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|
///////////////////////////////////////////////////////////////
// Copyright 2011 - 2025 John Maddock.
// Copyright Christopher Kormanyos 2002 - 2025.
// Distributed under the Boost
// Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at https://www.boost.org/LICENSE_1_0.txt
//
// This work is based on an earlier work:
// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations",
// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469
#ifdef _MSC_VER
#define _SCL_SECURE_NO_WARNINGS
#pragma warning(disable : 4127)
#endif
#include <test.hpp>
#include <boost/detail/lightweight_test.hpp>
#include <boost/math/constants/constants.hpp>
#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) && !defined(TEST_CPP_DOUBLE_FLOAT)
#define TEST_MPF_50
//#define TEST_MPF
#define TEST_BACKEND
#define TEST_CPP_DEC_FLOAT
#define TEST_MPFI_50
#define TEST_FLOAT128
#define TEST_CPP_BIN_FLOAT
#define TEST_CPP_DOUBLE_FLOAT
#ifdef _MSC_VER
#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
#endif
#ifdef __GNUC__
#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
#endif
#endif
#include <test_traits.hpp> // Note: include this AFTER the test-backends are defined
#if defined(TEST_MPF_50)
#include <boost/multiprecision/gmp.hpp>
#endif
#if defined(TEST_MPFR_50)
#include <boost/multiprecision/mpfr.hpp>
#endif
#if defined(TEST_MPFI_50)
#include <boost/multiprecision/mpfi.hpp>
#endif
#ifdef TEST_BACKEND
#include <boost/multiprecision/concepts/mp_number_archetypes.hpp>
#endif
#ifdef TEST_CPP_DEC_FLOAT
#include <boost/multiprecision/cpp_dec_float.hpp>
#endif
#ifdef TEST_FLOAT128
#include <boost/multiprecision/float128.hpp>
#endif
#ifdef TEST_CPP_BIN_FLOAT
#include <boost/multiprecision/cpp_bin_float.hpp>
#endif
#ifdef TEST_CPP_DOUBLE_FLOAT
#include <boost/multiprecision/cpp_double_fp.hpp>
#endif
#include <array>
#include <ctime>
#include <random>
template<typename FloatType> auto my_zero() -> FloatType&;
template<typename FloatType> auto my_one() -> FloatType&;
template <class T>
void test()
{
std::cout << "Testing type " << typeid(T).name() << std::endl;
unsigned max_err = 0;
BOOST_IF_CONSTEXPR (std::numeric_limits<T>::is_specialized && (std::numeric_limits<T>::max_exponent10 > 4000))
{
using table_data_array_type = std::array<const char*, 51u>;
static const table_data_array_type table_data =
{{
"1.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"9.47747587596218770242116751705184563668845029215054154915126374673142219159548534317576897266130328412495991561490384353e76",
"8.98225489794452370997623936390755615068333094834545092387689795875746440121970819499035111276893290879203289092353747850e153",
"8.51291041070124257524798251795398355552294928156627848633073113916721592074889256105483993631579761345100284245144410506e230",
"8.06809030516483860484254925989129017112482132468761563276276594763374886826841745433660192438855214332469192411759402790e307",
"7.64651312322841630493169711336894888932951818957138997327518186691187347879142222644283389432604713409023263917264358401e384",
"7.24696436606255985380192585665173794455118215150711210905481870053193336336731228464367470327868286988180495111406609690e461",
"6.86829299533155197480610865771404565313986987801060270120621935139741577246731459024227828759564450034267891072352816870e538",
"6.50940811722948585242669672360741252715012399316164518226061001845519670701239429603657927628755169479689062519606799624e615",
"6.16927583978348964454665652571294215251327375137123272041877979478545511090085756858225302357977159539777447847855503405e692",
"5.84691629437043896753869572004324228849833391140408095171257918435296982661233664069534601413835876272500275725690968474e769",
"5.54140081286660645835370762406928689330724181979654545550204201113926269281603301564114980528619942840737770415885783439e846",
"5.25184925229805200184933663459660562493261505058724212670923083643709964294855282715531768162298567379648573804433968486e923",
"4.97742745928448409225535325233998957076879979440190164347796593390995994951755710667491911026476108957070504003155645761e1000",
"4.71734486697204622371883518659702954552385115723942808636490157561056417525827884479573988899517566587636669779645610803e1077",
"4.47085221753216236037602345430121605512330975424643767098987010800161616413051148037751552110081034066081309007796182114e1154",
"4.23723940366531198300986713567588008777043812458400705569721660157434941774066620870256745107265536124077734836797938268e1231",
"4.01583342289144005397455901781647949754375366066998182220342540048111140676724909947493787596336610499122085983712119281e1308",
"3.80599643873362813900306284477369187319506389058898599816705625750135796510808933786432614186155972485637939057212164098e1385",
"3.60712394320959592074309301816510372687695286650188776957291994751966018917404878612237961367128638199290387601511358836e1462",
"3.41864301533745457066062991907289263038319874930395315315257927161138360206596116102724713069518697248463965164712972907e1539",
"3.24001067063873569456703204286462007769933831045558617578289414699244767403736057931834775727420762410328297596596814910e1616",
"3.07071229688386868087623659761166306563170839771162347830514606977592027644137144160294469813988158463967740978461420862e1693",
"2.91026017157373047094077218552378456052150304677863670611408570458991015300131731261787644801415538043027268185097710615e1770",
"2.75819205688636078700279174380111581147323147951670302427494196210176478494486073721584055059489736040565979466551070179e1847",
"2.61406986804110104534167739704643351039975992759905579635058824027507742375380077276380178376470686987855503581867681046e1924",
"2.47747841124391945459619002346303925269640785743990333362087223895627681769816204236257960940497519376881830373722711456e2001",
"2.34802418757813746316913800667907927718925648696508255347624141597281474683823345136640610924639820192825966082309575303e2078",
"2.22533425939475124828943430510333464605535146852848680647615867629953075390889821397228584866395924176189346073006180260e2155",
"2.10905517593659363154553947631071808925462553114068144748077359132255993441363479041540672158497404660986163617828972963e2232",
"1.99885195510122536266653916064141606295420554580140619900425370702471778604391774578696867899999534265169574306808906810e2309",
"1.89440711840917173277691572886942144916664047407963356271198286654087884646102070148271284410118233470318337745546895603e2386",
"1.79541977639739687088375911648976940254141946934175300605485966288703931992861387257771264702798405630917098672594899744e2463",
"1.70160476180317540861346545791118106171203487587101437710693054174454895160403997508137760007058856854991413121389834429e2540",
"1.61269180804119796097157014527479883521656118500417752963675677684343588976915851637637232001139108420659882326614772004e2617",
"1.52842477060722969066998464046690349841548269556677423378408183476489015878816585045578141383463708674469365281537792914e2694",
"1.44856088916530600122626623629347336702026699647293500058111037526381692645547938577338582002157148103479049071921438452e2771",
"1.37287008819265239873777879432333192404914357037749380145412895230166352318128978403808382142784030558123748263528360645e2848",
"1.30113431416759441771790128053911040907207490879890145597562380328956450092799014856149474809345424672958343296615764490e2925",
"1.23314690739099822369963411660419632130352733806319401863570442920347696015409870236230656305563674376063778482449716744e3002",
"1.16871200663155636468514484039368694043851858077879103221831997264419096417014996945143145495038265243932745953706526253e3079",
"1.10764398487979357804590117089134596938734185016144401218934115168561552640448889215089150481162977776214124397487013110e3156",
"1.04976691458528698318220729857405616816444374000182094405930946710168752954926612218474430081526312018810817657409158490e3233",
"9.94914060836531582868347569174220216007647278536863127198023584205669825317884219144692385409156165042162234017403353704e3309",
"9.42927401023380446961314339401657458785389811652244742482194123119943160577946366372207045050095290781679375214307398844e3386",
"8.93657169598281164656322298275337750103095739790107943666668184304335665562867744740310577868880098719252549186849812451e3463",
"8.46961426624835911826517103631490619655296714141872141145089865045804196205328364155921945616925875458926717336478525196e3540",
"8.02705648870740089929294815816002943860908317454595055392168733404583122074223427054310572378841634984243492063192095337e3617",
"7.60762342267101369970765191988545810374824800500875923752736467467657167098026707905341603949108433696304383346239333297e3694",
"7.21010674617694221027190468649359000420209460539838589305387835463807416706224777302997789297329446308541513638035437482e3771",
"6.83336127500041943234365059231968669406267422759442985746460610830503287734479988530512309065240678799786759250323660701e3848",
}};
const T pi = static_cast<T>("3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609");
for (unsigned k = 0u; k < static_cast<unsigned>(std::tuple_size<table_data_array_type>::value); ++k)
{
T val = exp(sqrt((pi * (100u * k)) * (100u * k)));
T e = relative_error(val, T(table_data[k]));
unsigned err = e.template convert_to<unsigned>();
if (err > max_err)
{
max_err = err;
}
val = exp(-sqrt((pi * (100u * k)) * (100u * k)));
e = relative_error(val, T(1 / T(table_data[k])));
err = e.template convert_to<unsigned>();
if (err > max_err)
{
max_err = err;
}
}
std::cout << "Max error table_data was: " << max_err << std::endl;
#if defined(BOOST_INTEL) && defined(TEST_FLOAT128)
BOOST_TEST(max_err < 40000);
#elif defined(TEST_CPP_BIN_FLOAT)
BOOST_TEST(max_err < 6200);
#else
BOOST_TEST(max_err < 5000);
#endif
} // (std::numeric_limits<T>::max_exponent10 > 4000)
using std::ldexp;
using exact_data_pair_type = std::array<T, 2>;
using exact_data_array_type = std::array<exact_data_pair_type, 12>;
static const exact_data_array_type exact_data =
{{
{{ldexp(1.0, -50), static_cast<T>("1.000000000000000888178419700125626769357944978675730736309709508287711059579809241499236575743374705946980126761002249532899810120773330275600867188192232364653350140592709328919189811425580736404494785")}},
{{ldexp(1.0, -20), static_cast<T>("1.00000095367477115374544678824955687428365188553281789775169686343569285229334215539516690752571791280462887427635269562079697496032436580742164524046357050365736415701568566320292733574692386949329504")}},
{{ldexp(1.0, -10), static_cast<T>("1.00097703949241653524284529261160650646585162918174419940186408264916250428896869173656853690882467186075613761065459260696969179898943231122954769049191889764955875334240964352999872451396042953452219")}},
{{0.25, static_cast<T>("1.28402541668774148407342056806243645833628086528146308921750729687220776586723800275330641943955356890166283174967968730585475423604648842750177989872959231004569930548795441439028562847893962382677678")}},
{{0.5, static_cast<T>("1.64872127070012814684865078781416357165377610071014801157507931164066102119421560863277652005636664300286663775630779700467116697521960915984097145249005979692942265909840391471994846465948924489686891")}},
{{0.75, static_cast<T>("2.11700001661267466854536981983709561013449158470240342177913303081098453336401282000279156026661579821888590471901551426235852033897220601942873096478507538156877637403469865756763918374951675146515683")}},
{{10, static_cast<T>("22026.4657948067165169579006452842443663535126185567810742354263552252028185707925751991209681645258954515555010924578366524232916065228951662224801377289728734855778378472751954806100958814170558886579")}},
{{10.5, static_cast<T>("36315.5026742466377389120269013166179689315579671275857607480190550842856628099187749764427758174866310742771977376827511779240563292392413797025035252944088473059613508585937585174897482367249804575829")}},
{{25, static_cast<T>("7.20048993373858725241613514661261579152235338133952787362213864472320593107782569745000325654258093194727871848859163683530731259683905547347259346394203424381962487428148616548084393082148632398178103e10")}},
{{31.25, static_cast<T>("3.72994612957188849046766396046821396700589012875701157893019118883826370993674081486706667149871508642909416337810227575115729423667289322729813729072376711271966343652718317681492250090327804073781915e13")}},
// N[Log[39614081257132168796771975168], 201]
{{static_cast<T>("65.8489821531948043946370515385267739671725127642242491414646009018723940871209979825570160646597753164901406969542151447001244223970224029181037214053322163834191192286952863430791686692697089797567183"), static_cast<T>("39614081257132168796771975168.0")}},
// N[Log[19807040628566084398385987584], 201]
{{static_cast<T>("65.1558349726348590852198194170685973990970126298639938873439208923790004651513032669511527376633566289481392159336444589664389021612642723610710506536971404214883916578669149078888616306458173062855949"), static_cast<T>("19807040628566084398385987584.0")}},
}};
max_err = 0;
for (unsigned k = 0u; k < static_cast<unsigned>(std::tuple_size<exact_data_array_type>::value); ++k)
{
T val = exp(exact_data[k][0]);
T e = relative_error(val, exact_data[k][1]);
unsigned err = e.template convert_to<unsigned>();
if (err > max_err)
{
max_err = err;
}
val = exp(-exact_data[k][0]);
e = relative_error(val, T(1 / exact_data[k][1]));
err = e.template convert_to<unsigned>();
if (err > max_err)
{
max_err = err;
}
}
std::cout << "Max error exact_data was: " << max_err << std::endl;
BOOST_TEST(max_err < 60);
BOOST_IF_CONSTEXPR (!boost::multiprecision::is_interval_number<T>::value)
{
std::mt19937_64 gen { };
gen.seed(static_cast<typename std::mt19937_64::result_type>(std::clock()));
std::uniform_real_distribution<float>
dist
(
static_cast<float>(1.01L),
static_cast<float>(1.04L)
);
for (int index = 0; index < 8; ++index)
{
static_cast<void>(index);
const T val_zero { ::my_zero<T>() * dist(gen) };
const T exp_zero = exp(val_zero);
BOOST_CHECK(exp_zero == ::my_one<T>());
}
BOOST_IF_CONSTEXPR (std::numeric_limits<T>::is_specialized)
{
for (int index = 0; index < 8; ++index)
{
static_cast<void>(index);
const T val_one(static_cast<int>(::my_one<T>() * dist(gen)));
const T exp_one = exp(val_one);
BOOST_CHECK_CLOSE_FRACTION(exp_one, boost::math::constants::e<T>(), std::numeric_limits<T>::epsilon() * 4);
}
}
T bug_case = -1.05 * log((std::numeric_limits<T>::max)());
for (unsigned i = 0U; bug_case > -20 / std::numeric_limits<T>::epsilon(); ++i, bug_case *= 1.05)
{
static_cast<void>(i);
BOOST_IF_CONSTEXPR (std::numeric_limits<T>::has_infinity)
{
BOOST_CHECK_EQUAL(exp(bug_case), 0);
}
else
{
BOOST_CHECK_LE(exp(bug_case), (std::numeric_limits<T>::min)());
}
}
BOOST_IF_CONSTEXPR (::has_poor_exp_range_or_precision_support<T>::value)
{
bug_case = log(T(1) / (std::numeric_limits<T>::min)()) / -1.0005;
}
else
{
bug_case = log((std::numeric_limits<T>::max)()) / -1.0005;
}
for (unsigned i { 0U }; i < 20U; ++i, bug_case /= static_cast<T>(1.05L))
{
static_cast<void>(i);
BOOST_CHECK_GE(exp(bug_case), (std::numeric_limits<T>::min)());
}
}
}
int main()
{
#ifdef TEST_BACKEND
test<boost::multiprecision::number<boost::multiprecision::concepts::number_backend_float_architype> >();
#endif
#ifdef TEST_MPF_50
test<boost::multiprecision::mpf_float_50>();
test<boost::multiprecision::mpf_float_100>();
#endif
#ifdef TEST_MPFR_50
test<boost::multiprecision::mpfr_float_50>();
test<boost::multiprecision::mpfr_float_100>();
#endif
#ifdef TEST_MPFI_50
test<boost::multiprecision::mpfi_float_50>();
test<boost::multiprecision::mpfi_float_100>();
#endif
#ifdef TEST_CPP_DEC_FLOAT
test<boost::multiprecision::cpp_dec_float_50>();
test<boost::multiprecision::cpp_dec_float_100>();
#ifndef SLOW_COMPILER
// Some "peculiar" digit counts which stress our code:
test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<65> > >();
test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<64> > >();
test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<63> > >();
test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<62> > >();
test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<61, long long> > >();
test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<60, long long> > >();
test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<59, long long, std::allocator<char> > > >();
test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<58, long long, std::allocator<char> > > >();
// Check low multiprecision digit counts.
test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<9> > >();
test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<18> > >();
#endif
#endif
#ifdef TEST_FLOAT128
test<boost::multiprecision::float128>();
#endif
#ifdef TEST_CPP_BIN_FLOAT
test<boost::multiprecision::cpp_bin_float_50>();
test<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<35, boost::multiprecision::digit_base_10, std::allocator<char>, long long> > >();
#endif
#ifdef TEST_CPP_DOUBLE_FLOAT
test<boost::multiprecision::cpp_double_float>();
test<boost::multiprecision::cpp_double_double>();
test<boost::multiprecision::cpp_double_long_double>();
#if defined(BOOST_MP_CPP_DOUBLE_FP_HAS_FLOAT128)
test<boost::multiprecision::cpp_double_float128>();
#endif
#endif
return boost::report_errors();
}
template<typename FloatType> auto my_zero() -> FloatType&
{
using float_type = FloatType;
static float_type my_val_zero(0);
return my_val_zero;
}
template<typename FloatType> auto my_one() -> FloatType&
{
using float_type = FloatType;
static float_type my_val_one(1);
return my_val_one;
}
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