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// test file for special_functions.hpp
// (C) Copyright Hubert Holin 2001. Permission to copy, use, modify, sell and
// distribute this software is granted provided this copyright notice appears
// in all copies. This software is provided "as is" without express or implied
// warranty, and with no claim as to its suitability for any purpose.
#include <algorithm>
#include <iostream>
#include <iomanip>
#include <complex>
#include <boost/math/special_functions/atanh.hpp>
#include <boost/math/special_functions/asinh.hpp>
#include <boost/math/special_functions/acosh.hpp>
#include <boost/math/special_functions/sinc.hpp>
#include <boost/math/special_functions/sinhc.hpp>
#include <boost/config.hpp>
#ifdef BOOST_NO_STDC_NAMESPACE
namespace std {
using ::abs;
using ::cosh;
using ::log;
using ::sin;
using ::sinh;
using ::sqrt;
using ::tanh;
}
#endif
#define BOOST_INCLUDE_MAIN // for testing, include rather than link
#include <boost/test/test_tools.hpp>
template<typename T>
T atanh_error_evaluator(T x)
{
using ::std::abs;
using ::std::tanh;
using ::std::cosh;
using ::std::numeric_limits;
using ::boost::math::atanh;
static T const epsilon = numeric_limits<float>::epsilon();
T y = tanh(x);
T z = atanh(y);
T absolute_error = abs(z-x);
T relative_error = absolute_error/(cosh(x)*cosh(x));
T scaled_error = relative_error/epsilon;
return(scaled_error);
}
template<typename T>
T asinh_error_evaluator(T x)
{
using ::std::abs;
using ::std::sinh;
using ::std::cosh;
using ::std::numeric_limits;
using ::boost::math::asinh;
static T const epsilon = numeric_limits<float>::epsilon();
T y = sinh(x);
T z = asinh(y);
T absolute_error = abs(z-x);
T relative_error = absolute_error*cosh(x);
T scaled_error = relative_error/epsilon;
return(scaled_error);
}
template<typename T>
T acosh_error_evaluator(T x)
{
using ::std::abs;
using ::std::sinh;
using ::std::cosh;
using ::std::numeric_limits;
using ::boost::math::acosh;
static T const epsilon = numeric_limits<float>::epsilon();
T y = cosh(x);
T z = acosh(y);
T absolute_error = abs(z-abs(x));
T relative_error = absolute_error*abs(sinh(x));
T scaled_error = relative_error/epsilon;
return(scaled_error);
}
int test_main(int, char *[])
{
using ::std::abs;
using ::std::sin;
using ::std::log;
using ::std::tanh;
using ::std::sinh;
using ::std::cosh;
using ::std::numeric_limits;
using ::boost::math::atanh;
using ::boost::math::asinh;
using ::boost::math::acosh;
using ::boost::math::sinc_pi;
using ::boost::math::sinhc_pi;
// tests for evaluation by humans
// tests for evaluation by scripts
#define BOOST_SPECIAL_FUNCTIONS_TEST_ATANH(type) \
\
::std::cout << "Testing atanh in the real domain." << ::std::endl; \
\
BOOST_TEST(abs(atanh<type>(static_cast<type>(0))) <= \
numeric_limits<type>::epsilon()); \
\
BOOST_TEST(abs(atanh<type>(static_cast<type>(3)/5)- \
log(static_cast<type>(2))) <= \
numeric_limits<type>::epsilon()); \
\
BOOST_TEST(abs(atanh<type>(static_cast<type>(-3)/5)+ \
log(static_cast<type>(2))) <= \
numeric_limits<type>::epsilon()); \
\
for (int i = 0; i <= 100; i++) \
{ \
type x = static_cast<type>(i-50)/static_cast<type>(5); \
type y = tanh(x); \
\
if ( \
(abs(y-static_cast<type>(1)) >= \
numeric_limits<type>::epsilon())&& \
(abs(y+static_cast<type>(1)) >= \
numeric_limits<type>::epsilon()) \
) \
{ \
BOOST_TEST(atanh_error_evaluator(x) <= static_cast<type>(4)); \
} \
}
#define BOOST_SPECIAL_FUNCTIONS_TEST_ASINH(type) \
\
::std::cout << "Testing asinh in the real domain." << ::std::endl; \
\
for (int i = 0; i <= 100; i++) \
{ \
type x = static_cast<type>(i-50)/static_cast<type>(5); \
\
BOOST_TEST(asinh_error_evaluator(x) <= static_cast<type>(4)); \
}
#define BOOST_SPECIAL_FUNCTIONS_TEST_ACOSH(type) \
\
::std::cout << "Testing acosh in the real domain." << ::std::endl; \
\
for (int i = 0; i <= 100; i++) \
{ \
type x = static_cast<type>(i-50)/static_cast<type>(5); \
\
BOOST_TEST(acosh_error_evaluator(x) <= static_cast<type>(4)); \
}
#define BOOST_SPECIAL_FUNCTIONS_TEST_SINC_PI(type) \
\
::std::cout << "Testing sinc_pi in the real domain." << ::std::endl; \
\
BOOST_TEST(abs(sinc_pi<type>(static_cast<type>(0))- \
static_cast<type>(1)) <= \
numeric_limits<type>::epsilon());
#define BOOST_SPECIAL_FUNCTIONS_TEST_SINC_PI_FOR_C(type) \
\
::std::cout << "Testing sinc_pi in the complex domain." << ::std::endl; \
\
BOOST_TEST(abs(sinc_pi<type>(::std::complex<type>(0, 1))- \
::std::complex<type>(sinh(static_cast<type>(1)))) <= \
numeric_limits<type>::epsilon());
#define BOOST_SPECIAL_FUNCTIONS_TEST_SINHC_PI(type) \
\
::std::cout << "Testing sinhc_pi in the real domain." << ::std::endl; \
\
BOOST_TEST(abs(sinhc_pi<type>(static_cast<type>(0))- \
static_cast<type>(1)) <= \
numeric_limits<type>::epsilon());
#define BOOST_SPECIAL_FUNCTIONS_TEST_SINHC_PI_FOR_C(type) \
\
::std::cout << "Testing sinhc_pi in the complex domain." << ::std::endl;\
\
BOOST_TEST(abs(sinhc_pi<type>(::std::complex<type>(0, 1))- \
::std::complex<type>(sin(static_cast<type>(1)))) <= \
numeric_limits<type>::epsilon());
#if defined(__GNUC__) || defined(__COMO__) || \
(defined(__MWERKS__) && (__MWERKS__ <= 0x2301))
#define BOOST_SPECIAL_FUNCTIONS_TEST(type) \
::std::cout << "Testing " << #type << "." << std::endl; \
BOOST_SPECIAL_FUNCTIONS_TEST_ATANH(type) \
BOOST_SPECIAL_FUNCTIONS_TEST_ASINH(type) \
BOOST_SPECIAL_FUNCTIONS_TEST_ACOSH(type) \
BOOST_SPECIAL_FUNCTIONS_TEST_SINC_PI(type) \
BOOST_SPECIAL_FUNCTIONS_TEST_SINHC_PI(type)
#else
#define BOOST_SPECIAL_FUNCTIONS_TEST(type) \
::std::cout << "Testing " << #type << "." << std::endl; \
BOOST_SPECIAL_FUNCTIONS_TEST_ATANH(type) \
BOOST_SPECIAL_FUNCTIONS_TEST_ASINH(type) \
BOOST_SPECIAL_FUNCTIONS_TEST_ACOSH(type) \
BOOST_SPECIAL_FUNCTIONS_TEST_SINC_PI(type) \
BOOST_SPECIAL_FUNCTIONS_TEST_SINHC_PI(type) \
BOOST_SPECIAL_FUNCTIONS_TEST_SINC_PI_FOR_C(type) \
BOOST_SPECIAL_FUNCTIONS_TEST_SINHC_PI_FOR_C(type)
#endif
BOOST_SPECIAL_FUNCTIONS_TEST(float)
BOOST_SPECIAL_FUNCTIONS_TEST(double)
BOOST_SPECIAL_FUNCTIONS_TEST(long double)
#undef BOOST_SPECIAL_FUNCTIONS_TEST
#undef BOOST_SPECIAL_FUNCTIONS_TEST_ATANH
#undef BOOST_SPECIAL_FUNCTIONS_TEST_ASINH
#undef BOOST_SPECIAL_FUNCTIONS_TEST_ACOSH
#undef BOOST_SPECIAL_FUNCTIONS_TEST_SINC_PI
#undef BOOST_SPECIAL_FUNCTIONS_TEST_SINC_PI_FOR_C
#undef BOOST_SPECIAL_FUNCTIONS_TEST_SINHC_PI
#undef BOOST_SPECIAL_FUNCTIONS_TEST_SINHC_PI_FOR_C
return(::boost::exit_success);
}
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