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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 <boost/math/concepts/real_concept.hpp>
#include <boost/test/included/test_exec_monitor.hpp>
#include <boost/test/floating_point_comparison.hpp>
#include <boost/math/special_functions/digamma.hpp>
#include <boost/array.hpp>
#include "functor.hpp"
#include "handle_test_result.hpp"
//
// DESCRIPTION:
// ~~~~~~~~~~~~
//
// This file tests the digamma function. There are two sets of tests, spot
// tests which compare our results with selected values computed
// using the online special function calculator at
// functions.wolfram.com, while the bulk of the 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.
//
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
".*", // test type(s)
".*Negative.*", // test data group
".*", 300, 40); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
".*", // test type(s)
".*", // test data group
".*", 3, 3); // test function
//
// Finish off by printing out the compiler/stdlib/platform names,
// we do this to make it easier to mark up expected error rates.
//
std::cout << "Tests run with " << BOOST_COMPILER << ", "
<< BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
}
template <class T>
void do_test_digamma(const T& data, const char* type_name, const char* test_name)
{
typedef typename T::value_type row_type;
typedef typename row_type::value_type value_type;
typedef value_type (*pg)(value_type);
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
pg funcp = boost::math::digamma<value_type>;
#else
pg funcp = boost::math::digamma;
#endif
boost::math::tools::test_result<value_type> result;
std::cout << "Testing " << test_name << " with type " << type_name
<< "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
//
// test digamma against data:
//
result = boost::math::tools::test(
data,
bind_func(funcp, 0),
extract_result(1));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::digamma", test_name);
std::cout << std::endl;
}
template <class T>
void test_digamma(T, const char* name)
{
//
// The actual test data is rather verbose, so it's in a separate file
//
// The contents are as follows, each row of data contains
// three items, input value a, input value b and erf(a, b):
//
# include "digamma_data.ipp"
do_test_digamma(digamma_data, name, "Digamma Function: Large Values");
# include "digamma_root_data.ipp"
do_test_digamma(digamma_root_data, name, "Digamma Function: Near the Positive Root");
# include "digamma_small_data.ipp"
do_test_digamma(digamma_small_data, name, "Digamma Function: Near Zero");
# include "digamma_neg_data.ipp"
do_test_digamma(digamma_neg_data, name, "Digamma Function: Negative Values");
}
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 3 epsilon expressed as a percentage:
//
T tolerance = boost::math::tools::epsilon<T>() * 300;
//
// Special tolerance (200eps) for when we're very near the root,
// and T has more than 64-bits in it's mantissa:
//
BOOST_CHECK_CLOSE(::boost::math::digamma(static_cast<T>(0.125)), static_cast<T>(-8.3884926632958548678027429230863430000514460424495L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::digamma(static_cast<T>(0.5)), static_cast<T>(-1.9635100260214234794409763329987555671931596046604L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::digamma(static_cast<T>(1)), static_cast<T>(-0.57721566490153286060651209008240243104215933593992L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::digamma(static_cast<T>(1.5)), static_cast<T>(0.036489973978576520559023667001244432806840395339566L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::digamma(static_cast<T>(1.5) - static_cast<T>(1)/32), static_cast<T>(0.00686541147073577672813890866512415766586241385896200579891429L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::digamma(static_cast<T>(2)), static_cast<T>(0.42278433509846713939348790991759756895784066406008L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::digamma(static_cast<T>(8)), static_cast<T>(2.0156414779556099965363450527747404261006978069172L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::digamma(static_cast<T>(12)), static_cast<T>(2.4426616799758120167383652547949424463027180089374L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::digamma(static_cast<T>(22)), static_cast<T>(3.0681430398611966699248760264450329818421699570581L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::digamma(static_cast<T>(50)), static_cast<T>(3.9019896734278921969539597028823666609284424880275L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::digamma(static_cast<T>(500)), static_cast<T>(6.2136077650889917423827750552855712637776544784569L), tolerance);
//
// negative values:
//
BOOST_CHECK_CLOSE(::boost::math::digamma(static_cast<T>(-0.125)), static_cast<T>(7.1959829284523046176757814502538535827603450463013L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::digamma(static_cast<T>(-10.125)), static_cast<T>(9.9480538258660761287008034071425343357982429855241L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::digamma(static_cast<T>(-10.875)), static_cast<T>(-5.1527360383841562620205965901515879492020193154231L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::digamma(static_cast<T>(-1.5)), static_cast<T>(0.70315664064524318722569033366791109947350706200623L), tolerance);
}
int test_main(int, char* [])
{
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");
test_spots(boost::math::concepts::real_concept(0.1), "real_concept");
#endif
expected_results();
test_digamma(0.1F, "float");
test_digamma(0.1, "double");
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_digamma(0.1L, "long double");
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
test_digamma(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::cout;
#endif
return 0;
}
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