400 lines
42 KiB
C++
400 lines
42 KiB
C++
///////////////////////////////////////////////////////////////
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// Copyright 2011 John Maddock.
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// Copyright Christopher Kormanyos 2002 - 2011, 2021 - 2023.
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// Distributed under the Boost
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// Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at https://www.boost.org/LICENSE_1_0.txt
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//
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// This work is based on an earlier work:
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// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations",
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// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469
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#ifdef _MSC_VER
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#define _SCL_SECURE_NO_WARNINGS
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#endif
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#include <array>
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#include <boost/detail/lightweight_test.hpp>
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#include "test.hpp"
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#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)
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#define TEST_MPF_50
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//# define TEST_MPF
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#define TEST_BACKEND
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#define TEST_CPP_DEC_FLOAT
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#define TEST_MPFI_50
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#define TEST_FLOAT128
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#define TEST_CPP_BIN_FLOAT
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#ifdef _MSC_VER
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#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
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#endif
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#ifdef __GNUC__
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#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
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#endif
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#endif
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#if defined(TEST_MPF_50)
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#include <boost/multiprecision/gmp.hpp>
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#endif
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#if defined(TEST_MPFR_50)
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#include <boost/multiprecision/mpfr.hpp>
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#endif
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#if defined(TEST_MPFI_50)
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#include <boost/multiprecision/mpfi.hpp>
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#endif
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#ifdef TEST_BACKEND
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#include <boost/multiprecision/concepts/mp_number_archetypes.hpp>
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#endif
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#ifdef TEST_CPP_DEC_FLOAT
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#include <boost/multiprecision/cpp_dec_float.hpp>
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#endif
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#ifdef TEST_FLOAT128
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#include <boost/multiprecision/float128.hpp>
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#endif
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#ifdef TEST_CPP_BIN_FLOAT
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#include <boost/multiprecision/cpp_bin_float.hpp>
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#endif
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template <class T>
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struct has_poor_large_value_support
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{
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static const bool value = false;
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};
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#ifdef TEST_CPP_DEC_FLOAT
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template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
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struct has_poor_large_value_support<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >
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{
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static const bool value = true;
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};
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#endif
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#ifdef TEST_CPP_BIN_FLOAT
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template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
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struct has_poor_large_value_support<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >
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{
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static const bool value = true;
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};
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#endif
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template <class T>
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void test()
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{
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std::cout << "Testing type " << typeid(T).name() << std::endl;
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const auto cos_of_zero = T(cos(T(0)));
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BOOST_CHECK_EQUAL(cos_of_zero, 1);
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static const std::array<const char*, 101u> data =
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{{
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// Table[N[Cos[(EulerGamma (50 (k - 50))) + (1/3)], 101], {k, 0, 100, 1}]
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// https://www.wolframalpha.com/input?i=Table%5BN%5BCos%5B%28EulerGamma+%2850+%28k+-+50%29%29%29+%2B+%281%2F3%29%5D%2C+101%5D%2C+%7Bk%2C+0%2C+100%2C+1%7D%5D
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"-0.75522374473812163631247515025564476422080272582805459124567972288992315002544650231456719260290393448",
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"+0.99177424050987078305718234392165209340174111849152986876930620518345872463813104258276605250076220663",
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"-0.89689535276576538239644024438717681824282288472937517213933743060538230305159711263242684254310859234",
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"+0.50229354250194163406402444743126210856418051761353638078567538573056810464940493618249607403769334413",
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"+0.060163846517213110495287865058512375888082770374979708375285005467173639623078062471046383014515380996",
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"-0.60251578638607408174153719680359969947476728639803494484820646313503151632712613434560482463290488079",
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"+0.94352005308100229868799635617405658297966684706744151395996633902114927491997597132128885613329389184",
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"-0.96922043633697497987077257420678251646692088115397631948484267792712783259753785690156175358973573557",
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"+0.67102842696437132362827617078550998722111278607793021204511545683902259100708741304116648970083436434",
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"-0.14859330984974745992272920792717978661579314375359758114387480429193700838163076982617783925777397623",
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"-0.42349846002565357573365455360406295360291020120814581939274933215133262161146147516778593641957000198",
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"+0.85406625418854044598614364153638681043157422531602182215249899433267238156387976169098669141854998543",
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"-0.99922367919132422838657467493172243168181683868937611097856546175284000911167457842760193265495953203",
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"+0.81046228027046067495614314199303621444645130977947720666442275111980794261672954029491798338934451875",
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"-0.35086201203716198404328235709545190783118545884247873839607445427060857629766360107570120021791028545",
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"-0.22598871058263736136516291182461668924243911095074926945449406494728550496842048843097143688103987908",
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"+0.72731892059924520594527209903849754939694753641298338102456622953608055530121553480066103566210034169",
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"-0.98559496402477645306083135240176869391975635559119525068139061020445764612654272982720172292426927267",
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"+0.91450660375786130812133846970712948206225066805832917629074209522096757147701670666806677721715862998",
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"-0.53781002387352078753790249970598443140406130738935012929335126485714251196092676630650434978293588028",
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"-0.018610970479793824535307037396406173322070897066017309400218317442212007537213255858425537054901896002",
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"+0.56881258322305698577134931632431934991811068305525973179026972435784678522446841874188003459725604730",
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"-0.92892940036126409890648687321813757912651437960485020765259774993199116136800989769046446194331809685",
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"+0.97861821290317516082616722229830324093528716301944391082069364731686136547408498003774673683179652478",
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"-0.70127410025725103160150311578948263037084041007140675810945025654503083857262818357789579087591073306",
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"+0.18957943359370310949801083045314453042403073680869382856983464079803868643616706133133497219616261998",
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"+0.38546855707929266664330738987106107335039407316978720671565144595988915060029219518206727857702464106",
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"-0.83170133858547559325384069672828458256943495557617267420842105366092894324362767728660335424583663624",
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"+0.99999761936646980659302392326222396230076214076136855560607516508271413544520473671424617757874760592",
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"-0.83411644224780740443802393353020152783160510191961705252957863713647472470375365559904177259187032448",
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"+0.38949168928016399258808272596658145954990693720386670813704609135112298719325919417196919969498883218",
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"+0.18529271614660048029315220499213983006230385399299594837689217603034218043881070792505299960141731679",
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"-0.69815632531344755495700074773208771239898066007179029522226572749684739033568507165044356992389239467",
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"+0.97771127304805875096302055471671824364193338048399119877771520276962441938659312922663310577377347126",
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"-0.93053637517160684333270118579141243377979081347694605522369074735665128048522422922379139880141336351",
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"+0.57239645666339138305164823585263582086346745852115860611744965932539674466112705167914143310030833324",
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"-0.022974089983222970830270121659136692983063119181552057636409006089581052645850719938940036838401762616",
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"-0.53412571796227096080994662710632991361380393795391666637696090635450395630095712094676329023219063753",
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"+0.91273232635340845454758777790750127904169646034026720933263598021195491604840880331172364189164448082",
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"-0.98632364005128638348610546126594143395327821574637246152782508176423353395239564173232123321538804827",
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"+0.73030704237484385669793900616084298051587357008524403352896223441031971226523011713445590901246148922",
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"-0.23023771279124249360719018936374840860483418487190460124805174881167754482919756584350885282964064996",
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"-0.34677205353255107074270940867264936293128503186690652696555560490176129639151046331855509327353844213",
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"+0.80789814065962078162313696756687436253043490028550710874505170068001452327852828904563185936688869192",
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"-0.99904223817102218283832272688639131610080353233814416591680405810797978558749707525581732505124214045",
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"+0.85632814540204599001582879323425306505411102223821276435786962913932902973605403140120634952390573031",
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"-0.42744780861773083218365996941251378635523098677286723863217304183495948410925049529229414119217940065",
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"-0.14427629029388624828563673013117761585712703183837121638265706309202788675650509211809621258800717782",
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"+0.66778639050003757770042983790178833901857696290038360580016134476447713018265947477815538331712639770",
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"-0.96813680104745915791757369634017171023781067151805502453542500434184038180057018467751587787337527038",
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"+0.94495694631473766438828400767588060784585269956514073767764573375009956219650036482442815880569855659",
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"-0.60599302967180876433192089403903382676733032699457512605380116754407375824151847505870667726411990809",
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"+0.064519420766880040668086393166826714652900698681390119541316116106285520418852040768474032966065220233",
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"+0.49851517548389238812231814352883990560131103141543242099327299178614042214389615971698396067885275938",
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"-0.89495684107033980596249111108748935211258747875381139757010736656960740465630823081614003389578616333",
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"+0.99232339258974947226158529887397235761590778641642735410948555747216288771085708807697173754437759902",
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"-0.75807704591036921414806386154596439746990180773273952751370978554489147303459869793293976479662356164",
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"+0.27049783604387208956248334636803857985987733007195915812457458733890546430548186222577271587703639893",
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"+0.30747586823528866168770660981205288634457626510884032545099935495924822143910388598536053259197272980",
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"-0.78269782388783280482361748835867896803255997742596959775194684920345165036689112142387879582846627403",
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"+0.99635918777003290709807818665535559293474138203590483515902518300402312609399774335339576355333952179",
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"-0.87705897846879139053941506456466256927752398912716371586342594693678656106829528188553032627321900324",
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"+0.46466473156528608535236715320072651871225412877113468500031440934682825703791733051544707991905349587",
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"+0.10301036377512723883847711006256865159971781034753925458956857734851463788769146246092185776635806217",
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"-0.63626163566134131474313450299794745201479025797366608278399127639461917220225941446148571679304922282",
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"+0.95688810540143750738270690895076937926058404500815546016423545895252255902306584174530871277725113912",
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"-0.95774337932603188692331901043750504222894892926477655472723219653630628365847577870373636148725970599",
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"+0.63854164348877737693852565104404930720866348110108520102588257405131332886001427789504420806630591991",
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"-0.10595317647176727636297995805751591205912221750713937829868315960580969943647593100213172740088126842",
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"-0.46204253800665223955545454438703785831518341476259256062152846465385993424324136704174839658870857065",
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"+0.87563368411181055059238471728955721925243516244878366366341074667761930173559838380680631168677342978",
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"-0.99660709499358106945251812531715152455888413445624154722189389121490103660209506826260807242464254862",
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"+0.78453608748892561465296993626136148899426878839890563401365975442481908889851258205156656425919578781",
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"-0.31029018049432190022601573322920317880148331049704223634856275455292554678122209723430782687385842749",
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"-0.26764795708230086746325105426297564262004630406879417208512648033578386950681688131973949509628569692",
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"+0.75614396782019777225973639390917818172269805798719508815698039477125953731450344867748759490583650876",
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"-0.99195310803094461279631432580877677399015713092500048795389926800713260997627477770848085391297670965",
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"+0.89627309109004451865841185971014320250257719291218301784622876930391012650997775213580143671067644992",
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"-0.50107809794941083740383264238863411430805627677286465718420205008190236166779077055406083046177226456",
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"-0.061566298808816960775765112659677250214449360721731762985376022632705898105308711264437732575923183725",
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"+0.60363657735938799049962139931230574782532058104694186882410982905431042314299584563647039422322732601",
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"-0.94398463876607540862169012201410217551959626821280074360146361680269973765925720214764017351637782709",
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"+0.96887356230098908018012044617847428126677191495505927930545620653954823087945830214113311025316456165",
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"-0.66998601096684128132696349534681627659808566271749039790384265051291248269448698253804864759632904293",
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"+0.14720370464810205394666752863705707879664514114344071425531921187048125868439366797325106243253408120",
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"+0.42477087859213565028850083700927112079154974120724572930357442458726728780667660495786723233601909925",
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"-0.85479627150564771610785173189883706686353873834567424296532543518652621816359548381683573703506486761",
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"+0.99916733934703343498941571697876191831435191797013968660764149081333476511095596166993279378639305054",
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"-0.80963841081553687650244093926565278259801002131655992334985017661642748628153083132625615583968346335",
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"+0.34954593222712704243773218900662710602266514803559232616137133889665523090852229527293791807869966914",
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"+0.22735719549545777590639612962755842542265259235462442701733905212357623140678183504162894293905368751",
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"-0.72828249271680441204059068763641241558372744757192990213682578184830485204394460015577981511832535424",
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"+0.98583161849974998971487434912965720276095235749163612899712018135045118998280333947926532890806156807",
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"-0.91393725581113006404986951724190889152954788855325137557250209500165949001753443894409978034652860192",
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"+0.53662493720753194861847829399392196230738295128876969910948236088619178011187682842129855738933292994",
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"+0.020015765672806574062770584104635787267073042966637437669478451568439132509223934385280964429092007474",
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"-0.56996763493902980612150959017737976930155662510050132522665741443022870977912293609746998693648905727",
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"+0.92944871543510228552616355260521062687374496892416215528634792079607107380916491379221669185331365082",
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"-0.97832824753051029640282164383239113461178867037876402416828361520985847551699363184953653080593019924",
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"+0.70027175455988286614347083279168308367959753235381072861043358026854887124970773344589632560717267396",
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"-0.18819966970613688381679196216129711654052637441272557548297575087510716490244958558866873725348050513"
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}};
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static const T euler_gamma = static_cast<T>("5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1");
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static const T one_third = static_cast<T>(static_cast<T>(1) / 3);
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std::uintmax_t max_err = UINTMAX_C(0);
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for (unsigned k = 0; k < data.size(); k++)
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{
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const auto k_factor = static_cast<long>(50L * (static_cast<long>(k) - 50L));
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const T arg = T((euler_gamma * k_factor) + one_third);
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T val = cos(arg);
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T e = relative_error(val, T(data[k]));
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unsigned err = e.template convert_to<unsigned>();
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if (err > max_err)
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max_err = err;
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val = cos(-arg);
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e = relative_error(val, T(data[k]));
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err = e.template convert_to<unsigned>();
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if (err > max_err)
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max_err = err;
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}
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std::cout << "Max error was: " << max_err << std::endl;
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BOOST_TEST(max_err < UINTMAX_C(1000000));
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static const std::array<const char*, 51u> near_one =
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{{
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"0.001103662615143147017601393734232421549156847219973314118949247990939859507971857976111288683988415478257878902917354105871236439563170045857810738102729287303674642020538722348587741395785016549139854168605590336633274890874911975139498047488076101124170425114828336211817830671418321600962996502656221412102902998671173649312277667706874059520046508702908872747388744526457997404065469953155187340837",
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|
|
"0.087035466793942804442393380943589773874807384137701777807755858606555806090045313793349743667697666495784828540247587627381581545620918795107877715086227932192756144780086856515641298195558204484728115519445514732755572178929839231921546119143469647706999890259163924570037168105911942268212237224359201159897493303064534985539474450028748960081579369980283792804593122976296597796047722827878891322393",
|
|
"0.088940096619320340510800454481897179643787714504988904779549430422905882044782054375828906100456879992313640144934242418129400679706865644316664458061953684856607341811667576418163339843372041295322709797007871604740491453013916791024918954258557372755707588171502529270934617054742841996068375532958173787119651672031238405892943090742861150287144368470297356054911834742041692715934237148148936307154",
|
|
"0.090844401286964974994199780075024285173534240616972938308566124002318176156233343333797652771250228033597767340846476094210813299723066344955542455246897302945908336756464582189829335315055318509171623072382573656172991307091055717376996812421994002305994837615827430425975713541786272473174908117299253875064746541808768776888139494200307162476704515967971265236163183394620211890252072718610942571965",
|
|
"0.092748373834894294768837248013614869545920040757666771889792264347367335922283987944081370356939214799510822558638935486112190359701790662792925773186897671244831971450474952036618937833706899006048469791213129922302798462311426294239282200248625552430083292818594731518350634587677158329361662244008606299358410273467156168469937529868888478684257396004386633746334360279683178784117372066095688934486",
|
|
"0.094652007302340089278624856973167138217258137565762699413364163993950641989798336903224059425798872308451866930780842878435503832366316245159154044350517727312654980455290163514021860802028251981954724580292247887851185639950862672925642859475325430465650514258094310141033116303195908372018392349011340787373492402788283020594141795669947097771918542864972570255253465754192708165241608041715996375567",
|
|
"0.09655529472977379853549858833033074225823562054271495313739665642376685099661084023094270272485976247900824483810911634635819558334630910267353320029261330296977292720266655308513559530586843550229208517388789783011887450865488554143475302590353915732321663418057567573042594801866258948380684000769091353165879953111046260532796891917772727185993569684246844052518121013717183610828519193371796413317",
|
|
}};
|
|
|
|
T half_pi = static_cast<T>("1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399107404325664115332354692230477529111586267970406424055872514205135096926055277982231147447746519098221440548783296672306423782411689339158263560095457282428346173017430522716332410669680363012457064");
|
|
|
|
max_err = 0;
|
|
for (unsigned k = 0; k < near_one.size(); k++)
|
|
{
|
|
T val = cos(half_pi - (euler_gamma + k) / 523);
|
|
T e = relative_error(val, T(near_one[k]));
|
|
unsigned err = e.template convert_to<unsigned>();
|
|
if (err > max_err)
|
|
max_err = err;
|
|
val = cos(-half_pi + (euler_gamma + k) / 523);
|
|
e = relative_error(val, T(near_one[k]));
|
|
err = e.template convert_to<unsigned>();
|
|
if (err > max_err)
|
|
max_err = err;
|
|
}
|
|
std::cout << "Max error was: " << max_err << std::endl;
|
|
#if defined(BOOST_INTEL) && defined(TEST_FLOAT128)
|
|
BOOST_TEST(max_err < 8000);
|
|
#else
|
|
BOOST_TEST(max_err < 750);
|
|
#endif
|
|
|
|
//
|
|
// Test with some exact binary values as input - this tests our code
|
|
// rather than the test data:
|
|
//
|
|
static const std::array<std::array<T, 2>, 8> exact_data =
|
|
{{{{0.5, static_cast<T>("0.877582561890372716116281582603829651991645197109744052997610868315950763274213947405794184084682258355478400593109053993")}},
|
|
{{0.25, static_cast<T>("0.968912421710644784144595449494189199804134190287442831148128124288942561184523327264655202799685025510352709626116202617")}},
|
|
{{0.75, static_cast<T>("0.731688868873820886311838753000084543840541276050772482507683220220750082501569499540967562610201174960122884908227300721")}},
|
|
{{std::ldexp(1.0, -20), static_cast<T>("0.99999999999954525264911357034690133684385823577463126432241468890539365027135494672267164697779879113636143901797362388")}},
|
|
{{2, static_cast<T>("-0.416146836547142386997568229500762189766000771075544890755149973781964936124079169074531777860169140367366791365215728559")}},
|
|
{{5, static_cast<T>("0.283662185463226264466639171513557308334422592252215944930359066586151456767382702286176981668344573238827368717546699737")}},
|
|
{{10, static_cast<T>("-0.839071529076452452258863947824064834519930165133168546835953731048792586866270768400933712760422138927451054405350243624")}},
|
|
{{8.5, static_cast<T>("-0.60201190268482361534842652295699870029606776360435523539636606145572515876770619546025351418378467287262574566665150299")}}}};
|
|
max_err = 0;
|
|
for (unsigned k = 0; k < exact_data.size(); k++)
|
|
{
|
|
T val = cos(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 = cos(-exact_data[k][0]);
|
|
e = relative_error(val, exact_data[k][1]);
|
|
err = e.template convert_to<unsigned>();
|
|
if (err > max_err)
|
|
max_err = err;
|
|
}
|
|
std::cout << "Max error was: " << max_err << std::endl;
|
|
BOOST_TEST(max_err < 20);
|
|
|
|
BOOST_TEST(cos(T(0)) == 1);
|
|
#if defined(BOOST_INTEL) && defined(TEST_FLOAT128)
|
|
BOOST_TEST(fabs(cos(half_pi)) < 4 * std::numeric_limits<T>::epsilon());
|
|
#else
|
|
BOOST_TEST(fabs(cos(half_pi)) < std::numeric_limits<T>::epsilon());
|
|
#endif
|
|
|
|
#include "sincos.ipp"
|
|
max_err = 0;
|
|
for (unsigned k = 0; k < sincos.size(); k++)
|
|
{
|
|
T val = cos(sincos[k][0]);
|
|
T e = relative_error(val, sincos[k][2]);
|
|
unsigned err = e.template convert_to<unsigned>();
|
|
if (err > max_err)
|
|
max_err = err;
|
|
}
|
|
std::cout << "Max error was: " << max_err << std::endl;
|
|
BOOST_TEST(max_err < 20);
|
|
|
|
if (has_poor_large_value_support<T>::value)
|
|
{
|
|
T bug_value = 12 / std::numeric_limits<T>::epsilon();
|
|
for (unsigned i = 0; i < 20; ++i, bug_value *= 1.1)
|
|
{
|
|
BOOST_TEST(cos(bug_value) == 1);
|
|
}
|
|
}
|
|
}
|
|
|
|
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_COMPLER
|
|
// 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> > > >();
|
|
#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
|
|
return boost::report_errors();
|
|
}
|