diff options
Diffstat (limited to 'modules/fdlibm')
89 files changed, 12341 insertions, 0 deletions
diff --git a/modules/fdlibm/moz.build b/modules/fdlibm/moz.build new file mode 100644 index 0000000000..4ee1eb1a3e --- /dev/null +++ b/modules/fdlibm/moz.build @@ -0,0 +1,10 @@ +# -*- Mode: python; indent-tabs-mode: nil; tab-width: 40 -*- +# vim: set filetype=python: +# This Source Code Form is subject to the terms of the Mozilla Public +# License, v. 2.0. If a copy of the MPL was not distributed with this +# file, You can obtain one at http://mozilla.org/MPL/2.0/. + +with Files('**'): + BUG_COMPONENT = ('Core', 'JavaScript Engine') + +DIRS += ['src'] diff --git a/modules/fdlibm/moz.yaml b/modules/fdlibm/moz.yaml new file mode 100644 index 0000000000..52fda3d63b --- /dev/null +++ b/modules/fdlibm/moz.yaml @@ -0,0 +1,113 @@ +# Version of this schema +schema: 1 + +bugzilla: + product: "Core" + component: "JavaScript Engine" + +origin: + name: "fdlibm" + description: "The fdlibm library imported from freebsd" + + url: "https://github.com/freebsd/freebsd/tree/master/lib/msun/src" + + # Human-readable identifier for this version/release + # Generally "version NNN", "tag SSS", "bookmark SSS" + release: "commit 369ea0520a3061c07400d7cd32172efb6af39815 (2022-08-04T17:33:34Z)" + + # Revision to pull in + # Must be a long or short commit SHA (long preferred) + revision: bd5e624a861433dee76fe00a8acedc9564425332 + + license: "BSD-2-Clause" + license-file: LICENSE + +vendoring: + url: https://github.com/freebsd/freebsd/ + flavor: individual-files + source-hosting: github + vendor-directory: modules/fdlibm/src + + individual-files-default-upstream: 'lib/msun/src/' + individual-files-default-destination: '{vendor_dir}/' + individual-files-list: + - math_private.h + - math.h + - e_acos.c + - e_acosf.c + - e_acosh.c + - e_asin.c + - e_asinf.c + - e_atan2.c + - e_atanh.c + - e_cosh.c + - e_exp.c + - e_expf.c + - e_hypot.c + - e_log10.c + - e_log2.c + - e_log.c + - e_logf.c + - e_pow.c + - e_powf.c + - e_rem_pio2.c + - e_rem_pio2f.c + - e_sinh.c + - e_sqrtf.c + - k_cos.c + - k_cosf.c + - k_exp.c + - k_expf.c + - k_log.h + - k_rem_pio2.c + - k_sin.c + - k_sinf.c + - k_tan.c + - k_tanf.c + - s_asinh.c + - s_atan.c + - s_atanf.c + - s_cbrt.c + - s_ceil.c + - s_ceilf.c + - s_copysign.c + - s_cos.c + - s_cosf.c + - s_expm1.c + - s_exp2.c + - s_exp2f.c + - s_fabs.c + - s_fabsf.c + - s_floor.c + - s_floorf.c + - s_log1p.c + - s_nearbyint.c + - s_rint.c + - s_rintf.c + - s_scalbn.c + - s_scalbnf.c + - s_sin.c + - s_sinf.c + - s_tan.c + - s_tanf.c + - s_tanh.c + - s_trunc.c + - s_truncf.c + + update-actions: + - action: 'move-file' + from: '{vendor_dir}/math.h' + to: '{vendor_dir}/fdlibm.h' + - action: 'run-script' + script: '{yaml_dir}/rename_c_to_cpp.sh' + cwd: '{vendor_dir}' + + patches: + - 'patches/*.patch' + +updatebot: + maintainer-phab: arai + maintainer-bz: arai.unmht@gmail.com + tasks: + - type: vendoring + enabled: false diff --git a/modules/fdlibm/patches/01_remove_unused_declarations_from_fdlibm_h.patch b/modules/fdlibm/patches/01_remove_unused_declarations_from_fdlibm_h.patch new file mode 100644 index 0000000000..6365f71488 --- /dev/null +++ b/modules/fdlibm/patches/01_remove_unused_declarations_from_fdlibm_h.patch @@ -0,0 +1,511 @@ +diff --git a/fdlibm.h b/fdlibm.h +--- a/fdlibm.h ++++ b/fdlibm.h +@@ -12,504 +12,66 @@ + /* + * from: @(#)fdlibm.h 5.1 93/09/24 + * $FreeBSD$ + */ + + #ifndef _MATH_H_ + #define _MATH_H_ + +-#include <sys/cdefs.h> +-#include <sys/_types.h> +-#include <machine/_limits.h> +- +-/* +- * ANSI/POSIX +- */ +-extern const union __infinity_un { +- unsigned char __uc[8]; +- double __ud; +-} __infinity; +- +-extern const union __nan_un { +- unsigned char __uc[sizeof(float)]; +- float __uf; +-} __nan; +- +-#if __GNUC_PREREQ__(3, 3) +-#define __MATH_BUILTIN_CONSTANTS +-#endif +- +-#if __GNUC_PREREQ__(3, 0) +-#define __MATH_BUILTIN_RELOPS +-#endif +- +-#ifdef __MATH_BUILTIN_CONSTANTS +-#define HUGE_VAL __builtin_huge_val() +-#else +-#define HUGE_VAL (__infinity.__ud) +-#endif +- +-#if __ISO_C_VISIBLE >= 1999 +-#define FP_ILOGB0 (-__INT_MAX) +-#define FP_ILOGBNAN __INT_MAX +- +-#ifdef __MATH_BUILTIN_CONSTANTS +-#define HUGE_VALF __builtin_huge_valf() +-#define HUGE_VALL __builtin_huge_vall() +-#define INFINITY __builtin_inff() +-#define NAN __builtin_nanf("") +-#else +-#define HUGE_VALF (float)HUGE_VAL +-#define HUGE_VALL (long double)HUGE_VAL +-#define INFINITY HUGE_VALF +-#define NAN (__nan.__uf) +-#endif /* __MATH_BUILTIN_CONSTANTS */ +- +-#define MATH_ERRNO 1 +-#define MATH_ERREXCEPT 2 +-#define math_errhandling MATH_ERREXCEPT +- +-#define FP_FAST_FMAF 1 +- +-/* Symbolic constants to classify floating point numbers. */ +-#define FP_INFINITE 0x01 +-#define FP_NAN 0x02 +-#define FP_NORMAL 0x04 +-#define FP_SUBNORMAL 0x08 +-#define FP_ZERO 0x10 +- +-#if __STDC_VERSION__ >= 201112L || __has_extension(c_generic_selections) +-#define __fp_type_select(x, f, d, ld) __extension__ _Generic((x), \ +- float: f(x), \ +- double: d(x), \ +- long double: ld(x)) +-#elif __GNUC_PREREQ__(3, 1) && !defined(__cplusplus) +-#define __fp_type_select(x, f, d, ld) __builtin_choose_expr( \ +- __builtin_types_compatible_p(__typeof(x), long double), ld(x), \ +- __builtin_choose_expr( \ +- __builtin_types_compatible_p(__typeof(x), double), d(x), \ +- __builtin_choose_expr( \ +- __builtin_types_compatible_p(__typeof(x), float), f(x), (void)0))) +-#else +-#define __fp_type_select(x, f, d, ld) \ +- ((sizeof(x) == sizeof(float)) ? f(x) \ +- : (sizeof(x) == sizeof(double)) ? d(x) \ +- : ld(x)) +-#endif +- +-#define fpclassify(x) \ +- __fp_type_select(x, __fpclassifyf, __fpclassifyd, __fpclassifyl) +-#define isfinite(x) __fp_type_select(x, __isfinitef, __isfinite, __isfinitel) +-#define isinf(x) __fp_type_select(x, __isinff, __isinf, __isinfl) +-#define isnan(x) \ +- __fp_type_select(x, __inline_isnanf, __inline_isnan, __inline_isnanl) +-#define isnormal(x) __fp_type_select(x, __isnormalf, __isnormal, __isnormall) +- +-#ifdef __MATH_BUILTIN_RELOPS +-#define isgreater(x, y) __builtin_isgreater((x), (y)) +-#define isgreaterequal(x, y) __builtin_isgreaterequal((x), (y)) +-#define isless(x, y) __builtin_isless((x), (y)) +-#define islessequal(x, y) __builtin_islessequal((x), (y)) +-#define islessgreater(x, y) __builtin_islessgreater((x), (y)) +-#define isunordered(x, y) __builtin_isunordered((x), (y)) +-#else +-#define isgreater(x, y) (!isunordered((x), (y)) && (x) > (y)) +-#define isgreaterequal(x, y) (!isunordered((x), (y)) && (x) >= (y)) +-#define isless(x, y) (!isunordered((x), (y)) && (x) < (y)) +-#define islessequal(x, y) (!isunordered((x), (y)) && (x) <= (y)) +-#define islessgreater(x, y) (!isunordered((x), (y)) && \ +- ((x) > (y) || (y) > (x))) +-#define isunordered(x, y) (isnan(x) || isnan(y)) +-#endif /* __MATH_BUILTIN_RELOPS */ +- +-#define signbit(x) __fp_type_select(x, __signbitf, __signbit, __signbitl) +- +-typedef __double_t double_t; +-typedef __float_t float_t; +-#endif /* __ISO_C_VISIBLE >= 1999 */ +- +-/* +- * XOPEN/SVID +- */ +-#if __BSD_VISIBLE || __XSI_VISIBLE +-#define M_E 2.7182818284590452354 /* e */ +-#define M_LOG2E 1.4426950408889634074 /* log 2e */ +-#define M_LOG10E 0.43429448190325182765 /* log 10e */ +-#define M_LN2 0.69314718055994530942 /* log e2 */ +-#define M_LN10 2.30258509299404568402 /* log e10 */ +-#define M_PI 3.14159265358979323846 /* pi */ + #define M_PI_2 1.57079632679489661923 /* pi/2 */ +-#define M_PI_4 0.78539816339744830962 /* pi/4 */ +-#define M_1_PI 0.31830988618379067154 /* 1/pi */ +-#define M_2_PI 0.63661977236758134308 /* 2/pi */ +-#define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */ +-#define M_SQRT2 1.41421356237309504880 /* sqrt(2) */ +-#define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */ +- +-#define MAXFLOAT ((float)3.40282346638528860e+38) +-extern int signgam; +-#endif /* __BSD_VISIBLE || __XSI_VISIBLE */ +- +-#if __BSD_VISIBLE +-#if 0 +-/* Old value from 4.4BSD-Lite math.h; this is probably better. */ +-#define HUGE HUGE_VAL +-#else +-#define HUGE MAXFLOAT +-#endif +-#endif /* __BSD_VISIBLE */ +- +-/* +- * Most of these functions depend on the rounding mode and have the side +- * effect of raising floating-point exceptions, so they are not declared +- * as __pure2. In C99, FENV_ACCESS affects the purity of these functions. +- */ +-__BEGIN_DECLS +-/* +- * ANSI/POSIX +- */ +-int __fpclassifyd(double) __pure2; +-int __fpclassifyf(float) __pure2; +-int __fpclassifyl(long double) __pure2; +-int __isfinitef(float) __pure2; +-int __isfinite(double) __pure2; +-int __isfinitel(long double) __pure2; +-int __isinff(float) __pure2; +-int __isinf(double) __pure2; +-int __isinfl(long double) __pure2; +-int __isnormalf(float) __pure2; +-int __isnormal(double) __pure2; +-int __isnormall(long double) __pure2; +-int __signbit(double) __pure2; +-int __signbitf(float) __pure2; +-int __signbitl(long double) __pure2; +- +-static __inline int +-__inline_isnan(__const double __x) +-{ +- +- return (__x != __x); +-} +- +-static __inline int +-__inline_isnanf(__const float __x) +-{ +- +- return (__x != __x); +-} +- +-static __inline int +-__inline_isnanl(__const long double __x) +-{ +- +- return (__x != __x); +-} +- +-/* +- * Define the following aliases, for compatibility with glibc and CUDA. +- */ +-#define __isnan __inline_isnan +-#define __isnanf __inline_isnanf +- +-/* +- * Version 2 of the Single UNIX Specification (UNIX98) defined isnan() and +- * isinf() as functions taking double. C99, and the subsequent POSIX revisions +- * (SUSv3, POSIX.1-2001, define it as a macro that accepts any real floating +- * point type. If we are targeting SUSv2 and C99 or C11 (or C++11) then we +- * expose the newer definition, assuming that the language spec takes +- * precedence over the operating system interface spec. +- */ +-#if __XSI_VISIBLE > 0 && __XSI_VISIBLE < 600 && __ISO_C_VISIBLE < 1999 +-#undef isinf +-#undef isnan +-int isinf(double); +-int isnan(double); +-#endif +- + double acos(double); + double asin(double); + double atan(double); + double atan2(double, double); + double cos(double); + double sin(double); + double tan(double); + + double cosh(double); + double sinh(double); + double tanh(double); + + double exp(double); +-double frexp(double, int *); /* fundamentally !__pure2 */ +-double ldexp(double, int); + double log(double); + double log10(double); +-double modf(double, double *); /* fundamentally !__pure2 */ + + double pow(double, double); +-double sqrt(double); + + double ceil(double); +-double fabs(double) __pure2; ++double fabs(double); + double floor(double); +-double fmod(double, double); + +-/* +- * These functions are not in C90. +- */ +-#if __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 || __XSI_VISIBLE + double acosh(double); + double asinh(double); + double atanh(double); + double cbrt(double); +-double erf(double); +-double erfc(double); + double exp2(double); + double expm1(double); +-double fma(double, double, double); + double hypot(double, double); +-int ilogb(double) __pure2; +-double lgamma(double); +-long long llrint(double); +-long long llround(double); + double log1p(double); + double log2(double); +-double logb(double); +-long lrint(double); +-long lround(double); +-double nan(const char *) __pure2; +-double nextafter(double, double); +-double remainder(double, double); +-double remquo(double, double, int *); + double rint(double); +-#endif /* __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 || __XSI_VISIBLE */ +- +-#if __BSD_VISIBLE || __XSI_VISIBLE +-double j0(double); +-double j1(double); +-double jn(int, double); +-double y0(double); +-double y1(double); +-double yn(int, double); +- +-#if __XSI_VISIBLE <= 500 || __BSD_VISIBLE +-double gamma(double); +-#endif +- +-#if __XSI_VISIBLE <= 600 || __BSD_VISIBLE +-double scalb(double, double); +-#endif +-#endif /* __BSD_VISIBLE || __XSI_VISIBLE */ +- +-#if __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 +-double copysign(double, double) __pure2; +-double fdim(double, double); +-double fmax(double, double) __pure2; +-double fmin(double, double) __pure2; ++double copysign(double, double); + double nearbyint(double); +-double round(double); +-double scalbln(double, long); + double scalbn(double, int); +-double tgamma(double); + double trunc(double); +-#endif +- +-/* +- * BSD math library entry points +- */ +-#if __BSD_VISIBLE +-double drem(double, double); +-int finite(double) __pure2; +-int isnanf(float) __pure2; +- +-/* +- * Reentrant version of gamma & lgamma; passes signgam back by reference +- * as the second argument; user must allocate space for signgam. +- */ +-double gamma_r(double, int *); +-double lgamma_r(double, int *); +- +-/* +- * IEEE Test Vector +- */ +-double significand(double); +-#endif /* __BSD_VISIBLE */ +- +-/* float versions of ANSI/POSIX functions */ +-#if __ISO_C_VISIBLE >= 1999 + float acosf(float); + float asinf(float); + float atanf(float); +-float atan2f(float, float); + float cosf(float); + float sinf(float); + float tanf(float); +- +-float coshf(float); +-float sinhf(float); +-float tanhf(float); +- + float exp2f(float); + float expf(float); +-float expm1f(float); +-float frexpf(float, int *); /* fundamentally !__pure2 */ +-int ilogbf(float) __pure2; +-float ldexpf(float, int); +-float log10f(float); +-float log1pf(float); +-float log2f(float); + float logf(float); +-float modff(float, float *); /* fundamentally !__pure2 */ +- + float powf(float, float); + float sqrtf(float); + + float ceilf(float); +-float fabsf(float) __pure2; ++float fabsf(float); + float floorf(float); +-float fmodf(float, float); +-float roundf(float); +- +-float erff(float); +-float erfcf(float); +-float hypotf(float, float); +-float lgammaf(float); +-float tgammaf(float); +- +-float acoshf(float); +-float asinhf(float); +-float atanhf(float); +-float cbrtf(float); +-float logbf(float); +-float copysignf(float, float) __pure2; +-long long llrintf(float); +-long long llroundf(float); +-long lrintf(float); +-long lroundf(float); +-float nanf(const char *) __pure2; + float nearbyintf(float); +-float nextafterf(float, float); +-float remainderf(float, float); +-float remquof(float, float, int *); + float rintf(float); +-float scalblnf(float, long); + float scalbnf(float, int); + float truncf(float); + +-float fdimf(float, float); +-float fmaf(float, float, float); +-float fmaxf(float, float) __pure2; +-float fminf(float, float) __pure2; +-#endif +- +-/* +- * float versions of BSD math library entry points +- */ +-#if __BSD_VISIBLE +-float dremf(float, float); +-int finitef(float) __pure2; +-float gammaf(float); +-float j0f(float); +-float j1f(float); +-float jnf(int, float); +-float scalbf(float, float); +-float y0f(float); +-float y1f(float); +-float ynf(int, float); +- +-/* +- * Float versions of reentrant version of gamma & lgamma; passes +- * signgam back by reference as the second argument; user must +- * allocate space for signgam. +- */ +-float gammaf_r(float, int *); +-float lgammaf_r(float, int *); +- +-/* +- * float version of IEEE Test Vector +- */ +-float significandf(float); +-#endif /* __BSD_VISIBLE */ +- +-/* +- * long double versions of ISO/POSIX math functions +- */ +-#if __ISO_C_VISIBLE >= 1999 +-long double acoshl(long double); +-long double acosl(long double); +-long double asinhl(long double); +-long double asinl(long double); +-long double atan2l(long double, long double); +-long double atanhl(long double); +-long double atanl(long double); +-long double cbrtl(long double); +-long double ceill(long double); +-long double copysignl(long double, long double) __pure2; +-long double coshl(long double); +-long double cosl(long double); +-long double erfcl(long double); +-long double erfl(long double); +-long double exp2l(long double); +-long double expl(long double); +-long double expm1l(long double); +-long double fabsl(long double) __pure2; +-long double fdiml(long double, long double); +-long double floorl(long double); +-long double fmal(long double, long double, long double); +-long double fmaxl(long double, long double) __pure2; +-long double fminl(long double, long double) __pure2; +-long double fmodl(long double, long double); +-long double frexpl(long double, int *); /* fundamentally !__pure2 */ +-long double hypotl(long double, long double); +-int ilogbl(long double) __pure2; +-long double ldexpl(long double, int); +-long double lgammal(long double); +-long long llrintl(long double); +-long long llroundl(long double); +-long double log10l(long double); +-long double log1pl(long double); +-long double log2l(long double); +-long double logbl(long double); +-long double logl(long double); +-long lrintl(long double); +-long lroundl(long double); +-long double modfl(long double, long double *); /* fundamentally !__pure2 */ +-long double nanl(const char *) __pure2; +-long double nearbyintl(long double); +-long double nextafterl(long double, long double); +-double nexttoward(double, long double); +-float nexttowardf(float, long double); +-long double nexttowardl(long double, long double); +-long double powl(long double, long double); +-long double remainderl(long double, long double); +-long double remquol(long double, long double, int *); +-long double rintl(long double); +-long double roundl(long double); +-long double scalblnl(long double, long); +-long double scalbnl(long double, int); +-long double sinhl(long double); +-long double sinl(long double); +-long double sqrtl(long double); +-long double tanhl(long double); +-long double tanl(long double); +-long double tgammal(long double); +-long double truncl(long double); +-#endif /* __ISO_C_VISIBLE >= 1999 */ +- +-#if __BSD_VISIBLE +-long double lgammal_r(long double, int *); +-void sincos(double, double *, double *); +-void sincosf(float, float *, float *); +-void sincosl(long double, long double *, long double *); +-double cospi(double); +-float cospif(float); +-long double cospil(long double); +-double sinpi(double); +-float sinpif(float); +-long double sinpil(long double); +-double tanpi(double); +-float tanpif(float); +-long double tanpil(long double); +-#endif +- +-__END_DECLS +- + #endif /* !_MATH_H_ */ diff --git a/modules/fdlibm/patches/02_change_include_guard_in_fdlibm_h.patch b/modules/fdlibm/patches/02_change_include_guard_in_fdlibm_h.patch new file mode 100644 index 0000000000..e89eadbe32 --- /dev/null +++ b/modules/fdlibm/patches/02_change_include_guard_in_fdlibm_h.patch @@ -0,0 +1,37 @@ +--- a/fdlibm.h 2022-12-13 14:27:29.092805897 -0500 ++++ b/fdlibm.h 2022-12-13 14:27:37.444836016 -0500 +@@ -9,18 +9,21 @@ + * ==================================================== + */ + + /* + * from: @(#)fdlibm.h 5.1 93/09/24 + * $FreeBSD$ + */ + +-#ifndef _MATH_H_ +-#define _MATH_H_ ++#ifndef mozilla_imported_fdlibm_h ++#define mozilla_imported_fdlibm_h + ++#ifndef M_PI_2 + #define M_PI_2 1.57079632679489661923 /* pi/2 */ ++#endif ++ + double acos(double); + double asin(double); + double atan(double); + double atan2(double, double); + double cos(double); + double sin(double); +@@ -69,9 +72,9 @@ + float ceilf(float); + float fabsf(float); + float floorf(float); + float nearbyintf(float); + float rintf(float); + float scalbnf(float, int); + float truncf(float); + +-#endif /* !_MATH_H_ */ ++#endif /* !mozilla_imported_fdlibm_h */ diff --git a/modules/fdlibm/patches/03_put_fdlibm_functions_into_fdlibm_namespace.patch b/modules/fdlibm/patches/03_put_fdlibm_functions_into_fdlibm_namespace.patch new file mode 100644 index 0000000000..2a2b147381 --- /dev/null +++ b/modules/fdlibm/patches/03_put_fdlibm_functions_into_fdlibm_namespace.patch @@ -0,0 +1,36 @@ +--- a/fdlibm.h 2022-12-13 14:28:36.393051585 -0500 ++++ b/fdlibm.h 2022-12-13 14:28:47.533092878 -0500 +@@ -12,19 +12,21 @@ + /* + * from: @(#)fdlibm.h 5.1 93/09/24 + * $FreeBSD$ + */ + + #ifndef mozilla_imported_fdlibm_h + #define mozilla_imported_fdlibm_h + ++namespace fdlibm { ++ + #ifndef M_PI_2 + #define M_PI_2 1.57079632679489661923 /* pi/2 */ + #endif + + double acos(double); + double asin(double); + double atan(double); + double atan2(double, double); + double cos(double); + double sin(double); + double tan(double); +@@ -69,9 +71,11 @@ + float ceilf(float); + float fabsf(float); + float floorf(float); + float nearbyintf(float); + float rintf(float); + float scalbnf(float, int); + float truncf(float); + ++} /* namespace fdlibm */ ++ + #endif /* !mozilla_imported_fdlibm_h */ diff --git a/modules/fdlibm/patches/04_include_fdlibm_h_from_math_private_h.patch b/modules/fdlibm/patches/04_include_fdlibm_h_from_math_private_h.patch new file mode 100644 index 0000000000..8531976f89 --- /dev/null +++ b/modules/fdlibm/patches/04_include_fdlibm_h_from_math_private_h.patch @@ -0,0 +1,1214 @@ +diff --git a/e_acos.cpp b/e_acos.cpp +--- a/e_acos.cpp ++++ b/e_acos.cpp +@@ -35,17 +35,16 @@ __FBSDID("$FreeBSD$"); + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + * Function needed: sqrt + */ + + #include <float.h> + +-#include "math.h" + #include "math_private.h" + + static const double + one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ + pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ + pio2_hi = 1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */ + static volatile double + pio2_lo = 6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */ +diff --git a/e_acosh.cpp b/e_acosh.cpp +--- a/e_acosh.cpp ++++ b/e_acosh.cpp +@@ -26,17 +26,16 @@ __FBSDID("$FreeBSD$"); + * + * Special cases: + * acosh(x) is NaN with signal if x<1. + * acosh(NaN) is NaN without signal. + */ + + #include <float.h> + +-#include "math.h" + #include "math_private.h" + + static const double + one = 1.0, + ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ + + double + __ieee754_acosh(double x) +diff --git a/e_asin.cpp b/e_asin.cpp +--- a/e_asin.cpp ++++ b/e_asin.cpp +@@ -41,17 +41,16 @@ __FBSDID("$FreeBSD$"); + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + */ + + #include <float.h> + +-#include "math.h" + #include "math_private.h" + + static const double + one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ + huge = 1.000e+300, + pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ + pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ + pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */ +diff --git a/e_atan2.cpp b/e_atan2.cpp +--- a/e_atan2.cpp ++++ b/e_atan2.cpp +@@ -39,17 +39,16 @@ __FBSDID("$FreeBSD$"); + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + + #include <float.h> + +-#include "math.h" + #include "math_private.h" + + static volatile double + tiny = 1.0e-300; + static const double + zero = 0.0, + pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ + pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ +diff --git a/e_atanh.cpp b/e_atanh.cpp +--- a/e_atanh.cpp ++++ b/e_atanh.cpp +@@ -30,17 +30,16 @@ __FBSDID("$FreeBSD$"); + * atanh(x) is NaN if |x| > 1 with signal; + * atanh(NaN) is that NaN with no signal; + * atanh(+-1) is +-INF with signal. + * + */ + + #include <float.h> + +-#include "math.h" + #include "math_private.h" + + static const double one = 1.0, huge = 1e300; + static const double zero = 0.0; + + double + __ieee754_atanh(double x) + { +diff --git a/e_cosh.cpp b/e_cosh.cpp +--- a/e_cosh.cpp ++++ b/e_cosh.cpp +@@ -32,17 +32,16 @@ __FBSDID("$FreeBSD$"); + * + * Special cases: + * cosh(x) is |x| if x is +INF, -INF, or NaN. + * only cosh(0)=1 is exact for finite x. + */ + + #include <float.h> + +-#include "math.h" + #include "math_private.h" + + static const double one = 1.0, half=0.5, huge = 1.0e300; + + double + __ieee754_cosh(double x) + { + double t,w; +diff --git a/e_exp.cpp b/e_exp.cpp +--- a/e_exp.cpp ++++ b/e_exp.cpp +@@ -73,17 +73,16 @@ __FBSDID("$FreeBSD$"); + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + + #include <float.h> + +-#include "math.h" + #include "math_private.h" + + static const double + one = 1.0, + halF[2] = {0.5,-0.5,}, + o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */ + u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */ + ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */ +diff --git a/e_hypot.cpp b/e_hypot.cpp +--- a/e_hypot.cpp ++++ b/e_hypot.cpp +@@ -43,17 +43,16 @@ __FBSDID("$FreeBSD$"); + * + * Accuracy: + * hypot(x,y) returns sqrt(x^2+y^2) with error less + * than 1 ulps (units in the last place) + */ + + #include <float.h> + +-#include "math.h" + #include "math_private.h" + + double + __ieee754_hypot(double x, double y) + { + double a,b,t1,t2,y1,y2,w; + int32_t j,k,ha,hb; + +diff --git a/e_log.cpp b/e_log.cpp +--- a/e_log.cpp ++++ b/e_log.cpp +@@ -62,17 +62,16 @@ __FBSDID("$FreeBSD$"); + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + + #include <float.h> + +-#include "math.h" + #include "math_private.h" + + static const double + ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ + ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ + two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ + Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ + Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ +diff --git a/e_log10.cpp b/e_log10.cpp +--- a/e_log10.cpp ++++ b/e_log10.cpp +@@ -19,17 +19,16 @@ __FBSDID("$FreeBSD$"); + * comments. + * + * log10(x) = (f - 0.5*f*f + k_log1p(f)) / ln10 + k * log10(2) + * in not-quite-routine extra precision. + */ + + #include <float.h> + +-#include "math.h" + #include "math_private.h" + #include "k_log.h" + + static const double + two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ + ivln10hi = 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */ + ivln10lo = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */ + log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ +diff --git a/e_log2.cpp b/e_log2.cpp +--- a/e_log2.cpp ++++ b/e_log2.cpp +@@ -21,17 +21,16 @@ __FBSDID("$FreeBSD$"); + * This reduces x to {k, 1+f} exactly as in e_log.c, then calls the kernel, + * then does the combining and scaling steps + * log2(x) = (f - 0.5*f*f + k_log1p(f)) / ln2 + k + * in not-quite-routine extra precision. + */ + + #include <float.h> + +-#include "math.h" + #include "math_private.h" + #include "k_log.h" + + static const double + two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ + ivln2hi = 1.44269504072144627571e+00, /* 0x3ff71547, 0x65200000 */ + ivln2lo = 1.67517131648865118353e-10; /* 0x3de705fc, 0x2eefa200 */ + +diff --git a/e_pow.cpp b/e_pow.cpp +--- a/e_pow.cpp ++++ b/e_pow.cpp +@@ -53,17 +53,16 @@ __FBSDID("$FreeBSD$"); + * Constants : + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + + #include <float.h> +-#include "math.h" + #include "math_private.h" + + static const double + bp[] = {1.0, 1.5,}, + dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ + dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ + zero = 0.0, + half = 0.5, +diff --git a/e_rem_pio2.cpp b/e_rem_pio2.cpp +--- a/e_rem_pio2.cpp ++++ b/e_rem_pio2.cpp +@@ -19,17 +19,16 @@ __FBSDID("$FreeBSD$"); + /* __ieee754_rem_pio2(x,y) + * + * return the remainder of x rem pi/2 in y[0]+y[1] + * use __kernel_rem_pio2() + */ + + #include <float.h> + +-#include "math.h" + #include "math_private.h" + + /* + * invpio2: 53 bits of 2/pi + * pio2_1: first 33 bit of pi/2 + * pio2_1t: pi/2 - pio2_1 + * pio2_2: second 33 bit of pi/2 + * pio2_2t: pi/2 - (pio2_1+pio2_2) +diff --git a/e_sinh.cpp b/e_sinh.cpp +--- a/e_sinh.cpp ++++ b/e_sinh.cpp +@@ -29,17 +29,16 @@ __FBSDID("$FreeBSD$"); + * + * Special cases: + * sinh(x) is |x| if x is +INF, -INF, or NaN. + * only sinh(0)=0 is exact for finite x. + */ + + #include <float.h> + +-#include "math.h" + #include "math_private.h" + + static const double one = 1.0, shuge = 1.0e307; + + double + __ieee754_sinh(double x) + { + double t,h; +diff --git a/k_cos.cpp b/k_cos.cpp +--- a/k_cos.cpp ++++ b/k_cos.cpp +@@ -48,17 +48,16 @@ __FBSDID("$FreeBSD$"); + * and tmp having the same precision as x. If they have extra + * precision due to compiler bugs, then the extra precision is + * only good provided it is retained in all terms of the final + * expression for cos(). Retention happens in all cases tested + * under FreeBSD, so don't pessimize things by forcibly clipping + * any extra precision in w. + */ + +-#include "math.h" + #include "math_private.h" + + static const double + one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ + C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ + C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ + C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ + C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ +diff --git a/k_exp.cpp b/k_exp.cpp +--- a/k_exp.cpp ++++ b/k_exp.cpp +@@ -26,17 +26,16 @@ + * SUCH DAMAGE. + */ + + #include <sys/cdefs.h> + __FBSDID("$FreeBSD$"); + + #include <complex.h> + +-#include "math.h" + #include "math_private.h" + + static const uint32_t k = 1799; /* constant for reduction */ + static const double kln2 = 1246.97177782734161156; /* k * ln2 */ + + /* + * Compute exp(x), scaled to avoid spurious overflow. An exponent is + * returned separately in 'expt'. +diff --git a/k_rem_pio2.cpp b/k_rem_pio2.cpp +--- a/k_rem_pio2.cpp ++++ b/k_rem_pio2.cpp +@@ -126,17 +126,16 @@ __FBSDID("$FreeBSD$"); + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + + #include <float.h> + +-#include "math.h" + #include "math_private.h" + + static const int init_jk[] = {3,4,4,6}; /* initial value for jk */ + + /* + * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi + * + * integer array, contains the (24*i)-th to (24*i+23)-th +diff --git a/k_sin.cpp b/k_sin.cpp +--- a/k_sin.cpp ++++ b/k_sin.cpp +@@ -39,17 +39,16 @@ __FBSDID("$FreeBSD$"); + * ~ sin(x) + (1-x*x/2)*y + * For better accuracy, let + * 3 2 2 2 2 + * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) + * then 3 2 + * sin(x) = x + (S1*x + (x *(r-y/2)+y)) + */ + +-#include "math.h" + #include "math_private.h" + + static const double + half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ + S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ + S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ + S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ + S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ +diff --git a/k_tan.cpp b/k_tan.cpp +--- a/k_tan.cpp ++++ b/k_tan.cpp +@@ -44,17 +44,16 @@ __FBSDID("$FreeBSD$"); + * 3 2 + * tan(x+y) = x + (T1*x + (x *(r+y)+y)) + * + * 4. For x in [0.67434,pi/4], let y = pi/4 - x, then + * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y)) + * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y))) + */ + +-#include "math.h" + #include "math_private.h" + static const double xxx[] = { + 3.33333333333334091986e-01, /* 3FD55555, 55555563 */ + 1.33333333333201242699e-01, /* 3FC11111, 1110FE7A */ + 5.39682539762260521377e-02, /* 3FABA1BA, 1BB341FE */ + 2.18694882948595424599e-02, /* 3F9664F4, 8406D637 */ + 8.86323982359930005737e-03, /* 3F8226E3, E96E8493 */ + 3.59207910759131235356e-03, /* 3F6D6D22, C9560328 */ +diff --git a/math_private.h b/math_private.h +--- a/math_private.h ++++ b/math_private.h +@@ -15,16 +15,18 @@ + */ + + #ifndef _MATH_PRIVATE_H_ + #define _MATH_PRIVATE_H_ + + #include <sys/types.h> + #include <machine/endian.h> + ++#include "fdlibm.h" ++ + /* + * The original fdlibm code used statements like: + * n0 = ((*(int*)&one)>>29)^1; * index of high word * + * ix0 = *(n0+(int*)&x); * high word of x * + * ix1 = *((1-n0)+(int*)&x); * low word of x * + * to dig two 32 bit words out of the 64 bit IEEE floating point + * value. That is non-ANSI, and, moreover, the gcc instruction + * scheduler gets it wrong. We instead use the following macros. +diff --git a/s_asinh.cpp b/s_asinh.cpp +--- a/s_asinh.cpp ++++ b/s_asinh.cpp +@@ -21,17 +21,16 @@ __FBSDID("$FreeBSD$"); + * asinh(x) := x if 1+x*x=1, + * := sign(x)*(log(x)+ln2)) for large |x|, else + * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else + * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) + */ + + #include <float.h> + +-#include "math.h" + #include "math_private.h" + + static const double + one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ + ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ + huge= 1.00000000000000000000e+300; + + double +diff --git a/s_atan.cpp b/s_atan.cpp +--- a/s_atan.cpp ++++ b/s_atan.cpp +@@ -30,17 +30,16 @@ __FBSDID("$FreeBSD$"); + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + + #include <float.h> + +-#include "math.h" + #include "math_private.h" + + static const double atanhi[] = { + 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */ + 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */ + 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */ + 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */ + }; +diff --git a/s_cbrt.cpp b/s_cbrt.cpp +--- a/s_cbrt.cpp ++++ b/s_cbrt.cpp +@@ -11,17 +11,16 @@ + * + * Optimized by Bruce D. Evans. + */ + + #include <sys/cdefs.h> + __FBSDID("$FreeBSD$"); + + #include <float.h> +-#include "math.h" + #include "math_private.h" + + /* cbrt(x) + * Return cube root of x + */ + static const u_int32_t + B1 = 715094163, /* B1 = (1023-1023/3-0.03306235651)*2**20 */ + B2 = 696219795; /* B2 = (1023-1023/3-54/3-0.03306235651)*2**20 */ +diff --git a/s_ceil.cpp b/s_ceil.cpp +--- a/s_ceil.cpp ++++ b/s_ceil.cpp +@@ -19,17 +19,16 @@ __FBSDID("$FreeBSD$"); + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to ceil(x). + */ + + #include <float.h> + +-#include "math.h" + #include "math_private.h" + + static const double huge = 1.0e300; + + double + ceil(double x) + { + int32_t i0,i1,j0; +diff --git a/s_ceilf.cpp b/s_ceilf.cpp +--- a/s_ceilf.cpp ++++ b/s_ceilf.cpp +@@ -11,17 +11,16 @@ + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + + #include <sys/cdefs.h> + __FBSDID("$FreeBSD$"); + +-#include "math.h" + #include "math_private.h" + + static const float huge = 1.0e30; + + float + ceilf(float x) + { + int32_t i0,j0; +diff --git a/s_copysign.cpp b/s_copysign.cpp +--- a/s_copysign.cpp ++++ b/s_copysign.cpp +@@ -14,17 +14,16 @@ + __FBSDID("$FreeBSD$"); + + /* + * copysign(double x, double y) + * copysign(x,y) returns a value with the magnitude of x and + * with the sign bit of y. + */ + +-#include "math.h" + #include "math_private.h" + + double + copysign(double x, double y) + { + u_int32_t hx,hy; + GET_HIGH_WORD(hx,x); + GET_HIGH_WORD(hy,y); +diff --git a/s_cos.cpp b/s_cos.cpp +--- a/s_cos.cpp ++++ b/s_cos.cpp +@@ -41,17 +41,16 @@ __FBSDID("$FreeBSD$"); + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + + #include <float.h> + +-#include "math.h" + #define INLINE_REM_PIO2 + #include "math_private.h" + #include "e_rem_pio2.c" + + double + cos(double x) + { + double y[2],z=0.0; +diff --git a/s_expm1.cpp b/s_expm1.cpp +--- a/s_expm1.cpp ++++ b/s_expm1.cpp +@@ -105,17 +105,16 @@ __FBSDID("$FreeBSD$"); + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + + #include <float.h> + +-#include "math.h" + #include "math_private.h" + + static const double + one = 1.0, + tiny = 1.0e-300, + o_threshold = 7.09782712893383973096e+02,/* 0x40862E42, 0xFEFA39EF */ + ln2_hi = 6.93147180369123816490e-01,/* 0x3fe62e42, 0xfee00000 */ + ln2_lo = 1.90821492927058770002e-10,/* 0x3dea39ef, 0x35793c76 */ +diff --git a/s_fabs.cpp b/s_fabs.cpp +--- a/s_fabs.cpp ++++ b/s_fabs.cpp +@@ -12,17 +12,16 @@ + + #include <sys/cdefs.h> + __FBSDID("$FreeBSD$"); + + /* + * fabs(x) returns the absolute value of x. + */ + +-#include "math.h" + #include "math_private.h" + + double + fabs(double x) + { + u_int32_t high; + GET_HIGH_WORD(high,x); + SET_HIGH_WORD(x,high&0x7fffffff); +diff --git a/s_floor.cpp b/s_floor.cpp +--- a/s_floor.cpp ++++ b/s_floor.cpp +@@ -19,17 +19,16 @@ __FBSDID("$FreeBSD$"); + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to floor(x). + */ + + #include <float.h> + +-#include "math.h" + #include "math_private.h" + + static const double huge = 1.0e300; + + double + floor(double x) + { + int32_t i0,i1,j0; +diff --git a/s_floorf.cpp b/s_floorf.cpp +--- a/s_floorf.cpp ++++ b/s_floorf.cpp +@@ -20,17 +20,16 @@ __FBSDID("$FreeBSD$"); + * floorf(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to floorf(x). + */ + +-#include "math.h" + #include "math_private.h" + + static const float huge = 1.0e30; + + float + floorf(float x) + { + int32_t i0,j0; +diff --git a/s_log1p.cpp b/s_log1p.cpp +--- a/s_log1p.cpp ++++ b/s_log1p.cpp +@@ -75,17 +75,16 @@ __FBSDID("$FreeBSD$"); + * if(u==1.0) return x ; else + * return log(u)*(x/(u-1.0)); + * + * See HP-15C Advanced Functions Handbook, p.193. + */ + + #include <float.h> + +-#include "math.h" + #include "math_private.h" + + static const double + ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ + ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ + two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ + Lp1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ + Lp2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ +diff --git a/s_nearbyint.cpp b/s_nearbyint.cpp +--- a/s_nearbyint.cpp ++++ b/s_nearbyint.cpp +@@ -25,17 +25,18 @@ + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + + #include <sys/cdefs.h> + __FBSDID("$FreeBSD$"); + + #include <fenv.h> +-#include <math.h> ++ ++#include "math_private.h" + + /* + * We save and restore the floating-point environment to avoid raising + * an inexact exception. We can get away with using fesetenv() + * instead of feclearexcept()/feupdateenv() to restore the environment + * because the only exception defined for rint() is overflow, and + * rounding can't overflow as long as emax >= p. + * +diff --git a/s_rint.cpp b/s_rint.cpp +--- a/s_rint.cpp ++++ b/s_rint.cpp +@@ -20,17 +20,16 @@ __FBSDID("$FreeBSD$"); + * Method: + * Using floating addition. + * Exception: + * Inexact flag raised if x not equal to rint(x). + */ + + #include <float.h> + +-#include "math.h" + #include "math_private.h" + + static const double + TWO52[2]={ + 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ + -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */ + }; + +diff --git a/s_rintf.cpp b/s_rintf.cpp +--- a/s_rintf.cpp ++++ b/s_rintf.cpp +@@ -14,17 +14,16 @@ + */ + + #include <sys/cdefs.h> + __FBSDID("$FreeBSD$"); + + #include <float.h> + #include <stdint.h> + +-#include "math.h" + #include "math_private.h" + + static const float + TWO23[2]={ + 8.3886080000e+06, /* 0x4b000000 */ + -8.3886080000e+06, /* 0xcb000000 */ + }; + +diff --git a/s_scalbn.cpp b/s_scalbn.cpp +--- a/s_scalbn.cpp ++++ b/s_scalbn.cpp +@@ -2,19 +2,20 @@ + * Copyright (c) 2005-2020 Rich Felker, et al. + * + * SPDX-License-Identifier: MIT + * + * Please see https://git.musl-libc.org/cgit/musl/tree/COPYRIGHT + * for all contributors to musl. + */ + #include <float.h> +-#include <math.h> + #include <stdint.h> + ++#include "math_private.h" ++ + double scalbn(double x, int n) + { + union {double f; uint64_t i;} u; + double_t y = x; + + if (n > 1023) { + y *= 0x1p1023; + n -= 1023; +diff --git a/s_scalbnf.cpp b/s_scalbnf.cpp +--- a/s_scalbnf.cpp ++++ b/s_scalbnf.cpp +@@ -8,16 +4,17 @@ + * SPDX-License-Identifier: MIT + * + * Please see https://git.musl-libc.org/cgit/musl/tree/COPYRIGHT + * for all contributors to musl. + */ +-#include <math.h> + #include <stdint.h> + ++#include "math_private.h" ++ + float scalbnf(float x, int n) + { + union {float f; uint32_t i;} u; + float_t y = x; + + if (n > 127) { + y *= 0x1p127f; + n -= 127; +diff --git a/s_sin.cpp b/s_sin.cpp +--- a/s_sin.cpp ++++ b/s_sin.cpp +@@ -41,17 +41,16 @@ __FBSDID("$FreeBSD$"); + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + + #include <float.h> + +-#include "math.h" + #define INLINE_REM_PIO2 + #include "math_private.h" + #include "e_rem_pio2.c" + + double + sin(double x) + { + double y[2],z=0.0; +diff --git a/s_tan.cpp b/s_tan.cpp +--- a/s_tan.cpp ++++ b/s_tan.cpp +@@ -40,17 +40,16 @@ __FBSDID("$FreeBSD$"); + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + + #include <float.h> + +-#include "math.h" + #define INLINE_REM_PIO2 + #include "math_private.h" + #include "e_rem_pio2.c" + + double + tan(double x) + { + double y[2],z=0.0; +diff --git a/s_tanh.cpp b/s_tanh.cpp +--- a/s_tanh.cpp ++++ b/s_tanh.cpp +@@ -34,17 +34,16 @@ __FBSDID("$FreeBSD$"); + * + * Special cases: + * tanh(NaN) is NaN; + * only tanh(0)=0 is exact for finite argument. + */ + + #include <float.h> + +-#include "math.h" + #include "math_private.h" + + static const volatile double tiny = 1.0e-300; + static const double one = 1.0, two = 2.0, huge = 1.0e300; + + double + tanh(double x) + { +diff --git a/s_trunc.cpp b/s_trunc.cpp +--- a/s_trunc.cpp ++++ b/s_trunc.cpp +@@ -19,17 +19,16 @@ __FBSDID("$FreeBSD$"); + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to trunc(x). + */ + + #include <float.h> + +-#include "math.h" + #include "math_private.h" + + static const double huge = 1.0e300; + + double + trunc(double x) + { + int32_t i0,i1,j0; +diff --git a/s_truncf.cpp b/s_truncf.cpp +--- a/s_truncf.cpp ++++ b/s_truncf.cpp +@@ -17,17 +17,16 @@ __FBSDID("$FreeBSD$"); + * truncf(x) + * Return x rounded toward 0 to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to truncf(x). + */ + +-#include "math.h" + #include "math_private.h" + + static const float huge = 1.0e30F; + + float + truncf(float x) + { + int32_t i0,j0; +--- a/e_acosf.cpp 2022-12-11 21:15:50.058431053 -0500 ++++ b/e_acosf.cpp_new 2022-12-11 21:13:10.532515637 -0500 +@@ -12,15 +12,14 @@ + * is preserved. + * ==================================================== + */ + + #include <sys/cdefs.h> + __FBSDID("$FreeBSD$"); + +-#include "math.h" + #include "math_private.h" + + static const float + one = 1.0000000000e+00, /* 0x3F800000 */ + pi = 3.1415925026e+00, /* 0x40490fda */ + pio2_hi = 1.5707962513e+00; /* 0x3fc90fda */ + static volatile float +--- a/e_asinf.cpp 2022-12-11 21:15:50.486437124 -0500 ++++ b/e_asinf.cpp_new 2022-12-11 21:13:07.876498396 -0500 +@@ -12,15 +12,14 @@ + * is preserved. + * ==================================================== + */ + + #include <sys/cdefs.h> + __FBSDID("$FreeBSD$"); + +-#include "math.h" + #include "math_private.h" + + static const float + one = 1.0000000000e+00, /* 0x3F800000 */ + huge = 1.000e+30, + /* coefficient for R(x^2) */ + pS0 = 1.6666586697e-01, +--- a/e_expf.cpp 2022-12-11 21:15:51.250447960 -0500 ++++ b/e_expf.cpp_new 2022-12-11 21:13:05.212481099 -0500 +@@ -14,15 +14,14 @@ + */ + + #include <sys/cdefs.h> + __FBSDID("$FreeBSD$"); + + #include <float.h> + +-#include "math.h" + #include "math_private.h" + + static const float + one = 1.0, + halF[2] = {0.5,-0.5,}, + o_threshold= 8.8721679688e+01, /* 0x42b17180 */ + u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */ +--- a/e_logf.cpp 2022-12-11 21:15:51.978458278 -0500 ++++ b/e_logf.cpp_new 2022-12-11 21:13:02.644464418 -0500 +@@ -12,15 +12,14 @@ + * is preserved. + * ==================================================== + */ + + #include <sys/cdefs.h> + __FBSDID("$FreeBSD$"); + +-#include "math.h" + #include "math_private.h" + + static const float + ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ + ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ + two25 = 3.355443200e+07, /* 0x4c000000 */ + /* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */ +--- a/e_powf.cpp 2022-12-11 21:15:52.242462016 -0500 ++++ b/e_powf.cpp_new 2022-12-11 21:13:00.164448306 -0500 +@@ -12,15 +12,14 @@ + * is preserved. + * ==================================================== + */ + + #include <sys/cdefs.h> + __FBSDID("$FreeBSD$"); + +-#include "math.h" + #include "math_private.h" + + static const float + bp[] = {1.0, 1.5,}, + dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */ + dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */ + zero = 0.0, +--- a/e_rem_pio2f.cpp 2022-12-11 21:15:52.626467454 -0500 ++++ b/e_rem_pio2f.cpp_new 2022-12-11 21:12:57.300429693 -0500 +@@ -22,15 +22,14 @@ + * return the remainder of x rem pi/2 in *y + * use double precision for everything except passing x + * use __kernel_rem_pio2() for large x + */ + + #include <float.h> + +-#include "math.h" + #include "math_private.h" + + /* + * invpio2: 53 bits of 2/pi + * pio2_1: first 25 bits of pi/2 + * pio2_1t: pi/2 - pio2_1 + */ +--- a/e_sqrtf.cpp 2022-12-11 21:15:52.922471645 -0500 ++++ b/e_sqrtf.cpp_new 2022-12-11 21:12:54.596412113 -0500 +@@ -13,15 +13,14 @@ + * ==================================================== + */ + + #ifndef lint + static char rcsid[] = "$FreeBSD$"; + #endif + +-#include "math.h" + #include "math_private.h" + + #ifdef USE_BUILTIN_SQRTF + float + __ieee754_sqrtf(float x) + { + return (__builtin_sqrtf(x)); +--- a/k_cosf.cpp 2022-12-11 21:15:53.178475268 -0500 ++++ b/k_cosf.cpp_new 2022-12-11 21:12:52.012395309 -0500 +@@ -15,15 +15,14 @@ + */ + + #ifndef INLINE_KERNEL_COSDF + #include <sys/cdefs.h> + __FBSDID("$FreeBSD$"); + #endif + +-#include "math.h" + #include "math_private.h" + + /* |cos(x) - c(x)| < 2**-34.1 (~[-5.37e-11, 5.295e-11]). */ + static const double + one = 1.0, + C0 = -0x1ffffffd0c5e81.0p-54, /* -0.499999997251031003120 */ + C1 = 0x155553e1053a42.0p-57, /* 0.0416666233237390631894 */ +--- a/k_expf.cpp 2022-12-11 21:15:53.434478888 -0500 ++++ b/k_expf.cpp_new 2022-12-11 21:12:49.012375792 -0500 +@@ -27,15 +27,14 @@ + */ + + #include <sys/cdefs.h> + __FBSDID("$FreeBSD$"); + + #include <complex.h> + +-#include "math.h" + #include "math_private.h" + + static const uint32_t k = 235; /* constant for reduction */ + static const float kln2 = 162.88958740F; /* k * ln2 */ + + /* + * See k_exp.c for details. +--- a/k_sinf.cpp 2022-12-11 21:15:53.946486130 -0500 ++++ b/k_sinf.cpp_new 2022-12-11 21:12:46.020356322 -0500 +@@ -15,15 +15,14 @@ + */ + + #ifndef INLINE_KERNEL_SINDF + #include <sys/cdefs.h> + __FBSDID("$FreeBSD$"); + #endif + +-#include "math.h" + #include "math_private.h" + + /* |sin(x)/x - s(x)| < 2**-37.5 (~[-4.89e-12, 4.824e-12]). */ + static const double + S1 = -0x15555554cbac77.0p-55, /* -0.166666666416265235595 */ + S2 = 0x111110896efbb2.0p-59, /* 0.0083333293858894631756 */ + S3 = -0x1a00f9e2cae774.0p-65, /* -0.000198393348360966317347 */ +--- a/k_tanf.cpp 2022-12-11 21:15:54.254490484 -0500 ++++ b/k_tanf.cpp_new 2022-12-11 21:12:42.972336479 -0500 +@@ -14,15 +14,14 @@ + */ + + #ifndef INLINE_KERNEL_TANDF + #include <sys/cdefs.h> + __FBSDID("$FreeBSD$"); + #endif + +-#include "math.h" + #include "math_private.h" + + /* |tan(x)/x - t(x)| < 2**-25.5 (~[-2e-08, 2e-08]). */ + static const double + T[] = { + 0x15554d3418c99f.0p-54, /* 0.333331395030791399758 */ + 0x1112fd38999f72.0p-55, /* 0.133392002712976742718 */ +--- a/s_atanf.cpp 2022-12-11 21:15:54.670496364 -0500 ++++ b/s_atanf.cpp_new 2022-12-11 21:12:39.940316733 -0500 +@@ -12,15 +12,14 @@ + * is preserved. + * ==================================================== + */ + + #include <sys/cdefs.h> + __FBSDID("$FreeBSD$"); + +-#include "math.h" + #include "math_private.h" + + static const float atanhi[] = { + 4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */ + 7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */ + 9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */ + 1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */ +--- a/s_cosf.cpp 2022-12-11 21:15:55.494508001 -0500 ++++ b/s_cosf.cpp_new 2022-12-11 21:12:37.396300160 -0500 +@@ -15,15 +15,14 @@ + */ + + #include <sys/cdefs.h> + __FBSDID("$FreeBSD$"); + + #include <float.h> + +-#include "math.h" + #define INLINE_KERNEL_COSDF + #define INLINE_KERNEL_SINDF + #define INLINE_REM_PIO2F + #include "math_private.h" + #include "e_rem_pio2f.c" + #include "k_cosf.c" + #include "k_sinf.c" +--- a/s_exp2.cpp 2022-12-11 21:15:55.790512181 -0500 ++++ b/s_exp2.cpp_new 2022-12-11 21:12:34.476281131 -0500 +@@ -27,15 +27,14 @@ + */ + + #include <sys/cdefs.h> + __FBSDID("$FreeBSD$"); + + #include <float.h> + +-#include "math.h" + #include "math_private.h" + + #define TBLBITS 8 + #define TBLSIZE (1 << TBLBITS) + + static const double + redux = 0x1.8p52 / TBLSIZE, +--- a/s_exp2f.cpp 2022-12-11 21:15:55.926514101 -0500 ++++ b/s_exp2f.cpp_new 2022-12-11 21:12:30.644256149 -0500 +@@ -27,15 +27,14 @@ + */ + + #include <sys/cdefs.h> + __FBSDID("$FreeBSD$"); + + #include <float.h> + +-#include "math.h" + #include "math_private.h" + + #define TBLBITS 4 + #define TBLSIZE (1 << TBLBITS) + + static const float + redux = 0x1.8p23f / TBLSIZE, +--- a/s_fabsf.cpp 2022-12-11 21:15:56.202517995 -0500 ++++ b/s_fabsf.cpp_new 2022-12-11 21:12:27.244233973 -0500 +@@ -16,15 +16,14 @@ + #include <sys/cdefs.h> + __FBSDID("$FreeBSD$"); + + /* + * fabsf(x) returns the absolute value of x. + */ + +-#include "math.h" + #include "math_private.h" + + float + fabsf(float x) + { + u_int32_t ix; + GET_FLOAT_WORD(ix,x); +--- a/s_sinf.cpp 2022-12-11 21:15:57.618537960 -0500 ++++ b/s_sinf.cpp_new 2022-12-11 21:12:24.684217270 -0500 +@@ -15,15 +15,14 @@ + */ + + #include <sys/cdefs.h> + __FBSDID("$FreeBSD$"); + + #include <float.h> + +-#include "math.h" + #define INLINE_KERNEL_COSDF + #define INLINE_KERNEL_SINDF + #define INLINE_REM_PIO2F + #include "math_private.h" + #include "e_rem_pio2f.c" + #include "k_cosf.c" + #include "k_sinf.c" +--- a/s_tanf.cpp 2022-12-11 21:15:57.930542357 -0500 ++++ b/s_tanf.cpp_new 2022-12-11 21:12:20.420189437 -0500 +@@ -15,15 +15,14 @@ + */ + + #include <sys/cdefs.h> + __FBSDID("$FreeBSD$"); + + #include <float.h> + +-#include "math.h" + #define INLINE_KERNEL_TANDF + #define INLINE_REM_PIO2F + #include "math_private.h" + #include "e_rem_pio2f.c" + #include "k_tanf.c" + + /* Small multiples of pi/2 rounded to double precision. */ diff --git a/modules/fdlibm/patches/05_include_stdint_h_in_math_private_h.patch b/modules/fdlibm/patches/05_include_stdint_h_in_math_private_h.patch new file mode 100644 index 0000000000..aec7d94738 --- /dev/null +++ b/modules/fdlibm/patches/05_include_stdint_h_in_math_private_h.patch @@ -0,0 +1,21 @@ +diff --git a/math_private.h b/math_private.h +--- a/math_private.h ++++ b/math_private.h +@@ -12,16 +12,17 @@ + /* + * from: @(#)fdlibm.h 5.1 93/09/24 + * $FreeBSD$ + */ + + #ifndef _MATH_PRIVATE_H_ + #define _MATH_PRIVATE_H_ + ++#include <stdint.h> + #include <sys/types.h> + #include <machine/endian.h> + + #include "fdlibm.h" + + /* + * The original fdlibm code used statements like: + * n0 = ((*(int*)&one)>>29)^1; * index of high word * diff --git a/modules/fdlibm/patches/06_use_mfbt_endian_h_in_math_private_h.patch b/modules/fdlibm/patches/06_use_mfbt_endian_h_in_math_private_h.patch new file mode 100644 index 0000000000..b4374fc948 --- /dev/null +++ b/modules/fdlibm/patches/06_use_mfbt_endian_h_in_math_private_h.patch @@ -0,0 +1,116 @@ +diff --git a/math_private.h b/math_private.h +--- a/math_private.h ++++ b/math_private.h +@@ -14,52 +14,38 @@ + * $FreeBSD$ + */ + + #ifndef _MATH_PRIVATE_H_ + #define _MATH_PRIVATE_H_ + + #include <stdint.h> + #include <sys/types.h> +-#include <machine/endian.h> ++ ++#include "mozilla/EndianUtils.h" + + #include "fdlibm.h" + + /* + * The original fdlibm code used statements like: + * n0 = ((*(int*)&one)>>29)^1; * index of high word * + * ix0 = *(n0+(int*)&x); * high word of x * + * ix1 = *((1-n0)+(int*)&x); * low word of x * + * to dig two 32 bit words out of the 64 bit IEEE floating point + * value. That is non-ANSI, and, moreover, the gcc instruction + * scheduler gets it wrong. We instead use the following macros. + * Unlike the original code, we determine the endianness at compile + * time, not at run time; I don't see much benefit to selecting + * endianness at run time. + */ + +-/* +- * A union which permits us to convert between a double and two 32 bit +- * ints. +- */ +- +-#ifdef __arm__ +-#if defined(__VFP_FP__) || defined(__ARM_EABI__) +-#define IEEE_WORD_ORDER BYTE_ORDER +-#else +-#define IEEE_WORD_ORDER BIG_ENDIAN +-#endif +-#else /* __arm__ */ +-#define IEEE_WORD_ORDER BYTE_ORDER +-#endif +- + /* A union which permits us to convert between a long double and + four 32 bit ints. */ + +-#if IEEE_WORD_ORDER == BIG_ENDIAN ++#if MOZ_BIG_ENDIAN() + + typedef union + { + long double value; + struct { + u_int32_t mswhi; + u_int32_t mswlo; + u_int32_t lswhi; +@@ -68,17 +54,17 @@ typedef union + struct { + u_int64_t msw; + u_int64_t lsw; + } parts64; + } ieee_quad_shape_type; + + #endif + +-#if IEEE_WORD_ORDER == LITTLE_ENDIAN ++#if MOZ_LITTLE_ENDIAN() + + typedef union + { + long double value; + struct { + u_int32_t lswlo; + u_int32_t lswhi; + u_int32_t mswlo; +@@ -87,17 +73,17 @@ typedef union + struct { + u_int64_t lsw; + u_int64_t msw; + } parts64; + } ieee_quad_shape_type; + + #endif + +-#if IEEE_WORD_ORDER == BIG_ENDIAN ++#if MOZ_BIG_ENDIAN() + + typedef union + { + double value; + struct + { + u_int32_t msw; + u_int32_t lsw; +@@ -105,17 +91,17 @@ typedef union + struct + { + u_int64_t w; + } xparts; + } ieee_double_shape_type; + + #endif + +-#if IEEE_WORD_ORDER == LITTLE_ENDIAN ++#if MOZ_LITTLE_ENDIAN() + + typedef union + { + double value; + struct + { + u_int32_t lsw; + u_int32_t msw; diff --git a/modules/fdlibm/patches/07_add_fdlibm_namespace_to_functions_defined_and_used_in_fdlibm.patch b/modules/fdlibm/patches/07_add_fdlibm_namespace_to_functions_defined_and_used_in_fdlibm.patch new file mode 100644 index 0000000000..37e0017cbc --- /dev/null +++ b/modules/fdlibm/patches/07_add_fdlibm_namespace_to_functions_defined_and_used_in_fdlibm.patch @@ -0,0 +1,71 @@ +diff --git a/math_private.h b/math_private.h +--- a/math_private.h ++++ b/math_private.h +@@ -867,16 +867,67 @@ irintl(long double x) + #define __ieee754_j1f j1f + #define __ieee754_y0f y0f + #define __ieee754_y1f y1f + #define __ieee754_jnf jnf + #define __ieee754_ynf ynf + #define __ieee754_remainderf remainderf + #define __ieee754_scalbf scalbf + ++#define acos fdlibm::acos ++#define acosf fdlibm::acosf ++#define asin fdlibm::asin ++#define asinf fdlibm::asinf ++#define atan fdlibm::atan ++#define atanf fdlibm::atanf ++#define atan2 fdlibm::atan2 ++#define cos fdlibm::cos ++#define cosf fdlibm::cosf ++#define sin fdlibm::sin ++#define sinf fdlibm::sinf ++#define tan fdlibm::tan ++#define tanf fdlibm::tanf ++#define cosh fdlibm::cosh ++#define sinh fdlibm::sinh ++#define tanh fdlibm::tanh ++#define exp fdlibm::exp ++#define expf fdlibm::expf ++#define exp2 fdlibm::exp2 ++#define exp2f fdlibm::exp2f ++#define log fdlibm::log ++#define logf fdlibm::logf ++#define log10 fdlibm::log10 ++#define pow fdlibm::pow ++#define powf fdlibm::powf ++#define ceil fdlibm::ceil ++#define ceilf fdlibm::ceilf ++#define fabs fdlibm::fabs ++#define fabsf fdlibm::fabsf ++#define floor fdlibm::floor ++#define acosh fdlibm::acosh ++#define asinh fdlibm::asinh ++#define atanh fdlibm::atanh ++#define cbrt fdlibm::cbrt ++#define expm1 fdlibm::expm1 ++#define hypot fdlibm::hypot ++#define log1p fdlibm::log1p ++#define log2 fdlibm::log2 ++#define scalb fdlibm::scalb ++#define copysign fdlibm::copysign ++#define scalbn fdlibm::scalbn ++#define scalbnf fdlibm::scalbnf ++#define trunc fdlibm::trunc ++#define truncf fdlibm::truncf ++#define floorf fdlibm::floorf ++#define nearbyint fdlibm::nearbyint ++#define nearbyintf fdlibm::nearbyintf ++#define rint fdlibm::rint ++#define rintf fdlibm::rintf ++#define sqrtf fdlibm::sqrtf ++ + /* fdlibm kernel function */ + int __kernel_rem_pio2(double*,double*,int,int,int); + + /* double precision kernel functions */ + #ifndef INLINE_REM_PIO2 + int __ieee754_rem_pio2(double,double*); + #endif + double __kernel_sin(double,double,int); diff --git a/modules/fdlibm/patches/08_remove_weak_reference_macro.patch b/modules/fdlibm/patches/08_remove_weak_reference_macro.patch new file mode 100644 index 0000000000..338ff92b60 --- /dev/null +++ b/modules/fdlibm/patches/08_remove_weak_reference_macro.patch @@ -0,0 +1,459 @@ +diff --git a/e_acos.cpp b/e_acos.cpp +--- a/e_acos.cpp ++++ b/e_acos.cpp +@@ -99,12 +99,8 @@ __ieee754_acos(double x) + c = (z-df*df)/(s+df); + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + r = p/q; + w = r*s+c; + return 2.0*(df+w); + } + } +- +-#if LDBL_MANT_DIG == 53 +-__weak_reference(acos, acosl); +-#endif +diff --git a/e_acosh.cpp b/e_acosh.cpp +--- a/e_acosh.cpp ++++ b/e_acosh.cpp +@@ -56,12 +56,8 @@ __ieee754_acosh(double x) + } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ + t=x*x; + return __ieee754_log(2.0*x-one/(x+sqrt(t-one))); + } else { /* 1<x<2 */ + t = x-one; + return log1p(t+sqrt(2.0*t+t*t)); + } + } +- +-#if LDBL_MANT_DIG == 53 +-__weak_reference(acosh, acoshl); +-#endif +diff --git a/e_asin.cpp b/e_asin.cpp +--- a/e_asin.cpp ++++ b/e_asin.cpp +@@ -105,12 +105,8 @@ __ieee754_asin(double x) + c = (t-w*w)/(s+w); + r = p/q; + p = 2.0*s*r-(pio2_lo-2.0*c); + q = pio4_hi-2.0*w; + t = pio4_hi-(p-q); + } + if(hx>0) return t; else return -t; + } +- +-#if LDBL_MANT_DIG == 53 +-__weak_reference(asin, asinl); +-#endif +diff --git a/e_atan2.cpp b/e_atan2.cpp +--- a/e_atan2.cpp ++++ b/e_atan2.cpp +@@ -117,12 +117,8 @@ __ieee754_atan2(double y, double x) + switch (m) { + case 0: return z ; /* atan(+,+) */ + case 1: return -z ; /* atan(-,+) */ + case 2: return pi-(z-pi_lo);/* atan(+,-) */ + default: /* case 3 */ + return (z-pi_lo)-pi;/* atan(-,-) */ + } + } +- +-#if LDBL_MANT_DIG == 53 +-__weak_reference(atan2, atan2l); +-#endif +diff --git a/e_atanh.cpp b/e_atanh.cpp +--- a/e_atanh.cpp ++++ b/e_atanh.cpp +@@ -56,12 +56,8 @@ __ieee754_atanh(double x) + SET_HIGH_WORD(x,ix); + if(ix<0x3fe00000) { /* x < 0.5 */ + t = x+x; + t = 0.5*log1p(t+t*x/(one-x)); + } else + t = 0.5*log1p((x+x)/(one-x)); + if(hx>=0) return t; else return -t; + } +- +-#if LDBL_MANT_DIG == 53 +-__weak_reference(atanh, atanhl); +-#endif +diff --git a/e_cosh.cpp b/e_cosh.cpp +--- a/e_cosh.cpp ++++ b/e_cosh.cpp +@@ -73,12 +73,8 @@ __ieee754_cosh(double x) + + /* |x| in [log(maxdouble), overflowthresold] */ + if (ix<=0x408633CE) + return __ldexp_exp(fabs(x), -1); + + /* |x| > overflowthresold, cosh(x) overflow */ + return huge*huge; + } +- +-#if (LDBL_MANT_DIG == 53) +-__weak_reference(cosh, coshl); +-#endif +diff --git a/e_exp.cpp b/e_exp.cpp +--- a/e_exp.cpp ++++ b/e_exp.cpp +@@ -152,12 +152,8 @@ __ieee754_exp(double x) /* default IEEE double exp */ + else y = one-((lo-(x*c)/(2.0-c))-hi); + if(k >= -1021) { + if (k==1024) return y*2.0*0x1p1023; + return y*twopk; + } else { + return y*twopk*twom1000; + } + } +- +-#if (LDBL_MANT_DIG == 53) +-__weak_reference(exp, expl); +-#endif +diff --git a/e_hypot.cpp b/e_hypot.cpp +--- a/e_hypot.cpp ++++ b/e_hypot.cpp +@@ -117,12 +117,8 @@ __ieee754_hypot(double x, double y) + w = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); + } + if(k!=0) { + t1 = 0.0; + SET_HIGH_WORD(t1,(1023+k)<<20); + return t1*w; + } else return w; + } +- +-#if LDBL_MANT_DIG == 53 +-__weak_reference(hypot, hypotl); +-#endif +diff --git a/e_log.cpp b/e_log.cpp +--- a/e_log.cpp ++++ b/e_log.cpp +@@ -135,12 +135,8 @@ __ieee754_log(double x) + hfsq=0.5*f*f; + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); + } else { + if(k==0) return f-s*(f-R); else + return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); + } + } +- +-#if (LDBL_MANT_DIG == 53) +-__weak_reference(log, logl); +-#endif +diff --git a/e_log10.cpp b/e_log10.cpp +--- a/e_log10.cpp ++++ b/e_log10.cpp +@@ -82,12 +82,8 @@ __ieee754_log10(double x) + * with some parallelism and it reduces the error for many args. + */ + w = y2 + val_hi; + val_lo += (y2 - w) + val_hi; + val_hi = w; + + return val_lo + val_hi; + } +- +-#if (LDBL_MANT_DIG == 53) +-__weak_reference(log10, log10l); +-#endif +diff --git a/e_log2.cpp b/e_log2.cpp +--- a/e_log2.cpp ++++ b/e_log2.cpp +@@ -105,12 +105,8 @@ __ieee754_log2(double x) + + /* spadd(val_hi, val_lo, y), except for not using double_t: */ + w = y + val_hi; + val_lo += (y - w) + val_hi; + val_hi = w; + + return val_lo + val_hi; + } +- +-#if (LDBL_MANT_DIG == 53) +-__weak_reference(log2, log2l); +-#endif +diff --git a/e_pow.cpp b/e_pow.cpp +--- a/e_pow.cpp ++++ b/e_pow.cpp +@@ -302,12 +302,8 @@ __ieee754_pow(double x, double y) + r = (z*t1)/(t1-two)-(w+z*w); + z = one-(r-z); + GET_HIGH_WORD(j,z); + j += (n<<20); + if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */ + else SET_HIGH_WORD(z,j); + return s*z; + } +- +-#if (LDBL_MANT_DIG == 53) +-__weak_reference(pow, powl); +-#endif +diff --git a/e_sinh.cpp b/e_sinh.cpp +--- a/e_sinh.cpp ++++ b/e_sinh.cpp +@@ -67,12 +67,8 @@ __ieee754_sinh(double x) + + /* |x| in [log(maxdouble), overflowthresold] */ + if (ix<=0x408633CE) + return h*2.0*__ldexp_exp(fabs(x), -1); + + /* |x| > overflowthresold, sinh(x) overflow */ + return x*shuge; + } +- +-#if (LDBL_MANT_DIG == 53) +-__weak_reference(sinh, sinhl); +-#endif +diff --git a/s_asinh.cpp b/s_asinh.cpp +--- a/s_asinh.cpp ++++ b/s_asinh.cpp +@@ -50,12 +50,8 @@ asinh(double x) + t = fabs(x); + w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t)); + } else { /* 2.0 > |x| > 2**-28 */ + t = x*x; + w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t))); + } + if(hx>0) return w; else return -w; + } +- +-#if LDBL_MANT_DIG == 53 +-__weak_reference(asinh, asinhl); +-#endif +diff --git a/s_atan.cpp b/s_atan.cpp +--- a/s_atan.cpp ++++ b/s_atan.cpp +@@ -112,12 +112,8 @@ atan(double x) + s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); + s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); + if (id<0) return x - x*(s1+s2); + else { + z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); + return (hx<0)? -z:z; + } + } +- +-#if LDBL_MANT_DIG == 53 +-__weak_reference(atan, atanl); +-#endif +diff --git a/s_cbrt.cpp b/s_cbrt.cpp +--- a/s_cbrt.cpp ++++ b/s_cbrt.cpp +@@ -106,12 +106,8 @@ cbrt(double x) + s=t*t; /* t*t is exact */ + r=x/s; /* error <= 0.5 ulps; |r| < |t| */ + w=t+t; /* t+t is exact */ + r=(r-t)/(w+r); /* r-t is exact; w+r ~= 3*t */ + t=t+t*r; /* error <= (0.5 + 0.5/3) * ulp */ + + return(t); + } +- +-#if (LDBL_MANT_DIG == 53) +-__weak_reference(cbrt, cbrtl); +-#endif +diff --git a/s_ceil.cpp b/s_ceil.cpp +--- a/s_ceil.cpp ++++ b/s_ceil.cpp +@@ -65,12 +65,8 @@ ceil(double x) + } + } + i1 &= (~i); + } + } + INSERT_WORDS(x,i0,i1); + return x; + } +- +-#if LDBL_MANT_DIG == 53 +-__weak_reference(ceil, ceill); +-#endif +diff --git a/s_cos.cpp b/s_cos.cpp +--- a/s_cos.cpp ++++ b/s_cos.cpp +@@ -77,12 +77,8 @@ cos(double x) + case 0: return __kernel_cos(y[0],y[1]); + case 1: return -__kernel_sin(y[0],y[1],1); + case 2: return -__kernel_cos(y[0],y[1]); + default: + return __kernel_sin(y[0],y[1],1); + } + } + } +- +-#if (LDBL_MANT_DIG == 53) +-__weak_reference(cos, cosl); +-#endif +diff --git a/s_expm1.cpp b/s_expm1.cpp +--- a/s_expm1.cpp ++++ b/s_expm1.cpp +@@ -210,12 +210,8 @@ expm1(double x) + SET_HIGH_WORD(t,((0x3ff-k)<<20)); /* 2^-k */ + y = x-(e+t); + y += one; + y = y*twopk; + } + } + return y; + } +- +-#if (LDBL_MANT_DIG == 53) +-__weak_reference(expm1, expm1l); +-#endif +diff --git a/s_floor.cpp b/s_floor.cpp +--- a/s_floor.cpp ++++ b/s_floor.cpp +@@ -66,12 +66,8 @@ floor(double x) + } + } + i1 &= (~i); + } + } + INSERT_WORDS(x,i0,i1); + return x; + } +- +-#if LDBL_MANT_DIG == 53 +-__weak_reference(floor, floorl); +-#endif +diff --git a/s_log1p.cpp b/s_log1p.cpp +--- a/s_log1p.cpp ++++ b/s_log1p.cpp +@@ -168,12 +168,8 @@ log1p(double x) + return k*ln2_hi-((R-(k*ln2_lo+c))-f); + } + s = f/(2.0+f); + z = s*s; + R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))); + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f); + } +- +-#if (LDBL_MANT_DIG == 53) +-__weak_reference(log1p, log1pl); +-#endif +diff --git a/s_rint.cpp b/s_rint.cpp +--- a/s_rint.cpp ++++ b/s_rint.cpp +@@ -80,12 +80,8 @@ rint(double x) + if((i1&i)==0) return x; /* x is integral */ + i>>=1; + if((i1&i)!=0) i1 = (i1&(~i))|((0x40000000)>>(j0-20)); + } + INSERT_WORDS(x,i0,i1); + STRICT_ASSIGN(double,w,TWO52[sx]+x); + return w-TWO52[sx]; + } +- +-#if (LDBL_MANT_DIG == 53) +-__weak_reference(rint, rintl); +-#endif +diff --git a/s_scalbn.cpp b/s_scalbn.cpp +--- a/s_scalbn.cpp ++++ b/s_scalbn.cpp +@@ -36,13 +36,8 @@ double scalbn(double x, int n) + if (n < -1022) + n = -1022; + } + } + u.i = (uint64_t)(0x3ff+n)<<52; + x = y * u.f; + return x; + } +- +-#if (LDBL_MANT_DIG == 53) && !defined(scalbn) +-__weak_reference(scalbn, ldexpl); +-__weak_reference(scalbn, scalbnl); +-#endif +diff --git a/s_sin.cpp b/s_sin.cpp +--- a/s_sin.cpp ++++ b/s_sin.cpp +@@ -77,12 +77,8 @@ sin(double x) + case 0: return __kernel_sin(y[0],y[1],1); + case 1: return __kernel_cos(y[0],y[1]); + case 2: return -__kernel_sin(y[0],y[1],1); + default: + return -__kernel_cos(y[0],y[1]); + } + } + } +- +-#if (LDBL_MANT_DIG == 53) +-__weak_reference(sin, sinl); +-#endif +diff --git a/s_tan.cpp b/s_tan.cpp +--- a/s_tan.cpp ++++ b/s_tan.cpp +@@ -71,12 +71,8 @@ tan(double x) + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2(x,y); + return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even + -1 -- n odd */ + } + } +- +-#if (LDBL_MANT_DIG == 53) +-__weak_reference(tan, tanl); +-#endif +diff --git a/s_tanh.cpp b/s_tanh.cpp +--- a/s_tanh.cpp ++++ b/s_tanh.cpp +@@ -72,12 +72,8 @@ tanh(double x) + z= -t/(t+two); + } + /* |x| >= 22, return +-1 */ + } else { + z = one - tiny; /* raise inexact flag */ + } + return (jx>=0)? z: -z; + } +- +-#if (LDBL_MANT_DIG == 53) +-__weak_reference(tanh, tanhl); +-#endif +diff --git a/s_trunc.cpp b/s_trunc.cpp +--- a/s_trunc.cpp ++++ b/s_trunc.cpp +@@ -55,12 +55,8 @@ trunc(double x) + i = ((u_int32_t)(0xffffffff))>>(j0-20); + if((i1&i)==0) return x; /* x is integral */ + if(huge+x>0.0) /* raise inexact flag */ + i1 &= (~i); + } + INSERT_WORDS(x,i0,i1); + return x; + } +- +-#if LDBL_MANT_DIG == 53 +-__weak_reference(trunc, truncl); +-#endif +--- a/s_exp2.cpp 2022-12-11 21:20:40.290068458 -0500 ++++ b/s_exp2.cpp_new 2022-12-11 21:20:57.490259247 -0500 +@@ -389,10 +389,6 @@ + return (r * 2.0 * 0x1p1023); + return (r * twopk); + } else { + return (r * twopkp1000 * twom1000); + } + } +- +-#if (LDBL_MANT_DIG == 53) +-__weak_reference(exp2, exp2l); +-#endif +--- a/s_scalbnf.cpp ++++ b/s_scalbnf.cpp +@@ -32,10 +34,8 @@ + if (n < -126) + n = -126; + } + } + u.i = (uint32_t)(0x7f+n)<<23; + x = y * u.f; + return x; + } +- +-__strong_reference(scalbnf, ldexpf); diff --git a/modules/fdlibm/patches/09_comment_out_rcsid_variable.patch b/modules/fdlibm/patches/09_comment_out_rcsid_variable.patch new file mode 100644 index 0000000000..715c859956 --- /dev/null +++ b/modules/fdlibm/patches/09_comment_out_rcsid_variable.patch @@ -0,0 +1,1362 @@ +diff --git a/e_acos.cpp b/e_acos.cpp +--- a/e_acos.cpp ++++ b/e_acos.cpp +@@ -6,18 +6,18 @@ + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* __ieee754_acos(x) + * Method : + * acos(x) = pi/2 - asin(x) + * acos(-x) = pi/2 + asin(x) + * For |x|<=0.5 + * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) + * For x>0.5 +diff --git a/e_acosh.cpp b/e_acosh.cpp +--- a/e_acosh.cpp ++++ b/e_acosh.cpp +@@ -7,18 +7,18 @@ + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* __ieee754_acosh(x) + * Method : + * Based on + * acosh(x) = log [ x + sqrt(x*x-1) ] + * we have + * acosh(x) := log(x)+ln2, if x is large; else + * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else +diff --git a/e_asin.cpp b/e_asin.cpp +--- a/e_asin.cpp ++++ b/e_asin.cpp +@@ -6,18 +6,18 @@ + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* __ieee754_asin(x) + * Method : + * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ... + * we approximate asin(x) on [0,0.5] by + * asin(x) = x + x*x^2*R(x^2) + * where + * R(x^2) is a rational approximation of (asin(x)-x)/x^3 +diff --git a/e_atan2.cpp b/e_atan2.cpp +--- a/e_atan2.cpp ++++ b/e_atan2.cpp +@@ -7,18 +7,18 @@ + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* __ieee754_atan2(y,x) + * Method : + * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). + * 2. Reduce x to positive by (if x and y are unexceptional): + * ARG (x+iy) = arctan(y/x) ... if x > 0, + * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, + * +diff --git a/e_atanh.cpp b/e_atanh.cpp +--- a/e_atanh.cpp ++++ b/e_atanh.cpp +@@ -7,18 +7,18 @@ + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* __ieee754_atanh(x) + * Method : + * 1.Reduced x to positive by atanh(-x) = -atanh(x) + * 2.For x>=0.5 + * 1 2x x + * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) + * 2 1 - x 1 - x +diff --git a/e_cosh.cpp b/e_cosh.cpp +--- a/e_cosh.cpp ++++ b/e_cosh.cpp +@@ -6,18 +6,18 @@ + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* __ieee754_cosh(x) + * Method : + * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 + * 1. Replace x by |x| (cosh(x) = cosh(-x)). + * 2. + * [ exp(x) - 1 ]^2 + * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- +diff --git a/e_exp.cpp b/e_exp.cpp +--- a/e_exp.cpp ++++ b/e_exp.cpp +@@ -5,18 +5,18 @@ + * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. + * + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* __ieee754_exp(x) + * Returns the exponential of x. + * + * Method + * 1. Argument reduction: + * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658. + * Given x, find r and integer k such that +diff --git a/e_hypot.cpp b/e_hypot.cpp +--- a/e_hypot.cpp ++++ b/e_hypot.cpp +@@ -6,18 +6,18 @@ + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* __ieee754_hypot(x,y) + * + * Method : + * If (assume round-to-nearest) z=x*x+y*y + * has error less than sqrt(2)/2 ulp, than + * sqrt(z) has error less than 1 ulp (exercise). + * +diff --git a/e_log.cpp b/e_log.cpp +--- a/e_log.cpp ++++ b/e_log.cpp +@@ -6,18 +6,18 @@ + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* __ieee754_log(x) + * Return the logrithm of x + * + * Method : + * 1. Argument Reduction: find k and f such that + * x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . +diff --git a/e_log10.cpp b/e_log10.cpp +--- a/e_log10.cpp ++++ b/e_log10.cpp +@@ -6,32 +6,32 @@ + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* + * Return the base 10 logarithm of x. See e_log.c and k_log.h for most + * comments. + * + * log10(x) = (f - 0.5*f*f + k_log1p(f)) / ln10 + k * log10(2) + * in not-quite-routine extra precision. + */ + + #include <float.h> + + #include "math_private.h" + #include "k_log.h" +- ++ + static const double + two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ + ivln10hi = 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */ + ivln10lo = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */ + log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ + log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ + + static const double zero = 0.0; +diff --git a/e_log2.cpp b/e_log2.cpp +--- a/e_log2.cpp ++++ b/e_log2.cpp +@@ -6,18 +6,18 @@ + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* + * Return the base 2 logarithm of x. See e_log.c and k_log.h for most + * comments. + * + * This reduces x to {k, 1+f} exactly as in e_log.c, then calls the kernel, + * then does the combining and scaling steps + * log2(x) = (f - 0.5*f*f + k_log1p(f)) / ln2 + k +diff --git a/e_pow.cpp b/e_pow.cpp +--- a/e_pow.cpp ++++ b/e_pow.cpp +@@ -4,18 +4,18 @@ + * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. + * + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* __ieee754_pow(x,y) return x**y + * + * n + * Method: Let x = 2 * (1+f) + * 1. Compute and return log2(x) in two pieces: + * log2(x) = w1 + w2, + * where w1 has 53-24 = 29 bit trailing zeros. +diff --git a/e_rem_pio2.cpp b/e_rem_pio2.cpp +--- a/e_rem_pio2.cpp ++++ b/e_rem_pio2.cpp +@@ -8,18 +8,18 @@ + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * Optimized by Bruce D. Evans. + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* __ieee754_rem_pio2(x,y) + * + * return the remainder of x rem pi/2 in y[0]+y[1] + * use __kernel_rem_pio2() + */ + + #include <float.h> +diff --git a/e_sinh.cpp b/e_sinh.cpp +--- a/e_sinh.cpp ++++ b/e_sinh.cpp +@@ -6,18 +6,18 @@ + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* __ieee754_sinh(x) + * Method : + * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 + * 1. Replace x by |x| (sinh(-x) = -sinh(x)). + * 2. + * E + E/(E+1) + * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x) +diff --git a/k_cos.cpp b/k_cos.cpp +--- a/k_cos.cpp ++++ b/k_cos.cpp +@@ -6,18 +6,18 @@ + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* + * __kernel_cos( x, y ) + * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * + * Algorithm +diff --git a/k_exp.cpp b/k_exp.cpp +--- a/k_exp.cpp ++++ b/k_exp.cpp +@@ -21,22 +21,22 @@ + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + #include <complex.h> + +-#include "math_private.h" ++ #include "math_private.h" + + static const uint32_t k = 1799; /* constant for reduction */ + static const double kln2 = 1246.97177782734161156; /* k * ln2 */ + + /* + * Compute exp(x), scaled to avoid spurious overflow. An exponent is + * returned separately in 'expt'. + * +diff --git a/k_log.h b/k_log.h +--- a/k_log.h ++++ b/k_log.h +@@ -6,18 +6,18 @@ + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* + * k_log1p(f): + * Return log(1+f) - f for 1+f in ~[sqrt(2)/2, sqrt(2)]. + * + * The following describes the overall strategy for computing + * logarithms in base e. The argument reduction and adding the final + * term of the polynomial are done by the caller for increased accuracy +diff --git a/k_rem_pio2.cpp b/k_rem_pio2.cpp +--- a/k_rem_pio2.cpp ++++ b/k_rem_pio2.cpp +@@ -6,18 +6,18 @@ + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* + * __kernel_rem_pio2(x,y,e0,nx,prec) + * double x[],y[]; int e0,nx,prec; + * + * __kernel_rem_pio2 return the last three digits of N with + * y = x - N*pi/2 + * so that |y| < pi/2. +diff --git a/k_sin.cpp b/k_sin.cpp +--- a/k_sin.cpp ++++ b/k_sin.cpp +@@ -6,18 +6,18 @@ + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* __kernel_sin( x, y, iy) + * kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). + * + * Algorithm +diff --git a/k_tan.cpp b/k_tan.cpp +--- a/k_tan.cpp ++++ b/k_tan.cpp +@@ -6,18 +6,18 @@ + * + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + + /* INDENT OFF */ +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* __kernel_tan( x, y, k ) + * kernel tan function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * Input k indicates whether tan (if k = 1) or -1/tan (if k = -1) is returned. + * + * Algorithm +diff --git a/s_asinh.cpp b/s_asinh.cpp +--- a/s_asinh.cpp ++++ b/s_asinh.cpp +@@ -5,18 +5,18 @@ + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* asinh(x) + * Method : + * Based on + * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] + * we have + * asinh(x) := x if 1+x*x=1, + * := sign(x)*(log(x)+ln2)) for large |x|, else +diff --git a/s_atan.cpp b/s_atan.cpp +--- a/s_atan.cpp ++++ b/s_atan.cpp +@@ -5,18 +5,18 @@ + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* atan(x) + * Method + * 1. Reduce x to positive by atan(x) = -atan(-x). + * 2. According to the integer k=4t+0.25 chopped, t=x, the argument + * is further reduced to one of the following intervals and the + * arctangent of t is evaluated by the corresponding formula: + * +diff --git a/s_cbrt.cpp b/s_cbrt.cpp +--- a/s_cbrt.cpp ++++ b/s_cbrt.cpp +@@ -7,18 +7,18 @@ + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * Optimized by Bruce D. Evans. + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + #include <float.h> + #include "math_private.h" + + /* cbrt(x) + * Return cube root of x + */ + static const u_int32_t +diff --git a/s_ceil.cpp b/s_ceil.cpp +--- a/s_ceil.cpp ++++ b/s_ceil.cpp +@@ -5,18 +5,18 @@ + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* + * ceil(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to ceil(x). +diff --git a/s_ceilf.cpp b/s_ceilf.cpp +--- a/s_ceilf.cpp ++++ b/s_ceilf.cpp +@@ -8,18 +8,18 @@ + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + #include "math_private.h" + + static const float huge = 1.0e30; + + float + ceilf(float x) + { +diff --git a/s_copysign.cpp b/s_copysign.cpp +--- a/s_copysign.cpp ++++ b/s_copysign.cpp +@@ -5,18 +5,18 @@ + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* + * copysign(double x, double y) + * copysign(x,y) returns a value with the magnitude of x and + * with the sign bit of y. + */ + + #include "math_private.h" +diff --git a/s_cos.cpp b/s_cos.cpp +--- a/s_cos.cpp ++++ b/s_cos.cpp +@@ -5,18 +5,18 @@ + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* cos(x) + * Return cosine function of x. + * + * kernel function: + * __kernel_sin ... sine function on [-pi/4,pi/4] + * __kernel_cos ... cosine function on [-pi/4,pi/4] + * __ieee754_rem_pio2 ... argument reduction routine +diff --git a/s_expm1.cpp b/s_expm1.cpp +--- a/s_expm1.cpp ++++ b/s_expm1.cpp +@@ -5,18 +5,18 @@ + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* expm1(x) + * Returns exp(x)-1, the exponential of x minus 1. + * + * Method + * 1. Argument reduction: + * Given x, find r and integer k such that + * +diff --git a/s_fabs.cpp b/s_fabs.cpp +--- a/s_fabs.cpp ++++ b/s_fabs.cpp +@@ -5,18 +5,18 @@ + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* + * fabs(x) returns the absolute value of x. + */ + + #include "math_private.h" + + double +diff --git a/s_floor.cpp b/s_floor.cpp +--- a/s_floor.cpp ++++ b/s_floor.cpp +@@ -5,18 +5,18 @@ + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* + * floor(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to floor(x). +diff --git a/s_floorf.cpp b/s_floorf.cpp +--- a/s_floorf.cpp ++++ b/s_floorf.cpp +@@ -8,18 +8,18 @@ + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* + * floorf(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to floorf(x). +diff --git a/s_log1p.cpp b/s_log1p.cpp +--- a/s_log1p.cpp ++++ b/s_log1p.cpp +@@ -5,18 +5,18 @@ + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* double log1p(double x) + * + * Method : + * 1. Argument Reduction: find k and f such that + * 1+x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * +diff --git a/s_nearbyint.cpp b/s_nearbyint.cpp +--- a/s_nearbyint.cpp ++++ b/s_nearbyint.cpp +@@ -21,18 +21,18 @@ + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + #include <fenv.h> + + #include "math_private.h" + + /* + * We save and restore the floating-point environment to avoid raising + * an inexact exception. We can get away with using fesetenv() +diff --git a/s_rint.cpp b/s_rint.cpp +--- a/s_rint.cpp ++++ b/s_rint.cpp +@@ -5,18 +5,18 @@ + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* + * rint(x) + * Return x rounded to integral value according to the prevailing + * rounding mode. + * Method: + * Using floating addition. + * Exception: +diff --git a/s_rintf.cpp b/s_rintf.cpp +--- a/s_rintf.cpp ++++ b/s_rintf.cpp +@@ -8,18 +8,18 @@ + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + #include <float.h> + #include <stdint.h> + + #include "math_private.h" + + static const float + TWO23[2]={ +diff --git a/s_sin.cpp b/s_sin.cpp +--- a/s_sin.cpp ++++ b/s_sin.cpp +@@ -5,18 +5,18 @@ + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* sin(x) + * Return sine function of x. + * + * kernel function: + * __kernel_sin ... sine function on [-pi/4,pi/4] + * __kernel_cos ... cose function on [-pi/4,pi/4] + * __ieee754_rem_pio2 ... argument reduction routine +diff --git a/s_tan.cpp b/s_tan.cpp +--- a/s_tan.cpp ++++ b/s_tan.cpp +@@ -5,18 +5,18 @@ + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* tan(x) + * Return tangent function of x. + * + * kernel function: + * __kernel_tan ... tangent function on [-pi/4,pi/4] + * __ieee754_rem_pio2 ... argument reduction routine + * +diff --git a/s_tanh.cpp b/s_tanh.cpp +--- a/s_tanh.cpp ++++ b/s_tanh.cpp +@@ -5,18 +5,18 @@ + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* Tanh(x) + * Return the Hyperbolic Tangent of x + * + * Method : + * x -x + * e - e + * 0. tanh(x) is defined to be ----------- +diff --git a/s_trunc.cpp b/s_trunc.cpp +--- a/s_trunc.cpp ++++ b/s_trunc.cpp +@@ -5,18 +5,18 @@ + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* + * trunc(x) + * Return x rounded toward 0 to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to trunc(x). +diff --git a/s_truncf.cpp b/s_truncf.cpp +--- a/s_truncf.cpp ++++ b/s_truncf.cpp +@@ -5,18 +5,18 @@ + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* + * truncf(x) + * Return x rounded toward 0 to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to truncf(x). +--- a/e_acosf.cpp 2022-12-11 21:20:40.290068458 -0500 ++++ b/e_acosf.cpp_new 2022-12-11 21:23:31.863880382 -0500 +@@ -9,16 +9,16 @@ + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + #include "math_private.h" + + static const float + one = 1.0000000000e+00, /* 0x3F800000 */ + pi = 3.1415925026e+00, /* 0x40490fda */ + pio2_hi = 1.5707962513e+00; /* 0x3fc90fda */ +--- a/e_asinf.cpp 2022-12-11 21:20:40.290068458 -0500 ++++ b/e_asinf.cpp_new 2022-12-11 21:23:31.875880502 -0500 +@@ -9,16 +9,16 @@ + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + #include "math_private.h" + + static const float + one = 1.0000000000e+00, /* 0x3F800000 */ + huge = 1.000e+30, + /* coefficient for R(x^2) */ +--- a/e_expf.cpp 2022-12-11 21:20:40.290068458 -0500 ++++ b/e_expf.cpp_new 2022-12-11 21:23:31.895880703 -0500 +@@ -9,16 +9,16 @@ + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + #include <float.h> + + #include "math_private.h" + + static const float + one = 1.0, +--- a/e_logf.cpp 2022-12-11 21:20:40.290068458 -0500 ++++ b/e_logf.cpp_new 2022-12-11 21:23:31.935881104 -0500 +@@ -9,16 +9,16 @@ + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + #include "math_private.h" + + static const float + ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ + ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ + two25 = 3.355443200e+07, /* 0x4c000000 */ +--- a/e_powf.cpp 2022-12-11 21:20:40.290068458 -0500 ++++ b/e_powf.cpp_new 2022-12-11 21:23:31.971881465 -0500 +@@ -9,16 +9,16 @@ + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + #include "math_private.h" + + static const float + bp[] = {1.0, 1.5,}, + dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */ + dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */ +--- a/e_rem_pio2f.cpp 2022-12-11 21:20:40.290068458 -0500 ++++ b/e_rem_pio2f.cpp_new 2022-12-11 21:23:32.015881905 -0500 +@@ -10,16 +10,16 @@ + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* __ieee754_rem_pio2f(x,y) + * + * return the remainder of x rem pi/2 in *y + * use double precision for everything except passing x + * use __kernel_rem_pio2() for large x + */ +--- b/k_cosf.cpp 2022-12-11 21:20:40.290068458 -0500 ++++ b/k_cosf.cpp_new 2022-12-11 21:23:32.051882266 -0500 +@@ -11,16 +11,16 @@ + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + + #ifndef INLINE_KERNEL_COSDF +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + #endif + + #include "math_private.h" + + /* |cos(x) - c(x)| < 2**-34.1 (~[-5.37e-11, 5.295e-11]). */ + static const double + one = 1.0, +--- b/k_expf.cpp 2022-12-11 21:20:40.290068458 -0500 ++++ b/k_expf.cpp_new 2022-12-11 21:23:32.087882627 -0500 +@@ -22,16 +22,16 @@ + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + #include <complex.h> + + #include "math_private.h" + + static const uint32_t k = 235; /* constant for reduction */ + static const float kln2 = 162.88958740F; /* k * ln2 */ +--- b/k_sinf.cpp 2022-12-11 21:20:40.290068458 -0500 ++++ b/k_sinf.cpp_new 2022-12-11 21:23:32.119882948 -0500 +@@ -11,16 +11,16 @@ + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + + #ifndef INLINE_KERNEL_SINDF +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + #endif + + #include "math_private.h" + + /* |sin(x)/x - s(x)| < 2**-37.5 (~[-4.89e-12, 4.824e-12]). */ + static const double + S1 = -0x15555554cbac77.0p-55, /* -0.166666666416265235595 */ +--- b/k_tanf.cpp 2022-12-11 21:20:40.290068458 -0500 ++++ b/k_tanf.cpp_new 2022-12-11 21:23:32.155883308 -0500 +@@ -10,16 +10,16 @@ + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + + #ifndef INLINE_KERNEL_TANDF +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + #endif + + #include "math_private.h" + + /* |tan(x)/x - t(x)| < 2**-25.5 (~[-2e-08, 2e-08]). */ + static const double + T[] = { +--- a/s_atanf.cpp 2022-12-11 21:20:40.290068458 -0500 ++++ b/s_atanf.cpp_new 2022-12-11 21:23:32.199883749 -0500 +@@ -9,16 +9,16 @@ + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + #include "math_private.h" + + static const float atanhi[] = { + 4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */ + 7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */ + 9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */ +--- a/s_cosf.cpp 2022-12-11 21:20:40.290068458 -0500 ++++ b/s_cosf.cpp_new 2022-12-11 21:23:32.235884110 -0500 +@@ -10,16 +10,16 @@ + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + #include <float.h> + + #define INLINE_KERNEL_COSDF + #define INLINE_KERNEL_SINDF + #define INLINE_REM_PIO2F + #include "math_private.h" +--- a/s_exp2.cpp 2022-12-11 21:20:40.290068458 -0500 ++++ b/s_exp2.cpp_new 2022-12-11 21:23:32.275884511 -0500 +@@ -22,16 +22,16 @@ + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + #include <float.h> + + #include "math_private.h" + + #define TBLBITS 8 + #define TBLSIZE (1 << TBLBITS) +--- a/s_exp2f.cpp 2022-12-11 21:20:40.290068458 -0500 ++++ b/s_exp2f.cpp_new 2022-12-11 21:23:32.311884872 -0500 +@@ -22,16 +22,16 @@ + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + #include <float.h> + + #include "math_private.h" + + #define TBLBITS 4 + #define TBLSIZE (1 << TBLBITS) +--- a/s_fabsf.cpp 2022-12-11 21:20:40.290068458 -0500 ++++ b/s_fabsf.cpp_new 2022-12-11 21:23:32.347885233 -0500 +@@ -9,16 +9,16 @@ + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + /* + * fabsf(x) returns the absolute value of x. + */ + + #include "math_private.h" + +--- a/s_sinf.cpp 2022-12-11 21:20:40.290068458 -0500 ++++ b/s_sinf.cpp_new 2022-12-11 21:23:32.383885594 -0500 +@@ -10,16 +10,16 @@ + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + #include <float.h> + + #define INLINE_KERNEL_COSDF + #define INLINE_KERNEL_SINDF + #define INLINE_REM_PIO2F + #include "math_private.h" +--- a/s_tanf.cpp 2022-12-11 21:20:40.290068458 -0500 ++++ b/s_tanf.cpp_new 2022-12-11 21:23:32.419885954 -0500 +@@ -10,16 +10,16 @@ + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#include <sys/cdefs.h> +-__FBSDID("$FreeBSD$"); ++//#include <sys/cdefs.h> ++//__FBSDID("$FreeBSD$"); + + #include <float.h> + + #define INLINE_KERNEL_TANDF + #define INLINE_REM_PIO2F + #include "math_private.h" + #include "e_rem_pio2f.c" +--- a/e_sqrtf.cpp 2022-12-13 14:30:13.113415455 -0500 ++++ b/e_sqrtf.cpp 2022-12-13 14:13:15.302434550 -0500 +@@ -8,19 +8,19 @@ + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +-#ifndef lint +-static char rcsid[] = "$FreeBSD$"; +-#endif ++//#ifndef lint ++//static char rcsid[] = "$FreeBSD$"; ++//#endif + + #include "math_private.h" + + #ifdef USE_BUILTIN_SQRTF + float + __ieee754_sqrtf(float x) + { + return (__builtin_sqrtf(x)); diff --git a/modules/fdlibm/patches/10_remove_unused_function_from_k_exp_cpp.patch b/modules/fdlibm/patches/10_remove_unused_function_from_k_exp_cpp.patch new file mode 100644 index 0000000000..0cd417bcd2 --- /dev/null +++ b/modules/fdlibm/patches/10_remove_unused_function_from_k_exp_cpp.patch @@ -0,0 +1,107 @@ +diff --git a/k_exp.cpp b/k_exp.cpp +--- a/k_exp.cpp ++++ b/k_exp.cpp +@@ -24,18 +24,16 @@ + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + + //#include <sys/cdefs.h> + //__FBSDID("$FreeBSD$"); + +-#include <complex.h> +- + #include "math_private.h" + + static const uint32_t k = 1799; /* constant for reduction */ + static const double kln2 = 1246.97177782734161156; /* k * ln2 */ + + /* + * Compute exp(x), scaled to avoid spurious overflow. An exponent is + * returned separately in 'expt'. +@@ -78,33 +76,8 @@ __ldexp_exp(double x, int expt) + double exp_x, scale; + int ex_expt; + + exp_x = __frexp_exp(x, &ex_expt); + expt += ex_expt; + INSERT_WORDS(scale, (0x3ff + expt) << 20, 0); + return (exp_x * scale); + } +- +-double complex +-__ldexp_cexp(double complex z, int expt) +-{ +- double c, exp_x, s, scale1, scale2, x, y; +- int ex_expt, half_expt; +- +- x = creal(z); +- y = cimag(z); +- exp_x = __frexp_exp(x, &ex_expt); +- expt += ex_expt; +- +- /* +- * Arrange so that scale1 * scale2 == 2**expt. We use this to +- * compensate for scalbn being horrendously slow. +- */ +- half_expt = expt / 2; +- INSERT_WORDS(scale1, (0x3ff + half_expt) << 20, 0); +- half_expt = expt - half_expt; +- INSERT_WORDS(scale2, (0x3ff + half_expt) << 20, 0); +- +- sincos(y, &s, &c); +- return (CMPLX(c * exp_x * scale1 * scale2, +- s * exp_x * scale1 * scale2)); +-} +--- a/k_expf.cpp 2022-12-13 14:39:11.791594163 -0500 ++++ b/k_expf.cpp 2022-12-13 14:39:18.631622916 -0500 +@@ -24,18 +24,16 @@ + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + + //#include <sys/cdefs.h> + //__FBSDID("$FreeBSD$"); + +-#include <complex.h> +- + #include "math_private.h" + + static const uint32_t k = 235; /* constant for reduction */ + static const float kln2 = 162.88958740F; /* k * ln2 */ + + /* + * See k_exp.c for details. + * +@@ -61,29 +59,8 @@ + float exp_x, scale; + int ex_expt; + + exp_x = __frexp_expf(x, &ex_expt); + expt += ex_expt; + SET_FLOAT_WORD(scale, (0x7f + expt) << 23); + return (exp_x * scale); + } +- +-float complex +-__ldexp_cexpf(float complex z, int expt) +-{ +- float c, exp_x, s, scale1, scale2, x, y; +- int ex_expt, half_expt; +- +- x = crealf(z); +- y = cimagf(z); +- exp_x = __frexp_expf(x, &ex_expt); +- expt += ex_expt; +- +- half_expt = expt / 2; +- SET_FLOAT_WORD(scale1, (0x7f + half_expt) << 23); +- half_expt = expt - half_expt; +- SET_FLOAT_WORD(scale2, (0x7f + half_expt) << 23); +- +- sincosf(y, &s, &c); +- return (CMPLXF(c * exp_x * scale1 * scale2, +- s * exp_x * scale1 * scale2)); +-} diff --git a/modules/fdlibm/patches/11_include_cfloat_to_use_flt_eval_method.patch b/modules/fdlibm/patches/11_include_cfloat_to_use_flt_eval_method.patch new file mode 100644 index 0000000000..a2b7d959a6 --- /dev/null +++ b/modules/fdlibm/patches/11_include_cfloat_to_use_flt_eval_method.patch @@ -0,0 +1,21 @@ +diff --git a/math_private.h b/math_private.h +--- a/math_private.h ++++ b/math_private.h +@@ -12,16 +12,17 @@ + /* + * from: @(#)fdlibm.h 5.1 93/09/24 + * $FreeBSD$ + */ + + #ifndef _MATH_PRIVATE_H_ + #define _MATH_PRIVATE_H_ + ++#include <cfloat> + #include <stdint.h> + #include <sys/types.h> + + #include "mozilla/EndianUtils.h" + + #include "fdlibm.h" + + /* diff --git a/modules/fdlibm/patches/12_define_u_int32_t_and_u_int64_t_on_windows.patch b/modules/fdlibm/patches/12_define_u_int32_t_and_u_int64_t_on_windows.patch new file mode 100644 index 0000000000..895509c8d2 --- /dev/null +++ b/modules/fdlibm/patches/12_define_u_int32_t_and_u_int64_t_on_windows.patch @@ -0,0 +1,27 @@ +diff --git a/math_private.h b/math_private.h +--- a/math_private.h ++++ b/math_private.h +@@ -33,16 +33,23 @@ + * to dig two 32 bit words out of the 64 bit IEEE floating point + * value. That is non-ANSI, and, moreover, the gcc instruction + * scheduler gets it wrong. We instead use the following macros. + * Unlike the original code, we determine the endianness at compile + * time, not at run time; I don't see much benefit to selecting + * endianness at run time. + */ + ++#ifndef u_int32_t ++#define u_int32_t uint32_t ++#endif ++#ifndef u_int64_t ++#define u_int64_t uint64_t ++#endif ++ + /* A union which permits us to convert between a long double and + four 32 bit ints. */ + + #if MOZ_BIG_ENDIAN() + + typedef union + { + long double value; diff --git a/modules/fdlibm/patches/13_define_strict_assign_even_if_flt_eval_method_is_not_defined.patch b/modules/fdlibm/patches/13_define_strict_assign_even_if_flt_eval_method_is_not_defined.patch new file mode 100644 index 0000000000..a0417602d5 --- /dev/null +++ b/modules/fdlibm/patches/13_define_strict_assign_even_if_flt_eval_method_is_not_defined.patch @@ -0,0 +1,31 @@ +diff --git a/math_private.h b/math_private.h +--- a/math_private.h ++++ b/math_private.h +@@ -323,16 +323,27 @@ do { \ + if (sizeof(type) >= sizeof(long double)) \ + (lval) = (rval); \ + else { \ + __lval = (rval); \ + (lval) = __lval; \ + } \ + } while (0) + #endif ++#else ++#define STRICT_ASSIGN(type, lval, rval) do { \ ++ volatile type __lval; \ ++ \ ++ if (sizeof(type) >= sizeof(long double)) \ ++ (lval) = (rval); \ ++ else { \ ++ __lval = (rval); \ ++ (lval) = __lval; \ ++ } \ ++} while (0) + #endif /* FLT_EVAL_METHOD */ + + /* Support switching the mode to FP_PE if necessary. */ + #if defined(__i386__) && !defined(NO_FPSETPREC) + #define ENTERI() ENTERIT(long double) + #define ENTERIT(returntype) \ + returntype __retval; \ + fp_prec_t __oprec; \ diff --git a/modules/fdlibm/patches/14_do_not_use_hexadecimal_floating_point_number.patch b/modules/fdlibm/patches/14_do_not_use_hexadecimal_floating_point_number.patch new file mode 100644 index 0000000000..151a7a3b11 --- /dev/null +++ b/modules/fdlibm/patches/14_do_not_use_hexadecimal_floating_point_number.patch @@ -0,0 +1,68 @@ +diff --git a/e_exp.cpp b/e_exp.cpp +--- a/e_exp.cpp ++++ b/e_exp.cpp +@@ -146,14 +146,17 @@ __ieee754_exp(double x) /* default IEEE double exp */ + if(k >= -1021) + INSERT_WORDS(twopk,((u_int32_t)(0x3ff+k))<<20, 0); + else + INSERT_WORDS(twopk,((u_int32_t)(0x3ff+(k+1000)))<<20, 0); + c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); + if(k==0) return one-((x*c)/(c-2.0)-x); + else y = one-((lo-(x*c)/(2.0-c))-hi); + if(k >= -1021) { +- if (k==1024) return y*2.0*0x1p1023; ++ if (k==1024) { ++ double const_0x1p1023 = pow(2, 1023); ++ return y*2.0*const_0x1p1023; ++ } + return y*twopk; + } else { + return y*twopk*twom1000; + } + } +diff --git a/s_expm1.cpp b/s_expm1.cpp +--- a/s_expm1.cpp ++++ b/s_expm1.cpp +@@ -192,17 +192,20 @@ expm1(double x) + e -= hxs; + if(k== -1) return 0.5*(x-e)-0.5; + if(k==1) { + if(x < -0.25) return -2.0*(e-(x+0.5)); + else return one+2.0*(x-e); + } + if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ + y = one-(e-x); +- if (k == 1024) y = y*2.0*0x1p1023; ++ if (k == 1024) { ++ double const_0x1p1023 = pow(2, 1023); ++ y = y*2.0*const_0x1p1023; ++ } + else y = y*twopk; + return y-one; + } + t = one; + if(k<20) { + SET_HIGH_WORD(t,0x3ff00000 - (0x200000>>k)); /* t=1-2^-k */ + y = t-(e-x); + y = y*twopk; +--- a/s_exp2.cpp 2022-12-11 21:26:36.045643147 -0500 ++++ b/s_exp2.cpp_new 2022-12-11 21:28:42.058769925 -0500 +@@ -381,14 +381,16 @@ + INSERT_WORDS(twopk, 0x3ff00000 + k, 0); + else + INSERT_WORDS(twopkp1000, 0x3ff00000 + k + (1000 << 20), 0); + r = t + t * z * (P1 + z * (P2 + z * (P3 + z * (P4 + z * P5)))); + + /* Scale by 2**(k>>20). */ + if(k >= -(1021 << 20)) { +- if (k == 1024 << 20) +- return (r * 2.0 * 0x1p1023); ++ if (k == 1024 << 20) { ++ double const_0x1p1023 = pow(2, 1023); ++ return (r * 2.0 * const_0x1p1023); ++ } + return (r * twopk); + } else { + return (r * twopkp1000 * twom1000); + } + } diff --git a/modules/fdlibm/patches/15_remove_unused_rintl_function_from_s_nearbyint_cpp.patch b/modules/fdlibm/patches/15_remove_unused_rintl_function_from_s_nearbyint_cpp.patch new file mode 100644 index 0000000000..8c4f45a75a --- /dev/null +++ b/modules/fdlibm/patches/15_remove_unused_rintl_function_from_s_nearbyint_cpp.patch @@ -0,0 +1,13 @@ +diff --git a/s_nearbyint.cpp b/s_nearbyint.cpp +--- a/s_nearbyint.cpp ++++ b/s_nearbyint.cpp +@@ -54,9 +54,8 @@ fn(type x) \ + fegetenv(&env); \ + ret = rint(x); \ + fesetenv(&env); \ + return (ret); \ + } + + DECL(double, nearbyint, rint) + DECL(float, nearbyintf, rintf) +-DECL(long double, nearbyintl, rintl) diff --git a/modules/fdlibm/patches/16_use_safer_strict_assign_on_visual_studio.patch b/modules/fdlibm/patches/16_use_safer_strict_assign_on_visual_studio.patch new file mode 100644 index 0000000000..9f834149c6 --- /dev/null +++ b/modules/fdlibm/patches/16_use_safer_strict_assign_on_visual_studio.patch @@ -0,0 +1,22 @@ +diff --git a/math_private.h b/math_private.h +--- a/math_private.h ++++ b/math_private.h +@@ -309,17 +309,17 @@ do { \ + /* The above works on non-i386 too, but we use this to check v. */ + #define LD80C(m, ex, v) { .e = (v), } + #endif + + #ifdef FLT_EVAL_METHOD + /* + * Attempt to get strict C99 semantics for assignment with non-C99 compilers. + */ +-#if FLT_EVAL_METHOD == 0 || __GNUC__ == 0 ++#if !defined(_MSC_VER) && (FLT_EVAL_METHOD == 0 || __GNUC__ == 0) + #define STRICT_ASSIGN(type, lval, rval) ((lval) = (rval)) + #else + #define STRICT_ASSIGN(type, lval, rval) do { \ + volatile type __lval; \ + \ + if (sizeof(type) >= sizeof(long double)) \ + (lval) = (rval); \ + else { \ diff --git a/modules/fdlibm/patches/17_exp_exact_result_for_positive_one.patch b/modules/fdlibm/patches/17_exp_exact_result_for_positive_one.patch new file mode 100644 index 0000000000..ada59b23a2 --- /dev/null +++ b/modules/fdlibm/patches/17_exp_exact_result_for_positive_one.patch @@ -0,0 +1,40 @@ +diff --git a/e_exp.cpp b/e_exp.cpp +--- a/e_exp.cpp ++++ b/e_exp.cpp +@@ -91,16 +91,18 @@ ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */ + -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */ + invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */ + P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ + P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ + P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ + P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ + P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */ + ++static const double E = 2.7182818284590452354; /* e */ ++ + static volatile double + huge = 1.0e+300, + twom1000= 9.33263618503218878990e-302; /* 2**-1000=0x01700000,0*/ + + double + __ieee754_exp(double x) /* default IEEE double exp */ + { + double y,hi=0.0,lo=0.0,c,t,twopk; +@@ -122,16 +124,17 @@ __ieee754_exp(double x) /* default IEEE double exp */ + } + if(x > o_threshold) return huge*huge; /* overflow */ + if(x < u_threshold) return twom1000*twom1000; /* underflow */ + } + + /* argument reduction */ + if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ + if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ ++ if (x == 1.0) return E; + hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; + } else { + k = (int)(invln2*x+halF[xsb]); + t = k; + hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ + lo = t*ln2LO[0]; + } + STRICT_ASSIGN(double, x, hi - lo); diff --git a/modules/fdlibm/patches/18_use_stdlib_sqrt.patch b/modules/fdlibm/patches/18_use_stdlib_sqrt.patch new file mode 100644 index 0000000000..a4f9f3f003 --- /dev/null +++ b/modules/fdlibm/patches/18_use_stdlib_sqrt.patch @@ -0,0 +1,289 @@ +diff --git a/e_acos.cpp b/e_acos.cpp +--- a/e_acos.cpp ++++ b/e_acos.cpp +@@ -33,16 +33,17 @@ + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + * Function needed: sqrt + */ + ++#include <cmath> + #include <float.h> + + #include "math_private.h" + + static const double + one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ + pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ + pio2_hi = 1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */ +@@ -82,23 +83,23 @@ __ieee754_acos(double x) + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + r = p/q; + return pio2_hi - (x - (pio2_lo-x*r)); + } else if (hx<0) { /* x < -0.5 */ + z = (one+x)*0.5; + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); +- s = sqrt(z); ++ s = std::sqrt(z); + r = p/q; + w = r*s-pio2_lo; + return pi - 2.0*(s+w); + } else { /* x > 0.5 */ + z = (one-x)*0.5; +- s = sqrt(z); ++ s = std::sqrt(z); + df = s; + SET_LOW_WORD(df,0); + c = (z-df*df)/(s+df); + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + r = p/q; + w = r*s+c; + return 2.0*(df+w); +diff --git a/e_acosh.cpp b/e_acosh.cpp +--- a/e_acosh.cpp ++++ b/e_acosh.cpp +@@ -24,16 +24,17 @@ + * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else + * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. + * + * Special cases: + * acosh(x) is NaN with signal if x<1. + * acosh(NaN) is NaN without signal. + */ + ++#include <cmath> + #include <float.h> + + #include "math_private.h" + + static const double + one = 1.0, + ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ + +@@ -50,14 +51,14 @@ __ieee754_acosh(double x) + if(hx >=0x7ff00000) { /* x is inf of NaN */ + return x+x; + } else + return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */ + } else if(((hx-0x3ff00000)|lx)==0) { + return 0.0; /* acosh(1) = 0 */ + } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ + t=x*x; +- return __ieee754_log(2.0*x-one/(x+sqrt(t-one))); ++ return __ieee754_log(2.0*x-one/(x+std::sqrt(t-one))); + } else { /* 1<x<2 */ + t = x-one; +- return log1p(t+sqrt(2.0*t+t*t)); ++ return log1p(t+std::sqrt(2.0*t+t*t)); + } + } +diff --git a/e_asin.cpp b/e_asin.cpp +--- a/e_asin.cpp ++++ b/e_asin.cpp +@@ -39,16 +39,17 @@ + * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c)) + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + */ + ++#include <cmath> + #include <float.h> + + #include "math_private.h" + + static const double + one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ + huge = 1.000e+300, + pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ +@@ -90,17 +91,17 @@ __ieee754_asin(double x) + w = p/q; + return x+x*w; + } + /* 1> |x|>= 0.5 */ + w = one-fabs(x); + t = w*0.5; + p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); + q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); +- s = sqrt(t); ++ s = std::sqrt(t); + if(ix>=0x3FEF3333) { /* if |x| > 0.975 */ + w = p/q; + t = pio2_hi-(2.0*(s+s*w)-pio2_lo); + } else { + w = s; + SET_LOW_WORD(w,0); + c = (t-w*w)/(s+w); + r = p/q; +diff --git a/e_hypot.cpp b/e_hypot.cpp +--- a/e_hypot.cpp ++++ b/e_hypot.cpp +@@ -41,16 +41,17 @@ + * hypot(x,y) is INF if x or y is +INF or -INF; else + * hypot(x,y) is NAN if x or y is NAN. + * + * Accuracy: + * hypot(x,y) returns sqrt(x^2+y^2) with error less + * than 1 ulps (units in the last place) + */ + ++#include <cmath> + #include <float.h> + + #include "math_private.h" + + double + __ieee754_hypot(double x, double y) + { + double a,b,t1,t2,y1,y2,w; +@@ -100,25 +101,25 @@ __ieee754_hypot(double x, double y) + } + } + /* medium size a and b */ + w = a-b; + if (w>b) { + t1 = 0; + SET_HIGH_WORD(t1,ha); + t2 = a-t1; +- w = sqrt(t1*t1-(b*(-b)-t2*(a+t1))); ++ w = std::sqrt(t1*t1-(b*(-b)-t2*(a+t1))); + } else { + a = a+a; + y1 = 0; + SET_HIGH_WORD(y1,hb); + y2 = b - y1; + t1 = 0; + SET_HIGH_WORD(t1,ha+0x00100000); + t2 = a - t1; +- w = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); ++ w = std::sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); + } + if(k!=0) { + t1 = 0.0; + SET_HIGH_WORD(t1,(1023+k)<<20); + return t1*w; + } else return w; + } +diff --git a/e_pow.cpp b/e_pow.cpp +--- a/e_pow.cpp ++++ b/e_pow.cpp +@@ -52,16 +52,17 @@ + * + * Constants : + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + ++#include <cmath> + #include <float.h> + #include "math_private.h" + + static const double + bp[] = {1.0, 1.5,}, + dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ + dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ + zero = 0.0, +@@ -151,17 +152,17 @@ __ieee754_pow(double x, double y) + return (hy<0)?-y: zero; + } + if(iy==0x3ff00000) { /* y is +-1 */ + if(hy<0) return one/x; else return x; + } + if(hy==0x40000000) return x*x; /* y is 2 */ + if(hy==0x3fe00000) { /* y is 0.5 */ + if(hx>=0) /* x >= +0 */ +- return sqrt(x); ++ return std::sqrt(x); + } + } + + ax = fabs(x); + /* special value of x */ + if(lx==0) { + if(ix==0x7ff00000||ix==0||ix==0x3ff00000){ + z = ax; /*x is +-0,+-inf,+-1*/ +diff --git a/s_asinh.cpp b/s_asinh.cpp +--- a/s_asinh.cpp ++++ b/s_asinh.cpp +@@ -19,16 +19,17 @@ + * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] + * we have + * asinh(x) := x if 1+x*x=1, + * := sign(x)*(log(x)+ln2)) for large |x|, else + * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else + * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) + */ + ++#include <cmath> + #include <float.h> + + #include "math_private.h" + + static const double + one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ + ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ + huge= 1.00000000000000000000e+300; +@@ -43,15 +44,15 @@ asinh(double x) + if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ + if(ix< 0x3e300000) { /* |x|<2**-28 */ + if(huge+x>one) return x; /* return x inexact except 0 */ + } + if(ix>0x41b00000) { /* |x| > 2**28 */ + w = __ieee754_log(fabs(x))+ln2; + } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ + t = fabs(x); +- w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t)); ++ w = __ieee754_log(2.0*t+one/(std::sqrt(x*x+one)+t)); + } else { /* 2.0 > |x| > 2**-28 */ + t = x*x; +- w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t))); ++ w =log1p(fabs(x)+t/(one+std::sqrt(one+t))); + } + if(hx>0) return w; else return -w; + } +--- a/e_asinf.cpp 2022-12-13 14:45:17.953154257 -0500 ++++ b/e_asinf.cpp 2022-12-13 14:45:03.425091710 -0500 +@@ -11,16 +11,18 @@ + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + + //#include <sys/cdefs.h> + //__FBSDID("$FreeBSD$"); + ++#include <cmath> ++ + #include "math_private.h" + + static const float + one = 1.0000000000e+00, /* 0x3F800000 */ + huge = 1.000e+30, + /* coefficient for R(x^2) */ + pS0 = 1.6666586697e-01, + pS1 = -4.2743422091e-02, +@@ -52,13 +54,13 @@ + w = p/q; + return x+x*w; + } + /* 1> |x|>= 0.5 */ + w = one-fabsf(x); + t = w*(float)0.5; + p = t*(pS0+t*(pS1+t*pS2)); + q = one+t*qS1; +- s = sqrt(t); ++ s = std::sqrt(t); + w = p/q; + t = pio2-2.0*(s+s*w); + if(hx>0) return t; else return -t; + } diff --git a/modules/fdlibm/patches/19_remove_unneeded_round_to_integer_helpers.patch b/modules/fdlibm/patches/19_remove_unneeded_round_to_integer_helpers.patch new file mode 100644 index 0000000000..8720d8c0ed --- /dev/null +++ b/modules/fdlibm/patches/19_remove_unneeded_round_to_integer_helpers.patch @@ -0,0 +1,50 @@ +diff --git a/math_private.h b/math_private.h +--- a/math_private.h ++++ b/math_private.h +@@ -612,46 +612,16 @@ rnint(__double_t x) + * magic number would need to be variable. Assuming that the + * rounding precision is always the default is too fragile. This + * and many other complications will move when the default is + * changed to FP_PE. + */ + return ((double)(x + 0x1.8p52) - 0x1.8p52); + } + +-static inline float +-rnintf(__float_t x) +-{ +- /* +- * As for rnint(), except we could just call that to handle the +- * extra precision case, usually without losing efficiency. +- */ +- return ((float)(x + 0x1.8p23F) - 0x1.8p23F); +-} +- +-#ifdef LDBL_MANT_DIG +-/* +- * The complications for extra precision are smaller for rnintl() since it +- * can safely assume that the rounding precision has been increased from +- * its default to FP_PE on x86. We don't exploit that here to get small +- * optimizations from limiting the rangle to double. We just need it for +- * the magic number to work with long doubles. ld128 callers should use +- * rnint() instead of this if possible. ld80 callers should prefer +- * rnintl() since for amd64 this avoids swapping the register set, while +- * for i386 it makes no difference (assuming FP_PE), and for other arches +- * it makes little difference. +- */ +-static inline long double +-rnintl(long double x) +-{ +- return (x + __CONCAT(0x1.8p, LDBL_MANT_DIG) / 2 - +- __CONCAT(0x1.8p, LDBL_MANT_DIG) / 2); +-} +-#endif /* LDBL_MANT_DIG */ +- + /* + * irint() and i64rint() give the same result as casting to their integer + * return type provided their arg is a floating point integer. They can + * sometimes be more efficient because no rounding is required. + */ + #if defined(amd64) || defined(__i386__) + #define irint(x) \ + (sizeof(x) == sizeof(float) && \ diff --git a/modules/fdlibm/patches/20_emulate_freebsd_internal_double_types.patch b/modules/fdlibm/patches/20_emulate_freebsd_internal_double_types.patch new file mode 100644 index 0000000000..d22073391e --- /dev/null +++ b/modules/fdlibm/patches/20_emulate_freebsd_internal_double_types.patch @@ -0,0 +1,28 @@ +diff --git a/math_private.h b/math_private.h +--- a/math_private.h ++++ b/math_private.h +@@ -20,16 +20,24 @@ + #include <cfloat> + #include <stdint.h> + #include <sys/types.h> + + #include "mozilla/EndianUtils.h" + + #include "fdlibm.h" + ++/* ++ * Emulate FreeBSD internal double types. ++ * Adapted from https://github.com/freebsd/freebsd-src/search?q=__double_t ++ */ ++ ++typedef double __double_t; ++typedef __double_t double_t; ++ + /* + * The original fdlibm code used statements like: + * n0 = ((*(int*)&one)>>29)^1; * index of high word * + * ix0 = *(n0+(int*)&x); * high word of x * + * ix1 = *((1-n0)+(int*)&x); * low word of x * + * to dig two 32 bit words out of the 64 bit IEEE floating point + * value. That is non-ANSI, and, moreover, the gcc instruction + * scheduler gets it wrong. We instead use the following macros. diff --git a/modules/fdlibm/patches/21_rem_pio_fixups.patch b/modules/fdlibm/patches/21_rem_pio_fixups.patch new file mode 100644 index 0000000000..8961db62c3 --- /dev/null +++ b/modules/fdlibm/patches/21_rem_pio_fixups.patch @@ -0,0 +1,226 @@ +diff --git a/e_rem_pio2.cpp b/e_rem_pio2.cpp +--- a/e_rem_pio2.cpp ++++ b/e_rem_pio2.cpp +@@ -43,17 +43,17 @@ invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ + pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ + pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ + pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ + pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ + pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ + pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ + + #ifdef INLINE_REM_PIO2 +-static __inline __always_inline ++static inline + #endif + int + __ieee754_rem_pio2(double x, double *y) + { + double z,w,t,r,fn; + double tx[3],ty[2]; + int32_t e0,i,j,nx,n,ix,hx; + u_int32_t low; +diff --git a/k_rem_pio2.cpp b/k_rem_pio2.cpp +--- a/k_rem_pio2.cpp ++++ b/k_rem_pio2.cpp +@@ -305,17 +305,18 @@ __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec) + q0 = e0-24*(jv+1); + + /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ + j = jv-jx; m = jx+jk; + for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j]; + + /* compute q[0],q[1],...q[jk] */ + for (i=0;i<=jk;i++) { +- for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw; ++ for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; ++ q[i] = fw; + } + + jz = jk; + recompute: + /* distill q[] into iq[] reversingly */ + for(i=0,j=jz,z=q[jz];j>0;i++,j--) { + fw = (double)((int32_t)(twon24* z)); + iq[i] = (int32_t)(z-two24*fw); +diff --git a/s_cos.cpp b/s_cos.cpp +--- a/s_cos.cpp ++++ b/s_cos.cpp +@@ -43,17 +43,17 @@ + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + + #include <float.h> + + #define INLINE_REM_PIO2 + #include "math_private.h" +-#include "e_rem_pio2.c" ++#include "e_rem_pio2.cpp" + + double + cos(double x) + { + double y[2],z=0.0; + int32_t n, ix; + + /* High word of x. */ +diff --git a/s_sin.cpp b/s_sin.cpp +--- a/s_sin.cpp ++++ b/s_sin.cpp +@@ -43,17 +43,17 @@ + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + + #include <float.h> + + #define INLINE_REM_PIO2 + #include "math_private.h" +-#include "e_rem_pio2.c" ++#include "e_rem_pio2.cpp" + + double + sin(double x) + { + double y[2],z=0.0; + int32_t n, ix; + + /* High word of x. */ +diff --git a/s_tan.cpp b/s_tan.cpp +--- a/s_tan.cpp ++++ b/s_tan.cpp +@@ -42,17 +42,17 @@ + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + + #include <float.h> + + #define INLINE_REM_PIO2 + #include "math_private.h" +-#include "e_rem_pio2.c" ++#include "e_rem_pio2.cpp" + + double + tan(double x) + { + double y[2],z=0.0; + int32_t n, ix; + + /* High word of x. */ +--- a/s_cosf.cpp 2022-12-11 21:26:36.041643110 -0500 ++++ b/s_cosf.cpp 2022-12-11 21:34:08.197486828 -0500 +@@ -18,19 +18,19 @@ + //__FBSDID("$FreeBSD$"); + + #include <float.h> + + #define INLINE_KERNEL_COSDF + #define INLINE_KERNEL_SINDF + #define INLINE_REM_PIO2F + #include "math_private.h" +-#include "e_rem_pio2f.c" +-#include "k_cosf.c" +-#include "k_sinf.c" ++#include "e_rem_pio2f.cpp" ++#include "k_cosf.cpp" ++#include "k_sinf.cpp" + + /* Small multiples of pi/2 rounded to double precision. */ + static const double + c1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */ + c2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */ + c3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */ + c4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */ + +--- a/s_sinf.cpp 2022-12-11 21:26:36.045643147 -0500 ++++ b/s_sinf.cpp 2022-12-11 21:33:52.741362926 -0500 +@@ -18,19 +18,19 @@ + //__FBSDID("$FreeBSD$"); + + #include <float.h> + + #define INLINE_KERNEL_COSDF + #define INLINE_KERNEL_SINDF + #define INLINE_REM_PIO2F + #include "math_private.h" +-#include "e_rem_pio2f.c" +-#include "k_cosf.c" +-#include "k_sinf.c" ++#include "e_rem_pio2f.cpp" ++#include "k_cosf.cpp" ++#include "k_sinf.cpp" + + /* Small multiples of pi/2 rounded to double precision. */ + static const double + s1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */ + s2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */ + s3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */ + s4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */ + +--- a/s_tanf.cpp 2022-12-11 21:26:36.045643147 -0500 ++++ b/s_tanf.cpp 2022-12-11 21:33:45.269302886 -0500 +@@ -17,18 +17,18 @@ + //#include <sys/cdefs.h> + //__FBSDID("$FreeBSD$"); + + #include <float.h> + + #define INLINE_KERNEL_TANDF + #define INLINE_REM_PIO2F + #include "math_private.h" +-#include "e_rem_pio2f.c" +-#include "k_tanf.c" ++#include "e_rem_pio2f.cpp" ++#include "k_tanf.cpp" + + /* Small multiples of pi/2 rounded to double precision. */ + static const double + t1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */ + t2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */ + t3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */ + t4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */ + +--- a/e_rem_pio2f.cpp 2022-12-13 14:50:12.582776365 -0500 ++++ b/e_rem_pio2f.cpp 2022-12-13 14:51:05.003200166 -0500 +@@ -35,17 +35,17 @@ + */ + + static const double + invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ + pio2_1 = 1.57079631090164184570e+00, /* 0x3FF921FB, 0x50000000 */ + pio2_1t = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */ + + #ifdef INLINE_REM_PIO2F +-static __inline __always_inline ++static inline + #endif + int + __ieee754_rem_pio2f(float x, double *y) + { + double w,r,fn; + double tx[1],ty[1]; + float z; + int32_t e0,n,ix,hx; +--- a/e_powf.cpp ++++ b/e_powf.cpp +@@ -11,16 +11,18 @@ + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + + //#include <sys/cdefs.h> + //__FBSDID("$FreeBSD$"); + ++#include "s_scalbnf.cpp" ++ + #include "math_private.h" + + static const float + bp[] = {1.0, 1.5,}, + dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */ + dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */ + zero = 0.0, + half = 0.5, diff --git a/modules/fdlibm/patches/22_add_float_types.patch b/modules/fdlibm/patches/22_add_float_types.patch new file mode 100644 index 0000000000..39b991a486 --- /dev/null +++ b/modules/fdlibm/patches/22_add_float_types.patch @@ -0,0 +1,66 @@ +diff --git a/math_private.h b/math_private.h +--- a/math_private.h ++++ b/math_private.h +@@ -27,16 +27,17 @@ + + /* + * Emulate FreeBSD internal double types. + * Adapted from https://github.com/freebsd/freebsd-src/search?q=__double_t + */ + + typedef double __double_t; + typedef __double_t double_t; ++typedef float __float_t; + + /* + * The original fdlibm code used statements like: + * n0 = ((*(int*)&one)>>29)^1; * index of high word * + * ix0 = *(n0+(int*)&x); * high word of x * + * ix1 = *((1-n0)+(int*)&x); * low word of x * + * to dig two 32 bit words out of the 64 bit IEEE floating point + * value. That is non-ANSI, and, moreover, the gcc instruction +diff --git a/e_rem_pio2f.cpp b/e_rem_pio2f.cpp +--- a/e_rem_pio2f.cpp ++++ b/e_rem_pio2f.cpp +@@ -49,17 +49,17 @@ int + double tx[1],ty[1]; + float z; + int32_t e0,n,ix,hx; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + /* 33+53 bit pi is good enough for medium size */ + if(ix<0x4dc90fdb) { /* |x| ~< 2^28*(pi/2), medium size */ +- fn = rnint((float_t)x*invpio2); ++ fn = rnint((float)x*invpio2); + n = irint(fn); + r = x-fn*pio2_1; + w = fn*pio2_1t; + *y = r-w; + return n; + } + /* + * all other (large) arguments +diff --git a/s_scalbnf.cpp b/s_scalbnf.cpp +--- a/s_scalbnf.cpp ++++ b/s_scalbnf.cpp +@@ -7,18 +7,18 @@ + * for all contributors to musl. + */ + #include <stdint.h> + + #include "math_private.h" + + float scalbnf(float x, int n) + { + union {float f; uint32_t i;} u; +- float_t y = x; ++ float y = x; + + if (n > 127) { + y *= 0x1p127f; + n -= 127; + if (n > 127) { + y *= 0x1p127f; + n -= 127; + if (n > 127) diff --git a/modules/fdlibm/rename_c_to_cpp.sh b/modules/fdlibm/rename_c_to_cpp.sh new file mode 100755 index 0000000000..1b7855bc11 --- /dev/null +++ b/modules/fdlibm/rename_c_to_cpp.sh @@ -0,0 +1,7 @@ +#!/bin/sh + +set -e + +for i in *.c; do + mv "$i" "${i}pp" +done
\ No newline at end of file diff --git a/modules/fdlibm/src/LICENSE b/modules/fdlibm/src/LICENSE new file mode 100644 index 0000000000..d28d5c912d --- /dev/null +++ b/modules/fdlibm/src/LICENSE @@ -0,0 +1,11 @@ +Copyright 1992-2022 The FreeBSD Project. + +Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: + + Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. + + Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. + +THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + +The views and conclusions contained in the software and documentation are those of the authors and should not be interpreted as representing official policies, either expressed or implied, of the FreeBSD Project. diff --git a/modules/fdlibm/src/e_acos.cpp b/modules/fdlibm/src/e_acos.cpp new file mode 100644 index 0000000000..4f497b3b3f --- /dev/null +++ b/modules/fdlibm/src/e_acos.cpp @@ -0,0 +1,107 @@ + +/* @(#)e_acos.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* __ieee754_acos(x) + * Method : + * acos(x) = pi/2 - asin(x) + * acos(-x) = pi/2 + asin(x) + * For |x|<=0.5 + * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) + * For x>0.5 + * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) + * = 2asin(sqrt((1-x)/2)) + * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) + * = 2f + (2c + 2s*z*R(z)) + * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term + * for f so that f+c ~ sqrt(z). + * For x<-0.5 + * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) + * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + * Function needed: sqrt + */ + +#include <cmath> +#include <float.h> + +#include "math_private.h" + +static const double +one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ +pio2_hi = 1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */ +static volatile double +pio2_lo = 6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */ +static const double +pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ +pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ +pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ +pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ +pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ +pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ +qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ +qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ +qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ +qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ + +double +__ieee754_acos(double x) +{ + double z,p,q,r,w,s,c,df; + int32_t hx,ix; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x3ff00000) { /* |x| >= 1 */ + u_int32_t lx; + GET_LOW_WORD(lx,x); + if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */ + if(hx>0) return 0.0; /* acos(1) = 0 */ + else return pi+2.0*pio2_lo; /* acos(-1)= pi */ + } + return (x-x)/(x-x); /* acos(|x|>1) is NaN */ + } + if(ix<0x3fe00000) { /* |x| < 0.5 */ + if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ + z = x*x; + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + r = p/q; + return pio2_hi - (x - (pio2_lo-x*r)); + } else if (hx<0) { /* x < -0.5 */ + z = (one+x)*0.5; + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + s = std::sqrt(z); + r = p/q; + w = r*s-pio2_lo; + return pi - 2.0*(s+w); + } else { /* x > 0.5 */ + z = (one-x)*0.5; + s = std::sqrt(z); + df = s; + SET_LOW_WORD(df,0); + c = (z-df*df)/(s+df); + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + r = p/q; + w = r*s+c; + return 2.0*(df+w); + } +} diff --git a/modules/fdlibm/src/e_acosf.cpp b/modules/fdlibm/src/e_acosf.cpp new file mode 100644 index 0000000000..79f07a98b0 --- /dev/null +++ b/modules/fdlibm/src/e_acosf.cpp @@ -0,0 +1,76 @@ +/* e_acosf.c -- float version of e_acos.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +#include "math_private.h" + +static const float +one = 1.0000000000e+00, /* 0x3F800000 */ +pi = 3.1415925026e+00, /* 0x40490fda */ +pio2_hi = 1.5707962513e+00; /* 0x3fc90fda */ +static volatile float +pio2_lo = 7.5497894159e-08; /* 0x33a22168 */ +static const float +pS0 = 1.6666586697e-01, +pS1 = -4.2743422091e-02, +pS2 = -8.6563630030e-03, +qS1 = -7.0662963390e-01; + +float +__ieee754_acosf(float x) +{ + float z,p,q,r,w,s,c,df; + int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x3f800000) { /* |x| >= 1 */ + if(ix==0x3f800000) { /* |x| == 1 */ + if(hx>0) return 0.0; /* acos(1) = 0 */ + else return pi+(float)2.0*pio2_lo; /* acos(-1)= pi */ + } + return (x-x)/(x-x); /* acos(|x|>1) is NaN */ + } + if(ix<0x3f000000) { /* |x| < 0.5 */ + if(ix<=0x32800000) return pio2_hi+pio2_lo;/*if|x|<2**-26*/ + z = x*x; + p = z*(pS0+z*(pS1+z*pS2)); + q = one+z*qS1; + r = p/q; + return pio2_hi - (x - (pio2_lo-x*r)); + } else if (hx<0) { /* x < -0.5 */ + z = (one+x)*(float)0.5; + p = z*(pS0+z*(pS1+z*pS2)); + q = one+z*qS1; + s = sqrtf(z); + r = p/q; + w = r*s-pio2_lo; + return pi - (float)2.0*(s+w); + } else { /* x > 0.5 */ + int32_t idf; + z = (one-x)*(float)0.5; + s = sqrtf(z); + df = s; + GET_FLOAT_WORD(idf,df); + SET_FLOAT_WORD(df,idf&0xfffff000); + c = (z-df*df)/(s+df); + p = z*(pS0+z*(pS1+z*pS2)); + q = one+z*qS1; + r = p/q; + w = r*s+c; + return (float)2.0*(df+w); + } +} diff --git a/modules/fdlibm/src/e_acosh.cpp b/modules/fdlibm/src/e_acosh.cpp new file mode 100644 index 0000000000..ce52d5aaa7 --- /dev/null +++ b/modules/fdlibm/src/e_acosh.cpp @@ -0,0 +1,64 @@ + +/* @(#)e_acosh.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* __ieee754_acosh(x) + * Method : + * Based on + * acosh(x) = log [ x + sqrt(x*x-1) ] + * we have + * acosh(x) := log(x)+ln2, if x is large; else + * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else + * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. + * + * Special cases: + * acosh(x) is NaN with signal if x<1. + * acosh(NaN) is NaN without signal. + */ + +#include <cmath> +#include <float.h> + +#include "math_private.h" + +static const double +one = 1.0, +ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ + +double +__ieee754_acosh(double x) +{ + double t; + int32_t hx; + u_int32_t lx; + EXTRACT_WORDS(hx,lx,x); + if(hx<0x3ff00000) { /* x < 1 */ + return (x-x)/(x-x); + } else if(hx >=0x41b00000) { /* x > 2**28 */ + if(hx >=0x7ff00000) { /* x is inf of NaN */ + return x+x; + } else + return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */ + } else if(((hx-0x3ff00000)|lx)==0) { + return 0.0; /* acosh(1) = 0 */ + } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ + t=x*x; + return __ieee754_log(2.0*x-one/(x+std::sqrt(t-one))); + } else { /* 1<x<2 */ + t = x-one; + return log1p(t+std::sqrt(2.0*t+t*t)); + } +} diff --git a/modules/fdlibm/src/e_asin.cpp b/modules/fdlibm/src/e_asin.cpp new file mode 100644 index 0000000000..e896bde9ea --- /dev/null +++ b/modules/fdlibm/src/e_asin.cpp @@ -0,0 +1,113 @@ + +/* @(#)e_asin.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* __ieee754_asin(x) + * Method : + * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ... + * we approximate asin(x) on [0,0.5] by + * asin(x) = x + x*x^2*R(x^2) + * where + * R(x^2) is a rational approximation of (asin(x)-x)/x^3 + * and its remez error is bounded by + * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75) + * + * For x in [0.5,1] + * asin(x) = pi/2-2*asin(sqrt((1-x)/2)) + * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2; + * then for x>0.98 + * asin(x) = pi/2 - 2*(s+s*z*R(z)) + * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo) + * For x<=0.98, let pio4_hi = pio2_hi/2, then + * f = hi part of s; + * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z) + * and + * asin(x) = pi/2 - 2*(s+s*z*R(z)) + * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo) + * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c)) + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + */ + +#include <cmath> +#include <float.h> + +#include "math_private.h" + +static const double +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +huge = 1.000e+300, +pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ +pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ +pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */ + /* coefficient for R(x^2) */ +pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ +pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ +pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ +pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ +pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ +pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ +qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ +qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ +qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ +qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ + +double +__ieee754_asin(double x) +{ + double t=0.0,w,p,q,c,r,s; + int32_t hx,ix; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>= 0x3ff00000) { /* |x|>= 1 */ + u_int32_t lx; + GET_LOW_WORD(lx,x); + if(((ix-0x3ff00000)|lx)==0) + /* asin(1)=+-pi/2 with inexact */ + return x*pio2_hi+x*pio2_lo; + return (x-x)/(x-x); /* asin(|x|>1) is NaN */ + } else if (ix<0x3fe00000) { /* |x|<0.5 */ + if(ix<0x3e500000) { /* if |x| < 2**-26 */ + if(huge+x>one) return x;/* return x with inexact if x!=0*/ + } + t = x*x; + p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); + q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); + w = p/q; + return x+x*w; + } + /* 1> |x|>= 0.5 */ + w = one-fabs(x); + t = w*0.5; + p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); + q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); + s = std::sqrt(t); + if(ix>=0x3FEF3333) { /* if |x| > 0.975 */ + w = p/q; + t = pio2_hi-(2.0*(s+s*w)-pio2_lo); + } else { + w = s; + SET_LOW_WORD(w,0); + c = (t-w*w)/(s+w); + r = p/q; + p = 2.0*s*r-(pio2_lo-2.0*c); + q = pio4_hi-2.0*w; + t = pio4_hi-(p-q); + } + if(hx>0) return t; else return -t; +} diff --git a/modules/fdlibm/src/e_asinf.cpp b/modules/fdlibm/src/e_asinf.cpp new file mode 100644 index 0000000000..62727032c9 --- /dev/null +++ b/modules/fdlibm/src/e_asinf.cpp @@ -0,0 +1,66 @@ +/* e_asinf.c -- float version of e_asin.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +#include <cmath> + +#include "math_private.h" + +static const float +one = 1.0000000000e+00, /* 0x3F800000 */ +huge = 1.000e+30, + /* coefficient for R(x^2) */ +pS0 = 1.6666586697e-01, +pS1 = -4.2743422091e-02, +pS2 = -8.6563630030e-03, +qS1 = -7.0662963390e-01; + +static const double +pio2 = 1.570796326794896558e+00; + +float +__ieee754_asinf(float x) +{ + double s; + float t,w,p,q; + int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x3f800000) { /* |x| >= 1 */ + if(ix==0x3f800000) /* |x| == 1 */ + return x*pio2; /* asin(+-1) = +-pi/2 with inexact */ + return (x-x)/(x-x); /* asin(|x|>1) is NaN */ + } else if (ix<0x3f000000) { /* |x|<0.5 */ + if(ix<0x39800000) { /* |x| < 2**-12 */ + if(huge+x>one) return x;/* return x with inexact if x!=0*/ + } + t = x*x; + p = t*(pS0+t*(pS1+t*pS2)); + q = one+t*qS1; + w = p/q; + return x+x*w; + } + /* 1> |x|>= 0.5 */ + w = one-fabsf(x); + t = w*(float)0.5; + p = t*(pS0+t*(pS1+t*pS2)); + q = one+t*qS1; + s = std::sqrt(t); + w = p/q; + t = pio2-2.0*(s+s*w); + if(hx>0) return t; else return -t; +} diff --git a/modules/fdlibm/src/e_atan2.cpp b/modules/fdlibm/src/e_atan2.cpp new file mode 100644 index 0000000000..f45ad187fa --- /dev/null +++ b/modules/fdlibm/src/e_atan2.cpp @@ -0,0 +1,124 @@ + +/* @(#)e_atan2.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* __ieee754_atan2(y,x) + * Method : + * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). + * 2. Reduce x to positive by (if x and y are unexceptional): + * ARG (x+iy) = arctan(y/x) ... if x > 0, + * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, + * + * Special cases: + * + * ATAN2((anything), NaN ) is NaN; + * ATAN2(NAN , (anything) ) is NaN; + * ATAN2(+-0, +(anything but NaN)) is +-0 ; + * ATAN2(+-0, -(anything but NaN)) is +-pi ; + * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; + * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; + * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; + * ATAN2(+-INF,+INF ) is +-pi/4 ; + * ATAN2(+-INF,-INF ) is +-3pi/4; + * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include <float.h> + +#include "math_private.h" + +static volatile double +tiny = 1.0e-300; +static const double +zero = 0.0, +pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ +pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ +pi = 3.1415926535897931160E+00; /* 0x400921FB, 0x54442D18 */ +static volatile double +pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ + +double +__ieee754_atan2(double y, double x) +{ + double z; + int32_t k,m,hx,hy,ix,iy; + u_int32_t lx,ly; + + EXTRACT_WORDS(hx,lx,x); + ix = hx&0x7fffffff; + EXTRACT_WORDS(hy,ly,y); + iy = hy&0x7fffffff; + if(((ix|((lx|-lx)>>31))>0x7ff00000)|| + ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ + return nan_mix(x, y); + if(hx==0x3ff00000&&lx==0) return atan(y); /* x=1.0 */ + m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ + + /* when y = 0 */ + if((iy|ly)==0) { + switch(m) { + case 0: + case 1: return y; /* atan(+-0,+anything)=+-0 */ + case 2: return pi+tiny;/* atan(+0,-anything) = pi */ + case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ + } + } + /* when x = 0 */ + if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* when x is INF */ + if(ix==0x7ff00000) { + if(iy==0x7ff00000) { + switch(m) { + case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ + case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ + case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ + case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ + } + } else { + switch(m) { + case 0: return zero ; /* atan(+...,+INF) */ + case 1: return -zero ; /* atan(-...,+INF) */ + case 2: return pi+tiny ; /* atan(+...,-INF) */ + case 3: return -pi-tiny ; /* atan(-...,-INF) */ + } + } + } + /* when y is INF */ + if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* compute y/x */ + k = (iy-ix)>>20; + if(k > 60) { /* |y/x| > 2**60 */ + z=pi_o_2+0.5*pi_lo; + m&=1; + } + else if(hx<0&&k<-60) z=0.0; /* 0 > |y|/x > -2**-60 */ + else z=atan(fabs(y/x)); /* safe to do y/x */ + switch (m) { + case 0: return z ; /* atan(+,+) */ + case 1: return -z ; /* atan(-,+) */ + case 2: return pi-(z-pi_lo);/* atan(+,-) */ + default: /* case 3 */ + return (z-pi_lo)-pi;/* atan(-,-) */ + } +} diff --git a/modules/fdlibm/src/e_atanh.cpp b/modules/fdlibm/src/e_atanh.cpp new file mode 100644 index 0000000000..a8f0f8deb3 --- /dev/null +++ b/modules/fdlibm/src/e_atanh.cpp @@ -0,0 +1,63 @@ + +/* @(#)e_atanh.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* __ieee754_atanh(x) + * Method : + * 1.Reduced x to positive by atanh(-x) = -atanh(x) + * 2.For x>=0.5 + * 1 2x x + * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) + * 2 1 - x 1 - x + * + * For x<0.5 + * atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) + * + * Special cases: + * atanh(x) is NaN if |x| > 1 with signal; + * atanh(NaN) is that NaN with no signal; + * atanh(+-1) is +-INF with signal. + * + */ + +#include <float.h> + +#include "math_private.h" + +static const double one = 1.0, huge = 1e300; +static const double zero = 0.0; + +double +__ieee754_atanh(double x) +{ + double t; + int32_t hx,ix; + u_int32_t lx; + EXTRACT_WORDS(hx,lx,x); + ix = hx&0x7fffffff; + if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */ + return (x-x)/(x-x); + if(ix==0x3ff00000) + return x/zero; + if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */ + SET_HIGH_WORD(x,ix); + if(ix<0x3fe00000) { /* x < 0.5 */ + t = x+x; + t = 0.5*log1p(t+t*x/(one-x)); + } else + t = 0.5*log1p((x+x)/(one-x)); + if(hx>=0) return t; else return -t; +} diff --git a/modules/fdlibm/src/e_cosh.cpp b/modules/fdlibm/src/e_cosh.cpp new file mode 100644 index 0000000000..42cb277d49 --- /dev/null +++ b/modules/fdlibm/src/e_cosh.cpp @@ -0,0 +1,80 @@ + +/* @(#)e_cosh.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* __ieee754_cosh(x) + * Method : + * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 + * 1. Replace x by |x| (cosh(x) = cosh(-x)). + * 2. + * [ exp(x) - 1 ]^2 + * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- + * 2*exp(x) + * + * exp(x) + 1/exp(x) + * ln2/2 <= x <= 22 : cosh(x) := ------------------- + * 2 + * 22 <= x <= lnovft : cosh(x) := exp(x)/2 + * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) + * ln2ovft < x : cosh(x) := huge*huge (overflow) + * + * Special cases: + * cosh(x) is |x| if x is +INF, -INF, or NaN. + * only cosh(0)=1 is exact for finite x. + */ + +#include <float.h> + +#include "math_private.h" + +static const double one = 1.0, half=0.5, huge = 1.0e300; + +double +__ieee754_cosh(double x) +{ + double t,w; + int32_t ix; + + /* High word of |x|. */ + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7ff00000) return x*x; + + /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ + if(ix<0x3fd62e43) { + t = expm1(fabs(x)); + w = one+t; + if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */ + return one+(t*t)/(w+w); + } + + /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ + if (ix < 0x40360000) { + t = __ieee754_exp(fabs(x)); + return half*t+half/t; + } + + /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ + if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + if (ix<=0x408633CE) + return __ldexp_exp(fabs(x), -1); + + /* |x| > overflowthresold, cosh(x) overflow */ + return huge*huge; +} diff --git a/modules/fdlibm/src/e_exp.cpp b/modules/fdlibm/src/e_exp.cpp new file mode 100644 index 0000000000..92af819ce5 --- /dev/null +++ b/modules/fdlibm/src/e_exp.cpp @@ -0,0 +1,165 @@ + +/* @(#)e_exp.c 1.6 04/04/22 */ +/* + * ==================================================== + * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. + * + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* __ieee754_exp(x) + * Returns the exponential of x. + * + * Method + * 1. Argument reduction: + * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658. + * Given x, find r and integer k such that + * + * x = k*ln2 + r, |r| <= 0.5*ln2. + * + * Here r will be represented as r = hi-lo for better + * accuracy. + * + * 2. Approximation of exp(r) by a special rational function on + * the interval [0,0.34658]: + * Write + * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ... + * We use a special Remes algorithm on [0,0.34658] to generate + * a polynomial of degree 5 to approximate R. The maximum error + * of this polynomial approximation is bounded by 2**-59. In + * other words, + * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5 + * (where z=r*r, and the values of P1 to P5 are listed below) + * and + * | 5 | -59 + * | 2.0+P1*z+...+P5*z - R(z) | <= 2 + * | | + * The computation of exp(r) thus becomes + * 2*r + * exp(r) = 1 + ------- + * R - r + * r*R1(r) + * = 1 + r + ----------- (for better accuracy) + * 2 - R1(r) + * where + * 2 4 10 + * R1(r) = r - (P1*r + P2*r + ... + P5*r ). + * + * 3. Scale back to obtain exp(x): + * From step 1, we have + * exp(x) = 2^k * exp(r) + * + * Special cases: + * exp(INF) is INF, exp(NaN) is NaN; + * exp(-INF) is 0, and + * for finite argument, only exp(0)=1 is exact. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Misc. info. + * For IEEE double + * if x > 7.09782712893383973096e+02 then exp(x) overflow + * if x < -7.45133219101941108420e+02 then exp(x) underflow + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include <float.h> + +#include "math_private.h" + +static const double +one = 1.0, +halF[2] = {0.5,-0.5,}, +o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */ +u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */ +ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */ + -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */ +ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */ + -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */ +invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */ +P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ +P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ +P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ +P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ +P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */ + +static const double E = 2.7182818284590452354; /* e */ + +static volatile double +huge = 1.0e+300, +twom1000= 9.33263618503218878990e-302; /* 2**-1000=0x01700000,0*/ + +double +__ieee754_exp(double x) /* default IEEE double exp */ +{ + double y,hi=0.0,lo=0.0,c,t,twopk; + int32_t k=0,xsb; + u_int32_t hx; + + GET_HIGH_WORD(hx,x); + xsb = (hx>>31)&1; /* sign bit of x */ + hx &= 0x7fffffff; /* high word of |x| */ + + /* filter out non-finite argument */ + if(hx >= 0x40862E42) { /* if |x|>=709.78... */ + if(hx>=0x7ff00000) { + u_int32_t lx; + GET_LOW_WORD(lx,x); + if(((hx&0xfffff)|lx)!=0) + return x+x; /* NaN */ + else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ + } + if(x > o_threshold) return huge*huge; /* overflow */ + if(x < u_threshold) return twom1000*twom1000; /* underflow */ + } + + /* argument reduction */ + if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ + if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ + if (x == 1.0) return E; + hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; + } else { + k = (int)(invln2*x+halF[xsb]); + t = k; + hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ + lo = t*ln2LO[0]; + } + STRICT_ASSIGN(double, x, hi - lo); + } + else if(hx < 0x3e300000) { /* when |x|<2**-28 */ + if(huge+x>one) return one+x;/* trigger inexact */ + } + else k = 0; + + /* x is now in primary range */ + t = x*x; + if(k >= -1021) + INSERT_WORDS(twopk,((u_int32_t)(0x3ff+k))<<20, 0); + else + INSERT_WORDS(twopk,((u_int32_t)(0x3ff+(k+1000)))<<20, 0); + c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); + if(k==0) return one-((x*c)/(c-2.0)-x); + else y = one-((lo-(x*c)/(2.0-c))-hi); + if(k >= -1021) { + if (k==1024) { + double const_0x1p1023 = pow(2, 1023); + return y*2.0*const_0x1p1023; + } + return y*twopk; + } else { + return y*twopk*twom1000; + } +} diff --git a/modules/fdlibm/src/e_expf.cpp b/modules/fdlibm/src/e_expf.cpp new file mode 100644 index 0000000000..dd5b665d6f --- /dev/null +++ b/modules/fdlibm/src/e_expf.cpp @@ -0,0 +1,97 @@ +/* e_expf.c -- float version of e_exp.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +#include <float.h> + +#include "math_private.h" + +static const float +one = 1.0, +halF[2] = {0.5,-0.5,}, +o_threshold= 8.8721679688e+01, /* 0x42b17180 */ +u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */ +ln2HI[2] ={ 6.9314575195e-01, /* 0x3f317200 */ + -6.9314575195e-01,}, /* 0xbf317200 */ +ln2LO[2] ={ 1.4286067653e-06, /* 0x35bfbe8e */ + -1.4286067653e-06,}, /* 0xb5bfbe8e */ +invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */ +/* + * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]: + * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74 + */ +P1 = 1.6666625440e-1, /* 0xaaaa8f.0p-26 */ +P2 = -2.7667332906e-3; /* -0xb55215.0p-32 */ + +static volatile float +huge = 1.0e+30, +twom100 = 7.8886090522e-31; /* 2**-100=0x0d800000 */ + +float +__ieee754_expf(float x) +{ + float y,hi=0.0,lo=0.0,c,t,twopk; + int32_t k=0,xsb; + u_int32_t hx; + + GET_FLOAT_WORD(hx,x); + xsb = (hx>>31)&1; /* sign bit of x */ + hx &= 0x7fffffff; /* high word of |x| */ + + /* filter out non-finite argument */ + if(hx >= 0x42b17218) { /* if |x|>=88.721... */ + if(hx>0x7f800000) + return x+x; /* NaN */ + if(hx==0x7f800000) + return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ + if(x > o_threshold) return huge*huge; /* overflow */ + if(x < u_threshold) return twom100*twom100; /* underflow */ + } + + /* argument reduction */ + if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ + if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ + hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; + } else { + k = invln2*x+halF[xsb]; + t = k; + hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ + lo = t*ln2LO[0]; + } + STRICT_ASSIGN(float, x, hi - lo); + } + else if(hx < 0x39000000) { /* when |x|<2**-14 */ + if(huge+x>one) return one+x;/* trigger inexact */ + } + else k = 0; + + /* x is now in primary range */ + t = x*x; + if(k >= -125) + SET_FLOAT_WORD(twopk,((u_int32_t)(0x7f+k))<<23); + else + SET_FLOAT_WORD(twopk,((u_int32_t)(0x7f+(k+100)))<<23); + c = x - t*(P1+t*P2); + if(k==0) return one-((x*c)/(c-(float)2.0)-x); + else y = one-((lo-(x*c)/((float)2.0-c))-hi); + if(k >= -125) { + if(k==128) return y*2.0F*0x1p127F; + return y*twopk; + } else { + return y*twopk*twom100; + } +} diff --git a/modules/fdlibm/src/e_hypot.cpp b/modules/fdlibm/src/e_hypot.cpp new file mode 100644 index 0000000000..fff4797897 --- /dev/null +++ b/modules/fdlibm/src/e_hypot.cpp @@ -0,0 +1,125 @@ + +/* @(#)e_hypot.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* __ieee754_hypot(x,y) + * + * Method : + * If (assume round-to-nearest) z=x*x+y*y + * has error less than sqrt(2)/2 ulp, than + * sqrt(z) has error less than 1 ulp (exercise). + * + * So, compute sqrt(x*x+y*y) with some care as + * follows to get the error below 1 ulp: + * + * Assume x>y>0; + * (if possible, set rounding to round-to-nearest) + * 1. if x > 2y use + * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y + * where x1 = x with lower 32 bits cleared, x2 = x-x1; else + * 2. if x <= 2y use + * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) + * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, + * y1= y with lower 32 bits chopped, y2 = y-y1. + * + * NOTE: scaling may be necessary if some argument is too + * large or too tiny + * + * Special cases: + * hypot(x,y) is INF if x or y is +INF or -INF; else + * hypot(x,y) is NAN if x or y is NAN. + * + * Accuracy: + * hypot(x,y) returns sqrt(x^2+y^2) with error less + * than 1 ulps (units in the last place) + */ + +#include <cmath> +#include <float.h> + +#include "math_private.h" + +double +__ieee754_hypot(double x, double y) +{ + double a,b,t1,t2,y1,y2,w; + int32_t j,k,ha,hb; + + GET_HIGH_WORD(ha,x); + ha &= 0x7fffffff; + GET_HIGH_WORD(hb,y); + hb &= 0x7fffffff; + if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} + a = fabs(a); + b = fabs(b); + if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ + k=0; + if(ha > 0x5f300000) { /* a>2**500 */ + if(ha >= 0x7ff00000) { /* Inf or NaN */ + u_int32_t low; + /* Use original arg order iff result is NaN; quieten sNaNs. */ + w = fabsl(x+0.0L)-fabs(y+0); + GET_LOW_WORD(low,a); + if(((ha&0xfffff)|low)==0) w = a; + GET_LOW_WORD(low,b); + if(((hb^0x7ff00000)|low)==0) w = b; + return w; + } + /* scale a and b by 2**-600 */ + ha -= 0x25800000; hb -= 0x25800000; k += 600; + SET_HIGH_WORD(a,ha); + SET_HIGH_WORD(b,hb); + } + if(hb < 0x20b00000) { /* b < 2**-500 */ + if(hb <= 0x000fffff) { /* subnormal b or 0 */ + u_int32_t low; + GET_LOW_WORD(low,b); + if((hb|low)==0) return a; + t1=0; + SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */ + b *= t1; + a *= t1; + k -= 1022; + } else { /* scale a and b by 2^600 */ + ha += 0x25800000; /* a *= 2^600 */ + hb += 0x25800000; /* b *= 2^600 */ + k -= 600; + SET_HIGH_WORD(a,ha); + SET_HIGH_WORD(b,hb); + } + } + /* medium size a and b */ + w = a-b; + if (w>b) { + t1 = 0; + SET_HIGH_WORD(t1,ha); + t2 = a-t1; + w = std::sqrt(t1*t1-(b*(-b)-t2*(a+t1))); + } else { + a = a+a; + y1 = 0; + SET_HIGH_WORD(y1,hb); + y2 = b - y1; + t1 = 0; + SET_HIGH_WORD(t1,ha+0x00100000); + t2 = a - t1; + w = std::sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); + } + if(k!=0) { + t1 = 0.0; + SET_HIGH_WORD(t1,(1023+k)<<20); + return t1*w; + } else return w; +} diff --git a/modules/fdlibm/src/e_log.cpp b/modules/fdlibm/src/e_log.cpp new file mode 100644 index 0000000000..fa2da8fcb0 --- /dev/null +++ b/modules/fdlibm/src/e_log.cpp @@ -0,0 +1,142 @@ + +/* @(#)e_log.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* __ieee754_log(x) + * Return the logrithm of x + * + * Method : + * 1. Argument Reduction: find k and f such that + * x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * + * 2. Approximation of log(1+f). + * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * = 2s + s*R + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error + * of this polynomial approximation is bounded by 2**-58.45. In + * other words, + * 2 4 6 8 10 12 14 + * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s + * (the values of Lg1 to Lg7 are listed in the program) + * and + * | 2 14 | -58.45 + * | Lg1*s +...+Lg7*s - R(z) | <= 2 + * | | + * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. + * In order to guarantee error in log below 1ulp, we compute log + * by + * log(1+f) = f - s*(f - R) (if f is not too large) + * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) + * + * 3. Finally, log(x) = k*ln2 + log(1+f). + * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) + * Here ln2 is split into two floating point number: + * ln2_hi + ln2_lo, + * where n*ln2_hi is always exact for |n| < 2000. + * + * Special cases: + * log(x) is NaN with signal if x < 0 (including -INF) ; + * log(+INF) is +INF; log(0) is -INF with signal; + * log(NaN) is that NaN with no signal. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include <float.h> + +#include "math_private.h" + +static const double +ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ +ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ +two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ +Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ +Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ +Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ +Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ +Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ +Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ +Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ + +static const double zero = 0.0; +static volatile double vzero = 0.0; + +double +__ieee754_log(double x) +{ + double hfsq,f,s,z,R,w,t1,t2,dk; + int32_t k,hx,i,j; + u_int32_t lx; + + EXTRACT_WORDS(hx,lx,x); + + k=0; + if (hx < 0x00100000) { /* x < 2**-1022 */ + if (((hx&0x7fffffff)|lx)==0) + return -two54/vzero; /* log(+-0)=-inf */ + if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 54; x *= two54; /* subnormal number, scale up x */ + GET_HIGH_WORD(hx,x); + } + if (hx >= 0x7ff00000) return x+x; + k += (hx>>20)-1023; + hx &= 0x000fffff; + i = (hx+0x95f64)&0x100000; + SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */ + k += (i>>20); + f = x-1.0; + if((0x000fffff&(2+hx))<3) { /* -2**-20 <= f < 2**-20 */ + if(f==zero) { + if(k==0) { + return zero; + } else { + dk=(double)k; + return dk*ln2_hi+dk*ln2_lo; + } + } + R = f*f*(0.5-0.33333333333333333*f); + if(k==0) return f-R; else {dk=(double)k; + return dk*ln2_hi-((R-dk*ln2_lo)-f);} + } + s = f/(2.0+f); + dk = (double)k; + z = s*s; + i = hx-0x6147a; + w = z*z; + j = 0x6b851-hx; + t1= w*(Lg2+w*(Lg4+w*Lg6)); + t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); + i |= j; + R = t2+t1; + if(i>0) { + hfsq=0.5*f*f; + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); + } else { + if(k==0) return f-s*(f-R); else + return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); + } +} diff --git a/modules/fdlibm/src/e_log10.cpp b/modules/fdlibm/src/e_log10.cpp new file mode 100644 index 0000000000..ed68798859 --- /dev/null +++ b/modules/fdlibm/src/e_log10.cpp @@ -0,0 +1,89 @@ + +/* @(#)e_log10.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* + * Return the base 10 logarithm of x. See e_log.c and k_log.h for most + * comments. + * + * log10(x) = (f - 0.5*f*f + k_log1p(f)) / ln10 + k * log10(2) + * in not-quite-routine extra precision. + */ + +#include <float.h> + +#include "math_private.h" +#include "k_log.h" + +static const double +two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ +ivln10hi = 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */ +ivln10lo = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */ +log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ +log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ + +static const double zero = 0.0; +static volatile double vzero = 0.0; + +double +__ieee754_log10(double x) +{ + double f,hfsq,hi,lo,r,val_hi,val_lo,w,y,y2; + int32_t i,k,hx; + u_int32_t lx; + + EXTRACT_WORDS(hx,lx,x); + + k=0; + if (hx < 0x00100000) { /* x < 2**-1022 */ + if (((hx&0x7fffffff)|lx)==0) + return -two54/vzero; /* log(+-0)=-inf */ + if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 54; x *= two54; /* subnormal number, scale up x */ + GET_HIGH_WORD(hx,x); + } + if (hx >= 0x7ff00000) return x+x; + if (hx == 0x3ff00000 && lx == 0) + return zero; /* log(1) = +0 */ + k += (hx>>20)-1023; + hx &= 0x000fffff; + i = (hx+0x95f64)&0x100000; + SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */ + k += (i>>20); + y = (double)k; + f = x - 1.0; + hfsq = 0.5*f*f; + r = k_log1p(f); + + /* See e_log2.c for most details. */ + hi = f - hfsq; + SET_LOW_WORD(hi,0); + lo = (f - hi) - hfsq + r; + val_hi = hi*ivln10hi; + y2 = y*log10_2hi; + val_lo = y*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi; + + /* + * Extra precision in for adding y*log10_2hi is not strictly needed + * since there is no very large cancellation near x = sqrt(2) or + * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs + * with some parallelism and it reduces the error for many args. + */ + w = y2 + val_hi; + val_lo += (y2 - w) + val_hi; + val_hi = w; + + return val_lo + val_hi; +} diff --git a/modules/fdlibm/src/e_log2.cpp b/modules/fdlibm/src/e_log2.cpp new file mode 100644 index 0000000000..5649fec443 --- /dev/null +++ b/modules/fdlibm/src/e_log2.cpp @@ -0,0 +1,112 @@ + +/* @(#)e_log10.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* + * Return the base 2 logarithm of x. See e_log.c and k_log.h for most + * comments. + * + * This reduces x to {k, 1+f} exactly as in e_log.c, then calls the kernel, + * then does the combining and scaling steps + * log2(x) = (f - 0.5*f*f + k_log1p(f)) / ln2 + k + * in not-quite-routine extra precision. + */ + +#include <float.h> + +#include "math_private.h" +#include "k_log.h" + +static const double +two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ +ivln2hi = 1.44269504072144627571e+00, /* 0x3ff71547, 0x65200000 */ +ivln2lo = 1.67517131648865118353e-10; /* 0x3de705fc, 0x2eefa200 */ + +static const double zero = 0.0; +static volatile double vzero = 0.0; + +double +__ieee754_log2(double x) +{ + double f,hfsq,hi,lo,r,val_hi,val_lo,w,y; + int32_t i,k,hx; + u_int32_t lx; + + EXTRACT_WORDS(hx,lx,x); + + k=0; + if (hx < 0x00100000) { /* x < 2**-1022 */ + if (((hx&0x7fffffff)|lx)==0) + return -two54/vzero; /* log(+-0)=-inf */ + if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 54; x *= two54; /* subnormal number, scale up x */ + GET_HIGH_WORD(hx,x); + } + if (hx >= 0x7ff00000) return x+x; + if (hx == 0x3ff00000 && lx == 0) + return zero; /* log(1) = +0 */ + k += (hx>>20)-1023; + hx &= 0x000fffff; + i = (hx+0x95f64)&0x100000; + SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */ + k += (i>>20); + y = (double)k; + f = x - 1.0; + hfsq = 0.5*f*f; + r = k_log1p(f); + + /* + * f-hfsq must (for args near 1) be evaluated in extra precision + * to avoid a large cancellation when x is near sqrt(2) or 1/sqrt(2). + * This is fairly efficient since f-hfsq only depends on f, so can + * be evaluated in parallel with R. Not combining hfsq with R also + * keeps R small (though not as small as a true `lo' term would be), + * so that extra precision is not needed for terms involving R. + * + * Compiler bugs involving extra precision used to break Dekker's + * theorem for spitting f-hfsq as hi+lo, unless double_t was used + * or the multi-precision calculations were avoided when double_t + * has extra precision. These problems are now automatically + * avoided as a side effect of the optimization of combining the + * Dekker splitting step with the clear-low-bits step. + * + * y must (for args near sqrt(2) and 1/sqrt(2)) be added in extra + * precision to avoid a very large cancellation when x is very near + * these values. Unlike the above cancellations, this problem is + * specific to base 2. It is strange that adding +-1 is so much + * harder than adding +-ln2 or +-log10_2. + * + * This uses Dekker's theorem to normalize y+val_hi, so the + * compiler bugs are back in some configurations, sigh. And I + * don't want to used double_t to avoid them, since that gives a + * pessimization and the support for avoiding the pessimization + * is not yet available. + * + * The multi-precision calculations for the multiplications are + * routine. + */ + hi = f - hfsq; + SET_LOW_WORD(hi,0); + lo = (f - hi) - hfsq + r; + val_hi = hi*ivln2hi; + val_lo = (lo+hi)*ivln2lo + lo*ivln2hi; + + /* spadd(val_hi, val_lo, y), except for not using double_t: */ + w = y + val_hi; + val_lo += (y - w) + val_hi; + val_hi = w; + + return val_lo + val_hi; +} diff --git a/modules/fdlibm/src/e_logf.cpp b/modules/fdlibm/src/e_logf.cpp new file mode 100644 index 0000000000..a878e9d32d --- /dev/null +++ b/modules/fdlibm/src/e_logf.cpp @@ -0,0 +1,88 @@ +/* e_logf.c -- float version of e_log.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +#include "math_private.h" + +static const float +ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ +ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ +two25 = 3.355443200e+07, /* 0x4c000000 */ +/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */ +Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */ +Lg2 = 0xccce13.0p-25, /* 0.40000972152 */ +Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */ +Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */ + +static const float zero = 0.0; +static volatile float vzero = 0.0; + +float +__ieee754_logf(float x) +{ + float hfsq,f,s,z,R,w,t1,t2,dk; + int32_t k,ix,i,j; + + GET_FLOAT_WORD(ix,x); + + k=0; + if (ix < 0x00800000) { /* x < 2**-126 */ + if ((ix&0x7fffffff)==0) + return -two25/vzero; /* log(+-0)=-inf */ + if (ix<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 25; x *= two25; /* subnormal number, scale up x */ + GET_FLOAT_WORD(ix,x); + } + if (ix >= 0x7f800000) return x+x; + k += (ix>>23)-127; + ix &= 0x007fffff; + i = (ix+(0x95f64<<3))&0x800000; + SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */ + k += (i>>23); + f = x-(float)1.0; + if((0x007fffff&(0x8000+ix))<0xc000) { /* -2**-9 <= f < 2**-9 */ + if(f==zero) { + if(k==0) { + return zero; + } else { + dk=(float)k; + return dk*ln2_hi+dk*ln2_lo; + } + } + R = f*f*((float)0.5-(float)0.33333333333333333*f); + if(k==0) return f-R; else {dk=(float)k; + return dk*ln2_hi-((R-dk*ln2_lo)-f);} + } + s = f/((float)2.0+f); + dk = (float)k; + z = s*s; + i = ix-(0x6147a<<3); + w = z*z; + j = (0x6b851<<3)-ix; + t1= w*(Lg2+w*Lg4); + t2= z*(Lg1+w*Lg3); + i |= j; + R = t2+t1; + if(i>0) { + hfsq=(float)0.5*f*f; + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); + } else { + if(k==0) return f-s*(f-R); else + return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); + } +} diff --git a/modules/fdlibm/src/e_pow.cpp b/modules/fdlibm/src/e_pow.cpp new file mode 100644 index 0000000000..8e10035599 --- /dev/null +++ b/modules/fdlibm/src/e_pow.cpp @@ -0,0 +1,310 @@ +/* @(#)e_pow.c 1.5 04/04/22 SMI */ +/* + * ==================================================== + * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. + * + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* __ieee754_pow(x,y) return x**y + * + * n + * Method: Let x = 2 * (1+f) + * 1. Compute and return log2(x) in two pieces: + * log2(x) = w1 + w2, + * where w1 has 53-24 = 29 bit trailing zeros. + * 2. Perform y*log2(x) = n+y' by simulating multi-precision + * arithmetic, where |y'|<=0.5. + * 3. Return x**y = 2**n*exp(y'*log2) + * + * Special cases: + * 1. (anything) ** 0 is 1 + * 2. (anything) ** 1 is itself + * 3. (anything) ** NAN is NAN except 1 ** NAN = 1 + * 4. NAN ** (anything except 0) is NAN + * 5. +-(|x| > 1) ** +INF is +INF + * 6. +-(|x| > 1) ** -INF is +0 + * 7. +-(|x| < 1) ** +INF is +0 + * 8. +-(|x| < 1) ** -INF is +INF + * 9. +-1 ** +-INF is 1 + * 10. +0 ** (+anything except 0, NAN) is +0 + * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 + * 12. +0 ** (-anything except 0, NAN) is +INF + * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF + * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) + * 15. +INF ** (+anything except 0,NAN) is +INF + * 16. +INF ** (-anything except 0,NAN) is +0 + * 17. -INF ** (anything) = -0 ** (-anything) + * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) + * 19. (-anything except 0 and inf) ** (non-integer) is NAN + * + * Accuracy: + * pow(x,y) returns x**y nearly rounded. In particular + * pow(integer,integer) + * always returns the correct integer provided it is + * representable. + * + * Constants : + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include <cmath> +#include <float.h> +#include "math_private.h" + +static const double +bp[] = {1.0, 1.5,}, +dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ +dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ +zero = 0.0, +half = 0.5, +qrtr = 0.25, +thrd = 3.3333333333333331e-01, /* 0x3fd55555, 0x55555555 */ +one = 1.0, +two = 2.0, +two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */ +huge = 1.0e300, +tiny = 1.0e-300, + /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ +L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */ +L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */ +L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */ +L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */ +L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */ +L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */ +P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ +P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ +P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ +P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ +P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */ +lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ +lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */ +lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */ +ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */ +cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */ +cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */ +cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/ +ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */ +ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/ +ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ + +double +__ieee754_pow(double x, double y) +{ + double z,ax,z_h,z_l,p_h,p_l; + double y1,t1,t2,r,s,t,u,v,w; + int32_t i,j,k,yisint,n; + int32_t hx,hy,ix,iy; + u_int32_t lx,ly; + + EXTRACT_WORDS(hx,lx,x); + EXTRACT_WORDS(hy,ly,y); + ix = hx&0x7fffffff; iy = hy&0x7fffffff; + + /* y==zero: x**0 = 1 */ + if((iy|ly)==0) return one; + + /* x==1: 1**y = 1, even if y is NaN */ + if (hx==0x3ff00000 && lx == 0) return one; + + /* y!=zero: result is NaN if either arg is NaN */ + if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) || + iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) + return nan_mix(x, y); + + /* determine if y is an odd int when x < 0 + * yisint = 0 ... y is not an integer + * yisint = 1 ... y is an odd int + * yisint = 2 ... y is an even int + */ + yisint = 0; + if(hx<0) { + if(iy>=0x43400000) yisint = 2; /* even integer y */ + else if(iy>=0x3ff00000) { + k = (iy>>20)-0x3ff; /* exponent */ + if(k>20) { + j = ly>>(52-k); + if(((u_int32_t)j<<(52-k))==ly) yisint = 2-(j&1); + } else if(ly==0) { + j = iy>>(20-k); + if((j<<(20-k))==iy) yisint = 2-(j&1); + } + } + } + + /* special value of y */ + if(ly==0) { + if (iy==0x7ff00000) { /* y is +-inf */ + if(((ix-0x3ff00000)|lx)==0) + return one; /* (-1)**+-inf is 1 */ + else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */ + return (hy>=0)? y: zero; + else /* (|x|<1)**-,+inf = inf,0 */ + return (hy<0)?-y: zero; + } + if(iy==0x3ff00000) { /* y is +-1 */ + if(hy<0) return one/x; else return x; + } + if(hy==0x40000000) return x*x; /* y is 2 */ + if(hy==0x3fe00000) { /* y is 0.5 */ + if(hx>=0) /* x >= +0 */ + return std::sqrt(x); + } + } + + ax = fabs(x); + /* special value of x */ + if(lx==0) { + if(ix==0x7ff00000||ix==0||ix==0x3ff00000){ + z = ax; /*x is +-0,+-inf,+-1*/ + if(hy<0) z = one/z; /* z = (1/|x|) */ + if(hx<0) { + if(((ix-0x3ff00000)|yisint)==0) { + z = (z-z)/(z-z); /* (-1)**non-int is NaN */ + } else if(yisint==1) + z = -z; /* (x<0)**odd = -(|x|**odd) */ + } + return z; + } + } + + /* CYGNUS LOCAL + fdlibm-5.3 fix: This used to be + n = (hx>>31)+1; + but ANSI C says a right shift of a signed negative quantity is + implementation defined. */ + n = ((u_int32_t)hx>>31)-1; + + /* (x<0)**(non-int) is NaN */ + if((n|yisint)==0) return (x-x)/(x-x); + + s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ + if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */ + + /* |y| is huge */ + if(iy>0x41e00000) { /* if |y| > 2**31 */ + if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */ + if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny; + if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny; + } + /* over/underflow if x is not close to one */ + if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny; + if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny; + /* now |1-x| is tiny <= 2**-20, suffice to compute + log(x) by x-x^2/2+x^3/3-x^4/4 */ + t = ax-one; /* t has 20 trailing zeros */ + w = (t*t)*(half-t*(thrd-t*qrtr)); + u = ivln2_h*t; /* ivln2_h has 21 sig. bits */ + v = t*ivln2_l-w*ivln2; + t1 = u+v; + SET_LOW_WORD(t1,0); + t2 = v-(t1-u); + } else { + double ss,s2,s_h,s_l,t_h,t_l; + n = 0; + /* take care subnormal number */ + if(ix<0x00100000) + {ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); } + n += ((ix)>>20)-0x3ff; + j = ix&0x000fffff; + /* determine interval */ + ix = j|0x3ff00000; /* normalize ix */ + if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */ + else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */ + else {k=0;n+=1;ix -= 0x00100000;} + SET_HIGH_WORD(ax,ix); + + /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ + u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */ + v = one/(ax+bp[k]); + ss = u*v; + s_h = ss; + SET_LOW_WORD(s_h,0); + /* t_h=ax+bp[k] High */ + t_h = zero; + SET_HIGH_WORD(t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18)); + t_l = ax - (t_h-bp[k]); + s_l = v*((u-s_h*t_h)-s_h*t_l); + /* compute log(ax) */ + s2 = ss*ss; + r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); + r += s_l*(s_h+ss); + s2 = s_h*s_h; + t_h = 3+s2+r; + SET_LOW_WORD(t_h,0); + t_l = r-((t_h-3)-s2); + /* u+v = ss*(1+...) */ + u = s_h*t_h; + v = s_l*t_h+t_l*ss; + /* 2/(3log2)*(ss+...) */ + p_h = u+v; + SET_LOW_WORD(p_h,0); + p_l = v-(p_h-u); + z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ + z_l = cp_l*p_h+p_l*cp+dp_l[k]; + /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */ + t = n; + t1 = (((z_h+z_l)+dp_h[k])+t); + SET_LOW_WORD(t1,0); + t2 = z_l-(((t1-t)-dp_h[k])-z_h); + } + + /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ + y1 = y; + SET_LOW_WORD(y1,0); + p_l = (y-y1)*t1+y*t2; + p_h = y1*t1; + z = p_l+p_h; + EXTRACT_WORDS(j,i,z); + if (j>=0x40900000) { /* z >= 1024 */ + if(((j-0x40900000)|i)!=0) /* if z > 1024 */ + return s*huge*huge; /* overflow */ + else { + if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */ + } + } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */ + if(((j-0xc090cc00)|i)!=0) /* z < -1075 */ + return s*tiny*tiny; /* underflow */ + else { + if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ + } + } + /* + * compute 2**(p_h+p_l) + */ + i = j&0x7fffffff; + k = (i>>20)-0x3ff; + n = 0; + if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ + n = j+(0x00100000>>(k+1)); + k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */ + t = zero; + SET_HIGH_WORD(t,n&~(0x000fffff>>k)); + n = ((n&0x000fffff)|0x00100000)>>(20-k); + if(j<0) n = -n; + p_h -= t; + } + t = p_l+p_h; + SET_LOW_WORD(t,0); + u = t*lg2_h; + v = (p_l-(t-p_h))*lg2+t*lg2_l; + z = u+v; + w = v-(z-u); + t = z*z; + t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); + r = (z*t1)/(t1-two)-(w+z*w); + z = one-(r-z); + GET_HIGH_WORD(j,z); + j += (n<<20); + if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */ + else SET_HIGH_WORD(z,j); + return s*z; +} diff --git a/modules/fdlibm/src/e_powf.cpp b/modules/fdlibm/src/e_powf.cpp new file mode 100644 index 0000000000..0337fc989a --- /dev/null +++ b/modules/fdlibm/src/e_powf.cpp @@ -0,0 +1,253 @@ +/* e_powf.c -- float version of e_pow.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +#include "s_scalbnf.cpp" + +#include "math_private.h" + +static const float +bp[] = {1.0, 1.5,}, +dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */ +dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */ +zero = 0.0, +half = 0.5, +qrtr = 0.25, +thrd = 3.33333343e-01, /* 0x3eaaaaab */ +one = 1.0, +two = 2.0, +two24 = 16777216.0, /* 0x4b800000 */ +huge = 1.0e30, +tiny = 1.0e-30, + /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ +L1 = 6.0000002384e-01, /* 0x3f19999a */ +L2 = 4.2857143283e-01, /* 0x3edb6db7 */ +L3 = 3.3333334327e-01, /* 0x3eaaaaab */ +L4 = 2.7272811532e-01, /* 0x3e8ba305 */ +L5 = 2.3066075146e-01, /* 0x3e6c3255 */ +L6 = 2.0697501302e-01, /* 0x3e53f142 */ +P1 = 1.6666667163e-01, /* 0x3e2aaaab */ +P2 = -2.7777778450e-03, /* 0xbb360b61 */ +P3 = 6.6137559770e-05, /* 0x388ab355 */ +P4 = -1.6533901999e-06, /* 0xb5ddea0e */ +P5 = 4.1381369442e-08, /* 0x3331bb4c */ +lg2 = 6.9314718246e-01, /* 0x3f317218 */ +lg2_h = 6.93145752e-01, /* 0x3f317200 */ +lg2_l = 1.42860654e-06, /* 0x35bfbe8c */ +ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */ +cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */ +cp_h = 9.6191406250e-01, /* 0x3f764000 =12b cp */ +cp_l = -1.1736857402e-04, /* 0xb8f623c6 =tail of cp_h */ +ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */ +ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/ +ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/ + +float +__ieee754_powf(float x, float y) +{ + float z,ax,z_h,z_l,p_h,p_l; + float y1,t1,t2,r,s,sn,t,u,v,w; + int32_t i,j,k,yisint,n; + int32_t hx,hy,ix,iy,is; + + GET_FLOAT_WORD(hx,x); + GET_FLOAT_WORD(hy,y); + ix = hx&0x7fffffff; iy = hy&0x7fffffff; + + /* y==zero: x**0 = 1 */ + if(iy==0) return one; + + /* x==1: 1**y = 1, even if y is NaN */ + if (hx==0x3f800000) return one; + + /* y!=zero: result is NaN if either arg is NaN */ + if(ix > 0x7f800000 || + iy > 0x7f800000) + return nan_mix(x, y); + + /* determine if y is an odd int when x < 0 + * yisint = 0 ... y is not an integer + * yisint = 1 ... y is an odd int + * yisint = 2 ... y is an even int + */ + yisint = 0; + if(hx<0) { + if(iy>=0x4b800000) yisint = 2; /* even integer y */ + else if(iy>=0x3f800000) { + k = (iy>>23)-0x7f; /* exponent */ + j = iy>>(23-k); + if((j<<(23-k))==iy) yisint = 2-(j&1); + } + } + + /* special value of y */ + if (iy==0x7f800000) { /* y is +-inf */ + if (ix==0x3f800000) + return one; /* (-1)**+-inf is NaN */ + else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */ + return (hy>=0)? y: zero; + else /* (|x|<1)**-,+inf = inf,0 */ + return (hy<0)?-y: zero; + } + if(iy==0x3f800000) { /* y is +-1 */ + if(hy<0) return one/x; else return x; + } + if(hy==0x40000000) return x*x; /* y is 2 */ + if(hy==0x3f000000) { /* y is 0.5 */ + if(hx>=0) /* x >= +0 */ + return __ieee754_sqrtf(x); + } + + ax = fabsf(x); + /* special value of x */ + if(ix==0x7f800000||ix==0||ix==0x3f800000){ + z = ax; /*x is +-0,+-inf,+-1*/ + if(hy<0) z = one/z; /* z = (1/|x|) */ + if(hx<0) { + if(((ix-0x3f800000)|yisint)==0) { + z = (z-z)/(z-z); /* (-1)**non-int is NaN */ + } else if(yisint==1) + z = -z; /* (x<0)**odd = -(|x|**odd) */ + } + return z; + } + + n = ((u_int32_t)hx>>31)-1; + + /* (x<0)**(non-int) is NaN */ + if((n|yisint)==0) return (x-x)/(x-x); + + sn = one; /* s (sign of result -ve**odd) = -1 else = 1 */ + if((n|(yisint-1))==0) sn = -one;/* (-ve)**(odd int) */ + + /* |y| is huge */ + if(iy>0x4d000000) { /* if |y| > 2**27 */ + /* over/underflow if x is not close to one */ + if(ix<0x3f7ffff6) return (hy<0)? sn*huge*huge:sn*tiny*tiny; + if(ix>0x3f800007) return (hy>0)? sn*huge*huge:sn*tiny*tiny; + /* now |1-x| is tiny <= 2**-20, suffice to compute + log(x) by x-x^2/2+x^3/3-x^4/4 */ + t = ax-1; /* t has 20 trailing zeros */ + w = (t*t)*(half-t*(thrd-t*qrtr)); + u = ivln2_h*t; /* ivln2_h has 16 sig. bits */ + v = t*ivln2_l-w*ivln2; + t1 = u+v; + GET_FLOAT_WORD(is,t1); + SET_FLOAT_WORD(t1,is&0xfffff000); + t2 = v-(t1-u); + } else { + float s2,s_h,s_l,t_h,t_l; + n = 0; + /* take care subnormal number */ + if(ix<0x00800000) + {ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); } + n += ((ix)>>23)-0x7f; + j = ix&0x007fffff; + /* determine interval */ + ix = j|0x3f800000; /* normalize ix */ + if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */ + else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */ + else {k=0;n+=1;ix -= 0x00800000;} + SET_FLOAT_WORD(ax,ix); + + /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ + u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */ + v = one/(ax+bp[k]); + s = u*v; + s_h = s; + GET_FLOAT_WORD(is,s_h); + SET_FLOAT_WORD(s_h,is&0xfffff000); + /* t_h=ax+bp[k] High */ + is = ((ix>>1)&0xfffff000)|0x20000000; + SET_FLOAT_WORD(t_h,is+0x00400000+(k<<21)); + t_l = ax - (t_h-bp[k]); + s_l = v*((u-s_h*t_h)-s_h*t_l); + /* compute log(ax) */ + s2 = s*s; + r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); + r += s_l*(s_h+s); + s2 = s_h*s_h; + t_h = 3+s2+r; + GET_FLOAT_WORD(is,t_h); + SET_FLOAT_WORD(t_h,is&0xfffff000); + t_l = r-((t_h-3)-s2); + /* u+v = s*(1+...) */ + u = s_h*t_h; + v = s_l*t_h+t_l*s; + /* 2/(3log2)*(s+...) */ + p_h = u+v; + GET_FLOAT_WORD(is,p_h); + SET_FLOAT_WORD(p_h,is&0xfffff000); + p_l = v-(p_h-u); + z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ + z_l = cp_l*p_h+p_l*cp+dp_l[k]; + /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ + t = n; + t1 = (((z_h+z_l)+dp_h[k])+t); + GET_FLOAT_WORD(is,t1); + SET_FLOAT_WORD(t1,is&0xfffff000); + t2 = z_l-(((t1-t)-dp_h[k])-z_h); + } + + /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ + GET_FLOAT_WORD(is,y); + SET_FLOAT_WORD(y1,is&0xfffff000); + p_l = (y-y1)*t1+y*t2; + p_h = y1*t1; + z = p_l+p_h; + GET_FLOAT_WORD(j,z); + if (j>0x43000000) /* if z > 128 */ + return sn*huge*huge; /* overflow */ + else if (j==0x43000000) { /* if z == 128 */ + if(p_l+ovt>z-p_h) return sn*huge*huge; /* overflow */ + } + else if ((j&0x7fffffff)>0x43160000) /* z <= -150 */ + return sn*tiny*tiny; /* underflow */ + else if (j==0xc3160000){ /* z == -150 */ + if(p_l<=z-p_h) return sn*tiny*tiny; /* underflow */ + } + /* + * compute 2**(p_h+p_l) + */ + i = j&0x7fffffff; + k = (i>>23)-0x7f; + n = 0; + if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */ + n = j+(0x00800000>>(k+1)); + k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */ + SET_FLOAT_WORD(t,n&~(0x007fffff>>k)); + n = ((n&0x007fffff)|0x00800000)>>(23-k); + if(j<0) n = -n; + p_h -= t; + } + t = p_l+p_h; + GET_FLOAT_WORD(is,t); + SET_FLOAT_WORD(t,is&0xffff8000); + u = t*lg2_h; + v = (p_l-(t-p_h))*lg2+t*lg2_l; + z = u+v; + w = v-(z-u); + t = z*z; + t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); + r = (z*t1)/(t1-two)-(w+z*w); + z = one-(r-z); + GET_FLOAT_WORD(j,z); + j += (n<<23); + if((j>>23)<=0) z = scalbnf(z,n); /* subnormal output */ + else SET_FLOAT_WORD(z,j); + return sn*z; +} diff --git a/modules/fdlibm/src/e_rem_pio2.cpp b/modules/fdlibm/src/e_rem_pio2.cpp new file mode 100644 index 0000000000..1e5e1cc9f4 --- /dev/null +++ b/modules/fdlibm/src/e_rem_pio2.cpp @@ -0,0 +1,179 @@ + +/* @(#)e_rem_pio2.c 1.4 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * Optimized by Bruce D. Evans. + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* __ieee754_rem_pio2(x,y) + * + * return the remainder of x rem pi/2 in y[0]+y[1] + * use __kernel_rem_pio2() + */ + +#include <float.h> + +#include "math_private.h" + +/* + * invpio2: 53 bits of 2/pi + * pio2_1: first 33 bit of pi/2 + * pio2_1t: pi/2 - pio2_1 + * pio2_2: second 33 bit of pi/2 + * pio2_2t: pi/2 - (pio2_1+pio2_2) + * pio2_3: third 33 bit of pi/2 + * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) + */ + +static const double +zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ +two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ +invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ +pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ +pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ +pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ +pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ +pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ +pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ + +#ifdef INLINE_REM_PIO2 +static inline +#endif +int +__ieee754_rem_pio2(double x, double *y) +{ + double z,w,t,r,fn; + double tx[3],ty[2]; + int32_t e0,i,j,nx,n,ix,hx; + u_int32_t low; + + GET_HIGH_WORD(hx,x); /* high word of x */ + ix = hx&0x7fffffff; +#if 0 /* Must be handled in caller. */ + if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ + {y[0] = x; y[1] = 0; return 0;} +#endif + if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */ + if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */ + goto medium; /* cancellation -- use medium case */ + if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */ + if (hx > 0) { + z = x - pio2_1; /* one round good to 85 bits */ + y[0] = z - pio2_1t; + y[1] = (z-y[0])-pio2_1t; + return 1; + } else { + z = x + pio2_1; + y[0] = z + pio2_1t; + y[1] = (z-y[0])+pio2_1t; + return -1; + } + } else { + if (hx > 0) { + z = x - 2*pio2_1; + y[0] = z - 2*pio2_1t; + y[1] = (z-y[0])-2*pio2_1t; + return 2; + } else { + z = x + 2*pio2_1; + y[0] = z + 2*pio2_1t; + y[1] = (z-y[0])+2*pio2_1t; + return -2; + } + } + } + if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */ + if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */ + if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */ + goto medium; + if (hx > 0) { + z = x - 3*pio2_1; + y[0] = z - 3*pio2_1t; + y[1] = (z-y[0])-3*pio2_1t; + return 3; + } else { + z = x + 3*pio2_1; + y[0] = z + 3*pio2_1t; + y[1] = (z-y[0])+3*pio2_1t; + return -3; + } + } else { + if (ix == 0x401921fb) /* |x| ~= 4pi/2 */ + goto medium; + if (hx > 0) { + z = x - 4*pio2_1; + y[0] = z - 4*pio2_1t; + y[1] = (z-y[0])-4*pio2_1t; + return 4; + } else { + z = x + 4*pio2_1; + y[0] = z + 4*pio2_1t; + y[1] = (z-y[0])+4*pio2_1t; + return -4; + } + } + } + if(ix<0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */ +medium: + fn = rnint((double_t)x*invpio2); + n = irint(fn); + r = x-fn*pio2_1; + w = fn*pio2_1t; /* 1st round good to 85 bit */ + { + u_int32_t high; + j = ix>>20; + y[0] = r-w; + GET_HIGH_WORD(high,y[0]); + i = j-((high>>20)&0x7ff); + if(i>16) { /* 2nd iteration needed, good to 118 */ + t = r; + w = fn*pio2_2; + r = t-w; + w = fn*pio2_2t-((t-r)-w); + y[0] = r-w; + GET_HIGH_WORD(high,y[0]); + i = j-((high>>20)&0x7ff); + if(i>49) { /* 3rd iteration need, 151 bits acc */ + t = r; /* will cover all possible cases */ + w = fn*pio2_3; + r = t-w; + w = fn*pio2_3t-((t-r)-w); + y[0] = r-w; + } + } + } + y[1] = (r-y[0])-w; + return n; + } + /* + * all other (large) arguments + */ + if(ix>=0x7ff00000) { /* x is inf or NaN */ + y[0]=y[1]=x-x; return 0; + } + /* set z = scalbn(|x|,ilogb(x)-23) */ + GET_LOW_WORD(low,x); + e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ + INSERT_WORDS(z, ix - ((int32_t)(e0<<20)), low); + for(i=0;i<2;i++) { + tx[i] = (double)((int32_t)(z)); + z = (z-tx[i])*two24; + } + tx[2] = z; + nx = 3; + while(tx[nx-1]==zero) nx--; /* skip zero term */ + n = __kernel_rem_pio2(tx,ty,e0,nx,1); + if(hx<0) {y[0] = -ty[0]; y[1] = -ty[1]; return -n;} + y[0] = ty[0]; y[1] = ty[1]; return n; +} diff --git a/modules/fdlibm/src/e_rem_pio2f.cpp b/modules/fdlibm/src/e_rem_pio2f.cpp new file mode 100644 index 0000000000..49a30a6fa1 --- /dev/null +++ b/modules/fdlibm/src/e_rem_pio2f.cpp @@ -0,0 +1,77 @@ +/* e_rem_pio2f.c -- float version of e_rem_pio2.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + * Debugged and optimized by Bruce D. Evans. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* __ieee754_rem_pio2f(x,y) + * + * return the remainder of x rem pi/2 in *y + * use double precision for everything except passing x + * use __kernel_rem_pio2() for large x + */ + +#include <float.h> + +#include "math_private.h" + +/* + * invpio2: 53 bits of 2/pi + * pio2_1: first 25 bits of pi/2 + * pio2_1t: pi/2 - pio2_1 + */ + +static const double +invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ +pio2_1 = 1.57079631090164184570e+00, /* 0x3FF921FB, 0x50000000 */ +pio2_1t = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */ + +#ifdef INLINE_REM_PIO2F +static inline +#endif +int +__ieee754_rem_pio2f(float x, double *y) +{ + double w,r,fn; + double tx[1],ty[1]; + float z; + int32_t e0,n,ix,hx; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + /* 33+53 bit pi is good enough for medium size */ + if(ix<0x4dc90fdb) { /* |x| ~< 2^28*(pi/2), medium size */ + fn = rnint((float)x*invpio2); + n = irint(fn); + r = x-fn*pio2_1; + w = fn*pio2_1t; + *y = r-w; + return n; + } + /* + * all other (large) arguments + */ + if(ix>=0x7f800000) { /* x is inf or NaN */ + *y=x-x; return 0; + } + /* set z = scalbn(|x|,ilogb(|x|)-23) */ + e0 = (ix>>23)-150; /* e0 = ilogb(|x|)-23; */ + SET_FLOAT_WORD(z, ix - ((int32_t)(e0<<23))); + tx[0] = z; + n = __kernel_rem_pio2(tx,ty,e0,1,0); + if(hx<0) {*y = -ty[0]; return -n;} + *y = ty[0]; return n; +} diff --git a/modules/fdlibm/src/e_sinh.cpp b/modules/fdlibm/src/e_sinh.cpp new file mode 100644 index 0000000000..c3418e6875 --- /dev/null +++ b/modules/fdlibm/src/e_sinh.cpp @@ -0,0 +1,74 @@ + +/* @(#)e_sinh.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* __ieee754_sinh(x) + * Method : + * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 + * 1. Replace x by |x| (sinh(-x) = -sinh(x)). + * 2. + * E + E/(E+1) + * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x) + * 2 + * + * 22 <= x <= lnovft : sinh(x) := exp(x)/2 + * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2) + * ln2ovft < x : sinh(x) := x*shuge (overflow) + * + * Special cases: + * sinh(x) is |x| if x is +INF, -INF, or NaN. + * only sinh(0)=0 is exact for finite x. + */ + +#include <float.h> + +#include "math_private.h" + +static const double one = 1.0, shuge = 1.0e307; + +double +__ieee754_sinh(double x) +{ + double t,h; + int32_t ix,jx; + + /* High word of |x|. */ + GET_HIGH_WORD(jx,x); + ix = jx&0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7ff00000) return x+x; + + h = 0.5; + if (jx<0) h = -h; + /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ + if (ix < 0x40360000) { /* |x|<22 */ + if (ix<0x3e300000) /* |x|<2**-28 */ + if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ + t = expm1(fabs(x)); + if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one)); + return h*(t+t/(t+one)); + } + + /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ + if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + if (ix<=0x408633CE) + return h*2.0*__ldexp_exp(fabs(x), -1); + + /* |x| > overflowthresold, sinh(x) overflow */ + return x*shuge; +} diff --git a/modules/fdlibm/src/e_sqrtf.cpp b/modules/fdlibm/src/e_sqrtf.cpp new file mode 100644 index 0000000000..78e01a76ae --- /dev/null +++ b/modules/fdlibm/src/e_sqrtf.cpp @@ -0,0 +1,96 @@ +/* e_sqrtf.c -- float version of e_sqrt.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#ifndef lint +//static char rcsid[] = "$FreeBSD$"; +//#endif + +#include "math_private.h" + +#ifdef USE_BUILTIN_SQRTF +float +__ieee754_sqrtf(float x) +{ + return (__builtin_sqrtf(x)); +} +#else +static const float one = 1.0, tiny=1.0e-30; + +float +__ieee754_sqrtf(float x) +{ + float z; + int32_t sign = (int)0x80000000; + int32_t ix,s,q,m,t,i; + u_int32_t r; + + GET_FLOAT_WORD(ix,x); + + /* take care of Inf and NaN */ + if((ix&0x7f800000)==0x7f800000) { + return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf + sqrt(-inf)=sNaN */ + } + /* take care of zero */ + if(ix<=0) { + if((ix&(~sign))==0) return x;/* sqrt(+-0) = +-0 */ + else if(ix<0) + return (x-x)/(x-x); /* sqrt(-ve) = sNaN */ + } + /* normalize x */ + m = (ix>>23); + if(m==0) { /* subnormal x */ + for(i=0;(ix&0x00800000)==0;i++) ix<<=1; + m -= i-1; + } + m -= 127; /* unbias exponent */ + ix = (ix&0x007fffff)|0x00800000; + if(m&1) /* odd m, double x to make it even */ + ix += ix; + m >>= 1; /* m = [m/2] */ + + /* generate sqrt(x) bit by bit */ + ix += ix; + q = s = 0; /* q = sqrt(x) */ + r = 0x01000000; /* r = moving bit from right to left */ + + while(r!=0) { + t = s+r; + if(t<=ix) { + s = t+r; + ix -= t; + q += r; + } + ix += ix; + r>>=1; + } + + /* use floating add to find out rounding direction */ + if(ix!=0) { + z = one-tiny; /* trigger inexact flag */ + if (z>=one) { + z = one+tiny; + if (z>one) + q += 2; + else + q += (q&1); + } + } + ix = (q>>1)+0x3f000000; + ix += (m <<23); + SET_FLOAT_WORD(z,ix); + return z; +} +#endif diff --git a/modules/fdlibm/src/fdlibm.h b/modules/fdlibm/src/fdlibm.h new file mode 100644 index 0000000000..048e763952 --- /dev/null +++ b/modules/fdlibm/src/fdlibm.h @@ -0,0 +1,84 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * from: @(#)fdlibm.h 5.1 93/09/24 + * $FreeBSD$ + */ + +#ifndef mozilla_imported_fdlibm_h +#define mozilla_imported_fdlibm_h + +namespace fdlibm { + +#ifndef M_PI_2 +#define M_PI_2 1.57079632679489661923 /* pi/2 */ +#endif + +double acos(double); +double asin(double); +double atan(double); +double atan2(double, double); +double cos(double); +double sin(double); +double tan(double); + +double cosh(double); +double sinh(double); +double tanh(double); + +double exp(double); +double log(double); +double log10(double); + +double pow(double, double); + +double ceil(double); +double fabs(double); +double floor(double); + +double acosh(double); +double asinh(double); +double atanh(double); +double cbrt(double); +double exp2(double); +double expm1(double); +double hypot(double, double); +double log1p(double); +double log2(double); +double rint(double); +double copysign(double, double); +double nearbyint(double); +double scalbn(double, int); +double trunc(double); +float acosf(float); +float asinf(float); +float atanf(float); +float cosf(float); +float sinf(float); +float tanf(float); +float exp2f(float); +float expf(float); +float logf(float); +float powf(float, float); +float sqrtf(float); + +float ceilf(float); +float fabsf(float); +float floorf(float); +float nearbyintf(float); +float rintf(float); +float scalbnf(float, int); +float truncf(float); + +} /* namespace fdlibm */ + +#endif /* !mozilla_imported_fdlibm_h */ diff --git a/modules/fdlibm/src/k_cos.cpp b/modules/fdlibm/src/k_cos.cpp new file mode 100644 index 0000000000..5bee28daf3 --- /dev/null +++ b/modules/fdlibm/src/k_cos.cpp @@ -0,0 +1,78 @@ + +/* @(#)k_cos.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* + * __kernel_cos( x, y ) + * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * + * Algorithm + * 1. Since cos(-x) = cos(x), we need only to consider positive x. + * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0. + * 3. cos(x) is approximated by a polynomial of degree 14 on + * [0,pi/4] + * 4 14 + * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x + * where the remez error is + * + * | 2 4 6 8 10 12 14 | -58 + * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 + * | | + * + * 4 6 8 10 12 14 + * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then + * cos(x) ~ 1 - x*x/2 + r + * since cos(x+y) ~ cos(x) - sin(x)*y + * ~ cos(x) - x*y, + * a correction term is necessary in cos(x) and hence + * cos(x+y) = 1 - (x*x/2 - (r - x*y)) + * For better accuracy, rearrange to + * cos(x+y) ~ w + (tmp + (r-x*y)) + * where w = 1 - x*x/2 and tmp is a tiny correction term + * (1 - x*x/2 == w + tmp exactly in infinite precision). + * The exactness of w + tmp in infinite precision depends on w + * and tmp having the same precision as x. If they have extra + * precision due to compiler bugs, then the extra precision is + * only good provided it is retained in all terms of the final + * expression for cos(). Retention happens in all cases tested + * under FreeBSD, so don't pessimize things by forcibly clipping + * any extra precision in w. + */ + +#include "math_private.h" + +static const double +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ +C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ +C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ +C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ +C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ +C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ + +double +__kernel_cos(double x, double y) +{ + double hz,z,r,w; + + z = x*x; + w = z*z; + r = z*(C1+z*(C2+z*C3)) + w*w*(C4+z*(C5+z*C6)); + hz = 0.5*z; + w = one-hz; + return w + (((one-w)-hz) + (z*r-x*y)); +} diff --git a/modules/fdlibm/src/k_cosf.cpp b/modules/fdlibm/src/k_cosf.cpp new file mode 100644 index 0000000000..db8e8744ca --- /dev/null +++ b/modules/fdlibm/src/k_cosf.cpp @@ -0,0 +1,45 @@ +/* k_cosf.c -- float version of k_cos.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + * Debugged and optimized by Bruce D. Evans. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#ifndef INLINE_KERNEL_COSDF +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); +#endif + +#include "math_private.h" + +/* |cos(x) - c(x)| < 2**-34.1 (~[-5.37e-11, 5.295e-11]). */ +static const double +one = 1.0, +C0 = -0x1ffffffd0c5e81.0p-54, /* -0.499999997251031003120 */ +C1 = 0x155553e1053a42.0p-57, /* 0.0416666233237390631894 */ +C2 = -0x16c087e80f1e27.0p-62, /* -0.00138867637746099294692 */ +C3 = 0x199342e0ee5069.0p-68; /* 0.0000243904487962774090654 */ + +#ifdef INLINE_KERNEL_COSDF +static __inline +#endif +float +__kernel_cosdf(double x) +{ + double r, w, z; + + /* Try to optimize for parallel evaluation as in k_tanf.c. */ + z = x*x; + w = z*z; + r = C2+z*C3; + return ((one+z*C0) + w*C1) + (w*z)*r; +} diff --git a/modules/fdlibm/src/k_exp.cpp b/modules/fdlibm/src/k_exp.cpp new file mode 100644 index 0000000000..9394c8fd8d --- /dev/null +++ b/modules/fdlibm/src/k_exp.cpp @@ -0,0 +1,83 @@ +/*- + * SPDX-License-Identifier: BSD-2-Clause-FreeBSD + * + * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG> + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + + #include "math_private.h" + +static const uint32_t k = 1799; /* constant for reduction */ +static const double kln2 = 1246.97177782734161156; /* k * ln2 */ + +/* + * Compute exp(x), scaled to avoid spurious overflow. An exponent is + * returned separately in 'expt'. + * + * Input: ln(DBL_MAX) <= x < ln(2 * DBL_MAX / DBL_MIN_DENORM) ~= 1454.91 + * Output: 2**1023 <= y < 2**1024 + */ +static double +__frexp_exp(double x, int *expt) +{ + double exp_x; + uint32_t hx; + + /* + * We use exp(x) = exp(x - kln2) * 2**k, carefully chosen to + * minimize |exp(kln2) - 2**k|. We also scale the exponent of + * exp_x to MAX_EXP so that the result can be multiplied by + * a tiny number without losing accuracy due to denormalization. + */ + exp_x = exp(x - kln2); + GET_HIGH_WORD(hx, exp_x); + *expt = (hx >> 20) - (0x3ff + 1023) + k; + SET_HIGH_WORD(exp_x, (hx & 0xfffff) | ((0x3ff + 1023) << 20)); + return (exp_x); +} + +/* + * __ldexp_exp(x, expt) and __ldexp_cexp(x, expt) compute exp(x) * 2**expt. + * They are intended for large arguments (real part >= ln(DBL_MAX)) + * where care is needed to avoid overflow. + * + * The present implementation is narrowly tailored for our hyperbolic and + * exponential functions. We assume expt is small (0 or -1), and the caller + * has filtered out very large x, for which overflow would be inevitable. + */ + +double +__ldexp_exp(double x, int expt) +{ + double exp_x, scale; + int ex_expt; + + exp_x = __frexp_exp(x, &ex_expt); + expt += ex_expt; + INSERT_WORDS(scale, (0x3ff + expt) << 20, 0); + return (exp_x * scale); +} diff --git a/modules/fdlibm/src/k_expf.cpp b/modules/fdlibm/src/k_expf.cpp new file mode 100644 index 0000000000..57f7c08499 --- /dev/null +++ b/modules/fdlibm/src/k_expf.cpp @@ -0,0 +1,66 @@ +/*- + * SPDX-License-Identifier: BSD-2-Clause-FreeBSD + * + * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG> + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +#include "math_private.h" + +static const uint32_t k = 235; /* constant for reduction */ +static const float kln2 = 162.88958740F; /* k * ln2 */ + +/* + * See k_exp.c for details. + * + * Input: ln(FLT_MAX) <= x < ln(2 * FLT_MAX / FLT_MIN_DENORM) ~= 192.7 + * Output: 2**127 <= y < 2**128 + */ +static float +__frexp_expf(float x, int *expt) +{ + float exp_x; + uint32_t hx; + + exp_x = expf(x - kln2); + GET_FLOAT_WORD(hx, exp_x); + *expt = (hx >> 23) - (0x7f + 127) + k; + SET_FLOAT_WORD(exp_x, (hx & 0x7fffff) | ((0x7f + 127) << 23)); + return (exp_x); +} + +float +__ldexp_expf(float x, int expt) +{ + float exp_x, scale; + int ex_expt; + + exp_x = __frexp_expf(x, &ex_expt); + expt += ex_expt; + SET_FLOAT_WORD(scale, (0x7f + expt) << 23); + return (exp_x * scale); +} diff --git a/modules/fdlibm/src/k_log.h b/modules/fdlibm/src/k_log.h new file mode 100644 index 0000000000..0efa020f63 --- /dev/null +++ b/modules/fdlibm/src/k_log.h @@ -0,0 +1,100 @@ + +/* @(#)e_log.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* + * k_log1p(f): + * Return log(1+f) - f for 1+f in ~[sqrt(2)/2, sqrt(2)]. + * + * The following describes the overall strategy for computing + * logarithms in base e. The argument reduction and adding the final + * term of the polynomial are done by the caller for increased accuracy + * when different bases are used. + * + * Method : + * 1. Argument Reduction: find k and f such that + * x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * + * 2. Approximation of log(1+f). + * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * = 2s + s*R + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error + * of this polynomial approximation is bounded by 2**-58.45. In + * other words, + * 2 4 6 8 10 12 14 + * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s + * (the values of Lg1 to Lg7 are listed in the program) + * and + * | 2 14 | -58.45 + * | Lg1*s +...+Lg7*s - R(z) | <= 2 + * | | + * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. + * In order to guarantee error in log below 1ulp, we compute log + * by + * log(1+f) = f - s*(f - R) (if f is not too large) + * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) + * + * 3. Finally, log(x) = k*ln2 + log(1+f). + * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) + * Here ln2 is split into two floating point number: + * ln2_hi + ln2_lo, + * where n*ln2_hi is always exact for |n| < 2000. + * + * Special cases: + * log(x) is NaN with signal if x < 0 (including -INF) ; + * log(+INF) is +INF; log(0) is -INF with signal; + * log(NaN) is that NaN with no signal. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +static const double +Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ +Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ +Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ +Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ +Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ +Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ +Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ + +/* + * We always inline k_log1p(), since doing so produces a + * substantial performance improvement (~40% on amd64). + */ +static inline double +k_log1p(double f) +{ + double hfsq,s,z,R,w,t1,t2; + + s = f/(2.0+f); + z = s*s; + w = z*z; + t1= w*(Lg2+w*(Lg4+w*Lg6)); + t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); + R = t2+t1; + hfsq=0.5*f*f; + return s*(hfsq+R); +} diff --git a/modules/fdlibm/src/k_rem_pio2.cpp b/modules/fdlibm/src/k_rem_pio2.cpp new file mode 100644 index 0000000000..22b098af74 --- /dev/null +++ b/modules/fdlibm/src/k_rem_pio2.cpp @@ -0,0 +1,443 @@ + +/* @(#)k_rem_pio2.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* + * __kernel_rem_pio2(x,y,e0,nx,prec) + * double x[],y[]; int e0,nx,prec; + * + * __kernel_rem_pio2 return the last three digits of N with + * y = x - N*pi/2 + * so that |y| < pi/2. + * + * The method is to compute the integer (mod 8) and fraction parts of + * (2/pi)*x without doing the full multiplication. In general we + * skip the part of the product that are known to be a huge integer ( + * more accurately, = 0 mod 8 ). Thus the number of operations are + * independent of the exponent of the input. + * + * (2/pi) is represented by an array of 24-bit integers in ipio2[]. + * + * Input parameters: + * x[] The input value (must be positive) is broken into nx + * pieces of 24-bit integers in double precision format. + * x[i] will be the i-th 24 bit of x. The scaled exponent + * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0 + * match x's up to 24 bits. + * + * Example of breaking a double positive z into x[0]+x[1]+x[2]: + * e0 = ilogb(z)-23 + * z = scalbn(z,-e0) + * for i = 0,1,2 + * x[i] = floor(z) + * z = (z-x[i])*2**24 + * + * + * y[] output result in an array of double precision numbers. + * The dimension of y[] is: + * 24-bit precision 1 + * 53-bit precision 2 + * 64-bit precision 2 + * 113-bit precision 3 + * The actual value is the sum of them. Thus for 113-bit + * precision, one may have to do something like: + * + * long double t,w,r_head, r_tail; + * t = (long double)y[2] + (long double)y[1]; + * w = (long double)y[0]; + * r_head = t+w; + * r_tail = w - (r_head - t); + * + * e0 The exponent of x[0]. Must be <= 16360 or you need to + * expand the ipio2 table. + * + * nx dimension of x[] + * + * prec an integer indicating the precision: + * 0 24 bits (single) + * 1 53 bits (double) + * 2 64 bits (extended) + * 3 113 bits (quad) + * + * External function: + * double scalbn(), floor(); + * + * + * Here is the description of some local variables: + * + * jk jk+1 is the initial number of terms of ipio2[] needed + * in the computation. The minimum and recommended value + * for jk is 3,4,4,6 for single, double, extended, and quad. + * jk+1 must be 2 larger than you might expect so that our + * recomputation test works. (Up to 24 bits in the integer + * part (the 24 bits of it that we compute) and 23 bits in + * the fraction part may be lost to cancellation before we + * recompute.) + * + * jz local integer variable indicating the number of + * terms of ipio2[] used. + * + * jx nx - 1 + * + * jv index for pointing to the suitable ipio2[] for the + * computation. In general, we want + * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8 + * is an integer. Thus + * e0-3-24*jv >= 0 or (e0-3)/24 >= jv + * Hence jv = max(0,(e0-3)/24). + * + * jp jp+1 is the number of terms in PIo2[] needed, jp = jk. + * + * q[] double array with integral value, representing the + * 24-bits chunk of the product of x and 2/pi. + * + * q0 the corresponding exponent of q[0]. Note that the + * exponent for q[i] would be q0-24*i. + * + * PIo2[] double precision array, obtained by cutting pi/2 + * into 24 bits chunks. + * + * f[] ipio2[] in floating point + * + * iq[] integer array by breaking up q[] in 24-bits chunk. + * + * fq[] final product of x*(2/pi) in fq[0],..,fq[jk] + * + * ih integer. If >0 it indicates q[] is >= 0.5, hence + * it also indicates the *sign* of the result. + * + */ + + +/* + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include <float.h> + +#include "math_private.h" + +static const int init_jk[] = {3,4,4,6}; /* initial value for jk */ + +/* + * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi + * + * integer array, contains the (24*i)-th to (24*i+23)-th + * bit of 2/pi after binary point. The corresponding + * floating value is + * + * ipio2[i] * 2^(-24(i+1)). + * + * NB: This table must have at least (e0-3)/24 + jk terms. + * For quad precision (e0 <= 16360, jk = 6), this is 686. + */ +static const int32_t ipio2[] = { +0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, +0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, +0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, +0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, +0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, +0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, +0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, +0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, +0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, +0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, +0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, + +#if LDBL_MAX_EXP > 1024 +#if LDBL_MAX_EXP > 16384 +#error "ipio2 table needs to be expanded" +#endif +0x47C419, 0xC367CD, 0xDCE809, 0x2A8359, 0xC4768B, 0x961CA6, +0xDDAF44, 0xD15719, 0x053EA5, 0xFF0705, 0x3F7E33, 0xE832C2, +0xDE4F98, 0x327DBB, 0xC33D26, 0xEF6B1E, 0x5EF89F, 0x3A1F35, +0xCAF27F, 0x1D87F1, 0x21907C, 0x7C246A, 0xFA6ED5, 0x772D30, +0x433B15, 0xC614B5, 0x9D19C3, 0xC2C4AD, 0x414D2C, 0x5D000C, +0x467D86, 0x2D71E3, 0x9AC69B, 0x006233, 0x7CD2B4, 0x97A7B4, +0xD55537, 0xF63ED7, 0x1810A3, 0xFC764D, 0x2A9D64, 0xABD770, +0xF87C63, 0x57B07A, 0xE71517, 0x5649C0, 0xD9D63B, 0x3884A7, +0xCB2324, 0x778AD6, 0x23545A, 0xB91F00, 0x1B0AF1, 0xDFCE19, +0xFF319F, 0x6A1E66, 0x615799, 0x47FBAC, 0xD87F7E, 0xB76522, +0x89E832, 0x60BFE6, 0xCDC4EF, 0x09366C, 0xD43F5D, 0xD7DE16, +0xDE3B58, 0x929BDE, 0x2822D2, 0xE88628, 0x4D58E2, 0x32CAC6, +0x16E308, 0xCB7DE0, 0x50C017, 0xA71DF3, 0x5BE018, 0x34132E, +0x621283, 0x014883, 0x5B8EF5, 0x7FB0AD, 0xF2E91E, 0x434A48, +0xD36710, 0xD8DDAA, 0x425FAE, 0xCE616A, 0xA4280A, 0xB499D3, +0xF2A606, 0x7F775C, 0x83C2A3, 0x883C61, 0x78738A, 0x5A8CAF, +0xBDD76F, 0x63A62D, 0xCBBFF4, 0xEF818D, 0x67C126, 0x45CA55, +0x36D9CA, 0xD2A828, 0x8D61C2, 0x77C912, 0x142604, 0x9B4612, +0xC459C4, 0x44C5C8, 0x91B24D, 0xF31700, 0xAD43D4, 0xE54929, +0x10D5FD, 0xFCBE00, 0xCC941E, 0xEECE70, 0xF53E13, 0x80F1EC, +0xC3E7B3, 0x28F8C7, 0x940593, 0x3E71C1, 0xB3092E, 0xF3450B, +0x9C1288, 0x7B20AB, 0x9FB52E, 0xC29247, 0x2F327B, 0x6D550C, +0x90A772, 0x1FE76B, 0x96CB31, 0x4A1679, 0xE27941, 0x89DFF4, +0x9794E8, 0x84E6E2, 0x973199, 0x6BED88, 0x365F5F, 0x0EFDBB, +0xB49A48, 0x6CA467, 0x427271, 0x325D8D, 0xB8159F, 0x09E5BC, +0x25318D, 0x3974F7, 0x1C0530, 0x010C0D, 0x68084B, 0x58EE2C, +0x90AA47, 0x02E774, 0x24D6BD, 0xA67DF7, 0x72486E, 0xEF169F, +0xA6948E, 0xF691B4, 0x5153D1, 0xF20ACF, 0x339820, 0x7E4BF5, +0x6863B2, 0x5F3EDD, 0x035D40, 0x7F8985, 0x295255, 0xC06437, +0x10D86D, 0x324832, 0x754C5B, 0xD4714E, 0x6E5445, 0xC1090B, +0x69F52A, 0xD56614, 0x9D0727, 0x50045D, 0xDB3BB4, 0xC576EA, +0x17F987, 0x7D6B49, 0xBA271D, 0x296996, 0xACCCC6, 0x5414AD, +0x6AE290, 0x89D988, 0x50722C, 0xBEA404, 0x940777, 0x7030F3, +0x27FC00, 0xA871EA, 0x49C266, 0x3DE064, 0x83DD97, 0x973FA3, +0xFD9443, 0x8C860D, 0xDE4131, 0x9D3992, 0x8C70DD, 0xE7B717, +0x3BDF08, 0x2B3715, 0xA0805C, 0x93805A, 0x921110, 0xD8E80F, +0xAF806C, 0x4BFFDB, 0x0F9038, 0x761859, 0x15A562, 0xBBCB61, +0xB989C7, 0xBD4010, 0x04F2D2, 0x277549, 0xF6B6EB, 0xBB22DB, +0xAA140A, 0x2F2689, 0x768364, 0x333B09, 0x1A940E, 0xAA3A51, +0xC2A31D, 0xAEEDAF, 0x12265C, 0x4DC26D, 0x9C7A2D, 0x9756C0, +0x833F03, 0xF6F009, 0x8C402B, 0x99316D, 0x07B439, 0x15200C, +0x5BC3D8, 0xC492F5, 0x4BADC6, 0xA5CA4E, 0xCD37A7, 0x36A9E6, +0x9492AB, 0x6842DD, 0xDE6319, 0xEF8C76, 0x528B68, 0x37DBFC, +0xABA1AE, 0x3115DF, 0xA1AE00, 0xDAFB0C, 0x664D64, 0xB705ED, +0x306529, 0xBF5657, 0x3AFF47, 0xB9F96A, 0xF3BE75, 0xDF9328, +0x3080AB, 0xF68C66, 0x15CB04, 0x0622FA, 0x1DE4D9, 0xA4B33D, +0x8F1B57, 0x09CD36, 0xE9424E, 0xA4BE13, 0xB52333, 0x1AAAF0, +0xA8654F, 0xA5C1D2, 0x0F3F0B, 0xCD785B, 0x76F923, 0x048B7B, +0x721789, 0x53A6C6, 0xE26E6F, 0x00EBEF, 0x584A9B, 0xB7DAC4, +0xBA66AA, 0xCFCF76, 0x1D02D1, 0x2DF1B1, 0xC1998C, 0x77ADC3, +0xDA4886, 0xA05DF7, 0xF480C6, 0x2FF0AC, 0x9AECDD, 0xBC5C3F, +0x6DDED0, 0x1FC790, 0xB6DB2A, 0x3A25A3, 0x9AAF00, 0x9353AD, +0x0457B6, 0xB42D29, 0x7E804B, 0xA707DA, 0x0EAA76, 0xA1597B, +0x2A1216, 0x2DB7DC, 0xFDE5FA, 0xFEDB89, 0xFDBE89, 0x6C76E4, +0xFCA906, 0x70803E, 0x156E85, 0xFF87FD, 0x073E28, 0x336761, +0x86182A, 0xEABD4D, 0xAFE7B3, 0x6E6D8F, 0x396795, 0x5BBF31, +0x48D784, 0x16DF30, 0x432DC7, 0x356125, 0xCE70C9, 0xB8CB30, +0xFD6CBF, 0xA200A4, 0xE46C05, 0xA0DD5A, 0x476F21, 0xD21262, +0x845CB9, 0x496170, 0xE0566B, 0x015299, 0x375550, 0xB7D51E, +0xC4F133, 0x5F6E13, 0xE4305D, 0xA92E85, 0xC3B21D, 0x3632A1, +0xA4B708, 0xD4B1EA, 0x21F716, 0xE4698F, 0x77FF27, 0x80030C, +0x2D408D, 0xA0CD4F, 0x99A520, 0xD3A2B3, 0x0A5D2F, 0x42F9B4, +0xCBDA11, 0xD0BE7D, 0xC1DB9B, 0xBD17AB, 0x81A2CA, 0x5C6A08, +0x17552E, 0x550027, 0xF0147F, 0x8607E1, 0x640B14, 0x8D4196, +0xDEBE87, 0x2AFDDA, 0xB6256B, 0x34897B, 0xFEF305, 0x9EBFB9, +0x4F6A68, 0xA82A4A, 0x5AC44F, 0xBCF82D, 0x985AD7, 0x95C7F4, +0x8D4D0D, 0xA63A20, 0x5F57A4, 0xB13F14, 0x953880, 0x0120CC, +0x86DD71, 0xB6DEC9, 0xF560BF, 0x11654D, 0x6B0701, 0xACB08C, +0xD0C0B2, 0x485551, 0x0EFB1E, 0xC37295, 0x3B06A3, 0x3540C0, +0x7BDC06, 0xCC45E0, 0xFA294E, 0xC8CAD6, 0x41F3E8, 0xDE647C, +0xD8649B, 0x31BED9, 0xC397A4, 0xD45877, 0xC5E369, 0x13DAF0, +0x3C3ABA, 0x461846, 0x5F7555, 0xF5BDD2, 0xC6926E, 0x5D2EAC, +0xED440E, 0x423E1C, 0x87C461, 0xE9FD29, 0xF3D6E7, 0xCA7C22, +0x35916F, 0xC5E008, 0x8DD7FF, 0xE26A6E, 0xC6FDB0, 0xC10893, +0x745D7C, 0xB2AD6B, 0x9D6ECD, 0x7B723E, 0x6A11C6, 0xA9CFF7, +0xDF7329, 0xBAC9B5, 0x5100B7, 0x0DB2E2, 0x24BA74, 0x607DE5, +0x8AD874, 0x2C150D, 0x0C1881, 0x94667E, 0x162901, 0x767A9F, +0xBEFDFD, 0xEF4556, 0x367ED9, 0x13D9EC, 0xB9BA8B, 0xFC97C4, +0x27A831, 0xC36EF1, 0x36C594, 0x56A8D8, 0xB5A8B4, 0x0ECCCF, +0x2D8912, 0x34576F, 0x89562C, 0xE3CE99, 0xB920D6, 0xAA5E6B, +0x9C2A3E, 0xCC5F11, 0x4A0BFD, 0xFBF4E1, 0x6D3B8E, 0x2C86E2, +0x84D4E9, 0xA9B4FC, 0xD1EEEF, 0xC9352E, 0x61392F, 0x442138, +0xC8D91B, 0x0AFC81, 0x6A4AFB, 0xD81C2F, 0x84B453, 0x8C994E, +0xCC2254, 0xDC552A, 0xD6C6C0, 0x96190B, 0xB8701A, 0x649569, +0x605A26, 0xEE523F, 0x0F117F, 0x11B5F4, 0xF5CBFC, 0x2DBC34, +0xEEBC34, 0xCC5DE8, 0x605EDD, 0x9B8E67, 0xEF3392, 0xB817C9, +0x9B5861, 0xBC57E1, 0xC68351, 0x103ED8, 0x4871DD, 0xDD1C2D, +0xA118AF, 0x462C21, 0xD7F359, 0x987AD9, 0xC0549E, 0xFA864F, +0xFC0656, 0xAE79E5, 0x362289, 0x22AD38, 0xDC9367, 0xAAE855, +0x382682, 0x9BE7CA, 0xA40D51, 0xB13399, 0x0ED7A9, 0x480569, +0xF0B265, 0xA7887F, 0x974C88, 0x36D1F9, 0xB39221, 0x4A827B, +0x21CF98, 0xDC9F40, 0x5547DC, 0x3A74E1, 0x42EB67, 0xDF9DFE, +0x5FD45E, 0xA4677B, 0x7AACBA, 0xA2F655, 0x23882B, 0x55BA41, +0x086E59, 0x862A21, 0x834739, 0xE6E389, 0xD49EE5, 0x40FB49, +0xE956FF, 0xCA0F1C, 0x8A59C5, 0x2BFA94, 0xC5C1D3, 0xCFC50F, +0xAE5ADB, 0x86C547, 0x624385, 0x3B8621, 0x94792C, 0x876110, +0x7B4C2A, 0x1A2C80, 0x12BF43, 0x902688, 0x893C78, 0xE4C4A8, +0x7BDBE5, 0xC23AC4, 0xEAF426, 0x8A67F7, 0xBF920D, 0x2BA365, +0xB1933D, 0x0B7CBD, 0xDC51A4, 0x63DD27, 0xDDE169, 0x19949A, +0x9529A8, 0x28CE68, 0xB4ED09, 0x209F44, 0xCA984E, 0x638270, +0x237C7E, 0x32B90F, 0x8EF5A7, 0xE75614, 0x08F121, 0x2A9DB5, +0x4D7E6F, 0x5119A5, 0xABF9B5, 0xD6DF82, 0x61DD96, 0x023616, +0x9F3AC4, 0xA1A283, 0x6DED72, 0x7A8D39, 0xA9B882, 0x5C326B, +0x5B2746, 0xED3400, 0x7700D2, 0x55F4FC, 0x4D5901, 0x8071E0, +#endif + +}; + +static const double PIo2[] = { + 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */ + 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */ + 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */ + 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */ + 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */ + 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */ + 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */ + 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */ +}; + +static const double +zero = 0.0, +one = 1.0, +two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ +twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */ + +int +__kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec) +{ + int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; + double z,fw,f[20],fq[20],q[20]; + + /* initialize jk*/ + jk = init_jk[prec]; + jp = jk; + + /* determine jx,jv,q0, note that 3>q0 */ + jx = nx-1; + jv = (e0-3)/24; if(jv<0) jv=0; + q0 = e0-24*(jv+1); + + /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ + j = jv-jx; m = jx+jk; + for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j]; + + /* compute q[0],q[1],...q[jk] */ + for (i=0;i<=jk;i++) { + for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; + q[i] = fw; + } + + jz = jk; +recompute: + /* distill q[] into iq[] reversingly */ + for(i=0,j=jz,z=q[jz];j>0;i++,j--) { + fw = (double)((int32_t)(twon24* z)); + iq[i] = (int32_t)(z-two24*fw); + z = q[j-1]+fw; + } + + /* compute n */ + z = scalbn(z,q0); /* actual value of z */ + z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */ + n = (int32_t) z; + z -= (double)n; + ih = 0; + if(q0>0) { /* need iq[jz-1] to determine n */ + i = (iq[jz-1]>>(24-q0)); n += i; + iq[jz-1] -= i<<(24-q0); + ih = iq[jz-1]>>(23-q0); + } + else if(q0==0) ih = iq[jz-1]>>23; + else if(z>=0.5) ih=2; + + if(ih>0) { /* q > 0.5 */ + n += 1; carry = 0; + for(i=0;i<jz ;i++) { /* compute 1-q */ + j = iq[i]; + if(carry==0) { + if(j!=0) { + carry = 1; iq[i] = 0x1000000- j; + } + } else iq[i] = 0xffffff - j; + } + if(q0>0) { /* rare case: chance is 1 in 12 */ + switch(q0) { + case 1: + iq[jz-1] &= 0x7fffff; break; + case 2: + iq[jz-1] &= 0x3fffff; break; + } + } + if(ih==2) { + z = one - z; + if(carry!=0) z -= scalbn(one,q0); + } + } + + /* check if recomputation is needed */ + if(z==zero) { + j = 0; + for (i=jz-1;i>=jk;i--) j |= iq[i]; + if(j==0) { /* need recomputation */ + for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ + + for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ + f[jx+i] = (double) ipio2[jv+i]; + for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; + q[i] = fw; + } + jz += k; + goto recompute; + } + } + + /* chop off zero terms */ + if(z==0.0) { + jz -= 1; q0 -= 24; + while(iq[jz]==0) { jz--; q0-=24;} + } else { /* break z into 24-bit if necessary */ + z = scalbn(z,-q0); + if(z>=two24) { + fw = (double)((int32_t)(twon24*z)); + iq[jz] = (int32_t)(z-two24*fw); + jz += 1; q0 += 24; + iq[jz] = (int32_t) fw; + } else iq[jz] = (int32_t) z ; + } + + /* convert integer "bit" chunk to floating-point value */ + fw = scalbn(one,q0); + for(i=jz;i>=0;i--) { + q[i] = fw*(double)iq[i]; fw*=twon24; + } + + /* compute PIo2[0,...,jp]*q[jz,...,0] */ + for(i=jz;i>=0;i--) { + for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; + fq[jz-i] = fw; + } + + /* compress fq[] into y[] */ + switch(prec) { + case 0: + fw = 0.0; + for (i=jz;i>=0;i--) fw += fq[i]; + y[0] = (ih==0)? fw: -fw; + break; + case 1: + case 2: + fw = 0.0; + for (i=jz;i>=0;i--) fw += fq[i]; + STRICT_ASSIGN(double,fw,fw); + y[0] = (ih==0)? fw: -fw; + fw = fq[0]-fw; + for (i=1;i<=jz;i++) fw += fq[i]; + y[1] = (ih==0)? fw: -fw; + break; + case 3: /* painful */ + for (i=jz;i>0;i--) { + fw = fq[i-1]+fq[i]; + fq[i] += fq[i-1]-fw; + fq[i-1] = fw; + } + for (i=jz;i>1;i--) { + fw = fq[i-1]+fq[i]; + fq[i] += fq[i-1]-fw; + fq[i-1] = fw; + } + for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; + if(ih==0) { + y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; + } else { + y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; + } + } + return n&7; +} diff --git a/modules/fdlibm/src/k_sin.cpp b/modules/fdlibm/src/k_sin.cpp new file mode 100644 index 0000000000..f45165f62e --- /dev/null +++ b/modules/fdlibm/src/k_sin.cpp @@ -0,0 +1,69 @@ + +/* @(#)k_sin.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* __kernel_sin( x, y, iy) + * kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). + * + * Algorithm + * 1. Since sin(-x) = -sin(x), we need only to consider positive x. + * 2. Callers must return sin(-0) = -0 without calling here since our + * odd polynomial is not evaluated in a way that preserves -0. + * Callers may do the optimization sin(x) ~ x for tiny x. + * 3. sin(x) is approximated by a polynomial of degree 13 on + * [0,pi/4] + * 3 13 + * sin(x) ~ x + S1*x + ... + S6*x + * where + * + * |sin(x) 2 4 6 8 10 12 | -58 + * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 + * | x | + * + * 4. sin(x+y) = sin(x) + sin'(x')*y + * ~ sin(x) + (1-x*x/2)*y + * For better accuracy, let + * 3 2 2 2 2 + * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) + * then 3 2 + * sin(x) = x + (S1*x + (x *(r-y/2)+y)) + */ + +#include "math_private.h" + +static const double +half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ +S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ +S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ +S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ +S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ +S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ + +double +__kernel_sin(double x, double y, int iy) +{ + double z,r,v,w; + + z = x*x; + w = z*z; + r = S2+z*(S3+z*S4) + z*w*(S5+z*S6); + v = z*x; + if(iy==0) return x+v*(S1+z*r); + else return x-((z*(half*y-v*r)-y)-v*S1); +} diff --git a/modules/fdlibm/src/k_sinf.cpp b/modules/fdlibm/src/k_sinf.cpp new file mode 100644 index 0000000000..c1108625d7 --- /dev/null +++ b/modules/fdlibm/src/k_sinf.cpp @@ -0,0 +1,45 @@ +/* k_sinf.c -- float version of k_sin.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + * Optimized by Bruce D. Evans. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#ifndef INLINE_KERNEL_SINDF +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); +#endif + +#include "math_private.h" + +/* |sin(x)/x - s(x)| < 2**-37.5 (~[-4.89e-12, 4.824e-12]). */ +static const double +S1 = -0x15555554cbac77.0p-55, /* -0.166666666416265235595 */ +S2 = 0x111110896efbb2.0p-59, /* 0.0083333293858894631756 */ +S3 = -0x1a00f9e2cae774.0p-65, /* -0.000198393348360966317347 */ +S4 = 0x16cd878c3b46a7.0p-71; /* 0.0000027183114939898219064 */ + +#ifdef INLINE_KERNEL_SINDF +static __inline +#endif +float +__kernel_sindf(double x) +{ + double r, s, w, z; + + /* Try to optimize for parallel evaluation as in k_tanf.c. */ + z = x*x; + w = z*z; + r = S3+z*S4; + s = z*x; + return (x + s*(S1+z*S2)) + s*w*r; +} diff --git a/modules/fdlibm/src/k_tan.cpp b/modules/fdlibm/src/k_tan.cpp new file mode 100644 index 0000000000..de08717983 --- /dev/null +++ b/modules/fdlibm/src/k_tan.cpp @@ -0,0 +1,131 @@ +/* @(#)k_tan.c 1.5 04/04/22 SMI */ + +/* + * ==================================================== + * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. + * + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* INDENT OFF */ +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* __kernel_tan( x, y, k ) + * kernel tan function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * Input k indicates whether tan (if k = 1) or -1/tan (if k = -1) is returned. + * + * Algorithm + * 1. Since tan(-x) = -tan(x), we need only to consider positive x. + * 2. Callers must return tan(-0) = -0 without calling here since our + * odd polynomial is not evaluated in a way that preserves -0. + * Callers may do the optimization tan(x) ~ x for tiny x. + * 3. tan(x) is approximated by a odd polynomial of degree 27 on + * [0,0.67434] + * 3 27 + * tan(x) ~ x + T1*x + ... + T13*x + * where + * + * |tan(x) 2 4 26 | -59.2 + * |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2 + * | x | + * + * Note: tan(x+y) = tan(x) + tan'(x)*y + * ~ tan(x) + (1+x*x)*y + * Therefore, for better accuracy in computing tan(x+y), let + * 3 2 2 2 2 + * r = x *(T2+x *(T3+x *(...+x *(T12+x *T13)))) + * then + * 3 2 + * tan(x+y) = x + (T1*x + (x *(r+y)+y)) + * + * 4. For x in [0.67434,pi/4], let y = pi/4 - x, then + * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y)) + * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y))) + */ + +#include "math_private.h" +static const double xxx[] = { + 3.33333333333334091986e-01, /* 3FD55555, 55555563 */ + 1.33333333333201242699e-01, /* 3FC11111, 1110FE7A */ + 5.39682539762260521377e-02, /* 3FABA1BA, 1BB341FE */ + 2.18694882948595424599e-02, /* 3F9664F4, 8406D637 */ + 8.86323982359930005737e-03, /* 3F8226E3, E96E8493 */ + 3.59207910759131235356e-03, /* 3F6D6D22, C9560328 */ + 1.45620945432529025516e-03, /* 3F57DBC8, FEE08315 */ + 5.88041240820264096874e-04, /* 3F4344D8, F2F26501 */ + 2.46463134818469906812e-04, /* 3F3026F7, 1A8D1068 */ + 7.81794442939557092300e-05, /* 3F147E88, A03792A6 */ + 7.14072491382608190305e-05, /* 3F12B80F, 32F0A7E9 */ + -1.85586374855275456654e-05, /* BEF375CB, DB605373 */ + 2.59073051863633712884e-05, /* 3EFB2A70, 74BF7AD4 */ +/* one */ 1.00000000000000000000e+00, /* 3FF00000, 00000000 */ +/* pio4 */ 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */ +/* pio4lo */ 3.06161699786838301793e-17 /* 3C81A626, 33145C07 */ +}; +#define one xxx[13] +#define pio4 xxx[14] +#define pio4lo xxx[15] +#define T xxx +/* INDENT ON */ + +double +__kernel_tan(double x, double y, int iy) { + double z, r, v, w, s; + int32_t ix, hx; + + GET_HIGH_WORD(hx,x); + ix = hx & 0x7fffffff; /* high word of |x| */ + if (ix >= 0x3FE59428) { /* |x| >= 0.6744 */ + if (hx < 0) { + x = -x; + y = -y; + } + z = pio4 - x; + w = pio4lo - y; + x = z + w; + y = 0.0; + } + z = x * x; + w = z * z; + /* + * Break x^5*(T[1]+x^2*T[2]+...) into + * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + + * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) + */ + r = T[1] + w * (T[3] + w * (T[5] + w * (T[7] + w * (T[9] + + w * T[11])))); + v = z * (T[2] + w * (T[4] + w * (T[6] + w * (T[8] + w * (T[10] + + w * T[12]))))); + s = z * x; + r = y + z * (s * (r + v) + y); + r += T[0] * s; + w = x + r; + if (ix >= 0x3FE59428) { + v = (double) iy; + return (double) (1 - ((hx >> 30) & 2)) * + (v - 2.0 * (x - (w * w / (w + v) - r))); + } + if (iy == 1) + return w; + else { + /* + * if allow error up to 2 ulp, simply return + * -1.0 / (x+r) here + */ + /* compute -1.0 / (x+r) accurately */ + double a, t; + z = w; + SET_LOW_WORD(z,0); + v = r - (z - x); /* z+v = r+x */ + t = a = -1.0 / w; /* a = -1.0/w */ + SET_LOW_WORD(t,0); + s = 1.0 + t * z; + return t + a * (s + t * v); + } +} diff --git a/modules/fdlibm/src/k_tanf.cpp b/modules/fdlibm/src/k_tanf.cpp new file mode 100644 index 0000000000..7f40783061 --- /dev/null +++ b/modules/fdlibm/src/k_tanf.cpp @@ -0,0 +1,65 @@ +/* k_tanf.c -- float version of k_tan.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + * Optimized by Bruce D. Evans. + */ + +/* + * ==================================================== + * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. + * + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#ifndef INLINE_KERNEL_TANDF +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); +#endif + +#include "math_private.h" + +/* |tan(x)/x - t(x)| < 2**-25.5 (~[-2e-08, 2e-08]). */ +static const double +T[] = { + 0x15554d3418c99f.0p-54, /* 0.333331395030791399758 */ + 0x1112fd38999f72.0p-55, /* 0.133392002712976742718 */ + 0x1b54c91d865afe.0p-57, /* 0.0533812378445670393523 */ + 0x191df3908c33ce.0p-58, /* 0.0245283181166547278873 */ + 0x185dadfcecf44e.0p-61, /* 0.00297435743359967304927 */ + 0x1362b9bf971bcd.0p-59, /* 0.00946564784943673166728 */ +}; + +#ifdef INLINE_KERNEL_TANDF +static __inline +#endif +float +__kernel_tandf(double x, int iy) +{ + double z,r,w,s,t,u; + + z = x*x; + /* + * Split up the polynomial into small independent terms to give + * opportunities for parallel evaluation. The chosen splitting is + * micro-optimized for Athlons (XP, X64). It costs 2 multiplications + * relative to Horner's method on sequential machines. + * + * We add the small terms from lowest degree up for efficiency on + * non-sequential machines (the lowest degree terms tend to be ready + * earlier). Apart from this, we don't care about order of + * operations, and don't need to care since we have precision to + * spare. However, the chosen splitting is good for accuracy too, + * and would give results as accurate as Horner's method if the + * small terms were added from highest degree down. + */ + r = T[4]+z*T[5]; + t = T[2]+z*T[3]; + w = z*z; + s = z*x; + u = T[0]+z*T[1]; + r = (x+s*u)+(s*w)*(t+w*r); + if(iy==1) return r; + else return -1.0/r; +} diff --git a/modules/fdlibm/src/math_private.h b/modules/fdlibm/src/math_private.h new file mode 100644 index 0000000000..f4373f2783 --- /dev/null +++ b/modules/fdlibm/src/math_private.h @@ -0,0 +1,962 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * from: @(#)fdlibm.h 5.1 93/09/24 + * $FreeBSD$ + */ + +#ifndef _MATH_PRIVATE_H_ +#define _MATH_PRIVATE_H_ + +#include <cfloat> +#include <stdint.h> +#include <sys/types.h> + +#include "mozilla/EndianUtils.h" + +#include "fdlibm.h" + +/* + * Emulate FreeBSD internal double types. + * Adapted from https://github.com/freebsd/freebsd-src/search?q=__double_t + */ + +typedef double __double_t; +typedef __double_t double_t; +typedef float __float_t; + +/* + * The original fdlibm code used statements like: + * n0 = ((*(int*)&one)>>29)^1; * index of high word * + * ix0 = *(n0+(int*)&x); * high word of x * + * ix1 = *((1-n0)+(int*)&x); * low word of x * + * to dig two 32 bit words out of the 64 bit IEEE floating point + * value. That is non-ANSI, and, moreover, the gcc instruction + * scheduler gets it wrong. We instead use the following macros. + * Unlike the original code, we determine the endianness at compile + * time, not at run time; I don't see much benefit to selecting + * endianness at run time. + */ + +#ifndef u_int32_t +#define u_int32_t uint32_t +#endif +#ifndef u_int64_t +#define u_int64_t uint64_t +#endif + +/* A union which permits us to convert between a long double and + four 32 bit ints. */ + +#if MOZ_BIG_ENDIAN() + +typedef union +{ + long double value; + struct { + u_int32_t mswhi; + u_int32_t mswlo; + u_int32_t lswhi; + u_int32_t lswlo; + } parts32; + struct { + u_int64_t msw; + u_int64_t lsw; + } parts64; +} ieee_quad_shape_type; + +#endif + +#if MOZ_LITTLE_ENDIAN() + +typedef union +{ + long double value; + struct { + u_int32_t lswlo; + u_int32_t lswhi; + u_int32_t mswlo; + u_int32_t mswhi; + } parts32; + struct { + u_int64_t lsw; + u_int64_t msw; + } parts64; +} ieee_quad_shape_type; + +#endif + +#if MOZ_BIG_ENDIAN() + +typedef union +{ + double value; + struct + { + u_int32_t msw; + u_int32_t lsw; + } parts; + struct + { + u_int64_t w; + } xparts; +} ieee_double_shape_type; + +#endif + +#if MOZ_LITTLE_ENDIAN() + +typedef union +{ + double value; + struct + { + u_int32_t lsw; + u_int32_t msw; + } parts; + struct + { + u_int64_t w; + } xparts; +} ieee_double_shape_type; + +#endif + +/* Get two 32 bit ints from a double. */ + +#define EXTRACT_WORDS(ix0,ix1,d) \ +do { \ + ieee_double_shape_type ew_u; \ + ew_u.value = (d); \ + (ix0) = ew_u.parts.msw; \ + (ix1) = ew_u.parts.lsw; \ +} while (0) + +/* Get a 64-bit int from a double. */ +#define EXTRACT_WORD64(ix,d) \ +do { \ + ieee_double_shape_type ew_u; \ + ew_u.value = (d); \ + (ix) = ew_u.xparts.w; \ +} while (0) + +/* Get the more significant 32 bit int from a double. */ + +#define GET_HIGH_WORD(i,d) \ +do { \ + ieee_double_shape_type gh_u; \ + gh_u.value = (d); \ + (i) = gh_u.parts.msw; \ +} while (0) + +/* Get the less significant 32 bit int from a double. */ + +#define GET_LOW_WORD(i,d) \ +do { \ + ieee_double_shape_type gl_u; \ + gl_u.value = (d); \ + (i) = gl_u.parts.lsw; \ +} while (0) + +/* Set a double from two 32 bit ints. */ + +#define INSERT_WORDS(d,ix0,ix1) \ +do { \ + ieee_double_shape_type iw_u; \ + iw_u.parts.msw = (ix0); \ + iw_u.parts.lsw = (ix1); \ + (d) = iw_u.value; \ +} while (0) + +/* Set a double from a 64-bit int. */ +#define INSERT_WORD64(d,ix) \ +do { \ + ieee_double_shape_type iw_u; \ + iw_u.xparts.w = (ix); \ + (d) = iw_u.value; \ +} while (0) + +/* Set the more significant 32 bits of a double from an int. */ + +#define SET_HIGH_WORD(d,v) \ +do { \ + ieee_double_shape_type sh_u; \ + sh_u.value = (d); \ + sh_u.parts.msw = (v); \ + (d) = sh_u.value; \ +} while (0) + +/* Set the less significant 32 bits of a double from an int. */ + +#define SET_LOW_WORD(d,v) \ +do { \ + ieee_double_shape_type sl_u; \ + sl_u.value = (d); \ + sl_u.parts.lsw = (v); \ + (d) = sl_u.value; \ +} while (0) + +/* + * A union which permits us to convert between a float and a 32 bit + * int. + */ + +typedef union +{ + float value; + /* FIXME: Assumes 32 bit int. */ + unsigned int word; +} ieee_float_shape_type; + +/* Get a 32 bit int from a float. */ + +#define GET_FLOAT_WORD(i,d) \ +do { \ + ieee_float_shape_type gf_u; \ + gf_u.value = (d); \ + (i) = gf_u.word; \ +} while (0) + +/* Set a float from a 32 bit int. */ + +#define SET_FLOAT_WORD(d,i) \ +do { \ + ieee_float_shape_type sf_u; \ + sf_u.word = (i); \ + (d) = sf_u.value; \ +} while (0) + +/* + * Get expsign and mantissa as 16 bit and 64 bit ints from an 80 bit long + * double. + */ + +#define EXTRACT_LDBL80_WORDS(ix0,ix1,d) \ +do { \ + union IEEEl2bits ew_u; \ + ew_u.e = (d); \ + (ix0) = ew_u.xbits.expsign; \ + (ix1) = ew_u.xbits.man; \ +} while (0) + +/* + * Get expsign and mantissa as one 16 bit and two 64 bit ints from a 128 bit + * long double. + */ + +#define EXTRACT_LDBL128_WORDS(ix0,ix1,ix2,d) \ +do { \ + union IEEEl2bits ew_u; \ + ew_u.e = (d); \ + (ix0) = ew_u.xbits.expsign; \ + (ix1) = ew_u.xbits.manh; \ + (ix2) = ew_u.xbits.manl; \ +} while (0) + +/* Get expsign as a 16 bit int from a long double. */ + +#define GET_LDBL_EXPSIGN(i,d) \ +do { \ + union IEEEl2bits ge_u; \ + ge_u.e = (d); \ + (i) = ge_u.xbits.expsign; \ +} while (0) + +/* + * Set an 80 bit long double from a 16 bit int expsign and a 64 bit int + * mantissa. + */ + +#define INSERT_LDBL80_WORDS(d,ix0,ix1) \ +do { \ + union IEEEl2bits iw_u; \ + iw_u.xbits.expsign = (ix0); \ + iw_u.xbits.man = (ix1); \ + (d) = iw_u.e; \ +} while (0) + +/* + * Set a 128 bit long double from a 16 bit int expsign and two 64 bit ints + * comprising the mantissa. + */ + +#define INSERT_LDBL128_WORDS(d,ix0,ix1,ix2) \ +do { \ + union IEEEl2bits iw_u; \ + iw_u.xbits.expsign = (ix0); \ + iw_u.xbits.manh = (ix1); \ + iw_u.xbits.manl = (ix2); \ + (d) = iw_u.e; \ +} while (0) + +/* Set expsign of a long double from a 16 bit int. */ + +#define SET_LDBL_EXPSIGN(d,v) \ +do { \ + union IEEEl2bits se_u; \ + se_u.e = (d); \ + se_u.xbits.expsign = (v); \ + (d) = se_u.e; \ +} while (0) + +#ifdef __i386__ +/* Long double constants are broken on i386. */ +#define LD80C(m, ex, v) { \ + .xbits.man = __CONCAT(m, ULL), \ + .xbits.expsign = (0x3fff + (ex)) | ((v) < 0 ? 0x8000 : 0), \ +} +#else +/* The above works on non-i386 too, but we use this to check v. */ +#define LD80C(m, ex, v) { .e = (v), } +#endif + +#ifdef FLT_EVAL_METHOD +/* + * Attempt to get strict C99 semantics for assignment with non-C99 compilers. + */ +#if !defined(_MSC_VER) && (FLT_EVAL_METHOD == 0 || __GNUC__ == 0) +#define STRICT_ASSIGN(type, lval, rval) ((lval) = (rval)) +#else +#define STRICT_ASSIGN(type, lval, rval) do { \ + volatile type __lval; \ + \ + if (sizeof(type) >= sizeof(long double)) \ + (lval) = (rval); \ + else { \ + __lval = (rval); \ + (lval) = __lval; \ + } \ +} while (0) +#endif +#else +#define STRICT_ASSIGN(type, lval, rval) do { \ + volatile type __lval; \ + \ + if (sizeof(type) >= sizeof(long double)) \ + (lval) = (rval); \ + else { \ + __lval = (rval); \ + (lval) = __lval; \ + } \ +} while (0) +#endif /* FLT_EVAL_METHOD */ + +/* Support switching the mode to FP_PE if necessary. */ +#if defined(__i386__) && !defined(NO_FPSETPREC) +#define ENTERI() ENTERIT(long double) +#define ENTERIT(returntype) \ + returntype __retval; \ + fp_prec_t __oprec; \ + \ + if ((__oprec = fpgetprec()) != FP_PE) \ + fpsetprec(FP_PE) +#define RETURNI(x) do { \ + __retval = (x); \ + if (__oprec != FP_PE) \ + fpsetprec(__oprec); \ + RETURNF(__retval); \ +} while (0) +#define ENTERV() \ + fp_prec_t __oprec; \ + \ + if ((__oprec = fpgetprec()) != FP_PE) \ + fpsetprec(FP_PE) +#define RETURNV() do { \ + if (__oprec != FP_PE) \ + fpsetprec(__oprec); \ + return; \ +} while (0) +#else +#define ENTERI() +#define ENTERIT(x) +#define RETURNI(x) RETURNF(x) +#define ENTERV() +#define RETURNV() return +#endif + +/* Default return statement if hack*_t() is not used. */ +#define RETURNF(v) return (v) + +/* + * 2sum gives the same result as 2sumF without requiring |a| >= |b| or + * a == 0, but is slower. + */ +#define _2sum(a, b) do { \ + __typeof(a) __s, __w; \ + \ + __w = (a) + (b); \ + __s = __w - (a); \ + (b) = ((a) - (__w - __s)) + ((b) - __s); \ + (a) = __w; \ +} while (0) + +/* + * 2sumF algorithm. + * + * "Normalize" the terms in the infinite-precision expression a + b for + * the sum of 2 floating point values so that b is as small as possible + * relative to 'a'. (The resulting 'a' is the value of the expression in + * the same precision as 'a' and the resulting b is the rounding error.) + * |a| must be >= |b| or 0, b's type must be no larger than 'a's type, and + * exponent overflow or underflow must not occur. This uses a Theorem of + * Dekker (1971). See Knuth (1981) 4.2.2 Theorem C. The name "TwoSum" + * is apparently due to Skewchuk (1997). + * + * For this to always work, assignment of a + b to 'a' must not retain any + * extra precision in a + b. This is required by C standards but broken + * in many compilers. The brokenness cannot be worked around using + * STRICT_ASSIGN() like we do elsewhere, since the efficiency of this + * algorithm would be destroyed by non-null strict assignments. (The + * compilers are correct to be broken -- the efficiency of all floating + * point code calculations would be destroyed similarly if they forced the + * conversions.) + * + * Fortunately, a case that works well can usually be arranged by building + * any extra precision into the type of 'a' -- 'a' should have type float_t, + * double_t or long double. b's type should be no larger than 'a's type. + * Callers should use these types with scopes as large as possible, to + * reduce their own extra-precision and efficiciency problems. In + * particular, they shouldn't convert back and forth just to call here. + */ +#ifdef DEBUG +#define _2sumF(a, b) do { \ + __typeof(a) __w; \ + volatile __typeof(a) __ia, __ib, __r, __vw; \ + \ + __ia = (a); \ + __ib = (b); \ + assert(__ia == 0 || fabsl(__ia) >= fabsl(__ib)); \ + \ + __w = (a) + (b); \ + (b) = ((a) - __w) + (b); \ + (a) = __w; \ + \ + /* The next 2 assertions are weak if (a) is already long double. */ \ + assert((long double)__ia + __ib == (long double)(a) + (b)); \ + __vw = __ia + __ib; \ + __r = __ia - __vw; \ + __r += __ib; \ + assert(__vw == (a) && __r == (b)); \ +} while (0) +#else /* !DEBUG */ +#define _2sumF(a, b) do { \ + __typeof(a) __w; \ + \ + __w = (a) + (b); \ + (b) = ((a) - __w) + (b); \ + (a) = __w; \ +} while (0) +#endif /* DEBUG */ + +/* + * Set x += c, where x is represented in extra precision as a + b. + * x must be sufficiently normalized and sufficiently larger than c, + * and the result is then sufficiently normalized. + * + * The details of ordering are that |a| must be >= |c| (so that (a, c) + * can be normalized without extra work to swap 'a' with c). The details of + * the normalization are that b must be small relative to the normalized 'a'. + * Normalization of (a, c) makes the normalized c tiny relative to the + * normalized a, so b remains small relative to 'a' in the result. However, + * b need not ever be tiny relative to 'a'. For example, b might be about + * 2**20 times smaller than 'a' to give about 20 extra bits of precision. + * That is usually enough, and adding c (which by normalization is about + * 2**53 times smaller than a) cannot change b significantly. However, + * cancellation of 'a' with c in normalization of (a, c) may reduce 'a' + * significantly relative to b. The caller must ensure that significant + * cancellation doesn't occur, either by having c of the same sign as 'a', + * or by having |c| a few percent smaller than |a|. Pre-normalization of + * (a, b) may help. + * + * This is a variant of an algorithm of Kahan (see Knuth (1981) 4.2.2 + * exercise 19). We gain considerable efficiency by requiring the terms to + * be sufficiently normalized and sufficiently increasing. + */ +#define _3sumF(a, b, c) do { \ + __typeof(a) __tmp; \ + \ + __tmp = (c); \ + _2sumF(__tmp, (a)); \ + (b) += (a); \ + (a) = __tmp; \ +} while (0) + +/* + * Common routine to process the arguments to nan(), nanf(), and nanl(). + */ +void _scan_nan(uint32_t *__words, int __num_words, const char *__s); + +/* + * Mix 0, 1 or 2 NaNs. First add 0 to each arg. This normally just turns + * signaling NaNs into quiet NaNs by setting a quiet bit. We do this + * because we want to never return a signaling NaN, and also because we + * don't want the quiet bit to affect the result. Then mix the converted + * args using the specified operation. + * + * When one arg is NaN, the result is typically that arg quieted. When both + * args are NaNs, the result is typically the quietening of the arg whose + * mantissa is largest after quietening. When neither arg is NaN, the + * result may be NaN because it is indeterminate, or finite for subsequent + * construction of a NaN as the indeterminate 0.0L/0.0L. + * + * Technical complications: the result in bits after rounding to the final + * precision might depend on the runtime precision and/or on compiler + * optimizations, especially when different register sets are used for + * different precisions. Try to make the result not depend on at least the + * runtime precision by always doing the main mixing step in long double + * precision. Try to reduce dependencies on optimizations by adding the + * the 0's in different precisions (unless everything is in long double + * precision). + */ +#define nan_mix(x, y) (nan_mix_op((x), (y), +)) +#define nan_mix_op(x, y, op) (((x) + 0.0L) op ((y) + 0)) + +#ifdef _COMPLEX_H + +/* + * C99 specifies that complex numbers have the same representation as + * an array of two elements, where the first element is the real part + * and the second element is the imaginary part. + */ +typedef union { + float complex f; + float a[2]; +} float_complex; +typedef union { + double complex f; + double a[2]; +} double_complex; +typedef union { + long double complex f; + long double a[2]; +} long_double_complex; +#define REALPART(z) ((z).a[0]) +#define IMAGPART(z) ((z).a[1]) + +/* + * Inline functions that can be used to construct complex values. + * + * The C99 standard intends x+I*y to be used for this, but x+I*y is + * currently unusable in general since gcc introduces many overflow, + * underflow, sign and efficiency bugs by rewriting I*y as + * (0.0+I)*(y+0.0*I) and laboriously computing the full complex product. + * In particular, I*Inf is corrupted to NaN+I*Inf, and I*-0 is corrupted + * to -0.0+I*0.0. + * + * The C11 standard introduced the macros CMPLX(), CMPLXF() and CMPLXL() + * to construct complex values. Compilers that conform to the C99 + * standard require the following functions to avoid the above issues. + */ + +#ifndef CMPLXF +static __inline float complex +CMPLXF(float x, float y) +{ + float_complex z; + + REALPART(z) = x; + IMAGPART(z) = y; + return (z.f); +} +#endif + +#ifndef CMPLX +static __inline double complex +CMPLX(double x, double y) +{ + double_complex z; + + REALPART(z) = x; + IMAGPART(z) = y; + return (z.f); +} +#endif + +#ifndef CMPLXL +static __inline long double complex +CMPLXL(long double x, long double y) +{ + long_double_complex z; + + REALPART(z) = x; + IMAGPART(z) = y; + return (z.f); +} +#endif + +#endif /* _COMPLEX_H */ + +/* + * The rnint() family rounds to the nearest integer for a restricted range + * range of args (up to about 2**MANT_DIG). We assume that the current + * rounding mode is FE_TONEAREST so that this can be done efficiently. + * Extra precision causes more problems in practice, and we only centralize + * this here to reduce those problems, and have not solved the efficiency + * problems. The exp2() family uses a more delicate version of this that + * requires extracting bits from the intermediate value, so it is not + * centralized here and should copy any solution of the efficiency problems. + */ + +static inline double +rnint(__double_t x) +{ + /* + * This casts to double to kill any extra precision. This depends + * on the cast being applied to a double_t to avoid compiler bugs + * (this is a cleaner version of STRICT_ASSIGN()). This is + * inefficient if there actually is extra precision, but is hard + * to improve on. We use double_t in the API to minimise conversions + * for just calling here. Note that we cannot easily change the + * magic number to the one that works directly with double_t, since + * the rounding precision is variable at runtime on x86 so the + * magic number would need to be variable. Assuming that the + * rounding precision is always the default is too fragile. This + * and many other complications will move when the default is + * changed to FP_PE. + */ + return ((double)(x + 0x1.8p52) - 0x1.8p52); +} + +/* + * irint() and i64rint() give the same result as casting to their integer + * return type provided their arg is a floating point integer. They can + * sometimes be more efficient because no rounding is required. + */ +#if defined(amd64) || defined(__i386__) +#define irint(x) \ + (sizeof(x) == sizeof(float) && \ + sizeof(__float_t) == sizeof(long double) ? irintf(x) : \ + sizeof(x) == sizeof(double) && \ + sizeof(__double_t) == sizeof(long double) ? irintd(x) : \ + sizeof(x) == sizeof(long double) ? irintl(x) : (int)(x)) +#else +#define irint(x) ((int)(x)) +#endif + +#define i64rint(x) ((int64_t)(x)) /* only needed for ld128 so not opt. */ + +#if defined(__i386__) +static __inline int +irintf(float x) +{ + int n; + + __asm("fistl %0" : "=m" (n) : "t" (x)); + return (n); +} + +static __inline int +irintd(double x) +{ + int n; + + __asm("fistl %0" : "=m" (n) : "t" (x)); + return (n); +} +#endif + +#if defined(__amd64__) || defined(__i386__) +static __inline int +irintl(long double x) +{ + int n; + + __asm("fistl %0" : "=m" (n) : "t" (x)); + return (n); +} +#endif + +#ifdef DEBUG +#if defined(__amd64__) || defined(__i386__) +#define breakpoint() asm("int $3") +#else +#include <signal.h> + +#define breakpoint() raise(SIGTRAP) +#endif +#endif + +/* Write a pari script to test things externally. */ +#ifdef DOPRINT +#include <stdio.h> + +#ifndef DOPRINT_SWIZZLE +#define DOPRINT_SWIZZLE 0 +#endif + +#ifdef DOPRINT_LD80 + +#define DOPRINT_START(xp) do { \ + uint64_t __lx; \ + uint16_t __hx; \ + \ + /* Hack to give more-problematic args. */ \ + EXTRACT_LDBL80_WORDS(__hx, __lx, *xp); \ + __lx ^= DOPRINT_SWIZZLE; \ + INSERT_LDBL80_WORDS(*xp, __hx, __lx); \ + printf("x = %.21Lg; ", (long double)*xp); \ +} while (0) +#define DOPRINT_END1(v) \ + printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v)) +#define DOPRINT_END2(hi, lo) \ + printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \ + (long double)(hi), (long double)(lo)) + +#elif defined(DOPRINT_D64) + +#define DOPRINT_START(xp) do { \ + uint32_t __hx, __lx; \ + \ + EXTRACT_WORDS(__hx, __lx, *xp); \ + __lx ^= DOPRINT_SWIZZLE; \ + INSERT_WORDS(*xp, __hx, __lx); \ + printf("x = %.21Lg; ", (long double)*xp); \ +} while (0) +#define DOPRINT_END1(v) \ + printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v)) +#define DOPRINT_END2(hi, lo) \ + printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \ + (long double)(hi), (long double)(lo)) + +#elif defined(DOPRINT_F32) + +#define DOPRINT_START(xp) do { \ + uint32_t __hx; \ + \ + GET_FLOAT_WORD(__hx, *xp); \ + __hx ^= DOPRINT_SWIZZLE; \ + SET_FLOAT_WORD(*xp, __hx); \ + printf("x = %.21Lg; ", (long double)*xp); \ +} while (0) +#define DOPRINT_END1(v) \ + printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v)) +#define DOPRINT_END2(hi, lo) \ + printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \ + (long double)(hi), (long double)(lo)) + +#else /* !DOPRINT_LD80 && !DOPRINT_D64 (LD128 only) */ + +#ifndef DOPRINT_SWIZZLE_HIGH +#define DOPRINT_SWIZZLE_HIGH 0 +#endif + +#define DOPRINT_START(xp) do { \ + uint64_t __lx, __llx; \ + uint16_t __hx; \ + \ + EXTRACT_LDBL128_WORDS(__hx, __lx, __llx, *xp); \ + __llx ^= DOPRINT_SWIZZLE; \ + __lx ^= DOPRINT_SWIZZLE_HIGH; \ + INSERT_LDBL128_WORDS(*xp, __hx, __lx, __llx); \ + printf("x = %.36Lg; ", (long double)*xp); \ +} while (0) +#define DOPRINT_END1(v) \ + printf("y = %.36Lg; z = 0; show(x, y, z);\n", (long double)(v)) +#define DOPRINT_END2(hi, lo) \ + printf("y = %.36Lg; z = %.36Lg; show(x, y, z);\n", \ + (long double)(hi), (long double)(lo)) + +#endif /* DOPRINT_LD80 */ + +#else /* !DOPRINT */ +#define DOPRINT_START(xp) +#define DOPRINT_END1(v) +#define DOPRINT_END2(hi, lo) +#endif /* DOPRINT */ + +#define RETURNP(x) do { \ + DOPRINT_END1(x); \ + RETURNF(x); \ +} while (0) +#define RETURNPI(x) do { \ + DOPRINT_END1(x); \ + RETURNI(x); \ +} while (0) +#define RETURN2P(x, y) do { \ + DOPRINT_END2((x), (y)); \ + RETURNF((x) + (y)); \ +} while (0) +#define RETURN2PI(x, y) do { \ + DOPRINT_END2((x), (y)); \ + RETURNI((x) + (y)); \ +} while (0) +#ifdef STRUCT_RETURN +#define RETURNSP(rp) do { \ + if (!(rp)->lo_set) \ + RETURNP((rp)->hi); \ + RETURN2P((rp)->hi, (rp)->lo); \ +} while (0) +#define RETURNSPI(rp) do { \ + if (!(rp)->lo_set) \ + RETURNPI((rp)->hi); \ + RETURN2PI((rp)->hi, (rp)->lo); \ +} while (0) +#endif +#define SUM2P(x, y) ({ \ + const __typeof (x) __x = (x); \ + const __typeof (y) __y = (y); \ + \ + DOPRINT_END2(__x, __y); \ + __x + __y; \ +}) + +/* + * ieee style elementary functions + * + * We rename functions here to improve other sources' diffability + * against fdlibm. + */ +#define __ieee754_sqrt sqrt +#define __ieee754_acos acos +#define __ieee754_acosh acosh +#define __ieee754_log log +#define __ieee754_log2 log2 +#define __ieee754_atanh atanh +#define __ieee754_asin asin +#define __ieee754_atan2 atan2 +#define __ieee754_exp exp +#define __ieee754_cosh cosh +#define __ieee754_fmod fmod +#define __ieee754_pow pow +#define __ieee754_lgamma lgamma +#define __ieee754_gamma gamma +#define __ieee754_lgamma_r lgamma_r +#define __ieee754_gamma_r gamma_r +#define __ieee754_log10 log10 +#define __ieee754_sinh sinh +#define __ieee754_hypot hypot +#define __ieee754_j0 j0 +#define __ieee754_j1 j1 +#define __ieee754_y0 y0 +#define __ieee754_y1 y1 +#define __ieee754_jn jn +#define __ieee754_yn yn +#define __ieee754_remainder remainder +#define __ieee754_scalb scalb +#define __ieee754_sqrtf sqrtf +#define __ieee754_acosf acosf +#define __ieee754_acoshf acoshf +#define __ieee754_logf logf +#define __ieee754_atanhf atanhf +#define __ieee754_asinf asinf +#define __ieee754_atan2f atan2f +#define __ieee754_expf expf +#define __ieee754_coshf coshf +#define __ieee754_fmodf fmodf +#define __ieee754_powf powf +#define __ieee754_lgammaf lgammaf +#define __ieee754_gammaf gammaf +#define __ieee754_lgammaf_r lgammaf_r +#define __ieee754_gammaf_r gammaf_r +#define __ieee754_log10f log10f +#define __ieee754_log2f log2f +#define __ieee754_sinhf sinhf +#define __ieee754_hypotf hypotf +#define __ieee754_j0f j0f +#define __ieee754_j1f j1f +#define __ieee754_y0f y0f +#define __ieee754_y1f y1f +#define __ieee754_jnf jnf +#define __ieee754_ynf ynf +#define __ieee754_remainderf remainderf +#define __ieee754_scalbf scalbf + +#define acos fdlibm::acos +#define acosf fdlibm::acosf +#define asin fdlibm::asin +#define asinf fdlibm::asinf +#define atan fdlibm::atan +#define atanf fdlibm::atanf +#define atan2 fdlibm::atan2 +#define cos fdlibm::cos +#define cosf fdlibm::cosf +#define sin fdlibm::sin +#define sinf fdlibm::sinf +#define tan fdlibm::tan +#define tanf fdlibm::tanf +#define cosh fdlibm::cosh +#define sinh fdlibm::sinh +#define tanh fdlibm::tanh +#define exp fdlibm::exp +#define expf fdlibm::expf +#define exp2 fdlibm::exp2 +#define exp2f fdlibm::exp2f +#define log fdlibm::log +#define logf fdlibm::logf +#define log10 fdlibm::log10 +#define pow fdlibm::pow +#define powf fdlibm::powf +#define ceil fdlibm::ceil +#define ceilf fdlibm::ceilf +#define fabs fdlibm::fabs +#define fabsf fdlibm::fabsf +#define floor fdlibm::floor +#define acosh fdlibm::acosh +#define asinh fdlibm::asinh +#define atanh fdlibm::atanh +#define cbrt fdlibm::cbrt +#define expm1 fdlibm::expm1 +#define hypot fdlibm::hypot +#define log1p fdlibm::log1p +#define log2 fdlibm::log2 +#define scalb fdlibm::scalb +#define copysign fdlibm::copysign +#define scalbn fdlibm::scalbn +#define scalbnf fdlibm::scalbnf +#define trunc fdlibm::trunc +#define truncf fdlibm::truncf +#define floorf fdlibm::floorf +#define nearbyint fdlibm::nearbyint +#define nearbyintf fdlibm::nearbyintf +#define rint fdlibm::rint +#define rintf fdlibm::rintf +#define sqrtf fdlibm::sqrtf + +/* fdlibm kernel function */ +int __kernel_rem_pio2(double*,double*,int,int,int); + +/* double precision kernel functions */ +#ifndef INLINE_REM_PIO2 +int __ieee754_rem_pio2(double,double*); +#endif +double __kernel_sin(double,double,int); +double __kernel_cos(double,double); +double __kernel_tan(double,double,int); +double __ldexp_exp(double,int); +#ifdef _COMPLEX_H +double complex __ldexp_cexp(double complex,int); +#endif + +/* float precision kernel functions */ +#ifndef INLINE_REM_PIO2F +int __ieee754_rem_pio2f(float,double*); +#endif +#ifndef INLINE_KERNEL_SINDF +float __kernel_sindf(double); +#endif +#ifndef INLINE_KERNEL_COSDF +float __kernel_cosdf(double); +#endif +#ifndef INLINE_KERNEL_TANDF +float __kernel_tandf(double,int); +#endif +float __ldexp_expf(float,int); +#ifdef _COMPLEX_H +float complex __ldexp_cexpf(float complex,int); +#endif + +/* long double precision kernel functions */ +long double __kernel_sinl(long double, long double, int); +long double __kernel_cosl(long double, long double); +long double __kernel_tanl(long double, long double, int); + +#endif /* !_MATH_PRIVATE_H_ */ diff --git a/modules/fdlibm/src/moz.build b/modules/fdlibm/src/moz.build new file mode 100644 index 0000000000..438d862e71 --- /dev/null +++ b/modules/fdlibm/src/moz.build @@ -0,0 +1,92 @@ +# -*- Mode: python; indent-tabs-mode: nil; tab-width: 40 -*- +# vim: set filetype=python: +# This Source Code Form is subject to the terms of the Mozilla Public +# License, v. 2.0. If a copy of the MPL was not distributed with this +# file, You can obtain one at http://mozilla.org/MPL/2.0/. + +EXPORTS += [ + 'fdlibm.h', +] + +FINAL_LIBRARY = 'js' + +if CONFIG['CC_TYPE'] in ('clang', 'gcc'): + CXXFLAGS += [ + '-Wno-parentheses', + '-Wno-sign-compare', + ] + +if CONFIG['CC_TYPE'] == 'clang': + CXXFLAGS += [ + '-Wno-dangling-else', + ] + +if CONFIG['CC_TYPE'] == 'clang-cl': + CXXFLAGS += [ + '-Wno-sign-compare', + '-wd4146', # unary minus operator applied to unsigned type + '-wd4305', # truncation from 'double' to 'const float' + '-wd4723', # potential divide by 0 + '-wd4756', # overflow in constant arithmetic + ] + +# These sources can't be unified because there are too many conflicting global +# variables (e.g. almost every source file defines a `one` and a `huge`). +SOURCES += [ + 'e_acos.cpp', + 'e_acosf.cpp', + 'e_acosh.cpp', + 'e_asin.cpp', + 'e_asinf.cpp', + 'e_atan2.cpp', + 'e_atanh.cpp', + 'e_cosh.cpp', + 'e_exp.cpp', + 'e_expf.cpp', + 'e_hypot.cpp', + 'e_log.cpp', + 'e_log10.cpp', + 'e_log2.cpp', + 'e_logf.cpp', + 'e_pow.cpp', + 'e_powf.cpp', + 'e_sinh.cpp', + 'e_sqrtf.cpp', + 'k_cos.cpp', + 'k_cosf.cpp', + 'k_exp.cpp', + 'k_expf.cpp', + 'k_rem_pio2.cpp', + 'k_sin.cpp', + 'k_sinf.cpp', + 'k_tan.cpp', + 'k_tanf.cpp', + 's_asinh.cpp', + 's_atan.cpp', + 's_atanf.cpp', + 's_cbrt.cpp', + 's_ceil.cpp', + 's_ceilf.cpp', + # 's_copysign.cpp', # Unused file. + 's_cos.cpp', + 's_cosf.cpp', + 's_exp2.cpp', + 's_exp2f.cpp', + 's_expm1.cpp', + 's_fabs.cpp', + 's_fabsf.cpp', + 's_floor.cpp', + 's_floorf.cpp', + 's_log1p.cpp', + 's_nearbyint.cpp', + 's_rint.cpp', + 's_rintf.cpp', + 's_scalbn.cpp', + 's_sin.cpp', + 's_sinf.cpp', + 's_tan.cpp', + 's_tanf.cpp', + 's_tanh.cpp', + 's_trunc.cpp', + 's_truncf.cpp', +] diff --git a/modules/fdlibm/src/s_asinh.cpp b/modules/fdlibm/src/s_asinh.cpp new file mode 100644 index 0000000000..7ecc396bb8 --- /dev/null +++ b/modules/fdlibm/src/s_asinh.cpp @@ -0,0 +1,58 @@ +/* @(#)s_asinh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* asinh(x) + * Method : + * Based on + * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] + * we have + * asinh(x) := x if 1+x*x=1, + * := sign(x)*(log(x)+ln2)) for large |x|, else + * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else + * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) + */ + +#include <cmath> +#include <float.h> + +#include "math_private.h" + +static const double +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ +huge= 1.00000000000000000000e+300; + +double +asinh(double x) +{ + double t,w; + int32_t hx,ix; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ + if(ix< 0x3e300000) { /* |x|<2**-28 */ + if(huge+x>one) return x; /* return x inexact except 0 */ + } + if(ix>0x41b00000) { /* |x| > 2**28 */ + w = __ieee754_log(fabs(x))+ln2; + } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ + t = fabs(x); + w = __ieee754_log(2.0*t+one/(std::sqrt(x*x+one)+t)); + } else { /* 2.0 > |x| > 2**-28 */ + t = x*x; + w =log1p(fabs(x)+t/(one+std::sqrt(one+t))); + } + if(hx>0) return w; else return -w; +} diff --git a/modules/fdlibm/src/s_atan.cpp b/modules/fdlibm/src/s_atan.cpp new file mode 100644 index 0000000000..21bc0d8200 --- /dev/null +++ b/modules/fdlibm/src/s_atan.cpp @@ -0,0 +1,119 @@ +/* @(#)s_atan.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* atan(x) + * Method + * 1. Reduce x to positive by atan(x) = -atan(-x). + * 2. According to the integer k=4t+0.25 chopped, t=x, the argument + * is further reduced to one of the following intervals and the + * arctangent of t is evaluated by the corresponding formula: + * + * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) + * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) ) + * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) ) + * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) ) + * [39/16,INF] atan(x) = atan(INF) + atan( -1/t ) + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include <float.h> + +#include "math_private.h" + +static const double atanhi[] = { + 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */ + 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */ + 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */ + 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */ +}; + +static const double atanlo[] = { + 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */ + 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */ + 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */ + 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */ +}; + +static const double aT[] = { + 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */ + -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */ + 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */ + -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */ + 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */ + -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */ + 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */ + -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */ + 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */ + -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */ + 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */ +}; + + static const double +one = 1.0, +huge = 1.0e300; + +double +atan(double x) +{ + double w,s1,s2,z; + int32_t ix,hx,id; + + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x44100000) { /* if |x| >= 2^66 */ + u_int32_t low; + GET_LOW_WORD(low,x); + if(ix>0x7ff00000|| + (ix==0x7ff00000&&(low!=0))) + return x+x; /* NaN */ + if(hx>0) return atanhi[3]+*(volatile double *)&atanlo[3]; + else return -atanhi[3]-*(volatile double *)&atanlo[3]; + } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */ + if (ix < 0x3e400000) { /* |x| < 2^-27 */ + if(huge+x>one) return x; /* raise inexact */ + } + id = -1; + } else { + x = fabs(x); + if (ix < 0x3ff30000) { /* |x| < 1.1875 */ + if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */ + id = 0; x = (2.0*x-one)/(2.0+x); + } else { /* 11/16<=|x|< 19/16 */ + id = 1; x = (x-one)/(x+one); + } + } else { + if (ix < 0x40038000) { /* |x| < 2.4375 */ + id = 2; x = (x-1.5)/(one+1.5*x); + } else { /* 2.4375 <= |x| < 2^66 */ + id = 3; x = -1.0/x; + } + }} + /* end of argument reduction */ + z = x*x; + w = z*z; + /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ + s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); + s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); + if (id<0) return x - x*(s1+s2); + else { + z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); + return (hx<0)? -z:z; + } +} diff --git a/modules/fdlibm/src/s_atanf.cpp b/modules/fdlibm/src/s_atanf.cpp new file mode 100644 index 0000000000..fe99904cba --- /dev/null +++ b/modules/fdlibm/src/s_atanf.cpp @@ -0,0 +1,91 @@ +/* s_atanf.c -- float version of s_atan.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +#include "math_private.h" + +static const float atanhi[] = { + 4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */ + 7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */ + 9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */ + 1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */ +}; + +static const float atanlo[] = { + 5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */ + 3.7748947079e-08, /* atan(1.0)lo 0x33222168 */ + 3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */ + 7.5497894159e-08, /* atan(inf)lo 0x33a22168 */ +}; + +static const float aT[] = { + 3.3333328366e-01, + -1.9999158382e-01, + 1.4253635705e-01, + -1.0648017377e-01, + 6.1687607318e-02, +}; + +static const float +one = 1.0, +huge = 1.0e30; + +float +atanf(float x) +{ + float w,s1,s2,z; + int32_t ix,hx,id; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x4c800000) { /* if |x| >= 2**26 */ + if(ix>0x7f800000) + return x+x; /* NaN */ + if(hx>0) return atanhi[3]+*(volatile float *)&atanlo[3]; + else return -atanhi[3]-*(volatile float *)&atanlo[3]; + } if (ix < 0x3ee00000) { /* |x| < 0.4375 */ + if (ix < 0x39800000) { /* |x| < 2**-12 */ + if(huge+x>one) return x; /* raise inexact */ + } + id = -1; + } else { + x = fabsf(x); + if (ix < 0x3f980000) { /* |x| < 1.1875 */ + if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */ + id = 0; x = ((float)2.0*x-one)/((float)2.0+x); + } else { /* 11/16<=|x|< 19/16 */ + id = 1; x = (x-one)/(x+one); + } + } else { + if (ix < 0x401c0000) { /* |x| < 2.4375 */ + id = 2; x = (x-(float)1.5)/(one+(float)1.5*x); + } else { /* 2.4375 <= |x| < 2**26 */ + id = 3; x = -(float)1.0/x; + } + }} + /* end of argument reduction */ + z = x*x; + w = z*z; + /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ + s1 = z*(aT[0]+w*(aT[2]+w*aT[4])); + s2 = w*(aT[1]+w*aT[3]); + if (id<0) return x - x*(s1+s2); + else { + z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); + return (hx<0)? -z:z; + } +} diff --git a/modules/fdlibm/src/s_cbrt.cpp b/modules/fdlibm/src/s_cbrt.cpp new file mode 100644 index 0000000000..d1946781d1 --- /dev/null +++ b/modules/fdlibm/src/s_cbrt.cpp @@ -0,0 +1,113 @@ +/* @(#)s_cbrt.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * Optimized by Bruce D. Evans. + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +#include <float.h> +#include "math_private.h" + +/* cbrt(x) + * Return cube root of x + */ +static const u_int32_t + B1 = 715094163, /* B1 = (1023-1023/3-0.03306235651)*2**20 */ + B2 = 696219795; /* B2 = (1023-1023/3-54/3-0.03306235651)*2**20 */ + +/* |1/cbrt(x) - p(x)| < 2**-23.5 (~[-7.93e-8, 7.929e-8]). */ +static const double +P0 = 1.87595182427177009643, /* 0x3ffe03e6, 0x0f61e692 */ +P1 = -1.88497979543377169875, /* 0xbffe28e0, 0x92f02420 */ +P2 = 1.621429720105354466140, /* 0x3ff9f160, 0x4a49d6c2 */ +P3 = -0.758397934778766047437, /* 0xbfe844cb, 0xbee751d9 */ +P4 = 0.145996192886612446982; /* 0x3fc2b000, 0xd4e4edd7 */ + +double +cbrt(double x) +{ + int32_t hx; + union { + double value; + uint64_t bits; + } u; + double r,s,t=0.0,w; + u_int32_t sign; + u_int32_t high,low; + + EXTRACT_WORDS(hx,low,x); + sign=hx&0x80000000; /* sign= sign(x) */ + hx ^=sign; + if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */ + + /* + * Rough cbrt to 5 bits: + * cbrt(2**e*(1+m) ~= 2**(e/3)*(1+(e%3+m)/3) + * where e is integral and >= 0, m is real and in [0, 1), and "/" and + * "%" are integer division and modulus with rounding towards minus + * infinity. The RHS is always >= the LHS and has a maximum relative + * error of about 1 in 16. Adding a bias of -0.03306235651 to the + * (e%3+m)/3 term reduces the error to about 1 in 32. With the IEEE + * floating point representation, for finite positive normal values, + * ordinary integer division of the value in bits magically gives + * almost exactly the RHS of the above provided we first subtract the + * exponent bias (1023 for doubles) and later add it back. We do the + * subtraction virtually to keep e >= 0 so that ordinary integer + * division rounds towards minus infinity; this is also efficient. + */ + if(hx<0x00100000) { /* zero or subnormal? */ + if((hx|low)==0) + return(x); /* cbrt(0) is itself */ + SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */ + t*=x; + GET_HIGH_WORD(high,t); + INSERT_WORDS(t,sign|((high&0x7fffffff)/3+B2),0); + } else + INSERT_WORDS(t,sign|(hx/3+B1),0); + + /* + * New cbrt to 23 bits: + * cbrt(x) = t*cbrt(x/t**3) ~= t*P(t**3/x) + * where P(r) is a polynomial of degree 4 that approximates 1/cbrt(r) + * to within 2**-23.5 when |r - 1| < 1/10. The rough approximation + * has produced t such than |t/cbrt(x) - 1| ~< 1/32, and cubing this + * gives us bounds for r = t**3/x. + * + * Try to optimize for parallel evaluation as in k_tanf.c. + */ + r=(t*t)*(t/x); + t=t*((P0+r*(P1+r*P2))+((r*r)*r)*(P3+r*P4)); + + /* + * Round t away from zero to 23 bits (sloppily except for ensuring that + * the result is larger in magnitude than cbrt(x) but not much more than + * 2 23-bit ulps larger). With rounding towards zero, the error bound + * would be ~5/6 instead of ~4/6. With a maximum error of 2 23-bit ulps + * in the rounded t, the infinite-precision error in the Newton + * approximation barely affects third digit in the final error + * 0.667; the error in the rounded t can be up to about 3 23-bit ulps + * before the final error is larger than 0.667 ulps. + */ + u.value=t; + u.bits=(u.bits+0x80000000)&0xffffffffc0000000ULL; + t=u.value; + + /* one step Newton iteration to 53 bits with error < 0.667 ulps */ + s=t*t; /* t*t is exact */ + r=x/s; /* error <= 0.5 ulps; |r| < |t| */ + w=t+t; /* t+t is exact */ + r=(r-t)/(w+r); /* r-t is exact; w+r ~= 3*t */ + t=t+t*r; /* error <= (0.5 + 0.5/3) * ulp */ + + return(t); +} diff --git a/modules/fdlibm/src/s_ceil.cpp b/modules/fdlibm/src/s_ceil.cpp new file mode 100644 index 0000000000..67e9c1679e --- /dev/null +++ b/modules/fdlibm/src/s_ceil.cpp @@ -0,0 +1,72 @@ +/* @(#)s_ceil.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* + * ceil(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to ceil(x). + */ + +#include <float.h> + +#include "math_private.h" + +static const double huge = 1.0e300; + +double +ceil(double x) +{ + int32_t i0,i1,j0; + u_int32_t i,j; + EXTRACT_WORDS(i0,i1,x); + j0 = ((i0>>20)&0x7ff)-0x3ff; + if(j0<20) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0<0) {i0=0x80000000;i1=0;} + else if((i0|i1)!=0) { i0=0x3ff00000;i1=0;} + } + } else { + i = (0x000fffff)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0>0) i0 += (0x00100000)>>j0; + i0 &= (~i); i1=0; + } + } + } else if (j0>51) { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(j0-20); + if((i1&i)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0>0) { + if(j0==20) i0+=1; + else { + j = i1 + (1<<(52-j0)); + if(j<i1) i0+=1; /* got a carry */ + i1 = j; + } + } + i1 &= (~i); + } + } + INSERT_WORDS(x,i0,i1); + return x; +} diff --git a/modules/fdlibm/src/s_ceilf.cpp b/modules/fdlibm/src/s_ceilf.cpp new file mode 100644 index 0000000000..7b52deeed7 --- /dev/null +++ b/modules/fdlibm/src/s_ceilf.cpp @@ -0,0 +1,51 @@ +/* s_ceilf.c -- float version of s_ceil.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +#include "math_private.h" + +static const float huge = 1.0e30; + +float +ceilf(float x) +{ + int32_t i0,j0; + u_int32_t i; + + GET_FLOAT_WORD(i0,x); + j0 = ((i0>>23)&0xff)-0x7f; + if(j0<23) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>(float)0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0<0) {i0=0x80000000;} + else if(i0!=0) { i0=0x3f800000;} + } + } else { + i = (0x007fffff)>>j0; + if((i0&i)==0) return x; /* x is integral */ + if(huge+x>(float)0.0) { /* raise inexact flag */ + if(i0>0) i0 += (0x00800000)>>j0; + i0 &= (~i); + } + } + } else { + if(j0==0x80) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + SET_FLOAT_WORD(x,i0); + return x; +} diff --git a/modules/fdlibm/src/s_copysign.cpp b/modules/fdlibm/src/s_copysign.cpp new file mode 100644 index 0000000000..b150106fb2 --- /dev/null +++ b/modules/fdlibm/src/s_copysign.cpp @@ -0,0 +1,32 @@ +/* @(#)s_copysign.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* + * copysign(double x, double y) + * copysign(x,y) returns a value with the magnitude of x and + * with the sign bit of y. + */ + +#include "math_private.h" + +double +copysign(double x, double y) +{ + u_int32_t hx,hy; + GET_HIGH_WORD(hx,x); + GET_HIGH_WORD(hy,y); + SET_HIGH_WORD(x,(hx&0x7fffffff)|(hy&0x80000000)); + return x; +} diff --git a/modules/fdlibm/src/s_cos.cpp b/modules/fdlibm/src/s_cos.cpp new file mode 100644 index 0000000000..8c8bbfdc4c --- /dev/null +++ b/modules/fdlibm/src/s_cos.cpp @@ -0,0 +1,84 @@ +/* @(#)s_cos.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* cos(x) + * Return cosine function of x. + * + * kernel function: + * __kernel_sin ... sine function on [-pi/4,pi/4] + * __kernel_cos ... cosine function on [-pi/4,pi/4] + * __ieee754_rem_pio2 ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include <float.h> + +#define INLINE_REM_PIO2 +#include "math_private.h" +#include "e_rem_pio2.cpp" + +double +cos(double x) +{ + double y[2],z=0.0; + int32_t n, ix; + + /* High word of x. */ + GET_HIGH_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3fe921fb) { + if(ix<0x3e46a09e) /* if x < 2**-27 * sqrt(2) */ + if(((int)x)==0) return 1.0; /* generate inexact */ + return __kernel_cos(x,z); + } + + /* cos(Inf or NaN) is NaN */ + else if (ix>=0x7ff00000) return x-x; + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2(x,y); + switch(n&3) { + case 0: return __kernel_cos(y[0],y[1]); + case 1: return -__kernel_sin(y[0],y[1],1); + case 2: return -__kernel_cos(y[0],y[1]); + default: + return __kernel_sin(y[0],y[1],1); + } + } +} diff --git a/modules/fdlibm/src/s_cosf.cpp b/modules/fdlibm/src/s_cosf.cpp new file mode 100644 index 0000000000..324d849671 --- /dev/null +++ b/modules/fdlibm/src/s_cosf.cpp @@ -0,0 +1,86 @@ +/* s_cosf.c -- float version of s_cos.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + * Optimized by Bruce D. Evans. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +#include <float.h> + +#define INLINE_KERNEL_COSDF +#define INLINE_KERNEL_SINDF +#define INLINE_REM_PIO2F +#include "math_private.h" +#include "e_rem_pio2f.cpp" +#include "k_cosf.cpp" +#include "k_sinf.cpp" + +/* Small multiples of pi/2 rounded to double precision. */ +static const double +c1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */ +c2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */ +c3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */ +c4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */ + +float +cosf(float x) +{ + double y; + int32_t n, hx, ix; + + GET_FLOAT_WORD(hx,x); + ix = hx & 0x7fffffff; + + if(ix <= 0x3f490fda) { /* |x| ~<= pi/4 */ + if(ix<0x39800000) /* |x| < 2**-12 */ + if(((int)x)==0) return 1.0; /* 1 with inexact if x != 0 */ + return __kernel_cosdf(x); + } + if(ix<=0x407b53d1) { /* |x| ~<= 5*pi/4 */ + if(ix>0x4016cbe3) /* |x| ~> 3*pi/4 */ + return -__kernel_cosdf(x + (hx > 0 ? -c2pio2 : c2pio2)); + else { + if(hx>0) + return __kernel_sindf(c1pio2 - x); + else + return __kernel_sindf(x + c1pio2); + } + } + if(ix<=0x40e231d5) { /* |x| ~<= 9*pi/4 */ + if(ix>0x40afeddf) /* |x| ~> 7*pi/4 */ + return __kernel_cosdf(x + (hx > 0 ? -c4pio2 : c4pio2)); + else { + if(hx>0) + return __kernel_sindf(x - c3pio2); + else + return __kernel_sindf(-c3pio2 - x); + } + } + + /* cos(Inf or NaN) is NaN */ + else if (ix>=0x7f800000) return x-x; + + /* general argument reduction needed */ + else { + n = __ieee754_rem_pio2f(x,&y); + switch(n&3) { + case 0: return __kernel_cosdf(y); + case 1: return __kernel_sindf(-y); + case 2: return -__kernel_cosdf(y); + default: + return __kernel_sindf(y); + } + } +} diff --git a/modules/fdlibm/src/s_exp2.cpp b/modules/fdlibm/src/s_exp2.cpp new file mode 100644 index 0000000000..f736385bbc --- /dev/null +++ b/modules/fdlibm/src/s_exp2.cpp @@ -0,0 +1,396 @@ +/*- + * SPDX-License-Identifier: BSD-2-Clause-FreeBSD + * + * Copyright (c) 2005 David Schultz <das@FreeBSD.ORG> + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +#include <float.h> + +#include "math_private.h" + +#define TBLBITS 8 +#define TBLSIZE (1 << TBLBITS) + +static const double + redux = 0x1.8p52 / TBLSIZE, + P1 = 0x1.62e42fefa39efp-1, + P2 = 0x1.ebfbdff82c575p-3, + P3 = 0x1.c6b08d704a0a6p-5, + P4 = 0x1.3b2ab88f70400p-7, + P5 = 0x1.5d88003875c74p-10; + +static volatile double + huge = 0x1p1000, + twom1000 = 0x1p-1000; + +static const double tbl[TBLSIZE * 2] = { +/* exp2(z + eps) eps */ + 0x1.6a09e667f3d5dp-1, 0x1.9880p-44, + 0x1.6b052fa751744p-1, 0x1.8000p-50, + 0x1.6c012750bd9fep-1, -0x1.8780p-45, + 0x1.6cfdcddd476bfp-1, 0x1.ec00p-46, + 0x1.6dfb23c651a29p-1, -0x1.8000p-50, + 0x1.6ef9298593ae3p-1, -0x1.c000p-52, + 0x1.6ff7df9519386p-1, -0x1.fd80p-45, + 0x1.70f7466f42da3p-1, -0x1.c880p-45, + 0x1.71f75e8ec5fc3p-1, 0x1.3c00p-46, + 0x1.72f8286eacf05p-1, -0x1.8300p-44, + 0x1.73f9a48a58152p-1, -0x1.0c00p-47, + 0x1.74fbd35d7ccfcp-1, 0x1.f880p-45, + 0x1.75feb564267f1p-1, 0x1.3e00p-47, + 0x1.77024b1ab6d48p-1, -0x1.7d00p-45, + 0x1.780694fde5d38p-1, -0x1.d000p-50, + 0x1.790b938ac1d00p-1, 0x1.3000p-49, + 0x1.7a11473eb0178p-1, -0x1.d000p-49, + 0x1.7b17b0976d060p-1, 0x1.0400p-45, + 0x1.7c1ed0130c133p-1, 0x1.0000p-53, + 0x1.7d26a62ff8636p-1, -0x1.6900p-45, + 0x1.7e2f336cf4e3bp-1, -0x1.2e00p-47, + 0x1.7f3878491c3e8p-1, -0x1.4580p-45, + 0x1.80427543e1b4ep-1, 0x1.3000p-44, + 0x1.814d2add1071ap-1, 0x1.f000p-47, + 0x1.82589994ccd7ep-1, -0x1.1c00p-45, + 0x1.8364c1eb942d0p-1, 0x1.9d00p-45, + 0x1.8471a4623cab5p-1, 0x1.7100p-43, + 0x1.857f4179f5bbcp-1, 0x1.2600p-45, + 0x1.868d99b4491afp-1, -0x1.2c40p-44, + 0x1.879cad931a395p-1, -0x1.3000p-45, + 0x1.88ac7d98a65b8p-1, -0x1.a800p-45, + 0x1.89bd0a4785800p-1, -0x1.d000p-49, + 0x1.8ace5422aa223p-1, 0x1.3280p-44, + 0x1.8be05bad619fap-1, 0x1.2b40p-43, + 0x1.8cf3216b54383p-1, -0x1.ed00p-45, + 0x1.8e06a5e08664cp-1, -0x1.0500p-45, + 0x1.8f1ae99157807p-1, 0x1.8280p-45, + 0x1.902fed0282c0ep-1, -0x1.cb00p-46, + 0x1.9145b0b91ff96p-1, -0x1.5e00p-47, + 0x1.925c353aa2ff9p-1, 0x1.5400p-48, + 0x1.93737b0cdc64ap-1, 0x1.7200p-46, + 0x1.948b82b5f98aep-1, -0x1.9000p-47, + 0x1.95a44cbc852cbp-1, 0x1.5680p-45, + 0x1.96bdd9a766f21p-1, -0x1.6d00p-44, + 0x1.97d829fde4e2ap-1, -0x1.1000p-47, + 0x1.98f33e47a23a3p-1, 0x1.d000p-45, + 0x1.9a0f170ca0604p-1, -0x1.8a40p-44, + 0x1.9b2bb4d53ff89p-1, 0x1.55c0p-44, + 0x1.9c49182a3f15bp-1, 0x1.6b80p-45, + 0x1.9d674194bb8c5p-1, -0x1.c000p-49, + 0x1.9e86319e3238ep-1, 0x1.7d00p-46, + 0x1.9fa5e8d07f302p-1, 0x1.6400p-46, + 0x1.a0c667b5de54dp-1, -0x1.5000p-48, + 0x1.a1e7aed8eb8f6p-1, 0x1.9e00p-47, + 0x1.a309bec4a2e27p-1, 0x1.ad80p-45, + 0x1.a42c980460a5dp-1, -0x1.af00p-46, + 0x1.a5503b23e259bp-1, 0x1.b600p-47, + 0x1.a674a8af46213p-1, 0x1.8880p-44, + 0x1.a799e1330b3a7p-1, 0x1.1200p-46, + 0x1.a8bfe53c12e8dp-1, 0x1.6c00p-47, + 0x1.a9e6b5579fcd2p-1, -0x1.9b80p-45, + 0x1.ab0e521356fb8p-1, 0x1.b700p-45, + 0x1.ac36bbfd3f381p-1, 0x1.9000p-50, + 0x1.ad5ff3a3c2780p-1, 0x1.4000p-49, + 0x1.ae89f995ad2a3p-1, -0x1.c900p-45, + 0x1.afb4ce622f367p-1, 0x1.6500p-46, + 0x1.b0e07298db790p-1, 0x1.fd40p-45, + 0x1.b20ce6c9a89a9p-1, 0x1.2700p-46, + 0x1.b33a2b84f1a4bp-1, 0x1.d470p-43, + 0x1.b468415b747e7p-1, -0x1.8380p-44, + 0x1.b59728de5593ap-1, 0x1.8000p-54, + 0x1.b6c6e29f1c56ap-1, 0x1.ad00p-47, + 0x1.b7f76f2fb5e50p-1, 0x1.e800p-50, + 0x1.b928cf22749b2p-1, -0x1.4c00p-47, + 0x1.ba5b030a10603p-1, -0x1.d700p-47, + 0x1.bb8e0b79a6f66p-1, 0x1.d900p-47, + 0x1.bcc1e904bc1ffp-1, 0x1.2a00p-47, + 0x1.bdf69c3f3a16fp-1, -0x1.f780p-46, + 0x1.bf2c25bd71db8p-1, -0x1.0a00p-46, + 0x1.c06286141b2e9p-1, -0x1.1400p-46, + 0x1.c199bdd8552e0p-1, 0x1.be00p-47, + 0x1.c2d1cd9fa64eep-1, -0x1.9400p-47, + 0x1.c40ab5fffd02fp-1, -0x1.ed00p-47, + 0x1.c544778fafd15p-1, 0x1.9660p-44, + 0x1.c67f12e57d0cbp-1, -0x1.a100p-46, + 0x1.c7ba88988c1b6p-1, -0x1.8458p-42, + 0x1.c8f6d9406e733p-1, -0x1.a480p-46, + 0x1.ca3405751c4dfp-1, 0x1.b000p-51, + 0x1.cb720dcef9094p-1, 0x1.1400p-47, + 0x1.ccb0f2e6d1689p-1, 0x1.0200p-48, + 0x1.cdf0b555dc412p-1, 0x1.3600p-48, + 0x1.cf3155b5bab3bp-1, -0x1.6900p-47, + 0x1.d072d4a0789bcp-1, 0x1.9a00p-47, + 0x1.d1b532b08c8fap-1, -0x1.5e00p-46, + 0x1.d2f87080d8a85p-1, 0x1.d280p-46, + 0x1.d43c8eacaa203p-1, 0x1.1a00p-47, + 0x1.d5818dcfba491p-1, 0x1.f000p-50, + 0x1.d6c76e862e6a1p-1, -0x1.3a00p-47, + 0x1.d80e316c9834ep-1, -0x1.cd80p-47, + 0x1.d955d71ff6090p-1, 0x1.4c00p-48, + 0x1.da9e603db32aep-1, 0x1.f900p-48, + 0x1.dbe7cd63a8325p-1, 0x1.9800p-49, + 0x1.dd321f301b445p-1, -0x1.5200p-48, + 0x1.de7d5641c05bfp-1, -0x1.d700p-46, + 0x1.dfc97337b9aecp-1, -0x1.6140p-46, + 0x1.e11676b197d5ep-1, 0x1.b480p-47, + 0x1.e264614f5a3e7p-1, 0x1.0ce0p-43, + 0x1.e3b333b16ee5cp-1, 0x1.c680p-47, + 0x1.e502ee78b3fb4p-1, -0x1.9300p-47, + 0x1.e653924676d68p-1, -0x1.5000p-49, + 0x1.e7a51fbc74c44p-1, -0x1.7f80p-47, + 0x1.e8f7977cdb726p-1, -0x1.3700p-48, + 0x1.ea4afa2a490e8p-1, 0x1.5d00p-49, + 0x1.eb9f4867ccae4p-1, 0x1.61a0p-46, + 0x1.ecf482d8e680dp-1, 0x1.5500p-48, + 0x1.ee4aaa2188514p-1, 0x1.6400p-51, + 0x1.efa1bee615a13p-1, -0x1.e800p-49, + 0x1.f0f9c1cb64106p-1, -0x1.a880p-48, + 0x1.f252b376bb963p-1, -0x1.c900p-45, + 0x1.f3ac948dd7275p-1, 0x1.a000p-53, + 0x1.f50765b6e4524p-1, -0x1.4f00p-48, + 0x1.f6632798844fdp-1, 0x1.a800p-51, + 0x1.f7bfdad9cbe38p-1, 0x1.abc0p-48, + 0x1.f91d802243c82p-1, -0x1.4600p-50, + 0x1.fa7c1819e908ep-1, -0x1.b0c0p-47, + 0x1.fbdba3692d511p-1, -0x1.0e00p-51, + 0x1.fd3c22b8f7194p-1, -0x1.0de8p-46, + 0x1.fe9d96b2a23eep-1, 0x1.e430p-49, + 0x1.0000000000000p+0, 0x0.0000p+0, + 0x1.00b1afa5abcbep+0, -0x1.3400p-52, + 0x1.0163da9fb3303p+0, -0x1.2170p-46, + 0x1.02168143b0282p+0, 0x1.a400p-52, + 0x1.02c9a3e77806cp+0, 0x1.f980p-49, + 0x1.037d42e11bbcap+0, -0x1.7400p-51, + 0x1.04315e86e7f89p+0, 0x1.8300p-50, + 0x1.04e5f72f65467p+0, -0x1.a3f0p-46, + 0x1.059b0d315855ap+0, -0x1.2840p-47, + 0x1.0650a0e3c1f95p+0, 0x1.1600p-48, + 0x1.0706b29ddf71ap+0, 0x1.5240p-46, + 0x1.07bd42b72a82dp+0, -0x1.9a00p-49, + 0x1.0874518759bd0p+0, 0x1.6400p-49, + 0x1.092bdf66607c8p+0, -0x1.0780p-47, + 0x1.09e3ecac6f383p+0, -0x1.8000p-54, + 0x1.0a9c79b1f3930p+0, 0x1.fa00p-48, + 0x1.0b5586cf988fcp+0, -0x1.ac80p-48, + 0x1.0c0f145e46c8ap+0, 0x1.9c00p-50, + 0x1.0cc922b724816p+0, 0x1.5200p-47, + 0x1.0d83b23395dd8p+0, -0x1.ad00p-48, + 0x1.0e3ec32d3d1f3p+0, 0x1.bac0p-46, + 0x1.0efa55fdfa9a6p+0, -0x1.4e80p-47, + 0x1.0fb66affed2f0p+0, -0x1.d300p-47, + 0x1.1073028d7234bp+0, 0x1.1500p-48, + 0x1.11301d0125b5bp+0, 0x1.c000p-49, + 0x1.11edbab5e2af9p+0, 0x1.6bc0p-46, + 0x1.12abdc06c31d5p+0, 0x1.8400p-49, + 0x1.136a814f2047dp+0, -0x1.ed00p-47, + 0x1.1429aaea92de9p+0, 0x1.8e00p-49, + 0x1.14e95934f3138p+0, 0x1.b400p-49, + 0x1.15a98c8a58e71p+0, 0x1.5300p-47, + 0x1.166a45471c3dfp+0, 0x1.3380p-47, + 0x1.172b83c7d5211p+0, 0x1.8d40p-45, + 0x1.17ed48695bb9fp+0, -0x1.5d00p-47, + 0x1.18af9388c8d93p+0, -0x1.c880p-46, + 0x1.1972658375d66p+0, 0x1.1f00p-46, + 0x1.1a35beb6fcba7p+0, 0x1.0480p-46, + 0x1.1af99f81387e3p+0, -0x1.7390p-43, + 0x1.1bbe084045d54p+0, 0x1.4e40p-45, + 0x1.1c82f95281c43p+0, -0x1.a200p-47, + 0x1.1d4873168b9b2p+0, 0x1.3800p-49, + 0x1.1e0e75eb44031p+0, 0x1.ac00p-49, + 0x1.1ed5022fcd938p+0, 0x1.1900p-47, + 0x1.1f9c18438cdf7p+0, -0x1.b780p-46, + 0x1.2063b88628d8fp+0, 0x1.d940p-45, + 0x1.212be3578a81ep+0, 0x1.8000p-50, + 0x1.21f49917ddd41p+0, 0x1.b340p-45, + 0x1.22bdda2791323p+0, 0x1.9f80p-46, + 0x1.2387a6e7561e7p+0, -0x1.9c80p-46, + 0x1.2451ffb821427p+0, 0x1.2300p-47, + 0x1.251ce4fb2a602p+0, -0x1.3480p-46, + 0x1.25e85711eceb0p+0, 0x1.2700p-46, + 0x1.26b4565e27d16p+0, 0x1.1d00p-46, + 0x1.2780e341de00fp+0, 0x1.1ee0p-44, + 0x1.284dfe1f5633ep+0, -0x1.4c00p-46, + 0x1.291ba7591bb30p+0, -0x1.3d80p-46, + 0x1.29e9df51fdf09p+0, 0x1.8b00p-47, + 0x1.2ab8a66d10e9bp+0, -0x1.27c0p-45, + 0x1.2b87fd0dada3ap+0, 0x1.a340p-45, + 0x1.2c57e39771af9p+0, -0x1.0800p-46, + 0x1.2d285a6e402d9p+0, -0x1.ed00p-47, + 0x1.2df961f641579p+0, -0x1.4200p-48, + 0x1.2ecafa93e2ecfp+0, -0x1.4980p-45, + 0x1.2f9d24abd8822p+0, -0x1.6300p-46, + 0x1.306fe0a31b625p+0, -0x1.2360p-44, + 0x1.31432edeea50bp+0, -0x1.0df8p-40, + 0x1.32170fc4cd7b8p+0, -0x1.2480p-45, + 0x1.32eb83ba8e9a2p+0, -0x1.5980p-45, + 0x1.33c08b2641766p+0, 0x1.ed00p-46, + 0x1.3496266e3fa27p+0, -0x1.c000p-50, + 0x1.356c55f929f0fp+0, -0x1.0d80p-44, + 0x1.36431a2de88b9p+0, 0x1.2c80p-45, + 0x1.371a7373aaa39p+0, 0x1.0600p-45, + 0x1.37f26231e74fep+0, -0x1.6600p-46, + 0x1.38cae6d05d838p+0, -0x1.ae00p-47, + 0x1.39a401b713ec3p+0, -0x1.4720p-43, + 0x1.3a7db34e5a020p+0, 0x1.8200p-47, + 0x1.3b57fbfec6e95p+0, 0x1.e800p-44, + 0x1.3c32dc313a8f2p+0, 0x1.f800p-49, + 0x1.3d0e544ede122p+0, -0x1.7a00p-46, + 0x1.3dea64c1234bbp+0, 0x1.6300p-45, + 0x1.3ec70df1c4eccp+0, -0x1.8a60p-43, + 0x1.3fa4504ac7e8cp+0, -0x1.cdc0p-44, + 0x1.40822c367a0bbp+0, 0x1.5b80p-45, + 0x1.4160a21f72e95p+0, 0x1.ec00p-46, + 0x1.423fb27094646p+0, -0x1.3600p-46, + 0x1.431f5d950a920p+0, 0x1.3980p-45, + 0x1.43ffa3f84b9ebp+0, 0x1.a000p-48, + 0x1.44e0860618919p+0, -0x1.6c00p-48, + 0x1.45c2042a7d201p+0, -0x1.bc00p-47, + 0x1.46a41ed1d0016p+0, -0x1.2800p-46, + 0x1.4786d668b3326p+0, 0x1.0e00p-44, + 0x1.486a2b5c13c00p+0, -0x1.d400p-45, + 0x1.494e1e192af04p+0, 0x1.c200p-47, + 0x1.4a32af0d7d372p+0, -0x1.e500p-46, + 0x1.4b17dea6db801p+0, 0x1.7800p-47, + 0x1.4bfdad53629e1p+0, -0x1.3800p-46, + 0x1.4ce41b817c132p+0, 0x1.0800p-47, + 0x1.4dcb299fddddbp+0, 0x1.c700p-45, + 0x1.4eb2d81d8ab96p+0, -0x1.ce00p-46, + 0x1.4f9b2769d2d02p+0, 0x1.9200p-46, + 0x1.508417f4531c1p+0, -0x1.8c00p-47, + 0x1.516daa2cf662ap+0, -0x1.a000p-48, + 0x1.5257de83f51eap+0, 0x1.a080p-43, + 0x1.5342b569d4edap+0, -0x1.6d80p-45, + 0x1.542e2f4f6ac1ap+0, -0x1.2440p-44, + 0x1.551a4ca5d94dbp+0, 0x1.83c0p-43, + 0x1.56070dde9116bp+0, 0x1.4b00p-45, + 0x1.56f4736b529dep+0, 0x1.15a0p-43, + 0x1.57e27dbe2c40ep+0, -0x1.9e00p-45, + 0x1.58d12d497c76fp+0, -0x1.3080p-45, + 0x1.59c0827ff0b4cp+0, 0x1.dec0p-43, + 0x1.5ab07dd485427p+0, -0x1.4000p-51, + 0x1.5ba11fba87af4p+0, 0x1.0080p-44, + 0x1.5c9268a59460bp+0, -0x1.6c80p-45, + 0x1.5d84590998e3fp+0, 0x1.69a0p-43, + 0x1.5e76f15ad20e1p+0, -0x1.b400p-46, + 0x1.5f6a320dcebcap+0, 0x1.7700p-46, + 0x1.605e1b976dcb8p+0, 0x1.6f80p-45, + 0x1.6152ae6cdf715p+0, 0x1.1000p-47, + 0x1.6247eb03a5531p+0, -0x1.5d00p-46, + 0x1.633dd1d1929b5p+0, -0x1.2d00p-46, + 0x1.6434634ccc313p+0, -0x1.a800p-49, + 0x1.652b9febc8efap+0, -0x1.8600p-45, + 0x1.6623882553397p+0, 0x1.1fe0p-40, + 0x1.671c1c708328ep+0, -0x1.7200p-44, + 0x1.68155d44ca97ep+0, 0x1.6800p-49, + 0x1.690f4b19e9471p+0, -0x1.9780p-45, +}; + +/* + * exp2(x): compute the base 2 exponential of x + * + * Accuracy: Peak error < 0.503 ulp for normalized results. + * + * Method: (accurate tables) + * + * Reduce x: + * x = 2**k + y, for integer k and |y| <= 1/2. + * Thus we have exp2(x) = 2**k * exp2(y). + * + * Reduce y: + * y = i/TBLSIZE + z - eps[i] for integer i near y * TBLSIZE. + * Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z - eps[i]), + * with |z - eps[i]| <= 2**-9 + 2**-39 for the table used. + * + * We compute exp2(i/TBLSIZE) via table lookup and exp2(z - eps[i]) via + * a degree-5 minimax polynomial with maximum error under 1.3 * 2**-61. + * The values in exp2t[] and eps[] are chosen such that + * exp2t[i] = exp2(i/TBLSIZE + eps[i]), and eps[i] is a small offset such + * that exp2t[i] is accurate to 2**-64. + * + * Note that the range of i is +-TBLSIZE/2, so we actually index the tables + * by i0 = i + TBLSIZE/2. For cache efficiency, exp2t[] and eps[] are + * virtual tables, interleaved in the real table tbl[]. + * + * This method is due to Gal, with many details due to Gal and Bachelis: + * + * Gal, S. and Bachelis, B. An Accurate Elementary Mathematical Library + * for the IEEE Floating Point Standard. TOMS 17(1), 26-46 (1991). + */ +double +exp2(double x) +{ + double r, t, twopk, twopkp1000, z; + uint32_t hx, ix, lx, i0; + int k; + + /* Filter out exceptional cases. */ + GET_HIGH_WORD(hx,x); + ix = hx & 0x7fffffff; /* high word of |x| */ + if(ix >= 0x40900000) { /* |x| >= 1024 */ + if(ix >= 0x7ff00000) { + GET_LOW_WORD(lx,x); + if(((ix & 0xfffff) | lx) != 0 || (hx & 0x80000000) == 0) + return (x + x); /* x is NaN or +Inf */ + else + return (0.0); /* x is -Inf */ + } + if(x >= 0x1.0p10) + return (huge * huge); /* overflow */ + if(x <= -0x1.0ccp10) + return (twom1000 * twom1000); /* underflow */ + } else if (ix < 0x3c900000) { /* |x| < 0x1p-54 */ + return (1.0 + x); + } + + /* Reduce x, computing z, i0, and k. */ + STRICT_ASSIGN(double, t, x + redux); + GET_LOW_WORD(i0, t); + i0 += TBLSIZE / 2; + k = (i0 >> TBLBITS) << 20; + i0 = (i0 & (TBLSIZE - 1)) << 1; + t -= redux; + z = x - t; + + /* Compute r = exp2(y) = exp2t[i0] * p(z - eps[i]). */ + t = tbl[i0]; /* exp2t[i0] */ + z -= tbl[i0 + 1]; /* eps[i0] */ + if (k >= -(1021 << 20)) + INSERT_WORDS(twopk, 0x3ff00000 + k, 0); + else + INSERT_WORDS(twopkp1000, 0x3ff00000 + k + (1000 << 20), 0); + r = t + t * z * (P1 + z * (P2 + z * (P3 + z * (P4 + z * P5)))); + + /* Scale by 2**(k>>20). */ + if(k >= -(1021 << 20)) { + if (k == 1024 << 20) { + double const_0x1p1023 = pow(2, 1023); + return (r * 2.0 * const_0x1p1023); + } + return (r * twopk); + } else { + return (r * twopkp1000 * twom1000); + } +} diff --git a/modules/fdlibm/src/s_exp2f.cpp b/modules/fdlibm/src/s_exp2f.cpp new file mode 100644 index 0000000000..82ec98da94 --- /dev/null +++ b/modules/fdlibm/src/s_exp2f.cpp @@ -0,0 +1,138 @@ +/*- + * SPDX-License-Identifier: BSD-2-Clause-FreeBSD + * + * Copyright (c) 2005 David Schultz <das@FreeBSD.ORG> + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +#include <float.h> + +#include "math_private.h" + +#define TBLBITS 4 +#define TBLSIZE (1 << TBLBITS) + +static const float + redux = 0x1.8p23f / TBLSIZE, + P1 = 0x1.62e430p-1f, + P2 = 0x1.ebfbe0p-3f, + P3 = 0x1.c6b348p-5f, + P4 = 0x1.3b2c9cp-7f; + +static volatile float + huge = 0x1p100f, + twom100 = 0x1p-100f; + +static const double exp2ft[TBLSIZE] = { + 0x1.6a09e667f3bcdp-1, + 0x1.7a11473eb0187p-1, + 0x1.8ace5422aa0dbp-1, + 0x1.9c49182a3f090p-1, + 0x1.ae89f995ad3adp-1, + 0x1.c199bdd85529cp-1, + 0x1.d5818dcfba487p-1, + 0x1.ea4afa2a490dap-1, + 0x1.0000000000000p+0, + 0x1.0b5586cf9890fp+0, + 0x1.172b83c7d517bp+0, + 0x1.2387a6e756238p+0, + 0x1.306fe0a31b715p+0, + 0x1.3dea64c123422p+0, + 0x1.4bfdad5362a27p+0, + 0x1.5ab07dd485429p+0, +}; + +/* + * exp2f(x): compute the base 2 exponential of x + * + * Accuracy: Peak error < 0.501 ulp; location of peak: -0.030110927. + * + * Method: (equally-spaced tables) + * + * Reduce x: + * x = 2**k + y, for integer k and |y| <= 1/2. + * Thus we have exp2f(x) = 2**k * exp2(y). + * + * Reduce y: + * y = i/TBLSIZE + z for integer i near y * TBLSIZE. + * Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z), + * with |z| <= 2**-(TBLSIZE+1). + * + * We compute exp2(i/TBLSIZE) via table lookup and exp2(z) via a + * degree-4 minimax polynomial with maximum error under 1.4 * 2**-33. + * Using double precision for everything except the reduction makes + * roundoff error insignificant and simplifies the scaling step. + * + * This method is due to Tang, but I do not use his suggested parameters: + * + * Tang, P. Table-driven Implementation of the Exponential Function + * in IEEE Floating-Point Arithmetic. TOMS 15(2), 144-157 (1989). + */ +float +exp2f(float x) +{ + double tv, twopk, u, z; + float t; + uint32_t hx, ix, i0; + int32_t k; + + /* Filter out exceptional cases. */ + GET_FLOAT_WORD(hx, x); + ix = hx & 0x7fffffff; /* high word of |x| */ + if(ix >= 0x43000000) { /* |x| >= 128 */ + if(ix >= 0x7f800000) { + if ((ix & 0x7fffff) != 0 || (hx & 0x80000000) == 0) + return (x + x); /* x is NaN or +Inf */ + else + return (0.0); /* x is -Inf */ + } + if(x >= 0x1.0p7f) + return (huge * huge); /* overflow */ + if(x <= -0x1.2cp7f) + return (twom100 * twom100); /* underflow */ + } else if (ix <= 0x33000000) { /* |x| <= 0x1p-25 */ + return (1.0f + x); + } + + /* Reduce x, computing z, i0, and k. */ + STRICT_ASSIGN(float, t, x + redux); + GET_FLOAT_WORD(i0, t); + i0 += TBLSIZE / 2; + k = (i0 >> TBLBITS) << 20; + i0 &= TBLSIZE - 1; + t -= redux; + z = x - t; + INSERT_WORDS(twopk, 0x3ff00000 + k, 0); + + /* Compute r = exp2(y) = exp2ft[i0] * p(z). */ + tv = exp2ft[i0]; + u = tv * z; + tv = tv + u * (P1 + z * P2) + u * (z * z) * (P3 + z * P4); + + /* Scale by 2**(k>>20). */ + return (tv * twopk); +} diff --git a/modules/fdlibm/src/s_expm1.cpp b/modules/fdlibm/src/s_expm1.cpp new file mode 100644 index 0000000000..90ebc16988 --- /dev/null +++ b/modules/fdlibm/src/s_expm1.cpp @@ -0,0 +1,220 @@ +/* @(#)s_expm1.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* expm1(x) + * Returns exp(x)-1, the exponential of x minus 1. + * + * Method + * 1. Argument reduction: + * Given x, find r and integer k such that + * + * x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658 + * + * Here a correction term c will be computed to compensate + * the error in r when rounded to a floating-point number. + * + * 2. Approximating expm1(r) by a special rational function on + * the interval [0,0.34658]: + * Since + * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ... + * we define R1(r*r) by + * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r) + * That is, + * R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r) + * = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r)) + * = 1 - r^2/60 + r^4/2520 - r^6/100800 + ... + * We use a special Reme algorithm on [0,0.347] to generate + * a polynomial of degree 5 in r*r to approximate R1. The + * maximum error of this polynomial approximation is bounded + * by 2**-61. In other words, + * R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5 + * where Q1 = -1.6666666666666567384E-2, + * Q2 = 3.9682539681370365873E-4, + * Q3 = -9.9206344733435987357E-6, + * Q4 = 2.5051361420808517002E-7, + * Q5 = -6.2843505682382617102E-9; + * z = r*r, + * with error bounded by + * | 5 | -61 + * | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2 + * | | + * + * expm1(r) = exp(r)-1 is then computed by the following + * specific way which minimize the accumulation rounding error: + * 2 3 + * r r [ 3 - (R1 + R1*r/2) ] + * expm1(r) = r + --- + --- * [--------------------] + * 2 2 [ 6 - r*(3 - R1*r/2) ] + * + * To compensate the error in the argument reduction, we use + * expm1(r+c) = expm1(r) + c + expm1(r)*c + * ~ expm1(r) + c + r*c + * Thus c+r*c will be added in as the correction terms for + * expm1(r+c). Now rearrange the term to avoid optimization + * screw up: + * ( 2 2 ) + * ({ ( r [ R1 - (3 - R1*r/2) ] ) } r ) + * expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- ) + * ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 ) + * ( ) + * + * = r - E + * 3. Scale back to obtain expm1(x): + * From step 1, we have + * expm1(x) = either 2^k*[expm1(r)+1] - 1 + * = or 2^k*[expm1(r) + (1-2^-k)] + * 4. Implementation notes: + * (A). To save one multiplication, we scale the coefficient Qi + * to Qi*2^i, and replace z by (x^2)/2. + * (B). To achieve maximum accuracy, we compute expm1(x) by + * (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf) + * (ii) if k=0, return r-E + * (iii) if k=-1, return 0.5*(r-E)-0.5 + * (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E) + * else return 1.0+2.0*(r-E); + * (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1) + * (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else + * (vii) return 2^k(1-((E+2^-k)-r)) + * + * Special cases: + * expm1(INF) is INF, expm1(NaN) is NaN; + * expm1(-INF) is -1, and + * for finite argument, only expm1(0)=0 is exact. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Misc. info. + * For IEEE double + * if x > 7.09782712893383973096e+02 then expm1(x) overflow + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include <float.h> + +#include "math_private.h" + +static const double +one = 1.0, +tiny = 1.0e-300, +o_threshold = 7.09782712893383973096e+02,/* 0x40862E42, 0xFEFA39EF */ +ln2_hi = 6.93147180369123816490e-01,/* 0x3fe62e42, 0xfee00000 */ +ln2_lo = 1.90821492927058770002e-10,/* 0x3dea39ef, 0x35793c76 */ +invln2 = 1.44269504088896338700e+00,/* 0x3ff71547, 0x652b82fe */ +/* Scaled Q's: Qn_here = 2**n * Qn_above, for R(2*z) where z = hxs = x*x/2: */ +Q1 = -3.33333333333331316428e-02, /* BFA11111 111110F4 */ +Q2 = 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */ +Q3 = -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */ +Q4 = 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */ +Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */ + +static volatile double huge = 1.0e+300; + +double +expm1(double x) +{ + double y,hi,lo,c,t,e,hxs,hfx,r1,twopk; + int32_t k,xsb; + u_int32_t hx; + + GET_HIGH_WORD(hx,x); + xsb = hx&0x80000000; /* sign bit of x */ + hx &= 0x7fffffff; /* high word of |x| */ + + /* filter out huge and non-finite argument */ + if(hx >= 0x4043687A) { /* if |x|>=56*ln2 */ + if(hx >= 0x40862E42) { /* if |x|>=709.78... */ + if(hx>=0x7ff00000) { + u_int32_t low; + GET_LOW_WORD(low,x); + if(((hx&0xfffff)|low)!=0) + return x+x; /* NaN */ + else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ + } + if(x > o_threshold) return huge*huge; /* overflow */ + } + if(xsb!=0) { /* x < -56*ln2, return -1.0 with inexact */ + if(x+tiny<0.0) /* raise inexact */ + return tiny-one; /* return -1 */ + } + } + + /* argument reduction */ + if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ + if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ + if(xsb==0) + {hi = x - ln2_hi; lo = ln2_lo; k = 1;} + else + {hi = x + ln2_hi; lo = -ln2_lo; k = -1;} + } else { + k = invln2*x+((xsb==0)?0.5:-0.5); + t = k; + hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ + lo = t*ln2_lo; + } + STRICT_ASSIGN(double, x, hi - lo); + c = (hi-x)-lo; + } + else if(hx < 0x3c900000) { /* when |x|<2**-54, return x */ + t = huge+x; /* return x with inexact flags when x!=0 */ + return x - (t-(huge+x)); + } + else k = 0; + + /* x is now in primary range */ + hfx = 0.5*x; + hxs = x*hfx; + r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5)))); + t = 3.0-r1*hfx; + e = hxs*((r1-t)/(6.0 - x*t)); + if(k==0) return x - (x*e-hxs); /* c is 0 */ + else { + INSERT_WORDS(twopk,((u_int32_t)(0x3ff+k))<<20,0); /* 2^k */ + e = (x*(e-c)-c); + e -= hxs; + if(k== -1) return 0.5*(x-e)-0.5; + if(k==1) { + if(x < -0.25) return -2.0*(e-(x+0.5)); + else return one+2.0*(x-e); + } + if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ + y = one-(e-x); + if (k == 1024) { + double const_0x1p1023 = pow(2, 1023); + y = y*2.0*const_0x1p1023; + } + else y = y*twopk; + return y-one; + } + t = one; + if(k<20) { + SET_HIGH_WORD(t,0x3ff00000 - (0x200000>>k)); /* t=1-2^-k */ + y = t-(e-x); + y = y*twopk; + } else { + SET_HIGH_WORD(t,((0x3ff-k)<<20)); /* 2^-k */ + y = x-(e+t); + y += one; + y = y*twopk; + } + } + return y; +} diff --git a/modules/fdlibm/src/s_fabs.cpp b/modules/fdlibm/src/s_fabs.cpp new file mode 100644 index 0000000000..6ca84d71b7 --- /dev/null +++ b/modules/fdlibm/src/s_fabs.cpp @@ -0,0 +1,29 @@ +/* @(#)s_fabs.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* + * fabs(x) returns the absolute value of x. + */ + +#include "math_private.h" + +double +fabs(double x) +{ + u_int32_t high; + GET_HIGH_WORD(high,x); + SET_HIGH_WORD(x,high&0x7fffffff); + return x; +} diff --git a/modules/fdlibm/src/s_fabsf.cpp b/modules/fdlibm/src/s_fabsf.cpp new file mode 100644 index 0000000000..c14d562ade --- /dev/null +++ b/modules/fdlibm/src/s_fabsf.cpp @@ -0,0 +1,32 @@ +/* s_fabsf.c -- float version of s_fabs.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* + * fabsf(x) returns the absolute value of x. + */ + +#include "math_private.h" + +float +fabsf(float x) +{ + u_int32_t ix; + GET_FLOAT_WORD(ix,x); + SET_FLOAT_WORD(x,ix&0x7fffffff); + return x; +} diff --git a/modules/fdlibm/src/s_floor.cpp b/modules/fdlibm/src/s_floor.cpp new file mode 100644 index 0000000000..da57fc8283 --- /dev/null +++ b/modules/fdlibm/src/s_floor.cpp @@ -0,0 +1,73 @@ +/* @(#)s_floor.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* + * floor(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to floor(x). + */ + +#include <float.h> + +#include "math_private.h" + +static const double huge = 1.0e300; + +double +floor(double x) +{ + int32_t i0,i1,j0; + u_int32_t i,j; + EXTRACT_WORDS(i0,i1,x); + j0 = ((i0>>20)&0x7ff)-0x3ff; + if(j0<20) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0>=0) {i0=i1=0;} + else if(((i0&0x7fffffff)|i1)!=0) + { i0=0xbff00000;i1=0;} + } + } else { + i = (0x000fffff)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0<0) i0 += (0x00100000)>>j0; + i0 &= (~i); i1=0; + } + } + } else if (j0>51) { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(j0-20); + if((i1&i)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0<0) { + if(j0==20) i0+=1; + else { + j = i1+(1<<(52-j0)); + if(j<i1) i0 +=1 ; /* got a carry */ + i1=j; + } + } + i1 &= (~i); + } + } + INSERT_WORDS(x,i0,i1); + return x; +} diff --git a/modules/fdlibm/src/s_floorf.cpp b/modules/fdlibm/src/s_floorf.cpp new file mode 100644 index 0000000000..88511f2097 --- /dev/null +++ b/modules/fdlibm/src/s_floorf.cpp @@ -0,0 +1,60 @@ +/* s_floorf.c -- float version of s_floor.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* + * floorf(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to floorf(x). + */ + +#include "math_private.h" + +static const float huge = 1.0e30; + +float +floorf(float x) +{ + int32_t i0,j0; + u_int32_t i; + GET_FLOAT_WORD(i0,x); + j0 = ((i0>>23)&0xff)-0x7f; + if(j0<23) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>(float)0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0>=0) {i0=0;} + else if((i0&0x7fffffff)!=0) + { i0=0xbf800000;} + } + } else { + i = (0x007fffff)>>j0; + if((i0&i)==0) return x; /* x is integral */ + if(huge+x>(float)0.0) { /* raise inexact flag */ + if(i0<0) i0 += (0x00800000)>>j0; + i0 &= (~i); + } + } + } else { + if(j0==0x80) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + SET_FLOAT_WORD(x,i0); + return x; +} diff --git a/modules/fdlibm/src/s_log1p.cpp b/modules/fdlibm/src/s_log1p.cpp new file mode 100644 index 0000000000..afc6919c6f --- /dev/null +++ b/modules/fdlibm/src/s_log1p.cpp @@ -0,0 +1,175 @@ +/* @(#)s_log1p.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* double log1p(double x) + * + * Method : + * 1. Argument Reduction: find k and f such that + * 1+x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * + * Note. If k=0, then f=x is exact. However, if k!=0, then f + * may not be representable exactly. In that case, a correction + * term is need. Let u=1+x rounded. Let c = (1+x)-u, then + * log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u), + * and add back the correction term c/u. + * (Note: when x > 2**53, one can simply return log(x)) + * + * 2. Approximation of log1p(f). + * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * = 2s + s*R + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error + * of this polynomial approximation is bounded by 2**-58.45. In + * other words, + * 2 4 6 8 10 12 14 + * R(z) ~ Lp1*s +Lp2*s +Lp3*s +Lp4*s +Lp5*s +Lp6*s +Lp7*s + * (the values of Lp1 to Lp7 are listed in the program) + * and + * | 2 14 | -58.45 + * | Lp1*s +...+Lp7*s - R(z) | <= 2 + * | | + * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. + * In order to guarantee error in log below 1ulp, we compute log + * by + * log1p(f) = f - (hfsq - s*(hfsq+R)). + * + * 3. Finally, log1p(x) = k*ln2 + log1p(f). + * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) + * Here ln2 is split into two floating point number: + * ln2_hi + ln2_lo, + * where n*ln2_hi is always exact for |n| < 2000. + * + * Special cases: + * log1p(x) is NaN with signal if x < -1 (including -INF) ; + * log1p(+INF) is +INF; log1p(-1) is -INF with signal; + * log1p(NaN) is that NaN with no signal. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + * + * Note: Assuming log() return accurate answer, the following + * algorithm can be used to compute log1p(x) to within a few ULP: + * + * u = 1+x; + * if(u==1.0) return x ; else + * return log(u)*(x/(u-1.0)); + * + * See HP-15C Advanced Functions Handbook, p.193. + */ + +#include <float.h> + +#include "math_private.h" + +static const double +ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ +ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ +two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ +Lp1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ +Lp2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ +Lp3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ +Lp4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ +Lp5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ +Lp6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ +Lp7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ + +static const double zero = 0.0; +static volatile double vzero = 0.0; + +double +log1p(double x) +{ + double hfsq,f,c,s,z,R,u; + int32_t k,hx,hu,ax; + + GET_HIGH_WORD(hx,x); + ax = hx&0x7fffffff; + + k = 1; + if (hx < 0x3FDA827A) { /* 1+x < sqrt(2)+ */ + if(ax>=0x3ff00000) { /* x <= -1.0 */ + if(x==-1.0) return -two54/vzero; /* log1p(-1)=+inf */ + else return (x-x)/(x-x); /* log1p(x<-1)=NaN */ + } + if(ax<0x3e200000) { /* |x| < 2**-29 */ + if(two54+x>zero /* raise inexact */ + &&ax<0x3c900000) /* |x| < 2**-54 */ + return x; + else + return x - x*x*0.5; + } + if(hx>0||hx<=((int32_t)0xbfd2bec4)) { + k=0;f=x;hu=1;} /* sqrt(2)/2- <= 1+x < sqrt(2)+ */ + } + if (hx >= 0x7ff00000) return x+x; + if(k!=0) { + if(hx<0x43400000) { + STRICT_ASSIGN(double,u,1.0+x); + GET_HIGH_WORD(hu,u); + k = (hu>>20)-1023; + c = (k>0)? 1.0-(u-x):x-(u-1.0);/* correction term */ + c /= u; + } else { + u = x; + GET_HIGH_WORD(hu,u); + k = (hu>>20)-1023; + c = 0; + } + hu &= 0x000fffff; + /* + * The approximation to sqrt(2) used in thresholds is not + * critical. However, the ones used above must give less + * strict bounds than the one here so that the k==0 case is + * never reached from here, since here we have committed to + * using the correction term but don't use it if k==0. + */ + if(hu<0x6a09e) { /* u ~< sqrt(2) */ + SET_HIGH_WORD(u,hu|0x3ff00000); /* normalize u */ + } else { + k += 1; + SET_HIGH_WORD(u,hu|0x3fe00000); /* normalize u/2 */ + hu = (0x00100000-hu)>>2; + } + f = u-1.0; + } + hfsq=0.5*f*f; + if(hu==0) { /* |f| < 2**-20 */ + if(f==zero) { + if(k==0) { + return zero; + } else { + c += k*ln2_lo; + return k*ln2_hi+c; + } + } + R = hfsq*(1.0-0.66666666666666666*f); + if(k==0) return f-R; else + return k*ln2_hi-((R-(k*ln2_lo+c))-f); + } + s = f/(2.0+f); + z = s*s; + R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))); + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f); +} diff --git a/modules/fdlibm/src/s_nearbyint.cpp b/modules/fdlibm/src/s_nearbyint.cpp new file mode 100644 index 0000000000..773057431c --- /dev/null +++ b/modules/fdlibm/src/s_nearbyint.cpp @@ -0,0 +1,61 @@ +/*- + * SPDX-License-Identifier: BSD-2-Clause-FreeBSD + * + * Copyright (c) 2004 David Schultz <das@FreeBSD.ORG> + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +#include <fenv.h> + +#include "math_private.h" + +/* + * We save and restore the floating-point environment to avoid raising + * an inexact exception. We can get away with using fesetenv() + * instead of feclearexcept()/feupdateenv() to restore the environment + * because the only exception defined for rint() is overflow, and + * rounding can't overflow as long as emax >= p. + * + * The volatile keyword is needed below because clang incorrectly assumes + * that rint won't raise any floating-point exceptions. Declaring ret volatile + * is sufficient to trick the compiler into doing the right thing. + */ +#define DECL(type, fn, rint) \ +type \ +fn(type x) \ +{ \ + volatile type ret; \ + fenv_t env; \ + \ + fegetenv(&env); \ + ret = rint(x); \ + fesetenv(&env); \ + return (ret); \ +} + +DECL(double, nearbyint, rint) +DECL(float, nearbyintf, rintf) diff --git a/modules/fdlibm/src/s_rint.cpp b/modules/fdlibm/src/s_rint.cpp new file mode 100644 index 0000000000..19171f87f9 --- /dev/null +++ b/modules/fdlibm/src/s_rint.cpp @@ -0,0 +1,87 @@ +/* @(#)s_rint.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* + * rint(x) + * Return x rounded to integral value according to the prevailing + * rounding mode. + * Method: + * Using floating addition. + * Exception: + * Inexact flag raised if x not equal to rint(x). + */ + +#include <float.h> + +#include "math_private.h" + +static const double +TWO52[2]={ + 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ + -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */ +}; + +double +rint(double x) +{ + int32_t i0,j0,sx; + u_int32_t i,i1; + double w,t; + EXTRACT_WORDS(i0,i1,x); + sx = (i0>>31)&1; + j0 = ((i0>>20)&0x7ff)-0x3ff; + if(j0<20) { + if(j0<0) { + if(((i0&0x7fffffff)|i1)==0) return x; + i1 |= (i0&0x0fffff); + i0 &= 0xfffe0000; + i0 |= ((i1|-i1)>>12)&0x80000; + SET_HIGH_WORD(x,i0); + STRICT_ASSIGN(double,w,TWO52[sx]+x); + t = w-TWO52[sx]; + GET_HIGH_WORD(i0,t); + SET_HIGH_WORD(t,(i0&0x7fffffff)|(sx<<31)); + return t; + } else { + i = (0x000fffff)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + i>>=1; + if(((i0&i)|i1)!=0) { + /* + * Some bit is set after the 0.5 bit. To avoid the + * possibility of errors from double rounding in + * w = TWO52[sx]+x, adjust the 0.25 bit to a lower + * guard bit. We do this for all j0<=51. The + * adjustment is trickiest for j0==18 and j0==19 + * since then it spans the word boundary. + */ + if(j0==19) i1 = 0x40000000; else + if(j0==18) i1 = 0x80000000; else + i0 = (i0&(~i))|((0x20000)>>j0); + } + } + } else if (j0>51) { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(j0-20); + if((i1&i)==0) return x; /* x is integral */ + i>>=1; + if((i1&i)!=0) i1 = (i1&(~i))|((0x40000000)>>(j0-20)); + } + INSERT_WORDS(x,i0,i1); + STRICT_ASSIGN(double,w,TWO52[sx]+x); + return w-TWO52[sx]; +} diff --git a/modules/fdlibm/src/s_rintf.cpp b/modules/fdlibm/src/s_rintf.cpp new file mode 100644 index 0000000000..3a729b005d --- /dev/null +++ b/modules/fdlibm/src/s_rintf.cpp @@ -0,0 +1,52 @@ +/* s_rintf.c -- float version of s_rint.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +#include <float.h> +#include <stdint.h> + +#include "math_private.h" + +static const float +TWO23[2]={ + 8.3886080000e+06, /* 0x4b000000 */ + -8.3886080000e+06, /* 0xcb000000 */ +}; + +float +rintf(float x) +{ + int32_t i0,j0,sx; + float w,t; + GET_FLOAT_WORD(i0,x); + sx = (i0>>31)&1; + j0 = ((i0>>23)&0xff)-0x7f; + if(j0<23) { + if(j0<0) { + if((i0&0x7fffffff)==0) return x; + STRICT_ASSIGN(float,w,TWO23[sx]+x); + t = w-TWO23[sx]; + GET_FLOAT_WORD(i0,t); + SET_FLOAT_WORD(t,(i0&0x7fffffff)|(sx<<31)); + return t; + } + STRICT_ASSIGN(float,w,TWO23[sx]+x); + return w-TWO23[sx]; + } + if(j0==0x80) return x+x; /* inf or NaN */ + else return x; /* x is integral */ +} diff --git a/modules/fdlibm/src/s_scalbn.cpp b/modules/fdlibm/src/s_scalbn.cpp new file mode 100644 index 0000000000..13fa7f129d --- /dev/null +++ b/modules/fdlibm/src/s_scalbn.cpp @@ -0,0 +1,43 @@ +/* + * Copyright (c) 2005-2020 Rich Felker, et al. + * + * SPDX-License-Identifier: MIT + * + * Please see https://git.musl-libc.org/cgit/musl/tree/COPYRIGHT + * for all contributors to musl. + */ +#include <float.h> +#include <stdint.h> + +#include "math_private.h" + +double scalbn(double x, int n) +{ + union {double f; uint64_t i;} u; + double_t y = x; + + if (n > 1023) { + y *= 0x1p1023; + n -= 1023; + if (n > 1023) { + y *= 0x1p1023; + n -= 1023; + if (n > 1023) + n = 1023; + } + } else if (n < -1022) { + /* make sure final n < -53 to avoid double + rounding in the subnormal range */ + y *= 0x1p-1022 * 0x1p53; + n += 1022 - 53; + if (n < -1022) { + y *= 0x1p-1022 * 0x1p53; + n += 1022 - 53; + if (n < -1022) + n = -1022; + } + } + u.i = (uint64_t)(0x3ff+n)<<52; + x = y * u.f; + return x; +} diff --git a/modules/fdlibm/src/s_scalbnf.cpp b/modules/fdlibm/src/s_scalbnf.cpp new file mode 100644 index 0000000000..68eca80d90 --- /dev/null +++ b/modules/fdlibm/src/s_scalbnf.cpp @@ -0,0 +1,40 @@ +/* + * Copyright (c) 2005-2020 Rich Felker, et al. + * + * SPDX-License-Identifier: MIT + * + * Please see https://git.musl-libc.org/cgit/musl/tree/COPYRIGHT + * for all contributors to musl. + */ +#include <stdint.h> + +#include "math_private.h" + +float scalbnf(float x, int n) +{ + union {float f; uint32_t i;} u; + float y = x; + + if (n > 127) { + y *= 0x1p127f; + n -= 127; + if (n > 127) { + y *= 0x1p127f; + n -= 127; + if (n > 127) + n = 127; + } + } else if (n < -126) { + y *= 0x1p-126f * 0x1p24f; + n += 126 - 24; + if (n < -126) { + y *= 0x1p-126f * 0x1p24f; + n += 126 - 24; + if (n < -126) + n = -126; + } + } + u.i = (uint32_t)(0x7f+n)<<23; + x = y * u.f; + return x; +} diff --git a/modules/fdlibm/src/s_sin.cpp b/modules/fdlibm/src/s_sin.cpp new file mode 100644 index 0000000000..42cec47b2c --- /dev/null +++ b/modules/fdlibm/src/s_sin.cpp @@ -0,0 +1,84 @@ +/* @(#)s_sin.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* sin(x) + * Return sine function of x. + * + * kernel function: + * __kernel_sin ... sine function on [-pi/4,pi/4] + * __kernel_cos ... cose function on [-pi/4,pi/4] + * __ieee754_rem_pio2 ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include <float.h> + +#define INLINE_REM_PIO2 +#include "math_private.h" +#include "e_rem_pio2.cpp" + +double +sin(double x) +{ + double y[2],z=0.0; + int32_t n, ix; + + /* High word of x. */ + GET_HIGH_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3fe921fb) { + if(ix<0x3e500000) /* |x| < 2**-26 */ + {if((int)x==0) return x;} /* generate inexact */ + return __kernel_sin(x,z,0); + } + + /* sin(Inf or NaN) is NaN */ + else if (ix>=0x7ff00000) return x-x; + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2(x,y); + switch(n&3) { + case 0: return __kernel_sin(y[0],y[1],1); + case 1: return __kernel_cos(y[0],y[1]); + case 2: return -__kernel_sin(y[0],y[1],1); + default: + return -__kernel_cos(y[0],y[1]); + } + } +} diff --git a/modules/fdlibm/src/s_sinf.cpp b/modules/fdlibm/src/s_sinf.cpp new file mode 100644 index 0000000000..b4c5d74779 --- /dev/null +++ b/modules/fdlibm/src/s_sinf.cpp @@ -0,0 +1,84 @@ +/* s_sinf.c -- float version of s_sin.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + * Optimized by Bruce D. Evans. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +#include <float.h> + +#define INLINE_KERNEL_COSDF +#define INLINE_KERNEL_SINDF +#define INLINE_REM_PIO2F +#include "math_private.h" +#include "e_rem_pio2f.cpp" +#include "k_cosf.cpp" +#include "k_sinf.cpp" + +/* Small multiples of pi/2 rounded to double precision. */ +static const double +s1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */ +s2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */ +s3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */ +s4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */ + +float +sinf(float x) +{ + double y; + int32_t n, hx, ix; + + GET_FLOAT_WORD(hx,x); + ix = hx & 0x7fffffff; + + if(ix <= 0x3f490fda) { /* |x| ~<= pi/4 */ + if(ix<0x39800000) /* |x| < 2**-12 */ + if(((int)x)==0) return x; /* x with inexact if x != 0 */ + return __kernel_sindf(x); + } + if(ix<=0x407b53d1) { /* |x| ~<= 5*pi/4 */ + if(ix<=0x4016cbe3) { /* |x| ~<= 3pi/4 */ + if(hx>0) + return __kernel_cosdf(x - s1pio2); + else + return -__kernel_cosdf(x + s1pio2); + } else + return __kernel_sindf((hx > 0 ? s2pio2 : -s2pio2) - x); + } + if(ix<=0x40e231d5) { /* |x| ~<= 9*pi/4 */ + if(ix<=0x40afeddf) { /* |x| ~<= 7*pi/4 */ + if(hx>0) + return -__kernel_cosdf(x - s3pio2); + else + return __kernel_cosdf(x + s3pio2); + } else + return __kernel_sindf(x + (hx > 0 ? -s4pio2 : s4pio2)); + } + + /* sin(Inf or NaN) is NaN */ + else if (ix>=0x7f800000) return x-x; + + /* general argument reduction needed */ + else { + n = __ieee754_rem_pio2f(x,&y); + switch(n&3) { + case 0: return __kernel_sindf(y); + case 1: return __kernel_cosdf(y); + case 2: return __kernel_sindf(-y); + default: + return -__kernel_cosdf(y); + } + } +} diff --git a/modules/fdlibm/src/s_tan.cpp b/modules/fdlibm/src/s_tan.cpp new file mode 100644 index 0000000000..3bcb109761 --- /dev/null +++ b/modules/fdlibm/src/s_tan.cpp @@ -0,0 +1,78 @@ +/* @(#)s_tan.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* tan(x) + * Return tangent function of x. + * + * kernel function: + * __kernel_tan ... tangent function on [-pi/4,pi/4] + * __ieee754_rem_pio2 ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include <float.h> + +#define INLINE_REM_PIO2 +#include "math_private.h" +#include "e_rem_pio2.cpp" + +double +tan(double x) +{ + double y[2],z=0.0; + int32_t n, ix; + + /* High word of x. */ + GET_HIGH_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3fe921fb) { + if(ix<0x3e400000) /* x < 2**-27 */ + if((int)x==0) return x; /* generate inexact */ + return __kernel_tan(x,z,1); + } + + /* tan(Inf or NaN) is NaN */ + else if (ix>=0x7ff00000) return x-x; /* NaN */ + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2(x,y); + return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even + -1 -- n odd */ + } +} diff --git a/modules/fdlibm/src/s_tanf.cpp b/modules/fdlibm/src/s_tanf.cpp new file mode 100644 index 0000000000..f72d28382b --- /dev/null +++ b/modules/fdlibm/src/s_tanf.cpp @@ -0,0 +1,71 @@ +/* s_tanf.c -- float version of s_tan.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + * Optimized by Bruce D. Evans. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +#include <float.h> + +#define INLINE_KERNEL_TANDF +#define INLINE_REM_PIO2F +#include "math_private.h" +#include "e_rem_pio2f.cpp" +#include "k_tanf.cpp" + +/* Small multiples of pi/2 rounded to double precision. */ +static const double +t1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */ +t2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */ +t3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */ +t4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */ + +float +tanf(float x) +{ + double y; + int32_t n, hx, ix; + + GET_FLOAT_WORD(hx,x); + ix = hx & 0x7fffffff; + + if(ix <= 0x3f490fda) { /* |x| ~<= pi/4 */ + if(ix<0x39800000) /* |x| < 2**-12 */ + if(((int)x)==0) return x; /* x with inexact if x != 0 */ + return __kernel_tandf(x,1); + } + if(ix<=0x407b53d1) { /* |x| ~<= 5*pi/4 */ + if(ix<=0x4016cbe3) /* |x| ~<= 3pi/4 */ + return __kernel_tandf(x + (hx>0 ? -t1pio2 : t1pio2), -1); + else + return __kernel_tandf(x + (hx>0 ? -t2pio2 : t2pio2), 1); + } + if(ix<=0x40e231d5) { /* |x| ~<= 9*pi/4 */ + if(ix<=0x40afeddf) /* |x| ~<= 7*pi/4 */ + return __kernel_tandf(x + (hx>0 ? -t3pio2 : t3pio2), -1); + else + return __kernel_tandf(x + (hx>0 ? -t4pio2 : t4pio2), 1); + } + + /* tan(Inf or NaN) is NaN */ + else if (ix>=0x7f800000) return x-x; + + /* general argument reduction needed */ + else { + n = __ieee754_rem_pio2f(x,&y); + /* integer parameter: 1 -- n even; -1 -- n odd */ + return __kernel_tandf(y,1-((n&1)<<1)); + } +} diff --git a/modules/fdlibm/src/s_tanh.cpp b/modules/fdlibm/src/s_tanh.cpp new file mode 100644 index 0000000000..238973fce3 --- /dev/null +++ b/modules/fdlibm/src/s_tanh.cpp @@ -0,0 +1,79 @@ +/* @(#)s_tanh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* Tanh(x) + * Return the Hyperbolic Tangent of x + * + * Method : + * x -x + * e - e + * 0. tanh(x) is defined to be ----------- + * x -x + * e + e + * 1. reduce x to non-negative by tanh(-x) = -tanh(x). + * 2. 0 <= x < 2**-28 : tanh(x) := x with inexact if x != 0 + * -t + * 2**-28 <= x < 1 : tanh(x) := -----; t = expm1(-2x) + * t + 2 + * 2 + * 1 <= x < 22 : tanh(x) := 1 - -----; t = expm1(2x) + * t + 2 + * 22 <= x <= INF : tanh(x) := 1. + * + * Special cases: + * tanh(NaN) is NaN; + * only tanh(0)=0 is exact for finite argument. + */ + +#include <float.h> + +#include "math_private.h" + +static const volatile double tiny = 1.0e-300; +static const double one = 1.0, two = 2.0, huge = 1.0e300; + +double +tanh(double x) +{ + double t,z; + int32_t jx,ix; + + GET_HIGH_WORD(jx,x); + ix = jx&0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7ff00000) { + if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ + else return one/x-one; /* tanh(NaN) = NaN */ + } + + /* |x| < 22 */ + if (ix < 0x40360000) { /* |x|<22 */ + if (ix<0x3e300000) { /* |x|<2**-28 */ + if(huge+x>one) return x; /* tanh(tiny) = tiny with inexact */ + } + if (ix>=0x3ff00000) { /* |x|>=1 */ + t = expm1(two*fabs(x)); + z = one - two/(t+two); + } else { + t = expm1(-two*fabs(x)); + z= -t/(t+two); + } + /* |x| >= 22, return +-1 */ + } else { + z = one - tiny; /* raise inexact flag */ + } + return (jx>=0)? z: -z; +} diff --git a/modules/fdlibm/src/s_trunc.cpp b/modules/fdlibm/src/s_trunc.cpp new file mode 100644 index 0000000000..d2294a2723 --- /dev/null +++ b/modules/fdlibm/src/s_trunc.cpp @@ -0,0 +1,62 @@ +/* @(#)s_floor.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* + * trunc(x) + * Return x rounded toward 0 to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to trunc(x). + */ + +#include <float.h> + +#include "math_private.h" + +static const double huge = 1.0e300; + +double +trunc(double x) +{ + int32_t i0,i1,j0; + u_int32_t i; + EXTRACT_WORDS(i0,i1,x); + j0 = ((i0>>20)&0x7ff)-0x3ff; + if(j0<20) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0) {/* |x|<1, so return 0*sign(x) */ + i0 &= 0x80000000U; + i1 = 0; + } + } else { + i = (0x000fffff)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + i0 &= (~i); i1=0; + } + } + } else if (j0>51) { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(j0-20); + if((i1&i)==0) return x; /* x is integral */ + if(huge+x>0.0) /* raise inexact flag */ + i1 &= (~i); + } + INSERT_WORDS(x,i0,i1); + return x; +} diff --git a/modules/fdlibm/src/s_truncf.cpp b/modules/fdlibm/src/s_truncf.cpp new file mode 100644 index 0000000000..4853a44507 --- /dev/null +++ b/modules/fdlibm/src/s_truncf.cpp @@ -0,0 +1,52 @@ +/* @(#)s_floor.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//#include <sys/cdefs.h> +//__FBSDID("$FreeBSD$"); + +/* + * truncf(x) + * Return x rounded toward 0 to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to truncf(x). + */ + +#include "math_private.h" + +static const float huge = 1.0e30F; + +float +truncf(float x) +{ + int32_t i0,j0; + u_int32_t i; + GET_FLOAT_WORD(i0,x); + j0 = ((i0>>23)&0xff)-0x7f; + if(j0<23) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0F) /* |x|<1, so return 0*sign(x) */ + i0 &= 0x80000000; + } else { + i = (0x007fffff)>>j0; + if((i0&i)==0) return x; /* x is integral */ + if(huge+x>0.0F) /* raise inexact flag */ + i0 &= (~i); + } + } else { + if(j0==0x80) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + SET_FLOAT_WORD(x,i0); + return x; +} |