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+// (C) Copyright John Maddock 2006.
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0. (See accompanying file
+// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#include <pch.hpp>
+
+#include <boost/math/concepts/real_concept.hpp>
+#include <boost/math/special_functions/acosh.hpp>
+#include <boost/math/special_functions/asinh.hpp>
+#include <boost/math/special_functions/atanh.hpp>
+#define BOOST_TEST_MAIN
+#include <boost/test/unit_test.hpp>
+#include <boost/test/tools/floating_point_comparison.hpp>
+#include <boost/math/tools/stats.hpp>
+#include <boost/math/tools/test.hpp>
+#include <boost/math/constants/constants.hpp>
+#include <boost/type_traits/is_floating_point.hpp>
+#include <boost/array.hpp>
+#include "functor.hpp"
+
+#include "handle_test_result.hpp"
+#include "table_type.hpp"
+
+#include <iostream>
+#include <iomanip>
+//
+// DESCRIPTION:
+// ~~~~~~~~~~~~
+//
+// This file tests the inverse hyperbolic functions. There are two sets of tests:
+// 1) Sanity checks: comparison to test values created with the
+// online calculator at functions.wolfram.com
+// 2) Accuracy tests use values generated with NTL::RR at
+// 1000-bit precision and our generic versions of these functions.
+//
+// Note that when this file is first run on a new platform many of
+// these tests will fail: the default accuracy is 1 epsilon which
+// is too tight for most platforms. In this situation you will
+// need to cast a human eye over the error rates reported and make
+// a judgement as to whether they are acceptable. Either way please
+// report the results to the Boost mailing list. Acceptable rates of
+// error are marked up below as a series of regular expressions that
+// identify the compiler/stdlib/platform/data-type/test-data/test-function
+// along with the maximum expected peek and RMS mean errors for that
+// test.
+//
+
+void expected_results()
+{
+ //
+ // Define the max and mean errors expected for
+ // various compilers and platforms.
+ //
+ const char* largest_type;
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+ if(boost::math::policies::digits<double, boost::math::policies::policy<> >() == boost::math::policies::digits<long double, boost::math::policies::policy<> >())
+ {
+ largest_type = "(long\\s+)?double|real_concept";
+ }
+ else
+ {
+ largest_type = "long double|real_concept";
+ }
+#else
+ largest_type = "(long\\s+)?double";
+#endif
+
+ add_expected_result(
+ ".*", // compiler
+ ".*", // stdlib
+ ".*", // platform
+ largest_type, // test type(s)
+ "atanh.*", // test data group
+ ".*", 6, 1); // test function
+ add_expected_result(
+ ".*", // compiler
+ ".*", // stdlib
+ ".*", // platform
+ "real_concept", // test type(s)
+ ".*", // test data group
+ ".*", 4, 2); // test function
+ add_expected_result(
+ ".*", // compiler
+ ".*", // stdlib
+ ".*", // platform
+ largest_type, // test type(s)
+ ".*", // test data group
+ ".*", 4, 1); // test function
+
+ std::cout << "Tests run with " << BOOST_COMPILER << ", "
+ << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+template <class Real, class T>
+void do_test_asinh(const T& data, const char* type_name, const char* test_name)
+{
+ //
+ // test asinh(T) against data:
+ //
+ using namespace std;
+ typedef Real value_type;
+
+ std::cout << test_name << " with type " << type_name << std::endl;
+
+ typedef value_type (*pg)(value_type);
+#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
+ pg funcp = boost::math::asinh<value_type>;
+#else
+ pg funcp = boost::math::asinh;
+#endif
+
+ boost::math::tools::test_result<value_type> result;
+ //
+ // test asinh against data:
+ //
+ result = boost::math::tools::test_hetero<Real>(
+ data,
+ bind_func<Real>(funcp, 0),
+ extract_result<Real>(1));
+ handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::asinh", test_name);
+ std::cout << std::endl;
+}
+
+template <class Real, class T>
+void do_test_acosh(const T& data, const char* type_name, const char* test_name)
+{
+ //
+ // test acosh(T) against data:
+ //
+ using namespace std;
+ typedef Real value_type;
+
+ std::cout << test_name << " with type " << type_name << std::endl;
+
+ typedef value_type (*pg)(value_type);
+#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
+ pg funcp = boost::math::acosh<value_type>;
+#else
+ pg funcp = boost::math::acosh;
+#endif
+
+ boost::math::tools::test_result<value_type> result;
+ //
+ // test acosh against data:
+ //
+ result = boost::math::tools::test_hetero<Real>(
+ data,
+ bind_func<Real>(funcp, 0),
+ extract_result<Real>(1));
+ handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::acosh", test_name);
+ std::cout << std::endl;
+}
+
+template <class Real, class T>
+void do_test_atanh(const T& data, const char* type_name, const char* test_name)
+{
+ //
+ // test atanh(T) against data:
+ //
+ using namespace std;
+ typedef Real value_type;
+
+ std::cout << test_name << " with type " << type_name << std::endl;
+
+ typedef value_type (*pg)(value_type);
+#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
+ pg funcp = boost::math::atanh<value_type>;
+#else
+ pg funcp = boost::math::atanh;
+#endif
+
+ boost::math::tools::test_result<value_type> result;
+ //
+ // test atanh against data:
+ //
+ result = boost::math::tools::test_hetero<Real>(
+ data,
+ bind_func<Real>(funcp, 0),
+ extract_result<Real>(1));
+ handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::atanh", test_name);
+ std::cout << std::endl;
+}
+
+template <class T>
+void test_inv_hyperbolics(T, const char* name)
+{
+ // function values calculated on http://functions.wolfram.com/
+ #define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L))
+ static const boost::array<boost::array<typename table_type<T>::type, 2>, 16> data1 = {{
+ {{ SC_(1.0), SC_(0.0) }},
+ {{ SC_(18014398509481985.0)/SC_(18014398509481984.0), (SC_(18014398509481985.0)/SC_(18014398509481984.0) == 1 ? 0 : SC_(1.05367121277235078980001569764860129317209081216314559121044e-8)) }},
+ {{ SC_(140737488355329.0)/SC_(140737488355328.0), (SC_(140737488355329.0)/SC_(140737488355328.0) == 1 ? 0 : SC_(1.19209289550781179413921062141751258430803882725295121500042e-7)) }},
+ {{ SC_(1073741825.0)/SC_(1073741824.0), (SC_(1073741825.0)/SC_(1073741824.0) == 1 ? 0 : SC_(0.0000431583728718059579720327225039166883356735150941350459126580)) }},
+ {{ SC_(32769.0)/32768, (SC_(32769.0)/32768 == 1 ? 0 : SC_(0.00781248013192149783598227588546120945538554063153555218442060)) }},
+ {{ SC_(1025.0)/1024, SC_(0.0441905780831100944299637635287994671116916497867872322058681) }},
+ {{ SC_(513.0)/512, SC_(0.0624898319417098609694799246056217361555882834152944713872228) }},
+ {{ SC_(129.0)/128, SC_(0.124918762511080617606418193883982155828039646714882611321039) }},
+ {{ SC_(33.0)/32, SC_(0.249353493842885487851439075410018843027071727873456825299808) }},
+ {{ SC_(5.0)/4, SC_(0.693147180559945309417232121458176568075500134360255254120680) }},
+ {{ SC_(3.0)/2, SC_(0.962423650119206894995517826848736846270368668771321039322036) }},
+ {{ SC_(1.75), SC_(1.15881036042994681173087299087873019318368454205435905403767) }},
+ {{ SC_(2.0), SC_(1.31695789692481670862504634730796844402698197146751647976847) }},
+ {{ SC_(20.0), SC_(3.68825386736129666761816757203235188783315569765587425882926) }},
+ {{ SC_(200.0), SC_(5.99145829704938742305501213819154333467246121857058747847273) }},
+ {{ SC_(2000.0), SC_(8.29404957760202181151262480475259799729149903827743516943515) }},
+ }};
+ #undef SC_
+
+ //
+ // The actual test data is rather verbose, so it's in a separate file
+ //
+#include "asinh_data.ipp"
+ do_test_asinh<T>(asinh_data, name, "asinh");
+#include "acosh_data.ipp"
+ do_test_acosh<T>(data1, name, "acosh: Mathworld Data");
+ do_test_acosh<T>(acosh_data, name, "acosh");
+#include "atanh_data.ipp"
+ do_test_atanh<T>(atanh_data, name, "atanh");
+}
+
+extern "C" double zetac(double);
+
+template <class T>
+void test_spots(T, const char* t)
+{
+ std::cout << "Testing basic sanity checks for type " << t << std::endl;
+ //
+ // Basic sanity checks, tolerance is either 5 or 10 epsilon
+ // expressed as a percentage:
+ //
+ T tolerance = boost::math::tools::epsilon<T>() * 100 *
+ (boost::is_floating_point<T>::value ? 5 : 10);
+ BOOST_CHECK_CLOSE(::boost::math::acosh(static_cast<T>(262145)/262144L), static_cast<T>(0.00276213498595136093375633956331651432309750291610866833462649L), tolerance);
+ BOOST_CHECK_CLOSE(::boost::math::acosh(static_cast<T>(2)), static_cast<T>(1.31695789692481670862504634730796844402698197146751647976847L), tolerance);
+ BOOST_CHECK_CLOSE(::boost::math::acosh(static_cast<T>(40)), static_cast<T>(4.38187034804006698696313269586603717076961771721038534547948L), tolerance);
+ BOOST_CHECK_CLOSE(::boost::math::acosh(static_cast<T>(262145L)), static_cast<T>(13.1698002453253126137651962522659827810753786944786303017757L), tolerance);
+
+ BOOST_CHECK_CLOSE(::boost::math::asinh(static_cast<T>(0)), static_cast<T>(0), tolerance);
+ BOOST_CHECK_CLOSE(::boost::math::asinh(static_cast<T>(1)/262145L), static_cast<T>(3.81468271375603081996185039385472561751449912305225962381803e-6L), tolerance);
+ BOOST_CHECK_CLOSE(::boost::math::asinh(static_cast<T>(0.25)), static_cast<T>(0.247466461547263452944781549788359289253766903098567696469117L), tolerance);
+ BOOST_CHECK_CLOSE(::boost::math::asinh(static_cast<T>(1)), static_cast<T>(0.881373587019543025232609324979792309028160328261635410753296L), tolerance);
+ BOOST_CHECK_CLOSE(::boost::math::asinh(static_cast<T>(10)), static_cast<T>(2.99822295029796973884659553759645347660705805487730365573446L), tolerance);
+ BOOST_CHECK_CLOSE(::boost::math::asinh(static_cast<T>(262145L)), static_cast<T>(13.1698002453325885158685460826511173257938039316922010439486L), tolerance);
+
+ BOOST_CHECK_CLOSE(::boost::math::atanh(static_cast<T>(0)), static_cast<T>(0), tolerance);
+ BOOST_CHECK_CLOSE(::boost::math::atanh(static_cast<T>(1)/262145L), static_cast<T>(3.81468271378378607794264842456613940280945630999769224301574e-6L), tolerance);
+ BOOST_CHECK_CLOSE(::boost::math::atanh(static_cast<T>(-1)/262145L), static_cast<T>(-3.81468271378378607794264842456613940280945630999769224301574e-6L), tolerance);
+ BOOST_CHECK_CLOSE(::boost::math::atanh(static_cast<T>(0.5)), static_cast<T>(0.549306144334054845697622618461262852323745278911374725867347L), tolerance);
+ BOOST_CHECK_CLOSE(::boost::math::atanh(static_cast<T>(-0.5)), static_cast<T>(-0.549306144334054845697622618461262852323745278911374725867347L), tolerance);
+}
+
+BOOST_AUTO_TEST_CASE( test_main )
+{
+ expected_results();
+ BOOST_MATH_CONTROL_FP;
+
+ test_spots(0.0f, "float");
+ test_spots(0.0, "double");
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+ test_spots(0.0L, "long double");
+#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
+ test_spots(boost::math::concepts::real_concept(0.1), "real_concept");
+#endif
+#else
+ std::cout << "<note>The long double tests have been disabled on this platform "
+ "either because the long double overloads of the usual math functions are "
+ "not available at all, or because they are too inaccurate for these tests "
+ "to pass.</note>" << std::endl;
+#endif
+
+ test_inv_hyperbolics(0.1F, "float");
+ test_inv_hyperbolics(0.1, "double");
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+ test_inv_hyperbolics(0.1L, "long double");
+#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
+ test_inv_hyperbolics(boost::math::concepts::real_concept(0.1), "real_concept");
+#endif
+#else
+ std::cout << "<note>The long double tests have been disabled on this platform "
+ "either because the long double overloads of the usual math functions are "
+ "not available at all, or because they are too inaccurate for these tests "
+ "to pass.</note>" << std::endl;
+#endif
+
+}
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