns)</span> + </p> + </td> +<td> + <p> + <span class="red">8.40<br> (1722ns)</span> + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + cyl_bessel_k<br> (187/279 tests selected) + </p> + </td> +<td> + <p> + <span class="red">19.68<br> (6847ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (348ns)</span> + </p> + </td> +<td> + <p> + <span class="red">6.31<br> (2196ns)</span> + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + cyl_neumann (integer order)<br> (424/428 tests selected) + </p> + </td> +<td> + <p> + <span class="red">2.13<br> (348ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.55<br> (252ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.83<br> (624ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (163ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + cyl_neumann<br> (428/450 tests selected) + </p> + </td> +<td> + <p> + <span class="red">12.46<br> (10032ns)</span> + </p> + </td> +<td> + <p> + <span class="red">7.10<br> (5715ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (805ns)</span> + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ellint_1 (complete)<br> (109/109 tests selected) + </p> + </td> +<td> + <p> + <span class="blue">1.64<br> (77ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (47ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.36<br> (111ns)</span> + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ellint_1<br> (627/629 tests selected) + </p> + </td> +<td> + <p> + <span class="blue">1.41<br> (349ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (248ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.09<br> (270ns)</span> + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ellint_2 (complete)<br> (110/110 tests selected) + </p> + </td> +<td> + <p> + <span class="red">2.11<br> (57ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (27ns)</span> + </p> + </td> +<td> + <p> + <span class="red">9.37<br> (253ns)</span> + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ellint_2<br> (527/530 tests selected) + </p> + </td> +<td> + <p> + <span class="blue">1.50<br> (583ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (388ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (412ns)</span> + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ellint_3 (complete)<br> (0/500 tests selected) + </p> + </td> +<td> + <p> + <span class="green">nan<br> (0ns)</span> + </p> + </td> +<td> + <p> + <span class="green">nan<br> (0ns)</span> + </p> + </td> +<td> + <p> + <span class="green">nan<br> (0ns)</span> + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + ellint_3<br> (22/845 tests selected) + </p> + </td> +<td> + <p> + <span class="red">2.58<br> (670ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.53<br> (398ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (260ns)</span> + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + erf<br> (950/950 tests selected) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (33ns)</span> + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +<td> + <p> + <span class="green">1.15<br> (38ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.30<br> (43ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + erfc<br> (950/950 tests selected) + </p> + </td> +<td> + <p> + <span class="blue">1.76<br> (90ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (51ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (55ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.25<br> (64ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + expint<br> (436/436 tests selected) + </p> + </td> +<td> + <p> + <span class="blue">1.53<br> (92ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (60ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.83<br> (110ns)</span> + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + expm1<br> (80/80 tests selected) + </p> + </td> +<td> + <p> + <span class="blue">1.38<br> (33ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (26ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (24ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (24ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + laguerre<br> (280/280 tests selected) + </p> + </td> +<td> + <p> + <span class="green">1.07<br> (112ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (105ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (108ns)</span> + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + legendre<br> (300/300 tests selected) + </p> + </td> +<td> + <p> + <span class="blue">1.25<br> (320ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (255ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.27<br> (323ns)</span> + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + lgamma<br> (400/400 tests selected) + </p> + </td> +<td> + <p> + <span class="red">3.40<br> (214ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.54<br> (160ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (63ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (64ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + log1p<br> (80/80 tests selected) + </p> + </td> +<td> + <p> + <span class="blue">1.71<br> (29ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (17ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.53<br> (26ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.71<br> (29ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + sph_bessel<br> (483/483 tests selected) + </p> + </td> +<td> + <p> + <span class="blue">1.48<br> (975ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (661ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.02<br> (1999ns)</span> + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + sph_neumann<br> (284/284 tests selected) + </p> + </td> +<td> + <p> + <span class="red">2.96<br> (3153ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1064ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.73<br> (2906ns)</span> + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma<br> (400/400 tests selected) + </p> + </td> +<td> + <p> + <span class="red">3.32<br> (259ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.03<br> (158ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (79ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (78ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + zeta<br> (448/448 tests selected) + </p> + </td> +<td> + <p> + <span class="blue">1.40<br> (310ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (221ns)</span> + </p> + </td> +<td> + <p> + <span class="red">918.24<br> (202930ns)</span> + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_and_distributio.section_Library_Comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64"></a><a class="link" href="index.html#special_function_and_distributio.section_Library_Comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64" title="Library Comparison with Microsoft Visual C++ version 14.2 on Windows x64">Library + Comparison with Microsoft Visual C++ version 14.2 on Windows x64</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_and_distributio.section_Library_Comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64.table_Library_Comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64"></a><p class="title"><b>Table 8. Library Comparison with Microsoft Visual C++ version 14.2 on Windows + x64</b></p> +<div class="table-contents"><table class="table" summary="Library Comparison with Microsoft Visual C++ version 14.2 on Windows + x64"> +<colgroup> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Function + </p> + </th> +<th> + <p> + boost 1.73 + </p> + </th> +<th> + <p> + math.h + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cbrt<br> (85/85 tests selected) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (51ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.22<br> (62ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + cyl_bessel_j (integer order)<br> (267/268 tests selected) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (123ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.50<br> (185ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + cyl_neumann (integer order)<br> (428/428 tests selected) + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (158ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (156ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + erf<br> (950/950 tests selected) + </p> + </td> +<td> + <p> + <span class="red">2.15<br> (43ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (20ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + erfc<br> (950/950 tests selected) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (54ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.09<br> (59ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + expm1<br> (80/80 tests selected) + </p> + </td> +<td> + <p> + <span class="green">1.10<br> (11ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (10ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + lgamma<br> (400/400 tests selected) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (80ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.60<br> (128ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + log1p<br> (80/80 tests selected) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (14ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.07<br> (15ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + tgamma<br> (400/400 tests selected) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (74ns)</span> + </p> + </td> +<td> + <p> + <span class="red">12.53<br> (927ns)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_and_distributio.section_Polynomial_Arithmetic_GNU_C_version_9_2_0_Windows_x64_"></a><a class="link" href="index.html#special_function_and_distributio.section_Polynomial_Arithmetic_GNU_C_version_9_2_0_Windows_x64_" title="Polynomial Arithmetic (GNU C++ version 9.2.0, Windows x64)">Polynomial + Arithmetic (GNU C++ version 9.2.0, Windows x64)</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_and_distributio.section_Polynomial_Arithmetic_GNU_C_version_9_2_0_Windows_x64_.table_Polynomial_Arithmetic_GNU_C_version_9_2_0_Windows_x64_"></a><p class="title"><b>Table 9. Polynomial Arithmetic (GNU C++ version 9.2.0, Windows x64)</b></p> +<div class="table-contents"><table class="table" summary="Polynomial Arithmetic (GNU C++ version 9.2.0, Windows x64)"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Function + </p> + </th> +<th> + <p> + boost::uint64_t + </p> + </th> +<th> + <p> + double + </p> + </th> +<th> + <p> + cpp_int + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + operator * + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (503ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (502ns)</span> + </p> + </td> +<td> + <p> + <span class="red">15.20<br> (7629ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator * (int) + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (114ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (109ns)</span> + </p> + </td> +<td> + <p> + <span class="red">6.04<br> (658ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator *= + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (223824ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (215955ns)</span> + </p> + </td> +<td> + <p> + <span class="red">19.30<br> (4168184ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator *= (int) + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (13931ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (13163ns)</span> + </p> + </td> +<td> + <p> + <span class="red">26.10<br> (343615ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator + + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (163ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.14<br> (186ns)</span> + </p> + </td> +<td> + <p> + <span class="red">6.04<br> (985ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator + (int) + </p> + </td> +<td> + <p> + <span class="green">1.16<br> (116ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (100ns)</span> + </p> + </td> +<td> + <p> + <span class="red">4.07<br> (407ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator += + </p> + </td> +<td> + <p> + <span class="green">1.12<br> (18ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (16ns)</span> + </p> + </td> +<td> + <p> + <span class="red">22.81<br> (365ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator += (int) + </p> + </td> +<td> + <p> + <span class="blue">1.33<br> (4ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (3ns)</span> + </p> + </td> +<td> + <p> + <span class="red">33.00<br> (99ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator - + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (159ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.16<br> (185ns)</span> + </p> + </td> +<td> + <p> + <span class="red">6.66<br> (1059ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator - (int) + </p> + </td> +<td> + <p> + <span class="green">1.11<br> (113ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (102ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.75<br> (382ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator -= + </p> + </td> +<td> + <p> + <span class="blue">1.38<br> (22ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (16ns)</span> + </p> + </td> +<td> + <p> + <span class="red">23.38<br> (374ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator -= (int) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (3ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (3ns)</span> + </p> + </td> +<td> + <p> + <span class="red">31.00<br> (93ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator / + </p> + </td> +<td> + <p> + <span class="blue">1.44<br> (767ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (533ns)</span> + </p> + </td> +<td> + <p> + <span class="red">41.38<br> (22054ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator / (int) + </p> + </td> +<td> + <p> + <span class="blue">1.29<br> (138ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (107ns)</span> + </p> + </td> +<td> + <p> + <span class="red">13.58<br> (1453ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator /= + </p> + </td> +<td> + <p> + <span class="green">1.10<br> (11ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (10ns)</span> + </p> + </td> +<td> + <p> + <span class="red">194.00<br> (1940ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator /= (int) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (679ns)</span> + </p> + </td> +<td> + <p> + <span class="red">21.14<br> (14351ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3447.12<br> (2340595ns)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_and_distributio.section_Polynomial_Arithmetic_Microsoft_Visual_C_version_14_2_Windows_x64_"></a><a class="link" href="index.html#special_function_and_distributio.section_Polynomial_Arithmetic_Microsoft_Visual_C_version_14_2_Windows_x64_" title="Polynomial Arithmetic (Microsoft Visual C++ version 14.2, Windows x64)">Polynomial + Arithmetic (Microsoft Visual C++ version 14.2, Windows x64)</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_and_distributio.section_Polynomial_Arithmetic_Microsoft_Visual_C_version_14_2_Windows_x64_.table_Polynomial_Arithmetic_Microsoft_Visual_C_version_14_2_Windows_x64_"></a><p class="title"><b>Table 10. Polynomial Arithmetic (Microsoft Visual C++ version 14.2, Windows x64)</b></p> +<div class="table-contents"><table class="table" summary="Polynomial Arithmetic (Microsoft Visual C++ version 14.2, Windows x64)"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Function + </p> + </th> +<th> + <p> + boost::uint64_t + </p> + </th> +<th> + <p> + double + </p> + </th> +<th> + <p> + cpp_int + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + operator * + </p> + </td> +<td> + <p> + <span class="blue">1.54<br> (951ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (617ns)</span> + </p> + </td> +<td> + <p> + <span class="red">15.22<br> (9391ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator * (int) + </p> + </td> +<td> + <p> + <span class="green">1.16<br> (135ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (116ns)</span> + </p> + </td> +<td> + <p> + <span class="red">5.22<br> (605ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator *= + </p> + </td> +<td> + <p> + <span class="blue">1.30<br> (371957ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (286462ns)</span> + </p> + </td> +<td> + <p> + <span class="red">17.11<br> (4901613ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator *= (int) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (14157ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (14670ns)</span> + </p> + </td> +<td> + <p> + <span class="red">19.69<br> (278738ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator + + </p> + </td> +<td> + <p> + <span class="blue">1.41<br> (273ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (194ns)</span> + </p> + </td> +<td> + <p> + <span class="red">6.20<br> (1203ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator + (int) + </p> + </td> +<td> + <p> + <span class="blue">1.25<br> (126ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (101ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.47<br> (350ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator += + </p> + </td> +<td> + <p> + <span class="blue">1.35<br> (42ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (31ns)</span> + </p> + </td> +<td> + <p> + <span class="red">11.16<br> (346ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator += (int) + </p> + </td> +<td> + <p> + <span class="blue">1.25<br> (5ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (4ns)</span> + </p> + </td> +<td> + <p> + <span class="red">25.50<br> (102ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator - + </p> + </td> +<td> + <p> + <span class="blue">1.20<br> (231ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (192ns)</span> + </p> + </td> +<td> + <p> + <span class="red">6.44<br> (1236ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator - (int) + </p> + </td> +<td> + <p> + <span class="green">1.20<br> (121ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (101ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.34<br> (337ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator -= + </p> + </td> +<td> + <p> + <span class="blue">1.35<br> (42ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (31ns)</span> + </p> + </td> +<td> + <p> + <span class="red">11.13<br> (345ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator -= (int) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (4ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (4ns)</span> + </p> + </td> +<td> + <p> + <span class="red">23.50<br> (94ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator / + </p> + </td> +<td> + <p> + <span class="red">2.17<br> (1164ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (537ns)</span> + </p> + </td> +<td> + <p> + <span class="red">51.34<br> (27568ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator / (int) + </p> + </td> +<td> + <p> + <span class="green">1.17<br> (138ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (118ns)</span> + </p> + </td> +<td> + <p> + <span class="red">9.73<br> (1148ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator /= + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (13ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (12ns)</span> + </p> + </td> +<td> + <p> + <span class="red">192.42<br> (2309ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + operator /= (int) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (697ns)</span> + </p> + </td> +<td> + <p> + <span class="red">36.29<br> (25293ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2700.21<br> (1882045ns)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_and_distributio.section_Polynomial_Method_Comparison_with_GNU_C_version_9_2_0_on_Windows_x64"></a><a class="link" href="index.html#special_function_and_distributio.section_Polynomial_Method_Comparison_with_GNU_C_version_9_2_0_on_Windows_x64" title="Polynomial Method Comparison with GNU C++ version 9.2.0 on Windows x64">Polynomial + Method Comparison with GNU C++ version 9.2.0 on Windows x64</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_and_distributio.section_Polynomial_Method_Comparison_with_GNU_C_version_9_2_0_on_Windows_x64.table_Polynomial_Method_Comparison_with_GNU_C_version_9_2_0_on_Windows_x64"></a><p class="title"><b>Table 11. Polynomial Method Comparison with GNU C++ version 9.2.0 on Windows x64</b></p> +<div class="table-contents"><table class="table" summary="Polynomial Method Comparison with GNU C++ version 9.2.0 on Windows x64"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Function + </p> + </th> +<th> + <p> + Method 0<br> (Double Coefficients) + </p> + </th> +<th> + <p> + Method 0<br> (Integer Coefficients) + </p> + </th> +<th> + <p> + Method 1<br> (Double Coefficients) + </p> + </th> +<th> + <p> + Method 1<br> (Integer Coefficients) + </p> + </th> +<th> + <p> + Method 2<br> (Double Coefficients) + </p> + </th> +<th> + <p> + Method 2<br> (Integer Coefficients) + </p> + </th> +<th> + <p> + Method 3<br> (Double Coefficients) + </p> + </th> +<th> + <p> + Method 3<br> (Integer Coefficients) + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Order 2 + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (6ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (6ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (6ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (6ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (6ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (6ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 3 + </p> + </td> +<td> + <p> + <span class="blue">1.56<br> (14ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.56<br> (23ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (9ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (9ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (9ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (9ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.11<br> (10ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (9ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 4 + </p> + </td> +<td> + <p> + <span class="blue">1.50<br> (18ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.42<br> (29ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (13ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (12ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (13ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (13ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (13ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (13ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 5 + </p> + </td> +<td> + <p> + <span class="blue">1.38<br> (22ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.31<br> (37ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (17ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (16ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (17ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.12<br> (18ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.12<br> (18ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.12<br> (18ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 6 + </p> + </td> +<td> + <p> + <span class="blue">1.48<br> (31ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.14<br> (45ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (21ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (21ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (22ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (22ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.24<br> (26ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (22ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 7 + </p> + </td> +<td> + <p> + <span class="blue">1.31<br> (34ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.15<br> (56ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (26ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (26ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (26ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.12<br> (29ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (27ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.19<br> (31ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 8 + </p> + </td> +<td> + <p> + <span class="blue">1.37<br> (41ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.23<br> (67ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.07<br> (32ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (31ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.10<br> (33ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (31ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.20<br> (36ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (30ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 9 + </p> + </td> +<td> + <p> + <span class="blue">1.58<br> (52ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.42<br> (80ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.15<br> (38ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.15<br> (38ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (33ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (33ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (33ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (34ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 10 + </p> + </td> +<td> + <p> + <span class="blue">1.51<br> (56ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.41<br> (89ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.22<br> (45ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.22<br> (45ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (37ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (38ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (39ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (39ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 11 + </p> + </td> +<td> + <p> + <span class="blue">1.56<br> (64ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.46<br> (101ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.27<br> (52ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.27<br> (52ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (41ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (41ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (41ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (41ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 12 + </p> + </td> +<td> + <p> + <span class="blue">1.70<br> (78ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.63<br> (121ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.30<br> (60ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.28<br> (59ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (46ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (48ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (47ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (47ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 13 + </p> + </td> +<td> + <p> + <span class="blue">1.78<br> (87ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.78<br> (136ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.29<br> (63ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.29<br> (63ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (49ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (50ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (49ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (49ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 14 + </p> + </td> +<td> + <p> + <span class="blue">1.79<br> (95ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.75<br> (146ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.43<br> (76ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.43<br> (76ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (53ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (54ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (53ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (53ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 15 + </p> + </td> +<td> + <p> + <span class="blue">1.63<br> (103ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.51<br> (158ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.33<br> (84ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.43<br> (90ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (64ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (64ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (63ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (64ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 16 + </p> + </td> +<td> + <p> + <span class="blue">1.61<br> (119ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.31<br> (171ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.31<br> (97ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.31<br> (97ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (75ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (75ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (75ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (74ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 17 + </p> + </td> +<td> + <p> + <span class="blue">1.67<br> (127ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.42<br> (184ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.42<br> (108ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.41<br> (107ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (76ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (76ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (77ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (77ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 18 + </p> + </td> +<td> + <p> + <span class="blue">1.66<br> (136ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.39<br> (196ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.41<br> (116ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.44<br> (118ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (86ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (84ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (87ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (82ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 19 + </p> + </td> +<td> + <p> + <span class="blue">1.72<br> (146ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.51<br> (213ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.59<br> (135ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.56<br> (133ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (86ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (86ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (85ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (87ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 20 + </p> + </td> +<td> + <p> + <span class="blue">1.70<br> (158ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.52<br> (234ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.55<br> (144ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.59<br> (148ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (98ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (95ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (93ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (99ns)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_and_distributio.section_Polynomial_Method_Comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64"></a><a class="link" href="index.html#special_function_and_distributio.section_Polynomial_Method_Comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64" title="Polynomial Method Comparison with Microsoft Visual C++ version 14.2 on Windows x64">Polynomial + Method Comparison with Microsoft Visual C++ version 14.2 on Windows x64</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_and_distributio.section_Polynomial_Method_Comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64.table_Polynomial_Method_Comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64"></a><p class="title"><b>Table 12. Polynomial Method Comparison with Microsoft Visual C++ version 14.2 + on Windows x64</b></p> +<div class="table-contents"><table class="table" summary="Polynomial Method Comparison with Microsoft Visual C++ version 14.2 + on Windows x64"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Function + </p> + </th> +<th> + <p> + Method 0<br> (Double Coefficients) + </p> + </th> +<th> + <p> + Method 0<br> (Integer Coefficients) + </p> + </th> +<th> + <p> + Method 1<br> (Double Coefficients) + </p> + </th> +<th> + <p> + Method 1<br> (Integer Coefficients) + </p> + </th> +<th> + <p> + Method 2<br> (Double Coefficients) + </p> + </th> +<th> + <p> + Method 2<br> (Integer Coefficients) + </p> + </th> +<th> + <p> + Method 3<br> (Double Coefficients) + </p> + </th> +<th> + <p> + Method 3<br> (Integer Coefficients) + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Order 2 + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (6ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (6ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (6ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (6ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (6ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (6ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 3 + </p> + </td> +<td> + <p> + <span class="red">2.33<br> (21ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.33<br> (30ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (9ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (9ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (9ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (9ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (9ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (9ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 4 + </p> + </td> +<td> + <p> + <span class="blue">2.00<br> (24ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.00<br> (36ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (12ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (12ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (12ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (12ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (13ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (13ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 5 + </p> + </td> +<td> + <p> + <span class="blue">1.56<br> (25ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.31<br> (37ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (16ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (16ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.13<br> (18ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.13<br> (18ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.56<br> (25ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.56<br> (25ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 6 + </p> + </td> +<td> + <p> + <span class="blue">1.48<br> (31ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.19<br> (46ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (22ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (21ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (21ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (21ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.29<br> (27ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.29<br> (27ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 7 + </p> + </td> +<td> + <p> + <span class="blue">1.54<br> (37ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.33<br> (56ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (26ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (26ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (25ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (24ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.13<br> (27ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.17<br> (28ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 8 + </p> + </td> +<td> + <p> + <span class="blue">1.53<br> (46ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.23<br> (67ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.07<br> (32ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.07<br> (32ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (30ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (30ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (31ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (31ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 9 + </p> + </td> +<td> + <p> + <span class="blue">1.35<br> (46ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.06<br> (70ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.18<br> (40ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.32<br> (45ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (34ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (34ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.09<br> (37ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (36ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 10 + </p> + </td> +<td> + <p> + <span class="blue">1.38<br> (54ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.13<br> (83ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.21<br> (47ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.15<br> (45ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (39ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (39ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (40ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (40ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 11 + </p> + </td> +<td> + <p> + <span class="blue">1.48<br> (62ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.24<br> (94ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.24<br> (52ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.26<br> (53ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.07<br> (45ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (42ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.10<br> (46ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (43ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 12 + </p> + </td> +<td> + <p> + <span class="blue">1.48<br> (71ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.27<br> (109ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.25<br> (60ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.27<br> (61ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (50ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (48ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (48ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (48ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 13 + </p> + </td> +<td> + <p> + <span class="blue">1.55<br> (76ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.33<br> (114ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.31<br> (64ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.31<br> (64ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (51ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (51ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (50ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (49ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 14 + </p> + </td> +<td> + <p> + <span class="blue">1.53<br> (84ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.40<br> (132ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.44<br> (79ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.40<br> (77ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (57ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (56ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (55ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (55ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 15 + </p> + </td> +<td> + <p> + <span class="blue">1.51<br> (95ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.33<br> (147ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.37<br> (86ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.38<br> (87ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (66ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (67ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (63ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (63ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 16 + </p> + </td> +<td> + <p> + <span class="blue">1.47<br> (106ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.18<br> (157ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.40<br> (101ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.33<br> (96ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (73ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (74ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (72ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (75ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 17 + </p> + </td> +<td> + <p> + <span class="blue">1.46<br> (114ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.08<br> (162ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.44<br> (112ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.44<br> (112ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (78ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (79ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (82ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (80ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 18 + </p> + </td> +<td> + <p> + <span class="blue">1.48<br> (126ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.08<br> (177ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.44<br> (122ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.46<br> (124ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (87ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (88ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (86ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (85ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 19 + </p> + </td> +<td> + <p> + <span class="blue">1.49<br> (136ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.07<br> (188ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.47<br> (134ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.47<br> (134ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (91ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (92ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (96ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (94ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 20 + </p> + </td> +<td> + <p> + <span class="blue">1.52<br> (150ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.05<br> (203ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.45<br> (144ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.46<br> (145ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (99ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (101ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (101ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (101ns)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_and_distributio.section_Rational_Method_Comparison_with_GNU_C_version_9_2_0_on_Windows_x64"></a><a class="link" href="index.html#special_function_and_distributio.section_Rational_Method_Comparison_with_GNU_C_version_9_2_0_on_Windows_x64" title="Rational Method Comparison with GNU C++ version 9.2.0 on Windows x64">Rational + Method Comparison with GNU C++ version 9.2.0 on Windows x64</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_and_distributio.section_Rational_Method_Comparison_with_GNU_C_version_9_2_0_on_Windows_x64.table_Rational_Method_Comparison_with_GNU_C_version_9_2_0_on_Windows_x64"></a><p class="title"><b>Table 13. Rational Method Comparison with GNU C++ version 9.2.0 on Windows x64</b></p> +<div class="table-contents"><table class="table" summary="Rational Method Comparison with GNU C++ version 9.2.0 on Windows x64"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Function + </p> + </th> +<th> + <p> + Method 0<br> (Double Coefficients) + </p> + </th> +<th> + <p> + Method 0<br> (Integer Coefficients) + </p> + </th> +<th> + <p> + Method 1<br> (Double Coefficients) + </p> + </th> +<th> + <p> + Method 1<br> (Integer Coefficients) + </p> + </th> +<th> + <p> + Method 2<br> (Double Coefficients) + </p> + </th> +<th> + <p> + Method 2<br> (Integer Coefficients) + </p> + </th> +<th> + <p> + Method 3<br> (Double Coefficients) + </p> + </th> +<th> + <p> + Method 3<br> (Integer Coefficients) + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Order 2 + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +<td> + <p> + <span class="blue">1.83<br> (22ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.83<br> (22ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (12ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (12ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.17<br> (14ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (13ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 3 + </p> + </td> +<td> + <p> + <span class="blue">1.83<br> (33ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.17<br> (39ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.56<br> (28ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.44<br> (26ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (18ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (18ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (18ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (18ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 4 + </p> + </td> +<td> + <p> + <span class="blue">1.65<br> (43ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">2.00<br> (52ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.46<br> (38ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.46<br> (38ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (26ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (26ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (27ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.12<br> (29ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 5 + </p> + </td> +<td> + <p> + <span class="green">1.17<br> (56ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.40<br> (67ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (49ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (48ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.12<br> (54ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.10<br> (53ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.17<br> (56ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.12<br> (54ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 6 + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (62ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.25<br> (76ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (61ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (61ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (62ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (62ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (64ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.30<br> (79ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 7 + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (74ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.29<br> (93ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (73ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (72ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (73ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (73ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (74ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (73ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 8 + </p> + </td> +<td> + <p> + <span class="green">1.10<br> (90ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.27<br> (104ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (82ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (82ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (82ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (84ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.12<br> (92ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (86ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 9 + </p> + </td> +<td> + <p> + <span class="blue">1.27<br> (119ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.66<br> (156ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (97ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (96ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (94ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (95ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (94ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (95ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 10 + </p> + </td> +<td> + <p> + <span class="blue">1.22<br> (128ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.40<br> (147ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (111ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.07<br> (112ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (105ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (107ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (105ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (113ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 11 + </p> + </td> +<td> + <p> + <span class="green">1.20<br> (140ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.44<br> (169ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.07<br> (125ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (124ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (117ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.07<br> (125ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (118ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (122ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 12 + </p> + </td> +<td> + <p> + <span class="blue">1.24<br> (155ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.32<br> (165ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.10<br> (137ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.12<br> (140ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (128ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.23<br> (154ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (130ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (125ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 13 + </p> + </td> +<td> + <p> + <span class="blue">1.27<br> (171ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.36<br> (183ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.18<br> (159ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.13<br> (153ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (143ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (135ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (136ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (138ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 14 + </p> + </td> +<td> + <p> + <span class="green">1.16<br> (178ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.28<br> (196ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.10<br> (168ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (166ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.14<br> (174ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.10<br> (168ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.13<br> (173ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (153ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 15 + </p> + </td> +<td> + <p> + <span class="blue">1.32<br> (196ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.47<br> (217ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.23<br> (182ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.22<br> (181ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (148ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (150ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.15<br> (170ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (152ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 16 + </p> + </td> +<td> + <p> + <span class="blue">1.31<br> (209ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.39<br> (223ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.26<br> (202ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.28<br> (205ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (160ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (161ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.09<br> (174ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (161ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 17 + </p> + </td> +<td> + <p> + <span class="blue">1.34<br> (221ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.46<br> (241ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.32<br> (217ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.37<br> (226ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (165ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (175ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (178ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (165ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 18 + </p> + </td> +<td> + <p> + <span class="blue">1.52<br> (264ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.53<br> (266ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.41<br> (246ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.43<br> (249ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.23<br> (214ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (179ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (174ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (182ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 19 + </p> + </td> +<td> + <p> + <span class="blue">1.35<br> (252ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.56<br> (292ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.54<br> (288ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.39<br> (259ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (187ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.22<br> (228ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (191ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (195ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 20 + </p> + </td> +<td> + <p> + <span class="blue">1.34<br> (271ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.59<br> (322ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.39<br> (280ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.46<br> (294ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (214ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (205ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (202ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (202ns)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_and_distributio.section_Rational_Method_Comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64"></a><a class="link" href="index.html#special_function_and_distributio.section_Rational_Method_Comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64" title="Rational Method Comparison with Microsoft Visual C++ version 14.2 on Windows x64">Rational + Method Comparison with Microsoft Visual C++ version 14.2 on Windows x64</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_and_distributio.section_Rational_Method_Comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64.table_Rational_Method_Comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64"></a><p class="title"><b>Table 14. Rational Method Comparison with Microsoft Visual C++ version 14.2 on + Windows x64</b></p> +<div class="table-contents"><table class="table" summary="Rational Method Comparison with Microsoft Visual C++ version 14.2 on + Windows x64"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Function + </p> + </th> +<th> + <p> + Method 0<br> (Double Coefficients) + </p> + </th> +<th> + <p> + Method 0<br> (Integer Coefficients) + </p> + </th> +<th> + <p> + Method 1<br> (Double Coefficients) + </p> + </th> +<th> + <p> + Method 1<br> (Integer Coefficients) + </p> + </th> +<th> + <p> + Method 2<br> (Double Coefficients) + </p> + </th> +<th> + <p> + Method 2<br> (Integer Coefficients) + </p> + </th> +<th> + <p> + Method 3<br> (Double Coefficients) + </p> + </th> +<th> + <p> + Method 3<br> (Integer Coefficients) + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Order 2 + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +<td> + <p> + <span class="grey">-</span> + </p> + </td> +<td> + <p> + <span class="blue">1.92<br> (23ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.92<br> (23ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (12ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.17<br> (14ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (12ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (12ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 3 + </p> + </td> +<td> + <p> + <span class="blue">1.89<br> (34ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.28<br> (41ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.67<br> (30ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.61<br> (29ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (19ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (18ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (18ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (18ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 4 + </p> + </td> +<td> + <p> + <span class="blue">1.72<br> (43ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.16<br> (54ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.64<br> (41ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.60<br> (40ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (25ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (25ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (25ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (26ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 5 + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (53ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.41<br> (69ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (49ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (49ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (53ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (53ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (49ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.10<br> (54ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 6 + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (65ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.42<br> (85ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (61ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (60ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (63ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.23<br> (74ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.25<br> (75ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.40<br> (84ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 7 + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (75ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.37<br> (97ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (72ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (71ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.14<br> (81ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (72ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.20<br> (85ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.35<br> (96ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 8 + </p> + </td> +<td> + <p> + <span class="green">1.07<br> (87ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.38<br> (112ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (84ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (83ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (82ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (81ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.49<br> (202ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.60<br> (211ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 9 + </p> + </td> +<td> + <p> + <span class="green">1.16<br> (103ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.61<br> (143ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.18<br> (105ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.27<br> (113ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (90ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (91ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (91ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (89ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 10 + </p> + </td> +<td> + <p> + <span class="green">1.15<br> (115ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.46<br> (146ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.14<br> (114ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.12<br> (112ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (101ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (102ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (101ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (100ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 11 + </p> + </td> +<td> + <p> + <span class="blue">1.21<br> (131ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.48<br> (160ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.17<br> (126ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.16<br> (125ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (108ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.27<br> (137ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (108ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (109ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 12 + </p> + </td> +<td> + <p> + <span class="blue">1.26<br> (148ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.53<br> (179ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.19<br> (139ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.19<br> (139ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (119ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.24<br> (145ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (117ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (117ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 13 + </p> + </td> +<td> + <p> + <span class="blue">1.31<br> (163ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.71<br> (212ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.23<br> (153ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.52<br> (189ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (125ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.29<br> (160ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (125ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (124ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 14 + </p> + </td> +<td> + <p> + <span class="blue">1.42<br> (190ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.56<br> (209ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.32<br> (177ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.47<br> (197ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (137ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.31<br> (175ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (134ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (136ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 15 + </p> + </td> +<td> + <p> + <span class="blue">1.34<br> (194ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.51<br> (219ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.36<br> (197ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.46<br> (212ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (148ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.30<br> (188ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (145ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.23<br> (323ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 16 + </p> + </td> +<td> + <p> + <span class="blue">1.38<br> (216ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.56<br> (244ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.36<br> (212ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.31<br> (204ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.15<br> (179ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.34<br> (209ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (156ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.10<br> (328ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 17 + </p> + </td> +<td> + <p> + <span class="blue">1.39<br> (227ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.67<br> (273ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.34<br> (218ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.69<br> (275ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (163ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.32<br> (215ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (167ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.53<br> (412ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 18 + </p> + </td> +<td> + <p> + <span class="blue">1.37<br> (242ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.73<br> (306ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.40<br> (248ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.56<br> (276ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (187ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.32<br> (233ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (177ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.15<br> (380ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 19 + </p> + </td> +<td> + <p> + <span class="blue">1.28<br> (254ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.60<br> (319ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.27<br> (253ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.51<br> (300ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (199ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.22<br> (243ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.80<br> (359ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.92<br> (382ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + Order 20 + </p> + </td> +<td> + <p> + <span class="blue">1.28<br> (268ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.62<br> (338ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.27<br> (265ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.56<br> (325ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (209ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.24<br> (259ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.87<br> (391ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.04<br> (427ns)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_and_distributio.section_gcd_method_comparison_with_GNU_C_version_9_2_0_on_Windows_x64"></a><a class="link" href="index.html#special_function_and_distributio.section_gcd_method_comparison_with_GNU_C_version_9_2_0_on_Windows_x64" title="gcd method comparison with GNU C++ version 9.2.0 on Windows x64">gcd + method comparison with GNU C++ version 9.2.0 on Windows x64</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_and_distributio.section_gcd_method_comparison_with_GNU_C_version_9_2_0_on_Windows_x64.table_gcd_method_comparison_with_GNU_C_version_9_2_0_on_Windows_x64"></a><p class="title"><b>Table 15. gcd method comparison with GNU C++ version 9.2.0 on Windows x64</b></p> +<div class="table-contents"><table class="table" summary="gcd method comparison with GNU C++ version 9.2.0 on Windows x64"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Function + </p> + </th> +<th> + <p> + gcd boost 1.73 + </p> + </th> +<th> + <p> + Euclid_gcd boost 1.73 + </p> + </th> +<th> + <p> + Stein_gcd boost 1.73 + </p> + </th> +<th> + <p> + mixed_binary_gcd boost 1.73 + </p> + </th> +<th> + <p> + Stein_gcd_textbook boost 1.73 + </p> + </th> +<th> + <p> + gcd_euclid_textbook boost 1.73 + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint1024_t> (Trivial cases) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (585ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.30<br> (761ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.82<br> (2237ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.97<br> (2321ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.43<br> (836ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.10<br> (645ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint1024_t> (adjacent Fibonacci + numbers) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (9970176ns)</span> + </p> + </td> +<td> + <p> + <span class="red">7.06<br> (70352275ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.96<br> (39452018ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.33<br> (33171075ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.04<br> (20368737ns)</span> + </p> + </td> +<td> + <p> + <span class="red">7.38<br> (73577712ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint1024_t> (permutations of Fibonacci + numbers) + </p> + </td> +<td> + <p> + <span class="red">3.58<br> (5700044700ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (1619575299ns)</span> + </p> + </td> +<td> + <p> + <span class="red">15.19<br> (24170880700ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.10<br> (4926301699ns)</span> + </p> + </td> +<td> + <p> + <span class="red">7.61<br> (12103557199ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1591386600ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint1024_t> (random prime number + products) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (776840ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.83<br> (1420825ns)</span> + </p> + </td> +<td> + <p> + <span class="red">7.78<br> (6040362ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.39<br> (1853658ns)</span> + </p> + </td> +<td> + <p> + <span class="red">4.19<br> (3251426ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.96<br> (1522179ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint1024_t> (uniform random numbers) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (55462256ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.02<br> (112246250ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.55<br> (141227725ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.21<br> (122643774ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.49<br> (82400762ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.99<br> (110242300ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint256_t> (Trivial cases) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (442ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (475ns)</span> + </p> + </td> +<td> + <p> + <span class="red">4.12<br> (1815ns)</span> + </p> + </td> +<td> + <p> + <span class="red">4.11<br> (1813ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.17<br> (515ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (441ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint256_t> (adjacent Fibonacci numbers) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (4055238ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.74<br> (15153867ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.14<br> (12714485ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.78<br> (11263817ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.83<br> (7405233ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.79<br> (15349360ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint256_t> (permutations of Fibonacci + numbers) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (2188053200ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.24<br> (4905530400ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.53<br> (7720779699ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.26<br> (4951713400ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.06<br> (4508168099ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.60<br> (5692910900ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint256_t> (random prime number + products) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (788189ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.65<br> (1298322ns)</span> + </p> + </td> +<td> + <p> + <span class="red">4.56<br> (3592013ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.51<br> (1186279ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.77<br> (2184586ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.70<br> (1337848ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint256_t> (uniform random numbers) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (5971862ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.75<br> (16440456ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.13<br> (18696806ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.48<br> (14818301ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.65<br> (9829225ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.16<br> (18848609ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint512_t> (Trivial cases) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (473ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.10<br> (522ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.35<br> (1113ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.54<br> (1201ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.30<br> (617ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (497ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint512_t> (adjacent Fibonacci numbers) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (8919442ns)</span> + </p> + </td> +<td> + <p> + <span class="red">4.88<br> (43541675ns)</span> + </p> + </td> +<td> + <p> + <span class="red">4.74<br> (42250737ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.64<br> (32424337ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.68<br> (14998360ns)</span> + </p> + </td> +<td> + <p> + <span class="red">4.90<br> (43720662ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint512_t> (permutations of Fibonacci + numbers) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (4874074099ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.22<br> (5941210899ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.28<br> (15985377299ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.50<br> (7304170300ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.76<br> (8559919799ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.23<br> (6002105200ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint512_t> (random prime number + products) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (829159ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.59<br> (1318798ns)</span> + </p> + </td> +<td> + <p> + <span class="red">8.12<br> (6731670ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.91<br> (1581731ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.08<br> (2551970ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.58<br> (1308443ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint512_t> (uniform random numbers) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (18120096ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.35<br> (42631487ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.97<br> (71846612ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.10<br> (56237574ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.49<br> (27081093ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.66<br> (48247731ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned long long> (Trivial cases) + </p> + </td> +<td> + <p> + <span class="blue">1.85<br> (109ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.44<br> (144ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (59ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.88<br> (111ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.68<br> (99ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.08<br> (123ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned long long> (adjacent Fibonacci numbers) + </p> + </td> +<td> + <p> + <span class="red">2.98<br> (17394ns)</span> + </p> + </td> +<td> + <p> + <span class="red">14.61<br> (85221ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (5832ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.98<br> (17351ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.20<br> (12805ns)</span> + </p> + </td> +<td> + <p> + <span class="red">14.60<br> (85125ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned long long> (permutations of Fibonacci numbers) + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (1203049ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.30<br> (1508607ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.13<br> (1307113ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1159442ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.23<br> (2585039ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.26<br> (1455556ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned long long> (random prime number products) + </p> + </td> +<td> + <p> + <span class="green">1.14<br> (267158ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.88<br> (441001ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (234725ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.07<br> (249997ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.02<br> (473466ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.78<br> (418669ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned long long> (uniform random numbers) + </p> + </td> +<td> + <p> + <span class="blue">1.39<br> (507147ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.14<br> (784228ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (365889ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.33<br> (488432ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.75<br> (641184ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.08<br> (760185ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned long> (Trivial cases) + </p> + </td> +<td> + <p> + <span class="blue">1.23<br> (70ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.16<br> (66ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (57ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.19<br> (68ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.63<br> (93ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.12<br> (64ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned long> (adjacent Fibonacci numbers) + </p> + </td> +<td> + <p> + <span class="blue">1.79<br> (2678ns)</span> + </p> + </td> +<td> + <p> + <span class="red">10.20<br> (15231ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1493ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.85<br> (2765ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.07<br> (3093ns)</span> + </p> + </td> +<td> + <p> + <span class="red">9.50<br> (14177ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned long> (permutations of Fibonacci numbers) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (130874ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.43<br> (187180ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.31<br> (171288ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (132289ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.45<br> (321281ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.30<br> (169852ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned long> (random prime number products) + </p> + </td> +<td> + <p> + <span class="green">1.02<br> (132073ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.56<br> (202025ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.11<br> (143913ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (129448ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.03<br> (263053ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.40<br> (181659ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned long> (uniform random numbers) + </p> + </td> +<td> + <p> + <span class="green">1.14<br> (209599ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.61<br> (296090ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (183672ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.17<br> (214530ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.76<br> (322600ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.55<br> (284838ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned short> (Trivial cases) + </p> + </td> +<td> + <p> + <span class="green">1.19<br> (74ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (65ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (62ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.29<br> (80ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.53<br> (95ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (67ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned short> (adjacent Fibonacci numbers) + </p> + </td> +<td> + <p> + <span class="blue">1.55<br> (694ns)</span> + </p> + </td> +<td> + <p> + <span class="red">6.51<br> (2915ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (448ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.65<br> (737ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.42<br> (634ns)</span> + </p> + </td> +<td> + <p> + <span class="red">6.06<br> (2716ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned short> (permutations of Fibonacci numbers) + </p> + </td> +<td> + <p> + <span class="blue">1.31<br> (10776ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.35<br> (19287ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (8206ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.41<br> (11598ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.63<br> (13337ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.21<br> (18163ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned short> (random prime number products) + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (48625ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.82<br> (84692ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (47933ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (46539ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.94<br> (136663ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.68<br> (78386ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned short> (uniform random numbers) + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (73231ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.72<br> (120140ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (69680ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (72636ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.51<br> (175204ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.70<br> (118679ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned> (Trivial cases) + </p> + </td> +<td> + <p> + <span class="blue">1.30<br> (73ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.14<br> (64ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (56ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.23<br> (69ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.62<br> (91ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.14<br> (64ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned> (adjacent Fibonacci numbers) + </p> + </td> +<td> + <p> + <span class="blue">1.81<br> (2689ns)</span> + </p> + </td> +<td> + <p> + <span class="red">10.14<br> (15051ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1485ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.92<br> (2845ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.10<br> (3117ns)</span> + </p> + </td> +<td> + <p> + <span class="red">9.74<br> (14464ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned> (permutations of Fibonacci numbers) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (125228ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.45<br> (182101ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.36<br> (169753ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (130303ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.50<br> (312889ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.41<br> (176940ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned> (random prime number products) + </p> + </td> +<td> + <p> + <span class="green">1.04<br> (133297ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.55<br> (199022ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (134178ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (128319ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.03<br> (260550ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.53<br> (196665ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned> (uniform random numbers) + </p> + </td> +<td> + <p> + <span class="green">1.15<br> (212670ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.61<br> (298254ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (184955ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.17<br> (216091ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.80<br> (332689ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.62<br> (299958ns)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="special_function_and_distributio.section_gcd_method_comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64"></a><a class="link" href="index.html#special_function_and_distributio.section_gcd_method_comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64" title="gcd method comparison with Microsoft Visual C++ version 14.2 on Windows x64">gcd + method comparison with Microsoft Visual C++ version 14.2 on Windows x64</a> +</h2></div></div></div> +<div class="table"> +<a name="special_function_and_distributio.section_gcd_method_comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64.table_gcd_method_comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64"></a><p class="title"><b>Table 16. gcd method comparison with Microsoft Visual C++ version 14.2 on Windows + x64</b></p> +<div class="table-contents"><table class="table" summary="gcd method comparison with Microsoft Visual C++ version 14.2 on Windows + x64"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Function + </p> + </th> +<th> + <p> + gcd boost 1.73 + </p> + </th> +<th> + <p> + Euclid_gcd boost 1.73 + </p> + </th> +<th> + <p> + Stein_gcd boost 1.73 + </p> + </th> +<th> + <p> + mixed_binary_gcd boost 1.73 + </p> + </th> +<th> + <p> + Stein_gcd_textbook boost 1.73 + </p> + </th> +<th> + <p> + gcd_euclid_textbook boost 1.73 + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint1024_t> (Trivial cases) + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (811ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (806ns)</span> + </p> + </td> +<td> + <p> + <span class="red">4.49<br> (3619ns)</span> + </p> + </td> +<td> + <p> + <span class="red">4.37<br> (3524ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.54<br> (1240ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.17<br> (947ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint1024_t> (adjacent Fibonacci + numbers) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (17221009ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.10<br> (53378856ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.49<br> (60085356ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.71<br> (46662362ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.43<br> (24687809ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.60<br> (62017387ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint1024_t> (permutations of Fibonacci + numbers) + </p> + </td> +<td> + <p> + <span class="red">4.79<br> (8947276300ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1869827499ns)</span> + </p> + </td> +<td> + <p> + <span class="red">16.49<br> (30836050300ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.95<br> (5512590399ns)</span> + </p> + </td> +<td> + <p> + <span class="red">9.35<br> (17476759399ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.59<br> (2969003299ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint1024_t> (random prime number + products) + </p> + </td> +<td> + <p> + <span class="green">1.15<br> (1366950ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1184715ns)</span> + </p> + </td> +<td> + <p> + <span class="red">6.07<br> (7192390ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.69<br> (2004764ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.88<br> (3414226ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (1223450ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint1024_t> (uniform random numbers) + </p> + </td> +<td> + <p> + <span class="green">1.13<br> (94422587ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.10<br> (91927462ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.46<br> (205656225ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.79<br> (150321950ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.26<br> (105849675ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (83747287ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint256_t> (Trivial cases) + </p> + </td> +<td> + <p> + <span class="green">1.12<br> (529ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.22<br> (578ns)</span> + </p> + </td> +<td> + <p> + <span class="red">5.71<br> (2706ns)</span> + </p> + </td> +<td> + <p> + <span class="red">5.01<br> (2376ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.62<br> (768ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (474ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint256_t> (adjacent Fibonacci numbers) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (6910946ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.03<br> (14038607ns)</span> + </p> + </td> +<td> + <p> + <span class="red">4.15<br> (28656946ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.36<br> (16280003ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.83<br> (12632765ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.79<br> (12358175ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint256_t> (permutations of Fibonacci + numbers) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (3546690299ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.24<br> (4410071600ns)</span> + </p> + </td> +<td> + <p> + <span class="red">4.54<br> (16088449000ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.08<br> (7376147399ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.87<br> (6630678299ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.11<br> (3921678899ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint256_t> (random prime number + products) + </p> + </td> +<td> + <p> + <span class="blue">1.24<br> (1402017ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.19<br> (1342771ns)</span> + </p> + </td> +<td> + <p> + <span class="red">10.57<br> (11937009ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.30<br> (2592407ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.17<br> (3578886ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1129228ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint256_t> (uniform random numbers) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (9555357ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.38<br> (13230160ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.58<br> (34160918ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.17<br> (20739521ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.66<br> (15830168ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.25<br> (11919907ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint512_t> (Trivial cases) + </p> + </td> +<td> + <p> + <span class="green">1.09<br> (610ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (586ns)</span> + </p> + </td> +<td> + <p> + <span class="red">4.52<br> (2524ns)</span> + </p> + </td> +<td> + <p> + <span class="red">5.42<br> (3032ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.53<br> (858ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (559ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint512_t> (adjacent Fibonacci numbers) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (15008157ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.19<br> (32823187ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.54<br> (53103662ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.51<br> (37681662ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.67<br> (25128434ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.06<br> (30897006ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint512_t> (permutations of Fibonacci + numbers) + </p> + </td> +<td> + <p> + <span class="blue">1.70<br> (7824618799ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.06<br> (4905917200ns)</span> + </p> + </td> +<td> + <p> + <span class="red">6.42<br> (29578499900ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.96<br> (9014054500ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.82<br> (12972133700ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (4607798200ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint512_t> (random prime number + products) + </p> + </td> +<td> + <p> + <span class="green">1.20<br> (1429033ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1192363ns)</span> + </p> + </td> +<td> + <p> + <span class="red">6.71<br> (8006331ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.66<br> (1983967ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.05<br> (3641579ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1193514ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<boost::multiprecision::uint512_t> (uniform random numbers) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (28993946ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.13<br> (32874618ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.71<br> (107613600ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.24<br> (64869562ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.39<br> (40246987ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.26<br> (36427993ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned long long> (Trivial cases) + </p> + </td> +<td> + <p> + <span class="blue">1.61<br> (143ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.88<br> (167ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.09<br> (97ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.66<br> (148ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (89ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.25<br> (111ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned long long> (adjacent Fibonacci numbers) + </p> + </td> +<td> + <p> + <span class="blue">1.65<br> (18657ns)</span> + </p> + </td> +<td> + <p> + <span class="red">9.12<br> (102852ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (11278ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.65<br> (18642ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.36<br> (15386ns)</span> + </p> + </td> +<td> + <p> + <span class="red">7.61<br> (85867ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned long long> (permutations of Fibonacci numbers) + </p> + </td> +<td> + <p> + <span class="green">1.18<br> (1759315ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.23<br> (1829739ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.48<br> (3696867ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.20<br> (1792095ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.92<br> (2869829ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (1493466ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned long long> (random prime number products) + </p> + </td> +<td> + <p> + <span class="green">1.03<br> (419624ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.26<br> (513559ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.66<br> (677592ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (407357ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.24<br> (505557ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (426446ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned long long> (uniform random numbers) + </p> + </td> +<td> + <p> + <span class="green">1.15<br> (802062ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.29<br> (895731ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.38<br> (959675ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.16<br> (810488ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (696259ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.10<br> (768043ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned long> (Trivial cases) + </p> + </td> +<td> + <p> + <span class="red">2.05<br> (115ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.61<br> (90ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.80<br> (101ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.98<br> (111ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.55<br> (87ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (56ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned long> (adjacent Fibonacci numbers) + </p> + </td> +<td> + <p> + <span class="blue">1.26<br> (3438ns)</span> + </p> + </td> +<td> + <p> + <span class="red">8.19<br> (22429ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (2739ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.30<br> (3567ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.15<br> (3146ns)</span> + </p> + </td> +<td> + <p> + <span class="red">5.44<br> (14903ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned long> (permutations of Fibonacci numbers) + </p> + </td> +<td> + <p> + <span class="green">1.17<br> (205858ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.52<br> (268100ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.43<br> (427978ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.13<br> (198590ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.02<br> (356193ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (175939ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned long> (random prime number products) + </p> + </td> +<td> + <p> + <span class="green">1.01<br> (214230ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.32<br> (278903ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.93<br> (406951ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.12<br> (237142ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.70<br> (358996ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (211247ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned long> (uniform random numbers) + </p> + </td> +<td> + <p> + <span class="blue">1.29<br> (382560ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.46<br> (431960ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.77<br> (524430ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.26<br> (373023ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.27<br> (377903ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (296476ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned short> (Trivial cases) + </p> + </td> +<td> + <p> + <span class="blue">1.79<br> (118ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.41<br> (93ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.47<br> (97ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.73<br> (114ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.42<br> (94ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (66ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned short> (adjacent Fibonacci numbers) + </p> + </td> +<td> + <p> + <span class="green">1.16<br> (821ns)</span> + </p> + </td> +<td> + <p> + <span class="red">7.62<br> (5377ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (706ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.17<br> (823ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.15<br> (810ns)</span> + </p> + </td> +<td> + <p> + <span class="red">5.04<br> (3557ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned short> (permutations of Fibonacci numbers) + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (11485ns)</span> + </p> + </td> +<td> + <p> + <span class="red">3.82<br> (43640ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.16<br> (13294ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (11428ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.19<br> (25029ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.11<br> (24145ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned short> (random prime number products) + </p> + </td> +<td> + <p> + <span class="blue">1.26<br> (123821ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.92<br> (188438ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.21<br> (216289ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.12<br> (109274ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.67<br> (163434ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (97914ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned short> (uniform random numbers) + </p> + </td> +<td> + <p> + <span class="green">1.16<br> (169639ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.44<br> (212132ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.62<br> (237308ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.16<br> (170196ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.30<br> (191524ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (146827ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned> (Trivial cases) + </p> + </td> +<td> + <p> + <span class="blue">1.98<br> (117ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.61<br> (95ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.90<br> (112ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">2.00<br> (118ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.61<br> (95ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (59ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned> (adjacent Fibonacci numbers) + </p> + </td> +<td> + <p> + <span class="blue">1.28<br> (3381ns)</span> + </p> + </td> +<td> + <p> + <span class="red">8.39<br> (22209ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (2648ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.30<br> (3436ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.34<br> (3540ns)</span> + </p> + </td> +<td> + <p> + <span class="red">5.64<br> (14937ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned> (permutations of Fibonacci numbers) + </p> + </td> +<td> + <p> + <span class="green">1.08<br> (197785ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.47<br> (269176ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.37<br> (435412ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.12<br> (205095ns)</span> + </p> + </td> +<td> + <p> + <span class="red">2.08<br> (382592ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (183636ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned> (random prime number products) + </p> + </td> +<td> + <p> + <span class="green">1.09<br> (214890ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.42<br> (279881ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.99<br> (392760ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.05<br> (206420ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.61<br> (317337ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (197431ns)</span> + </p> + </td> +</tr> +<tr> +<td> + <p> + gcd<unsigned> (uniform random numbers) + </p> + </td> +<td> + <p> + <span class="blue">1.26<br> (385229ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.35<br> (411167ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.68<br> (512335ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.23<br> (375323ns)</span> + </p> + </td> +<td> + <p> + <span class="blue">1.32<br> (402786ns)</span> + </p> + </td> +<td> + <p> + <span class="green">1.00<br> (305574ns)</span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"><p><small>Last revised: April 03, 2020 at 11:57:28 GMT</small></p></td> +<td align="right"><div class="copyright-footer"></div></td> +</tr></table> +<hr> +<div class="spirit-nav"></div> +</body> +</html> diff --git a/src/boost/libs/math/reporting/performance/is_intel_win.cpp b/src/boost/libs/math/reporting/performance/is_intel_win.cpp new file mode 100644 index 000000000..fd1d94d15 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/is_intel_win.cpp @@ -0,0 +1,10 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/config.hpp> + +#ifndef __ICL +#error "wrong compiler" +#endif diff --git a/src/boost/libs/math/reporting/performance/performance.hpp b/src/boost/libs/math/reporting/performance/performance.hpp new file mode 100644 index 000000000..baf27950c --- /dev/null +++ b/src/boost/libs/math/reporting/performance/performance.hpp @@ -0,0 +1,119 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef PERFORMANCE_HPP +#define PERFORMANCE_HPP + +#include <boost/math/special_functions/relative_difference.hpp> +#include <boost/array.hpp> +#include <boost/chrono.hpp> +#include <boost/regex.hpp> +#include <iostream> +#include <iomanip> + +extern std::vector<std::vector<double> > data; + +template <class Array> +void add_data(const Array& a) +{ + // + // This function is called multiple times to merge multiple data sets into one big table: + // + for(typename Array::const_iterator i = a.begin(); i != a.end(); ++i) + { + data.push_back(std::vector<double>()); + for(typename Array::value_type::const_iterator j = i->begin(); j != i->end(); ++j) + { + data.back().push_back(*j); + } + } +} + +template <class Func, class Result> +void screen_data(Func f, Result r) +{ + // + // If any of the implementations being tested produces garbage for one of our + // test cases (or else if we test a domain they don't support), then we remove that + // row from the table. This allows us to only test a common supported sub-set for performance: + // + for(std::vector<std::vector<double> >::size_type row = 0; row < data.size(); ++row) + { + try + { + double computed = f(data[row]); + double expected = r(data[row]); + double err = boost::math::relative_difference(computed, expected); + if(err > 1e-7) + { + std::cout << "Erasing row: "; + for(unsigned i = 0; i < data[row].size(); ++i) + { + std::cout << data[row][i] << " "; + } + std::cout << "Error was " << err << std::endl; + data.erase(data.begin() + row); + --row; + } + } + catch(const std::exception& e) + { + std::cout << "Erasing row: "; + for(unsigned i = 0; i < data[row].size(); ++i) + { + std::cout << data[row][i] << " "; + } + std::cout << "due to thrown exception: " << e.what() << std::endl; + data.erase(data.begin() + row); + --row; + } + } +} + +template <class Clock> +struct stopwatch +{ + typedef typename Clock::duration duration; + stopwatch() + { + m_start = Clock::now(); + } + duration elapsed() + { + return Clock::now() - m_start; + } + void reset() + { + m_start = Clock::now(); + } + +private: + typename Clock::time_point m_start; +}; + +double sum = 0; + +template <class Func> +double exec_timed_test(Func f) +{ + double t = 0; + unsigned repeats = 1; + do{ + stopwatch<boost::chrono::high_resolution_clock> w; + + for(unsigned count = 0; count < repeats; ++count) + { + for(std::vector<std::vector<double> >::const_iterator i = data.begin(); i != data.end(); ++i) + sum += f(*i); + } + + t = boost::chrono::duration_cast<boost::chrono::duration<double>>(w.elapsed()).count(); + if(t < 0.5) + repeats *= 2; + } while(t < 0.5); + return t / (repeats * data.size()); +} + +#endif // PERFORMANCE_HPP diff --git a/src/boost/libs/math/reporting/performance/table_helper.cpp b/src/boost/libs/math/reporting/performance/table_helper.cpp new file mode 100644 index 000000000..c8ecfe23c --- /dev/null +++ b/src/boost/libs/math/reporting/performance/table_helper.cpp @@ -0,0 +1,400 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/regex.hpp> +#include <boost/lexical_cast.hpp> +#include <boost/filesystem.hpp> +#include <boost/filesystem/fstream.hpp> +#include <boost/interprocess/sync/named_mutex.hpp> +#include <boost/interprocess/sync/scoped_lock.hpp> +#include <vector> +#include <set> +#include <iostream> +#include <sstream> +#include <iomanip> +#include "table_helper.hpp" + +void add_cell(boost::intmax_t val, const std::string& table_name, const std::string& row_name, const std::string& column_heading); +void add_to_all_sections(const std::string& id, std::string list_name = "performance_all_sections"); + +std::vector<std::vector<double> > data; +std::vector<std::tuple<double, std::string, std::string, std::string> > items_to_add; + +inline std::string sanitize_string(const std::string& s) +{ + static const boost::regex e("[^a-zA-Z0-9]+"); + std::string result = boost::regex_replace(s, e, "_"); + while(result[0] == '_') + result.erase(0); + return result; +} + +std::string format_precision(double val, int digits) +{ + std::stringstream ss; + ss << std::setprecision(digits); + ss << std::fixed; + ss << val; + return ss.str(); +} + +static std::string content; +boost::filesystem::path path_to_content; + +struct content_loader +{ + content_loader(){} + ~content_loader() + { + boost::interprocess::named_mutex mu(boost::interprocess::open_or_create, "handle_test_result"); + boost::interprocess::scoped_lock<boost::interprocess::named_mutex> lock(mu); + boost::filesystem::path p(__FILE__); + p = p.parent_path(); + p /= "doc"; + p /= "performance_tables.qbk"; + path_to_content = p; + if(boost::filesystem::exists(p)) + { + boost::filesystem::ifstream is(p); + if(is.good()) + { + do + { + char c = static_cast<char>(is.get()); + if(c != EOF) + content.append(1, c); + } while(is.good()); + } + } + // + // Now iterate through results and add them one at a time: + // + for(auto i = items_to_add.begin(); i != items_to_add.end(); ++i) + { + add_cell(static_cast<boost::uintmax_t>(std::get<0>(*i) / 1e-9), std::get<1>(*i), std::get<2>(*i), std::get<3>(*i)); + } + // + // Write out the results: + // + boost::filesystem::ofstream os(path_to_content); + os << content; + } + void instantiate()const + { + } +}; + +static const content_loader loader; + +void load_table(std::vector<std::vector<std::string> >& table, std::string::const_iterator begin, std::string::const_iterator end) +{ + static const boost::regex item_e( + "\\[" + "([^\\[\\]]*(?0)?)*" + "\\]" + ); + + boost::regex_token_iterator<std::string::const_iterator> i(begin, end, item_e), j; + + while(i != j) + { + // Add a row: + table.push_back(std::vector<std::string>()); + boost::regex_token_iterator<std::string::const_iterator> k(i->first + 1, i->second - 1, item_e); + while(k != j) + { + // Add a cell: + table.back().push_back(std::string(k->first + 1, k->second - 1)); + ++k; + } + ++i; + } +} + +std::string save_table(std::vector<std::vector<std::string> >& table) +{ + std::string result; + + for(std::vector<std::vector<std::string> >::const_iterator i = table.begin(), j = table.end(); i != j; ++i) + { + result += "["; + for(std::vector<std::string>::const_iterator k = i->begin(), l = i->end(); k != l; ++k) + { + result += "["; + result += *k; + result += "]"; + } + result += "]\n"; + } + return result; +} + +void add_to_all_sections(const std::string& id, std::string list_name) +{ + std::string::size_type pos = content.find("[template " + list_name + "[]"), end_pos; + if(pos == std::string::npos) + { + // + // Just append to the end: + // + content.append("\n[template ").append(list_name).append("[]\n[").append(id).append("]\n]\n"); + } + else + { + // + // Read in the all list of sections, add our new one (in alphabetical order), + // and then rewrite the whole thing: + // + static const boost::regex item_e( + "\\[" + "((?=[^\\]])[^\\[\\]]*+(?0)?+)*+" + "\\]|\\]" + ); + boost::regex_token_iterator<std::string::const_iterator> i(content.begin() + pos + 12 + list_name.size(), content.end(), item_e), j; + std::set<std::string> sections; + while(i != j) + { + if(i->length() == 1) + { + end_pos = i->first - content.begin(); + break; + } + sections.insert(std::string(i->first + 1, i->second - 1)); + ++i; + } + sections.insert(id); + std::string new_list = "\n"; + for(std::set<std::string>::const_iterator sec = sections.begin(); sec != sections.end(); ++sec) + { + new_list += "[" + *sec + "]\n"; + } + content.replace(pos + 12 + list_name.size(), end_pos - pos - 12 - list_name.size(), new_list); + } +} + +std::string get_colour(boost::uintmax_t val, boost::uintmax_t best) +{ + if(val <= best * 1.2) + return "green"; + if(val > best * 2) + return "red"; + return "blue"; +} + +boost::intmax_t get_value_from_cell(const std::string& cell) +{ + static const boost::regex time_e("(\\d+)ns"); + boost::smatch what; + if(regex_search(cell, what, time_e)) + { + return boost::lexical_cast<boost::uintmax_t>(what.str(1)); + } + return -1; +} + +void add_cell(boost::intmax_t val, const std::string& table_name, const std::string& row_name, const std::string& column_heading) +{ + // + // Load the table, add our data, and re-write: + // + std::string table_id = "table_" + sanitize_string(table_name); + boost::regex table_e("\\[table:" + table_id + + "\\s[^\\[]++" + "((\\[" + "([^\\[\\]]*+(?2)?+)*+" + "\\]\\s*+)*+\\s*+)" + "\\]" + ); + + boost::smatch table_location; + if(regex_search(content, table_location, table_e)) + { + std::vector<std::vector<std::string> > table_data; + load_table(table_data, table_location[1].first, table_location[1].second); + // + // Figure out which column we're on: + // + unsigned column_id = 1001u; + for(unsigned i = 0; i < table_data[0].size(); ++i) + { + if(table_data[0][i] == column_heading) + { + column_id = i; + break; + } + } + if(column_id > 1000) + { + // + // Need a new column, must be adding a new compiler to the table! + // + table_data[0].push_back(column_heading); + for(unsigned i = 1; i < table_data.size(); ++i) + table_data[i].push_back(std::string()); + column_id = table_data[0].size() - 1; + } + // + // Figure out the row: + // + unsigned row_id = 1001; + for(unsigned i = 1; i < table_data.size(); ++i) + { + if(table_data[i][0] == row_name) + { + row_id = i; + break; + } + } + if(row_id > 1000) + { + // + // Need a new row, add it now: + // + table_data.push_back(std::vector<std::string>()); + table_data.back().push_back(row_name); + for(unsigned i = 1; i < table_data[0].size(); ++i) + table_data.back().push_back(std::string()); + row_id = table_data.size() - 1; + } + // + // Find the best result in this row: + // + boost::uintmax_t best = (std::numeric_limits<boost::uintmax_t>::max)(); + std::vector<boost::intmax_t> values; + for(unsigned i = 1; i < table_data[row_id].size(); ++i) + { + if(i == column_id) + { + if(val < best) + best = val; + values.push_back(val); + } + else + { + std::cout << "Existing cell value was " << table_data[row_id][i] << std::endl; + boost::uintmax_t cell_val = get_value_from_cell(table_data[row_id][i]); + std::cout << "Extracted value: " << cell_val << std::endl; + if(cell_val < best) + best = cell_val; + values.push_back(cell_val); + } + } + // + // Update the row: + // + for(unsigned i = 1; i < table_data[row_id].size(); ++i) + { + std::string& s = table_data[row_id][i]; + s = "[role "; + if(values[i - 1] < 0) + { + s += "grey -]"; + } + else + { + s += get_colour(values[i - 1], best); + s += " "; + s += format_precision(static_cast<double>(values[i - 1]) / best, 2); + s += "[br]("; + s += boost::lexical_cast<std::string>(values[i - 1]) + "ns)]"; + } + } + // + // Convert back to a string and insert into content: + std::sort(table_data.begin() + 1, table_data.end(), [](std::vector<std::string> const& a, std::vector<std::string> const& b) { return a[0] < b[0]; } ); + std::string c = save_table(table_data); + content.replace(table_location.position(1), table_location.length(1), c); + } + else + { + // + // Create a new table and try again: + // + std::string new_table = "\n[template " + table_id; + new_table += "[]\n[table:" + table_id; + new_table += " "; + new_table += table_name; + new_table += "\n[[Function]["; + new_table += column_heading; + new_table += "]]\n"; + new_table += "[["; + new_table += row_name; + new_table += "][[role blue 1.00[br]("; + new_table += boost::lexical_cast<std::string>(val); + new_table += "ns)]]]\n]\n]\n"; + + std::string::size_type pos = content.find("[/tables:]"); + if(pos != std::string::npos) + content.insert(pos + 10, new_table); + else + content += "\n\n[/tables:]\n" + new_table; + // + // Add a section for this table as well: + // + std::string section_id = "section_" + sanitize_string(table_name); + if(content.find(section_id + "[]") == std::string::npos) + { + std::string new_section = "\n[template " + section_id + "[]\n[section:" + section_id + " " + table_name + "]\n[" + table_id + "]\n[endsect]\n]\n"; + pos = content.find("[/sections:]"); + if(pos != std::string::npos) + content.insert(pos + 12, new_section); + else + content += "\n\n[/sections:]\n" + new_section; + add_to_all_sections(section_id); + } + // + // Add to list of all tables (not in sections): + // + add_to_all_sections(table_id, "performance_all_tables"); + } +} + +void report_execution_time(double t, std::string table, std::string row, std::string heading) +{ + items_to_add.push_back(std::make_tuple(t, table, row, heading)); + //add_cell(static_cast<boost::uintmax_t>(t / 1e-9), table, row, heading); +} + +std::string get_compiler_options_name() +{ +#if defined(BOOST_MSVC) || defined(__ICL) + std::string result; +#ifdef BOOST_MSVC + result = "cl "; +#else + result = "icl "; +#endif +#ifdef _M_AMD64 +#ifdef __AVX__ + result += "/arch:AVX /Ox"; +#else + result += "/Ox"; +#endif + result += " (x64 build)"; +#else +#ifdef _DEBUG + result += "/Od"; +#elif defined(__AVX2__) + result += "/arch:AVX2 /Ox"; +#elif defined(__AVX__) + result += "/arch:AVX /Ox"; +#elif _M_IX86_FP == 2 + result += "/arch:sse2 /Ox"; +#else + result += "/arch:ia32 /Ox"; +#endif + result += " (x86 build)"; +#endif + std::cout << "Compiler options are found as: " << result << std::endl; + return result; +#else + return "Unknown"; +#endif +} + diff --git a/src/boost/libs/math/reporting/performance/table_helper.hpp b/src/boost/libs/math/reporting/performance/table_helper.hpp new file mode 100644 index 000000000..1eb3a5c1a --- /dev/null +++ b/src/boost/libs/math/reporting/performance/table_helper.hpp @@ -0,0 +1,325 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef TABLE_HELPER_HPP +#define TABLE_HELPER_HPP + +#include <vector> +#include <string> +#include <boost/version.hpp> +#include <boost/lexical_cast.hpp> + +// +// Also include headers for whatever else we may be testing: +// +#ifdef TEST_LIBSTDCXX +#include <tr1/cmath> +#include <stdexcept> +#endif +#ifdef TEST_GSL +#include <gsl/gsl_sf.h> +#include <gsl/gsl_errno.h> +#include <gsl/gsl_version.h> + +void gsl_handler(const char * reason, const char * file, int line, int gsl_errno) +{ + if(gsl_errno == GSL_ERANGE) return; // handle zero or infinity in our test code. +#ifdef DISTRIBUTIONS_TEST + return; +#else + throw std::domain_error(reason); +#endif +} + +struct gsl_error_handler_setter +{ + gsl_error_handler_t * old_handler; + gsl_error_handler_setter() + { + old_handler = gsl_set_error_handler(gsl_handler); + } + ~gsl_error_handler_setter() + { + gsl_set_error_handler(old_handler); + } +}; + +static const gsl_error_handler_setter handler; + +#endif + +#ifdef TEST_RMATH +// Rmath overloads ftrunc, leading to strange errors from GCC unless we include this: +#include <boost/math/special_functions.hpp> +#define MATHLIB_STANDALONE +#include <Rmath.h> +#endif + +#ifdef TEST_DCDFLIB +extern "C" { + extern void cdfbet(int*, double*, double*, double*, double*, double*, double*, int*, double*); + extern void cdfbin(int*, double*, double*, double*, double*, double*, double*, int*, double*); + extern void cdfchi(int*, double*, double*, double*, double*, int*, double*); + extern void cdfchn(int*, double*, double*, double*, double*, double*, int*, double*); + extern void cdff(int*, double*, double*, double*, double*, double*, int*, double*); + extern void cdffnc(int*, double*, double*, double*, double*, double*, double*, int*s, double*); + extern void cdfgam(int*, double*, double*, double*, double*, double*, int*, double*); + extern void cdfnbn(int*, double*, double*, double*, double*, double*, double*, int*, double*); + extern void cdfnor(int*, double*, double*, double*, double*, double*, int*, double*); + extern void cdfpoi(int*, double*, double*, double*, double*, int*, double*); + extern void cdft(int*, double*, double*, double*, double*, int*, double*); + //extern void cdftnc(int*, double*, double*, double*, double*, double*, int*, double*); +} + +inline double dcdflib_beta_cdf(double x, double a, double b) +{ + int what = 1; + int status = 0; + double p, q, bound, y(1-x); + cdfbet(&what, &p, &q, &x, &y, &a, &b, &status, &bound); + return p; +} + +inline double dcdflib_beta_quantile(double p, double a, double b) +{ + int what = 2; + int status = 0; + double x, y, bound, q(1 - p); + cdfbet(&what, &p, &q, &x, &y, &a, &b, &status, &bound); + return x; +} + +inline double dcdflib_binomial_cdf(double x, double s, double sf) +{ + int what = 1; + int status = 0; + double p, q, bound, sfc(1-sf); + cdfbin(&what, &p, &q, &x, &s, &sf, &sfc, &status, &bound); + return p; +} + +inline double dcdflib_binomial_quantile(double p, double s, double sf) +{ + int what = 2; + int status = 0; + double x, bound, q(1 - p), sfc(1-sf); + cdfbin(&what, &p, &q, &x, &s, &sf, &sfc, &status, &bound); + return x; +} + +inline double dcdflib_chi_cdf(double x, double df) +{ + int what = 1; + int status = 0; + double p, q, bound; + cdfchi(&what, &p, &q, &x, &df, &status, &bound); + return p; +} + +inline double dcdflib_chi_quantile(double p, double df) +{ + int what = 2; + int status = 0; + double x, bound, q(1 - p); + cdfchi(&what, &p, &q, &x, &df, &status, &bound); + return x; +} + +inline double dcdflib_chi_n_cdf(double x, double df, double nc) +{ + int what = 1; + int status = 0; + double p, q, bound; + cdfchn(&what, &p, &q, &x, &df, &nc, &status, &bound); + return p; +} + +inline double dcdflib_chi_n_quantile(double p, double df, double nc) +{ + int what = 2; + int status = 0; + double x, bound, q(1 - p); + cdfchn(&what, &p, &q, &x, &df, &nc, &status, &bound); + return x; +} + +inline double dcdflib_f_cdf(double x, double df1, double df2) +{ + int what = 1; + int status = 0; + double p, q, bound; + cdff(&what, &p, &q, &x, &df1, &df2, &status, &bound); + return p; +} + +inline double dcdflib_f_quantile(double p, double df1, double df2) +{ + int what = 2; + int status = 0; + double x, bound, q(1 - p); + cdff(&what, &p, &q, &x, &df1, &df2, &status, &bound); + return x; +} + +inline double dcdflib_f_n_cdf(double x, double df1, double df2, double nc) +{ + int what = 1; + int status = 0; + double p, q, bound; + cdffnc(&what, &p, &q, &x, &df1, &df2, &nc, &status, &bound); + return p; +} + +inline double dcdflib_f_n_quantile(double p, double df1, double df2, double nc) +{ + int what = 2; + int status = 0; + double x, bound, q(1 - p); + cdffnc(&what, &p, &q, &x, &df1, &df2, &nc, &status, &bound); + return x; +} + +inline double dcdflib_gamma_cdf(double x, double shape, double scale) +{ + int what = 1; + int status = 0; + double p, q, bound; + scale = 1 / scale; + cdfgam(&what, &p, &q, &x, &shape, &scale, &status, &bound); + return p; +} + +inline double dcdflib_gamma_quantile(double p, double shape, double scale) +{ + int what = 2; + int status = 0; + double x, bound, q(1 - p); + scale = 1 / scale; + cdfgam(&what, &p, &q, &x, &shape, &scale, &status, &bound); + return x; +} + +inline double dcdflib_nbin_cdf(double x, double r, double sf) +{ + int what = 1; + int status = 0; + double p, q, bound, sfc(1 - sf); + cdfnbn(&what, &p, &q, &x, &r, &sf, &sfc, &status, &bound); + return p; +} + +inline double dcdflib_nbin_quantile(double p, double r, double sf) +{ + int what = 2; + int status = 0; + double x, bound, q(1 - p), sfc(1 - sf); + cdfnbn(&what, &p, &q, &x, &r, &sf, &sfc, &status, &bound); + return x; +} + +inline double dcdflib_norm_cdf(double x, double mean, double sd) +{ + int what = 1; + int status = 0; + double p, q, bound; + cdfnor(&what, &p, &q, &x, &mean, &sd, &status, &bound); + return p; +} + +inline double dcdflib_norm_quantile(double p, double mean, double sd) +{ + int what = 2; + int status = 0; + double x, bound, q(1 - p); + cdfnor(&what, &p, &q, &x, &mean, &sd, &status, &bound); + return x; +} + +inline double dcdflib_poisson_cdf(double x, double param) +{ + int what = 1; + int status = 0; + double p, q, bound; + cdfpoi(&what, &p, &q, &x, ¶m, &status, &bound); + return p; +} + +inline double dcdflib_poisson_quantile(double p, double param) +{ + int what = 2; + int status = 0; + double x, bound, q(1 - p); + cdfpoi(&what, &p, &q, &x, ¶m, &status, &bound); + return x; +} + +inline double dcdflib_t_cdf(double x, double param) +{ + int what = 1; + int status = 0; + double p, q, bound; + cdft(&what, &p, &q, &x, ¶m, &status, &bound); + return p; +} + +inline double dcdflib_t_quantile(double p, double param) +{ + int what = 2; + int status = 0; + double x, bound, q(1 - p); + cdft(&what, &p, &q, &x, ¶m, &status, &bound); + return x; +} +/* +inline double dcdflib_t_n_cdf(double x, double param, double nc) +{ + int what = 1; + int status = 0; + double p, q, bound; + cdftnc(&what, &p, &q, &x, ¶m, &nc, &status, &bound); + return p; +} + +inline double dcdflib_t_n_quantile(double p, double param, double nc) +{ + int what = 2; + int status = 0; + double x, bound, q(1 - p); + cdftnc(&what, &p, &q, &x, ¶m, &nc, &status, &bound); + return x; +} +*/ +#endif + +extern std::vector<std::vector<double> > data; + +void report_execution_time(double t, std::string table, std::string row, std::string heading); +std::string get_compiler_options_name(); + +inline std::string boost_name() +{ + return "boost " + boost::lexical_cast<std::string>(BOOST_VERSION / 100000) + "." + boost::lexical_cast<std::string>((BOOST_VERSION / 100) % 1000); +} + +inline std::string compiler_name() +{ +#ifdef COMPILER_NAME + return COMPILER_NAME; +#else + return BOOST_COMPILER; +#endif +} + +inline std::string platform_name() +{ +#ifdef _WIN32 + return "Windows x64"; +#else + return BOOST_PLATFORM; +#endif +} + +#endif // TABLE_HELPER_HPP + diff --git a/src/boost/libs/math/reporting/performance/test_assoc_laguerre.cpp b/src/boost/libs/math/reporting/performance/test_assoc_laguerre.cpp new file mode 100644 index 000000000..0232bb4e8 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_assoc_laguerre.cpp @@ -0,0 +1,81 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/laguerre.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + +int main() +{ +# include "laguerre3.ipp" + + add_data(laguerre3); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::laguerre(v[0], v[1], v[2]); }, [](const std::vector<double>& v){ return v[3]; }); + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return std::tr1::assoc_laguerre(v[0], v[1], v[2]); }, [](const std::vector<double>& v){ return v[3]; }); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_laguerre_n(v[0], v[1], v[2]); }, [](const std::vector<double>& v){ return v[3]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "assoc_laguerre[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "assoc_laguerre"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::laguerre(v[0], v[1], v[2]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::laguerre(v[0], v[1], v[2], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::assoc_laguerre(v[0], v[1], v[2]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_laguerre_n(v[0], v[1], v[2]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif + + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_assoc_legendre.cpp b/src/boost/libs/math/reporting/performance/test_assoc_legendre.cpp new file mode 100644 index 000000000..8245f9f49 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_assoc_legendre.cpp @@ -0,0 +1,80 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/legendre.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + +int main() +{ +# include "assoc_legendre_p.ipp" + + add_data(assoc_legendre_p); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::legendre_p(v[0], v[1], v[2]); }, [](const std::vector<double>& v){ return v[3]; }); + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return std::tr1::assoc_legendre(v[0], v[1], v[2]); }, [](const std::vector<double>& v){ return v[3]; }); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_legendre_Plm(v[0], v[1], v[2]); }, [](const std::vector<double>& v){ return v[3]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "assoc_legendre[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "assoc_legendre"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::legendre_p(v[0], v[1], v[2]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::legendre_p(v[0], v[1], v[2], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::assoc_legendre(v[0], v[1], v[2]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_legendre_Plm(v[0], v[1], v[2]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_beta.cpp b/src/boost/libs/math/reporting/performance/test_beta.cpp new file mode 100644 index 000000000..7ed8cca86 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_beta.cpp @@ -0,0 +1,92 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/beta.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + +int main() +{ +# include "beta_small_data.ipp" +# include "beta_med_data.ipp" +# include "beta_exp_data.ipp" + + add_data(beta_small_data); + add_data(beta_med_data); + add_data(beta_exp_data); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::beta(v[0], v[1]); }, [](const std::vector<double>& v){ return v[2]; }); + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return std::tr1::beta(v[0], v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_beta(v[0], v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return beta(v[0], v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "beta[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "beta"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::beta(v[0], v[1]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::beta(v[0], v[1], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::beta(v[0], v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_beta(v[0], v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return beta(v[0], v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "Rmath " R_VERSION_STRING); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_beta_inc.cpp b/src/boost/libs/math/reporting/performance/test_beta_inc.cpp new file mode 100644 index 000000000..a9b78a87a --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_beta_inc.cpp @@ -0,0 +1,81 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/beta.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + + +int main() +{ +# include "ibeta_small_data.ipp" +# include "ibeta_data.ipp" +# include "ibeta_large_data.ipp" +# include "ibeta_int_data.ipp" + + add_data(ibeta_small_data); + add_data(ibeta_data); + add_data(ibeta_large_data); + add_data(ibeta_int_data); + + unsigned data_total = data.size(); + + std::cout << "Screening boost data:\n"; + screen_data([](const std::vector<double>& v){ return boost::math::ibeta(v[0], v[1], v[2]); }, [](const std::vector<double>& v){ return v[5]; }); + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + std::cout << "Screening gsl data:\n"; + screen_data([](const std::vector<double>& v){ return gsl_sf_beta_inc(v[0], v[1], v[2]); }, [](const std::vector<double>& v){ return v[5]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "beta (incomplete)[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "beta (incomplete)"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::beta(v[0], v[1], v[2]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::beta(v[0], v[1], v[2], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_beta_inc(v[0], v[1], v[2]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_cbrt.cpp b/src/boost/libs/math/reporting/performance/test_cbrt.cpp new file mode 100644 index 000000000..8be48f900 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_cbrt.cpp @@ -0,0 +1,81 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/cbrt.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +int main() +{ + typedef double T; +#define SC_(x) static_cast<double>(x) +# include "../../test/cbrt_data.ipp" + + add_data(cbrt_data); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::cbrt(v[1]); }, [](const std::vector<double>& v){ return v[0]; }); + +#if defined(TEST_C99) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return ::cbrt(v[1]); }, [](const std::vector<double>& v){ return v[0]; }); +#endif +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return std::tr1::cbrt(v[1]); }, [](const std::vector<double>& v){ return v[0]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "cbrt[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "cbrt"; + + double time = exec_timed_test([](const std::vector<double>& v){ return boost::math::cbrt(v[1]); }); + std::cout << time << std::endl; +#if defined(COMPILER_COMPARISON_TABLES) + report_execution_time(time, std::string("Compiler Option Comparison on ") + platform_name(), "boost::math::cbrt", get_compiler_options_name()); +#else +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_C99) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); +#endif + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + double time = exec_timed_test([](const std::vector<double>& v){ return boost::math::cbrt(v[1], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_C99) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_C99) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return ::cbrt(v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "math.h"); +#endif +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::cbrt(v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif + + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_cn.cpp b/src/boost/libs/math/reporting/performance/test_cn.cpp new file mode 100644 index 000000000..eac28da75 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_cn.cpp @@ -0,0 +1,135 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/jacobi_elliptic.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + static const boost::array<boost::array<T, 5>, 36> data1 = {{ + {{ SC_(0.0), SC_(0.0), SC_(0.0), SC_(1.0), SC_(1.0) }}, + {{ ldexp(T(1), -25), ldexp(T(1), -25), SC_(2.98023223876953080883700663838486782870427050521881839342311e-8), SC_(0.99999999999999955591079014993741669975171697261290223678373), SC_(0.99999999999999999999999999999960556954738949421406900774443) }}, + {{ -ldexp(T(1), -25), ldexp(T(1), -25), SC_(-2.98023223876953080883700663838486782870427050521881839342311e-8), SC_(0.99999999999999955591079014993741669975171697261290223678373), SC_(0.99999999999999999999999999999960556954738949421406900774443) }}, + {{ SC_(0.25), ldexp(T(1), -25), SC_(0.247403959254522927383635623557663763268693729825996390997241), SC_(0.968912421710644784709721529742747886950140086772629513814665), SC_(0.99999999999999997281786831901333837240938011109848356555885) }}, + {{ SC_(-0.25), ldexp(T(1), -25), SC_(-0.247403959254522927383635623557663763268693729825996390997241), SC_(0.968912421710644784709721529742747886950140086772629513814665), SC_(0.99999999999999997281786831901333837240938011109848356555885) }}, + {{ SC_(1.25), ldexp(T(1), -25), SC_(0.948984619355586147780156037971989352776684194861616269831136), SC_(0.315322362395268865789580233344649598639316847638615703458263), SC_(0.99999999999999960006577747263860127231780811081154547949983) }}, + {{ SC_(-1.25), ldexp(T(1), -25), SC_(-0.948984619355586147780156037971989352776684194861616269831136), SC_(0.315322362395268865789580233344649598639316847638615703458263), SC_(0.99999999999999960006577747263860127231780811081154547949983) }}, + {{ SC_(25.0), ldexp(T(1), -25), SC_(-0.132351750097778560056127137329035522219365438979106560464704), SC_(0.991202811863472859528158119981178957382802975691690722810123), SC_(0.99999999999999999222089563757583834413059580275315226870704) }}, + {{ SC_(-25.0), ldexp(T(1), -25), SC_(0.132351750097778560056127137329035522219365438979106560464704), SC_(0.991202811863472859528158119981178957382802975691690722810123), SC_(0.99999999999999999222089563757583834413059580275315226870704) }}, + {{ ldexp(T(1), -25), SC_(0.5), SC_(2.98023223876953058825550995757802173334628440851964836958219e-8), SC_(0.99999999999999955591079014993744956895610118130967536624417), SC_(0.99999999999999988897769753748438088116649141278818704012037) }}, + {{ -ldexp(T(1), -25), SC_(0.5), SC_(-2.98023223876953058825550995757802173334628440851964836958219e-8), SC_(0.99999999999999955591079014993744956895610118130967536624417), SC_(0.99999999999999988897769753748438088116649141278818704012037) }}, + {{ SC_(0.25), SC_(0.5), SC_(0.246781405136141600483623741101255389743847413013817188632739), SC_(0.969071172865559727608777289021929824625726812182428398055476), SC_(0.992358168465276394946615469032829292963938826683866720698130) }}, + {{ SC_(-0.25), SC_(0.5), SC_(-0.246781405136141600483623741101255389743847413013817188632739), SC_(0.969071172865559727608777289021929824625726812182428398055476), SC_(0.992358168465276394946615469032829292963938826683866720698130) }}, + {{ SC_(1.25), SC_(0.5), SC_(0.928561236426319775700204388269999130782711902203415239399579), SC_(0.371179242693370810357222594552131893184749696381729988511999), SC_(0.885688154799196841458565445994481097477880319663264816077719) }}, + {{ SC_(-1.25), SC_(0.5), SC_(-0.928561236426319775700204388269999130782711902203415239399579), SC_(0.371179242693370810357222594552131893184749696381729988511999), SC_(0.885688154799196841458565445994481097477880319663264816077719) }}, + {{ SC_(25.0), SC_(0.5), SC_(-0.969223071486651608400225080456020493867827336842041561445359), SC_(-0.246184154035106463351874891855925292474628176040625311168501), SC_(0.874729477852721764836147376110255133761608728373832418508248) }}, + {{ SC_(-25.0), SC_(0.5), SC_(0.969223071486651608400225080456020493867827336842041561445359), SC_(-0.246184154035106463351874891855925292474628176040625311168501), SC_(0.874729477852721764836147376110255133761608728373832418508248) }}, + {{ ldexp(T(1), -25), 1 - ldexp(T(1), -9), SC_(2.98023223876953036939562331632512854347569015560128614888589e-8), SC_(0.99999999999999955591079014993754766348947956082687878223721), SC_(0.99999999999999955764381956001984590118394542979655101564079) }}, + {{ -ldexp(T(1), -25), 1 - ldexp(T(1), -9), SC_(-2.98023223876953036939562331632512854347569015560128614888589e-8), SC_(0.99999999999999955591079014993754766348947956082687878223721), SC_(0.99999999999999955764381956001984590118394542979655101564079) }}, + {{ SC_(0.25), 1 - ldexp(T(1), -9), SC_(0.244928335616519632082236089277654937383208524525331032303082), SC_(0.969541185516180906431546524888118346090913555188425579774305), SC_(0.969661908643964623248878987955178702010392829596222190545649) }}, + {{ SC_(-0.25), 1 - ldexp(T(1), -9), SC_(-0.244928335616519632082236089277654937383208524525331032303082), SC_(0.969541185516180906431546524888118346090913555188425579774305), SC_(0.969661908643964623248878987955178702010392829596222190545649) }}, + {{ SC_(1.25), 1 - ldexp(T(1), -9), SC_(0.848768940045053312079390719205939167551169094157365783446523), SC_(0.528763923140371497228677918580246099580380684604621321430057), SC_(0.531415689278260818860813380561526095359692710060403584603095) }}, + {{ SC_(-1.25), 1 - ldexp(T(1), -9), SC_(-0.848768940045053312079390719205939167551169094157365783446523), SC_(0.528763923140371497228677918580246099580380684604621321430057), SC_(0.531415689278260818860813380561526095359692710060403584603095) }}, + {{ SC_(25.0), 1 - ldexp(T(1), -9), SC_(-0.0252326124525503880903568715488227138184083895871544015366337), SC_(-0.999681606947341709011836635135181960590782564534371631099332), SC_(0.999682849652724146508471774051629114156076052044812654903417) }}, + {{ SC_(-25.0), 1 - ldexp(T(1), -9), SC_(0.0252326124525503880903568715488227138184083895871544015366337), SC_(-0.999681606947341709011836635135181960590782564534371631099332), SC_(0.999682849652724146508471774051629114156076052044812654903417) }}, + + // Try modulus > 1 + {{ ldexp(T(1), -25), SC_(1.5), SC_(2.98023223876952981622027157475276613133414644789222481971590e-8), SC_(0.999999999999999555910790149937712522591174851747994454928040), SC_(0.999999999999999000799277837359575841918151654603571877092161) }}, + {{ -ldexp(T(1), -25), SC_(1.5), SC_(-2.98023223876952981622027157475276613133414644789222481971590e-8), SC_(0.999999999999999555910790149937712522591174851747994454928040), SC_(0.999999999999999000799277837359575841918151654603571877092161) }}, + {{ SC_(0.25), SC_(1.5), SC_(0.241830488135945315134822478837394038661484435596992059686086), SC_(0.970318512143270619246031961334217540099946232418710982266812), SC_(0.931888155181641649031244632258710371461078255228024421800363) }}, + {{ SC_(-0.25), SC_(1.5), SC_(-0.241830488135945315134822478837394038661484435596992059686086), SC_(0.970318512143270619246031961334217540099946232418710982266812), SC_(0.931888155181641649031244632258710371461078255228024421800363) }}, + {{ SC_(1.25), SC_(1.5), SC_(0.665875890711922169121186264316618499018039094009893317545462), SC_(0.746062529663971452521312655373498959968622875614588791642250), SC_(-0.0486921028438866868299166778939466685768843580182675008164949) }}, + {{ SC_(-1.25), SC_(1.5), SC_(-0.665875890711922169121186264316618499018039094009893317545462), SC_(0.746062529663971452521312655373498959968622875614588791642250), SC_(-0.0486921028438866868299166778939466685768843580182675008164949) }}, + {{ SC_(25.0), SC_(1.5), SC_(0.618665338981368217712277210270169521641154921220796362724248), SC_(0.785654630447163313102421517325310755764805805534154371583941), SC_(0.372585153048138377269609818284480926623056458773704266654150) }}, + {{ SC_(-25.0), SC_(1.5), SC_(-0.618665338981368217712277210270169521641154921220796362724248), SC_(0.785654630447163313102421517325310755764805805534154371583941), SC_(0.372585153048138377269609818284480926623056458773704266654150) }}, + + // Special Values: + {{ SC_(0.0), SC_(0.5), SC_(0.0), SC_(1.0), SC_(1.0) }}, + {{ SC_(5.0), SC_(0.0), SC_(-0.958924274663138468893154406155993973352461543964601778131672), SC_(0.283662185463226264466639171513557308334422592252215944930359), SC_(1.0) }}, + {{ SC_(5.0), SC_(1.0), SC_(0.999909204262595131210990447534473021089812615990547862736429), SC_(0.0134752822213045573055191382448821552908373539417006868332819), SC_(0.0134752822213045573055191382448821552908373539417006868332819) }}, + }}; + + +int main() +{ +#include "jacobi_elliptic.ipp" +#include "jacobi_elliptic_small.ipp" +#include "jacobi_near_1.ipp" +#include "jacobi_large_phi.ipp" + + add_data(data1); + add_data(jacobi_elliptic); + add_data(jacobi_elliptic_small); + add_data(jacobi_near_1); + add_data(jacobi_large_phi); + + unsigned data_total = data.size(); + + + std::cout << "Screening Boost data:\n"; + screen_data([](const std::vector<double>& v){ return boost::math::jacobi_cn(v[1], v[0]); }, [](const std::vector<double>& v){ return v[3]; }); + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + std::cout << "Screening GSL data:\n"; + screen_data([](const std::vector<double>& v) + { + double s, c, d; + gsl_sf_elljac_e(v[0], v[1] * v[1], &s, &c, &d); + return c; + }, [](const std::vector<double>& v){ return v[3]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "jacobi_cn[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "jacobi_cn"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::jacobi_cn(v[1], v[2]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::jacobi_cn(v[1], v[0], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v) + { + double s, c, d; + gsl_sf_elljac_e(v[0], v[1] * v[1], &s, &c, &d); + return c; + }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_digamma.cpp b/src/boost/libs/math/reporting/performance/test_digamma.cpp new file mode 100644 index 000000000..57a598e16 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_digamma.cpp @@ -0,0 +1,100 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/digamma.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +int main() +{ + typedef double T; +#define SC_(x) static_cast<double>(x) +# include "digamma_data.ipp" +# include "digamma_root_data.ipp" +# include "digamma_small_data.ipp" +# include "digamma_neg_data.ipp" + static const boost::array<boost::array<T, 2>, 5> digamma_bugs = {{ + // Test cases from Rocco Romeo: + {{ static_cast<T>(std::ldexp(1.0, -100)), SC_(-1.26765060022822940149670320537657721566490153286060651209008e30) }}, + {{ static_cast<T>(-std::ldexp(1.0, -100)), SC_(1.26765060022822940149670320537542278433509846713939348790992e30) }}, + {{ static_cast<T>(1), SC_(-0.577215664901532860606512090082402431042159335939923598805767) }}, + {{ static_cast<T>(-1) + static_cast<T>(std::ldexp(1.0, -20)), SC_(-1.04857557721314249602848739817764518743062133735858753112190e6) }}, + {{ static_cast<T>(-1) - static_cast<T>(std::ldexp(1.0, -20)), SC_(1.04857642278181269259522681939281063878220298942888100442172e6) }}, + }}; + static const boost::array<boost::array<T, 2>, 40> digamma_integers = { { + { 1, SC_(-0.57721566490153286060651209008240243) }, { 2, SC_(0.42278433509846713939348790991759757) }, { 3, SC_(0.92278433509846713939348790991759757) }, { 4, SC_(1.2561176684318004727268212432509309) }, { 5, SC_(1.5061176684318004727268212432509309) }, { 6, SC_(1.7061176684318004727268212432509309) }, { 7, SC_(1.8727843350984671393934879099175976) }, { 8, SC_(2.0156414779556099965363450527747404) }, { 9, SC_(2.1406414779556099965363450527747404) }, { SC_(10.0), SC_(2.2517525890667211076474561638858515) }, { SC_(11.0), SC_(2.3517525890667211076474561638858515) }, { SC_(12.0), SC_(2.4426616799758120167383652547949424) }, { SC_(13.0), SC_(2.5259950133091453500716985881282758) }, { SC_(14.0), SC_(2.6029180902322222731486216650513527) }, { SC_(15.0), SC_(2.6743466616607937017200502364799241) }, { SC_(16.0), SC_(2.7410133283274603683867169031465908) }, { SC_(17.0), SC_(2.8035133283274603683867169031465908) }, { SC_(18.0), SC_(2.8623368577392250742690698443230614) }, { SC_(19.0), SC_(2.9178924132947806298246253998786169) }, { SC_(20.0), SC_(2.9705239922421490508772569788259854) }, { SC_(21.0), SC_(3.0205239922421490508772569788259854) }, { SC_(22.0), SC_(3.0681430398611966699248760264450330) }, { SC_(23.0), SC_(3.1135975853157421244703305718995784) }, { SC_(24.0), SC_(3.1570758461853073418616349197256654) }, { SC_(25.0), SC_(3.1987425128519740085283015863923321) }, { SC_(26.0), SC_(3.2387425128519740085283015863923321) }, { SC_(27.0), SC_(3.2772040513135124700667631248538705) }, { SC_(28.0), SC_(3.3142410883505495071038001618909076) }, { SC_(29.0), SC_(3.3499553740648352213895144476051933) }, { SC_(30.0), SC_(3.3844381326855248765619282407086415) }, { SC_(31.0), SC_(3.4177714660188582098952615740419749) }, { SC_(32.0), SC_(3.4500295305349872421533260901710071) }, { SC_(33.0), SC_(3.4812795305349872421533260901710071) }, { SC_(34.0), SC_(3.5115825608380175451836291204740374) }, { SC_(35.0), SC_(3.5409943255438998981248055910622727) }, { SC_(36.0), SC_(3.5695657541153284695533770196337013) }, { SC_(37.0), SC_(3.5973435318931062473311547974114791) }, { SC_(38.0), SC_(3.6243705589201332743581818244385061) }, { SC_(39.0), SC_(3.6506863483938174848844976139121903) }, { SC_(40.0), SC_(3.6763273740348431259101386395532160) } + } }; + static const boost::array<boost::array<T, 2>, 41> digamma_half_integers = { { + { SC_(0.5), SC_(-1.9635100260214234794409763329987556) }, { SC_(1.5), SC_(0.036489973978576520559023667001244433) }, { SC_(2.5), SC_(0.70315664064524318722569033366791110) }, { SC_(3.5), SC_(1.1031566406452431872256903336679111) }, { SC_(4.5), SC_(1.3888709263595289015114046193821968) }, { SC_(5.5), SC_(1.6110931485817511237336268416044190) }, { SC_(6.5), SC_(1.7929113303999329419154450234226009) }, { SC_(7.5), SC_(1.9467574842460867880692911772687547) }, { SC_(8.5), SC_(2.0800908175794201214026245106020880) }, { SC_(9.5), SC_(2.1977378764029495331673303929550292) }, { SC_(10.5), SC_(2.3030010342976863752725935508497661) }, { SC_(11.5), SC_(2.3982391295357816133678316460878613) }, { SC_(12.5), SC_(2.4851956512749120481504403417400352) }, { SC_(13.5), SC_(2.5651956512749120481504403417400352) }, { SC_(14.5), SC_(2.6392697253489861222245144158141093) }, { SC_(15.5), SC_(2.7082352425903654325693420020210058) }, { SC_(16.5), SC_(2.7727513716226234970854710342790703) }, { SC_(17.5), SC_(2.8333574322286841031460770948851310) }, { SC_(18.5), SC_(2.8905002893715412460032199520279881) }, { SC_(19.5), SC_(2.9445543434255953000572740060820421) }, { SC_(20.5), SC_(2.9958363947076465821085560573640934) }, { SC_(21.5), SC_(3.0446168825125246308890438622421422) }, { SC_(22.5), SC_(3.0911285104195013750750903738700492) }, { SC_(23.5), SC_(3.1355729548639458195195348183144936) }, { SC_(24.5), SC_(3.1781261463533075216471943927825787) }, { SC_(25.5), SC_(3.2189424728839197665451535764560481) }, { SC_(26.5), SC_(3.2581581591584295704667222039070285) }, { SC_(27.5), SC_(3.2958940082150333440516278642843870) }, { SC_(28.5), SC_(3.3322576445786697076879915006480234) }, { SC_(29.5), SC_(3.3673453638769153217230792199462690) }, { SC_(30.5), SC_(3.4012436689616610844349436267259300) }, { SC_(31.5), SC_(3.4340305542075627237792059218078972) }, { SC_(32.5), SC_(3.4657765859535944698109519535539290) }, { SC_(33.5), SC_(3.4965458167228252390417211843231597) }, { SC_(34.5), SC_(3.5263965629914819554596316320843538) }, { SC_(35.5), SC_(3.5553820702378587670538345306350784) }, { SC_(36.5), SC_(3.5835510843223658093073556573956418) }, { SC_(37.5), SC_(3.6109483445963384120470816847929021) }, { SC_(38.5), SC_(3.6376150112630050787137483514595687) }, { SC_(39.5), SC_(3.6635890372370310527397223774335947) }, { SC_(40.5), SC_(3.6889054929332335843852919976867593) } + } }; + + add_data(digamma_data); + add_data(digamma_root_data); + add_data(digamma_small_data); + add_data(digamma_neg_data); + add_data(digamma_bugs); + add_data(digamma_integers); + add_data(digamma_half_integers); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::digamma(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_psi(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return ::digamma(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "digamma[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "digamma"; + + double time = exec_timed_test([](const std::vector<double>& v){ return boost::math::digamma(v[0]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + double time = exec_timed_test([](const std::vector<double>& v){ return boost::math::digamma(v[0], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_psi(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return ::digamma(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "Rmath " R_VERSION_STRING); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_distributions.cpp b/src/boost/libs/math/reporting/performance/test_distributions.cpp new file mode 100644 index 000000000..ddd72ee96 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_distributions.cpp @@ -0,0 +1,750 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error +#define DISTRIBUTIONS_TEST + +#include <boost/math/distributions.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +#ifdef TEST_GSL +#include <gsl/gsl_cdf.h> +#endif + +class distribution_tester +{ + std::string distro_name; + static const double quantiles[19]; + double sum; + + struct param_info + { + std::vector<double> params; + std::vector<double> x_values; + }; + std::vector<param_info> tests; + double sanitize_x(double x) + { + if(x > boost::math::tools::max_value<float>() / 2) + return boost::math::tools::max_value<float>() / 2; + if(x < -boost::math::tools::max_value<float>() / 2) + return -boost::math::tools::max_value<float>() / 2; + return x; + } +public: + distribution_tester(const char* name) : distro_name(name), sum(0) {} + + template <class F> + void add_test_case(F f) + { + tests.push_back(param_info()); + for(unsigned i = 0; i < sizeof(quantiles) / sizeof(quantiles[0]); ++i) + { + tests.back().x_values.push_back(sanitize_x(f(quantiles[i]))); + } + } + template <class F> + void add_test_case(double p1, F f) + { + tests.push_back(param_info()); + tests.back().params.push_back(p1); + for(unsigned i = 0; i < sizeof(quantiles) / sizeof(quantiles[0]); ++i) + { + tests.back().x_values.push_back(sanitize_x(f(p1, quantiles[i]))); + } + } + template <class F> + void add_test_case(double p1, double p2, F f) + { + tests.push_back(param_info()); + tests.back().params.push_back(p1); + tests.back().params.push_back(p2); + for(unsigned i = 0; i < sizeof(quantiles) / sizeof(quantiles[0]); ++i) + { + tests.back().x_values.push_back(sanitize_x(f(p1, p2, quantiles[i]))); + } + } + template <class F> + void add_test_case(double p1, double p2, double p3, F f) + { + tests.push_back(param_info()); + tests.back().params.push_back(p1); + tests.back().params.push_back(p2); + tests.back().params.push_back(p3); + for(unsigned i = 0; i < sizeof(quantiles) / sizeof(quantiles[0]); ++i) + { + tests.back().x_values.push_back(sanitize_x(f(p1, p2, p3, quantiles[i]))); + } + } + + enum + { + main_table = 1, + boost_only_table = 2, + both_tables = 3 + }; + + template <class F> + void run_timed_tests(F f, std::string sub_name, std::string column, bool p_value = false, int where = main_table) + { + std::cout << "Testing " << distro_name + " (" + std::string(sub_name) + ")" << " with library " << column << std::endl; + try{ + double t = 0; + unsigned repeats = 1; + unsigned data_size; + do{ + data_size = 0; + stopwatch<boost::chrono::high_resolution_clock> w; + + for(unsigned count = 0; count < repeats; ++count) + { + for(unsigned i = 0; i < tests.size(); ++i) + { + for(unsigned j = 0; j < tests[i].x_values.size(); ++j) + { + if((boost::math::isfinite)(tests[i].x_values[j])) + sum += f(tests[i].params, p_value ? quantiles[j] : tests[i].x_values[j]); + ++data_size; + } + } + } + + t = boost::chrono::duration_cast<boost::chrono::duration<double>>(w.elapsed()).count(); + if(t < 0.5) + repeats *= 2; + } while(t < 0.5); + + static const std::string main_table_name = std::string("Distribution performance comparison with ") + compiler_name() + std::string(" on ") + platform_name(); + static const std::string boost_table_name = std::string("Distribution performance comparison for different performance options with ") + compiler_name() + std::string(" on ") + platform_name(); + + if (where & 1) + { + report_execution_time( + t / data_size, + main_table_name, + distro_name + " (" + std::string(sub_name) + ")", + column); + } + if (where & 2) + { + report_execution_time( + t / data_size, + boost_table_name, + distro_name + " (" + std::string(sub_name) + ")", + column); + } + } + catch(const std::exception& e) + { + std::cerr << "Aborting due to exception: " << e.what() << std::endl; + std::cerr << "In " << distro_name + " (" + std::string(sub_name) + ")" << std::endl; + report_execution_time( + (std::numeric_limits<boost::uintmax_t>::max)(), + std::string("Distribution performance comparison with ") + compiler_name() + std::string(" on ") + platform_name(), + distro_name + " (" + std::string(sub_name) + ")", + column); + } + } +}; + +const double distribution_tester::quantiles[19] = +{ + 0.000001, + 0.00001, + 0.0001, + 0.001, + 0.01, + 0.1, + 0.2, + 0.3, + 0.4, + 0.5, + 0.6, + 0.7, + 0.8, + 0.9, + 0.99, + 0.999, + 0.9999, + 0.99999, + 0.999999 +}; + +template <class D> +struct three_param_quantile +{ + template <class T, class U, class V, class X> + double operator()(T x, U y, V z, X q)const + { + return quantile(D(x, y, z), q); + } +}; + +template <class D> +struct two_param_quantile +{ + template <class T, class U, class V> + double operator()(T x, U y, V q)const + { + return quantile(D(x, y), q); + } +}; + +template <class D> +struct one_param_quantile +{ + template <class T, class V> + double operator()(T x, V q)const + { + return quantile(D(x), q); + } +}; + +template <template <class T, class U> class D> +void test_boost_1_param(distribution_tester& tester) +{ + // + // Define some custom policies to test: + // + typedef boost::math::policies::policy<> default_policy; + typedef boost::math::policies::policy<boost::math::policies::promote_double<false> > no_promote_double_policy; + typedef boost::math::policies::policy<boost::math::policies::promote_double<false>, boost::math::policies::digits10<10> > no_promote_double_10_digits_policy; + typedef boost::math::policies::policy<boost::math::policies::promote_float<false> > no_promote_float_policy; + + tester.run_timed_tests([](const std::vector<double>& v, double x){ return pdf(D<double, default_policy>(v[0]), x); }, "PDF", boost_name(), false, distribution_tester::both_tables); + tester.run_timed_tests([](const std::vector<double>& v, double x){ return cdf(D<double, default_policy>(v[0]), x); }, "CDF", boost_name(), false, distribution_tester::both_tables); + tester.run_timed_tests([](const std::vector<double>& v, double x){ return quantile(D<double, default_policy>(v[0]), x); }, "quantile", boost_name(), true, distribution_tester::both_tables); + if(sizeof(double) != sizeof(long double)) + { + tester.run_timed_tests([](const std::vector<double>& v, double x){ return pdf(D<double, no_promote_double_policy>(v[0]), x); }, "PDF", "Boost[br]promote_double<false>", false, distribution_tester::both_tables); + tester.run_timed_tests([](const std::vector<double>& v, double x){ return cdf(D<double, no_promote_double_policy>(v[0]), x); }, "CDF", "Boost[br]promote_double<false>", false, distribution_tester::both_tables); + tester.run_timed_tests([](const std::vector<double>& v, double x){ return quantile(D<double, no_promote_double_policy>(v[0]), x); }, "quantile", "Boost[br]promote_double<false>", true, distribution_tester::both_tables); + } + tester.run_timed_tests([](const std::vector<double>& v, double x){ return pdf(D<double, no_promote_double_10_digits_policy>(v[0]), x); }, "PDF", "Boost[br]promote_double<false>[br]digits10<10>", false, distribution_tester::boost_only_table); + tester.run_timed_tests([](const std::vector<double>& v, double x){ return cdf(D<double, no_promote_double_10_digits_policy>(v[0]), x); }, "CDF", "Boost[br]promote_double<false>[br]digits10<10>", false, distribution_tester::boost_only_table); + tester.run_timed_tests([](const std::vector<double>& v, double x){ return quantile(D<double, no_promote_double_10_digits_policy>(v[0]), x); }, "quantile", "Boost[br]promote_double<false>[br]digits10<10>", true, distribution_tester::boost_only_table); + + tester.run_timed_tests([](const std::vector<double>& v, double x){ return pdf(D<float, no_promote_float_policy>(static_cast<float>(v[0])), static_cast<float>(x)); }, "PDF", "Boost[br]float[br]promote_float<false>", false, distribution_tester::boost_only_table); + tester.run_timed_tests([](const std::vector<double>& v, double x){ return cdf(D<float, no_promote_float_policy>(static_cast<float>(v[0])), static_cast<float>(x)); }, "CDF", "Boost[br]float[br]promote_float<false>", false, distribution_tester::boost_only_table); + tester.run_timed_tests([](const std::vector<double>& v, double x){ return quantile(D<float, no_promote_float_policy>(static_cast<float>(v[0])), static_cast<float>(x)); }, "quantile", "Boost[br]float[br]promote_float<false>", true, distribution_tester::boost_only_table); +} + +template <template <class T, class U> class D> +void test_boost_2_param(distribution_tester& tester) +{ + // + // Define some custom policies to test: + // + typedef boost::math::policies::policy<> default_policy; + typedef boost::math::policies::policy<boost::math::policies::promote_double<false> > no_promote_double_policy; + typedef boost::math::policies::policy<boost::math::policies::promote_double<false>, boost::math::policies::digits10<10> > no_promote_double_10_digits_policy; + typedef boost::math::policies::policy<boost::math::policies::promote_float<false> > no_promote_float_policy; + + tester.run_timed_tests([](const std::vector<double>& v, double x){ return pdf(D<double, default_policy>(v[0], v[1]), x); }, "PDF", boost_name(), false, distribution_tester::both_tables); + tester.run_timed_tests([](const std::vector<double>& v, double x){ return cdf(D<double, default_policy>(v[0], v[1]), x); }, "CDF", boost_name(), false, distribution_tester::both_tables); + tester.run_timed_tests([](const std::vector<double>& v, double x){ return quantile(D<double, default_policy>(v[0], v[1]), x); }, "quantile", boost_name(), true, distribution_tester::both_tables); + if(sizeof(double) != sizeof(long double)) + { + tester.run_timed_tests([](const std::vector<double>& v, double x){ return pdf(D<double, no_promote_double_policy>(v[0], v[1]), x); }, "PDF", "Boost[br]promote_double<false>", false, distribution_tester::both_tables); + tester.run_timed_tests([](const std::vector<double>& v, double x){ return cdf(D<double, no_promote_double_policy>(v[0], v[1]), x); }, "CDF", "Boost[br]promote_double<false>", false, distribution_tester::both_tables); + tester.run_timed_tests([](const std::vector<double>& v, double x){ return quantile(D<double, no_promote_double_policy>(v[0], v[1]), x); }, "quantile", "Boost[br]promote_double<false>", true, distribution_tester::both_tables); + } + tester.run_timed_tests([](const std::vector<double>& v, double x){ return pdf(D<double, no_promote_double_10_digits_policy>(v[0], v[1]), x); }, "PDF", "Boost[br]promote_double<false>[br]digits10<10>", false, distribution_tester::boost_only_table); + tester.run_timed_tests([](const std::vector<double>& v, double x){ return cdf(D<double, no_promote_double_10_digits_policy>(v[0], v[1]), x); }, "CDF", "Boost[br]promote_double<false>[br]digits10<10>", false, distribution_tester::boost_only_table); + tester.run_timed_tests([](const std::vector<double>& v, double x){ return quantile(D<double, no_promote_double_10_digits_policy>(v[0], v[1]), x); }, "quantile", "Boost[br]promote_double<false>[br]digits10<10>", true, distribution_tester::boost_only_table); + + tester.run_timed_tests([](const std::vector<double>& v, double x){ return pdf(D<float, no_promote_float_policy>(static_cast<float>(v[0]), static_cast<float>(v[1])), static_cast<float>(x)); }, "PDF", "Boost[br]float[br]promote_float<false>", false, distribution_tester::boost_only_table); + tester.run_timed_tests([](const std::vector<double>& v, double x){ return cdf(D<float, no_promote_float_policy>(static_cast<float>(v[0]), static_cast<float>(v[1])), static_cast<float>(x)); }, "CDF", "Boost[br]float[br]promote_float<false>", false, distribution_tester::boost_only_table); + tester.run_timed_tests([](const std::vector<double>& v, double x){ return quantile(D<float, no_promote_float_policy>(static_cast<float>(v[0]), static_cast<float>(v[1])), static_cast<float>(x)); }, "quantile", "Boost[br]float[br]promote_float<false>", true, distribution_tester::boost_only_table); +} + +template <template <class T, class U> class D> +void test_boost_3_param(distribution_tester& tester) +{ + // + // Define some custom policies to test: + // + typedef boost::math::policies::policy<> default_policy; + typedef boost::math::policies::policy<boost::math::policies::promote_double<false> > no_promote_double_policy; + typedef boost::math::policies::policy<boost::math::policies::promote_double<false>, boost::math::policies::digits10<10> > no_promote_double_10_digits_policy; + typedef boost::math::policies::policy<boost::math::policies::promote_float<false> > no_promote_float_policy; + + tester.run_timed_tests([](const std::vector<double>& v, double x){ return pdf(D<double, default_policy>(v[0], v[1], v[2]), x); }, "PDF", boost_name(), false, distribution_tester::both_tables); + tester.run_timed_tests([](const std::vector<double>& v, double x){ return cdf(D<double, default_policy>(v[0], v[1], v[2]), x); }, "CDF", boost_name(), false, distribution_tester::both_tables); + tester.run_timed_tests([](const std::vector<double>& v, double x){ return quantile(D<double, default_policy>(v[0], v[1], v[2]), x); }, "quantile", boost_name(), true, distribution_tester::both_tables); + if(sizeof(double) != sizeof(long double)) + { + tester.run_timed_tests([](const std::vector<double>& v, double x){ return pdf(D<double, no_promote_double_policy>(v[0], v[1], v[2]), x); }, "PDF", "Boost[br]promote_double<false>", false, distribution_tester::both_tables); + tester.run_timed_tests([](const std::vector<double>& v, double x){ return cdf(D<double, no_promote_double_policy>(v[0], v[1], v[2]), x); }, "CDF", "Boost[br]promote_double<false>", false, distribution_tester::both_tables); + tester.run_timed_tests([](const std::vector<double>& v, double x){ return quantile(D<double, no_promote_double_policy>(v[0], v[1], v[2]), x); }, "quantile", "Boost[br]promote_double<false>", true, distribution_tester::both_tables); + } + tester.run_timed_tests([](const std::vector<double>& v, double x){ return pdf(D<double, no_promote_double_10_digits_policy>(v[0], v[1], v[2]), x); }, "PDF", "Boost[br]promote_double<false>[br]digits10<10>", false, distribution_tester::boost_only_table); + tester.run_timed_tests([](const std::vector<double>& v, double x){ return cdf(D<double, no_promote_double_10_digits_policy>(v[0], v[1], v[2]), x); }, "CDF", "Boost[br]promote_double<false>[br]digits10<10>", false, distribution_tester::boost_only_table); + tester.run_timed_tests([](const std::vector<double>& v, double x){ return quantile(D<double, no_promote_double_10_digits_policy>(v[0], v[1], v[2]), x); }, "quantile", "Boost[br]promote_double<false>[br]digits10<10>", true, distribution_tester::boost_only_table); + + tester.run_timed_tests([](const std::vector<double>& v, double x){ return pdf(D<float, no_promote_float_policy>(static_cast<float>(v[0]), static_cast<float>(v[1]), static_cast<float>(v[2])), static_cast<float>(x)); }, "PDF", "Boost[br]float[br]promote_float<false>", false, distribution_tester::boost_only_table); + tester.run_timed_tests([](const std::vector<double>& v, double x){ return cdf(D<float, no_promote_float_policy>(static_cast<float>(v[0]), static_cast<float>(v[1]), static_cast<float>(v[2])), static_cast<float>(x)); }, "CDF", "Boost[br]float[br]promote_float<false>", false, distribution_tester::boost_only_table); + tester.run_timed_tests([](const std::vector<double>& v, double x){ return quantile(D<float, no_promote_float_policy>(static_cast<float>(v[0]), static_cast<float>(v[1]), static_cast<float>(v[2])), static_cast<float>(x)); }, "quantile", "Boost[br]float[br]promote_float<false>", true, distribution_tester::boost_only_table); +} + +int main() +{ + try { + // + // Normal: + // + distribution_tester n("Normal"); + n.add_test_case(0, 1, two_param_quantile<boost::math::normal_distribution<> >()); + n.add_test_case(20, 20, two_param_quantile<boost::math::normal_distribution<> >()); + n.add_test_case(-20, 0.0125, two_param_quantile<boost::math::normal_distribution<> >()); + + test_boost_2_param<boost::math::normal_distribution>(n); + + distribution_tester arcsine("ArcSine"); + arcsine.add_test_case(0, 1, two_param_quantile<boost::math::arcsine_distribution<> >()); + arcsine.add_test_case(20, 500, two_param_quantile<boost::math::arcsine_distribution<> >()); + arcsine.add_test_case(-20, 100000, two_param_quantile<boost::math::arcsine_distribution<> >()); + + test_boost_2_param<boost::math::arcsine_distribution>(arcsine); + + distribution_tester beta("Beta"); + beta.add_test_case(1, 4, two_param_quantile<boost::math::beta_distribution<> >()); + beta.add_test_case(20, 500, two_param_quantile<boost::math::beta_distribution<> >()); + beta.add_test_case(0.1, 0.01, two_param_quantile<boost::math::beta_distribution<> >()); + + test_boost_2_param<boost::math::beta_distribution>(beta); + + distribution_tester binomial("Binomial"); + binomial.add_test_case(5, 0.125, two_param_quantile<boost::math::binomial_distribution<> >()); + binomial.add_test_case(200, 0.75, two_param_quantile<boost::math::binomial_distribution<> >()); + binomial.add_test_case(2000, 0.5, two_param_quantile<boost::math::binomial_distribution<> >()); + binomial.add_test_case(20000, 0.001, two_param_quantile<boost::math::binomial_distribution<> >()); + binomial.add_test_case(200000, 0.99, two_param_quantile<boost::math::binomial_distribution<> >()); + + test_boost_2_param<boost::math::binomial_distribution>(binomial); + + distribution_tester cauchy("Cauchy"); + cauchy.add_test_case(0, 1, two_param_quantile<boost::math::cauchy_distribution<> >()); + cauchy.add_test_case(20, 20, two_param_quantile<boost::math::cauchy_distribution<> >()); + cauchy.add_test_case(-20, 0.0125, two_param_quantile<boost::math::cauchy_distribution<> >()); + + test_boost_2_param<boost::math::cauchy_distribution>(cauchy); + + distribution_tester chi_squared("ChiSquared"); + chi_squared.add_test_case(3, one_param_quantile<boost::math::chi_squared_distribution<> >()); + chi_squared.add_test_case(20, one_param_quantile<boost::math::chi_squared_distribution<> >()); + chi_squared.add_test_case(200, one_param_quantile<boost::math::chi_squared_distribution<> >()); + chi_squared.add_test_case(2000, one_param_quantile<boost::math::chi_squared_distribution<> >()); + chi_squared.add_test_case(20000, one_param_quantile<boost::math::chi_squared_distribution<> >()); + chi_squared.add_test_case(200000, one_param_quantile<boost::math::chi_squared_distribution<> >()); + + test_boost_1_param<boost::math::chi_squared_distribution>(chi_squared); + + distribution_tester exponential("Exponential"); + exponential.add_test_case(0.001, one_param_quantile<boost::math::exponential_distribution<> >()); + exponential.add_test_case(0.01, one_param_quantile<boost::math::exponential_distribution<> >()); + exponential.add_test_case(0.1, one_param_quantile<boost::math::exponential_distribution<> >()); + exponential.add_test_case(1, one_param_quantile<boost::math::exponential_distribution<> >()); + exponential.add_test_case(10, one_param_quantile<boost::math::exponential_distribution<> >()); + exponential.add_test_case(100, one_param_quantile<boost::math::exponential_distribution<> >()); + exponential.add_test_case(1000, one_param_quantile<boost::math::exponential_distribution<> >()); + + test_boost_1_param<boost::math::exponential_distribution>(exponential); + + distribution_tester extreme_value("ExtremeValue"); + extreme_value.add_test_case(0, 1, two_param_quantile<boost::math::extreme_value_distribution<> >()); + extreme_value.add_test_case(20, 20, two_param_quantile<boost::math::extreme_value_distribution<> >()); + extreme_value.add_test_case(-20, 0.0125, two_param_quantile<boost::math::extreme_value_distribution<> >()); + + test_boost_2_param<boost::math::extreme_value_distribution>(extreme_value); + + distribution_tester fisher("F"); + for (unsigned i = 2; i <= 200000; i *= 10) + { + for (unsigned j = 2; j <= 200000; j *= 10) + { + fisher.add_test_case(i, j, two_param_quantile<boost::math::fisher_f_distribution<> >()); + } + } + test_boost_2_param<boost::math::fisher_f_distribution>(fisher); + + distribution_tester gamma("Gamma"); + gamma.add_test_case(0.1, 1, two_param_quantile<boost::math::gamma_distribution<> >()); + gamma.add_test_case(20, 20, two_param_quantile<boost::math::gamma_distribution<> >()); + gamma.add_test_case(200, 0.0125, two_param_quantile<boost::math::gamma_distribution<> >()); + gamma.add_test_case(2000, 500, two_param_quantile<boost::math::gamma_distribution<> >()); + + test_boost_2_param<boost::math::gamma_distribution>(gamma); + + distribution_tester geometric("Geometric"); + geometric.add_test_case(0.001, one_param_quantile<boost::math::geometric_distribution<> >()); + geometric.add_test_case(0.01, one_param_quantile<boost::math::geometric_distribution<> >()); + geometric.add_test_case(0.1, one_param_quantile<boost::math::geometric_distribution<> >()); + geometric.add_test_case(0.5, one_param_quantile<boost::math::geometric_distribution<> >()); + geometric.add_test_case(0.9, one_param_quantile<boost::math::geometric_distribution<> >()); + geometric.add_test_case(0.99, one_param_quantile<boost::math::geometric_distribution<> >()); + geometric.add_test_case(0.999, one_param_quantile<boost::math::geometric_distribution<> >()); + + test_boost_1_param<boost::math::geometric_distribution>(geometric); + + distribution_tester hypergeometric("Hypergeometric"); + hypergeometric.add_test_case(10, 5, 100, three_param_quantile<boost::math::hypergeometric_distribution<> >()); + hypergeometric.add_test_case(50, 75, 100, three_param_quantile<boost::math::hypergeometric_distribution<> >()); + hypergeometric.add_test_case(30, 20, 100, three_param_quantile<boost::math::hypergeometric_distribution<> >()); + hypergeometric.add_test_case(100, 50, 1000000, three_param_quantile<boost::math::hypergeometric_distribution<> >()); + hypergeometric.add_test_case(500000, 3000, 1000000, three_param_quantile<boost::math::hypergeometric_distribution<> >()); + hypergeometric.add_test_case(20000, 800000, 1000000, three_param_quantile<boost::math::hypergeometric_distribution<> >()); + hypergeometric.add_test_case(100, 5, 1000, three_param_quantile<boost::math::hypergeometric_distribution<> >()); + hypergeometric.add_test_case(500, 50, 1000, three_param_quantile<boost::math::hypergeometric_distribution<> >()); + hypergeometric.add_test_case(2, 25, 1000, three_param_quantile<boost::math::hypergeometric_distribution<> >()); + hypergeometric.add_test_case(1, 5, 1000, three_param_quantile<boost::math::hypergeometric_distribution<> >()); + hypergeometric.add_test_case(100, 500, 1000, three_param_quantile<boost::math::hypergeometric_distribution<> >()); + + test_boost_3_param<boost::math::hypergeometric_distribution>(hypergeometric); + + distribution_tester inverse_chi_squared("InverseChiSquared"); + inverse_chi_squared.add_test_case(5, 0.125, two_param_quantile<boost::math::inverse_chi_squared_distribution<> >()); + inverse_chi_squared.add_test_case(200, 0.75, two_param_quantile<boost::math::inverse_chi_squared_distribution<> >()); + inverse_chi_squared.add_test_case(2000, 1, two_param_quantile<boost::math::inverse_chi_squared_distribution<> >()); + inverse_chi_squared.add_test_case(20000, 10, two_param_quantile<boost::math::inverse_chi_squared_distribution<> >()); + inverse_chi_squared.add_test_case(200000, 100, two_param_quantile<boost::math::inverse_chi_squared_distribution<> >()); + + test_boost_2_param<boost::math::inverse_chi_squared_distribution>(inverse_chi_squared); + + distribution_tester inverse_gamma("InverseGamma"); + inverse_gamma.add_test_case(0.1, 1, two_param_quantile<boost::math::inverse_gamma_distribution<> >()); + inverse_gamma.add_test_case(20, 20, two_param_quantile<boost::math::inverse_gamma_distribution<> >()); + inverse_gamma.add_test_case(200, 0.0125, two_param_quantile<boost::math::inverse_gamma_distribution<> >()); + inverse_gamma.add_test_case(2000, 500, two_param_quantile<boost::math::inverse_gamma_distribution<> >()); + + test_boost_2_param<boost::math::inverse_gamma_distribution>(inverse_gamma); + + distribution_tester inverse_gaussian("InverseGaussian"); + inverse_gaussian.add_test_case(0.001, 1, two_param_quantile<boost::math::inverse_gaussian_distribution<> >()); + inverse_gaussian.add_test_case(20, 20, two_param_quantile<boost::math::inverse_gaussian_distribution<> >()); + + test_boost_2_param<boost::math::inverse_gaussian_distribution>(inverse_gaussian); + + distribution_tester laplace("Laplace"); + laplace.add_test_case(0, 1, two_param_quantile<boost::math::laplace_distribution<> >()); + laplace.add_test_case(20, 20, two_param_quantile<boost::math::laplace_distribution<> >()); + laplace.add_test_case(-20, 0.0125, two_param_quantile<boost::math::laplace_distribution<> >()); + + test_boost_2_param<boost::math::laplace_distribution>(laplace); + + distribution_tester logistic("Logistic"); + logistic.add_test_case(0, 1, two_param_quantile<boost::math::logistic_distribution<> >()); + logistic.add_test_case(20, 20, two_param_quantile<boost::math::logistic_distribution<> >()); + logistic.add_test_case(-20, 0.0125, two_param_quantile<boost::math::logistic_distribution<> >()); + + test_boost_2_param<boost::math::logistic_distribution>(logistic); + + distribution_tester lognormal("LogNormal"); + lognormal.add_test_case(0, 1, two_param_quantile<boost::math::lognormal_distribution<> >()); + lognormal.add_test_case(20, 20, two_param_quantile<boost::math::lognormal_distribution<> >()); + lognormal.add_test_case(-20, 0.0125, two_param_quantile<boost::math::lognormal_distribution<> >()); + + test_boost_2_param<boost::math::lognormal_distribution>(lognormal); + + distribution_tester negative_binomial("NegativeBinomial"); + negative_binomial.add_test_case(5, 0.125, two_param_quantile<boost::math::negative_binomial_distribution<> >()); + negative_binomial.add_test_case(200, 0.75, two_param_quantile<boost::math::negative_binomial_distribution<> >()); + negative_binomial.add_test_case(2000, 0.001, two_param_quantile<boost::math::negative_binomial_distribution<> >()); + negative_binomial.add_test_case(20000, 0.5, two_param_quantile<boost::math::negative_binomial_distribution<> >()); + negative_binomial.add_test_case(200000, 0.99, two_param_quantile<boost::math::negative_binomial_distribution<> >()); + + test_boost_2_param<boost::math::negative_binomial_distribution>(negative_binomial); + + distribution_tester non_central_beta("NonCentralBeta"); + non_central_beta.add_test_case(2, 5, 2.1, three_param_quantile<boost::math::non_central_beta_distribution<> >()); + non_central_beta.add_test_case(0.25, 0.01, 20, three_param_quantile<boost::math::non_central_beta_distribution<> >()); + non_central_beta.add_test_case(20, 3, 30, three_param_quantile<boost::math::non_central_beta_distribution<> >()); + non_central_beta.add_test_case(100, 200, 400, three_param_quantile<boost::math::non_central_beta_distribution<> >()); + non_central_beta.add_test_case(100, 0.25, 20, three_param_quantile<boost::math::non_central_beta_distribution<> >()); + + test_boost_3_param<boost::math::non_central_beta_distribution>(non_central_beta); + + distribution_tester non_central_chi_squared("NonCentralChiSquared"); + non_central_chi_squared.add_test_case(5, 0.5, two_param_quantile<boost::math::non_central_chi_squared_distribution<> >()); + non_central_chi_squared.add_test_case(200, 2, two_param_quantile<boost::math::non_central_chi_squared_distribution<> >()); + non_central_chi_squared.add_test_case(2000, 20, two_param_quantile<boost::math::non_central_chi_squared_distribution<> >()); + non_central_chi_squared.add_test_case(20000, 10, two_param_quantile<boost::math::non_central_chi_squared_distribution<> >()); + non_central_chi_squared.add_test_case(200000, 50, two_param_quantile<boost::math::non_central_chi_squared_distribution<> >()); + + test_boost_2_param<boost::math::non_central_chi_squared_distribution>(non_central_chi_squared); + + distribution_tester non_central_f("NonCentralF"); + non_central_f.add_test_case(20, 20, 3, three_param_quantile<boost::math::non_central_f_distribution<> >()); + non_central_f.add_test_case(20, 50, 20, three_param_quantile<boost::math::non_central_f_distribution<> >()); + non_central_f.add_test_case(100, 20, 30, three_param_quantile<boost::math::non_central_f_distribution<> >()); + non_central_f.add_test_case(100, 200, 100, three_param_quantile<boost::math::non_central_f_distribution<> >()); + non_central_f.add_test_case(1000, 100000, 20, three_param_quantile<boost::math::non_central_f_distribution<> >()); + + test_boost_3_param<boost::math::non_central_f_distribution>(non_central_f); + + distribution_tester non_central_t("NonCentralT"); + non_central_t.add_test_case(5, 0.5, two_param_quantile<boost::math::non_central_t_distribution<> >()); + non_central_t.add_test_case(200, 2, two_param_quantile<boost::math::non_central_t_distribution<> >()); + non_central_t.add_test_case(2000, 20, two_param_quantile<boost::math::non_central_t_distribution<> >()); + non_central_t.add_test_case(20000, 10, two_param_quantile<boost::math::non_central_t_distribution<> >()); + non_central_t.add_test_case(200000, 50, two_param_quantile<boost::math::non_central_t_distribution<> >()); + + test_boost_2_param<boost::math::non_central_t_distribution>(non_central_t); + + distribution_tester pareto("Pareto"); + pareto.add_test_case(0.1, 1, two_param_quantile<boost::math::pareto_distribution<> >()); + pareto.add_test_case(20, 20, two_param_quantile<boost::math::pareto_distribution<> >()); + pareto.add_test_case(200, 0.0125, two_param_quantile<boost::math::pareto_distribution<> >()); + pareto.add_test_case(2000, 500, two_param_quantile<boost::math::pareto_distribution<> >()); + + test_boost_2_param<boost::math::pareto_distribution>(pareto); + + distribution_tester poisson("Poisson"); + poisson.add_test_case(0.001, one_param_quantile<boost::math::poisson_distribution<> >()); + poisson.add_test_case(0.01, one_param_quantile<boost::math::poisson_distribution<> >()); + poisson.add_test_case(0.1, one_param_quantile<boost::math::poisson_distribution<> >()); + poisson.add_test_case(1, one_param_quantile<boost::math::poisson_distribution<> >()); + poisson.add_test_case(10, one_param_quantile<boost::math::poisson_distribution<> >()); + poisson.add_test_case(100, one_param_quantile<boost::math::poisson_distribution<> >()); + poisson.add_test_case(1000, one_param_quantile<boost::math::poisson_distribution<> >()); + + test_boost_1_param<boost::math::poisson_distribution>(poisson); + + distribution_tester rayleigh("Rayleigh"); + rayleigh.add_test_case(0.001, one_param_quantile<boost::math::rayleigh_distribution<> >()); + rayleigh.add_test_case(0.01, one_param_quantile<boost::math::rayleigh_distribution<> >()); + rayleigh.add_test_case(0.1, one_param_quantile<boost::math::rayleigh_distribution<> >()); + rayleigh.add_test_case(1, one_param_quantile<boost::math::rayleigh_distribution<> >()); + rayleigh.add_test_case(10, one_param_quantile<boost::math::rayleigh_distribution<> >()); + rayleigh.add_test_case(100, one_param_quantile<boost::math::rayleigh_distribution<> >()); + rayleigh.add_test_case(1000, one_param_quantile<boost::math::rayleigh_distribution<> >()); + + test_boost_1_param<boost::math::rayleigh_distribution>(rayleigh); + + distribution_tester skew_norm("SkewNormal"); + skew_norm.add_test_case(0, 1, 0.1, three_param_quantile<boost::math::skew_normal_distribution<> >()); + skew_norm.add_test_case(20, 20, 30, three_param_quantile<boost::math::skew_normal_distribution<> >()); + skew_norm.add_test_case(-20, 0.0125, 10, three_param_quantile<boost::math::skew_normal_distribution<> >()); + + test_boost_3_param<boost::math::skew_normal_distribution>(skew_norm); + + distribution_tester students_t("StudentsT"); + students_t.add_test_case(3, one_param_quantile<boost::math::students_t_distribution<> >()); + students_t.add_test_case(20, one_param_quantile<boost::math::students_t_distribution<> >()); + students_t.add_test_case(200, one_param_quantile<boost::math::students_t_distribution<> >()); + students_t.add_test_case(2000, one_param_quantile<boost::math::students_t_distribution<> >()); + students_t.add_test_case(20000, one_param_quantile<boost::math::students_t_distribution<> >()); + students_t.add_test_case(200000, one_param_quantile<boost::math::students_t_distribution<> >()); + + test_boost_1_param<boost::math::students_t_distribution>(students_t); + + distribution_tester weibull("Weibull"); + weibull.add_test_case(0.1, 1, two_param_quantile<boost::math::weibull_distribution<> >()); + weibull.add_test_case(20, 20, two_param_quantile<boost::math::weibull_distribution<> >()); + weibull.add_test_case(200, 0.0125, two_param_quantile<boost::math::weibull_distribution<> >()); + weibull.add_test_case(2000, 500, two_param_quantile<boost::math::weibull_distribution<> >()); + + test_boost_2_param<boost::math::weibull_distribution>(weibull); + +#ifdef TEST_GSL + // normal, note no location param + n.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_gaussian_P(x, v[1]); }, "CDF", "GSL"); + n.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_gaussian_Pinv(x, v[1]); }, "quantile", "GSL", true); + // exponential: + exponential.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_exponential_P(x, 1 / v[0]); }, "CDF", "GSL"); + exponential.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_exponential_Pinv(x, 1 / v[0]); }, "quantile", "GSL", true); + // laplace, note no location param: + laplace.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_laplace_P(x, v[1]); }, "CDF", "GSL"); + laplace.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_laplace_Pinv(x, v[1]); }, "quantile", "GSL", true); + // cauchy, note no location param: + cauchy.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_cauchy_P(x, v[1]); }, "CDF", "GSL"); + cauchy.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_cauchy_Pinv(x, v[1]); }, "quantile", "GSL", true); + // rayleigh: + rayleigh.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_rayleigh_P(x, v[0]); }, "CDF", "GSL"); + rayleigh.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_rayleigh_Pinv(x, v[0]); }, "quantile", "GSL", true); + // gamma: + gamma.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_gamma_P(x, v[0], v[1]); }, "CDF", "GSL"); + gamma.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_gamma_Pinv(x, v[0], v[1]); }, "quantile", "GSL", true); + // lognormal: + lognormal.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_lognormal_P(x, v[0], v[1]); }, "CDF", "GSL"); + lognormal.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_lognormal_Pinv(x, v[0], v[1]); }, "quantile", "GSL", true); + // chi squared: + chi_squared.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_chisq_P(x, v[0]); }, "CDF", "GSL"); + chi_squared.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_chisq_Pinv(x, v[0]); }, "quantile", "GSL", true); + // F: + fisher.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_fdist_P(x, v[0], v[1]); }, "CDF", "GSL"); + fisher.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_fdist_Pinv(x, v[0], v[1]); }, "quantile", "GSL", true); + // T: + students_t.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_tdist_P(x, v[0]); }, "CDF", "GSL"); + students_t.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_tdist_Pinv(x, v[0]); }, "quantile", "GSL", true); + // beta: + beta.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_beta_P(x, v[0], v[1]); }, "CDF", "GSL"); + beta.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_beta_Pinv(x, v[0], v[1]); }, "quantile", "GSL", true); + // logistic, note no location param + logistic.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_logistic_P(x, v[1]); }, "CDF", "GSL"); + logistic.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_logistic_Pinv(x, v[1]); }, "quantile", "GSL", true); + // pareto: + pareto.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_pareto_P(x, v[1], v[0]); }, "CDF", "GSL"); + pareto.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_pareto_Pinv(x, v[1], v[0]); }, "quantile", "GSL", true); + // weibull: + weibull.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_weibull_P(x, v[1], v[0]); }, "CDF", "GSL"); + weibull.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_weibull_Pinv(x, v[1], v[0]); }, "quantile", "GSL", true); + // poisson: + poisson.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_poisson_P(x, v[0]); }, "CDF", "GSL"); + //poisson.run_timed_tests([](const std::vector<double>& v, double x){ return gsl_cdf_poisson_Pinv(x, v[0]); }, "quantile", "GSL", true); + // binomial: + binomial.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_binomial_P(x, v[1], v[0]); }, "CDF", "GSL"); + //binomial.run_timed_tests([](const std::vector<double>& v, double x){ return gsl_cdf_binomial_Pinv(x, v[1], v[0]); }, "quantile", "GSL", true); + // negative_binomial: + negative_binomial.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_negative_binomial_P(x, v[1], v[0]); }, "CDF", "GSL"); + //negative_binomial.run_timed_tests([](const std::vector<double>& v, double x){ return gsl_cdf_negative_binomial_Pinv(x, v[1], v[0]); }, "quantile", "GSL", true); + // geometric: + geometric.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_geometric_P(x + 1, v[0]); }, "CDF", "GSL"); + //geometric.run_timed_tests([](const std::vector<double>& v, double x){ return gsl_cdf_geometric_Pinv(x, v[0]) - 1; }, "quantile", "GSL", true); + // hypergeometric: + hypergeometric.run_timed_tests([](const std::vector<double>& v, double x) { return gsl_cdf_hypergeometric_P(x, v[0], v[2] - v[0], v[1]); }, "CDF", "GSL"); + //hypergeometric.run_timed_tests([](const std::vector<double>& v, double x){ return gsl_cdf_hypergeometric_Pinv(x, v[0], v[2] - v[0], v[1]); }, "quantile", "GSL", true); +#endif + +#ifdef TEST_RMATH + // beta + beta.run_timed_tests([](const std::vector<double>& v, double x) { return dbeta(x, v[0], v[1], 0); }, "PDF", "Rmath " R_VERSION_STRING); + beta.run_timed_tests([](const std::vector<double>& v, double x) { return pbeta(x, v[0], v[1], 1, 0); }, "CDF", "Rmath " R_VERSION_STRING); + beta.run_timed_tests([](const std::vector<double>& v, double x) { return qbeta(x, v[0], v[1], 1, 0); }, "quantile", "Rmath " R_VERSION_STRING, true); + // non-central beta + non_central_beta.run_timed_tests([](const std::vector<double>& v, double x) { return dnbeta(x, v[0], v[1], v[2], 0); }, "PDF", "Rmath " R_VERSION_STRING); + non_central_beta.run_timed_tests([](const std::vector<double>& v, double x) { return pnbeta(x, v[0], v[1], v[2], 1, 0); }, "CDF", "Rmath " R_VERSION_STRING); + non_central_beta.run_timed_tests([](const std::vector<double>& v, double x) { return qnbeta(x, v[0], v[1], v[2], 1, 0); }, "quantile", "Rmath " R_VERSION_STRING, true); + // binomial + binomial.run_timed_tests([](const std::vector<double>& v, double x) { return dbinom(x, v[0], v[1], 0); }, "PDF", "Rmath " R_VERSION_STRING); + binomial.run_timed_tests([](const std::vector<double>& v, double x) { return pbinom(x, v[0], v[1], 1, 0); }, "CDF", "Rmath " R_VERSION_STRING); + binomial.run_timed_tests([](const std::vector<double>& v, double x) { return qbinom(x, v[0], v[1], 1, 0); }, "quantile", "Rmath " R_VERSION_STRING, true); + // cauchy + cauchy.run_timed_tests([](const std::vector<double>& v, double x) { return dcauchy(x, v[0], v[1], 0); }, "PDF", "Rmath " R_VERSION_STRING); + cauchy.run_timed_tests([](const std::vector<double>& v, double x) { return pcauchy(x, v[0], v[1], 1, 0); }, "CDF", "Rmath " R_VERSION_STRING); + cauchy.run_timed_tests([](const std::vector<double>& v, double x) { return qcauchy(x, v[0], v[1], 1, 0); }, "quantile", "Rmath " R_VERSION_STRING, true); + // chi squared + chi_squared.run_timed_tests([](const std::vector<double>& v, double x) { return dchisq(x, v[0], 0); }, "PDF", "Rmath " R_VERSION_STRING); + chi_squared.run_timed_tests([](const std::vector<double>& v, double x) { return pchisq(x, v[0], 1, 0); }, "CDF", "Rmath " R_VERSION_STRING); + chi_squared.run_timed_tests([](const std::vector<double>& v, double x) { return qchisq(x, v[0], 1, 0); }, "quantile", "Rmath " R_VERSION_STRING, true); + // non central chi squared + non_central_chi_squared.run_timed_tests([](const std::vector<double>& v, double x) { return dnchisq(x, v[0], v[1], 0); }, "PDF", "Rmath " R_VERSION_STRING); + non_central_chi_squared.run_timed_tests([](const std::vector<double>& v, double x) { return pnchisq(x, v[0], v[1], 1, 0); }, "CDF", "Rmath " R_VERSION_STRING); + non_central_chi_squared.run_timed_tests([](const std::vector<double>& v, double x) { return qnchisq(x, v[0], v[1], 1, 0); }, "quantile", "Rmath " R_VERSION_STRING, true); + // exponential + exponential.run_timed_tests([](const std::vector<double>& v, double x) { return dexp(x, 1 / v[0], 0); }, "PDF", "Rmath " R_VERSION_STRING); + exponential.run_timed_tests([](const std::vector<double>& v, double x) { return pexp(x, 1 / v[0], 1, 0); }, "CDF", "Rmath " R_VERSION_STRING); + exponential.run_timed_tests([](const std::vector<double>& v, double x) { return qexp(x, 1 / v[0], 1, 0); }, "quantile", "Rmath " R_VERSION_STRING, true); + // F + fisher.run_timed_tests([](const std::vector<double>& v, double x) { return df(x, v[0], v[1], 0); }, "PDF", "Rmath " R_VERSION_STRING); + fisher.run_timed_tests([](const std::vector<double>& v, double x) { return pf(x, v[0], v[1], 1, 0); }, "CDF", "Rmath " R_VERSION_STRING); + fisher.run_timed_tests([](const std::vector<double>& v, double x) { return qf(x, v[0], v[1], 1, 0); }, "quantile", "Rmath " R_VERSION_STRING, true); + // non central F + non_central_f.run_timed_tests([](const std::vector<double>& v, double x) { return dnf(x, v[0], v[1], v[2], 0); }, "PDF", "Rmath " R_VERSION_STRING); + non_central_f.run_timed_tests([](const std::vector<double>& v, double x) { return pnf(x, v[0], v[1], v[2], 1, 0); }, "CDF", "Rmath " R_VERSION_STRING); + non_central_f.run_timed_tests([](const std::vector<double>& v, double x) { return qnf(x, v[0], v[1], v[2], 1, 0); }, "quantile", "Rmath " R_VERSION_STRING, true); + // gamma + gamma.run_timed_tests([](const std::vector<double>& v, double x) { return dgamma(x, v[0], v[1], 0); }, "PDF", "Rmath " R_VERSION_STRING); + gamma.run_timed_tests([](const std::vector<double>& v, double x) { return pgamma(x, v[0], v[1], 1, 0); }, "CDF", "Rmath " R_VERSION_STRING); + gamma.run_timed_tests([](const std::vector<double>& v, double x) { return qgamma(x, v[0], v[1], 1, 0); }, "quantile", "Rmath " R_VERSION_STRING, true); + // geometric + geometric.run_timed_tests([](const std::vector<double>& v, double x) { return dgeom(x, v[0], 0); }, "PDF", "Rmath " R_VERSION_STRING); + geometric.run_timed_tests([](const std::vector<double>& v, double x) { return pgeom(x, v[0], 1, 0); }, "CDF", "Rmath " R_VERSION_STRING); + geometric.run_timed_tests([](const std::vector<double>& v, double x) { return qgeom(x, v[0], 1, 0); }, "quantile", "Rmath " R_VERSION_STRING, true); + // hypergeometric + hypergeometric.run_timed_tests([](const std::vector<double>& v, double x) { return dhyper(x, v[0], v[2] - v[0], v[1], 0); }, "PDF", "Rmath " R_VERSION_STRING); + hypergeometric.run_timed_tests([](const std::vector<double>& v, double x) { return phyper(x, v[0], v[2] - v[0], v[1], 1, 0); }, "CDF", "Rmath " R_VERSION_STRING); + hypergeometric.run_timed_tests([](const std::vector<double>& v, double x) { return qhyper(x, v[0], v[2] - v[0], v[1], 1, 0); }, "quantile", "Rmath " R_VERSION_STRING, true); + // logistic + logistic.run_timed_tests([](const std::vector<double>& v, double x) { return dlogis(x, v[0], v[1], 0); }, "PDF", "Rmath " R_VERSION_STRING); + logistic.run_timed_tests([](const std::vector<double>& v, double x) { return plogis(x, v[0], v[1], 1, 0); }, "CDF", "Rmath " R_VERSION_STRING); + logistic.run_timed_tests([](const std::vector<double>& v, double x) { return qlogis(x, v[0], v[1], 1, 0); }, "quantile", "Rmath " R_VERSION_STRING, true); + // lognormal + lognormal.run_timed_tests([](const std::vector<double>& v, double x) { return dlnorm(x, v[0], v[1], 0); }, "PDF", "Rmath " R_VERSION_STRING); + lognormal.run_timed_tests([](const std::vector<double>& v, double x) { return plnorm(x, v[0], v[1], 1, 0); }, "CDF", "Rmath " R_VERSION_STRING); + lognormal.run_timed_tests([](const std::vector<double>& v, double x) { return qlnorm(x, v[0], v[1], 1, 0); }, "quantile", "Rmath " R_VERSION_STRING, true); + // negative_binomial + negative_binomial.run_timed_tests([](const std::vector<double>& v, double x) { return dnbinom(x, v[0], v[1], 0); }, "PDF", "Rmath " R_VERSION_STRING); + negative_binomial.run_timed_tests([](const std::vector<double>& v, double x) { return pnbinom(x, v[0], v[1], 1, 0); }, "CDF", "Rmath " R_VERSION_STRING); + negative_binomial.run_timed_tests([](const std::vector<double>& v, double x) { return qnbinom(x, v[0], v[1], 1, 0); }, "quantile", "Rmath " R_VERSION_STRING, true); + // normal + n.run_timed_tests([](const std::vector<double>& v, double x) { return dnorm(x, v[0], v[1], 0); }, "PDF", "Rmath " R_VERSION_STRING); + n.run_timed_tests([](const std::vector<double>& v, double x) { return pnorm(x, v[0], v[1], 1, 0); }, "CDF", "Rmath " R_VERSION_STRING); + n.run_timed_tests([](const std::vector<double>& v, double x) { return qnorm(x, v[0], v[1], 1, 0); }, "quantile", "Rmath " R_VERSION_STRING, true); + // poisson + poisson.run_timed_tests([](const std::vector<double>& v, double x) { return dpois(x, v[0], 0); }, "PDF", "Rmath " R_VERSION_STRING); + poisson.run_timed_tests([](const std::vector<double>& v, double x) { return ppois(x, v[0], 1, 0); }, "CDF", "Rmath " R_VERSION_STRING); + poisson.run_timed_tests([](const std::vector<double>& v, double x) { return qpois(x, v[0], 1, 0); }, "quantile", "Rmath " R_VERSION_STRING, true); + // T + students_t.run_timed_tests([](const std::vector<double>& v, double x) { return dt(x, v[0], 0); }, "PDF", "Rmath " R_VERSION_STRING); + students_t.run_timed_tests([](const std::vector<double>& v, double x) { return pt(x, v[0], 1, 0); }, "CDF", "Rmath " R_VERSION_STRING); + students_t.run_timed_tests([](const std::vector<double>& v, double x) { return qt(x, v[0], 1, 0); }, "quantile", "Rmath " R_VERSION_STRING, true); + // non central T + non_central_t.run_timed_tests([](const std::vector<double>& v, double x) { return dnt(x, v[0], v[1], 0); }, "PDF", "Rmath " R_VERSION_STRING); + non_central_t.run_timed_tests([](const std::vector<double>& v, double x) { return pnt(x, v[0], v[1], 1, 0); }, "CDF", "Rmath " R_VERSION_STRING); + non_central_t.run_timed_tests([](const std::vector<double>& v, double x) { return qnt(x, v[0], v[1], 1, 0); }, "quantile", "Rmath " R_VERSION_STRING, true); + // weibull + weibull.run_timed_tests([](const std::vector<double>& v, double x) { return dweibull(x, v[0], v[1], 0); }, "PDF", "Rmath " R_VERSION_STRING); + weibull.run_timed_tests([](const std::vector<double>& v, double x) { return pweibull(x, v[0], v[1], 1, 0); }, "CDF", "Rmath " R_VERSION_STRING); + weibull.run_timed_tests([](const std::vector<double>& v, double x) { return qweibull(x, v[0], v[1], 1, 0); }, "quantile", "Rmath " R_VERSION_STRING, true); + +#endif + +#ifdef TEST_DCDFLIB + n.run_timed_tests([](const std::vector<double>& v, double x) { return dcdflib_norm_cdf(x, v[0], v[1]); }, "CDF", "DCDFLIB"); + n.run_timed_tests([](const std::vector<double>& v, double x) { return dcdflib_norm_quantile(x, v[0], v[1]); }, "quantile", "DCDFLIB", true); + + beta.run_timed_tests([](const std::vector<double>& v, double x) { return dcdflib_beta_cdf(x, v[0], v[1]); }, "CDF", "DCDFLIB"); + beta.run_timed_tests([](const std::vector<double>& v, double x) { return dcdflib_beta_quantile(x, v[0], v[1]); }, "quantile", "DCDFLIB", true); + + binomial.run_timed_tests([](const std::vector<double>& v, double x) { return dcdflib_binomial_cdf(x, v[0], v[1]); }, "CDF", "DCDFLIB"); + binomial.run_timed_tests([](const std::vector<double>& v, double x) { return dcdflib_binomial_quantile(x, v[0], v[1]); }, "quantile", "DCDFLIB", true); + + chi_squared.run_timed_tests([](const std::vector<double>& v, double x) { return dcdflib_chi_cdf(x, v[0]); }, "CDF", "DCDFLIB"); + chi_squared.run_timed_tests([](const std::vector<double>& v, double x) { return dcdflib_chi_quantile(x, v[0]); }, "quantile", "DCDFLIB", true); + + non_central_chi_squared.run_timed_tests([](const std::vector<double>& v, double x) { return dcdflib_chi_n_cdf(x, v[0], v[1]); }, "CDF", "DCDFLIB"); + non_central_chi_squared.run_timed_tests([](const std::vector<double>& v, double x) { return dcdflib_chi_n_quantile(x, v[0], v[1]); }, "quantile", "DCDFLIB", true); + + fisher.run_timed_tests([](const std::vector<double>& v, double x) { return dcdflib_f_cdf(x, v[0], v[1]); }, "CDF", "DCDFLIB"); + fisher.run_timed_tests([](const std::vector<double>& v, double x) { return dcdflib_f_quantile(x, v[0], v[1]); }, "quantile", "DCDFLIB", true); + + non_central_f.run_timed_tests([](const std::vector<double>& v, double x) { return dcdflib_f_n_cdf(x, v[0], v[1], v[2]); }, "CDF", "DCDFLIB"); + non_central_f.run_timed_tests([](const std::vector<double>& v, double x) { return dcdflib_f_n_quantile(x, v[0], v[1], v[2]); }, "quantile", "DCDFLIB", true); + + gamma.run_timed_tests([](const std::vector<double>& v, double x) { return dcdflib_gamma_cdf(x, v[0], v[1]); }, "CDF", "DCDFLIB"); + gamma.run_timed_tests([](const std::vector<double>& v, double x) { return dcdflib_gamma_quantile(x, v[0], v[1]); }, "quantile", "DCDFLIB", true); + + negative_binomial.run_timed_tests([](const std::vector<double>& v, double x) { return dcdflib_nbin_cdf(x, v[0], v[1]); }, "CDF", "DCDFLIB"); + negative_binomial.run_timed_tests([](const std::vector<double>& v, double x) { return dcdflib_nbin_quantile(x, v[0], v[1]); }, "quantile", "DCDFLIB", true); + + poisson.run_timed_tests([](const std::vector<double>& v, double x) { return dcdflib_poisson_cdf(x, v[0]); }, "CDF", "DCDFLIB"); + poisson.run_timed_tests([](const std::vector<double>& v, double x) { return dcdflib_poisson_quantile(x, v[0]); }, "quantile", "DCDFLIB", true); + + students_t.run_timed_tests([](const std::vector<double>& v, double x) { return dcdflib_t_cdf(x, v[0]); }, "CDF", "DCDFLIB"); + students_t.run_timed_tests([](const std::vector<double>& v, double x) { return dcdflib_t_quantile(x, v[0]); }, "quantile", "DCDFLIB", true); + + //non_central_t.run_timed_tests([](const std::vector<double>& v, double x) { return dcdflib_t_n_cdf(x, v[0], v[1]); }, "CDF", "DCDFLIB"); + //non_central_t.run_timed_tests([](const std::vector<double>& v, double x) { return dcdflib_t_n_quantile(x, v[0], v[1]); }, "quantile", "DCDFLIB", true); +#endif + + } + catch(const std::exception& e) + { + std::cout << "Test run aborted due to thrown exception: " << e.what() << std::endl; + return 1; + } + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_dn.cpp b/src/boost/libs/math/reporting/performance/test_dn.cpp new file mode 100644 index 000000000..4abe1e68c --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_dn.cpp @@ -0,0 +1,135 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/jacobi_elliptic.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + static const boost::array<boost::array<T, 5>, 36> data1 = {{ + {{ SC_(0.0), SC_(0.0), SC_(0.0), SC_(1.0), SC_(1.0) }}, + {{ ldexp(T(1), -25), ldexp(T(1), -25), SC_(2.98023223876953080883700663838486782870427050521881839342311e-8), SC_(0.99999999999999955591079014993741669975171697261290223678373), SC_(0.99999999999999999999999999999960556954738949421406900774443) }}, + {{ -ldexp(T(1), -25), ldexp(T(1), -25), SC_(-2.98023223876953080883700663838486782870427050521881839342311e-8), SC_(0.99999999999999955591079014993741669975171697261290223678373), SC_(0.99999999999999999999999999999960556954738949421406900774443) }}, + {{ SC_(0.25), ldexp(T(1), -25), SC_(0.247403959254522927383635623557663763268693729825996390997241), SC_(0.968912421710644784709721529742747886950140086772629513814665), SC_(0.99999999999999997281786831901333837240938011109848356555885) }}, + {{ SC_(-0.25), ldexp(T(1), -25), SC_(-0.247403959254522927383635623557663763268693729825996390997241), SC_(0.968912421710644784709721529742747886950140086772629513814665), SC_(0.99999999999999997281786831901333837240938011109848356555885) }}, + {{ SC_(1.25), ldexp(T(1), -25), SC_(0.948984619355586147780156037971989352776684194861616269831136), SC_(0.315322362395268865789580233344649598639316847638615703458263), SC_(0.99999999999999960006577747263860127231780811081154547949983) }}, + {{ SC_(-1.25), ldexp(T(1), -25), SC_(-0.948984619355586147780156037971989352776684194861616269831136), SC_(0.315322362395268865789580233344649598639316847638615703458263), SC_(0.99999999999999960006577747263860127231780811081154547949983) }}, + {{ SC_(25.0), ldexp(T(1), -25), SC_(-0.132351750097778560056127137329035522219365438979106560464704), SC_(0.991202811863472859528158119981178957382802975691690722810123), SC_(0.99999999999999999222089563757583834413059580275315226870704) }}, + {{ SC_(-25.0), ldexp(T(1), -25), SC_(0.132351750097778560056127137329035522219365438979106560464704), SC_(0.991202811863472859528158119981178957382802975691690722810123), SC_(0.99999999999999999222089563757583834413059580275315226870704) }}, + {{ ldexp(T(1), -25), SC_(0.5), SC_(2.98023223876953058825550995757802173334628440851964836958219e-8), SC_(0.99999999999999955591079014993744956895610118130967536624417), SC_(0.99999999999999988897769753748438088116649141278818704012037) }}, + {{ -ldexp(T(1), -25), SC_(0.5), SC_(-2.98023223876953058825550995757802173334628440851964836958219e-8), SC_(0.99999999999999955591079014993744956895610118130967536624417), SC_(0.99999999999999988897769753748438088116649141278818704012037) }}, + {{ SC_(0.25), SC_(0.5), SC_(0.246781405136141600483623741101255389743847413013817188632739), SC_(0.969071172865559727608777289021929824625726812182428398055476), SC_(0.992358168465276394946615469032829292963938826683866720698130) }}, + {{ SC_(-0.25), SC_(0.5), SC_(-0.246781405136141600483623741101255389743847413013817188632739), SC_(0.969071172865559727608777289021929824625726812182428398055476), SC_(0.992358168465276394946615469032829292963938826683866720698130) }}, + {{ SC_(1.25), SC_(0.5), SC_(0.928561236426319775700204388269999130782711902203415239399579), SC_(0.371179242693370810357222594552131893184749696381729988511999), SC_(0.885688154799196841458565445994481097477880319663264816077719) }}, + {{ SC_(-1.25), SC_(0.5), SC_(-0.928561236426319775700204388269999130782711902203415239399579), SC_(0.371179242693370810357222594552131893184749696381729988511999), SC_(0.885688154799196841458565445994481097477880319663264816077719) }}, + {{ SC_(25.0), SC_(0.5), SC_(-0.969223071486651608400225080456020493867827336842041561445359), SC_(-0.246184154035106463351874891855925292474628176040625311168501), SC_(0.874729477852721764836147376110255133761608728373832418508248) }}, + {{ SC_(-25.0), SC_(0.5), SC_(0.969223071486651608400225080456020493867827336842041561445359), SC_(-0.246184154035106463351874891855925292474628176040625311168501), SC_(0.874729477852721764836147376110255133761608728373832418508248) }}, + {{ ldexp(T(1), -25), 1 - ldexp(T(1), -9), SC_(2.98023223876953036939562331632512854347569015560128614888589e-8), SC_(0.99999999999999955591079014993754766348947956082687878223721), SC_(0.99999999999999955764381956001984590118394542979655101564079) }}, + {{ -ldexp(T(1), -25), 1 - ldexp(T(1), -9), SC_(-2.98023223876953036939562331632512854347569015560128614888589e-8), SC_(0.99999999999999955591079014993754766348947956082687878223721), SC_(0.99999999999999955764381956001984590118394542979655101564079) }}, + {{ SC_(0.25), 1 - ldexp(T(1), -9), SC_(0.244928335616519632082236089277654937383208524525331032303082), SC_(0.969541185516180906431546524888118346090913555188425579774305), SC_(0.969661908643964623248878987955178702010392829596222190545649) }}, + {{ SC_(-0.25), 1 - ldexp(T(1), -9), SC_(-0.244928335616519632082236089277654937383208524525331032303082), SC_(0.969541185516180906431546524888118346090913555188425579774305), SC_(0.969661908643964623248878987955178702010392829596222190545649) }}, + {{ SC_(1.25), 1 - ldexp(T(1), -9), SC_(0.848768940045053312079390719205939167551169094157365783446523), SC_(0.528763923140371497228677918580246099580380684604621321430057), SC_(0.531415689278260818860813380561526095359692710060403584603095) }}, + {{ SC_(-1.25), 1 - ldexp(T(1), -9), SC_(-0.848768940045053312079390719205939167551169094157365783446523), SC_(0.528763923140371497228677918580246099580380684604621321430057), SC_(0.531415689278260818860813380561526095359692710060403584603095) }}, + {{ SC_(25.0), 1 - ldexp(T(1), -9), SC_(-0.0252326124525503880903568715488227138184083895871544015366337), SC_(-0.999681606947341709011836635135181960590782564534371631099332), SC_(0.999682849652724146508471774051629114156076052044812654903417) }}, + {{ SC_(-25.0), 1 - ldexp(T(1), -9), SC_(0.0252326124525503880903568715488227138184083895871544015366337), SC_(-0.999681606947341709011836635135181960590782564534371631099332), SC_(0.999682849652724146508471774051629114156076052044812654903417) }}, + + // Try modulus > 1 + {{ ldexp(T(1), -25), SC_(1.5), SC_(2.98023223876952981622027157475276613133414644789222481971590e-8), SC_(0.999999999999999555910790149937712522591174851747994454928040), SC_(0.999999999999999000799277837359575841918151654603571877092161) }}, + {{ -ldexp(T(1), -25), SC_(1.5), SC_(-2.98023223876952981622027157475276613133414644789222481971590e-8), SC_(0.999999999999999555910790149937712522591174851747994454928040), SC_(0.999999999999999000799277837359575841918151654603571877092161) }}, + {{ SC_(0.25), SC_(1.5), SC_(0.241830488135945315134822478837394038661484435596992059686086), SC_(0.970318512143270619246031961334217540099946232418710982266812), SC_(0.931888155181641649031244632258710371461078255228024421800363) }}, + {{ SC_(-0.25), SC_(1.5), SC_(-0.241830488135945315134822478837394038661484435596992059686086), SC_(0.970318512143270619246031961334217540099946232418710982266812), SC_(0.931888155181641649031244632258710371461078255228024421800363) }}, + {{ SC_(1.25), SC_(1.5), SC_(0.665875890711922169121186264316618499018039094009893317545462), SC_(0.746062529663971452521312655373498959968622875614588791642250), SC_(-0.0486921028438866868299166778939466685768843580182675008164949) }}, + {{ SC_(-1.25), SC_(1.5), SC_(-0.665875890711922169121186264316618499018039094009893317545462), SC_(0.746062529663971452521312655373498959968622875614588791642250), SC_(-0.0486921028438866868299166778939466685768843580182675008164949) }}, + {{ SC_(25.0), SC_(1.5), SC_(0.618665338981368217712277210270169521641154921220796362724248), SC_(0.785654630447163313102421517325310755764805805534154371583941), SC_(0.372585153048138377269609818284480926623056458773704266654150) }}, + {{ SC_(-25.0), SC_(1.5), SC_(-0.618665338981368217712277210270169521641154921220796362724248), SC_(0.785654630447163313102421517325310755764805805534154371583941), SC_(0.372585153048138377269609818284480926623056458773704266654150) }}, + + // Special Values: + {{ SC_(0.0), SC_(0.5), SC_(0.0), SC_(1.0), SC_(1.0) }}, + {{ SC_(5.0), SC_(0.0), SC_(-0.958924274663138468893154406155993973352461543964601778131672), SC_(0.283662185463226264466639171513557308334422592252215944930359), SC_(1.0) }}, + {{ SC_(5.0), SC_(1.0), SC_(0.999909204262595131210990447534473021089812615990547862736429), SC_(0.0134752822213045573055191382448821552908373539417006868332819), SC_(0.0134752822213045573055191382448821552908373539417006868332819) }}, + }}; + + +int main() +{ +#include "jacobi_elliptic.ipp" +#include "jacobi_elliptic_small.ipp" +#include "jacobi_near_1.ipp" +#include "jacobi_large_phi.ipp" + + add_data(data1); + add_data(jacobi_elliptic); + add_data(jacobi_elliptic_small); + add_data(jacobi_near_1); + add_data(jacobi_large_phi); + + unsigned data_total = data.size(); + + + std::cout << "Screening Boost data:\n"; + screen_data([](const std::vector<double>& v){ return boost::math::jacobi_dn(v[1], v[0]); }, [](const std::vector<double>& v){ return v[4]; }); + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + std::cout << "Screening GSL data:\n"; + screen_data([](const std::vector<double>& v) + { + double s, c, d; + gsl_sf_elljac_e(v[0], v[1] * v[1], &s, &c, &d); + return d; + }, [](const std::vector<double>& v){ return v[4]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "jacobi_dn[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "jacobi_dn"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::jacobi_dn(v[1], v[2]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::jacobi_dn(v[1], v[0], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v) + { + double s, c, d; + gsl_sf_elljac_e(v[0], v[1] * v[1], &s, &c, &d); + return d; + }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_ellint_1.cpp b/src/boost/libs/math/reporting/performance/test_ellint_1.cpp new file mode 100644 index 000000000..17941a388 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_ellint_1.cpp @@ -0,0 +1,102 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/ellint_1.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) +static const boost::array<boost::array<T, 3>, 19> data1 = { { + { { SC_(0.0), SC_(0.0), SC_(0.0) } }, + { { SC_(-10.0), SC_(0.0), SC_(-10.0) } }, + { { SC_(-1.0), SC_(-1.0), SC_(-1.2261911708835170708130609674719067527242483502207) } }, + { { SC_(-4.0), SC_(0.875), SC_(-5.3190556182262405182189463092940736859067548232647) } }, + { { SC_(8.0), SC_(-0.625), SC_(9.0419973860310100524448893214394562615252527557062) } }, + { { SC_(1e-05), SC_(0.875), SC_(0.000010000000000127604166668510945638036143355898993088) } }, + { { SC_(1e+05), T(10) / 1024, SC_(100002.38431454899771096037307519328741455615271038) } }, + { { SC_(1e-20), SC_(1.0), SC_(1.0000000000000000000000000000000000000000166666667e-20) } }, + { { SC_(1e-20), SC_(1e-20), SC_(1.000000000000000e-20) } }, + { { SC_(1e+20), T(400) / 1024, SC_(1.0418143796499216839719289963154558027005142709763e20) } }, + { { SC_(1e+50), SC_(0.875), SC_(1.3913251718238765549409892714295358043696028445944e50) } }, + { { SC_(2.0), SC_(0.5), SC_(2.1765877052210673672479877957388515321497888026770) } }, + { { SC_(4.0), SC_(0.5), SC_(4.2543274975235836861894752787874633017836785640477) } }, + { { SC_(6.0), SC_(0.5), SC_(6.4588766202317746302999080620490579800463614807916) } }, + { { SC_(10.0), SC_(0.5), SC_(10.697409951222544858346795279378531495869386960090) } }, + { { SC_(-2.0), SC_(0.5), SC_(-2.1765877052210673672479877957388515321497888026770) } }, + { { SC_(-4.0), SC_(0.5), SC_(-4.2543274975235836861894752787874633017836785640477) } }, + { { SC_(-6.0), SC_(0.5), SC_(-6.4588766202317746302999080620490579800463614807916) } }, + { { SC_(-10.0), SC_(0.5), SC_(-10.697409951222544858346795279378531495869386960090) } }, + } }; + +int main() +{ +#include "ellint_f_data.ipp" + + add_data(data1); + add_data(ellint_f_data); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::ellint_1(v[1], v[0]); }, [](const std::vector<double>& v){ return v[2]; }); + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return std::tr1::ellint_1(v[1], v[0]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_ellint_F(v[0], v[1], GSL_PREC_DOUBLE); }, [](const std::vector<double>& v){ return v[2]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "ellint_1[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "ellint_1"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ellint_1(v[1], v[0]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ellint_1(v[1], v[0], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::ellint_1(v[1], v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_ellint_F(v[0], v[1], GSL_PREC_DOUBLE); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_ellint_1c.cpp b/src/boost/libs/math/reporting/performance/test_ellint_1c.cpp new file mode 100644 index 000000000..e73d29c30 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_ellint_1c.cpp @@ -0,0 +1,92 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/ellint_1.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) +static const boost::array<boost::array<T, 2>, 9> data2 = { { + { { SC_(0.0), SC_(1.5707963267948966192313216916397514420985846996876) } }, + { { SC_(0.125), SC_(1.5769867712158131421244030532288080803822271060839) } }, + { { SC_(0.25), SC_(1.5962422221317835101489690714979498795055744578951) } }, + { { T(300) / 1024, SC_(1.6062331054696636704261124078746600894998873503208) } }, + { { T(400) / 1024, SC_(1.6364782007562008756208066125715722889067992997614) } }, + { { SC_(-0.5), SC_(1.6857503548125960428712036577990769895008008941411) } }, + { { SC_(-0.75), SC_(1.9109897807518291965531482187613425592531451316788) } }, + { { 1 - T(1) / 8, SC_(2.185488469278223686913080323730158689730428415766) } }, + { { 1 - T(1) / 1024, SC_(4.5074135978990422666372495313621124487894807327687) } }, + } }; + +int main() +{ +#include "ellint_k_data.ipp" + + add_data(data2); + add_data(ellint_k_data); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::ellint_1(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return std::tr1::comp_ellint_1(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_ellint_Kcomp(v[0], GSL_PREC_DOUBLE); }, [](const std::vector<double>& v){ return v[1]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "ellint_1 (complete)[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "ellint_1 (complete)"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ellint_1(v[0]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ellint_1(v[0], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::comp_ellint_1(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_ellint_Kcomp(v[0], GSL_PREC_DOUBLE); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_ellint_2.cpp b/src/boost/libs/math/reporting/performance/test_ellint_2.cpp new file mode 100644 index 000000000..96365597e --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_ellint_2.cpp @@ -0,0 +1,93 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/ellint_2.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) +static const boost::array<boost::array<T, 3>, 10> data1 = { { + { { SC_(0.0), SC_(0.0), SC_(0.0) } }, + { { SC_(-10.0), SC_(0.0), SC_(-10.0) } }, + { { SC_(-1.0), SC_(-1.0), SC_(-0.84147098480789650665250232163029899962256306079837) } }, + { { SC_(-4.0), T(900) / 1024, SC_(-3.1756145986492562317862928524528520686391383168377) } }, + { { SC_(8.0), T(-600) / 1024, SC_(7.2473147180505693037677015377802777959345489333465) } }, + { { SC_(1e-05), T(800) / 1024, SC_(9.999999999898274739584436515967055859383969942432E-6) } }, + { { SC_(1e+05), T(100) / 1024, SC_(99761.153306972066658135668386691227343323331995888) } }, + { { SC_(1e+10), SC_(-0.5), SC_(9.3421545766487137036576748555295222252286528414669e9) } }, + { { static_cast<T>(ldexp(T(1), 66)), T(400) / 1024, SC_(7.0886102721911705466476846969992069994308167515242e19) } }, + { { static_cast<T>(ldexp(T(1), 166)), T(900) / 1024, SC_(7.1259011068364515942912094521783688927118026465790e49) } }, + } }; + +int main() +{ +#include "ellint_e2_data.ipp" + + add_data(data1); + add_data(ellint_e2_data); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::ellint_2(v[1], v[0]); }, [](const std::vector<double>& v){ return v[2]; }); + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return std::tr1::ellint_2(v[1], v[0]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_ellint_E(v[0], v[1], GSL_PREC_DOUBLE); }, [](const std::vector<double>& v){ return v[2]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "ellint_2[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "ellint_2"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ellint_2(v[1], v[0]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ellint_2(v[1], v[0], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::ellint_2(v[1], v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_ellint_E(v[0], v[1], GSL_PREC_DOUBLE); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_ellint_2c.cpp b/src/boost/libs/math/reporting/performance/test_ellint_2c.cpp new file mode 100644 index 000000000..f59037a95 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_ellint_2c.cpp @@ -0,0 +1,93 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/ellint_2.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) +static const boost::array<boost::array<T, 2>, 10> data2 = { { + { { SC_(-1.0), SC_(1.0) } }, + { { SC_(0.0), SC_(1.5707963267948966192313216916397514420985846996876) } }, + { { T(100) / 1024, SC_(1.5670445330545086723323795143598956428788609133377) } }, + { { T(200) / 1024, SC_(1.5557071588766556854463404816624361127847775545087) } }, + { { T(300) / 1024, SC_(1.5365278991162754883035625322482669608948678755743) } }, + { { T(400) / 1024, SC_(1.5090417763083482272165682786143770446401437564021) } }, + { { SC_(-0.5), SC_(1.4674622093394271554597952669909161360253617523272) } }, + { { T(-600) / 1024, SC_(1.4257538571071297192428217218834579920545946473778) } }, + { { T(-800) / 1024, SC_(1.2927868476159125056958680222998765985004489572909) } }, + { { T(-900) / 1024, SC_(1.1966864890248739524112920627353824133420353430982) } }, + } }; + +int main() +{ +#include "ellint_e_data.ipp" + + add_data(data2); + add_data(ellint_e_data); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::ellint_2(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return std::tr1::comp_ellint_2(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_ellint_Ecomp(v[0], GSL_PREC_DOUBLE); }, [](const std::vector<double>& v){ return v[1]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "ellint_2 (complete)[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "ellint_2 (complete)"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ellint_2(v[0]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ellint_2(v[0], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::comp_ellint_2(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_ellint_Ecomp(v[0], GSL_PREC_DOUBLE); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_ellint_3.cpp b/src/boost/libs/math/reporting/performance/test_ellint_3.cpp new file mode 100644 index 000000000..0484fb4a0 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_ellint_3.cpp @@ -0,0 +1,162 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/ellint_3.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) +static const boost::array<boost::array<T, 4>, 65> data1 = { { + { { SC_(1.0), SC_(-1.0), SC_(0.0), SC_(-1.557407724654902230506974807458360173087) } }, + { { SC_(0.0), SC_(-4.0), SC_(0.4), SC_(-4.153623371196831087495427530365430979011) } }, + { { SC_(0.0), SC_(8.0), SC_(-0.6), SC_(8.935930619078575123490612395578518914416) } }, + { { SC_(0.0), SC_(0.5), SC_(0.25), SC_(0.501246705365439492445236118603525029757890291780157969500480) } }, + { { SC_(0.0), SC_(0.5), SC_(0.0), SC_(0.5) } }, + { { SC_(-2.0), SC_(0.5), SC_(0.0), SC_(0.437501067017546278595664813509803743009132067629603474488486) } }, + { { SC_(0.25), SC_(0.5), SC_(0.0), SC_(0.510269830229213412212501938035914557628394166585442994564135) } }, + { { SC_(0.75), SC_(0.5), SC_(0.0), SC_(0.533293253875952645421201146925578536430596894471541312806165) } }, + { { SC_(0.75), SC_(0.75), SC_(0.0), SC_(0.871827580412760575085768367421866079353646112288567703061975) } }, + { { SC_(1.0), SC_(0.25), SC_(0.0), SC_(0.255341921221036266504482236490473678204201638800822621740476) } }, + { { SC_(2.0), SC_(0.25), SC_(0.0), SC_(0.261119051639220165094943572468224137699644963125853641716219) } }, + { { T(1023) / 1024, SC_(1.5), SC_(0.0), SC_(13.2821612239764190363647953338544569682942329604483733197131) } }, + { { SC_(0.5), SC_(-1.0), SC_(0.5), SC_(-1.228014414316220642611298946293865487807) } }, + { { SC_(0.5), SC_(1e+10), SC_(0.5), SC_(1.536591003599172091573590441336982730551e+10) } }, + { { SC_(-1e+05), SC_(10.0), SC_(0.75), SC_(0.0347926099493147087821620459290460547131012904008557007934290) } }, + { { SC_(-1e+10), SC_(10.0), SC_(0.875), SC_(0.000109956202759561502329123384755016959364346382187364656768212) } }, + { { SC_(-1e+10), SC_(1e+20), SC_(0.875), SC_(1.00000626665567332602765201107198822183913978895904937646809e15) } }, + { { SC_(-1e+10), T(1608) / 1024, SC_(0.875), SC_(0.0000157080616044072676127333183571107873332593142625043567690379) } }, + { { 1 - T(1) / 1024, SC_(1e+20), SC_(0.875), SC_(6.43274293944380717581167058274600202023334985100499739678963e21) } }, + { { SC_(50.0), SC_(0.125), SC_(0.25), SC_(0.196321043776719739372196642514913879497104766409504746018939) } }, + { { SC_(1.125), SC_(1.0), SC_(0.25), SC_(1.77299767784815770192352979665283069318388205110727241629752) } }, + { { SC_(1.125), SC_(10.0), SC_(0.25), SC_(0.662467818678976949597336360256848770217429434745967677192487) } }, + { { SC_(1.125), SC_(3.0), SC_(0.25), SC_(-0.142697285116693775525461312178015106079842313950476205580178) } }, + { { T(257) / 256, SC_(1.5), SC_(0.125), SC_(22.2699300473528164111357290313578126108398839810535700884237) } }, + { { T(257) / 256, SC_(21.5), SC_(0.125), SC_(-0.535406081652313940727588125663856894154526187713506526799429) } }, + // Bug cases from Rocco Romeo: + { { SC_(-1E-170), boost::math::constants::pi<T>() / 4, SC_(1E-164), SC_(0.785398163397448309615660845819875721049292349843776455243736) } }, + { { SC_(-1E-170), boost::math::constants::pi<T>() / 4, SC_(-1E-164), SC_(0.785398163397448309615660845819875721049292349843776455243736) } }, + { { -ldexp(T(1.0), -52), boost::math::constants::pi<T>() / 4, SC_(0.9375), SC_(0.866032844934895872810905364370384153285798081574191920571016) } }, + { { -ldexp(T(1.0), -52), boost::math::constants::pi<T>() / 4, SC_(-0.9375), SC_(0.866032844934895872810905364370384153285798081574191920571016) } }, + { { std::numeric_limits<T>::max_exponent > 600 ? -ldexp(T(1), 604) : T(0), -ldexp(T(1), -816), ldexp(T(1), -510), std::numeric_limits<T>::max_exponent > 600 ? SC_(-2.28835573409367516299079046268930870596307631872422530813192e-246) : SC_(-2.28835573409367516299079046268930870596307631872422530813192e-246) } }, + { { std::numeric_limits<T>::max_exponent > 600 ? -ldexp(T(1), 604) : T(0), -ldexp(T(1), -816), -ldexp(T(1), -510), std::numeric_limits<T>::max_exponent > 600 ? SC_(-2.28835573409367516299079046268930870596307631872422530813192e-246) : SC_(-2.28835573409367516299079046268930870596307631872422530813192e-246) } }, + { { -ldexp(T(1), -622), -ldexp(T(1), -800), ldexp(T(1), -132), SC_(-1.49969681389563095481764443762806535353996169623910829793733e-241) } }, + { { -ldexp(T(1), -622), -ldexp(T(1), -800), -ldexp(T(1), -132), SC_(-1.49969681389563095481764443762806535353996169623910829793733e-241) } }, + { { -ldexp(T(1), -562), ldexp(T(1), -140), ldexp(T(1), -256), SC_(7.174648137343063403129495466444370592154941142407760751e-43) } }, + { { -ldexp(T(1), -562), -ldexp(T(1), -140), ldexp(T(1), -256), SC_(-7.17464813734306340312949546644437059215494114240776075e-43) } }, + { { ldexp(T(1), -688), -ldexp(T(1), -243), ldexp(T(1), -193), SC_(-7.07474928033336903711649944600608732865822749854620171e-74) } }, + { { -ldexp(T(1), -688), -ldexp(T(1), -243), ldexp(T(1), -193), SC_(-7.07474928033336903711649944600608732865822749854620171e-74) } }, + // Special cases where k = 0: + { { SC_(0.5), SC_(1.0), SC_(0.0), SC_(1.17881507892743738986863357869566288974084658835353613038547) } }, + { { SC_(-0.5), SC_(1.0), SC_(0.0), SC_(0.888286691263535380266337576823783210424994266596287990733270) } }, + { { SC_(0.5), SC_(-1.0), SC_(0.0), SC_(-1.17881507892743738986863357869566288974084658835353613038547) } }, + { { SC_(-0.5), SC_(-1.0), SC_(0.0), SC_(-0.888286691263535380266337576823783210424994266596287990733270) } }, + // k == 0 and phi > pi/2: + { { SC_(0.5), SC_(2.0), SC_(0.0), SC_(3.03379730757207227653600089552126882582809860566558143254794) } }, + { { SC_(-0.5), SC_(2.0), SC_(0.0), SC_(1.57453655812023739911111328195028658229986230310938753315640) } }, + { { SC_(0.5), SC_(-2.0), SC_(0.0), SC_(-3.03379730757207227653600089552126882582809860566558143254794) } }, + { { SC_(-0.5), SC_(-2.0), SC_(0.0), SC_(-1.57453655812023739911111328195028658229986230310938753315640) } }, + // Special cases where k = 1: + { { SC_(0.5), SC_(1.0), SC_(1.0), SC_(1.4830998734200773326887632776553375078936815318419194718912351) } }, + { { SC_(-0.5), SC_(1.0), SC_(1.0), SC_(1.07048347329000030842347009377117215811122412769516781788253) } }, + { { SC_(0.5), SC_(-1.0), SC_(1.0), SC_(-1.4830998734200773326887632776553375078936815318419194718912) } }, + { { SC_(-0.5), SC_(-1.0), SC_(1.0), SC_(-1.07048347329000030842347009377117215811122412769516781788253) } }, + // special cases where v = 1: + { { SC_(1.0), SC_(0.5), SC_(0.5), SC_(0.55225234291197632914658859230278152249148960801635386133501) } }, + { { SC_(1.0), SC_(-0.5), SC_(0.5), SC_(-0.55225234291197632914658859230278152249148960801635386133501) } }, + { { SC_(1.0), SC_(2.0), SC_(0.5), SC_(-2.87534521505997989921579168327307068134740792740155171368532) } }, + { { SC_(1.0), SC_(-2.0), SC_(0.5), SC_(2.87534521505997989921579168327307068134740792740155171368532) } }, + { { SC_(1.0), SC_(2.0), ldexp(T(1), -200), SC_(-2.18503986326151899164330610231368254343201774622766316456295) } }, + { { SC_(1.0), SC_(-2.0), ldexp(T(1), -200), SC_(2.18503986326151899164330610231368254343201774622766316456295) } }, + { { SC_(1.0), ldexp(T(1.0), -150), ldexp(T(1), -200), SC_(7.006492321624085354618647916449580656401309709382578858e-46) } }, + { { SC_(1.0), -ldexp(T(1.0), -150), ldexp(T(1), -200), SC_(-7.006492321624085354618647916449580656401309709382578858e-46) } }, + // Previously unsupported region with v > 1 and |phi| > PI/2, this is the only region + // with high-ish error rates caused by argument reduction by Pi: + { { SC_(20.0), ldexp(T(1647611), -19), SC_(0.5), SC_(0.000975940902692994840122139131147517258405256880370413541280) } }, + { { SC_(20.0), -ldexp(T(1647611), -19), SC_(0.5), SC_(-0.000975940902692994840122139131147517258405256880370413541280) } }, + { { T(1.0) + ldexp(T(1), -6), ldexp(T(889085), -19), SC_(0.5), SC_(-27.1647225624906589308619292363045712770651414487085887109197) } }, + { { T(1.0) + ldexp(T(1), -6), -ldexp(T(889085), -19), SC_(0.5), SC_(27.1647225624906589308619292363045712770651414487085887109197) } }, + // Phi = 0: + { { SC_(1.0), SC_(0.0), SC_(0.5), SC_(0.0) } }, + { { SC_(-1.0), SC_(0.0), SC_(0.5), SC_(0.0) } }, + { { SC_(100.0), SC_(0.0), SC_(0.5), SC_(0.0) } }, + { { SC_(-100.0), SC_(0.0), SC_(0.5), SC_(0.0) } }, + } }; + + +int main() +{ +#include "ellint_pi3_data.ipp" +#include "ellint_pi3_large_data.ipp" + + add_data(data1); + add_data(ellint_pi3_data); + add_data(ellint_pi3_large_data); + + unsigned data_total = data.size(); + + std::cout << "Screening boost data:\n"; + screen_data([](const std::vector<double>& v){ return boost::math::ellint_3(v[2], v[0], v[1]); }, [](const std::vector<double>& v){ return v[3]; }); + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + std::cout << "Screening libstdc++ data:\n"; + screen_data([](const std::vector<double>& v){ return std::tr1 ::ellint_3(v[2], -v[0], v[1]); }, [](const std::vector<double>& v){ return v[3]; }); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + std::cout << "Screening libstdc++ data:\n"; + screen_data([](const std::vector<double>& v){ return gsl_sf_ellint_P(v[1], v[2], -v[0], GSL_PREC_DOUBLE); }, [](const std::vector<double>& v){ return v[3]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "ellint_3[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "ellint_3"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ellint_3(v[2], v[0], v[1]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ellint_3(v[2], v[0], v[1], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::ellint_3(v[2], -v[0], v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_ellint_P(v[1], v[2], -v[0], GSL_PREC_DOUBLE); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_ellint_3c.cpp b/src/boost/libs/math/reporting/performance/test_ellint_3c.cpp new file mode 100644 index 000000000..f8da39d1a --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_ellint_3c.cpp @@ -0,0 +1,80 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/ellint_3.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + +int main() +{ +#include "ellint_pi2_data.ipp" + + add_data(ellint_pi2_data); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::ellint_3(v[1], v[0]); }, [](const std::vector<double>& v){ return v[2]; }); + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return std::tr1::comp_ellint_3(v[1], -v[0]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_ellint_Pcomp(v[1], -v[0], GSL_PREC_DOUBLE); }, [](const std::vector<double>& v){ return v[2]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "ellint_3 (complete)[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "ellint_3 (complete)"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ellint_3(v[1], v[0]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ellint_3(v[1], v[0], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::comp_ellint_3(v[1], -v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_ellint_Pcomp(v[1], -v[0], GSL_PREC_DOUBLE); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_ellint_rc.cpp b/src/boost/libs/math/reporting/performance/test_ellint_rc.cpp new file mode 100644 index 000000000..9f1e22698 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_ellint_rc.cpp @@ -0,0 +1,72 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/ellint_rc.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + +int main() +{ +#include "ellint_rc_data.ipp" + + add_data(ellint_rc_data); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::ellint_rc(v[0], v[1]); }, [](const std::vector<double>& v){ return v[2]; }); + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_ellint_RC(v[0], v[1], GSL_PREC_DOUBLE); }, [](const std::vector<double>& v){ return v[2]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "ellint_rc[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "ellint_rc"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ellint_rc(v[0], v[1]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ellint_rc(v[0], v[1], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_ellint_RC(v[0], v[1], GSL_PREC_DOUBLE); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_ellint_rd.cpp b/src/boost/libs/math/reporting/performance/test_ellint_rd.cpp new file mode 100644 index 000000000..b89709898 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_ellint_rd.cpp @@ -0,0 +1,82 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/ellint_rd.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + +int main() +{ +#include "ellint_rd_data.ipp" +#include "ellint_rd_xyy.ipp" +#include "ellint_rd_xxz.ipp" +#include "ellint_rd_0yy.ipp" +#include "ellint_rd_xxx.ipp" +#include "ellint_rd_0xy.ipp" + + add_data(ellint_rd_data); + add_data(ellint_rd_xyy); + add_data(ellint_rd_xxz); + add_data(ellint_rd_0yy); + add_data(ellint_rd_xxx); + add_data(ellint_rd_0xy); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::ellint_rd(v[0], v[1], v[2]); }, [](const std::vector<double>& v){ return v[3]; }); + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_ellint_RD(v[0], v[1], v[2], GSL_PREC_DOUBLE); }, [](const std::vector<double>& v){ return v[3]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "ellint_rd[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "ellint_rd"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ellint_rd(v[0], v[1], v[2]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ellint_rd(v[0], v[1], v[2], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_ellint_RD(v[0], v[1], v[2], GSL_PREC_DOUBLE); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_ellint_rf.cpp b/src/boost/libs/math/reporting/performance/test_ellint_rf.cpp new file mode 100644 index 000000000..e7c5aeacc --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_ellint_rf.cpp @@ -0,0 +1,80 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/ellint_rf.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + +int main() +{ +#include "ellint_rf_data.ipp" +#include "ellint_rf_xxx.ipp" +#include "ellint_rf_xyy.ipp" +#include "ellint_rf_0yy.ipp" +#include "ellint_rf_xy0.ipp" + + add_data(ellint_rf_data); + add_data(ellint_rf_xxx); + add_data(ellint_rf_xyy); + add_data(ellint_rf_0yy); + add_data(ellint_rf_xy0); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::ellint_rf(v[0], v[1], v[2]); }, [](const std::vector<double>& v){ return v[3]; }); + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_ellint_RF(v[0], v[1], v[2], GSL_PREC_DOUBLE); }, [](const std::vector<double>& v){ return v[3]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "ellint_rf[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "ellint_rf"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ellint_rf(v[0], v[1], v[2]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ellint_rf(v[0], v[1], v[2], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_ellint_RF(v[0], v[1], v[2], GSL_PREC_DOUBLE); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_ellint_rj.cpp b/src/boost/libs/math/reporting/performance/test_ellint_rj.cpp new file mode 100644 index 000000000..841195aa9 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_ellint_rj.cpp @@ -0,0 +1,80 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/ellint_rj.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + +int main() +{ +#include "ellint_rj_data.ipp" +#include "ellint_rj_e4.ipp" +#include "ellint_rj_e3.ipp" +#include "ellint_rj_e2.ipp" +#include "ellint_rj_zp.ipp" + + add_data(ellint_rj_data); + add_data(ellint_rj_e4); + add_data(ellint_rj_e3); + add_data(ellint_rj_e2); + add_data(ellint_rj_zp); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::ellint_rj(v[0], v[1], v[2], v[3]); }, [](const std::vector<double>& v){ return v[4]; }); + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_ellint_RJ(v[0], v[1], v[2], v[3], GSL_PREC_DOUBLE); }, [](const std::vector<double>& v){ return v[4]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "ellint_rj[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "ellint_rj"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ellint_rj(v[0], v[1], v[2], v[3]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ellint_rj(v[0], v[1], v[2], v[3], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_ellint_RJ(v[0], v[1], v[2], v[3], GSL_PREC_DOUBLE); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_erf.cpp b/src/boost/libs/math/reporting/performance/test_erf.cpp new file mode 100644 index 000000000..5c9025168 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_erf.cpp @@ -0,0 +1,89 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/erf.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +int main() +{ + typedef double T; +#define SC_(x) static_cast<double>(x) +# include "erf_small_data.ipp" +# include "erf_data.ipp" +# include "erf_large_data.ipp" + + add_data(erf_small_data); + add_data(erf_data); + add_data(erf_large_data); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::erf(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); + + +#if defined(TEST_C99) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return ::erf(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); +#endif +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return std::tr1::erf(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_erf(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); +#endif + unsigned data_used = data.size(); + std::string function = "erf[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "erf"; + + double time = exec_timed_test([](const std::vector<double>& v){ return boost::math::erf(v[0]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_C99) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + double time = exec_timed_test([](const std::vector<double>& v){ return boost::math::erf(v[0], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_C99) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_C99) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return ::erf(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "math.h"); +#endif +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::erf(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_erf(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif + + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_erfc.cpp b/src/boost/libs/math/reporting/performance/test_erfc.cpp new file mode 100644 index 000000000..6c09df1cb --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_erfc.cpp @@ -0,0 +1,91 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/erf.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +int main() +{ + typedef double T; +#define SC_(x) static_cast<double>(x) +# include "erf_small_data.ipp" +# include "erf_data.ipp" +# include "erf_large_data.ipp" + + add_data(erf_small_data); + add_data(erf_data); + add_data(erf_large_data); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::erfc(v[0]); }, [](const std::vector<double>& v){ return v[2]; }); + + +#if defined(TEST_C99) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return ::erfc(v[0]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return std::tr1::erfc(v[0]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_erfc(v[0]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "erfc[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "erfc"; + + double time = exec_timed_test([](const std::vector<double>& v){ return boost::math::erfc(v[0]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_C99) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + double time = exec_timed_test([](const std::vector<double>& v){ return boost::math::erfc(v[0], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_C99) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_C99) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return ::erfc(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "math.h"); +#endif + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::erfc(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_erfc(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif + + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_expint.cpp b/src/boost/libs/math/reporting/performance/test_expint.cpp new file mode 100644 index 000000000..2a2f44afb --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_expint.cpp @@ -0,0 +1,82 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/expint.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + +int main() +{ +#include "expinti_data.ipp" +#include "expinti_data_double.ipp" + + add_data(expinti_data); + add_data(expinti_data_double); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::expint(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return std::tr1::expint(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_expint_Ei(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "expint[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "expint"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::expint(v[0]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::expint(v[0], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::expint(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_expint_Ei(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_expint_n.cpp b/src/boost/libs/math/reporting/performance/test_expint_n.cpp new file mode 100644 index 000000000..413598d28 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_expint_n.cpp @@ -0,0 +1,76 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/expint.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + +int main() +{ +#include "expint_data.ipp" +#include "expint_small_data.ipp" +#include "expint_1_data.ipp" + + add_data(expint_data); + add_data(expint_small_data); + add_data(expint_1_data); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::expint(static_cast<int>(v[0]), v[1]); }, [](const std::vector<double>& v){ return v[2]; }); + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_expint_En(static_cast<int>(v[0]), v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "expint (En)[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "expint (En)"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::expint(static_cast<int>(v[0]), v[1]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::expint(static_cast<int>(v[0]), v[1], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_expint_En(static_cast<int>(v[0]), v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_expm1.cpp b/src/boost/libs/math/reporting/performance/test_expm1.cpp new file mode 100644 index 000000000..027f020a1 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_expm1.cpp @@ -0,0 +1,78 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/expm1.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +int main() +{ + typedef double T; +#define SC_(x) static_cast<double>(x) +# include "../../test/log1p_expm1_data.ipp" + + add_data(log1p_expm1_data); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::expm1(v[0]); }, [](const std::vector<double>& v){ return v[2]; }); + + +#if defined(TEST_C99) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return ::expm1(v[0]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return std::tr1::expm1(v[0]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "expm1[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "expm1"; + + double time = exec_timed_test([](const std::vector<double>& v){ return boost::math::expm1(v[0]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_C99) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + double time = exec_timed_test([](const std::vector<double>& v){ return boost::math::expm1(v[0], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_C99) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_C99) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return ::expm1(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "math.h"); +#endif +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::expm1(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif + + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_gamma_p.cpp b/src/boost/libs/math/reporting/performance/test_gamma_p.cpp new file mode 100644 index 000000000..4d11da845 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_gamma_p.cpp @@ -0,0 +1,86 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/gamma.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + +int main() +{ +# include "igamma_med_data.ipp" +# include "igamma_small_data.ipp" +# include "igamma_big_data.ipp" +# include "igamma_int_data.ipp" + + add_data(igamma_med_data); + add_data(igamma_small_data); + add_data(igamma_big_data); + add_data(igamma_int_data); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::gamma_p(v[0], v[1]); }, [](const std::vector<double>& v){ return v[5]; }); + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_gamma_inc_P(v[0], v[1]); }, [](const std::vector<double>& v){ return v[5]; }); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return pgamma(v[1], v[0], 1.0, 1, 0); }, [](const std::vector<double>& v){ return v[5]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "gamma_p[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "gamma_p"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::gamma_p(v[0], v[1]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::gamma_p(v[0], v[1], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_gamma_inc_P(v[0], v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return pgamma(v[1], v[0], 1.0, 1, 0); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "Rmath " R_VERSION_STRING); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_gamma_p_inv.cpp b/src/boost/libs/math/reporting/performance/test_gamma_p_inv.cpp new file mode 100644 index 000000000..a825957bc --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_gamma_p_inv.cpp @@ -0,0 +1,78 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/gamma.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + +int main() +{ +# include "gamma_inv_data.ipp" +# include "gamma_inv_big_data.ipp" +# include "gamma_inv_small_data.ipp" + + add_data(gamma_inv_data); + add_data(gamma_inv_big_data); + add_data(gamma_inv_small_data); + + unsigned data_total = data.size(); + + std::cout << "screening Boost data:\n"; + screen_data([](const std::vector<double>& v){ return boost::math::gamma_p_inv(v[0], v[1]); }, [](const std::vector<double>& v){ return v[2]; }); + + +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + std::cout << "screening Rmath data:\n"; + screen_data([](const std::vector<double>& v){ return qgamma(v[1], v[0], 1.0, 1, 0); }, [](const std::vector<double>& v){ return v[2]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "gamma_p_inv[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "gamma_p_inv"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::gamma_p_inv(v[0], v[1]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::gamma_p_inv(v[0], v[1], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return qgamma(v[1], v[0], 1.0, 1, 0); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "Rmath " R_VERSION_STRING); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_gamma_q.cpp b/src/boost/libs/math/reporting/performance/test_gamma_q.cpp new file mode 100644 index 000000000..1651dd6d9 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_gamma_q.cpp @@ -0,0 +1,90 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/gamma.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + +int main() +{ +# include "igamma_med_data.ipp" +# include "igamma_small_data.ipp" +# include "igamma_big_data.ipp" +# include "igamma_int_data.ipp" + + add_data(igamma_med_data); + add_data(igamma_small_data); + add_data(igamma_big_data); + add_data(igamma_int_data); + + unsigned data_total = data.size(); + + + std::cout << "Screening Boost data:\n"; + screen_data([](const std::vector<double>& v){ return boost::math::gamma_q(v[0], v[1]); }, [](const std::vector<double>& v){ return v[3]; }); + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + std::cout << "Screening GSL data:\n"; + screen_data([](const std::vector<double>& v){ return gsl_sf_gamma_inc_Q(v[0], v[1]); }, [](const std::vector<double>& v){ return v[3]; }); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + std::cout << "Screening GSL data:\n"; + screen_data([](const std::vector<double>& v){ return pgamma(v[1], v[0], 1.0, 0, 0); }, [](const std::vector<double>& v){ return v[3]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "gamma_q[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "gamma_q"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::gamma_q(v[0], v[1]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::gamma_q(v[0], v[1], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_gamma_inc_Q(v[0], v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return pgamma(v[1], v[0], 1.0, 0, 0); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "Rmath " R_VERSION_STRING); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_gamma_q_inv.cpp b/src/boost/libs/math/reporting/performance/test_gamma_q_inv.cpp new file mode 100644 index 000000000..923ef5d51 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_gamma_q_inv.cpp @@ -0,0 +1,78 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/gamma.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + +int main() +{ +# include "gamma_inv_data.ipp" +# include "gamma_inv_big_data.ipp" +# include "gamma_inv_small_data.ipp" + + add_data(gamma_inv_data); + add_data(gamma_inv_big_data); + add_data(gamma_inv_small_data); + + unsigned data_total = data.size(); + + std::cout << "screening Boost data:\n"; + screen_data([](const std::vector<double>& v){ return boost::math::gamma_q_inv(v[0], v[1]); }, [](const std::vector<double>& v){ return v[3]; }); + + +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + std::cout << "screening Rmath data:\n"; + screen_data([](const std::vector<double>& v){ return qgamma(v[1], v[0], 1.0, 0, 0); }, [](const std::vector<double>& v){ return v[2]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "gamma_q_inv[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "gamma_q_inv"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::gamma_q_inv(v[0], v[1]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::gamma_q_inv(v[0], v[1], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return qgamma(v[1], v[0], 1.0, 0, 0); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "Rmath " R_VERSION_STRING); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_gcd.cpp b/src/boost/libs/math/reporting/performance/test_gcd.cpp new file mode 100644 index 000000000..f9793a02b --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_gcd.cpp @@ -0,0 +1,478 @@ +// Copyright Jeremy Murphy 2016. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/integer/common_factor_rt.hpp> +#include <boost/math/special_functions/prime.hpp> +#include <boost/multiprecision/cpp_int.hpp> +#include <boost/multiprecision/integer.hpp> +#include <boost/random.hpp> +#include <boost/array.hpp> +#include <iostream> +#include <algorithm> +#include <numeric> +#include <string> +#include <tuple> +#include <type_traits> +#include <vector> +#include <functional> +#include "fibonacci.hpp" +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" + + +using namespace std; + +boost::multiprecision::cpp_int total_sum(0); + +template <typename Func, class Table> +double exec_timed_test_foo(Func f, const Table& data, double min_elapsed = 0.5) +{ + double t = 0; + unsigned repeats = 1; + typename Table::value_type::first_type sum{0}; + stopwatch<boost::chrono::high_resolution_clock> w; + do + { + for(unsigned count = 0; count < repeats; ++count) + { + for(typename Table::size_type n = 0; n < data.size(); ++n) + sum += f(data[n].first, data[n].second); + } + + t = boost::chrono::duration_cast<boost::chrono::duration<double>>(w.elapsed()).count(); + if(t < min_elapsed) + repeats *= 2; + } + while(t < min_elapsed); + total_sum += sum; + return t / repeats; +} + + +template <typename T> +struct test_function_template +{ + vector<pair<T, T> > const & data; + const char* data_name; + + test_function_template(vector<pair<T, T> > const &data, const char* name) : data(data), data_name(name) {} + + template <typename Function> + void operator()(pair<Function, string> const &f) const + { + auto result = exec_timed_test_foo(f.first, data); + auto table_name = string("gcd method comparison with ") + compiler_name() + string(" on ") + platform_name(); + + report_execution_time(result, + table_name, + string(data_name), + string(f.second) + "\n" + boost_name()); + } +}; + +boost::random::mt19937 rng; +boost::random::uniform_int_distribution<> d_0_6(0, 6); +boost::random::uniform_int_distribution<> d_1_20(1, 20); + +template <class T> +T get_prime_products() +{ + int n_primes = d_0_6(rng); + switch(n_primes) + { + case 0: + // Generate a power of 2: + return static_cast<T>(1u) << d_1_20(rng); + case 1: + // prime number: + return boost::math::prime(d_1_20(rng) + 3); + } + T result = 1; + for(int i = 0; i < n_primes; ++i) + result *= boost::math::prime(d_1_20(rng) + 3) * boost::math::prime(d_1_20(rng) + 3) * boost::math::prime(d_1_20(rng) + 3) * boost::math::prime(d_1_20(rng) + 3) * boost::math::prime(d_1_20(rng) + 3); + return result; +} + +template <class T> +T get_uniform_random() +{ + static boost::random::uniform_int_distribution<T> minimax((std::numeric_limits<T>::min)(), (std::numeric_limits<T>::max)()); + return minimax(rng); +} + +template <class T> +inline bool even(T const& val) +{ + return !(val & 1u); +} + +template <class Backend, boost::multiprecision::expression_template_option ExpressionTemplates> +inline bool even(boost::multiprecision::number<Backend, ExpressionTemplates> const& val) +{ + return !bit_test(val, 0); +} + +template <class T> +T euclid_textbook(T a, T b) +{ + using std::swap; + if(a < b) + swap(a, b); + while(b) + { + T t = b; + b = a % b; + a = t; + } + return a; +} + +template <class T> +T binary_textbook(T u, T v) +{ + if(u && v) + { + unsigned shifts = (std::min)(boost::multiprecision::lsb(u), boost::multiprecision::lsb(v)); + if(shifts) + { + u >>= shifts; + v >>= shifts; + } + while(u) + { + unsigned bit_index = boost::multiprecision::lsb(u); + if(bit_index) + { + u >>= bit_index; + } + else if(bit_index = boost::multiprecision::lsb(v)) + { + v >>= bit_index; + } + else + { + if(u < v) + v = (v - u) >> 1u; + else + u = (u - v) >> 1u; + } + } + return v << shifts; + } + return u + v; +} + +template <typename Integer> +inline BOOST_CXX14_CONSTEXPR Integer gcd_default(Integer a, Integer b) BOOST_GCD_NOEXCEPT(Integer) +{ + using boost::integer::gcd; + return gcd(a, b); +} + + +template <class T> +void test_type(const char* name) +{ + using namespace boost::integer::gcd_detail; + typedef T int_type; + std::vector<pair<int_type, int_type> > data; + + for(unsigned i = 0; i < 1000; ++i) + { + data.push_back(std::make_pair(get_prime_products<T>(), get_prime_products<T>())); + } + std::string row_name("gcd<"); + row_name += name; + row_name += "> (random prime number products)"; + + typedef pair< function<int_type(int_type, int_type)>, string> f_test; + array<f_test, 6> test_functions{ { + { gcd_default<int_type>, "gcd" }, + { Euclid_gcd<int_type>, "Euclid_gcd" }, + { Stein_gcd<int_type>, "Stein_gcd" } , + { mixed_binary_gcd<int_type>, "mixed_binary_gcd" }, + { binary_textbook<int_type>, "Stein_gcd_textbook" }, + { euclid_textbook<int_type>, "gcd_euclid_textbook" }, + } }; + for_each(begin(test_functions), end(test_functions), test_function_template<int_type>(data, row_name.c_str())); + + data.clear(); + for(unsigned i = 0; i < 1000; ++i) + { + data.push_back(std::make_pair(get_uniform_random<T>(), get_uniform_random<T>())); + } + row_name.erase(); + row_name += "gcd<"; + row_name += name; + row_name += "> (uniform random numbers)"; + for_each(begin(test_functions), end(test_functions), test_function_template<int_type>(data, row_name.c_str())); + + // Fibonacci number tests: + row_name.erase(); + row_name += "gcd<"; + row_name += name; + row_name += "> (adjacent Fibonacci numbers)"; + for_each(begin(test_functions), end(test_functions), test_function_template<int_type>(fibonacci_numbers_permution_1<T>(), row_name.c_str())); + + row_name.erase(); + row_name += "gcd<"; + row_name += name; + row_name += "> (permutations of Fibonacci numbers)"; + for_each(begin(test_functions), end(test_functions), test_function_template<int_type>(fibonacci_numbers_permution_2<T>(), row_name.c_str())); + + row_name.erase(); + row_name += "gcd<"; + row_name += name; + row_name += "> (Trivial cases)"; + for_each(begin(test_functions), end(test_functions), test_function_template<int_type>(trivial_gcd_test_cases<T>(), row_name.c_str())); +} + +/*******************************************************************************************************************/ + +template <class T> +T generate_random(unsigned bits_wanted) +{ + static boost::random::mt19937 gen; + typedef boost::random::mt19937::result_type random_type; + + T max_val; + unsigned digits; + if(std::numeric_limits<T>::is_bounded && (bits_wanted == (unsigned)std::numeric_limits<T>::digits)) + { + max_val = (std::numeric_limits<T>::max)(); + digits = std::numeric_limits<T>::digits; + } + else + { + max_val = T(1) << bits_wanted; + digits = bits_wanted; + } + + unsigned bits_per_r_val = std::numeric_limits<random_type>::digits - 1; + while((random_type(1) << bits_per_r_val) > (gen.max)()) --bits_per_r_val; + + unsigned terms_needed = digits / bits_per_r_val + 1; + + T val = 0; + for(unsigned i = 0; i < terms_needed; ++i) + { + val *= (gen.max)(); + val += gen(); + } + val %= max_val; + return val; +} + +template <typename N> +N gcd_stein(N m, N n) +{ + BOOST_ASSERT(m >= static_cast<N>(0)); + BOOST_ASSERT(n >= static_cast<N>(0)); + if(m == N(0)) return n; + if(n == N(0)) return m; + // m > 0 && n > 0 + unsigned d_m = 0; + while(even(m)) { m >>= 1; d_m++; } + unsigned d_n = 0; + while(even(n)) { n >>= 1; d_n++; } + // odd(m) && odd(n) + while(m != n) { + if(n > m) swap(n, m); + m -= n; + do m >>= 1; while(even(m)); + // m == n + } + return m << (std::min)(d_m, d_n); +} + + +boost::multiprecision::cpp_int big_gcd(const boost::multiprecision::cpp_int& a, const boost::multiprecision::cpp_int& b) +{ + return boost::multiprecision::gcd(a, b); +} + +namespace boost { namespace multiprecision { namespace backends { + +template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1> +inline typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type + eval_gcd_new( + cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, + const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a, + const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& b) +{ + using default_ops::eval_lsb; + using default_ops::eval_is_zero; + using default_ops::eval_get_sign; + + if(a.size() == 1) + { + eval_gcd(result, b, *a.limbs()); + return; + } + if(b.size() == 1) + { + eval_gcd(result, a, *b.limbs()); + return; + } + + int shift; + + cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> u(a), v(b), mod; + + int s = eval_get_sign(u); + + /* GCD(0,x) := x */ + if(s < 0) + { + u.negate(); + } + else if(s == 0) + { + result = v; + return; + } + s = eval_get_sign(v); + if(s < 0) + { + v.negate(); + } + else if(s == 0) + { + result = u; + return; + } + + /* Let shift := lg K, where K is the greatest power of 2 + dividing both u and v. */ + + unsigned us = eval_lsb(u); + unsigned vs = eval_lsb(v); + shift = (std::min)(us, vs); + eval_right_shift(u, us); + eval_right_shift(v, vs); + + // From now on access u and v via pointers, that way we have a trivial swap: + cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>* up(&u), *vp(&v), *mp(&mod); + + do + { + /* Now u and v are both odd, so diff(u, v) is even. + Let u = min(u, v), v = diff(u, v)/2. */ + s = up->compare(*vp); + if(s > 0) + std::swap(up, vp); + if(s == 0) + break; + if(vp->size() <= 2) + { + if(vp->size() == 1) + *up = boost::integer::gcd_detail::mixed_binary_gcd(*vp->limbs(), *up->limbs()); + else + { + double_limb_type i, j; + i = vp->limbs()[0] | (static_cast<double_limb_type>(vp->limbs()[1]) << sizeof(limb_type) * CHAR_BIT); + j = (up->size() == 1) ? *up->limbs() : up->limbs()[0] | (static_cast<double_limb_type>(up->limbs()[1]) << sizeof(limb_type) * CHAR_BIT); + u = boost::integer::gcd_detail::mixed_binary_gcd(i, j); + } + break; + } + if(vp->size() > up->size() /*eval_msb(*vp) > eval_msb(*up) + 32*/) + { + eval_modulus(*mp, *vp, *up); + std::swap(vp, mp); + eval_subtract(*up, *vp); + if(eval_is_zero(*vp) == 0) + { + vs = eval_lsb(*vp); + eval_right_shift(*vp, vs); + } + else + break; + if(eval_is_zero(*up) == 0) + { + vs = eval_lsb(*up); + eval_right_shift(*up, vs); + } + else + { + std::swap(up, vp); + break; + } + } + else + { + eval_subtract(*vp, *up); + vs = eval_lsb(*vp); + eval_right_shift(*vp, vs); + } + } + while(true); + + result = *up; + eval_left_shift(result, shift); +} + +}}} + + +boost::multiprecision::cpp_int big_gcd_new(const boost::multiprecision::cpp_int& a, const boost::multiprecision::cpp_int& b) +{ + boost::multiprecision::cpp_int result; + boost::multiprecision::backends::eval_gcd_new(result.backend(), a.backend(), b.backend()); + return result; +} + +#if 0 +void test_n_bits(unsigned n, std::string data_name, const std::vector<pair<boost::multiprecision::cpp_int, boost::multiprecision::cpp_int> >* p_data = 0) +{ + using namespace boost::math::detail; + typedef boost::multiprecision::cpp_int int_type; + std::vector<pair<int_type, int_type> > data, data2; + + for(unsigned i = 0; i < 1000; ++i) + { + data.push_back(std::make_pair(generate_random<int_type>(n), generate_random<int_type>(n))); + } + + typedef pair< function<int_type(int_type, int_type)>, string> f_test; + array<f_test, 2> test_functions{ { /*{ Stein_gcd<int_type>, "Stein_gcd" } ,{ Euclid_gcd<int_type>, "Euclid_gcd" },{ binary_textbook<int_type>, "Stein_gcd_textbook" },{ euclid_textbook<int_type>, "gcd_euclid_textbook" },{ mixed_binary_gcd<int_type>, "mixed_binary_gcd" },{ gcd_stein<int_type>, "gcd_stein" },*/{ big_gcd, "boost::multiprecision::gcd" },{ big_gcd_new, "big_gcd_new" } } }; + for_each(begin(test_functions), end(test_functions), test_function_template<int_type>(p_data ? *p_data : data, data_name.c_str(), true)); +} +#endif + +int main() +{ + test_type<unsigned short>("unsigned short"); + test_type<unsigned>("unsigned"); + test_type<unsigned long>("unsigned long"); + test_type<unsigned long long>("unsigned long long"); + + test_type<boost::multiprecision::uint256_t>("boost::multiprecision::uint256_t"); + test_type<boost::multiprecision::uint512_t>("boost::multiprecision::uint512_t"); + test_type<boost::multiprecision::uint1024_t>("boost::multiprecision::uint1024_t"); + + /* + test_n_bits(16, " 16 bit random values"); + test_n_bits(32, " 32 bit random values"); + test_n_bits(64, " 64 bit random values"); + test_n_bits(125, " 125 bit random values"); + test_n_bits(250, " 250 bit random values"); + test_n_bits(500, " 500 bit random values"); + test_n_bits(1000, " 1000 bit random values"); + test_n_bits(5000, " 5000 bit random values"); + test_n_bits(10000, "10000 bit random values"); + //test_n_bits(100000); + //test_n_bits(1000000); + + test_n_bits(0, "consecutive first 1000 fibonacci numbers", &fibonacci_numbers_cpp_int_permution_1()); + test_n_bits(0, "permutations of first 1000 fibonacci numbers", &fibonacci_numbers_cpp_int_permution_2()); + */ + return 0; +} diff --git a/src/boost/libs/math/reporting/performance/test_ibeta.cpp b/src/boost/libs/math/reporting/performance/test_ibeta.cpp new file mode 100644 index 000000000..59a53e4af --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_ibeta.cpp @@ -0,0 +1,81 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/beta.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + + +int main() +{ +# include "ibeta_small_data.ipp" +# include "ibeta_data.ipp" +# include "ibeta_large_data.ipp" +# include "ibeta_int_data.ipp" + + add_data(ibeta_small_data); + add_data(ibeta_data); + add_data(ibeta_large_data); + add_data(ibeta_int_data); + + unsigned data_total = data.size(); + + std::cout << "Screening boost data:\n"; + screen_data([](const std::vector<double>& v){ return boost::math::ibeta(v[0], v[1], v[2]); }, [](const std::vector<double>& v){ return v[5]; }); + + +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + std::cout << "Screening libstdc++ data:\n"; + screen_data([](const std::vector<double>& v){ return ::pbeta(v[2], v[0], v[1], 1, 0); }, [](const std::vector<double>& v){ return v[5]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "ibeta[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "ibeta"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ibeta(v[0], v[1], v[2]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ibeta(v[0], v[1], v[2], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return ::pbeta(v[2], v[0], v[1], 1, 0); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "Rmath " R_VERSION_STRING); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_ibeta_inv.cpp b/src/boost/libs/math/reporting/performance/test_ibeta_inv.cpp new file mode 100644 index 000000000..68488cdef --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_ibeta_inv.cpp @@ -0,0 +1,79 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/beta.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + + +int main() +{ +# include "ibeta_inv_data.ipp" + + add_data(ibeta_inv_data); + + unsigned data_total = data.size(); + + std::cout << "Screening boost data:\n"; + screen_data([](const std::vector<double>& v){ return boost::math::ibeta_inv(v[0], v[1], v[2]); }, [](const std::vector<double>& v){ return v[3]; }); + + +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + std::cout << "Screening libstdc++ data:\n"; + screen_data([](const std::vector<double>& v){ return ::qbeta(v[2], v[0], v[1], 1, 0); }, [](const std::vector<double>& v){ return v[3]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "ibeta_inv[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "ibeta_inv"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ibeta_inv(v[0], v[1], v[2]); }); + std::cout << time << std::endl; +#if defined(COMPILER_COMPARISON_TABLES) + report_execution_time(time, std::string("Compiler Option Comparison on ") + platform_name(), "boost::math::ibeta_inv", get_compiler_options_name()); +#else +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); +#endif + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ibeta_inv(v[0], v[1], v[2], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return ::qbeta(v[2], v[0], v[1], 1, 0); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "Rmath " R_VERSION_STRING); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_ibetac.cpp b/src/boost/libs/math/reporting/performance/test_ibetac.cpp new file mode 100644 index 000000000..33eadbeb9 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_ibetac.cpp @@ -0,0 +1,81 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/beta.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + + +int main() +{ +# include "ibeta_small_data.ipp" +# include "ibeta_data.ipp" +# include "ibeta_large_data.ipp" +# include "ibeta_int_data.ipp" + + add_data(ibeta_small_data); + add_data(ibeta_data); + add_data(ibeta_large_data); + add_data(ibeta_int_data); + + unsigned data_total = data.size(); + + std::cout << "Screening boost data:\n"; + screen_data([](const std::vector<double>& v){ return boost::math::ibetac(v[0], v[1], v[2]); }, [](const std::vector<double>& v){ return v[6]; }); + + +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + std::cout << "Screening libstdc++ data:\n"; + screen_data([](const std::vector<double>& v){ return ::pbeta(v[2], v[0], v[1], 0, 0); }, [](const std::vector<double>& v){ return v[6]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "ibetac[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "ibetac"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ibetac(v[0], v[1], v[2]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ibetac(v[0], v[1], v[2], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return ::pbeta(v[2], v[0], v[1], 0, 0); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "Rmath " R_VERSION_STRING); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_ibetac_inv.cpp b/src/boost/libs/math/reporting/performance/test_ibetac_inv.cpp new file mode 100644 index 000000000..5889acaf4 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_ibetac_inv.cpp @@ -0,0 +1,75 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/beta.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + + +int main() +{ +# include "ibeta_inv_data.ipp" + + add_data(ibeta_inv_data); + + unsigned data_total = data.size(); + + std::cout << "Screening boost data:\n"; + screen_data([](const std::vector<double>& v){ return boost::math::ibetac_inv(v[0], v[1], v[2]); }, [](const std::vector<double>& v){ return v[4]; }); + + +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + std::cout << "Screening libstdc++ data:\n"; + screen_data([](const std::vector<double>& v){ return ::qbeta(v[2], v[0], v[1], 0, 0); }, [](const std::vector<double>& v){ return v[4]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "ibetac_inv[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "ibetac_inv"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ibetac_inv(v[0], v[1], v[2]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::ibetac_inv(v[0], v[1], v[2], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return ::qbeta(v[2], v[0], v[1], 0, 0); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "Rmath " R_VERSION_STRING); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_igamma.cpp b/src/boost/libs/math/reporting/performance/test_igamma.cpp new file mode 100644 index 000000000..48c31d3ec --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_igamma.cpp @@ -0,0 +1,78 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/gamma.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + +int main() +{ +# include "igamma_med_data.ipp" +# include "igamma_small_data.ipp" +# include "igamma_big_data.ipp" +# include "igamma_int_data.ipp" + + add_data(igamma_med_data); + add_data(igamma_small_data); + add_data(igamma_big_data); + add_data(igamma_int_data); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::tgamma(v[0], v[1]); }, [](const std::vector<double>& v){ return v[2]; }); + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_gamma_inc(v[0], v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "tgamma (incomplete)[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "tgamma (incomplete)"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::tgamma(v[0], v[1]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::tgamma(v[0], v[1], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_gamma_inc(v[0], v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_in.cpp b/src/boost/libs/math/reporting/performance/test_in.cpp new file mode 100644 index 000000000..6a56bf71f --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_in.cpp @@ -0,0 +1,127 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/bessel.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) +static const boost::array<boost::array<T, 3>, 10> i0_data = { { + { { SC_(0.0), SC_(0.0), SC_(1.0) } }, + { { SC_(0.0), SC_(1.0), SC_(1.26606587775200833559824462521471753760767031135496220680814) } }, + { { SC_(0.0), SC_(-2.0), SC_(2.27958530233606726743720444081153335328584110278545905407084) } }, + { { SC_(0.0), SC_(4.0), SC_(11.3019219521363304963562701832171024974126165944353377060065) } }, + { { SC_(0.0), SC_(-7.0), SC_(168.593908510289698857326627187500840376522679234531714193194) } }, + { { SC_(0.0), T(1) / 1024, SC_(1.00000023841859331241759166109699567801556273303717896447683) } }, + { { SC_(0.0), T(SC_(1.0)) / (1024 * 1024), SC_(1.00000000000022737367544324498417583090700894607432256476338) } }, + { { SC_(0.0), SC_(-1.0), SC_(1.26606587775200833559824462521471753760767031135496220680814) } }, + { { SC_(0.0), SC_(100.0), SC_(1.07375170713107382351972085760349466128840319332527279540154e42) } }, + { { SC_(0.0), SC_(200.0), SC_(2.03968717340972461954167312677945962233267573614834337894328e85) } }, + } }; +static const boost::array<boost::array<T, 3>, 10> i1_data = { { + { { SC_(1.0), SC_(0.0), SC_(0.0) } }, + { { SC_(1.0), SC_(1.0), SC_(0.565159103992485027207696027609863307328899621621092009480294) } }, + { { SC_(1.0), SC_(-2.0), SC_(-1.59063685463732906338225442499966624795447815949553664713229) } }, + { { SC_(1.0), SC_(4.0), SC_(9.75946515370444990947519256731268090005597033325296730692753) } }, + { { SC_(1.0), SC_(-8.0), SC_(-399.873136782560098219083086145822754889628443904067647306574) } }, + { { SC_(1.0), T(SC_(1.0)) / 1024, SC_(0.000488281308207663226432087816784315537514225208473395063575150) } }, + { { SC_(1.0), T(SC_(1.0)) / (1024 * 1024), SC_(4.76837158203179210108624277276025646653133998635956784292029E-7) } }, + { { SC_(1.0), SC_(-10.0), SC_(-2670.98830370125465434103196677215254914574515378753771310849) } }, + { { SC_(1.0), SC_(100.0), SC_(1.06836939033816248120614576322429526544612284405623226965918e42) } }, + { { SC_(1.0), SC_(200.0), SC_(2.03458154933206270342742797713906950389661161681122964159220e85) } }, + } }; +static const boost::array<boost::array<T, 3>, 11> in_data = { { + { { SC_(-2.0), SC_(0.0), SC_(0.0) } }, + { { SC_(2.0), T(SC_(1.0)) / (1024 * 1024), SC_(1.13686837721624646204093977095674566928522671779753217215467e-13) } }, + { { SC_(5.0), SC_(10.0), SC_(777.188286403259959907293484802339632852674154572666041953297) } }, + { { SC_(-5.0), SC_(100.0), SC_(9.47009387303558124618275555002161742321578485033007130107740e41) } }, + { { SC_(-5.0), SC_(-1.0), SC_(-0.000271463155956971875181073905153777342383564426758143634974124) } }, + { { SC_(10.0), SC_(20.0), SC_(3.54020020901952109905289138244985607057267103782948493874391e6) } }, + { { SC_(10.0), SC_(-5.0), SC_(0.00458004441917605126118647027872016953192323139337073320016447) } }, + { { SC_(1e+02), SC_(9.0), SC_(2.74306601746058997093587654668959071522869282506446891736820e-93) } }, + { { SC_(1e+02), SC_(80.0), SC_(4.65194832850610205318128191404145885093970505338730540776711e8) } }, + { { SC_(-100.0), SC_(-200.0), SC_(4.35275044972702191438729017441198257508190719030765213981307e74) } }, + { { SC_(10.0), SC_(1e-100), SC_(2.69114445546737213403880070546737213403880070546737213403880e-1010) } }, + } }; + +int main() +{ +#include "bessel_i_int_data.ipp" + + add_data(i0_data); + add_data(i1_data); + add_data(in_data); + add_data(bessel_i_int_data); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::cyl_bessel_i(static_cast<int>(v[0]), v[1]); }, [](const std::vector<double>& v){ return v[2]; }); + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return std::tr1::cyl_bessel_i(static_cast<int>(v[0]), v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_bessel_In(static_cast<int>(v[0]), v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return bessel_i(v[1], static_cast<int>(v[0]), 1); }, [](const std::vector<double>& v){ return v[2]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "cyl_bessel_i (integer order)[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "cyl_bessel_i (integer order)"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::cyl_bessel_i(static_cast<int>(v[0]), v[1]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::cyl_bessel_i(static_cast<int>(v[0]), v[1], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::cyl_bessel_i(static_cast<int>(v[0]), v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_bessel_In(static_cast<int>(v[0]), v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return bessel_i(v[1], static_cast<int>(v[0]), 1); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "Rmath " R_VERSION_STRING); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_iv.cpp b/src/boost/libs/math/reporting/performance/test_iv.cpp new file mode 100644 index 000000000..585c36bb7 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_iv.cpp @@ -0,0 +1,113 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/bessel.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) +static const boost::array<boost::array<T, 3>, 10> iv_data = { { + { { SC_(2.25), T(1) / (1024 * 1024), SC_(2.34379212133481347189068464680335815256364262507955635911656e-15) } }, + { { SC_(5.5), SC_(3.125), SC_(0.0583514045989371500460946536220735787163510569634133670181210) } }, + { { T(-5) + T(1) / 1024, SC_(2.125), SC_(0.0267920938009571023702933210070984416052633027166975342895062) } }, + { { SC_(-5.5), SC_(10.0), SC_(597.577606961369169607937419869926705730305175364662688426534) } }, + { { SC_(-5.5), SC_(100.0), SC_(9.22362906144706871737354069133813819358704200689067071415379e41) } }, + { { T(-10486074) / (1024 * 1024), T(1) / 1024, SC_(1.41474005665181350367684623930576333542989766867888186478185e35) } }, + { { T(-10486074) / (1024 * 1024), SC_(50.0), SC_(1.07153277202900671531087024688681954238311679648319534644743e20) } }, + { { T(144794) / 1024, SC_(100.0), SC_(2066.27694757392660413922181531984160871678224178890247540320) } }, + { { T(144794) / 1024, SC_(200.0), SC_(2.23699739472246928794922868978337381373643889659337595319774e64) } }, + { { T(-144794) / 1024, SC_(100.0), SC_(2066.27694672763190927440969155740243346136463461655104698748) } }, + } }; +static const boost::array<boost::array<T, 3>, 5> iv_large_data = { { + // Bug report https://svn.boost.org/trac/boost/ticket/5560: + { { SC_(-1.0), static_cast<T>(ldexp(0.5, -512)), SC_(1.86458518280005168582274132886573345934411788365010172356788e-155) } }, + { { SC_(1.0), static_cast<T>(ldexp(0.5, -512)), SC_(1.86458518280005168582274132886573345934411788365010172356788e-155) } }, + { { SC_(-1.125), static_cast<T>(ldexp(0.5, -512)), SC_(-1.34963720853101363690381585556234820027343435206156667634081e173) } }, + { { SC_(1.125), static_cast<T>(ldexp(0.5, -512)), SC_(8.02269390325932403421158766283366891170783955777638875887348e-175) } }, + { { SC_(0.5), static_cast<T>(ldexp(0.5, -683)), SC_(8.90597649117647254543282704099383321071493400182381039079219e-104) } }, + } }; + +int main() +{ +#include "bessel_i_data.ipp" + + add_data(iv_data); + add_data(iv_large_data); + add_data(bessel_i_data); + + unsigned data_total = data.size(); + + std::cout << "Screening boost data:\n"; + screen_data([](const std::vector<double>& v){ return boost::math::cyl_bessel_i(v[0], v[1]); }, [](const std::vector<double>& v){ return v[2]; }); + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + std::cout << "Screening libstdc++ data:\n"; + screen_data([](const std::vector<double>& v){ return std::tr1::cyl_bessel_i(v[0], v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + std::cout << "Screening GSL data:\n"; + screen_data([](const std::vector<double>& v){ return gsl_sf_bessel_Inu(v[0], v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + std::cout << "Screening GSL data:\n"; + screen_data([](const std::vector<double>& v){ return bessel_i(v[1], v[0], 1); }, [](const std::vector<double>& v){ return v[2]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "cyl_bessel_i[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "cyl_bessel_i"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::cyl_bessel_i(v[0], v[1]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::cyl_bessel_i(v[0], v[1], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::cyl_bessel_i(v[0], v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_bessel_Inu(v[0], v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return bessel_i(v[1], v[0], 1); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "Rmath " R_VERSION_STRING); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_jn.cpp b/src/boost/libs/math/reporting/performance/test_jn.cpp new file mode 100644 index 000000000..48dee7a1f --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_jn.cpp @@ -0,0 +1,168 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/bessel.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) +static const boost::array<boost::array<typename table_type<T>::type, 3>, 8> j0_data = { { + { { SC_(0.0), SC_(0.0), SC_(1.0) } }, + { { SC_(0.0), SC_(1.0), SC_(0.7651976865579665514497175261026632209093) } }, + { { SC_(0.0), SC_(-2.0), SC_(0.2238907791412356680518274546499486258252) } }, + { { SC_(0.0), SC_(4.0), SC_(-0.3971498098638473722865907684516980419756) } }, + { { SC_(0.0), SC_(-8.0), SC_(0.1716508071375539060908694078519720010684) } }, + { { SC_(0.0), SC_(1e-05), SC_(0.999999999975000000000156249999999565972) } }, + { { SC_(0.0), SC_(1e-10), SC_(0.999999999999999999997500000000000000000) } }, + { { SC_(0.0), SC_(-1e+01), SC_(-0.2459357644513483351977608624853287538296) } }, + } }; +static const boost::array<boost::array<T, 3>, 6> j0_tricky = { { + // Big numbers make the accuracy of std::sin the limiting factor: + { { SC_(0.0), SC_(1e+03), SC_(0.02478668615242017456133073111569370878617) } }, + { { SC_(0.0), SC_(1e+05), SC_(-0.001719201116235972192570601477073201747532) } }, + // test at the roots: + { { SC_(0.0), T(2521642.0) / (1024 * 1024), SC_(1.80208819970046790002973759410972422387259992955354630042138e-7) } }, + { { SC_(0.0), T(5788221.0) / (1024 * 1024), SC_(-1.37774249380686777043369399806210229535671843632174587432454e-7) } }, + { { SC_(0.0), T(9074091.0) / (1024 * 1024), SC_(1.03553057441100845081018471279571355857520645127532785991335e-7) } }, + { { SC_(0.0), T(12364320.0) / (1024 * 1024), SC_(-3.53017140778223781420794006033810387155048392363051866610931e-9) } } + } }; + +static const boost::array<boost::array<typename table_type<T>::type, 3>, 8> j1_data = { { + { { SC_(1.0), SC_(0.0), SC_(0.0) } }, + { { SC_(1.0), SC_(1.0), SC_(0.4400505857449335159596822037189149131274) } }, + { { SC_(1.0), SC_(-2.0), SC_(-0.5767248077568733872024482422691370869203) } }, + { { SC_(1.0), SC_(4.0), SC_(-6.604332802354913614318542080327502872742e-02) } }, + { { SC_(1.0), SC_(-8.0), SC_(-0.2346363468539146243812766515904546115488) } }, + { { SC_(1.0), SC_(1e-05), SC_(4.999999999937500000000260416666666124132e-06) } }, + { { SC_(1.0), SC_(1e-10), SC_(4.999999999999999999993750000000000000000e-11) } }, + { { SC_(1.0), SC_(-1e+01), SC_(-4.347274616886143666974876802585928830627e-02) } }, + } }; +static const boost::array<boost::array<T, 3>, 5> j1_tricky = { { + // Big numbers make the accuracy of std::sin the limiting factor: + { { SC_(1.0), SC_(1e+03), SC_(4.728311907089523917576071901216916285418e-03) } }, + { { SC_(1.0), SC_(1e+05), SC_(1.846757562882567716362123967114215743694e-03) } }, + // test zeros: + { { SC_(1.0), T(4017834) / (1024 * 1024), SC_(3.53149033321258645807835062770856949751958513973522222203044e-7) } }, + { { SC_(1.0), T(7356375) / (1024 * 1024), SC_(-2.31227973111067286051984021150135526024117175836722748404342e-7) } }, + { { SC_(1.0), T(10667654) / (1024 * 1024), SC_(1.24591331097191900488116495350277530373473085499043086981229e-7) } }, + } }; + +static const boost::array<boost::array<typename table_type<T>::type, 3>, 17> jn_data = { { + // This first one is a modified test case from https://svn.boost.org/trac/boost/ticket/2733 + { { SC_(-1.0), SC_(1.25), SC_(-0.510623260319880467069474837274910375352924050139633057168856) } }, + { { SC_(2.0), SC_(0.0), SC_(0.0) } }, + { { SC_(-2.0), SC_(0.0), SC_(0.0) } }, + { { SC_(2.0), SC_(1e-02), SC_(1.249989583365885362413250958437642113452e-05) } }, + { { SC_(5.0), SC_(10.0), SC_(-0.2340615281867936404436949416457777864635) } }, + { { SC_(5.0), SC_(-10.0), SC_(0.2340615281867936404436949416457777864635) } }, + { { SC_(-5.0), SC_(1e+06), SC_(7.259643842453285052375779970433848914846e-04) } }, + { { SC_(5.0), SC_(1e+06), SC_(-0.000725964384245328505237577997043384891484649290328285235308619) } }, + { { SC_(-5.0), SC_(-1.0), SC_(2.497577302112344313750655409880451981584e-04) } }, + { { SC_(10.0), SC_(10.0), SC_(0.2074861066333588576972787235187534280327) } }, + { { SC_(10.0), SC_(-10.0), SC_(0.2074861066333588576972787235187534280327) } }, + { { SC_(10.0), SC_(-5.0), SC_(1.467802647310474131107532232606627020895e-03) } }, + { { SC_(-10.0), SC_(1e+06), SC_(-3.310793117604488741264958559035744460210e-04) } }, + { { SC_(10.0), SC_(1e+06), SC_(-0.000331079311760448874126495855903574446020957243277028930713243) } }, + { { SC_(1e+02), SC_(8e+01), SC_(4.606553064823477354141298259169874909670e-06) } }, + { { SC_(1e+03), SC_(1e+05), SC_(1.283178112502480365195139312635384057363e-03) } }, + { { SC_(10.0), SC_(1e-100), SC_(2.69114445546737213403880070546737213403880070546737213403880e-1010) } }, + } }; + + +int main() +{ +#include "bessel_j_int_data.ipp" + + add_data(j0_data); + add_data(j0_tricky); + add_data(j1_data); + add_data(j1_tricky); + add_data(jn_data); + add_data(bessel_j_int_data); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::cyl_bessel_j(static_cast<int>(v[0]), v[1]); }, [](const std::vector<double>& v){ return v[2]; }); + + +#if defined(TEST_C99) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return ::jn(static_cast<int>(v[0]), v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return std::tr1::cyl_bessel_j(static_cast<int>(v[0]), v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_bessel_Jn(static_cast<int>(v[0]), v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return bessel_j(v[1], static_cast<int>(v[0])); }, [](const std::vector<double>& v){ return v[2]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "cyl_bessel_j (integer order)[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "cyl_bessel_j (integer order)"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::cyl_bessel_j(static_cast<int>(v[0]), v[1]); }); + std::cout << time << std::endl; +#if defined(COMPILER_COMPARISON_TABLES) + report_execution_time(time, std::string("Compiler Option Comparison on ") + platform_name(), "boost::math::cyl_bessel_j (integer orders)", get_compiler_options_name()); +#else +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_C99) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); +#endif + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::cyl_bessel_j(static_cast<int>(v[0]), v[1], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_C99) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_C99) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return ::jn(static_cast<int>(v[0]), v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "math.h"); +#endif +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::cyl_bessel_j(static_cast<int>(v[0]), v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_bessel_Jn(static_cast<int>(v[0]), v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return bessel_j(v[1], static_cast<int>(v[0])); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "Rmath " R_VERSION_STRING); +#endif + + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_js.cpp b/src/boost/libs/math/reporting/performance/test_js.cpp new file mode 100644 index 000000000..72438b24f --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_js.cpp @@ -0,0 +1,80 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/bessel.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + +int main() +{ +#include "sph_bessel_data.ipp" + + add_data(sph_bessel_data); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::sph_bessel(static_cast<int>(v[0]), v[1]); }, [](const std::vector<double>& v){ return v[2]; }); + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return std::tr1::sph_bessel(static_cast<int>(v[0]), v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_bessel_jl(static_cast<int>(v[0]), v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "sph_bessel[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "sph_bessel"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::sph_bessel(static_cast<int>(v[0]), v[1]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::sph_bessel(static_cast<int>(v[0]), v[1], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::sph_bessel(static_cast<int>(v[0]), v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_bessel_jl(static_cast<int>(v[0]), v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif + + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_jv.cpp b/src/boost/libs/math/reporting/performance/test_jv.cpp new file mode 100644 index 000000000..ed6d7abc6 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_jv.cpp @@ -0,0 +1,119 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/bessel.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) +static const boost::array<boost::array<T, 3>, 21> jv_data = { { + //SC_(-2.4), {{ SC_(0.0), std::numeric_limits<T>::infinity() }}, + { { T(22.5), T(0.0), SC_(0.0) } }, + { { T(2457.0) / 1024, T(1.0) / 1024, SC_(3.80739920118603335646474073457326714709615200130620574875292e-9) } }, + { { SC_(5.5), T(3217) / 1024, SC_(0.0281933076257506091621579544064767140470089107926550720453038) } }, + { { SC_(-5.5), T(3217) / 1024, SC_(-2.55820064470647911823175836997490971806135336759164272675969) } }, + { { SC_(-5.5), SC_(1e+04), SC_(2.449843111985605522111159013846599118397e-03) } }, + { { SC_(5.5), SC_(1e+04), SC_(0.00759343502722670361395585198154817047185480147294665270646578) } }, + { { SC_(5.5), SC_(1e+06), SC_(-0.000747424248595630177396350688505919533097973148718960064663632) } }, + { { SC_(5.125), SC_(1e+06), SC_(-0.000776600124835704280633640911329691642748783663198207360238214) } }, + { { SC_(5.875), SC_(1e+06), SC_(-0.000466322721115193071631008581529503095819705088484386434589780) } }, + { { SC_(0.5), SC_(101.0), SC_(0.0358874487875643822020496677692429287863419555699447066226409) } }, + { { SC_(-5.5), SC_(1e+04), SC_(0.00244984311198560552211115901384659911839737686676766460822577) } }, + { { SC_(-5.5), SC_(1e+06), SC_(0.000279243200433579511095229508894156656558211060453622750659554) } }, + { { SC_(-0.5), SC_(101.0), SC_(0.0708184798097594268482290389188138201440114881159344944791454) } }, + { { T(-10486074) / (1024 * 1024), T(1) / 1024, SC_(1.41474013160494695750009004222225969090304185981836460288562e35) } }, + { { T(-10486074) / (1024 * 1024), SC_(15.0), SC_(-0.0902239288885423309568944543848111461724911781719692852541489) } }, + { { T(10486074) / (1024 * 1024), SC_(1e+02), SC_(-0.0547064914615137807616774867984047583596945624129838091326863) } }, + { { T(10486074) / (1024 * 1024), SC_(2e+04), SC_(-0.00556783614400875611650958980796060611309029233226596737701688) } }, + { { T(-10486074) / (1024 * 1024), SC_(1e+02), SC_(-0.0547613660316806551338637153942604550779513947674222863858713) } }, + // Bug report https://svn.boost.org/trac/boost/ticket/4812: + { { SC_(1.5), T(8034) / 1024, SC_(0.0339477646369710610146236955872928005087352629422508823945264) } }, + { { SC_(8.5), boost::math::constants::pi<T>() * 4, SC_(0.0436807946352780974532519564114026730332781693877984686758680) } }, + { { SC_(-8.5), boost::math::constants::pi<T>() * 4, SC_(-0.257086543428224355151772807588810984369026142375675714560864) } }, + } }; + +int main() +{ +#include "bessel_j_data.ipp" +#include "bessel_j_large_data.ipp" + + add_data(jv_data); + add_data(bessel_j_data); + add_data(bessel_j_large_data); + + unsigned data_total = data.size(); + + std::cout << "Screening boost data:\n"; + screen_data([](const std::vector<double>& v){ return boost::math::cyl_bessel_j(v[0], v[1]); }, [](const std::vector<double>& v){ return v[2]; }); + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + std::cout << "Screening libstdc++ data:\n"; + screen_data([](const std::vector<double>& v){ return std::tr1::cyl_bessel_j(v[0], v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + std::cout << "Screening libstdc++ data:\n"; + screen_data([](const std::vector<double>& v){ return gsl_sf_bessel_Jnu(v[0], v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + std::cout << "Screening libstdc++ data:\n"; + screen_data([](const std::vector<double>& v){ return bessel_j(v[1], v[0]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "cyl_bessel_j[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "cyl_bessel_j"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::cyl_bessel_j(v[0], v[1]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::cyl_bessel_j(v[0], v[1], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::cyl_bessel_j(v[0], v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_bessel_Jnu(v[0], v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return bessel_j(v[1], v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "Rmath " R_VERSION_STRING); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_kn.cpp b/src/boost/libs/math/reporting/performance/test_kn.cpp new file mode 100644 index 000000000..e5553cf56 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_kn.cpp @@ -0,0 +1,123 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/bessel.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) +static const boost::array<boost::array<T, 3>, 9> k0_data = { { + { { SC_(0.0), SC_(1.0), SC_(0.421024438240708333335627379212609036136219748226660472298970) } }, + { { SC_(0.0), SC_(2.0), SC_(0.113893872749533435652719574932481832998326624388808882892530) } }, + { { SC_(0.0), SC_(4.0), SC_(0.0111596760858530242697451959798334892250090238884743405382553) } }, + { { SC_(0.0), SC_(8.0), SC_(0.000146470705222815387096584408698677921967305368833759024089154) } }, + { { SC_(0.0), T(std::ldexp(1.0, -15)), SC_(10.5131392267382037062459525561594822400447325776672021972753) } }, + { { SC_(0.0), T(std::ldexp(1.0, -30)), SC_(20.9103469324567717360787328239372191382743831365906131108531) } }, + { { SC_(0.0), T(std::ldexp(1.0, -60)), SC_(41.7047623492551310138446473188663682295952219631968830346918) } }, + { { SC_(0.0), SC_(50.0), SC_(3.41016774978949551392067551235295223184502537762334808993276e-23) } }, + { { SC_(0.0), SC_(100.0), SC_(4.65662822917590201893900528948388635580753948544211387402671e-45) } }, + } }; +static const boost::array<boost::array<T, 3>, 9> k1_data = { { + { { SC_(1.0), SC_(1.0), SC_(0.601907230197234574737540001535617339261586889968106456017768) } }, + { { SC_(1.0), SC_(2.0), SC_(0.139865881816522427284598807035411023887234584841515530384442) } }, + { { SC_(1.0), SC_(4.0), SC_(0.0124834988872684314703841799808060684838415849886258457917076) } }, + { { SC_(1.0), SC_(8.0), SC_(0.000155369211805001133916862450622474621117065122872616157079566) } }, + { { SC_(1.0), T(std::ldexp(1.0, -15)), SC_(32767.9998319528316432647441316539139725104728341577594326513) } }, + { { SC_(1.0), T(std::ldexp(1.0, -30)), SC_(1.07374182399999999003003028572687332810353799544215073362305e9) } }, + { { SC_(1.0), T(std::ldexp(1.0, -60)), SC_(1.15292150460684697599999999999999998169660198868126604634036e18) } }, + { { SC_(1.0), SC_(50.0), SC_(3.44410222671755561259185303591267155099677251348256880221927e-23) } }, + { { SC_(1.0), SC_(100.0), SC_(4.67985373563690928656254424202433530797494354694335352937465e-45) } }, + } }; +static const boost::array<boost::array<T, 3>, 9> kn_data = { { + { { SC_(2.0), T(std::ldexp(1.0, -30)), SC_(2.30584300921369395150000000000000000234841952009593636868109e18) } }, + { { SC_(5.0), SC_(10.0), SC_(0.0000575418499853122792763740236992723196597629124356739596921536) } }, + { { SC_(-5.0), SC_(100.0), SC_(5.27325611329294989461777188449044716451716555009882448801072e-45) } }, + { { SC_(10.0), SC_(10.0), SC_(0.00161425530039067002345725193091329085443750382929208307802221) } }, + { { SC_(10.0), T(std::ldexp(1.0, -30)), SC_(3.78470202927236255215249281534478864916684072926050665209083e98) } }, + { { SC_(-10.0), SC_(1.0), SC_(1.80713289901029454691597861302340015908245782948536080022119e8) } }, + { { SC_(100.0), SC_(5.0), SC_(7.03986019306167654653386616796116726248616158936088056952477e115) } }, + { { SC_(100.0), SC_(80.0), SC_(8.39287107246490782848985384895907681748152272748337807033319e-12) } }, + { { SC_(-1000.0), SC_(700.0), SC_(6.51561979144735818903553852606383312984409361984128221539405e-31) } }, + } }; + +int main() +{ +#include "bessel_k_int_data.ipp" + + add_data(k0_data); + add_data(k1_data); + add_data(kn_data); + add_data(bessel_k_int_data); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::cyl_bessel_k(static_cast<int>(v[0]), v[1]); }, [](const std::vector<double>& v){ return v[2]; }); + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return std::tr1::cyl_bessel_k(static_cast<int>(v[0]), v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_bessel_Kn(static_cast<int>(v[0]), v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return bessel_k(v[1], static_cast<int>(v[0]), 1); }, [](const std::vector<double>& v){ return v[2]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "cyl_bessel_k (integer order)[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "cyl_bessel_k (integer order)"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::cyl_bessel_k(static_cast<int>(v[0]), v[1]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::cyl_bessel_k(static_cast<int>(v[0]), v[1], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::cyl_bessel_k(static_cast<int>(v[0]), v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_bessel_Kn(static_cast<int>(v[0]), v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return bessel_k(v[1], static_cast<int>(v[0]), 1); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "Rmath " R_VERSION_STRING); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_kv.cpp b/src/boost/libs/math/reporting/performance/test_kv.cpp new file mode 100644 index 000000000..8bf691276 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_kv.cpp @@ -0,0 +1,114 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/bessel.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) +static const boost::array<boost::array<T, 3>, 11> kv_data = { { + { { SC_(0.5), SC_(0.875), SC_(0.558532231646608646115729767013630967055657943463362504577189) } }, + { { SC_(0.5), SC_(1.125), SC_(0.383621010650189547146769320487006220295290256657827220786527) } }, + { { SC_(2.25), T(std::ldexp(1.0, -30)), SC_(5.62397392719283271332307799146649700147907612095185712015604e20) } }, + { { SC_(5.5), T(3217) / 1024, SC_(1.30623288775012596319554857587765179889689223531159532808379) } }, + { { SC_(-5.5), SC_(10.0), SC_(0.0000733045300798502164644836879577484533096239574909573072142667) } }, + { { SC_(-5.5), SC_(100.0), SC_(5.41274555306792267322084448693957747924412508020839543293369e-45) } }, + { { T(10240) / 1024, T(1) / 1024, SC_(2.35522579263922076203415803966825431039900000000993410734978e38) } }, + { { T(10240) / 1024, SC_(10.0), SC_(0.00161425530039067002345725193091329085443750382929208307802221) } }, + { { T(144793) / 1024, SC_(100.0), SC_(1.39565245860302528069481472855619216759142225046370312329416e-6) } }, + { { T(144793) / 1024, SC_(200.0), SC_(9.11950412043225432171915100042647230802198254567007382956336e-68) } }, + { { T(-144793) / 1024, SC_(50.0), SC_(1.30185229717525025165362673848737761549946548375142378172956e42) } }, + } }; +static const boost::array<boost::array<T, 3>, 5> kv_large_data = { { + // Bug report https://svn.boost.org/trac/boost/ticket/5560: + { { SC_(-1.0), static_cast<T>(ldexp(0.5, -512)), SC_(2.68156158598851941991480499964116922549587316411847867554471e154) } }, + { { SC_(1.0), static_cast<T>(ldexp(0.5, -512)), SC_(2.68156158598851941991480499964116922549587316411847867554471e154) } }, + { { SC_(-1.125), static_cast<T>(ldexp(0.5, -512)), SC_(5.53984048006472105611199242328122729730752165907526178753978e173) } }, + { { SC_(1.125), static_cast<T>(ldexp(0.5, -512)), SC_(5.53984048006472105611199242328122729730752165907526178753978e173) } }, + { { SC_(0.5), static_cast<T>(ldexp(0.5, -683)), SC_(1.12284149973980088540335945247019177715948513804063794284101e103) } }, + } }; + +int main() +{ +#include "bessel_k_data.ipp" + + add_data(kv_data); + add_data(kv_large_data); + add_data(bessel_k_data); + + unsigned data_total = data.size(); + + std::cout << "Screening boost data:\n"; + screen_data([](const std::vector<double>& v){ return boost::math::cyl_bessel_k(v[0], v[1]); }, [](const std::vector<double>& v){ return v[2]; }); + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + std::cout << "Screening libstdc++ data:\n"; + screen_data([](const std::vector<double>& v){ return std::tr1::cyl_bessel_k(v[0], v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + std::cout << "Screening libstdc++ data:\n"; + screen_data([](const std::vector<double>& v){ return gsl_sf_bessel_Knu(v[0], v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + std::cout << "Screening libstdc++ data:\n"; + screen_data([](const std::vector<double>& v){ return bessel_k(v[1], v[0], 1); }, [](const std::vector<double>& v){ return v[2]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "cyl_bessel_k[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "cyl_bessel_k"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::cyl_bessel_k(v[0], v[1]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::cyl_bessel_k(v[0], v[1], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::cyl_bessel_k(v[0], v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_bessel_Knu(v[0], v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return bessel_k(v[1], v[0], 1); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "Rmath " R_VERSION_STRING); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_laguerre.cpp b/src/boost/libs/math/reporting/performance/test_laguerre.cpp new file mode 100644 index 000000000..1174e64a4 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_laguerre.cpp @@ -0,0 +1,81 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/laguerre.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + +int main() +{ +# include "laguerre2.ipp" + + add_data(laguerre2); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::laguerre(v[0], v[1]); }, [](const std::vector<double>& v){ return v[2]; }); + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return std::tr1::laguerre(v[0], v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_laguerre_n(v[0], 0, v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "laguerre[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "laguerre"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::laguerre(v[0], v[1]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::laguerre(v[0], v[1], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::laguerre(v[0], v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_laguerre_n(v[0], 0, v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif + + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_legendre.cpp b/src/boost/libs/math/reporting/performance/test_legendre.cpp new file mode 100644 index 000000000..27c5e4a0a --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_legendre.cpp @@ -0,0 +1,82 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/legendre.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + +int main() +{ +# include "legendre_p.ipp" +# include "legendre_p_large.ipp" + + add_data(legendre_p); + add_data(legendre_p_large); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::legendre_p(v[0], v[1]); }, [](const std::vector<double>& v){ return v[2]; }); + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return std::tr1::legendre(v[0], v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_legendre_Pl(v[0], v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "legendre[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "legendre"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::legendre_p(v[0], v[1]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::legendre_p(v[0], v[1], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::legendre(v[0], v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_legendre_Pl(v[0], v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_legendre_q.cpp b/src/boost/libs/math/reporting/performance/test_legendre_q.cpp new file mode 100644 index 000000000..639ead4d8 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_legendre_q.cpp @@ -0,0 +1,74 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/legendre.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + +int main() +{ +# include "legendre_p.ipp" +# include "legendre_p_large.ipp" + + add_data(legendre_p); + add_data(legendre_p_large); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::legendre_q(v[0], v[1]); }, [](const std::vector<double>& v){ return v[3]; }); + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_legendre_Ql(v[0], v[1]); }, [](const std::vector<double>& v){ return v[3]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "legendre Q[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "legendre Q"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::legendre_q(v[0], v[1]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::legendre_q(v[0], v[1], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_legendre_Ql(v[0], v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_lgamma.cpp b/src/boost/libs/math/reporting/performance/test_lgamma.cpp new file mode 100644 index 000000000..1b0c7767e --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_lgamma.cpp @@ -0,0 +1,98 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/gamma.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +int main() +{ + typedef double T; +#define SC_(x) static_cast<double>(x) +# include "test_gamma_data.ipp" + + add_data(factorials); + add_data(near_0); + add_data(near_1); + add_data(near_2); + add_data(near_m10); + add_data(near_m55); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::lgamma(v[0]); }, [](const std::vector<double>& v){ return v[2]; }); + + +#if defined(TEST_C99) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return ::lgamma(v[0]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return std::tr1::lgamma(v[0]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_lngamma(v[0]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return lgammafn(v[0]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "lgamma[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "lgamma"; + + double time = exec_timed_test([](const std::vector<double>& v){ return boost::math::lgamma(v[0]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_C99) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + double time = exec_timed_test([](const std::vector<double>& v){ return boost::math::lgamma(v[0], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_C99) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_C99) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return ::lgamma(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "math.h"); +#endif +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::lgamma(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_lngamma(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return lgammafn(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "Rmath " R_VERSION_STRING); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_log1p.cpp b/src/boost/libs/math/reporting/performance/test_log1p.cpp new file mode 100644 index 000000000..bdc11f55e --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_log1p.cpp @@ -0,0 +1,77 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/log1p.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +int main() +{ + typedef double T; +#define SC_(x) static_cast<double>(x) +# include "../../test/log1p_expm1_data.ipp" + + add_data(log1p_expm1_data); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::log1p(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); + +#if defined(TEST_C99) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return ::log1p(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); +#endif +#ifdef TEST_LIBSTDCXX && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return std::tr1::log1p(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "log1p[br](" + boost::lexical_cast<std::string>(data_used)+"/" + boost::lexical_cast<std::string>(data_total)+" tests selected)"; + std::string function_short = "log1p"; + + double time = exec_timed_test([](const std::vector<double>& v){ return boost::math::log1p(v[0]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_C99) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + double time = exec_timed_test([](const std::vector<double>& v){ return boost::math::log1p(v[0], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_C99) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_C99) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return ::log1p(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "math.h"); +#endif +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::log1p(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif + + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_poly_method.cpp b/src/boost/libs/math/reporting/performance/test_poly_method.cpp new file mode 100644 index 000000000..752447000 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_poly_method.cpp @@ -0,0 +1,371 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +#define evaluate_polynomial_c_imp evaluate_polynomial_c_imp_1 +#undef BOOST_MATH_TOOLS_POLY_EVAL_20_HPP +#include <boost/math/tools/detail/polynomial_horner1_20.hpp> +#undef evaluate_polynomial_c_imp +#undef BOOST_MATH_TOOLS_POLY_EVAL_20_HPP +#define evaluate_polynomial_c_imp evaluate_polynomial_c_imp_2 +#include <boost/math/tools/detail/polynomial_horner2_20.hpp> +#undef evaluate_polynomial_c_imp +#undef BOOST_MATH_TOOLS_POLY_EVAL_20_HPP +#define evaluate_polynomial_c_imp evaluate_polynomial_c_imp_3 +#include <boost/math/tools/detail/polynomial_horner3_20.hpp> +#undef evaluate_polynomial_c_imp + +#undef BOOST_MATH_TOOLS_POLY_RAT_20_HPP +#define evaluate_rational_c_imp evaluate_rational_c_imp_1 +#include <boost/math/tools/detail/rational_horner1_20.hpp> +#undef evaluate_rational_c_imp +#undef BOOST_MATH_TOOLS_POLY_RAT_20_HPP +#define evaluate_rational_c_imp evaluate_rational_c_imp_2 +#include <boost/math/tools/detail/rational_horner2_20.hpp> +#undef evaluate_rational_c_imp +#undef BOOST_MATH_TOOLS_RAT_EVAL_20_HPP +#define evaluate_rational_c_imp evaluate_rational_c_imp_3 +#include <boost/math/tools/detail/rational_horner3_20.hpp> +#undef evaluate_rational_c_imp +#undef BOOST_MATH_TOOLS_POLY_RAT_20_HPP + +static const double num[21] = { + static_cast<double>(56906521.91347156388090791033559122686859L), + static_cast<double>(103794043.1163445451906271053616070238554L), + static_cast<double>(86363131.28813859145546927288977868422342L), + static_cast<double>(43338889.32467613834773723740590533316085L), + static_cast<double>(14605578.08768506808414169982791359218571L), + static_cast<double>(3481712.15498064590882071018964774556468L), + static_cast<double>(601859.6171681098786670226533699352302507L), + static_cast<double>(75999.29304014542649875303443598909137092L), + static_cast<double>(6955.999602515376140356310115515198987526L), + static_cast<double>(449.9445569063168119446858607650988409623L), + static_cast<double>(19.51992788247617482847860966235652136208L), + static_cast<double>(0.5098416655656676188125178644804694509993L), + static_cast<double>(0.006061842346248906525783753964555936883222L), + 0.0 +}; +static const double denom[20] = { + static_cast<double>(0u), + static_cast<double>(39916800u), + static_cast<double>(120543840u), + static_cast<double>(150917976u), + static_cast<double>(105258076u), + static_cast<double>(45995730u), + static_cast<double>(13339535u), + static_cast<double>(2637558u), + static_cast<double>(357423u), + static_cast<double>(32670u), + static_cast<double>(1925u), + static_cast<double>(66u), + static_cast<double>(1u), + 0.0 +}; +static const boost::uint32_t denom_int[20] = { + static_cast<boost::uint32_t>(0u), + static_cast<boost::uint32_t>(39916800u), + static_cast<boost::uint32_t>(120543840u), + static_cast<boost::uint32_t>(150917976u), + static_cast<boost::uint32_t>(105258076u), + static_cast<boost::uint32_t>(45995730u), + static_cast<boost::uint32_t>(13339535u), + static_cast<boost::uint32_t>(2637558u), + static_cast<boost::uint32_t>(357423u), + static_cast<boost::uint32_t>(32670u), + static_cast<boost::uint32_t>(1925u), + static_cast<boost::uint32_t>(66u), + static_cast<boost::uint32_t>(1u), + 0 +}; + +std::string make_order_string(int n) +{ + std::string result = boost::lexical_cast<std::string>(n); + if (result.size() < 2) + result.insert(result.begin(), ' '); + return result; +} + +void test_poly_1(const boost::integral_constant<int, 1>&) +{ +} + +template <int N> +void test_poly_1(const boost::integral_constant<int, N>&) +{ + test_poly_1(boost::integral_constant<int, N - 1>()); + + double time = exec_timed_test([](const std::vector<double>& v) + { + double result = 0; + for (unsigned i = 0; i < 10; ++i) + result += boost::math::tools::detail::evaluate_polynomial_c_imp_1(denom, v[0] + i, static_cast<boost::integral_constant<int, N>*>(0)); + return result; + }); + report_execution_time(time, std::string("Polynomial Method Comparison with ") + compiler_name() + std::string(" on ") + platform_name(), "Order " + make_order_string(N), "Method 1[br](Double Coefficients)"); + + time = exec_timed_test([](const std::vector<double>& v) + { + double result = 0; + for (unsigned i = 0; i < 10; ++i) + result += boost::math::tools::detail::evaluate_polynomial_c_imp_1(denom_int, v[0] + i, static_cast<boost::integral_constant<int, N>*>(0)); + return result; + }); + report_execution_time(time, std::string("Polynomial Method Comparison with ") + compiler_name() + std::string(" on ") + platform_name(), "Order " + make_order_string(N), "Method 1[br](Integer Coefficients)"); +} + + +void test_poly_2(const boost::integral_constant<int, 1>&) +{ +} + +template <int N> +void test_poly_2(const boost::integral_constant<int, N>&) +{ + test_poly_2(boost::integral_constant<int, N - 1>()); + + double time = exec_timed_test([](const std::vector<double>& v) + { + double result = 0; + for (unsigned i = 0; i < 10; ++i) + result += boost::math::tools::detail::evaluate_polynomial_c_imp_2(denom, v[0] + i, static_cast<boost::integral_constant<int, N>*>(0)); + return result; + }); + report_execution_time(time, std::string("Polynomial Method Comparison with ") + compiler_name() + std::string(" on ") + platform_name(), "Order " + make_order_string(N), "Method 2[br](Double Coefficients)"); + + time = exec_timed_test([](const std::vector<double>& v) + { + double result = 0; + for (unsigned i = 0; i < 10; ++i) + result += boost::math::tools::detail::evaluate_polynomial_c_imp_2(denom_int, v[0] + i, static_cast<boost::integral_constant<int, N>*>(0)); + return result; + }); + report_execution_time(time, std::string("Polynomial Method Comparison with ") + compiler_name() + std::string(" on ") + platform_name(), "Order " + make_order_string(N), "Method 2[br](Integer Coefficients)"); +} + +void test_poly_3(const boost::integral_constant<int, 1>&) +{ +} + +template <int N> +void test_poly_3(const boost::integral_constant<int, N>&) +{ + test_poly_3(boost::integral_constant<int, N - 1>()); + + double time = exec_timed_test([](const std::vector<double>& v) { double result = 0; + for (unsigned i = 0; i < 10; ++i) + result += boost::math::tools::detail::evaluate_polynomial_c_imp_3(denom, v[0] + i, static_cast<boost::integral_constant<int, N>*>(0)); + return result; + }); + report_execution_time(time, std::string("Polynomial Method Comparison with ") + compiler_name() + std::string(" on ") + platform_name(), "Order " + make_order_string(N), "Method 3[br](Double Coefficients)"); + + time = exec_timed_test([](const std::vector<double>& v) { double result = 0; + for (unsigned i = 0; i < 10; ++i) + result += boost::math::tools::detail::evaluate_polynomial_c_imp_3(denom_int, v[0] + i, static_cast<boost::integral_constant<int, N>*>(0)); + return result; + }); + report_execution_time(time, std::string("Polynomial Method Comparison with ") + compiler_name() + std::string(" on ") + platform_name(), "Order " + make_order_string(N), "Method 3[br](Integer Coefficients)"); +} + +template <class T, class U> +U evaluate_polynomial_0(const T* poly, U const& z, std::size_t count) +{ + U sum = static_cast<U>(poly[count - 1]); + for (int i = static_cast<int>(count) - 2; i >= 0; --i) + { + sum *= z; + sum += static_cast<U>(poly[i]); + } + return sum; +} + +void test_rat_1(const boost::integral_constant<int, 1>&) +{ +} + +template <int N> +void test_rat_1(const boost::integral_constant<int, N>&) +{ + test_rat_1(boost::integral_constant<int, N - 1>()); + + double time = exec_timed_test([](const std::vector<double>& v) + { + double result = 0; + for (unsigned i = 0; i < 10; ++i) + result += boost::math::tools::detail::evaluate_rational_c_imp_1(num, denom, v[0] + i, static_cast<boost::integral_constant<int, N>*>(0)); + return result; + }); + report_execution_time(time, std::string("Rational Method Comparison with ") + compiler_name() + std::string(" on ") + platform_name(), "Order " + make_order_string(N), "Method 1[br](Double Coefficients)"); + + time = exec_timed_test([](const std::vector<double>& v) + { + double result = 0; + for (unsigned i = 0; i < 10; ++i) + result += boost::math::tools::detail::evaluate_rational_c_imp_1(num, denom_int, v[0] + i, static_cast<boost::integral_constant<int, N>*>(0)); + return result; + }); + report_execution_time(time, std::string("Rational Method Comparison with ") + compiler_name() + std::string(" on ") + platform_name(), "Order " + make_order_string(N), "Method 1[br](Integer Coefficients)"); +} + +void test_rat_2(const boost::integral_constant<int, 1>&) +{ +} + +template <int N> +void test_rat_2(const boost::integral_constant<int, N>&) +{ + test_rat_2(boost::integral_constant<int, N - 1>()); + + double time = exec_timed_test([](const std::vector<double>& v) + { + double result = 0; + for (unsigned i = 0; i < 10; ++i) + result += boost::math::tools::detail::evaluate_rational_c_imp_2(num, denom, v[0] + i, static_cast<boost::integral_constant<int, N>*>(0)); + return result; + }); + report_execution_time(time, std::string("Rational Method Comparison with ") + compiler_name() + std::string(" on ") + platform_name(), "Order " + make_order_string(N), "Method 2[br](Double Coefficients)"); + + time = exec_timed_test([](const std::vector<double>& v) + { + double result = 0; + for (unsigned i = 0; i < 10; ++i) + result += boost::math::tools::detail::evaluate_rational_c_imp_2(num, denom_int, v[0] + i, static_cast<boost::integral_constant<int, N>*>(0)); + return result; + }); + report_execution_time(time, std::string("Rational Method Comparison with ") + compiler_name() + std::string(" on ") + platform_name(), "Order " + make_order_string(N), "Method 2[br](Integer Coefficients)"); +} + +void test_rat_3(const boost::integral_constant<int, 1>&) +{ +} + +template <int N> +void test_rat_3(const boost::integral_constant<int, N>&) +{ + test_rat_3(boost::integral_constant<int, N - 1>()); + + double time = exec_timed_test([](const std::vector<double>& v) + { + double result = 0; + for (unsigned i = 0; i < 10; ++i) + result += boost::math::tools::detail::evaluate_rational_c_imp_3(num, denom, v[0] + i, static_cast<boost::integral_constant<int, N>*>(0)); + return result; + }); + report_execution_time(time, std::string("Rational Method Comparison with ") + compiler_name() + std::string(" on ") + platform_name(), "Order " + make_order_string(N), "Method 3[br](Double Coefficients)"); + + time = exec_timed_test([](const std::vector<double>& v) + { + double result = 0; + for (unsigned i = 0; i < 10; ++i) + result += boost::math::tools::detail::evaluate_rational_c_imp_3(num, denom_int, v[0] + i, static_cast<boost::integral_constant<int, N>*>(0)); + return result; + }); + report_execution_time(time, std::string("Rational Method Comparison with ") + compiler_name() + std::string(" on ") + platform_name(), "Order " + make_order_string(N), "Method 3[br](Integer Coefficients)"); +} + +template <class T, class U, class V> +V evaluate_rational_0(const T* num, const U* denom, const V& z_, std::size_t count) +{ + V z(z_); + V s1, s2; + if (z <= 1) + { + s1 = static_cast<V>(num[count - 1]); + s2 = static_cast<V>(denom[count - 1]); + for (int i = (int)count - 2; i >= 0; --i) + { + s1 *= z; + s2 *= z; + s1 += num[i]; + s2 += denom[i]; + } + } + else + { + z = 1 / z; + s1 = static_cast<V>(num[0]); + s2 = static_cast<V>(denom[0]); + for (unsigned i = 1; i < count; ++i) + { + s1 *= z; + s2 *= z; + s1 += num[i]; + s2 += denom[i]; + } + } + return s1 / s2; +} + + +int main() +{ + double val = 0.001; + while (val < 1) + { + std::vector<double> v; + v.push_back(val); + data.push_back(v); + val *= 1.1; + } + + for (unsigned i = 3; i <= 20; ++i) + { + double time = exec_timed_test([&](const std::vector<double>& v) { + double result = 0; + for (unsigned j = 0; j < 10; ++j) + result += evaluate_polynomial_0(denom, v[0] + j, i); + return result; + }); + report_execution_time(time, std::string("Polynomial Method Comparison with ") + compiler_name() + std::string(" on ") + platform_name(), "Order " + make_order_string(i), "Method 0[br](Double Coefficients)"); + + time = exec_timed_test([&](const std::vector<double>& v) { + double result = 0; + for (unsigned j = 0; j < 10; ++j) + result += evaluate_polynomial_0(denom_int, v[0] + j, i); + return result; + }); + report_execution_time(time, std::string("Polynomial Method Comparison with ") + compiler_name() + std::string(" on ") + platform_name(), "Order " + make_order_string(i), "Method 0[br](Integer Coefficients)"); + } + + test_poly_1(boost::integral_constant<int, 20>()); + test_poly_2(boost::integral_constant<int, 20>()); + test_poly_3(boost::integral_constant<int, 20>()); + + for (unsigned i = 3; i <= 20; ++i) + { + double time = exec_timed_test([&](const std::vector<double>& v) { + double result = 0; + for (unsigned j = 0; j < 10; ++j) + result += evaluate_rational_0(num, denom, v[0] + j, i); + return result; + }); + report_execution_time(time, std::string("Rational Method Comparison with ") + compiler_name() + std::string(" on ") + platform_name(), "Order " + make_order_string(i), "Method 0[br](Double Coefficients)"); + + time = exec_timed_test([&](const std::vector<double>& v) { + double result = 0; + for (unsigned j = 0; j < 10; ++j) + result += evaluate_rational_0(num, denom_int, v[0] + j, i); + return result; + }); + report_execution_time(time, std::string("Rational Method Comparison with ") + compiler_name() + std::string(" on ") + platform_name(), "Order " + make_order_string(i), "Method 0[br](Integer Coefficients)"); + } + + test_rat_1(boost::integral_constant<int, 20>()); + test_rat_2(boost::integral_constant<int, 20>()); + test_rat_3(boost::integral_constant<int, 20>()); + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_polygamma.cpp b/src/boost/libs/math/reporting/performance/test_polygamma.cpp new file mode 100644 index 000000000..81ba5686e --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_polygamma.cpp @@ -0,0 +1,221 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/polygamma.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +typedef double value_type; +#define SC_(x) static_cast<double>(x) + boost::array<boost::array<value_type, 3>, 484> data1 = + { { + {{ 1, SC_(0.1250000), SC_(65.388133444988034473142999334395961) }}, {{ 1, SC_(2.250000), SC_(0.55732915450711073927131911933522402) }}, {{ 1, SC_(4.375000), SC_(0.25666408805722660683906428275458774) }}, {{ 1, SC_(6.500000), SC_(0.16628453574995823763989666631218566) }}, {{ 1, SC_(8.625000), SC_(0.12292237374423990274075995315923687) }}, {{ 1, SC_(10.75000), SC_(0.097483848201852104395946001854344927) }}, {{ 1, SC_(12.87500), SC_(0.080764208092843621858393487209278638) }}, {{ 1, SC_(15.00000), SC_(0.068938227847683806226155216756371670) }}, {{ 1, SC_(17.12500), SC_(0.060132263162293455894576107399989891) }}, {{ 1, SC_(19.25000), SC_(0.053320703915617277211139745531295189) }}, {{ 1, SC_(21.37500), SC_(0.047895038036916716105500109226810942) }}, {{ 1, SC_(23.50000), SC_(0.043471416266946770249685779030294199) }}, {{ 1, SC_(25.62500), SC_(0.039795743807625238080963836217545550) }}, {{ 1, SC_(27.75000), SC_(0.036693131333593477569076090983653779) }}, {{ 1, SC_(29.87500), SC_(0.034039266877179098641898178094001935) }}, {{ 1, SC_(32.00000), SC_(0.031743366520302090126581680438741427) }}, {{ 1, SC_(34.12500), SC_(0.029737585673522726661363528635488348) }}, {{ 1, SC_(36.25000), SC_(0.027970204614894933106878169214392067) }}, {{ 1, SC_(38.37500), SC_(0.026401106865951764123858232364900665) }}, {{ 1, SC_(40.50000), SC_(0.024998698201356741322280011143883922) }}, {{ 1, SC_(42.62500), SC_(0.023737757818075642720991864115881164) }}, {{ 1, SC_(44.75000), SC_(0.022597908441287364284087900916682571) }}, {{ 1, SC_(46.87500), SC_(0.021562506914486557632388530071308920) }}, {{ 1, SC_(49.00000), SC_(0.020617826354560516060031453062401102) }}, {{ 1, SC_(51.12500), SC_(0.019752444228552790805040230288386135) }}, {{ 1, SC_(53.25000), SC_(0.018956778300513446216011889734099110) }}, {{ 1, SC_(55.37500), SC_(0.018222730375562878627773770314126276) }}, {{ 1, SC_(57.50000), SC_(0.017543409716574620734228673575882677) }}, {{ 1, SC_(59.62500), SC_(0.016912916093398919581541485278641593) }}, {{ 1, SC_(61.75000), SC_(0.016326167985389235938281994221076159) }}, {{ 1, SC_(63.87500), SC_(0.015778765341125640054231784371915358) }}, {{ 1, SC_(66.00000), SC_(0.015266879048806385777045778219279459) }}, {{ 1, SC_(68.12500), SC_(0.014787161242916062152535888615850260) }}, {{ 1, SC_(70.25000), SC_(0.014336672004276912093324664070489886) }}, {{ 1, SC_(72.37500), SC_(0.013912819061256593888508241399678441) }}, {{ 1, SC_(74.50000), SC_(0.013513307879079644573772830117155790) }}, {{ 1, SC_(76.62500), SC_(0.013136100107643257539226305043251166) }}, {{ 1, SC_(78.75000), SC_(0.012779378799112389298746113446648982) }}, {{ 1, SC_(80.87500), SC_(0.012441519142554280549428650598112729) }}, {{ 1, SC_(83.00000), SC_(0.012121063720980953787190412456820037) }}, {{ 1, SC_(85.12500), SC_(0.011816701495952671887865236708275449) }}, {{ 1, SC_(87.25000), SC_(0.011527249880640584213306489206202069) }}, {{ 1, SC_(89.37500), SC_(0.011251639384481213426240562514542477) }}, {{ 1, SC_(91.50000), SC_(0.010988900409103388104670465071922664) }}, {{ 1, SC_(93.62500), SC_(0.010738151851930343087942933225290955) }}, {{ 1, SC_(95.75000), SC_(0.010498591235178571927709342934117247) }}, {{ 1, SC_(97.87500), SC_(0.010269486127251686167359605922136260) }}, {{ 1, SC_(100.0000), SC_(0.010050166663333571395245668465701423) }}, + {{ 2, SC_(0.1250000), -SC_(1025.7533381181356825956689300565174) }}, {{ 2, SC_(2.250000), -SC_(0.30373993753692033333796717884398989) }}, {{ 2, SC_(4.375000), -SC_(0.065528725397877855792664680804766330) }}, {{ 2, SC_(6.500000), -SC_(0.027587910706876798794117450572831562) }}, {{ 2, SC_(8.625000), -SC_(0.015091062676061564388822078971884395) }}, {{ 2, SC_(10.75000), -SC_(0.0094956196449265900776488965631791775) }}, {{ 2, SC_(12.87500), -SC_(0.0065193261909178260169885198194705291) }}, {{ 2, SC_(15.00000), -SC_(0.0047506027165515547467791223768191188) }}, {{ 2, SC_(17.12500), -SC_(0.0036148020016626802195565448384834283) }}, {{ 2, SC_(19.25000), -SC_(0.0028424250740909855631736845850335535) }}, {{ 2, SC_(21.37500), -SC_(0.0022934967923297751145806065882712900) }}, {{ 2, SC_(23.50000), -SC_(0.0018894667868625909895476094900477678) }}, {{ 2, SC_(25.62500), -SC_(0.0015834924252652953218803111387922996) }}, {{ 2, SC_(27.75000), -SC_(0.0013462349527320363170378913859580860) }}, {{ 2, SC_(29.87500), -SC_(0.0011585598948326545653381467670779893) }}, {{ 2, SC_(32.00000), -SC_(0.0010075567602140907392185110593117265) }}, {{ 2, SC_(34.12500), -SC_(0.00088425886906787461365402045268994574) }}, {{ 2, SC_(36.25000), -SC_(0.00078228136778540401396894643668418462) }}, {{ 2, SC_(38.37500), -SC_(0.00069697797537723210697105880606724159) }}, {{ 2, SC_(40.50000), -SC_(0.00062490237932923289658683588812998732) }}, {{ 2, SC_(42.62500), -SC_(0.00056345469641484389456121935536309197) }}, {{ 2, SC_(44.75000), -SC_(0.00051064374134295093656385520125286421) }}, {{ 2, SC_(46.87500), -SC_(0.00046492369550612086723038302919171885) }}, {{ 2, SC_(49.00000), -SC_(0.00042507970884222510504308867471824948) }}, {{ 2, SC_(51.12500), -SC_(0.00039014637079445100439645401142194535) }}, {{ 2, SC_(53.25000), -SC_(0.00035934868438211062777790080207505881) }}, {{ 2, SC_(55.37500), -SC_(0.00033205871518117505559928737076624192) }}, {{ 2, SC_(57.50000), -SC_(0.00030776333242771756953580263456220628) }}, {{ 2, SC_(59.62500), -SC_(0.00028603991345613245802207114123372414) }}, {{ 2, SC_(61.75000), -SC_(0.00026653784162151616772904552992231739) }}, {{ 2, SC_(63.87500), -SC_(0.00024896427102287300629668349085350311) }}, {{ 2, SC_(66.00000), -SC_(0.00023307306946180321476975587412226332) }}, {{ 2, SC_(68.12500), -SC_(0.00021865615382096049855997233359992101) }}, {{ 2, SC_(70.25000), -SC_(0.00020553664405312492990454318541834320) }}, {{ 2, SC_(72.37500), -SC_(0.00019356341228034103704385457246984425) }}, {{ 2, SC_(74.50000), -SC_(0.00018260671130395075946075978013398780) }}, {{ 2, SC_(76.62500), -SC_(0.00017255464497899193114313963889049197) }}, {{ 2, SC_(78.75000), -SC_(0.00016331030013937037094502788633900241) }}, {{ 2, SC_(80.87500), -SC_(0.00015478940207215993505449988937898640) }}, {{ 2, SC_(83.00000), -SC_(0.00014691838710034332570083901051760808) }}, {{ 2, SC_(85.12500), -SC_(0.00013963280957351165370765015817038278) }}, {{ 2, SC_(87.25000), -SC_(0.00013287601856558888563037791437997733) }}, {{ 2, SC_(89.37500), -SC_(0.00012659805332837531702241737466058293) }}, {{ 2, SC_(91.50000), -SC_(0.00012075471712784846612240303590084686) }}, {{ 2, SC_(93.62500), -SC_(0.00011530679728326736002584104318350829) }}, {{ 2, SC_(95.75000), -SC_(0.00011021940561565095981861374083495299) }}, {{ 2, SC_(97.87500), -SC_(0.00010546141852085692313553484671110170) }}, {{ 2, SC_(100.0000), -SC_(0.00010100499983334999700083300446059382) }}, + {{ 3, SC_(0.1250000), SC_(24580.143419063566218511004446647010) }}, + {{ 3, SC_(2.250000), SC_(0.32454400918839602279124382903505677) }}, + {{ 3, SC_(4.375000), SC_(0.033289201205556512286673394063908247) }}, + {{ 3, SC_(6.500000), SC_(0.0091336635043781405048050655353658508) }}, + {{ 3, SC_(8.625000), SC_(0.0037008460120616755687668778806054328) }}, + {{ 3, SC_(10.75000), SC_(0.0018484328773891268475922730275004208) }}, + {{ 3, SC_(12.87500), SC_(0.0010519186241203463873018930415985105) }}, + {{ 3, SC_(15.00000), SC_(0.00065447977828273734841733708901750530) }}, + {{ 3, SC_(17.12500), SC_(0.00043447135395979214393136263736764201) }}, + {{ 3, SC_(19.25000), SC_(0.00030297696415718385912539504824566570) }}, + {{ 3, SC_(21.37500), SC_(0.00021961042047214603636739002880115737) }}, + {{ 3, SC_(23.50000), SC_(0.00016422394665239820056068884910278128) }}, + {{ 3, SC_(25.62500), SC_(0.00012599930135391694524067581601102767) }}, + {{ 3, SC_(27.75000), SC_(0.000098773010741268191080883613389009048) }}, + {{ 3, SC_(29.87500), SC_(0.000078857844307768334137453508928722671) }}, + {{ 3, SC_(32.00000), SC_(0.000063955754777976299576673673574642423) }}, + {{ 3, SC_(34.12500), SC_(0.000052583702941352521813139097855885393) }}, + {{ 3, SC_(36.25000), SC_(0.000043755438122384003302367816109980192) }}, + {{ 3, SC_(38.37500), SC_(0.000036797707573246758497786056137200200) }}, + {{ 3, SC_(40.50000), SC_(0.000031240239710655936422248716017582946) }}, + {{ 3, SC_(42.62500), SC_(0.000026747791378195202271687207455056302) }}, + {{ 3, SC_(44.75000), SC_(0.000023076997706632396178157160717335565) }}, + {{ 3, SC_(46.87500), SC_(0.000020048287815935784161580614536631137) }}, + {{ 3, SC_(49.00000), SC_(0.000017527197874026635143654793647828466) }}, + {{ 3, SC_(51.12500), SC_(0.000015411686998050652806770684541876757) }}, + {{ 3, SC_(53.25000), SC_(0.000013623370966529973793708331754693666) }}, + {{ 3, SC_(55.37500), SC_(0.000012101363299593660023105041673385376) }}, + {{ 3, SC_(57.50000), SC_(0.000010797882726896889062768134787291884) }}, + {{ 3, SC_(59.62500), SC_(9.6750769605707758334815857396558355e-6) }}, + {{ 3, SC_(61.75000), SC_(8.7026966259856900409582330070865268e-6) }}, + {{ 3, SC_(63.87500), SC_(7.8563716857343030149244371160376495e-6) }}, + {{ 3, SC_(66.00000), SC_(7.1163203299934132027680033779014197e-6) }}, + {{ 3, SC_(68.12500), SC_(6.4663719906627627544882175944382226e-6) }}, + {{ 3, SC_(70.25000), SC_(5.8932210515208497328937862935232496e-6) }}, + {{ 3, SC_(72.37500), SC_(5.3858517367657111634358444590928906e-6) }}, + {{ 3, SC_(74.50000), SC_(4.9350912436686398240670814427342376e-6) }}, + {{ 3, SC_(76.62500), SC_(4.5332598242018110991734569100539592e-6) }}, + {{ 3, SC_(78.75000), SC_(4.1738947808706992483423293125251133e-6) }}, + {{ 3, SC_(80.87500), SC_(3.8515312659502461861484363442184908e-6) }}, + {{ 3, SC_(83.00000), SC_(3.5615270636518630626786644585266764e-6) }}, + {{ 3, SC_(85.12500), SC_(3.2999216708248315372665461067377996e-6) }}, + {{ 3, SC_(87.25000), SC_(3.0633223042636924720337703682152499e-6) }}, + {{ 3, SC_(89.37500), SC_(2.8488111819903247190925375784544775e-6) }}, + {{ 3, SC_(91.50000), SC_(2.6538697141941088454844912572034392e-6) }}, + {{ 3, SC_(93.62500), SC_(2.4763162120667457234467192228222670e-6) }}, + {{ 3, SC_(95.75000), SC_(2.3142544621402797124759791203351867e-6) }}, + {{ 3, SC_(97.87500), SC_(2.1660310796121506708372890790676070e-6) }}, + {{ 3, SC_(100.0000), SC_(2.0301999900013330334332872946449855e-6) }}, + + {{4, SC_(0.1250000), SC_(-786445.98543106378579320120709638297)}}, {{ 4, SC_(2.250000), SC_(-0.51106863793373355822715252195899576) }}, {{ 4, SC_(4.375000), SC_(-0.025241882074562753654505456518792508) }}, {{ 4, SC_(6.500000), SC_(-0.0045259302803220607103496010172883494) }}, {{ 4, SC_(8.625000), SC_(-0.0013596929106556359886012273921730071) }}, {{ 4, SC_(10.75000), SC_(-0.00053930828860547053427689740051604949) }}, {{ 4, SC_(12.87500), SC_(-0.00025445997266103206171225355293726865) }}, {{ 4, SC_(15.00000), SC_(-0.00013519619187519276575068431301221388) }}, {{ 4, SC_(17.12500), SC_(-0.000078306716822025065793290599586946118) }}, {{ 4, SC_(19.25000), SC_(-0.000048430513924395561509999792045098081) }}, {{ 4, SC_(21.37500), SC_(-0.000031536705873201397805285969259914559) }}, {{ 4, SC_(23.50000), SC_(-0.000021407049050977062373311093992814121) }}, {{ 4, SC_(25.62500), SC_(-0.000015036764178343754461565939319516893) }}, {{ 4, SC_(27.75000), SC_(-0.000010869219781124567432001391245344089) }}, {{ 4, SC_(29.87500), SC_(-8.0504604926168752698902834477348881e-6) }}, {{ 4, SC_(32.00000), SC_(-6.0889806370027137702207132674152980e-6) }}, {{ 4, SC_(34.12500), SC_(-4.6901011823268163094417546531023856e-6) }}, {{ 4, SC_(36.25000), SC_(-3.6708283086618325558290000911536581e-6) }}, {{ 4, SC_(38.37500), SC_(-2.9139932244650290336213711603586301e-6) }}, {{ 4, SC_(40.50000), SC_(-2.3425302303691304543510535971847968e-6) }}, {{ 4, SC_(42.62500), SC_(-1.9045296486050512642801504306671373e-6) }}, {{ 4, SC_(44.75000), SC_(-1.5642760453399369047824852836708697e-6) }}, {{ 4, SC_(46.87500), SC_(-1.2967233822729326645555539185332769e-6) }}, {{ 4, SC_(49.00000), SC_(-1.0840030171141394983603065427611252e-6) }}, {{ 4, SC_(51.12500), SC_(-9.1316643010960703020517255319750485e-7) }}, {{ 4, SC_(53.25000), SC_(-7.7469609700462921021995856208285815e-7) }}, {{ 4, SC_(55.37500), SC_(-6.6150474476547305805911346012045165e-7) }}, {{ 4, SC_(57.50000), SC_(-5.6825133351570053043820949353677183e-7) }}, {{ 4, SC_(59.62500), SC_(-4.9086620236193161135912086142572580e-7) }}, {{ 4, SC_(61.75000), SC_(-4.2621666772058776224801114961267801e-7) }}, {{ 4, SC_(63.87500), SC_(-3.7186839586672891333608898041067112e-7) }}, {{ 4, SC_(66.00000), SC_(-3.2591301914111222705427951896642626e-7) }}, {{ 4, SC_(68.12500), SC_(-2.8684217920848561693233665614958777e-7) }}, {{ 4, SC_(70.25000), SC_(-2.5345451083204479337777798526354757e-7) }}, {{ 4, SC_(72.37500), SC_(-2.2478626654835416271537021644553013e-7) }}, {{ 4, SC_(74.50000), SC_(-2.0005909073946645851596541397664333e-7) }}, {{ 4, SC_(76.62500), SC_(-1.7864035957298817513241281766878220e-7) }}, {{ 4, SC_(78.75000), SC_(-1.6001281551287093216803849072235519e-7) }}, {{ 4, SC_(80.87500), SC_(-1.4375113796429048125939526070340983e-7) }}, {{ 4, SC_(83.00000), SC_(-1.2950373350296884735201964028079076e-7) }}, {{ 4, SC_(85.12500), SC_(-1.1697848507486443027254417751822546e-7) }}, {{ 4, SC_(87.25000), SC_(-1.0593152651055065213702117539700727e-7) }}, {{ 4, SC_(89.37500), SC_(-9.6158345290200883062520858433963680e-8) }}, {{ 4, SC_(91.50000), SC_(-8.7486689164653963817234101603388082e-8) }}, {{ 4, SC_(93.62500), SC_(-7.9770879280803145900384972987304463e-8) }}, {{ 4, SC_(95.75000), SC_(-7.2887226653828502529665531368895369e-8) }}, {{ 4, SC_(97.87500), SC_(-6.6730319180606630829991063550458595e-8) }}, {{ 4, SC_(100.0000), SC_(-6.1209999300119967012993094755881001e-8) }}, + {{ 9, SC_(0.1250000), SC_(3.8963943320506514766700086867372762e14) }}, {{ 9, SC_(2.250000), SC_(112.10537259293726188704511169205760) }}, {{ 9, SC_(4.375000), SC_(0.16363919906361224458550935569570297) }}, {{ 9, SC_(6.500000), SC_(0.0036236228486465262827554601212241334) }}, {{ 9, SC_(8.625000), SC_(0.00024724827512609608284324030730925865) }}, {{ 9, SC_(10.75000), SC_(0.000031173409615380334086095590039151370) }}, {{ 9, SC_(12.87500), SC_(5.7824557132102074668570643058203530e-6) }}, {{ 9, SC_(15.00000), SC_(1.3980855499116564037825647833211369e-6) }}, {{ 9, SC_(17.12500), SC_(4.1002910484982160273499509487840966e-7) }}, {{ 9, SC_(19.25000), SC_(1.3928434419796988121776758599785632e-7) }}, {{ 9, SC_(21.37500), SC_(5.3108201638858702713365922453188085e-8) }}, {{ 9, SC_(23.50000), SC_(2.2228120959414339842295401083512930e-8) }}, {{ 9, SC_(25.62500), SC_(1.0046019155325212007574589173916857e-8) }}, {{ 9, SC_(27.75000), SC_(4.8421087709589697640039499715706350e-9) }}, {{ 9, SC_(29.87500), SC_(2.4651114661905897591489828702449678e-9) }}, {{ 9, SC_(32.00000), SC_(1.3154897461853304542190391130140025e-9) }}, {{ 9, SC_(34.12500), SC_(7.3134444425276046658844002904667737e-10) }}, {{ 9, SC_(36.25000), SC_(4.2146721224691157996140805304942419e-10) }}, {{ 9, SC_(38.37500), SC_(2.5073387292785072270991813660631786e-10) }}, {{ 9, SC_(40.50000), SC_(1.5344896969374692327054949367251260e-10) }}, {{ 9, SC_(42.62500), SC_(9.6326225603670754883495513330468241e-11) }}, {{ 9, SC_(44.75000), 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SC_(1.1791071073496904625468941445147639e7) }}, + {{ SC_(7.0), SC_(-12.750), SC_(3.3035269585550319411369451657990653e8) }}, {{ SC_(7.0), SC_(-12.250), SC_(3.3035269585550014530679554645726841e8) }}, {{ SC_(7.0), SC_(-11.750), SC_(3.3035269585549597724076958273392155e8) }}, {{ SC_(7.0), SC_(-11.250), SC_(3.3035269585549020632656302567379925e8) }}, {{ SC_(7.0), SC_(-10.750), SC_(3.3035269585548210560734246359421460e8) }}, {{ SC_(7.0), SC_(-10.250), SC_(3.3035269585547056321166932680182245e8) }}, {{ SC_(7.0), SC_(-9.7500), SC_(3.3035269585545384621477943726294791e8) }}, {{ SC_(7.0), SC_(-9.2500), SC_(3.3035269585542919758450034698830934e8) }}, {{ SC_(7.0), SC_(-8.7500), SC_(3.3035269585539213080586956648886140e8) }}, {{ SC_(7.0), SC_(-8.2500), SC_(3.3035269585533516103728829633890794e8) }}, {{ SC_(7.0), SC_(-7.7500), SC_(3.3035269585524545242332002141349801e8) }}, {{ SC_(7.0), SC_(-7.2500), SC_(3.3035269585510030650375087453009371e8) }}, {{ SC_(7.0), SC_(-6.7500), SC_(3.3035269585485817969386206988585281e8) }}, {{ SC_(7.0), SC_(-6.2500), SC_(3.3035269585444002902560781621765444e8) }}, {{ SC_(7.0), SC_(-5.7500), SC_(3.3035269585368867935011094629708018e8) }}, {{ SC_(7.0), SC_(-5.2500), SC_(3.3035269585227536550842381621765444e8) }}, {{ SC_(7.0), SC_(-4.7500), SC_(3.3035269584947086190323815702711063e8) }}, {{ SC_(7.0), SC_(-4.2500), SC_(3.3035269584354251332378488235637904e8) }}, {{ SC_(7.0), SC_(-3.7500), SC_(3.3035269583002256126086884537779074e8) }}, {{ SC_(7.0), SC_(-3.2500), SC_(3.3035269579619261006329391884897976e8) }}, {{ SC_(7.0), SC_(-2.7500), SC_(3.3035269570114408444331054633801022e8) }}, {{ SC_(7.0), SC_(-2.2500), SC_(3.3035269539127781220563177006740899e8) }}, {{ SC_(7.0), SC_(-1.7500), SC_(3.3035269416026348990428605870784761e8) }}, {{ SC_(7.0), SC_(-1.2500), SC_(3.3035268771818605685450990413016373e8) }}, {{ SC_(7.0), SC_(-0.75000), SC_(3.3035263686402030648824099487997220e8) }}, {{ SC_(7.0), SC_(-0.25000), SC_(3.3035184214649965685450990413016373e8) }}, + {{ SC_(8.0), SC_(-7.7500), SC_(-1.0569114259666913771892699180522388e10) }}, {{ SC_(8.0), SC_(-7.2500), SC_(1.0569114259666319911021283350705169e10) }}, {{ SC_(8.0), SC_(-6.7500), SC_(-1.0569114259667313537290849324034796e10) }}, {{ SC_(8.0), SC_(-6.2500), SC_(1.0569114259665591328976435838084546e10) }}, {{ SC_(8.0), SC_(-5.7500), SC_(-1.0569114259668699611772332137177045e10) }}, {{ SC_(8.0), SC_(-5.2500), SC_(1.0569114259662820559674440318084546e10) }}, {{ SC_(8.0), SC_(-4.7500), SC_(-1.0569114259674567879524502974422220e10) }}, {{ SC_(8.0), SC_(-4.2500), SC_(1.0569114259649513356345466704581650e10) }}, {{ SC_(8.0), SC_(-3.7500), SC_(-1.0569114259707322912185335499305285e10) }}, {{ SC_(8.0), SC_(-3.2500), SC_(1.0569114259560384126678660185038311e10) }}, {{ SC_(8.0), SC_(-2.7500), SC_(-1.0569114259982263662729459870590150e10) }}, {{ SC_(8.0), SC_(-2.2500), SC_(1.0569114258563670778105953357268290e10) }}, {{ SC_(8.0), SC_(-1.7500), 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SC_(-1.5220204740668360644738342521168221e13) }}, {{ SC_(10.0), SC_(-4.2500), SC_(1.5220204740668289586193246215389596e13) }}, {{ SC_(10.0), SC_(-3.7500), SC_(-1.5220204740668491301932335869743932e13) }}, {{ SC_(10.0), SC_(-3.2500), SC_(1.5220204740667845482073107110240315e13) }}, {{ SC_(10.0), SC_(-2.7500), SC_(-1.5220204740670250922735818265720155e13) }}, {{ SC_(10.0), SC_(-2.2500), SC_(1.5220204740659352776617813040228546e13) }}, {{ SC_(10.0), SC_(-1.7500), SC_(-1.5220204740723597111914149030851634e13) }}, {{ SC_(10.0), SC_(-1.2500), SC_(1.5220204740174337594057347065492760e13) }}, {{ SC_(10.0), SC_(-0.75000), SC_(-1.5220204748421004942502520332720988e13) }}, {{ SC_(10.0), SC_(-0.25000), SC_(1.5220204428462791119561347065492760e13) }}, + {{ SC_(11.0), SC_(-7.7500), SC_(6.6969403856797204470999075620782555e14)}}, {{ SC_(11.0), SC_(-7.2500), SC_(6.6969403856797204443997065278152669e14) }}, {{ SC_(11.0), SC_(-6.7500), SC_(6.6969403856797204385976298181981934e14) }}, {{ SC_(11.0), SC_(-6.2500), SC_(6.6969403856797204254719282828940321e14) }}, {{ SC_(11.0), SC_(-5.7500), SC_(6.6969403856797203939795943831775966e14) }}, {{ SC_(11.0), SC_(-5.2500), SC_(6.6969403856797203131161247792548979e14) }}, {{ SC_(11.0), SC_(-4.7500), SC_(6.6969403856797200883878751610651220e14) }}, {{ SC_(11.0), SC_(-4.2500), SC_(6.6969403856797194026913294831009712e14) }}, {{ SC_(11.0), SC_(-3.7500), SC_(6.6969403856797170626423300519402108e14) }}, {{ SC_(11.0), SC_(-3.2500), SC_(6.6969403856797079082317494121441662e14) }}, {{ SC_(11.0), SC_(-2.7500), SC_(6.6969403856796654470987612349915749e14) }}, {{ SC_(11.0), SC_(-2.2500), SC_(6.6969403856794204628163394590053064e14) }}, {{ SC_(11.0), SC_(-1.7500), SC_(6.6969403856775315995316280043863158e14) }}, {{ SC_(11.0), SC_(-1.2500), SC_(6.6969403856557086094467166780182235e14) }}, {{ SC_(11.0), SC_(-0.75000), SC_(6.6969403851936945358946446654116707e14) }}, {{ SC_(11.0), SC_(-0.25000), SC_(6.6969403582250925196910686780182235e14) }}, + {{ 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SC_(1.6715535177261375450685102745473439e18) }}, {{ SC_(13.0), SC_(-2.7500), SC_(1.6715535177261374960497681856044819e18) }}, {{ SC_(13.0), SC_(-2.2500), SC_(1.6715535177261371205337428998473234e18) }}, {{ SC_(13.0), SC_(-1.7500), SC_(1.6715535177261330943278445785436631e18) }}, {{ SC_(13.0), SC_(-1.2500), SC_(1.6715535177260640528966928029814669e18) }}, {{ SC_(13.0), SC_(-0.75000), SC_(1.6715535177236684875710325164741107e18) }}, {{ SC_(13.0), SC_(-0.25000), SC_(1.6715535174521967818565724133494669e18) }}, + {{ SC_(20.0), SC_(-7.7500), SC_(-1.0700016187896297695358366297227405e31)}}, {{ SC_(20.0), SC_(-7.2500), SC_(1.0700016187896297695358366297227207e31) }}, {{ SC_(20.0), SC_(-6.7500), SC_(-1.0700016187896297695358366297227919e31) }}, {{ SC_(20.0), SC_(-6.2500), SC_(1.0700016187896297695358366297225123e31) }}, {{ SC_(20.0), SC_(-5.7500), SC_(-1.0700016187896297695358366297237267e31) }}, {{ SC_(20.0), SC_(-5.2500), SC_(1.0700016187896297695358366297178064e31) }}, {{ SC_(20.0), SC_(-4.7500), SC_(-1.0700016187896297695358366297508349e31) }}, {{ SC_(20.0), SC_(-4.2500), SC_(1.0700016187896297695358366295346680e31) }}, {{ SC_(20.0), SC_(-3.7500), SC_(-1.0700016187896297695358366312489970e31) }}, {{ SC_(20.0), SC_(-3.2500), SC_(1.0700016187896297695358366140480322e31) }}, {{ SC_(20.0), SC_(-2.7500), SC_(-1.0700016187896297695358368457690989e31) }}, {{ SC_(20.0), SC_(-2.2500), SC_(1.0700016187896297695358322831891149e31) }}, {{ SC_(20.0), SC_(-1.7500), SC_(-1.0700016187896297695359814356987569e31) }}, {{ SC_(20.0), SC_(-1.2500), SC_(1.0700016187896297695260533442006924e31) }}, {{ SC_(20.0), SC_(-0.75000), SC_(-1.0700016187896297714516730336449055e31) }}, {{ SC_(20.0), SC_(-0.25000), SC_(1.0700016187896275255700182817756420e31) }}, + {{ SC_(23.0), SC_(-7.7500), SC_(7.2766958095269026379022334905108869e36)}}, {{ SC_(23.0), SC_(-7.2500), SC_(7.2766958095269026379022334905108869e36) }}, {{ SC_(23.0), SC_(-6.7500), SC_(7.2766958095269026379022334905108869e36) }}, {{ SC_(23.0), SC_(-6.2500), SC_(7.2766958095269026379022334905108868e36) }}, {{ SC_(23.0), SC_(-5.7500), SC_(7.2766958095269026379022334905108866e36) }}, {{ SC_(23.0), SC_(-5.2500), SC_(7.2766958095269026379022334905108848e36) }}, {{ SC_(23.0), SC_(-4.7500), SC_(7.2766958095269026379022334905108714e36) }}, {{ SC_(23.0), SC_(-4.2500), SC_(7.2766958095269026379022334905107503e36) }}, {{ SC_(23.0), SC_(-3.7500), SC_(7.2766958095269026379022334905093860e36) }}, {{ SC_(23.0), SC_(-3.2500), SC_(7.2766958095269026379022334904893135e36) }}, {{ SC_(23.0), SC_(-2.7500), SC_(7.2766958095269026379022334900771270e36) }}, {{ SC_(23.0), SC_(-2.2500), SC_(7.2766958095269026379022334770834817e36) }}, {{ SC_(23.0), SC_(-1.7500), SC_(7.2766958095269026379022327513062336e36) }}, {{ SC_(23.0), SC_(-1.2500), SC_(7.2766958095269026379021422520579094e36) }}, {{ SC_(23.0), SC_(-0.75000), SC_(7.2766958095269026378642504512809960e36) }}, {{ SC_(23.0), SC_(-0.25000), SC_(7.2766958095269025158194448897624671e36) }}, 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SC_(124.0), SC_(-18.50), SC_(-8.4019112566928602772066808945728022e45) }}, {{ SC_(124.0), SC_(-19.50), SC_(-1.6209265582255125824031570171026802e43) }}, {{ SC_(124.0), SC_(-20.50), SC_(-4.2125071484047517848318042867661534e40) }}, + {{ SC_(125.0), SC_(-1.500), SC_(3.2032092294989705945080639466924596e247) }}, {{ SC_(125.0), SC_(-2.500), SC_(3.2032092294989705945080639466924596e247) }}, {{ SC_(125.0), SC_(-3.500), SC_(3.2032092294989705945080639466924596e247) }}, {{ SC_(125.0), SC_(-4.500), SC_(3.2032092294989705945080639466924596e247) }}, {{ SC_(125.0), SC_(-5.500), SC_(3.2032092294989705945080639466924596e247) }}, {{ SC_(125.0), SC_(-6.500), SC_(3.2032092294989705945080639466924596e247) }}, {{ SC_(125.0), SC_(-7.500), SC_(3.2032092294989705945080639466924596e247) }}, {{ SC_(125.0), SC_(-8.500), SC_(3.2032092294989705945080639466924596e247) }}, {{ SC_(125.0), SC_(-9.500), SC_(3.2032092294989705945080639466924596e247) }}, {{ SC_(125.0), SC_(-10.50), SC_(3.2032092294989705945080639466924596e247) }}, {{ SC_(125.0), SC_(-11.50), SC_(3.2032092294989705945080639466924596e247) }}, {{ SC_(125.0), SC_(-12.50), SC_(3.2032092294989705945080639466924596e247) }}, {{ SC_(125.0), SC_(-13.50), SC_(3.2032092294989705945080639466924596e247) }}, {{ SC_(125.0), SC_(-14.50), SC_(3.2032092294989705945080639466924596e247) }}, {{ SC_(125.0), SC_(-15.50), SC_(3.2032092294989705945080639466924596e247) }}, {{ SC_(125.0), SC_(-16.50), SC_(3.2032092294989705945080639466924596e247) }}, {{ SC_(125.0), SC_(-17.50), SC_(3.2032092294989705945080639466924596e247) }}, {{ SC_(125.0), SC_(-18.50), SC_(3.2032092294989705945080639466924596e247) }}, {{ SC_(125.0), SC_(-19.50), SC_(3.2032092294989705945080639466924596e247) }}, {{ SC_(125.0), SC_(-20.50), SC_(3.2032092294989705945080639466924596e247) }}, + {{ SC_(125.0), SC_(-1.5000002384185791015625000000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-2.5000002384185791015625000000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-3.5000002384185791015625000000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-4.5000002384185791015625000000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-5.5000002384185791015625000000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-6.5000002384185791015625000000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-7.5000002384185791015625000000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-8.5000002384185791015625000000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-9.5000002384185791015625000000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-10.500000238418579101562500000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-11.500000238418579101562500000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-12.500000238418579101562500000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-13.500000238418579101562500000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-14.500000238418579101562500000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-15.500000238418579101562500000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-16.500000238418579101562500000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-17.500000238418579101562500000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-18.500000238418579101562500000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-19.500000238418579101562500000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-20.500000238418579101562500000000000), SC_(3.2032092353263025675858789018286326e247) }}, + {{ SC_(125.0), SC_(-1.4999997615814208984375000000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-2.4999997615814208984375000000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-3.4999997615814208984375000000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-4.4999997615814208984375000000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-5.4999997615814208984375000000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-6.4999997615814208984375000000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-7.4999997615814208984375000000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-8.4999997615814208984375000000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-9.4999997615814208984375000000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-10.499999761581420898437500000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-11.499999761581420898437500000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-12.499999761581420898437500000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-13.499999761581420898437500000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-14.499999761581420898437500000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-15.499999761581420898437500000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-16.499999761581420898437500000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-17.499999761581420898437500000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-18.499999761581420898437500000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-19.499999761581420898437500000000000), SC_(3.2032092353263025675858789018286326e247) }}, {{ SC_(125.0), SC_(-20.499999761581420898437500000000000), SC_(3.2032092353263025675858789018286326e247) }}, + } }; + boost::array<boost::array<value_type, 3>, 103> neg_double_data = + { { + { { SC_(124.0), SC_(-1.4999997615814208984375000000000000), SC_(7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-2.4999997615814208984375000000000000), SC_(7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-3.4999997615814208984375000000000000), SC_(7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-4.4999997615814208984375000000000000), SC_(7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-5.4999997615814208984375000000000000), SC_(7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-6.4999997615814208984375000000000000), SC_(7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-7.4999997615814208984375000000000000), SC_(7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-8.4999997615814208984375000000000000), SC_(7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-9.4999997615814208984375000000000000), SC_(7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-10.499999761581420898437500000000000), SC_(7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-11.499999761581420898437500000000000), SC_(7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-12.499999761581420898437500000000000), SC_(7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-13.499999761581420898437500000000000), SC_(7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-14.499999761581420898437500000000000), SC_(7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-15.499999761581420898437500000000000), SC_(7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-16.499999761581420898437500000000000), SC_(7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-17.499999761581420898437500000000000), SC_(7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-18.499999761581420898437500000000000), SC_(7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-19.499999761581420898437500000000000), SC_(7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-20.499999761581420898437500000000000), SC_(7.6370459352527012474320227016934851e240) } }, + { { SC_(124.0), SC_(-1.5000002384185791015625000000000000), SC_(-7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-2.5000002384185791015625000000000000), SC_(-7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-3.5000002384185791015625000000000000), SC_(-7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-4.5000002384185791015625000000000000), SC_(-7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-5.5000002384185791015625000000000000), SC_(-7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-6.5000002384185791015625000000000000), SC_(-7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-7.5000002384185791015625000000000000), SC_(-7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-8.5000002384185791015625000000000000), SC_(-7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-9.5000002384185791015625000000000000), SC_(-7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-10.500000238418579101562500000000000), SC_(-7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-11.500000238418579101562500000000000), SC_(-7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-12.500000238418579101562500000000000), SC_(-7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-13.500000238418579101562500000000000), SC_(-7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-14.500000238418579101562500000000000), SC_(-7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-15.500000238418579101562500000000000), SC_(-7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-16.500000238418579101562500000000000), SC_(-7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-17.500000238418579101562500000000000), SC_(-7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-18.500000238418579101562500000000000), SC_(-7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-19.500000238418579101562500000000000), SC_(-7.6370459352527012474320227016934851e240) } }, { { SC_(124.0), SC_(-20.500000238418579101562500000000000), SC_(-7.6370459352527012474320227016934851e240) } }, + { { SC_(1.0), SC_(-0.500), SC_(8.9348022005446793094172454999380756) } }, { { SC_(2.0), SC_(-0.500), SC_(-0.82879664423431999559633426116029987) } }, { { SC_(3.0), SC_(-0.500), SC_(193.40909103400243723644033268870511) } }, { { SC_(4.0), SC_(-0.500), SC_(-3.4742498266672251905359219240334210) } }, { { SC_(5.0), SC_(-0.500), SC_(15371.113548602435496241755549219359) } }, { { SC_(6.0), SC_(-0.500), SC_(-43.457923803023286231087958265415698) } }, { { SC_(7.0), SC_(-0.500), SC_(2.5806802181855980649694862685313201e6) } }, { { SC_(8.0), SC_(-0.500), SC_(-1059.9617600414264025178879353865365) } }, { { SC_(9.0), SC_(-0.500), SC_(7.4318457238509742722370782665375996e8) } }, { { SC_(10.), SC_(-0.500), SC_(-42108.858768975491796771277214753871) } }, { { SC_(11.), SC_(-0.500), SC_(3.2699873393475880004602936491973290e11) } }, { { SC_(12.), SC_(-0.500), SC_(-2.4644776094268285475780118302319831e6) } }, { { SC_(13.), SC_(-0.500), SC_(2.0404703892185195041277151739878551e14) } }, { { SC_(14.), SC_(-0.500), SC_(-1.9917964814708338071590970890436861e8) } }, { { SC_(15.), SC_(-0.500), SC_(1.7139949675391451725203269743703670e17) } }, { { SC_(16.), SC_(-0.500), SC_(-2.1239385116043117742696464301184360e10) } }, { { SC_(17.), SC_(-0.500), SC_(1.8648265054229230657699496051237022e20) } }, { { SC_(18.), SC_(-0.500), SC_(-2.8882421804274914449348671586694211e12) } }, { { SC_(19.), SC_(-0.500), SC_(2.5510826564916635359511595679555294e23) } }, { { SC_(20.), SC_(-0.500), SC_(-4.8777294946260987363553987421237456e14) } }, { { SC_(21.), SC_(-0.500), SC_(4.2858188623596794335838558079810850e26) } }, + { { SC_(1.0), SC_(-0.50000023841857910156250000000000000), SC_(8.9348023981506946089014375825505155) } }, { { SC_(2.0), SC_(-0.50000023841857910156250000000000000), SC_(-0.82884275655508842604754532179574729) } }, { { SC_(3.0), SC_(-0.50000023841857910156250000000000000), SC_(193.40909186276501767728859938348815) } }, { { SC_(4.0), SC_(-0.50000023841857910156250000000000000), SC_(-3.4779145857199327369685563062655118) } }, { { SC_(5.0), SC_(-0.50000023841857910156250000000000000), SC_(15371.113559036959283359095676640936) } }, { { SC_(6.0), SC_(-0.50000023841857910156250000000000000), SC_(-44.073205913790411411330389206216025) } }, { { SC_(7.0), SC_(-0.50000023841857910156250000000000000), SC_(2.5806802184594352176701819301926979e6) } }, { { SC_(8.0), SC_(-0.50000023841857910156250000000000000), SC_(-1237.1507698016190706446362670415721) } }, { { SC_(9.0), SC_(-0.50000023841857910156250000000000000), SC_(7.4318457240443082449903207673842183e8) } }, { { SC_(10.), SC_(-0.50000023841857910156250000000000000), SC_(-120071.43228224150936593763797588950) } }, { { SC_(11.), SC_(-0.50000023841857910156250000000000000), SC_(3.2699873394114574294629126382636465e11) } }, { { SC_(12.), SC_(-0.50000023841857910156250000000000000), SC_(-5.1113082699448800419004327980237078e7) } }, { { SC_(13.), SC_(-0.50000023841857910156250000000000000), SC_(2.0404703892677090523475108203530504e14) } }, { { SC_(14.), SC_(-0.50000023841857910156250000000000000), SC_(-4.1064004123360078851054877806228941e10) } }, { { SC_(15.), SC_(-0.50000023841857910156250000000000000), SC_(1.7139949675921973682361201187974158e17) } }, { { SC_(16.), SC_(-0.50000023841857910156250000000000000), SC_(-4.4482167955078907488604509935932075e13) } }, { { SC_(17.), SC_(-0.50000023841857910156250000000000000), SC_(1.8648265054954360818722434334340996e20) } }, { { SC_(18.), SC_(-0.50000023841857910156250000000000000), SC_(-6.0825438456286690418846111378451293e16) } }, { { SC_(19.), SC_(-0.50000023841857910156250000000000000), SC_(2.5510826566134749972709942636451521e23) } }, { { SC_(20.), SC_(-0.50000023841857910156250000000000000), SC_(-1.0218237211995580504353583819436291e20) } }, { { SC_(21.), SC_(-0.50000023841857910156250000000000000), SC_(4.2858188626062237162861505116019247e26) } }, + { { SC_(1.0), SC_(-0.49999976158142089843750000000000000), SC_(8.9348020029496580439061915046847633) } }, { { SC_(2.0), SC_(-0.49999976158142089843750000000000000), SC_(-0.82875053191374905338324754695139008) } }, { { SC_(3.0), SC_(-0.49999976158142089843750000000000000), SC_(193.40909020611360344139301017638823) } }, { { SC_(4.0), SC_(-0.49999976158142089843750000000000000), SC_(-3.4705850676169879410688441586536334) } }, { { SC_(5.0), SC_(-0.49999976158142089843750000000000000), SC_(15371.113538314606395712740903053532) } }, { { SC_(6.0), SC_(-0.49999976158142089843750000000000000), SC_(-42.842641692316412901148012739850716) } }, { { SC_(7.0), SC_(-0.49999976158142089843750000000000000), SC_(2.5806802179540060642078552424908302e6) } }, { { SC_(8.0), SC_(-0.49999976158142089843750000000000000), SC_(-882.77275028362734588789574976519641) } }, { { SC_(9.0), SC_(-0.49999976158142089843750000000000000), SC_(7.4318457238435175594844592942103986e8) } }, { { SC_(10.), SC_(-0.49999976158142089843750000000000000), SC_(35853.714744150436439369297880163123) } }, { { SC_(11.), SC_(-0.49999976158142089843750000000000000), SC_(3.2699873393997058844655604408250598e11) } }, { { SC_(12.), SC_(-0.49999976158142089843750000000000000), SC_(4.6184127480583821271680125577145403e7) } }, { { SC_(13.), SC_(-0.49999976158142089843750000000000000), SC_(2.0404703892667592897735663251491103e14) } }, { { SC_(14.), SC_(-0.49999976158142089843750000000000000), SC_(4.0665644827064704770358560360332387e10) } }, { { SC_(15.), SC_(-0.49999976158142089843750000000000000), SC_(1.7139949675920960909557128308150980e17) } }, { { SC_(16.), SC_(-0.49999976158142089843750000000000000), SC_(4.4439689184846657075559083382657063e13) } }, { { SC_(17.), SC_(-0.49999976158142089843750000000000000), SC_(1.8648265054954223096603082369745267e20) } }, { { SC_(18.), SC_(-0.49999976158142089843750000000000000), SC_(6.0819661971925807709274166342293111e16) } }, { { SC_(19.), SC_(-0.49999976158142089843750000000000000), SC_(2.5510826566134726713883235580466596e23) } }, { { SC_(20.), SC_(-0.49999976158142089843750000000000000), SC_(1.0218139657405687413065653078640133e20) } }, { { SC_(21.), SC_(-0.49999976158142089843750000000000000), SC_(4.2858188626062232387116210610555278e26) } }, + } }; + + boost::array<boost::array<value_type, 3>, 90> small_data = + { { + {{ SC_(0.0), SC_(0.12500000000000000000), SC_(-8.3884926632958548678027429230863430) }}, {{ SC_(0.0), SC_(0.062500000000000000000), SC_(-16.478853490060104366505723782801995) }}, {{ SC_(0.0), SC_(0.031250000000000000000), SC_(-32.526953288606118111369026129964135) }}, {{ SC_(0.0), SC_(0.015625000000000000000), SC_(-64.551802973167856670965920212624596) }}, {{ SC_(0.0), SC_(0.0078125000000000000000), SC_(-128.56443747297672763722041223143322) }}, {{ SC_(0.0), SC_(0.0039062500000000000000), SC_(-256.57080841886464838984737508407824) }}, {{ SC_(0.0), SC_(0.0019531250000000000000), SC_(-512.57400748048652546824732749592750) }}, {{ SC_(0.0), SC_(0.00097656250000000000000), SC_(-1024.5756104293406219086220979096446) }}, {{ SC_(0.0), SC_(0.00048828125000000000000), SC_(-2048.5764127609059633822989920937770) }}, {{ SC_(0.0), SC_(0.00024414062500000000000), SC_(-4096.5768141413027972625364884707221) }}, {{ SC_(0.0), SC_(0.00012207031250000000000), SC_(-8192.5770148851960259755970875167303) }}, {{ SC_(0.0), SC_(0.000061035156250000000000), SC_(-16384.577115270571506673278270921248) }}, {{ SC_(0.0), SC_(0.000030517578125000000000), SC_(-32768.577165466617109315191527852551) }}, {{ SC_(0.0), SC_(0.000015258789062500000000), SC_(-65536.577190565479456940587995127301) }}, {{ SC_(0.0), SC_(7.6293945312500000000e-6), SC_(-131072.57720311512052742189906385878) }}, {{ SC_(0.0), SC_(3.8146972656250000000e-6), SC_(-262144.57720938999353809133982546559) }}, {{ SC_(0.0), SC_(1.9073486328125000000e-6), SC_(-524288.57721252744316244096483807868) }}, {{ SC_(0.0), SC_(9.5367431640625000000e-7), SC_(-1.0485765772140961712543892173131386e6) }}, + {{ SC_(1.0), SC_(0.1250000000), SC_(65.388133444988034473142999334395961) }}, {{ SC_(1.0), SC_(0.06250000000), SC_(257.50642004291541426394984152786018) }}, {{ SC_(1.0), SC_(0.03125000000), SC_(1025.5728544782377088851896549789956) }}, {{ SC_(1.0), SC_(0.01562500000), SC_(4097.6081469812325471140472931934309) }}, {{ SC_(1.0), SC_(0.007812500000), SC_(16385.626348148031663597978251925972) }}, {{ SC_(1.0), SC_(0.003906250000), SC_(65537.635592296074077546680509110271) }}, {{ SC_(1.0), SC_(0.001953125000), SC_(262145.64025088744769438583827382756) }}, {{ SC_(1.0), SC_(0.0009765625000), SC_(1.0485776425893921526170408061678298e6) }}, + {{ SC_(2.0), SC_(0.1250000000), SC_(-1025.7533381181356825956689300565174) }}, {{ SC_(2.0), SC_(0.06250000000), SC_(-8194.0423055503627202407284588855458) }}, {{ SC_(2.0), SC_(0.03125000000), SC_(-65538.212736402744663973874571262931) }}, {{ SC_(2.0), SC_(0.01562500000), SC_(-524290.30560802491992997062359624105) }}, {{ SC_(2.0), SC_(0.007812500000), SC_(-4.1943063541297826472489756741474152e6) }}, {{ SC_(2.0), SC_(0.003906250000), SC_(-3.3554434378935516909394862712904232e7) }}, {{ SC_(2.0), SC_(0.001953125000), SC_(-2.6843545839147764655287988662280398e8) }}, {{ SC_(2.0), SC_(0.0009765625000), SC_(-2.1474836503977839163960630063909364e9) }}, + {{ SC_(3.0), SC_(0.1250000000), SC_(24580.143419063566218511004446647010) }}, {{ SC_(3.0), SC_(0.06250000000), SC_(393221.15036999967974263906424748910) }}, {{ SC_(3.0), SC_(0.03125000000), SC_(6.2914617723523498519444110540563165e6) }}, {{ SC_(3.0), SC_(0.01562500000), SC_(1.0066330211954465631968224525194028e8) }}, {{ SC_(3.0), SC_(0.007812500000), SC_(1.6106127423031841473495039368910042e9) }}, {{ SC_(3.0), SC_(0.003906250000), SC_(2.5769803782397651667126674423858834e10) }}, {{ SC_(3.0), SC_(0.001953125000), SC_(4.1231686042244556536661660289768233e11) }}, {{ SC_(3.0), SC_(0.0009765625000), SC_(6.5970697666624696945083422683684831e12) }}, + {{ SC_(4.0), SC_(0.1250000000), SC_(-786445.98543106378579320120709638297) }}, {{ SC_(4.0), SC_(0.06250000000), SC_(-2.5165842491343080297812493001330106e7) }}, {{ SC_(4.0), SC_(0.03125000000), SC_(-8.0530638940150780088628643019449463e8) }}, {{ SC_(4.0), SC_(0.01562500000), SC_(-2.5769803799064252508878172105001377e10) }}, {{ SC_(4.0), SC_(0.007812500000), SC_(-8.2463372085595426712260437166652246e11) }}, {{ SC_(4.0), SC_(0.003906250000), SC_(-2.6388279066648414875708308182697262e13) }}, {{ SC_(4.0), SC_(0.001953125000), SC_(-8.4442493013199264920484069629201316e14) }}, {{ SC_(4.0), SC_(0.0009765625000), SC_(-2.7021597764223000767391638642998277e16) }}, + {{ SC_(5.0), SC_(0.1250000000), SC_(3.1457340659602645662942019557433307e7) }}, {{ SC_(5.0), SC_(0.06250000000), SC_(2.0132660051504893647288429933363318e9) }}, {{ SC_(5.0), SC_(0.03125000000), SC_(1.2884901898167237155557768979087387e11) }}, {{ SC_(5.0), SC_(0.01562500000), SC_(8.2463372084313301694493047619778287e12) }}, {{ SC_(5.0), SC_(0.007812500000), SC_(5.2776558133259656048321206289799569e14) }}, {{ SC_(5.0), SC_(0.003906250000), SC_(3.3776997205278839283396175959111085e16) }}, {{ SC_(5.0), SC_(0.001953125000), SC_(2.1617278211378382006727785506307164e18) }}, {{ SC_(5.0), SC_(0.0009765625000), SC_(1.3835058055282163724137457865337740e20) }}, + {{ SC_(8.0), SC_(0.1250000000), SC_(-5.4116588069756277838328695722389595e12) }}, {{ SC_(8.0), SC_(0.06250000000), SC_(-2.7707693020189462516270216110672946e15) }}, {{ SC_(8.0), SC_(0.03125000000), SC_(-1.4186338826217368769684713903764732e18) }}, {{ SC_(8.0), SC_(0.01562500000), SC_(-7.2634054790231363002428528775599797e20) }}, {{ SC_(8.0), SC_(0.007812500000), SC_(-3.7188636052598456061623085548707189e23) }}, {{ SC_(8.0), SC_(0.003906250000), SC_(-1.9040581658930409501626172937578262e26) }}, {{ SC_(8.0), SC_(0.001953125000), SC_(-9.7487778093723696648306072338399010e28) }}, {{ SC_(8.0), SC_(0.0009765625000), SC_(-4.9913742383986532683932688751727976e31) }}, + {{ SC_(15.0), SC_(0.1250000000), SC_(3.6807761227792200230957850246407904e26) }}, {{ SC_(15.0), SC_(0.06250000000), SC_(2.4122334398245883325511911077327284e31) }}, {{ SC_(15.0), SC_(0.03125000000), SC_(1.5808813071234422095882610857505513e36) }}, {{ SC_(15.0), SC_(0.01562500000), SC_(1.0360463734364190864757622613687259e41) }}, {{ SC_(15.0), SC_(0.007812500000), SC_(6.7898335129529161251275555560392101e45) }}, {{ SC_(15.0), SC_(0.003906250000), SC_(4.4497852910488231117635948092058560e50) }}, {{ SC_(15.0), SC_(0.001953125000), SC_(2.9162112883417567145253894941611498e55) }}, {{ SC_(15.0), SC_(0.0009765625000), SC_(1.9111682299276536804313592588934511e60) }}, + {{ SC_(22.0), SC_(0.1250000000), SC_(-6.6349292044725783891012472579673570e41) }}, {{ SC_(22.0), SC_(0.06250000000), SC_(-5.5657820204072306855435555719642654e48) }}, {{ SC_(22.0), SC_(0.03125000000), SC_(-4.6689163582644258586596154617085763e55) }}, {{ SC_(22.0), SC_(0.01562500000), SC_(-3.9165709114267828873358919539012256e62) }}, {{ SC_(22.0), SC_(0.007812500000), SC_(-3.2854578080162002342968961931631453e69) }}, {{ SC_(22.0), SC_(0.003906250000), SC_(-2.7560417651987161415024817781137906e76) }}, {{ SC_(22.0), SC_(0.001953125000), SC_(-2.3119353999880071814336850663739568e83) }}, {{ SC_(22.0), SC_(0.0009765625000), SC_(-1.9393919791822596946232062017265105e90) }}, + {{ SC_(35.0), SC_(0.1250000000), SC_(3.3532982327901451846973629635910627e72) }}, {{ SC_(35.0), SC_(0.06250000000), SC_(2.3043689989709229438987285737704404e83) }}, {{ SC_(35.0), SC_(0.03125000000), SC_(1.5835503181594194718369731136519624e94) }}, {{ SC_(35.0), SC_(0.01562500000), SC_(1.0882074924904162473416628106826351e105) }}, {{ SC_(35.0), SC_(0.007812500000), SC_(7.4781049464136054012151819362261716e115) }}, {{ SC_(35.0), SC_(0.003906250000), SC_(5.1389145889443628300269064119650184e126) }}, {{ SC_(35.0), SC_(0.001953125000), SC_(3.5314352154325314429637711743107931e137) }}, {{ SC_(35.0), SC_(0.0009765625000), SC_(2.4267838013160699267233738410387795e148) }} + } }; + using std::ldexp; + + boost::array<boost::array<value_type, 3>, 23> bug_cases = + { { + {{ SC_(171.0), SC_(2.0), SC_(2.073093314165313149880140394410e257) }}, {{ SC_(171.0), SC_(5.0), SC_(7.42911976071332889749264626321716781e188) }}, + {{ SC_(166.0), SC_(2.0), SC_(-4.8129498903508823293044351695484095e247) }}, {{ SC_(166.0), SC_(3.0), SC_(-1.8843912448604502196243093626013895e218) }}, + {{ SC_(171.0), SC_(23.0), SC_(7.53143916217078889612817829861181739e74) }}, {{ SC_(168.0), SC_(150.0), SC_(-6.5266062780306068333215312257902920e-66) }}, + {{ SC_(169.0), SC_(202.0), SC_(9.2734049986021958613510169328055599e-88) }}, + {{ SC_(20.0), SC_(-9.5), SC_(-0.0010307637762451416598018081796345932)}}, {{ SC_(21.0), SC_(-9.5), SC_(4.2858188624279670465725116159418790e26) }}, {{ SC_(22.0), SC_(-9.5), SC_(-0.0041914420015886426448664611125724338) }}, {{ SC_(23.0), SC_(-9.5), SC_(8.6744973773084910367753904944787155e29) }}, {{ SC_(24.0), SC_(-9.5), SC_(-0.020482527998674199369359987617445420) }}, {{ SC_(25.0), SC_(-9.5), SC_(2.0818793705474855280713094147422278e33) }}, {{ SC_(26.0), SC_(-9.5), SC_(-0.11840299831136879082790399023048278) }}, {{ SC_(27.0), SC_(-9.5), SC_(5.8459172724952950454469355072783445e36) }}, {{ SC_(28.0), SC_(-9.5), SC_(-0.79896867888629450211348696225656872) }}, {{ SC_(29.0), SC_(-9.5), SC_(1.8987539301063980537054871851063348e40) }}, {{ SC_(30.0), SC_(-9.5), SC_(-6.2224465669723272001827279817965087) }}, + {{ SC_(1.0), ldexp(value_type(1), 120), SC_(7.5231638452626400509999138382223723e-37) }}, {{ SC_(2.0), ldexp(value_type(1), 120), SC_(-5.6597994242666952296931995568048699e-73) }}, {{ SC_(3.0), ldexp(value_type(1), 120), SC_(8.5159196800163014398201074324946177e-109) }}, {{ SC_(10.0), ldexp(value_type(1), 120), SC_(-2.1075031678562075551498983356333178e-356) }}, {{ SC_(15.0), ldexp(value_type(1), 120), SC_(1.2201582392961399809842378412624410e-531) }}, + } }; + +int main() +{ +#include "expint_data.ipp" +#include "expint_small_data.ipp" +#include "expint_1_data.ipp" + + add_data(data1); + add_data(big_data); + add_data(neg_data); + add_data(neg_double_data); + add_data(small_data); + add_data(bug_cases); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::polygamma(static_cast<int>(v[0]), v[1]); }, [](const std::vector<double>& v){ return v[2]; }); + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_psi_n(static_cast<int>(v[0]), v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return ::psigamma(v[1], static_cast<int>(v[0])); }, [](const std::vector<double>& v){ return v[2]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "polygamma[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "polygamma"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::polygamma(static_cast<int>(v[0]), v[1]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::polygamma(static_cast<int>(v[0]), v[1], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_psi_n(static_cast<int>(v[0]), v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return ::psigamma(v[1], static_cast<int>(v[0])); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "Rmath " R_VERSION_STRING); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_polynomial.cpp b/src/boost/libs/math/reporting/performance/test_polynomial.cpp new file mode 100644 index 000000000..4474ec881 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_polynomial.cpp @@ -0,0 +1,263 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2017 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#define BOOST_CHRONO_HEADER_ONLY + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + + +#include "performance.hpp" +#include "table_helper.hpp" +#include <boost/random.hpp> +#include <boost/math/tools/polynomial.hpp> +#include <boost/multiprecision/cpp_int.hpp> + +unsigned max_reps = 1000; + +template <class T> +struct tester +{ + tester() + { + a.assign(500, T()); + for(int i = 0; i < 500; ++i) + { + b.push_back(generate_random(false)); + c.push_back(generate_random(false)); + small.push_back(generate_random(true)); + } + } + double test_add() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for (unsigned repeats = 0; repeats < max_reps; ++repeats) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] + c[i]; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_subtract() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for (unsigned repeats = 0; repeats < max_reps; ++repeats) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] - c[i]; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_add_int() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for (unsigned repeats = 0; repeats < max_reps; ++repeats) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] + 1; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_subtract_int() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for (unsigned repeats = 0; repeats < max_reps; ++repeats) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] - 1; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_multiply() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for (unsigned repeats = 0; repeats < max_reps; ++repeats) + { + for(unsigned k = 0; k < b.size(); ++k) + a[k] = b[k] * c[k]; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_multiply_int() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for (unsigned repeats = 0; repeats < max_reps; ++repeats) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] * 3; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_divide() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for (unsigned repeats = 0; repeats < max_reps; ++repeats) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] / small[i]; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_divide_int() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for (unsigned repeats = 0; repeats < max_reps; ++repeats) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] / 3; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_gcd() + { + using boost::integer::gcd; + stopwatch<boost::chrono::high_resolution_clock> w; + for (unsigned repeats = 0; repeats < max_reps; ++repeats) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = gcd(b[i], c[i]); + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + + double test_inplace_add() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for (unsigned repeats = 0; repeats < max_reps; ++repeats) + { + for (unsigned i = 0; i < b.size(); ++i) + b[i] += c[i]; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_inplace_subtract() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for (unsigned repeats = 0; repeats < max_reps; ++repeats) + { + for (unsigned i = 0; i < b.size(); ++i) + b[i] -= c[i]; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_inplace_add_int() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for (unsigned repeats = 0; repeats < max_reps; ++repeats) + { + for (unsigned i = 0; i < b.size(); ++i) + b[i] += 1; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_inplace_subtract_int() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for (unsigned repeats = 0; repeats < max_reps; ++repeats) + { + for (unsigned i = 0; i < b.size(); ++i) + b[i] -= 1; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_inplace_multiply() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for (unsigned repeats = 0; repeats < max_reps; ++repeats) + { + for (unsigned k = 0; k < b.size(); ++k) + b[k] *= c[k]; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_inplace_multiply_int() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for (unsigned repeats = 0; repeats < max_reps; ++repeats) + { + for (unsigned i = 0; i < b.size(); ++i) + b[i] *= 3; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_inplace_divide() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for (unsigned repeats = 0; repeats < max_reps; ++repeats) + { + for (unsigned i = 0; i < b.size(); ++i) + a[i] /= small[i]; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_inplace_divide_int() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for (unsigned repeats = 0; repeats < max_reps; ++repeats) + { + for (unsigned i = 0; i < b.size(); ++i) + b[i] /= 3; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } +private: + T generate_random(bool issmall) + { + boost::uniform_int<> ui(2, issmall ? 5 : 40), ui2(1, 10000); + std::size_t len = ui(gen); + std::vector<typename T::value_type> values; + for (std::size_t i = 0; i < len; ++i) + { + values.push_back(static_cast<typename T::value_type>(ui2(gen))); + } + return T(values.begin(), values.end()); + } + std::vector<T> a, b, c, small; + static boost::random::mt19937 gen; +}; + +template <class N> +boost::random::mt19937 tester<N>::gen; + +template <class Number> +void test(const char* type) +{ + std::cout << "Testing type: " << type << std::endl; + tester<boost::math::tools::polynomial<Number> > t; + int count = 500 * max_reps; + std::string table_name = "Polynomial Arithmetic (" + compiler_name() + ", " + platform_name() + ")"; + // + // Now the actual tests: + // + report_execution_time(t.test_add() / count, table_name, "operator +", type); + report_execution_time(t.test_subtract() / count, table_name, "operator -", type); + report_execution_time(t.test_multiply() / count, table_name, "operator *", type); + report_execution_time(t.test_divide() / count, table_name, "operator /", type); + report_execution_time(t.test_add_int() / count, table_name, "operator + (int)", type); + report_execution_time(t.test_subtract_int() / count, table_name, "operator - (int)", type); + report_execution_time(t.test_multiply_int() / count, table_name, "operator * (int)", type); + report_execution_time(t.test_divide_int() / count, table_name, "operator / (int)", type); + report_execution_time(t.test_inplace_add() / count, table_name, "operator +=", type); + report_execution_time(t.test_inplace_subtract() / count, table_name, "operator -=", type); + report_execution_time(t.test_inplace_multiply() / count, table_name, "operator *=", type); + report_execution_time(t.test_inplace_divide() / count, table_name, "operator /=", type); + report_execution_time(t.test_inplace_add_int() / count, table_name, "operator += (int)", type); + report_execution_time(t.test_inplace_subtract_int() / count, table_name, "operator -= (int)", type); + report_execution_time(t.test_inplace_multiply_int() / count, table_name, "operator *= (int)", type); + report_execution_time(t.test_inplace_divide_int() / count, table_name, "operator /= (int)", type); + //report_execution_time(t.test_gcd() / count, table_name, "gcd", type); +} + + +int main() +{ + test<boost::uint64_t>("boost::uint64_t"); + test<double>("double"); + max_reps = 100; + test<boost::multiprecision::cpp_int>("cpp_int"); + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_sn.cpp b/src/boost/libs/math/reporting/performance/test_sn.cpp new file mode 100644 index 000000000..20d629a1e --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_sn.cpp @@ -0,0 +1,135 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/jacobi_elliptic.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + static const boost::array<boost::array<T, 5>, 36> data1 = {{ + {{ SC_(0.0), SC_(0.0), SC_(0.0), SC_(1.0), SC_(1.0) }}, + {{ ldexp(T(1), -25), ldexp(T(1), -25), SC_(2.98023223876953080883700663838486782870427050521881839342311e-8), SC_(0.99999999999999955591079014993741669975171697261290223678373), SC_(0.99999999999999999999999999999960556954738949421406900774443) }}, + {{ -ldexp(T(1), -25), ldexp(T(1), -25), SC_(-2.98023223876953080883700663838486782870427050521881839342311e-8), SC_(0.99999999999999955591079014993741669975171697261290223678373), SC_(0.99999999999999999999999999999960556954738949421406900774443) }}, + {{ SC_(0.25), ldexp(T(1), -25), SC_(0.247403959254522927383635623557663763268693729825996390997241), SC_(0.968912421710644784709721529742747886950140086772629513814665), SC_(0.99999999999999997281786831901333837240938011109848356555885) }}, + {{ SC_(-0.25), ldexp(T(1), -25), SC_(-0.247403959254522927383635623557663763268693729825996390997241), SC_(0.968912421710644784709721529742747886950140086772629513814665), SC_(0.99999999999999997281786831901333837240938011109848356555885) }}, + {{ SC_(1.25), ldexp(T(1), -25), SC_(0.948984619355586147780156037971989352776684194861616269831136), SC_(0.315322362395268865789580233344649598639316847638615703458263), SC_(0.99999999999999960006577747263860127231780811081154547949983) }}, + {{ SC_(-1.25), ldexp(T(1), -25), SC_(-0.948984619355586147780156037971989352776684194861616269831136), SC_(0.315322362395268865789580233344649598639316847638615703458263), SC_(0.99999999999999960006577747263860127231780811081154547949983) }}, + {{ SC_(25.0), ldexp(T(1), -25), SC_(-0.132351750097778560056127137329035522219365438979106560464704), SC_(0.991202811863472859528158119981178957382802975691690722810123), SC_(0.99999999999999999222089563757583834413059580275315226870704) }}, + {{ SC_(-25.0), ldexp(T(1), -25), SC_(0.132351750097778560056127137329035522219365438979106560464704), SC_(0.991202811863472859528158119981178957382802975691690722810123), SC_(0.99999999999999999222089563757583834413059580275315226870704) }}, + {{ ldexp(T(1), -25), SC_(0.5), SC_(2.98023223876953058825550995757802173334628440851964836958219e-8), SC_(0.99999999999999955591079014993744956895610118130967536624417), SC_(0.99999999999999988897769753748438088116649141278818704012037) }}, + {{ -ldexp(T(1), -25), SC_(0.5), SC_(-2.98023223876953058825550995757802173334628440851964836958219e-8), SC_(0.99999999999999955591079014993744956895610118130967536624417), SC_(0.99999999999999988897769753748438088116649141278818704012037) }}, + {{ SC_(0.25), SC_(0.5), SC_(0.246781405136141600483623741101255389743847413013817188632739), SC_(0.969071172865559727608777289021929824625726812182428398055476), SC_(0.992358168465276394946615469032829292963938826683866720698130) }}, + {{ SC_(-0.25), SC_(0.5), SC_(-0.246781405136141600483623741101255389743847413013817188632739), SC_(0.969071172865559727608777289021929824625726812182428398055476), SC_(0.992358168465276394946615469032829292963938826683866720698130) }}, + {{ SC_(1.25), SC_(0.5), SC_(0.928561236426319775700204388269999130782711902203415239399579), SC_(0.371179242693370810357222594552131893184749696381729988511999), SC_(0.885688154799196841458565445994481097477880319663264816077719) }}, + {{ SC_(-1.25), SC_(0.5), SC_(-0.928561236426319775700204388269999130782711902203415239399579), SC_(0.371179242693370810357222594552131893184749696381729988511999), SC_(0.885688154799196841458565445994481097477880319663264816077719) }}, + {{ SC_(25.0), SC_(0.5), SC_(-0.969223071486651608400225080456020493867827336842041561445359), SC_(-0.246184154035106463351874891855925292474628176040625311168501), SC_(0.874729477852721764836147376110255133761608728373832418508248) }}, + {{ SC_(-25.0), SC_(0.5), SC_(0.969223071486651608400225080456020493867827336842041561445359), SC_(-0.246184154035106463351874891855925292474628176040625311168501), SC_(0.874729477852721764836147376110255133761608728373832418508248) }}, + {{ ldexp(T(1), -25), 1 - ldexp(T(1), -9), SC_(2.98023223876953036939562331632512854347569015560128614888589e-8), SC_(0.99999999999999955591079014993754766348947956082687878223721), SC_(0.99999999999999955764381956001984590118394542979655101564079) }}, + {{ -ldexp(T(1), -25), 1 - ldexp(T(1), -9), SC_(-2.98023223876953036939562331632512854347569015560128614888589e-8), SC_(0.99999999999999955591079014993754766348947956082687878223721), SC_(0.99999999999999955764381956001984590118394542979655101564079) }}, + {{ SC_(0.25), 1 - ldexp(T(1), -9), SC_(0.244928335616519632082236089277654937383208524525331032303082), SC_(0.969541185516180906431546524888118346090913555188425579774305), SC_(0.969661908643964623248878987955178702010392829596222190545649) }}, + {{ SC_(-0.25), 1 - ldexp(T(1), -9), SC_(-0.244928335616519632082236089277654937383208524525331032303082), SC_(0.969541185516180906431546524888118346090913555188425579774305), SC_(0.969661908643964623248878987955178702010392829596222190545649) }}, + {{ SC_(1.25), 1 - ldexp(T(1), -9), SC_(0.848768940045053312079390719205939167551169094157365783446523), SC_(0.528763923140371497228677918580246099580380684604621321430057), SC_(0.531415689278260818860813380561526095359692710060403584603095) }}, + {{ SC_(-1.25), 1 - ldexp(T(1), -9), SC_(-0.848768940045053312079390719205939167551169094157365783446523), SC_(0.528763923140371497228677918580246099580380684604621321430057), SC_(0.531415689278260818860813380561526095359692710060403584603095) }}, + {{ SC_(25.0), 1 - ldexp(T(1), -9), SC_(-0.0252326124525503880903568715488227138184083895871544015366337), SC_(-0.999681606947341709011836635135181960590782564534371631099332), SC_(0.999682849652724146508471774051629114156076052044812654903417) }}, + {{ SC_(-25.0), 1 - ldexp(T(1), -9), SC_(0.0252326124525503880903568715488227138184083895871544015366337), SC_(-0.999681606947341709011836635135181960590782564534371631099332), SC_(0.999682849652724146508471774051629114156076052044812654903417) }}, + + // Try modulus > 1 + {{ ldexp(T(1), -25), SC_(1.5), SC_(2.98023223876952981622027157475276613133414644789222481971590e-8), SC_(0.999999999999999555910790149937712522591174851747994454928040), SC_(0.999999999999999000799277837359575841918151654603571877092161) }}, + {{ -ldexp(T(1), -25), SC_(1.5), SC_(-2.98023223876952981622027157475276613133414644789222481971590e-8), SC_(0.999999999999999555910790149937712522591174851747994454928040), SC_(0.999999999999999000799277837359575841918151654603571877092161) }}, + {{ SC_(0.25), SC_(1.5), SC_(0.241830488135945315134822478837394038661484435596992059686086), SC_(0.970318512143270619246031961334217540099946232418710982266812), SC_(0.931888155181641649031244632258710371461078255228024421800363) }}, + {{ SC_(-0.25), SC_(1.5), SC_(-0.241830488135945315134822478837394038661484435596992059686086), SC_(0.970318512143270619246031961334217540099946232418710982266812), SC_(0.931888155181641649031244632258710371461078255228024421800363) }}, + {{ SC_(1.25), SC_(1.5), SC_(0.665875890711922169121186264316618499018039094009893317545462), SC_(0.746062529663971452521312655373498959968622875614588791642250), SC_(-0.0486921028438866868299166778939466685768843580182675008164949) }}, + {{ SC_(-1.25), SC_(1.5), SC_(-0.665875890711922169121186264316618499018039094009893317545462), SC_(0.746062529663971452521312655373498959968622875614588791642250), SC_(-0.0486921028438866868299166778939466685768843580182675008164949) }}, + {{ SC_(25.0), SC_(1.5), SC_(0.618665338981368217712277210270169521641154921220796362724248), SC_(0.785654630447163313102421517325310755764805805534154371583941), SC_(0.372585153048138377269609818284480926623056458773704266654150) }}, + {{ SC_(-25.0), SC_(1.5), SC_(-0.618665338981368217712277210270169521641154921220796362724248), SC_(0.785654630447163313102421517325310755764805805534154371583941), SC_(0.372585153048138377269609818284480926623056458773704266654150) }}, + + // Special Values: + {{ SC_(0.0), SC_(0.5), SC_(0.0), SC_(1.0), SC_(1.0) }}, + {{ SC_(5.0), SC_(0.0), SC_(-0.958924274663138468893154406155993973352461543964601778131672), SC_(0.283662185463226264466639171513557308334422592252215944930359), SC_(1.0) }}, + {{ SC_(5.0), SC_(1.0), SC_(0.999909204262595131210990447534473021089812615990547862736429), SC_(0.0134752822213045573055191382448821552908373539417006868332819), SC_(0.0134752822213045573055191382448821552908373539417006868332819) }}, + }}; + + +int main() +{ +#include "jacobi_elliptic.ipp" +#include "jacobi_elliptic_small.ipp" +#include "jacobi_near_1.ipp" +#include "jacobi_large_phi.ipp" + + add_data(data1); + add_data(jacobi_elliptic); + add_data(jacobi_elliptic_small); + add_data(jacobi_near_1); + add_data(jacobi_large_phi); + + unsigned data_total = data.size(); + + + std::cout << "Screening Boost data:\n"; + screen_data([](const std::vector<double>& v){ return boost::math::jacobi_sn(v[1], v[0]); }, [](const std::vector<double>& v){ return v[2]; }); + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + std::cout << "Screening GSL data:\n"; + screen_data([](const std::vector<double>& v) + { + double s, c, d; + gsl_sf_elljac_e(v[0], v[1] * v[1], &s, &c, &d); + return s; + }, [](const std::vector<double>& v){ return v[2]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "jacobi_sn[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "jacobi_sn"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::jacobi_sn(v[1], v[2]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::jacobi_sn(v[1], v[0], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v) + { + double s, c, d; + gsl_sf_elljac_e(v[0], v[1] * v[1], &s, &c, &d); + return s; + }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_tgamma.cpp b/src/boost/libs/math/reporting/performance/test_tgamma.cpp new file mode 100644 index 000000000..4bd9b87e3 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_tgamma.cpp @@ -0,0 +1,98 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/gamma.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +int main() +{ + typedef double T; +#define SC_(x) static_cast<double>(x) +# include "test_gamma_data.ipp" + + add_data(factorials); + add_data(near_0); + add_data(near_1); + add_data(near_2); + add_data(near_m10); + add_data(near_m55); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::tgamma(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); + + +#if defined(TEST_C99) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return ::tgamma(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); +#endif +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return std::tr1::tgamma(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_gamma(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gammafn(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "tgamma[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "tgamma"; + + double time = exec_timed_test([](const std::vector<double>& v){ return boost::math::tgamma(v[0]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_C99) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + double time = exec_timed_test([](const std::vector<double>& v){ return boost::math::tgamma(v[0], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_C99) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_C99) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return ::tgamma(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "math.h"); +#endif +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::tgamma(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_gamma(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gammafn(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "Rmath " R_VERSION_STRING); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_trigamma.cpp b/src/boost/libs/math/reporting/performance/test_trigamma.cpp new file mode 100644 index 000000000..1ee1b2092 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_trigamma.cpp @@ -0,0 +1,84 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/trigamma.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +int main() +{ + typedef double T; +#define SC_(x) static_cast<double>(x) + boost::array<boost::array<T, 3>, 659> data = + { { + { SC_(1.0), SC_(1.6449340668482264364724151666460252) }, { SC_(2.0), SC_(0.64493406684822643647241516664602519) }, { SC_(3.0), SC_(0.39493406684822643647241516664602519) }, { SC_(4.0), SC_(0.28382295573711532536130405553491408) }, { SC_(5.0), SC_(0.22132295573711532536130405553491408) }, { SC_(6.0), SC_(0.18132295573711532536130405553491408) }, { SC_(7.0), SC_(0.15354517795933754758352627775713630) }, { SC_(8.0), SC_(0.13313701469403142513454668592040161) }, { SC_(9.0), SC_(0.11751201469403142513454668592040161) }, { SC_(10.0), SC_(0.10516633568168574612220100690805593) }, { SC_(11.0), SC_(0.095166335681685746122201006908055927) }, { SC_(12.0), SC_(0.086901872871768390750300180461774936) }, { SC_(13.0), SC_(0.079957428427323946305855736017330491) }, { SC_(14.0), SC_(0.074040268664010336838400114715555343) }, { SC_(15.0), SC_(0.068938227847683806226155216756371670) }, { SC_(16.0), SC_(0.064493783403239361781710772311927225) }, { SC_(17.0), SC_(0.060587533403239361781710772311927225) }, { SC_(18.0), SC_(0.057127325790782614376866481654487779) }, { SC_(19.0), SC_(0.054040906037696194623780061901401359) }, { SC_(20.0), SC_(0.051270822935203119831536294588381969) }, { SC_(21.0), SC_(0.048770822935203119831536294588381969) }, { SC_(22.0), SC_(0.046503249239057995114983006606522558) }, { SC_(23.0), SC_(0.044437133536578656272007799994952310) }, { SC_(24.0), SC_(0.042546774368336690298472828350339834) }, { SC_(25.0), SC_(0.040810663257225579187361717239228723) }, { SC_(26.0), SC_(0.039210663257225579187361717239228723) }, { SC_(27.0), SC_(0.037731373316397176820497811913784936) }, { SC_(28.0), SC_(0.036359631203914323596903847579079860) }, { SC_(29.0), SC_(0.035084120999832690943842623089283942) }, { SC_(30.0), SC_(0.033895060357739944213759388844337450) }, { SC_(31.0), SC_(0.032783949246628833102648277733226339) }, { SC_(32.0), SC_(0.031743366520302090126581680438741427) }, { SC_(33.0), SC_(0.030766804020302090126581680438741427) }, { SC_(34.0), SC_(0.029848530374755717307481588611376873) }, { SC_(35.0), SC_(0.028983478471641530456270515947017011) }, { SC_(36.0), SC_(0.028167151941029285558311332273547623) }, { SC_(37.0), SC_(0.027395547002757680620039727335276018) }, { SC_(38.0), SC_(0.026665086812838031240930888766977990) }, { SC_(39.0), SC_(0.025972566037214762542869946938723143) }, { SC_(40.0), SC_(0.025315103841291028157597100127414793) }, { SC_(41.0), SC_(0.024690103841291028157597100127414793) }, { SC_(42.0), SC_(0.024095219843670564148078956165487369) }, { SC_(43.0), SC_(0.023528326419634282968940634170022516) }, { SC_(44.0), SC_(0.022987493536995018501661023569698017) }, { SC_(45.0), SC_(0.022470964611375183790917221916805455) }, { SC_(46.0), SC_(0.021977137450881356630423394756311627) }, { SC_(47.0), SC_(0.021504547658820865137039651845158508) }, { SC_(48.0), SC_(0.021051854132338293837809230840178880) }, { SC_(49.0), SC_(0.020617826354560516060031453062401102) }, { SC_(50.0), SC_(0.020201333226697125805970645065733047) }, { SC_(51.0), SC_(0.019801333226697125805970645065733047) }, { SC_(52.0), SC_(0.019416865714201931649876834992684219) }, { SC_(53.0), SC_(0.019047043228994831058160858661323273) }, { SC_(54.0), SC_(0.018691044652989135080944767525687815) }, { SC_(55.0), SC_(0.018348109124868421775046276442011546) }, { SC_(56.0), SC_(0.018017530612471727560170243384160307) }, { SC_(57.0), SC_(0.017698653061451319396904937261711327) }, { SC_(58.0), SC_(0.017390866050063199975544518671375839) }, { SC_(59.0), SC_(0.017093600889540013293023710110139216) }, { SC_(60.0), SC_(0.016806327117635388185296045645904801) }, { SC_(61.0), SC_(0.016528549339857610407518267868127023) }, { SC_(62.0), SC_(0.016259804378825629757155462170733849) }, { SC_(63.0), SC_(0.015999658697243944013138812847112621) }, { SC_(64.0), SC_(0.015747706064338930155744003071350465) }, { SC_(65.0), SC_(0.015503565439338930155744003071350465) }, { SC_(66.0), SC_(0.015266879048806385777045778219279459) }, { SC_(67.0), SC_(0.015037310637419792572270755262438320) }, { SC_(68.0), SC_(0.014814543874220861852734110129892096) }, { SC_(69.0), SC_(0.014598280898442315139931341963802130) }, { SC_(70.0), SC_(0.014388240990859874476205234003289633) }, { SC_(71.0), SC_(0.014184159358206813251715438084922286) }, { SC_(72.0), SC_(0.013985786019583524221761063952805643) }, { SC_(73.0), SC_(0.013792884785015622987193162718237741) }, { SC_(74.0), SC_(0.013605232317385673653359422804557876) }, { SC_(75.0), SC_(0.013422617269905761308582213162483370) }, { SC_(76.0), SC_(0.013244839492127983530804435384705592) }, { SC_(77.0), SC_(0.013071709298222166356289199927641880) }, { SC_(78.0), SC_(0.012903046791897322369107550408330023) }, { SC_(79.0), SC_(0.012738681242916388772789338705502935) }, { SC_(80.0), SC_(0.012578450510661942369969277817824679) }, { SC_(81.0), SC_(0.012422200510661942369969277817824679) }, { SC_(82.0), SC_(0.012269784720386069789569948447301893) }, { SC_(83.0), SC_(0.012121063720980953787190412456820037) }, { SC_(84.0), SC_(0.011975904771931744903462730645236352) }, { SC_(85.0), SC_(0.011834181415922674608678150146370139) }, { SC_(86.0), SC_(0.011695773111424404712484378520072561) }, { SC_(87.0), SC_(0.011560564890764588595664475869991436) }, { SC_(88.0), SC_(0.011428447041643172292321894287219604) }, { SC_(89.0), SC_(0.011299314810238213614635943873996463) }, { SC_(90.0), SC_(0.011173068124213721757547192453721246) }, { SC_(91.0), SC_(0.011049611334090264967423735663597789) }, { SC_(92.0), SC_(0.010928852971573660692577702575806459) }, { SC_(93.0), SC_(0.010810705523558537819231766848018180) }, { SC_(94.0), SC_(0.010695085220633344155224367148630967) }, { SC_(95.0), SC_(0.010581911839012701330416761897386060) }, { SC_(96.0), SC_(0.010471108514912978338727011204865284) }, { SC_(97.0), SC_(0.010362601570468533894282566760420840) }, { SC_(98.0), SC_(0.010256320350360127049771991779020053) }, { SC_(99.0), SC_(0.010152197068394279486256789779853040) }, { SC_(100.0), SC_(0.010050166663333571395245668465701423) }, { SC_(101.0), SC_(0.0099501666633335713952456684657014225) }, { SC_(102.0), SC_(0.0098521370583928793062347871795530057) }, { SC_(103.0), SC_(0.0097560201802690807672113346612907989) }, { SC_(104.0), SC_(0.0096617605893557053312607266869294076) }, { SC_(105.0), SC_(0.0095693049680539301833317326040891709) }, { SC_(106.0), SC_(0.0094786020202081251946696010848147945) }, { SC_(107.0), SC_(0.0093896023762067012003655783009059301) }, { SC_(108.0), SC_(0.0093022585033793800369451922409880334) }, { SC_(109.0), SC_(0.0092165246213492017104705694700689662) }, { SC_(110.0), SC_(0.0091323566220225457050838175131629818) }, { SC_(111.0), SC_(0.0090497119939233721513648092487001719) }, { SC_(112.0), SC_(0.0089685497505989666647971605188892799) }, { SC_(113.0), SC_(0.0088888303628438646239808339882770350) }, { SC_(114.0), SC_(0.0088105156945064850327834027093985011) }, { SC_(115.0), SC_(0.0087335689416594551774432980618146291) }, { SC_(116.0), SC_(0.0086579545749297765385018991960301301) }, { SC_(117.0), SC_(0.0085836382847989798678716970557209743) }, { SC_(118.0), SC_(0.0085105869296963427139524918544644910) }, { SC_(119.0), SC_(0.0084387684867201864370205757384058871) }, { SC_(120.0), SC_(0.0083681520048333140410033453168254903) }, { SC_(121.0), SC_(0.0082987075603888695965589008723810458) }, { SC_(122.0), SC_(0.0082304062148523625273696378438993847) }, { SC_(123.0), SC_(0.0081632199745943673647789364195510913) }, { SC_(124.0), SC_(0.0080971217526365380303880315348924886) }, { SC_(125.0), SC_(0.0080320853322411165943838692039871816) }, { SC_(126.0), SC_(0.0079680853322411165943838692039871816) }, { SC_(127.0), SC_(0.0079050971740148631300351667600466424) }, { SC_(128.0), SC_(0.0078430970500146151295391657680446584) }, { SC_(129.0), SC_(0.0077820618937646151295391657680446584) }, { SC_(130.0), SC_(0.0077219693512491412998414312568974918) }, { SC_(131.0), SC_(0.0076627977536160052051668750438797403) }, { SC_(132.0), SC_(0.0076045260911254743503215863077920997) }, { SC_(133.0), SC_(0.0075471339882788260491278305685818151) }, { SC_(134.0), SC_(0.0074906016800646816656126516438263173) }, { SC_(135.0), SC_(0.0074349099892649489857284903606897613) }, { SC_(136.0), SC_(0.0073800403047656348567847317873015583) }, { SC_(137.0), SC_(0.0073259745608209981785840397457790669) }, { SC_(138.0), SC_(0.0072726952172225113119422367727916941) }, { SC_(139.0), SC_(0.0072201852403269011460107097826635698) }, { SC_(140.0), SC_(0.0071684280849001633995172570628250521) }, { SC_(141.0), SC_(0.0071174076767368980933948080832332154) }, { SC_(142.0), SC_(0.0070671083960166123934803168604577010) }, { SC_(143.0), SC_(0.0070175150613607901359917233274285402) }, { SC_(144.0), SC_(0.0069686129145565454296491148869180018) }, { SC_(145.0), SC_(0.0069203876059145701210071395782760264) }, { SC_(146.0), SC_(0.0068728251802308602518038102084781668) }, { SC_(147.0), SC_(0.0068259120633233729183453752300582005) }, { SC_(148.0), SC_(0.0067796350491163295567830632304284166) }, { SC_(149.0), SC_(0.0067339812872463514705887608199097899) }, { SC_(150.0), SC_(0.0066889382711659947299014043945235460) }, { SC_(151.0), SC_(0.0066444938267215502854569599500791016) }, { SC_(152.0), SC_(0.0066006361011831967044736697435092143) }, { SC_(153.0), 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SC_(-1.9990234375000000000000000000000000), SC_(1.0485788947897014608301106052600290e6) }, { SC_(-2.9990234375000000000000000000000000), SC_(1.0485790059731858715118158380121717e6) }, { SC_(-3.9990234375000000000000000000000000), SC_(1.0485790685037146291468005792240191e6) }, { SC_(-4.9990234375000000000000000000000000), SC_(1.0485791085193442079759033312640482e6) }, { SC_(-5.9990234375000000000000000000000000), SC_(1.0485791363061664391826604906353499e6) }, { SC_(-6.9990234375000000000000000000000000), SC_(1.0485791567200251382893770121774963e6) }, { SC_(-7.9990234375000000000000000000000000), SC_(1.0485791723488405341606371612842196e6) }, { SC_(-8.9990234375000000000000000000000000), SC_(1.0485791846971991664479297252200281e6) }, { SC_(-9.9990234375000000000000000000000000), SC_(1.0485791946991525775874820980861239e6) }, { SC_(-10.999023437500000000000000000000000), SC_(1.0485792029650829946601990955306663e6) }, { SC_(-11.999023437500000000000000000000000), SC_(1.0485792099106578577646272234105154e6) }, { SC_(-12.999023437500000000000000000000000), SC_(1.0485792158287067176193079741367670e6) }, { SC_(-13.999023437500000000000000000000000), SC_(1.0485792209314593886753540118883170e6) }, { SC_(-14.999023437500000000000000000000000), SC_(1.0485792253764825933424418561922499e6) }, { SC_(-15.999023437500000000000000000000000), SC_(1.0485792292832094741599436510420027e6) }, { SC_(-16.999023437500000000000000000000000), SC_(1.0485792327438146631093348182751076e6) }, { SC_(-17.999023437500000000000000000000000), SC_(1.0485792358305693414284737055180265e6) }, { SC_(-18.999023437500000000000000000000000), SC_(1.0485792386009372194851110066962854e6) }, { SC_(-19.999023437500000000000000000000000), SC_(1.0485792411011813779926686635901794e6) }, + { SC_(-1.0009765625000000000000000000000000), SC_(1.0485786453346669585098368000725210e6)}, { SC_(-2.0009765625000000000000000000000000), SC_(1.0485788950907050310998538089289880e6) }, { SC_(-3.0009765625000000000000000000000000), SC_(1.0485790061295134851948027406034007e6) }, { SC_(-4.0009765625000000000000000000000000), SC_(1.0485790685990070793038292171104670e6) }, { SC_(-5.0009765625000000000000000000000000), SC_(1.0485791085833866557487460417106589e6) }, { SC_(-6.0009765625000000000000000000000000), SC_(1.0485791363521243952566116253382220e6) }, { SC_(-7.0009765625000000000000000000000000), SC_(1.0485791567545946099550113256489222e6) }, { SC_(-8.0009765625000000000000000000000000), SC_(1.0485791723757806110676477942302156e6) }, { SC_(-9.0009765625000000000000000000000000), SC_(1.0485791847187808756018779739003157e6) }, { SC_(-10.000976562500000000000000000000000), SC_(1.0485791947168280366669245397313590e6) }, { SC_(-11.000976562500000000000000000000000), SC_(1.0485792029798236302523575048817360e6) }, { SC_(-12.000976562500000000000000000000000), SC_(1.0485792099231379319842508274674963e6) }, { SC_(-13.000976562500000000000000000000000), SC_(1.0485792158394087991015231685011609e6) }, { SC_(-14.000976562500000000000000000000000), SC_(1.0485792209407379096480891892744762e6) }, { SC_(-15.000976562500000000000000000000000), SC_(1.0485792253846037068979581619480639e6) }, { SC_(-16.000976562500000000000000000000000), SC_(1.0485792292903769133919482794005111e6) }, { SC_(-17.000976562500000000000000000000000), SC_(1.0485792327501870178663179616292787e6) }, { SC_(-18.000976562500000000000000000000000), SC_(1.0485792358362719002281530732844340e6) }, { SC_(-19.000976562500000000000000000000000), SC_(1.0485792386060702710649859237414384e6) }, { SC_(-20.000976562500000000000000000000000), SC_(1.0485792411058261483202152741904670e6) }, + } }; + + add_data(data); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::trigamma(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_psi_1(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return ::trigamma(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "trigamma[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "trigamma"; + + double time = exec_timed_test([](const std::vector<double>& v){ return boost::math::trigamma(v[0]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + double time = exec_timed_test([](const std::vector<double>& v){ return boost::math::trigamma(v[0], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_psi_1(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return ::trigamma(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "Rmath " R_VERSION_STRING); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_yn.cpp b/src/boost/libs/math/reporting/performance/test_yn.cpp new file mode 100644 index 000000000..6278be167 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_yn.cpp @@ -0,0 +1,135 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/bessel.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) +static const boost::array<boost::array<typename table_type<T>::type, 3>, 9> y0_data = { { + { { SC_(0.0), SC_(1.0), SC_(0.0882569642156769579829267660235151628278175230906755467110438) } }, + { { SC_(0.0), SC_(2.0), SC_(0.510375672649745119596606592727157873268139227085846135571839) } }, + { { SC_(0.0), SC_(4.0), SC_(-0.0169407393250649919036351344471532182404925898980149027169321) } }, + { { SC_(0.0), SC_(8.0), SC_(0.223521489387566220527323400498620359274814930781423577578334) } }, + { { SC_(0.0), SC_(1e-05), SC_(-7.40316028370197013259676050746759072070960287586102867247159) } }, + { { SC_(0.0), SC_(1e-10), SC_(-14.7325162726972420426916696426209144888762342592762415255386) } }, + { { SC_(0.0), SC_(1e-20), SC_(-29.3912282502857968601858410375186700783698345615477536431464) } }, + { { SC_(0.0), SC_(1e+03), SC_(0.00471591797762281339977326146566525500985900489680197718528000) } }, + { { SC_(0.0), SC_(1e+05), SC_(0.00184676615886506410434074102431546125884886798090392516843524) } } + } }; +static const boost::array<boost::array<typename table_type<T>::type, 3>, 9> y1_data = { { + { { SC_(1.0), SC_(1.0), SC_(-0.781212821300288716547150000047964820549906390716444607843833) } }, + { { SC_(1.0), SC_(2.0), SC_(-0.107032431540937546888370772277476636687480898235053860525795) } }, + { { SC_(1.0), SC_(4.0), SC_(0.397925710557100005253979972450791852271189181622908340876586) } }, + { { SC_(1.0), SC_(8.0), SC_(-0.158060461731247494255555266187483550327344049526705737651263) } }, + { { SC_(1.0), SC_(1e-10), SC_(-6.36619772367581343150789184284462611709080831190542841855708e9) } }, + { { SC_(1.0), SC_(1e-20), SC_(-6.36619772367581343075535053490057448139324059868649274367256e19) } }, + { { SC_(1.0), SC_(1e+01), SC_(0.249015424206953883923283474663222803260416543069658461246944) } }, + { { SC_(1.0), SC_(1e+03), SC_(-0.0247843312923517789148623560971412909386318548648705287583490) } }, + { { SC_(1.0), SC_(1e+05), SC_(0.00171921035008825630099494523539897102954509504993494957572726) } } + } }; +static const boost::array<boost::array<typename table_type<T>::type, 3>, 10> yn_data = { { + { { SC_(2.0), SC_(1e-20), SC_(-1.27323954473516268615107010698011489627570899691226996904849e40) } }, + { { SC_(5.0), SC_(10.0), SC_(0.135403047689362303197029014762241709088405766746419538495983) } }, + { { SC_(-5.0), SC_(1e+06), SC_(0.000331052088322609048503535570014688967096938338061796192422114) } }, + { { SC_(10.0), SC_(10.0), SC_(-0.359814152183402722051986577343560609358382147846904467526222) } }, + { { SC_(10.0), SC_(1e-10), SC_(-1.18280490494334933900960937719565669877576135140014365217993e108) } }, + { { SC_(-10.0), SC_(1e+06), SC_(0.000725951969295187086245251366365393653610914686201194434805730) } }, + { { SC_(1e+02), SC_(5.0), SC_(-5.08486391602022287993091563093082035595081274976837280338134e115) } }, + { { SC_(1e+03), SC_(1e+05), SC_(0.00217254919137684037092834146629212647764581965821326561261181) } }, + { { SC_(-1e+03), SC_(7e+02), SC_(-1.88753109980945889960843803284345261796244752396992106755091e77) } }, + { { SC_(-25.0), SC_(8.0), SC_(3.45113613777297661997458045843868931827873456761831907587263e8) } } + } }; + +int main() +{ +#include "bessel_y01_data.ipp" +#include "bessel_yn_data.ipp" + + add_data(y0_data); + add_data(y1_data); + add_data(yn_data); + add_data(bessel_y01_data); + add_data(bessel_yn_data); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::cyl_neumann(static_cast<int>(v[0]), v[1]); }, [](const std::vector<double>& v){ return v[2]; }); + + +#if defined(TEST_C99) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return ::yn(static_cast<int>(v[0]), v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return std::tr1::cyl_neumann(static_cast<int>(v[0]), v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_bessel_Yn(static_cast<int>(v[0]), v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return bessel_y(v[1], static_cast<int>(v[0])); }, [](const std::vector<double>& v){ return v[2]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "cyl_neumann (integer order)[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "cyl_neumann (integer order)"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::cyl_neumann(static_cast<int>(v[0]), v[1]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_C99) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::cyl_neumann(static_cast<int>(v[0]), v[1], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_C99) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_C99) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return ::yn(static_cast<int>(v[0]), v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "math.h"); +#endif +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::cyl_neumann(static_cast<int>(v[0]), v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_bessel_Yn(static_cast<int>(v[0]), v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return bessel_y(v[1], static_cast<int>(v[0])); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "Rmath " R_VERSION_STRING); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_ys.cpp b/src/boost/libs/math/reporting/performance/test_ys.cpp new file mode 100644 index 000000000..1c519ed66 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_ys.cpp @@ -0,0 +1,80 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/bessel.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) + +int main() +{ +#include "sph_neumann_data.ipp" + + add_data(sph_neumann_data); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::sph_neumann(static_cast<int>(v[0]), v[1]); }, [](const std::vector<double>& v){ return v[2]; }); + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return std::tr1::sph_neumann(static_cast<int>(v[0]), v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_bessel_yl(static_cast<int>(v[0]), v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "sph_neumann[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "sph_neumann"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::sph_neumann(static_cast<int>(v[0]), v[1]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::sph_neumann(static_cast<int>(v[0]), v[1], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::sph_neumann(static_cast<int>(v[0]), v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_bessel_yl(static_cast<int>(v[0]), v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_yv.cpp b/src/boost/libs/math/reporting/performance/test_yv.cpp new file mode 100644 index 000000000..2c9a50689 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_yv.cpp @@ -0,0 +1,118 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/bessel.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +typedef double T; +#define SC_(x) static_cast<double>(x) +static const boost::array<boost::array<T, 3>, 11> yv_data = { { + //SC_(2.25), {{ SC_(1.0) / 1024, SC_(-1.01759203636941035147948317764932151601257765988969544340275e7) }}, + { { SC_(0.5), T(1) / (1024 * 1024), SC_(-817.033790261762580469303126467917092806755460418223776544122) } }, + { { SC_(5.5), SC_(3.125), SC_(-2.61489440328417468776474188539366752698192046890955453259866) } }, + { { SC_(-5.5), SC_(3.125), SC_(-0.0274994493896489729948109971802244976377957234563871795364056) } }, + { { SC_(-5.5), SC_(1e+04), SC_(-0.00759343502722670361395585198154817047185480147294665270646578) } }, + { { T(-10486074) / (1024 * 1024), T(1) / 1024, SC_(-1.50382374389531766117868938966858995093408410498915220070230e38) } }, + { { T(-10486074) / (1024 * 1024), SC_(1e+02), SC_(0.0583041891319026009955779707640455341990844522293730214223545) } }, + { { SC_(141.75), SC_(1e+02), SC_(-5.38829231428696507293191118661269920130838607482708483122068e9) } }, + { { SC_(141.75), SC_(2e+04), SC_(-0.00376577888677186194728129112270988602876597726657372330194186) } }, + { { SC_(-141.75), SC_(1e+02), SC_(-3.81009803444766877495905954105669819951653361036342457919021e9) } }, + { { SC_(8.5), boost::math::constants::pi<T>() * 4, SC_(0.257086543428224355151772807588810984369026142375675714560864) } }, + { { SC_(-8.5), boost::math::constants::pi<T>() * 4, SC_(0.0436807946352780974532519564114026730332781693877984686758680) } }, + } }; +static const boost::array<boost::array<T, 3>, 7> yv_large_data = { { + // Bug report https://svn.boost.org/trac/boost/ticket/5560: + { { SC_(0.5), static_cast<T>(std::ldexp(0.5, -683)), SC_(-7.14823099969225685526188875418476476336424046896822867989728e102) } }, + { { SC_(-0.5), static_cast<T>(std::ldexp(0.5, -683)), SC_(8.90597649117647254543282704099383321071493400182381039079219e-104) } }, + { { SC_(0.0), static_cast<T>(std::ldexp(1.0, -53)), SC_(-23.4611779112897561252987257324561640034037313549011724328997) } }, + { { SC_(1.0), static_cast<T>(std::ldexp(1.0, -53)), SC_(-5.73416113922265864550047623401604244038331542638719289100990e15) } }, + { { SC_(2.0), static_cast<T>(std::ldexp(1.0, -53)), SC_(-1.03297463879542177245046832533417970379386617249046560049244e32) } }, + { { SC_(3.0), static_cast<T>(std::ldexp(1.0, -53)), SC_(-3.72168335868978735639260528876490232745489151562358712422544e48) } }, + { { SC_(10.0), static_cast<T>(std::ldexp(1.0, -53)), SC_(-4.15729476804920974669173904282420477878640623992500096231384e167) } }, + } }; + +int main() +{ +#include "bessel_yv_data.ipp" + + add_data(yv_data); + add_data(yv_large_data); + add_data(bessel_yv_data); + + unsigned data_total = data.size(); + + std::cout << "Screening boost data:\n"; + screen_data([](const std::vector<double>& v){ return boost::math::cyl_neumann(v[0], v[1]); }, [](const std::vector<double>& v){ return v[2]; }); + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + std::cout << "Screening libstdc++ data:\n"; + screen_data([](const std::vector<double>& v){ return std::tr1::cyl_neumann(v[0], v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + std::cout << "Screening GSL data:\n"; + screen_data([](const std::vector<double>& v){ return gsl_sf_bessel_Ynu(v[0], v[1]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + std::cout << "Screening Rmath data:\n"; + screen_data([](const std::vector<double>& v){ return bessel_y(v[1], v[0]); }, [](const std::vector<double>& v){ return v[2]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "cyl_neumann[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "cyl_neumann"; + + double time; + + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::cyl_neumann(v[0], v[1]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + time = exec_timed_test([](const std::vector<double>& v){ return boost::math::cyl_neumann(v[0], v[1], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::cyl_neumann(v[0], v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_bessel_Ynu(v[0], v[1]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif +#if defined(TEST_RMATH) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return bessel_y(v[1], v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "Rmath " R_VERSION_STRING); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/test_zeta.cpp b/src/boost/libs/math/reporting/performance/test_zeta.cpp new file mode 100644 index 000000000..bf54534e4 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/test_zeta.cpp @@ -0,0 +1,82 @@ +// Copyright John Maddock 2015. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4224) +#endif + +#include <boost/math/special_functions/zeta.hpp> +#include <boost/array.hpp> +#include <boost/lexical_cast.hpp> +#include "../../test/table_type.hpp" +#include "table_helper.hpp" +#include "performance.hpp" +#include <iostream> + +int main() +{ + typedef double T; +#define SC_(x) static_cast<double>(x) +#include "zeta_data.ipp" +#include "zeta_neg_data.ipp" +#include "zeta_1_up_data.ipp" +#include "zeta_1_below_data.ipp" + + add_data(zeta_data); + add_data(zeta_neg_data); + add_data(zeta_1_up_data); + add_data(zeta_1_below_data); + + unsigned data_total = data.size(); + + screen_data([](const std::vector<double>& v){ return boost::math::zeta(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return std::tr1::riemann_zeta(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + screen_data([](const std::vector<double>& v){ return gsl_sf_zeta(v[0]); }, [](const std::vector<double>& v){ return v[1]; }); +#endif + + unsigned data_used = data.size(); + std::string function = "zeta[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)"; + std::string function_short = "zeta"; + + double time = exec_timed_test([](const std::vector<double>& v){ return boost::math::zeta(v[0]); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name()); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name()); + // + // Boost again, but with promotion to long double turned off: + // +#if !defined(COMPILER_COMPARISON_TABLES) + if(sizeof(long double) != sizeof(double)) + { + double time = exec_timed_test([](const std::vector<double>& v){ return boost::math::zeta(v[0], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); }); + std::cout << time << std::endl; +#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH) || defined(TEST_LIBSTDCXX)) + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>"); +#endif + report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>"); + } +#endif + + +#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::riemann_zeta(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath"); +#endif +#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES) + time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_zeta(v[0]); }); + std::cout << time << std::endl; + report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION); +#endif + + return 0; +} + diff --git a/src/boost/libs/math/reporting/performance/third_party/dcdflib/readme.txt b/src/boost/libs/math/reporting/performance/third_party/dcdflib/readme.txt new file mode 100644 index 000000000..aec2d85f8 --- /dev/null +++ b/src/boost/libs/math/reporting/performance/third_party/dcdflib/readme.txt @@ -0,0 +1,6 @@ +Add the C source files for DCDFLIB here if you want them to be built and tested for performance comparisons. + +Copyright 2015 John Maddock and Paul A. Bristow. +Distributed under the Boost Software License, Version 1.0. +(See accompanying file LICENSE_1_0.txt or copy at +http://www.boost.org/LICENSE_1_0.txt). |