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e70f53e670a68ac704ea2382261e855bbe7ca29d
math/test/test_polygamma.hpp
jzmaddock e70f53e670 [Polygamma] Fix issues with small negative arguments for x. 
Tidy up a couple of cosmetic coding issues.
2014-10-31 18:51:14 +00:00

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// Copyright John Maddock 20
// Copyright Paul A. Bristow 2007, 2009
// 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)
#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
#include <boost/math/concepts/real_concept.hpp>
#include <boost/math/special_functions/math_fwd.hpp>
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp>
#include <boost/test/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"
#ifndef SC_
#ifndef BOOST_FLOAT128_C
#define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L))
#else
#define SC_(x) static_cast<typename table_type<T>::type>(BOOST_FLOAT128_C(x))
#endif
#endif
template <class Real, class T>
void do_test_polygamma(const T& data, const char* type_name, const char* test_name)
{
typedef Real value_type;
typedef value_type(*pg)(int, value_type);
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
pg funcp = boost::math::polygamma<value_type>;
#else
pg funcp = boost::math::polygamma;
#endif
boost::math::tools::test_result<value_type> result;
std::cout << "Testing " << test_name << " with type " << type_name
<< "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
//
// test polygamma against data:
//
result = boost::math::tools::test_hetero<Real>(
data,
bind_func_int1<Real>(funcp, 0, 1),
extract_result<Real>(2));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::polygamma", test_name);
std::cout << std::endl;
}
template <class T>
void test_polygamma(T, const char* name)
{
typedef typename table_type<T>::type value_type;
boost::array<boost::array<value_type, 3>, 384> data =
{ {
{ 1, SC_(0.1250000), SC_(65.388133444988034473142999334395961) }, { 1, SC_(2.250000), SC_(0.55732915450711073927131911933522402) }, { 1, SC_(4.375000), SC_(0.25666408805722660683906428275458774) }, { 1, SC_(6.500000), SC_(0.16628453574995823763989666631218566) }, { 1, SC_(8.625000), SC_(0.12292237374423990274075995315923687) }, { 1, SC_(10.75000), SC_(0.097483848201852104395946001854344927) }, { 1, SC_(12.87500), SC_(0.080764208092843621858393487209278638) }, { 1, SC_(15.00000), SC_(0.068938227847683806226155216756371670) }, { 1, SC_(17.12500), SC_(0.060132263162293455894576107399989891) }, { 1, SC_(19.25000), SC_(0.053320703915617277211139745531295189) }, { 1, SC_(21.37500), SC_(0.047895038036916716105500109226810942) }, { 1, SC_(23.50000), SC_(0.043471416266946770249685779030294199) }, { 1, SC_(25.62500), SC_(0.039795743807625238080963836217545550) }, { 1, SC_(27.75000), SC_(0.036693131333593477569076090983653779) }, { 1, SC_(29.87500), SC_(0.034039266877179098641898178094001935) }, { 1, SC_(32.00000), SC_(0.031743366520302090126581680438741427) }, { 1, SC_(34.12500), SC_(0.029737585673522726661363528635488348) }, { 1, SC_(36.25000), SC_(0.027970204614894933106878169214392067) }, { 1, SC_(38.37500), SC_(0.026401106865951764123858232364900665) }, { 1, SC_(40.50000), SC_(0.024998698201356741322280011143883922) }, { 1, SC_(42.62500), SC_(0.023737757818075642720991864115881164) }, { 1, SC_(44.75000), SC_(0.022597908441287364284087900916682571) }, { 1, SC_(46.87500), SC_(0.021562506914486557632388530071308920) }, { 1, SC_(49.00000), SC_(0.020617826354560516060031453062401102) }, { 1, SC_(51.12500), SC_(0.019752444228552790805040230288386135) }, { 1, SC_(53.25000), SC_(0.018956778300513446216011889734099110) }, { 1, SC_(55.37500), SC_(0.018222730375562878627773770314126276) }, { 1, SC_(57.50000), SC_(0.017543409716574620734228673575882677) }, { 1, SC_(59.62500), SC_(0.016912916093398919581541485278641593) }, { 1, SC_(61.75000), SC_(0.016326167985389235938281994221076159) }, { 1, SC_(63.87500), SC_(0.015778765341125640054231784371915358) }, { 1, SC_(66.00000), SC_(0.015266879048806385777045778219279459) }, { 1, SC_(68.12500), SC_(0.014787161242916062152535888615850260) }, { 1, SC_(70.25000), SC_(0.014336672004276912093324664070489886) }, { 1, SC_(72.37500), SC_(0.013912819061256593888508241399678441) }, { 1, SC_(74.50000), SC_(0.013513307879079644573772830117155790) }, { 1, SC_(76.62500), SC_(0.013136100107643257539226305043251166) }, { 1, SC_(78.75000), SC_(0.012779378799112389298746113446648982) }, { 1, SC_(80.87500), SC_(0.012441519142554280549428650598112729) }, { 1, SC_(83.00000), SC_(0.012121063720980953787190412456820037) }, { 1, SC_(85.12500), SC_(0.011816701495952671887865236708275449) }, { 1, SC_(87.25000), SC_(0.011527249880640584213306489206202069) }, { 1, SC_(89.37500), SC_(0.011251639384481213426240562514542477) }, { 1, SC_(91.50000), SC_(0.010988900409103388104670465071922664) }, { 1, SC_(93.62500), SC_(0.010738151851930343087942933225290955) }, { 1, SC_(95.75000), SC_(0.010498591235178571927709342934117247) }, { 1, SC_(97.87500), SC_(0.010269486127251686167359605922136260) }, { 1, SC_(100.0000), SC_(0.010050166663333571395245668465701423) },
{ 2, SC_(0.1250000), -SC_(1025.7533381181356825956689300565174) }, { 2, SC_(2.250000), -SC_(0.30373993753692033333796717884398989) }, { 2, SC_(4.375000), -SC_(0.065528725397877855792664680804766330) }, { 2, SC_(6.500000), -SC_(0.027587910706876798794117450572831562) }, { 2, SC_(8.625000), -SC_(0.015091062676061564388822078971884395) }, { 2, SC_(10.75000), -SC_(0.0094956196449265900776488965631791775) }, { 2, SC_(12.87500), -SC_(0.0065193261909178260169885198194705291) }, { 2, SC_(15.00000), -SC_(0.0047506027165515547467791223768191188) }, { 2, SC_(17.12500), -SC_(0.0036148020016626802195565448384834283) }, { 2, SC_(19.25000), -SC_(0.0028424250740909855631736845850335535) }, { 2, SC_(21.37500), -SC_(0.0022934967923297751145806065882712900) }, { 2, SC_(23.50000), -SC_(0.0018894667868625909895476094900477678) }, { 2, SC_(25.62500), -SC_(0.0015834924252652953218803111387922996) }, { 2, SC_(27.75000), -SC_(0.0013462349527320363170378913859580860) }, { 2, SC_(29.87500), -SC_(0.0011585598948326545653381467670779893) }, { 2, SC_(32.00000), -SC_(0.0010075567602140907392185110593117265) }, { 2, SC_(34.12500), -SC_(0.00088425886906787461365402045268994574) }, { 2, SC_(36.25000), -SC_(0.00078228136778540401396894643668418462) }, { 2, SC_(38.37500), -SC_(0.00069697797537723210697105880606724159) }, { 2, SC_(40.50000), -SC_(0.00062490237932923289658683588812998732) }, { 2, SC_(42.62500), -SC_(0.00056345469641484389456121935536309197) }, { 2, SC_(44.75000), -SC_(0.00051064374134295093656385520125286421) }, { 2, SC_(46.87500), -SC_(0.00046492369550612086723038302919171885) }, { 2, SC_(49.00000), -SC_(0.00042507970884222510504308867471824948) }, { 2, SC_(51.12500), -SC_(0.00039014637079445100439645401142194535) }, { 2, SC_(53.25000), -SC_(0.00035934868438211062777790080207505881) }, { 2, SC_(55.37500), -SC_(0.00033205871518117505559928737076624192) }, { 2, SC_(57.50000), -SC_(0.00030776333242771756953580263456220628) }, { 2, SC_(59.62500), -SC_(0.00028603991345613245802207114123372414) }, { 2, SC_(61.75000), -SC_(0.00026653784162151616772904552992231739) }, { 2, SC_(63.87500), -SC_(0.00024896427102287300629668349085350311) }, { 2, SC_(66.00000), -SC_(0.00023307306946180321476975587412226332) }, { 2, SC_(68.12500), -SC_(0.00021865615382096049855997233359992101) }, { 2, SC_(70.25000), -SC_(0.00020553664405312492990454318541834320) }, { 2, SC_(72.37500), -SC_(0.00019356341228034103704385457246984425) }, { 2, SC_(74.50000), -SC_(0.00018260671130395075946075978013398780) }, { 2, SC_(76.62500), -SC_(0.00017255464497899193114313963889049197) }, { 2, SC_(78.75000), -SC_(0.00016331030013937037094502788633900241) }, { 2, SC_(80.87500), -SC_(0.00015478940207215993505449988937898640) }, { 2, SC_(83.00000), -SC_(0.00014691838710034332570083901051760808) }, { 2, SC_(85.12500), -SC_(0.00013963280957351165370765015817038278) }, { 2, SC_(87.25000), -SC_(0.00013287601856558888563037791437997733) }, { 2, SC_(89.37500), -SC_(0.00012659805332837531702241737466058293) }, { 2, SC_(91.50000), -SC_(0.00012075471712784846612240303590084686) }, { 2, SC_(93.62500), -SC_(0.00011530679728326736002584104318350829) }, { 2, SC_(95.75000), -SC_(0.00011021940561565095981861374083495299) }, { 2, SC_(97.87500), -SC_(0.00010546141852085692313553484671110170) }, { 2, SC_(100.0000), -SC_(0.00010100499983334999700083300446059382) },
{ 3, SC_(0.1250000), SC_(24580.143419063566218511004446647010) },
{ 3, SC_(2.250000), SC_(0.32454400918839602279124382903505677) },
{ 3, SC_(4.375000), SC_(0.033289201205556512286673394063908247) },
{ 3, SC_(6.500000), SC_(0.0091336635043781405048050655353658508) },
{ 3, SC_(8.625000), SC_(0.0037008460120616755687668778806054328) },
{ 3, SC_(10.75000), SC_(0.0018484328773891268475922730275004208) },
{ 3, SC_(12.87500), SC_(0.0010519186241203463873018930415985105) },
{ 3, SC_(15.00000), SC_(0.00065447977828273734841733708901750530) },
{ 3, SC_(17.12500), SC_(0.00043447135395979214393136263736764201) },
{ 3, SC_(19.25000), SC_(0.00030297696415718385912539504824566570) },
{ 3, SC_(21.37500), SC_(0.00021961042047214603636739002880115737) },
{ 3, SC_(23.50000), SC_(0.00016422394665239820056068884910278128) },
{ 3, SC_(25.62500), SC_(0.00012599930135391694524067581601102767) },
{ 3, SC_(27.75000), SC_(0.000098773010741268191080883613389009048) },
{ 3, SC_(29.87500), SC_(0.000078857844307768334137453508928722671) },
{ 3, SC_(32.00000), SC_(0.000063955754777976299576673673574642423) },
{ 3, SC_(34.12500), SC_(0.000052583702941352521813139097855885393) },
{ 3, SC_(36.25000), SC_(0.000043755438122384003302367816109980192) },
{ 3, SC_(38.37500), SC_(0.000036797707573246758497786056137200200) },
{ 3, SC_(40.50000), SC_(0.000031240239710655936422248716017582946) },
{ 3, SC_(42.62500), SC_(0.000026747791378195202271687207455056302) },
{ 3, SC_(44.75000), SC_(0.000023076997706632396178157160717335565) },
{ 3, SC_(46.87500), SC_(0.000020048287815935784161580614536631137) },
{ 3, SC_(49.00000), SC_(0.000017527197874026635143654793647828466) },
{ 3, SC_(51.12500), SC_(0.000015411686998050652806770684541876757) },
{ 3, SC_(53.25000), SC_(0.000013623370966529973793708331754693666) },
{ 3, SC_(55.37500), SC_(0.000012101363299593660023105041673385376) },
{ 3, SC_(57.50000), SC_(0.000010797882726896889062768134787291884) },
{ 3, SC_(59.62500), SC_(9.6750769605707758334815857396558355e-6) },
{ 3, SC_(61.75000), SC_(8.7026966259856900409582330070865268e-6) },
{ 3, SC_(63.87500), SC_(7.8563716857343030149244371160376495e-6) },
{ 3, SC_(66.00000), SC_(7.1163203299934132027680033779014197e-6) },
{ 3, SC_(68.12500), SC_(6.4663719906627627544882175944382226e-6) },
{ 3, SC_(70.25000), SC_(5.8932210515208497328937862935232496e-6) },
{ 3, SC_(72.37500), SC_(5.3858517367657111634358444590928906e-6) },
{ 3, SC_(74.50000), SC_(4.9350912436686398240670814427342376e-6) },
{ 3, SC_(76.62500), SC_(4.5332598242018110991734569100539592e-6) },
{ 3, SC_(78.75000), SC_(4.1738947808706992483423293125251133e-6) },
{ 3, SC_(80.87500), SC_(3.8515312659502461861484363442184908e-6) },
{ 3, SC_(83.00000), SC_(3.5615270636518630626786644585266764e-6) },
{ 3, SC_(85.12500), SC_(3.2999216708248315372665461067377996e-6) },
{ 3, SC_(87.25000), SC_(3.0633223042636924720337703682152499e-6) },
{ 3, SC_(89.37500), SC_(2.8488111819903247190925375784544775e-6) },
{ 3, SC_(91.50000), SC_(2.6538697141941088454844912572034392e-6) },
{ 3, SC_(93.62500), SC_(2.4763162120667457234467192228222670e-6) },
{ 3, SC_(95.75000), SC_(2.3142544621402797124759791203351867e-6) },
{ 3, SC_(97.87500), SC_(2.1660310796121506708372890790676070e-6) },
{ 3, SC_(100.0000), SC_(2.0301999900013330334332872946449855e-6) },
{4, SC_(0.1250000), SC_(-786445.98543106378579320120709638297)}, { 4, SC_(2.250000), SC_(-0.51106863793373355822715252195899576) }, { 4, SC_(4.375000), SC_(-0.025241882074562753654505456518792508) }, { 4, SC_(6.500000), SC_(-0.0045259302803220607103496010172883494) }, { 4, SC_(8.625000), SC_(-0.0013596929106556359886012273921730071) }, { 4, SC_(10.75000), SC_(-0.00053930828860547053427689740051604949) }, { 4, SC_(12.87500), SC_(-0.00025445997266103206171225355293726865) }, { 4, SC_(15.00000), SC_(-0.00013519619187519276575068431301221388) }, { 4, SC_(17.12500), SC_(-0.000078306716822025065793290599586946118) }, { 4, SC_(19.25000), SC_(-0.000048430513924395561509999792045098081) }, { 4, SC_(21.37500), SC_(-0.000031536705873201397805285969259914559) }, { 4, SC_(23.50000), SC_(-0.000021407049050977062373311093992814121) }, { 4, SC_(25.62500), SC_(-0.000015036764178343754461565939319516893) }, { 4, SC_(27.75000), SC_(-0.000010869219781124567432001391245344089) }, { 4, SC_(29.87500), SC_(-8.0504604926168752698902834477348881e-6) }, { 4, SC_(32.00000), SC_(-6.0889806370027137702207132674152980e-6) }, { 4, SC_(34.12500), SC_(-4.6901011823268163094417546531023856e-6) }, { 4, SC_(36.25000), SC_(-3.6708283086618325558290000911536581e-6) }, { 4, SC_(38.37500), SC_(-2.9139932244650290336213711603586301e-6) }, { 4, SC_(40.50000), SC_(-2.3425302303691304543510535971847968e-6) }, { 4, SC_(42.62500), SC_(-1.9045296486050512642801504306671373e-6) }, { 4, SC_(44.75000), SC_(-1.5642760453399369047824852836708697e-6) }, { 4, SC_(46.87500), SC_(-1.2967233822729326645555539185332769e-6) }, { 4, SC_(49.00000), SC_(-1.0840030171141394983603065427611252e-6) }, { 4, SC_(51.12500), SC_(-9.1316643010960703020517255319750485e-7) }, { 4, SC_(53.25000), SC_(-7.7469609700462921021995856208285815e-7) }, { 4, SC_(55.37500), SC_(-6.6150474476547305805911346012045165e-7) }, { 4, SC_(57.50000), SC_(-5.6825133351570053043820949353677183e-7) }, { 4, SC_(59.62500), SC_(-4.9086620236193161135912086142572580e-7) }, { 4, SC_(61.75000), SC_(-4.2621666772058776224801114961267801e-7) }, { 4, SC_(63.87500), SC_(-3.7186839586672891333608898041067112e-7) }, { 4, SC_(66.00000), SC_(-3.2591301914111222705427951896642626e-7) }, { 4, SC_(68.12500), SC_(-2.8684217920848561693233665614958777e-7) }, { 4, SC_(70.25000), SC_(-2.5345451083204479337777798526354757e-7) }, { 4, SC_(72.37500), SC_(-2.2478626654835416271537021644553013e-7) }, { 4, SC_(74.50000), SC_(-2.0005909073946645851596541397664333e-7) }, { 4, SC_(76.62500), SC_(-1.7864035957298817513241281766878220e-7) }, { 4, SC_(78.75000), SC_(-1.6001281551287093216803849072235519e-7) }, { 4, SC_(80.87500), SC_(-1.4375113796429048125939526070340983e-7) }, { 4, SC_(83.00000), SC_(-1.2950373350296884735201964028079076e-7) }, { 4, SC_(85.12500), SC_(-1.1697848507486443027254417751822546e-7) }, { 4, SC_(87.25000), SC_(-1.0593152651055065213702117539700727e-7) }, { 4, SC_(89.37500), SC_(-9.6158345290200883062520858433963680e-8) }, { 4, SC_(91.50000), SC_(-8.7486689164653963817234101603388082e-8) }, { 4, SC_(93.62500), SC_(-7.9770879280803145900384972987304463e-8) }, { 4, SC_(95.75000), SC_(-7.2887226653828502529665531368895369e-8) }, { 4, SC_(97.87500), SC_(-6.6730319180606630829991063550458595e-8) }, { 4, SC_(100.0000), SC_(-6.1209999300119967012993094755881001e-8) },
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{ SC_(30.0), SC_(0.1250000), SC_(-2.6269370855717061268373196091559060e60) }, { SC_(30.0), SC_(2.250000), SC_(-3.2063201132225624894497621128724710e21) }, { SC_(30.0), SC_(4.375000), SC_(-3.5816122065666942298125086110013811e12) }, { SC_(30.0), SC_(6.500000), SC_(-1.6926495147567915305098150929608351e7) }, { SC_(30.0), SC_(8.625000), SC_(-2691.9893080722988179729741180559768) }, { SC_(30.0), SC_(10.75000), SC_(-3.0129827880548721952335149662772758) }, { SC_(30.0), SC_(12.87500), SC_(-0.011679541591944513522798667560485778) }, { SC_(30.0), SC_(15.00000), SC_(-0.00010699799160744992062995477402482814) }, { SC_(30.0), SC_(17.12500), SC_(-1.8412916811312822615145612742242341e-6) }, { SC_(30.0), SC_(19.25000), SC_(-5.1296809753659048984675389168991678e-8) }, { SC_(30.0), SC_(21.37500), SC_(-2.0897092756900426602247473552496515e-9) }, { SC_(30.0), SC_(23.50000), SC_(-1.1575741931670926101304469613657363e-10) }, { SC_(30.0), SC_(25.62500), SC_(-8.2634766034599236789755939810493909e-12) }, { SC_(30.0), SC_(27.75000), SC_(-7.2982420192371959627923444899651880e-13) }, { SC_(30.0), SC_(29.87500), SC_(-7.7259330615365968247618603604357394e-14) }, { SC_(30.0), SC_(32.00000), SC_(-9.5598830564651701596127591449043084e-15) }, { SC_(30.0), SC_(34.12500), SC_(-1.3549801683291963236022185422404195e-15) }, { SC_(30.0), SC_(36.25000), SC_(-2.1637420158752325246771018243486794e-16) }, { SC_(30.0), SC_(38.37500), SC_(-3.8399012944498044530335003629202925e-17) }, { SC_(30.0), SC_(40.50000), SC_(-7.4867790463777103523228388855693400e-18) }, { SC_(30.0), SC_(42.62500), SC_(-1.5882468053156791511681017429675896e-18) }, { SC_(30.0), SC_(44.75000), SC_(-3.6357619494056634364065401737558109e-19) }, { SC_(30.0), SC_(46.87500), SC_(-8.9173782150303341835362824820507660e-20) }, { SC_(30.0), SC_(49.00000), SC_(-2.3289849068324860513642836089935388e-20) }, { SC_(30.0), SC_(51.12500), SC_(-6.4424396179339080523684393804219419e-21) }, { SC_(30.0), SC_(53.25000), SC_(-1.8786312072016996388558435362347671e-21) }, { SC_(30.0), SC_(55.37500), SC_(-5.7508919690939180263189604207862429e-22) }, { SC_(30.0), SC_(57.50000), SC_(-1.8413295011736722141223685570224223e-22) }, { SC_(30.0), SC_(59.62500), SC_(-6.1461867250080302453576793713083061e-23) }, { SC_(30.0), SC_(61.75000), SC_(-2.1324740914631425269500808021967305e-23) }, { SC_(30.0), SC_(63.87500), SC_(-7.6704605421877601246419439338550908e-24) }, { SC_(30.0), SC_(66.00000), SC_(-2.8535639781622817027659809125071790e-24) }, { SC_(30.0), SC_(68.12500), SC_(-1.0955940788660649214956488504913491e-24) }, { SC_(30.0), SC_(70.25000), SC_(-4.3327278415671627426087404900842932e-25) }, { SC_(30.0), SC_(72.37500), SC_(-1.7617839186667213519985857533371320e-25) }, { SC_(30.0), SC_(74.50000), SC_(-7.3539453800410337613851853725254145e-26) }, { SC_(30.0), SC_(76.62500), SC_(-3.1464535209737263958150922875079198e-26) }, { SC_(30.0), SC_(78.75000), SC_(-1.3780503803711969857070836997294630e-26) }, { SC_(30.0), SC_(80.87500), SC_(-6.1703357256500029511495096803651889e-27) }, { SC_(30.0), SC_(83.00000), SC_(-2.8213173028841107933813502855693772e-27) }, { SC_(30.0), SC_(85.12500), SC_(-1.3159280846978733546278731706334709e-27) }, { SC_(30.0), SC_(87.25000), SC_(-6.2549157954995389707945629132366569e-28) }, { SC_(30.0), SC_(89.37500), SC_(-3.0270730786291364371674711274018267e-28) }, { SC_(30.0), SC_(91.50000), SC_(-1.4902791126813033033236323354658204e-28) }, { SC_(30.0), SC_(93.62500), SC_(-7.4578261147126651898615763642561310e-29) }, { SC_(30.0), SC_(95.75000), SC_(-3.7908508349033587121694154134344755e-29) }, { SC_(30.0), SC_(97.87500), SC_(-1.9558790071355202604313002586790408e-29) }, { SC_(30.0), SC_(100.0000), SC_(-1.0236429687189538253202730650097974e-29) }
}};
do_test_polygamma<T>(data, name, "Mathematica Data");
boost::array<boost::array<value_type, 3>, 284> big_data =
{ {
{ 1, SC_(2.0000000000000000000000000000000000), SC_(0.64493406684822643647241516664602519) }, { 1, SC_(4.0000000000000000000000000000000000), SC_(0.28382295573711532536130405553491408) }, { 1, SC_(8.0000000000000000000000000000000000), SC_(0.13313701469403142513454668592040161) }, { 1, SC_(16.000000000000000000000000000000000), SC_(0.064493783403239361781710772311927225) }, { 1, SC_(32.000000000000000000000000000000000), SC_(0.031743366520302090126581680438741427) }, { 1, SC_(64.000000000000000000000000000000000), SC_(0.015747706064338930155744003071350465) }, { 1, SC_(128.00000000000000000000000000000000), SC_(0.0078430970500146151295391657680446584) }, { 1, SC_(256.00000000000000000000000000000000), SC_(0.0039138893286083964054615299292933721) }, { 1, SC_(512.00000000000000000000000000000000), SC_(0.0019550335903952979329050939908745913) }, { 1, SC_(1024.0000000000000000000000000000000), SC_(0.00097703949237860262165259669085763056) },
{ 1, SC_(2048.0000000000000000000000000000000), SC_(0.00048840047869210349388677277938304048) }, { 1, SC_(4096.0000000000000000000000000000000), SC_(0.00024417042974770687112825193241674713) }, { 1, SC_(8192.0000000000000000000000000000000), SC_(0.00012207776338376182351559927851701587) }, { 1, SC_(16384.000000000000000000000000000000), SC_(0.000061037018933044843502668828413112893) }, { 1, SC_(32768.000000000000000000000000000000), SC_(0.000030518043791024259310109487753004549) },
{ 2, SC_(2.0000000000000000000000000000000000), SC_(-0.40411380631918857079947632302289998) }, { 2, SC_(4.0000000000000000000000000000000000), SC_(-0.080039732245114496725402248948825907) }, { 2, SC_(8.0000000000000000000000000000000000), SC_(-0.017699569195767773909291677736213879) }, { 2, SC_(16.000000000000000000000000000000000), SC_(-0.0041580101239589621541865297842265262) }, { 2, SC_(32.000000000000000000000000000000000), SC_(-0.0010075567602140907392185110593117265) }, { 2, SC_(64.000000000000000000000000000000000), SC_(-0.00024798512216328534949893202341675581) }, { 2, SC_(128.00000000000000000000000000000000), SC_(-0.000061513856015459056093727063597403146) }, { 2, SC_(256.00000000000000000000000000000000), SC_(-0.000015318510122005107648117663349723503) }, { 2, SC_(512.00000000000000000000000000000000), SC_(-3.8221551221702861883051574825692679e-6) }, { 2, SC_(1024.0000000000000000000000000000000), SC_(-9.5460609372807180482794242236285690e-7) }, { 2, SC_(2048.0000000000000000000000000000000), SC_(-2.3853502284509660646447307719091929e-7) }, { 2, SC_(4096.0000000000000000000000000000000), SC_(-5.9619198466975795959019740002484769e-8) }, { 2, SC_(8192.0000000000000000000000000000000), SC_(-1.4902980294273504017537750635770593e-8) }, { 2, SC_(16384.000000000000000000000000000000), SC_(-3.7255176790762511898502424554181168e-9) }, { 2, SC_(32768.000000000000000000000000000000), SC_(-9.3135099675858978849200435754135096e-10) }, { 2, SC_(65536.000000000000000000000000000000), SC_(-2.3283419639465348371721333739142464e-10) }, { 2, SC_(131072.00000000000000000000000000000), SC_(-5.8208105004371323183654400926421586e-11) }, { 2, SC_(262144.00000000000000000000000000000), SC_(-1.4551970739623962182873920142648449e-11) }, { 2, SC_(524288.00000000000000000000000000000), SC_(-3.6379857459922343037889500943887953e-12) }, { 2, SC_(1.0485760000000000000000000000000000e6), SC_(-9.0949556913507981662486265691361231e-13) }, { 2, SC_(2.0971520000000000000000000000000000e6), SC_(-2.2737378386347515742334544652596257e-13) }, { 2, SC_(4.1943040000000000000000000000000000e6), SC_(-5.6843432413336786525629259100975662e-14) }, { 2, SC_(8.3886080000000000000000000000000000e6), SC_(-1.4210856409267999200219031777240284e-14) }, { 2, SC_(1.6777216000000000000000000000000000e7), SC_(-3.5527138905587440538179478730582199e-15) }, { 2, SC_(3.3554432000000000000000000000000000e7), SC_(-8.8817844616990522846624354086352033e-16) }, { 2, SC_(6.7108864000000000000000000000000000e7), SC_(-2.2204460823375378294874032126041593e-16) }, { 2, SC_(1.3421772800000000000000000000000000e8), SC_(-5.5511151644848134838439376350034016e-17) }, { 2, SC_(2.6843545600000000000000000000000000e8), SC_(-1.3877787859513245136156122749960089e-17) }, { 2, SC_(5.3687091200000000000000000000000000e8), SC_(-3.4694469584159627304129087489268059e-18) }, { 2, SC_(1.0737418240000000000000000000000000e9), SC_(-8.6736173879619711452843652170069542e-19) }, { 2, 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SC_(-1.7662247842534755008372178353398608e-466) }, { SC_(30.0), SC_(7.2057594037927936000000000000000000e16), SC_(-1.6449250134206145379392674041454779e-475) }, { SC_(30.0), SC_(1.4411518807585587200000000000000000e17), SC_(-1.5319557985482871222587909400586267e-484) }, { SC_(30.0), SC_(2.8823037615171174400000000000000000e17), SC_(-1.4267450185011020326364788255126534e-493) }, { SC_(30.0), SC_(5.7646075230342348800000000000000000e17), SC_(-1.3287598439502548384585954790099239e-502) }, { SC_(30.0), SC_(1.1529215046068469760000000000000000e18), SC_(-1.2375040389134127843853680088571555e-511) }, { SC_(30.0), SC_(2.3058430092136939520000000000000000e18), SC_(-1.1525154476178928989312989675999669e-520) }, { SC_(30.0), SC_(4.6116860184273879040000000000000000e18), SC_(-1.0733636539596066765325327508232535e-529) }, { SC_(30.0), SC_(9.2233720368547758080000000000000000e18), SC_(-9.9964780170433844885501818972479211e-539) }, { SC_(30.0), SC_(1.8446744073709551616000000000000000e19), SC_(-9.3099456439198781553856371993072353e-548) }, { SC_(30.0), SC_(3.6893488147419103232000000000000000e19), SC_(-8.6705625466256198953841239814504762e-557) }, { SC_(30.0), SC_(7.3786976294838206464000000000000000e19), SC_(-8.0750906342879122995040411743125170e-566) }, { SC_(30.0), SC_(1.4757395258967641292800000000000000e20), SC_(-7.5205141997783559362248117439409145e-575) }, { SC_(30.0), SC_(2.9514790517935282585600000000000000e20), SC_(-7.0040246469698435960734303533011581e-584) }, { SC_(30.0), SC_(5.9029581035870565171200000000000000e20), SC_(-6.5230062668862227312246814035998837e-593) }, { SC_(30.0), SC_(1.1805916207174113034240000000000000e21), SC_(-6.0750229907093781336599992450810038e-602) }, { SC_(30.0), SC_(2.3611832414348226068480000000000000e21), SC_(-5.6578060525556822620531601462211155e-611) }, { SC_(30.0), SC_(4.7223664828696452136960000000000000e21), SC_(-5.2692424995411953535258666060047970e-620) }, { SC_(30.0), SC_(9.4447329657392904273920000000000000e21), SC_(-4.9073644909460054277605359114212468e-629) }, { SC_(30.0), SC_(1.8889465931478580854784000000000000e22), SC_(-4.5703393322844108825145652571006034e-638) }, { SC_(30.0), SC_(3.7778931862957161709568000000000000e22), SC_(-4.2564601938095045113123493445833636e-647) }, { SC_(30.0), SC_(7.5557863725914323419136000000000000e22), SC_(-3.9641374664469664090420159863859993e-656) }, { SC_(30.0), SC_(1.5111572745182864683827200000000000e23), SC_(-3.6918907113810688341424078675611601e-665) }, { SC_(30.0), SC_(3.0223145490365729367654400000000000e23), SC_(-3.4383411625223875363750612697898904e-674) }, { SC_(30.0), SC_(6.0446290980731458735308800000000000e23), SC_(-3.2022047438867274079238771888571055e-683) }, { SC_(30.0), SC_(1.2089258196146291747061760000000000e24), SC_(-2.9822855665224859564787125744222496e-692) }, { SC_(30.0), SC_(2.4178516392292583494123520000000000e24), SC_(-2.7774698720523025435197111896762965e-701) }, { SC_(30.0), SC_(4.8357032784585166988247040000000000e24), SC_(-2.5867203921566741015014262629362602e-710) }, { SC_(30.0), SC_(9.6714065569170333976494080000000000e24), SC_(-2.4090710954337139627909495039162813e-719) }, { SC_(30.0), SC_(1.9342813113834066795298816000000000e25), SC_(-2.2436222950310576360588405614024340e-728) }, { SC_(30.0), SC_(3.8685626227668133590597632000000000e25), SC_(-2.0895360922730133273255449640176061e-737) }, { SC_(30.0), SC_(7.7371252455336267181195264000000000e25), SC_(-1.9460321332076688551581879695116458e-746) }, { SC_(30.0), SC_(1.5474250491067253436239052800000000e26), SC_(-1.8123836565834180034307649180969011e-755) }, { SC_(30.0), SC_(3.0948500982134506872478105600000000e26), SC_(-1.6879138132402841033700526042422183e-764) }, { SC_(30.0), SC_(6.1897001964269013744956211200000000e26), SC_(-1.5719922382759713599179429591983936e-773) }, { SC_(30.0), SC_(1.2379400392853802748991242240000000e27), SC_(-1.4640318586267264186571752095136003e-782) }, { SC_(30.0), SC_(2.4758800785707605497982484480000000e27), SC_(-1.3634859198953271085928894585406723e-791) }, { SC_(30.0), SC_(4.9517601571415210995964968960000000e27), SC_(-1.2698452173688701433994709089494920e-800) }, { SC_(30.0), SC_(9.9035203142830421991929937920000000e27), SC_(-1.1826355172031280988822420193126128e-809) }, { SC_(30.0), SC_(1.9807040628566084398385987584000000e28), SC_(-1.1014151547133252945563215933898419e-818) }, { SC_(30.0), SC_(3.9614081257132168796771975168000000e28), SC_(-1.0257727976081197099353387886404875e-827) }, { SC_(30.0), SC_(7.9228162514264337593543950336000000e28), SC_(-9.5532536283891621039746216353614015e-837) }, { SC_(30.0), SC_(1.5845632502852867518708790067200000e29), SC_(-8.8971607651460562869670071028704372e-846) }, { SC_(30.0), SC_(3.1691265005705735037417580134400000e29), SC_(-8.2861266705636459281360796675545348e-855) }, { SC_(30.0), SC_(6.3382530011411470074835160268800000e29), SC_(-7.7170568244193177000955489160105929e-864) }, { SC_(30.0), SC_(1.2676506002282294014967032053760000e30), SC_(-7.1870692301721476950641245729469486e-873) },
{ SC_(31.0), SC_(2.0000000000000000000000000000000000), SC_(1.9145332544935048093264355986676073e24) }, { SC_(31.0), SC_(4.0000000000000000000000000000000000), SC_(4.4611518561919816922776795853710092e14) }, { SC_(31.0), SC_(8.0000000000000000000000000000000000), SC_(106267.95619808419253963903669279065) }, { SC_(31.0), SC_(16.000000000000000000000000000000000), SC_(0.000028318136062027075392587779376335821) }, { SC_(31.0), SC_(32.000000000000000000000000000000000), SC_(9.0814734303237413772295578988209818e-15) }
} };
do_test_polygamma<T>(big_data, name, "Mathematica Data - large arguments");
boost::array<boost::array<value_type, 3>, 399> neg_data =
{ {
{ 1, SC_(-12.750), SC_(19.663772856722737612034697464751605) }, { 1, SC_(-12.250), SC_(19.660817549236368273654684043826967) }, { 1, SC_(-11.750), SC_(19.657621376522814505537196503582823) }, { 1, SC_(-11.250), SC_(19.654153659190554029589711115880278) }, { 1, SC_(-10.750), SC_(19.650378280099093364749509767503149) }, { 1, SC_(-10.250), SC_(19.646252424622652795021809881312377) }, { 1, SC_(-9.7500), SC_(19.641724953976865133273035997897957) }, { 1, SC_(-9.2500), SC_(19.636734280660725370869519577921538) }, { 1, SC_(-8.7500), SC_(19.631205558842085383108670448917024) }, { 1, SC_(-8.2500), SC_(19.625046917622010980803778160828770) }, { 1, SC_(-7.7500), SC_(19.618144334352289464741323510141514) }, { 1, SC_(-7.2500), SC_(19.610354539293269015698176691590937) }, { 1, SC_(-6.7500), SC_(19.601495010731061577124257953429755) }, { 1, SC_(-6.2500), SC_(19.591329569019785068016844943671793) }, { 1, SC_(-5.7500), SC_(19.579547136931335925546754524074474) }, { 1, SC_(-5.2500), SC_(19.565729569019785068016844943671793) }, { 1, SC_(-4.7500), SC_(19.549301390239464469970194977760674) }, { 1, SC_(-4.2500), SC_(19.529448389881463072551992335962043) }, { 1, SC_(-3.7500), SC_(19.504980060599575273294294700752364) }, { 1, SC_(-3.2500), SC_(19.474085068082155114074483685443011) }, { 1, SC_(-2.7500), SC_(19.433868949488464162183183589641253) }, { 1, SC_(-2.2500), SC_(19.379410511869137362595193744614609) }, { 1, SC_(-1.7500), SC_(19.301637544529786476232770366500757) }, { 1, SC_(-1.2500), SC_(19.181879647671606498397662880417078) }, { 1, SC_(-0.75000), SC_(18.975106932284888517049096897113002) }, { 1, SC_(-0.25000), SC_(18.541879647671606498397662880417078) },
{ 2, SC_(-12.750), SC_(-124.03079461415823384604153251543681) }, { 2, SC_(-12.250), SC_(124.01896466745858356132308878716344) }, { 2, SC_(-11.750), SC_(-124.03175955222881001960976796032603) }, { 2, SC_(-11.250), SC_(124.01787668541028735821044014586602) }, { 2, SC_(-10.750), SC_(-124.03299241970518808612682102178640) }, { 2, SC_(-10.250), SC_(124.01647202148710491650947992638728) }, { 2, SC_(-9.7500), SC_(-124.03460234084420729198290916496876) }, { 2, SC_(-9.2500), SC_(124.01461482266526541911391108670126) }, { 2, SC_(-8.7500), SC_(-124.03676016548723903560636876475972) }, { 2, SC_(-8.2500), SC_(124.01208782525148933477537240192445) }, { 2, SC_(-7.7500), SC_(-124.03974558822776381694747663647984) }, { 2, SC_(-7.2500), SC_(124.00852603656573370687098416695770) }, { 2, SC_(-6.7500), SC_(-124.04404218787195165891317097369578) }, { 2, SC_(-6.2500), SC_(124.00327776890408296268303058132483) }, { 2, SC_(-5.7500), SC_(-124.05054526159038888901020902683808) }, { 2, SC_(-5.2500), SC_(123.99508576890408296268303058132483) }, { 2, SC_(-4.7500), SC_(-124.06106552130930069964553408642549) }, { 2, SC_(-4.2500), SC_(123.98126436732757934536308673076874) }, { 2, SC_(-3.7500), SC_(-124.07972713378925404561433420306057) }, { 2, SC_(-3.2500), SC_(123.95521103942202265902072971875978) }, { 2, SC_(-2.7500), SC_(-124.11765305971517997154026012898649) }, { 2, SC_(-2.2500), SC_(123.89694977406016558118732052440384) }, { 2, SC_(-1.7500), SC_(-124.21382135423058192495874247308867) }, { 2, SC_(-1.2500), SC_(123.72136678366236036856729308956159) }, { 2, SC_(-0.75000), SC_(-124.58699919679617959259722643810325) }, { 2, SC_(-0.25000), SC_(122.69736678366236036856729308956159) },
{ 3, SC_(-12.750), SC_(1558.5445992104061926890981987122713) }, { 3, SC_(-12.250), SC_(1558.5444945580353369268010524200916) }, { 3, SC_(-11.750), SC_(1558.5443721661542924129644962546503) }, { 3, SC_(-11.250), SC_(1558.5442281134520807137938731609983) }, { 3, SC_(-10.750), SC_(1558.5440573914794724810878018559796) }, { 3, SC_(-10.250), SC_(1558.5438535364058987293402837691373) }, { 3, SC_(-9.7500), SC_(1558.5436081111616066561977307462543) }, { 3, SC_(-9.2500), SC_(1558.5433099660190188764440197184975) }, { 3, SC_(-8.7500), SC_(1558.5429441651175968889289739463186) }, { 3, SC_(-8.2500), SC_(1558.5424903992902266328747639288402) }, { 3, SC_(-7.7500), SC_(1558.5419205916065598210405941045860) }, { 3, SC_(-7.2500), SC_(1558.5411952034044973136368045706704) }, { 3, SC_(-6.7500), SC_(1558.5402573917442935596345188772766) }, { 3, SC_(-6.2500), SC_(1558.5390235064410556263866168800637) }, { 3, SC_(-5.7500), SC_(1558.5373671367583214573691686314356) }, { 3, SC_(-5.2500), SC_(1558.5350913464410556263866168800637) }, { 3, SC_(-4.7500), SC_(1558.5318783056006283387768251220856) }, { 3, SC_(-4.2500), SC_(1558.5271934026830535593466489654603) }, { 3, SC_(-3.7500), SC_(1558.5200920240343420150070566273687) }, { 3, SC_(-3.2500), SC_(1558.5088028182791311925167498981598) }, { 3, SC_(-2.7500), SC_(1558.4897512832936012742663158866280) }, { 3, SC_(-2.2500), SC_(1558.4550231887143400437474491033697) }, { 3, SC_(-1.7500), SC_(1558.3848404165495264159916078748802) }, { 3, SC_(-1.2500), SC_(1558.2209125348505997602540791902467) }, { 3, SC_(-0.75000), SC_(1557.7451069721513589857542067919980) }, { 3, SC_(-0.25000), SC_(1555.7633125348505997602540791902467) },
{ 4, SC_(-12.750), SC_(-24481.574976569827769932951761311307) }, { 4, SC_(-12.250), SC_(24481.574556933476371183897773040987) }, { 4, SC_(-11.750), SC_(-24481.575047799396993548993707180364) }, { 4, SC_(-11.250), SC_(24481.574469931163471195977061446181) }, { 4, SC_(-10.750), SC_(-24481.575154956733102461973007401188) }, { 4, SC_(-10.250), SC_(24481.574336748213717601504674106852) }, { 4, SC_(-9.7500), SC_(-24481.575322130804866489839080372249) }, { 4, SC_(-9.2500), SC_(24481.574124623184691317447595452944) }, { 4, SC_(-8.7500), SC_(-24481.575594518925485881539083161966) }, { 4, SC_(-8.2500), SC_(24481.573770215950618995904133489849) }, { 4, SC_(-7.7500), SC_(-24481.576062438244817112573771089615) }, { 4, SC_(-7.2500), SC_(24481.573142242187841144152395619221) }, { 4, SC_(-6.7500), SC_(-24481.576920863980180344267229271453) }, { 4, SC_(-6.2500), SC_(24481.571944064552838833945395514059) }, { 4, SC_(-5.7500), SC_(-24481.578633607675571219683733120840) }, { 4, SC_(-5.2500), SC_(24481.569427482152838833945395514059) }, { 4, SC_(-4.7500), SC_(-24481.582451925002662084791450344735) }, { 4, SC_(-4.2500), SC_(24481.563410001194361068581610436266) }, { 4, SC_(-3.7500), SC_(-24481.592377214742692673229150129760) }, { 4, SC_(-3.2500), SC_(24481.546101215873022370388764255277) }, { 4, SC_(-2.7500), SC_(-24481.624740671532816130019273586550) }, { 4, SC_(-2.2500), SC_(24481.479910902562510187288086353997) }, { 4, SC_(-1.7500), SC_(-24481.777338295887834105691576149093) }, { 4, SC_(-1.2500), SC_(24481.063714184582527461077650952890) }, { 4, SC_(-0.75000), SC_(-24483.239586168797931089091350052823) }, { 4, SC_(-0.25000), SC_(24473.199394184582527461077650952890) },
{ 5, SC_(-12.750), SC_(492231.26705220367447285602722829798) }, { 5, SC_(-12.250), SC_(492231.26703986858726773334478356804) }, { 5, SC_(-11.750), SC_(492231.26702427051007143797156325129) }, { 5, SC_(-11.250), SC_(492231.26700435743914528929551352935) }, { 5, SC_(-10.750), SC_(492231.26697867164364211329952060413) }, { 5, SC_(-10.250), SC_(492231.26694516501703258064111915631) }, { 5, SC_(-9.7500), SC_(492231.26690091626142628638506805946) }, { 5, SC_(-9.2500), SC_(492231.26684168939311732012547103246) }, { 5, SC_(-8.7500), SC_(492231.26676123004572403423122047499) }, { 5, SC_(-8.2500), SC_(492231.26665011791524038956143753889) }, { 5, SC_(-7.7500), SC_(492231.26649384757753475935425594490) }, { 5, SC_(-7.2500), SC_(492231.26626952775598108546947519306) }, { 5, SC_(-6.7500), SC_(492231.26594002452246170664879905339) }, { 5, SC_(-6.2500), SC_(492231.26544319835253121636119925846) }, { 5, SC_(-5.7500), SC_(492231.26467132548883883596990731311) }, { 5, SC_(-5.2500), SC_(492231.26342993243253121636119925846) }, { 5, SC_(-4.7500), SC_(492231.26135104955223808370232711841) }, { 5, SC_(-4.2500), SC_(492231.25769899818636191601473727961) }, { 5, SC_(-3.7500), SC_(492231.25090337614167956955737997628) }, { 5, SC_(-3.2500), SC_(492231.23733572133772815343491824315) }, { 5, SC_(-2.7500), SC_(492231.20775210042151496050388203390) }, { 5, SC_(-2.2500), SC_(492231.13550447009078633328002916426) }, { 5, SC_(-1.7500), SC_(492230.93030187432148227746333192018) }, { 5, SC_(-1.2500), SC_(492230.21062287457971360836795049513) }, { 5, SC_(-0.75000), SC_(492226.75245080886406232489254933809) }, { 5, SC_(-0.25000), SC_(492198.75334287457971360836795049513) },
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{ SC_(20.0), SC_(-7.7500), SC_(-1.0700016187896297695358366297227405e31)}, { SC_(20.0), SC_(-7.2500), SC_(1.0700016187896297695358366297227207e31) }, { SC_(20.0), SC_(-6.7500), SC_(-1.0700016187896297695358366297227919e31) }, { SC_(20.0), SC_(-6.2500), SC_(1.0700016187896297695358366297225123e31) }, { SC_(20.0), SC_(-5.7500), SC_(-1.0700016187896297695358366297237267e31) }, { SC_(20.0), SC_(-5.2500), SC_(1.0700016187896297695358366297178064e31) }, { SC_(20.0), SC_(-4.7500), SC_(-1.0700016187896297695358366297508349e31) }, { SC_(20.0), SC_(-4.2500), SC_(1.0700016187896297695358366295346680e31) }, { SC_(20.0), SC_(-3.7500), SC_(-1.0700016187896297695358366312489970e31) }, { SC_(20.0), SC_(-3.2500), SC_(1.0700016187896297695358366140480322e31) }, { SC_(20.0), SC_(-2.7500), SC_(-1.0700016187896297695358368457690989e31) }, { SC_(20.0), SC_(-2.2500), SC_(1.0700016187896297695358322831891149e31) }, { SC_(20.0), SC_(-1.7500), SC_(-1.0700016187896297695359814356987569e31) }, { SC_(20.0), SC_(-1.2500), SC_(1.0700016187896297695260533442006924e31) }, { SC_(20.0), SC_(-0.75000), SC_(-1.0700016187896297714516730336449055e31) }, { SC_(20.0), SC_(-0.25000), SC_(1.0700016187896275255700182817756420e31) },
{ SC_(23.0), SC_(-7.7500), SC_(7.2766958095269026379022334905108869e36)}, { SC_(23.0), SC_(-7.2500), SC_(7.2766958095269026379022334905108869e36) }, { SC_(23.0), SC_(-6.7500), SC_(7.2766958095269026379022334905108869e36) }, { SC_(23.0), SC_(-6.2500), SC_(7.2766958095269026379022334905108868e36) }, { SC_(23.0), SC_(-5.7500), SC_(7.2766958095269026379022334905108866e36) }, { SC_(23.0), SC_(-5.2500), SC_(7.2766958095269026379022334905108848e36) }, { SC_(23.0), SC_(-4.7500), SC_(7.2766958095269026379022334905108714e36) }, { SC_(23.0), SC_(-4.2500), SC_(7.2766958095269026379022334905107503e36) }, { SC_(23.0), SC_(-3.7500), SC_(7.2766958095269026379022334905093860e36) }, { SC_(23.0), SC_(-3.2500), SC_(7.2766958095269026379022334904893135e36) }, { SC_(23.0), SC_(-2.7500), SC_(7.2766958095269026379022334900771270e36) }, { SC_(23.0), SC_(-2.2500), SC_(7.2766958095269026379022334770834817e36) }, { SC_(23.0), SC_(-1.7500), SC_(7.2766958095269026379022327513062336e36) }, { SC_(23.0), SC_(-1.2500), SC_(7.2766958095269026379021422520579094e36) }, { SC_(23.0), SC_(-0.75000), SC_(7.2766958095269026378642504512809960e36) }, { SC_(23.0), SC_(-0.25000), SC_(7.2766958095269025158194448897624671e36) },
{ SC_(3.0), -SC_(4.25), SC_(1558.5271934026830535593466489654603)}, { SC_(4.0), -SC_(4.25), SC_(24481.563410001194361068581610436266) }, { SC_(5.0), -SC_(4.25), SC_(492231.25769899818636191601473727961) }, { SC_(6.0), -SC_(4.25), SC_(1.1791224751536137687542195274483895e7) }, { SC_(7.0), -SC_(4.25), SC_(3.3035269584354251332378488235637904e8) }, { SC_(8.0), -SC_(4.25), SC_(1.0569114259649513356345466704581650e10) }, { SC_(9.0), -SC_(4.25), SC_(3.8051374324231168248427408936422641e11) }, { SC_(10.0), -SC_(4.25), SC_(1.5220204740668289586193246215389596e13) }, { SC_(11.0), -SC_(4.25), SC_(6.6969403856797194026913294831009712e14) }, { SC_(12.0), -SC_(4.25), SC_(3.2145233093874118103287175260580644e16) }, { SC_(13.0), -SC_(4.25), SC_(1.6715535177261375549959051229408070e18) }, { SC_(14.0), -SC_(4.25), SC_(9.3606970885707978198242133390297266e19) }, { SC_(15.0), -SC_(4.25), SC_(5.6164187748870728746250217782924909e21) }, { SC_(16.0), -SC_(4.25), SC_(3.5945079045721164734031460047595950e23) }, { SC_(17.0), -SC_(4.25), SC_(2.4442654003427929640663726375953543e25) }, { SC_(18.0), -SC_(4.25), SC_(1.7598710821897274459494049818707809e27) }, { SC_(19.0), -SC_(4.25), SC_(1.3375020239985042298043467701659026e29) }, { SC_(20.0), -SC_(4.25), SC_(1.0700016187896297695358366295346680e31) }, { SC_(21.0), -SC_(4.25), SC_(8.9880135989785359476536358803633961e32) }, { SC_(22.0), -SC_(4.25), SC_(7.9094519667650484338896180683524747e34) }, { SC_(23.0), -SC_(4.25), SC_(7.2766958095269026379022334905107503e36) },
{ SC_(3.0), SC_(-4.75), SC_(1558.5318783056006283387768251220856) }, { SC_(4.0), SC_(-4.75), SC_(-24481.582451925002662084791450344735) }, { SC_(5.0), SC_(-4.75), SC_(492231.26135104955223808370232711841) }, { SC_(6.0), SC_(-4.75), SC_(-1.1791224766632825018904254258839318e7) }, { SC_(7.0), SC_(-4.75), SC_(3.3035269584947086190323815702711063e8) }, { SC_(8.0), SC_(-4.75), SC_(-1.0569114259674567879524502974422220e10) }, { SC_(9.0), SC_(-4.75), SC_(3.8051374324232805216534792821594812e11) }, { SC_(10.0), SC_(-4.75), SC_(-1.5220204740668360644738342521168221e13) }, { SC_(11.0), SC_(-4.75), SC_(6.6969403856797200883878751610651220e14) }, { SC_(12.0), SC_(-4.75), SC_(-3.2145233093874118410246620594666049e16) }, { SC_(13.0), SC_(-4.75), SC_(1.6715535177261375554006502097069245e18) }, { SC_(14.0), SC_(-4.75), SC_(-9.3606970885707978200117071697879591e19) }, { SC_(15.0), SC_(-4.75), SC_(5.6164187748870728746282195405281448e21) }, { SC_(16.0), SC_(-4.75), SC_(-3.5945079045721164734032997263075953e23) }, { SC_(17.0), SC_(-4.75), SC_(2.4442654003427929640663758934254941e25) }, { SC_(18.0), SC_(-4.75), SC_(-1.7598710821897274459494051446575390e27) }, { SC_(19.0), SC_(-4.75), SC_(1.3375020239985042298043467743154361e29) }, { SC_(20.0), SC_(-4.75), SC_(-1.0700016187896297695358366297508349e31) }, { SC_(21.0), SC_(-4.75), SC_(8.9880135989785359476536358804280906e32) }, { SC_(22.0), SC_(-4.75), SC_(-7.9094519667650484338896180683559907e34) }, { SC_(23.0), SC_(-4.75), SC_(7.2766958095269026379022334905108714e36) },
{ SC_(1.0), SC_(-9.5), SC_(9.7696874450302318856305468284306792)}, { SC_(3.0), SC_(-9.5), SC_(194.81619198176773011863271713047162) }, { SC_(5.0), SC_(-9.5), SC_(15382.226860156995915624995579131219) }, { SC_(7.0), SC_(-9.5), SC_(2.5808804363008334969805587475917565e6) }, { SC_(9.0), SC_(-9.5), SC_(7.4319090477015599086877150154313919e8) }, { SC_(11.0), SC_(-9.5), SC_(3.2699904226951756570017589463296126e11) }, { SC_(13.0), SC_(-9.5), SC_(2.0404706026930390078103975418992502e14) }, { SC_(15.0), SC_(-9.5), SC_(1.7139949874533303450398622617829339e17) }, { SC_(17.0), SC_(-9.5), SC_(1.8648265078298896515398973583300966e20) }, { SC_(19.0), SC_(-9.5), SC_(2.5510826568574986072623191304028880e23) }, { SC_(21.0), SC_(-9.5), SC_(4.2858188624279670465725116159418790e26) },
{ SC_(2.0), SC_(-9.5), SC_(-0.0099751442477151692853059194570941025) }, { SC_(4.0), SC_(-9.5), SC_(-0.00059506011900940675655749713967447346) }, { SC_(6.0), SC_(-9.5), SC_(-0.00011794286977626608581527674104044053) }, { SC_(8.0), SC_(-9.5), SC_(-0.000048934615584055214532361558113243801) }, { SC_(10.0), SC_(-9.5), SC_(-0.000034696555222805555969152083201249795) }, { SC_(12.0), SC_(-9.5), SC_(-0.000037470635416758472254487967117333555) }, { SC_(14.0), SC_(-9.5), SC_(-0.000057218576281198884425118075685027774) }, { SC_(16.0), SC_(-9.5), SC_(-0.00011728023376485851827598955099805232) }, { SC_(18.0), SC_(-9.5), SC_(-0.00031049110045758006635527458576736345) }, { SC_(20.0), SC_(-9.5), SC_(-0.0010307637762451416598018081796345932) },
{ SC_(2.0), SC_(-9.5367431640625e-7), SC_(2.3058430092136939495958800005662742e18) }, { SC_(2.0), SC_(-5.960464477539063e-8), SC_(9.4447329657392904273895958858066118e21) }, { SC_(2.0), SC_(-3.725290298461914e-9), SC_(3.8685626227668133590597629595886169e25) }, { SC_(2.0), SC_(-2.3283064365386963e-10), SC_(1.5845632502852867518708790066959589e29) }, { SC_(2.0), SC_(-1.4551915228366852e-11), SC_(6.4903710731685345356631204115250960e32) }, { SC_(2.0), SC_(-9.094947017729282e-13), SC_(2.6584559915698317458076141205606891e36) }, { SC_(2.0), SC_(-5.684341886080802e-14), SC_(1.0889035741470030830827987437816583e40) }, { SC_(2.0), SC_(-3.552713678800501e-15), SC_(4.4601490397061246283071436545296723e43) }, { SC_(2.0), SC_(-2.220446049250313e-16), SC_(1.8268770466636286477546060408953538e47) }, { SC_(2.0), SC_(-1.3877787807814457e-17), SC_(7.4828883831342229412028663435073691e50) }, { SC_(2.0), SC_(-8.673617379884035e-19), SC_(3.0649910817317777167166940543006184e54) }, { SC_(2.0), SC_(-5.421010862427522e-20), SC_(1.2554203470773361527671578846415333e58) }, { SC_(2.0), SC_(-3.3881317890172014e-21), SC_(5.1422017416287688817342786954917203e61) },
{ SC_(3.0), SC_(-9.5367431640625e-7), SC_(7.2535549176877750482370624939631357e24) }, { SC_(3.0), SC_(-5.960464477539063e-8), SC_(4.7536897508558602556126370202249394e29) }, { SC_(3.0), SC_(-3.725290298461914e-9), SC_(3.1153781151208965771182977975320582e34) }, { SC_(3.0), SC_(-2.3283064365386963e-10), SC_(2.0416942015256307807802476445906093e39) }, { SC_(3.0), SC_(-1.4551915228366852e-11), SC_(1.3380447119118373884921430963589017e44) }, { SC_(3.0), SC_(-9.094947017729282e-13), SC_(8.7690098239854175092221089962976981e48) }, { SC_(3.0), SC_(-5.684341886080802e-14), SC_(5.7468582782470832188438013518136594e53) }, { SC_(3.0), SC_(-3.552713678800501e-15), SC_(3.7662610412320084583014736539245998e58) }, { SC_(3.0), SC_(-2.220446049250313e-16), SC_(2.4682568359818090632324537738360258e63) }, { SC_(3.0), SC_(-1.3877787807814457e-17), SC_(1.6175968000290383876800209052211778e68) }, { SC_(3.0), SC_(-8.673617379884035e-19), SC_(1.0601082388670305977499785004457511e73) }, { SC_(3.0), SC_(-5.421010862427522e-20), SC_(6.9475253542389717254142591005212745e77) }, { SC_(3.0), SC_(-3.3881317890172014e-21), SC_(4.5531302161540525099674888441176224e82) },
//{ SC_(20.0), SC_(-9.5), SC_(-0.0010307637762451416598018081796345932)}, { SC_(21.0), SC_(-9.5), SC_(4.2858188624279670465725116159418790e26) }, { SC_(22.0), SC_(-9.5), SC_(-0.0041914420015886426448664611125724338) }, { SC_(23.0), SC_(-9.5), SC_(8.6744973773084910367753904944787155e29) }, { SC_(24.0), SC_(-9.5), SC_(-0.020482527998674199369359987617445420) }, { SC_(25.0), SC_(-9.5), SC_(2.0818793705474855280713094147422278e33) }, { SC_(26.0), SC_(-9.5), SC_(-0.11840299831136879082790399023048278) }, { SC_(27.0), SC_(-9.5), SC_(5.8459172724952950454469355072783445e36) }, { SC_(28.0), SC_(-9.5), SC_(-0.79896867888629450211348696225656872) }, { SC_(29.0), SC_(-9.5), SC_(1.8987539301063980537054871851063348e40) }, { SC_(30.0), SC_(-9.5), SC_(-6.2224465669723272001827279817965087) }
} };
do_test_polygamma<T>(neg_data, name, "Mathematica Data - negative arguments");
boost::array<boost::array<value_type, 3>, 90> small_data =
{ {
{ SC_(0.0), SC_(0.12500000000000000000), SC_(-8.3884926632958548678027429230863430) }, { SC_(0.0), SC_(0.062500000000000000000), SC_(-16.478853490060104366505723782801995) }, { SC_(0.0), SC_(0.031250000000000000000), SC_(-32.526953288606118111369026129964135) }, { SC_(0.0), SC_(0.015625000000000000000), SC_(-64.551802973167856670965920212624596) }, { SC_(0.0), SC_(0.0078125000000000000000), SC_(-128.56443747297672763722041223143322) }, { SC_(0.0), SC_(0.0039062500000000000000), SC_(-256.57080841886464838984737508407824) }, { SC_(0.0), SC_(0.0019531250000000000000), SC_(-512.57400748048652546824732749592750) }, { SC_(0.0), SC_(0.00097656250000000000000), SC_(-1024.5756104293406219086220979096446) }, { SC_(0.0), SC_(0.00048828125000000000000), SC_(-2048.5764127609059633822989920937770) }, { SC_(0.0), SC_(0.00024414062500000000000), SC_(-4096.5768141413027972625364884707221) }, { SC_(0.0), SC_(0.00012207031250000000000), SC_(-8192.5770148851960259755970875167303) }, { SC_(0.0), SC_(0.000061035156250000000000), SC_(-16384.577115270571506673278270921248) }, { SC_(0.0), SC_(0.000030517578125000000000), SC_(-32768.577165466617109315191527852551) }, { SC_(0.0), SC_(0.000015258789062500000000), SC_(-65536.577190565479456940587995127301) }, { SC_(0.0), SC_(7.6293945312500000000e-6), SC_(-131072.57720311512052742189906385878) }, { SC_(0.0), SC_(3.8146972656250000000e-6), SC_(-262144.57720938999353809133982546559) }, { SC_(0.0), SC_(1.9073486328125000000e-6), SC_(-524288.57721252744316244096483807868) }, { SC_(0.0), SC_(9.5367431640625000000e-7), SC_(-1.0485765772140961712543892173131386e6) },
{ SC_(1.0), SC_(0.1250000000), SC_(65.388133444988034473142999334395961) }, { SC_(1.0), SC_(0.06250000000), SC_(257.50642004291541426394984152786018) }, { SC_(1.0), SC_(0.03125000000), SC_(1025.5728544782377088851896549789956) }, { SC_(1.0), SC_(0.01562500000), SC_(4097.6081469812325471140472931934309) }, { SC_(1.0), SC_(0.007812500000), SC_(16385.626348148031663597978251925972) }, { SC_(1.0), SC_(0.003906250000), SC_(65537.635592296074077546680509110271) }, { SC_(1.0), SC_(0.001953125000), SC_(262145.64025088744769438583827382756) }, { SC_(1.0), SC_(0.0009765625000), SC_(1.0485776425893921526170408061678298e6) },
{ SC_(2.0), SC_(0.1250000000), SC_(-1025.7533381181356825956689300565174) }, { SC_(2.0), SC_(0.06250000000), SC_(-8194.0423055503627202407284588855458) }, { SC_(2.0), SC_(0.03125000000), SC_(-65538.212736402744663973874571262931) }, { SC_(2.0), SC_(0.01562500000), SC_(-524290.30560802491992997062359624105) }, { SC_(2.0), SC_(0.007812500000), SC_(-4.1943063541297826472489756741474152e6) }, { SC_(2.0), SC_(0.003906250000), SC_(-3.3554434378935516909394862712904232e7) }, { SC_(2.0), SC_(0.001953125000), SC_(-2.6843545839147764655287988662280398e8) }, { SC_(2.0), SC_(0.0009765625000), SC_(-2.1474836503977839163960630063909364e9) },
{ SC_(3.0), SC_(0.1250000000), SC_(24580.143419063566218511004446647010) }, { SC_(3.0), SC_(0.06250000000), SC_(393221.15036999967974263906424748910) }, { SC_(3.0), SC_(0.03125000000), SC_(6.2914617723523498519444110540563165e6) }, { SC_(3.0), SC_(0.01562500000), SC_(1.0066330211954465631968224525194028e8) }, { SC_(3.0), SC_(0.007812500000), SC_(1.6106127423031841473495039368910042e9) }, { SC_(3.0), SC_(0.003906250000), SC_(2.5769803782397651667126674423858834e10) }, { SC_(3.0), SC_(0.001953125000), SC_(4.1231686042244556536661660289768233e11) }, { SC_(3.0), SC_(0.0009765625000), SC_(6.5970697666624696945083422683684831e12) },
{ SC_(4.0), SC_(0.1250000000), SC_(-786445.98543106378579320120709638297) }, { SC_(4.0), SC_(0.06250000000), SC_(-2.5165842491343080297812493001330106e7) }, { SC_(4.0), SC_(0.03125000000), SC_(-8.0530638940150780088628643019449463e8) }, { SC_(4.0), SC_(0.01562500000), SC_(-2.5769803799064252508878172105001377e10) }, { SC_(4.0), SC_(0.007812500000), SC_(-8.2463372085595426712260437166652246e11) }, { SC_(4.0), SC_(0.003906250000), SC_(-2.6388279066648414875708308182697262e13) }, { SC_(4.0), SC_(0.001953125000), SC_(-8.4442493013199264920484069629201316e14) }, { SC_(4.0), SC_(0.0009765625000), SC_(-2.7021597764223000767391638642998277e16) },
{ SC_(5.0), SC_(0.1250000000), SC_(3.1457340659602645662942019557433307e7) }, { SC_(5.0), SC_(0.06250000000), SC_(2.0132660051504893647288429933363318e9) }, { SC_(5.0), SC_(0.03125000000), SC_(1.2884901898167237155557768979087387e11) }, { SC_(5.0), SC_(0.01562500000), SC_(8.2463372084313301694493047619778287e12) }, { SC_(5.0), SC_(0.007812500000), SC_(5.2776558133259656048321206289799569e14) }, { SC_(5.0), SC_(0.003906250000), SC_(3.3776997205278839283396175959111085e16) }, { SC_(5.0), SC_(0.001953125000), SC_(2.1617278211378382006727785506307164e18) }, { SC_(5.0), SC_(0.0009765625000), SC_(1.3835058055282163724137457865337740e20) },
{ SC_(8.0), SC_(0.1250000000), SC_(-5.4116588069756277838328695722389595e12) }, { SC_(8.0), SC_(0.06250000000), SC_(-2.7707693020189462516270216110672946e15) }, { SC_(8.0), SC_(0.03125000000), SC_(-1.4186338826217368769684713903764732e18) }, { SC_(8.0), SC_(0.01562500000), SC_(-7.2634054790231363002428528775599797e20) }, { SC_(8.0), SC_(0.007812500000), SC_(-3.7188636052598456061623085548707189e23) }, { SC_(8.0), SC_(0.003906250000), SC_(-1.9040581658930409501626172937578262e26) }, { SC_(8.0), SC_(0.001953125000), SC_(-9.7487778093723696648306072338399010e28) }, { SC_(8.0), SC_(0.0009765625000), SC_(-4.9913742383986532683932688751727976e31) },
{ SC_(15.0), SC_(0.1250000000), SC_(3.6807761227792200230957850246407904e26) }, { SC_(15.0), SC_(0.06250000000), SC_(2.4122334398245883325511911077327284e31) }, { SC_(15.0), SC_(0.03125000000), SC_(1.5808813071234422095882610857505513e36) }, { SC_(15.0), SC_(0.01562500000), SC_(1.0360463734364190864757622613687259e41) }, { SC_(15.0), SC_(0.007812500000), SC_(6.7898335129529161251275555560392101e45) }, { SC_(15.0), SC_(0.003906250000), SC_(4.4497852910488231117635948092058560e50) }, { SC_(15.0), SC_(0.001953125000), SC_(2.9162112883417567145253894941611498e55) }, { SC_(15.0), SC_(0.0009765625000), SC_(1.9111682299276536804313592588934511e60) },
{ SC_(22.0), SC_(0.1250000000), SC_(-6.6349292044725783891012472579673570e41) }, { SC_(22.0), SC_(0.06250000000), SC_(-5.5657820204072306855435555719642654e48) }, { SC_(22.0), SC_(0.03125000000), SC_(-4.6689163582644258586596154617085763e55) }, { SC_(22.0), SC_(0.01562500000), SC_(-3.9165709114267828873358919539012256e62) }, { SC_(22.0), SC_(0.007812500000), SC_(-3.2854578080162002342968961931631453e69) }, { SC_(22.0), SC_(0.003906250000), SC_(-2.7560417651987161415024817781137906e76) }, { SC_(22.0), SC_(0.001953125000), SC_(-2.3119353999880071814336850663739568e83) }, { SC_(22.0), SC_(0.0009765625000), SC_(-1.9393919791822596946232062017265105e90) },
{ SC_(35.0), SC_(0.1250000000), SC_(3.3532982327901451846973629635910627e72) }, { SC_(35.0), SC_(0.06250000000), SC_(2.3043689989709229438987285737704404e83) }, { SC_(35.0), SC_(0.03125000000), SC_(1.5835503181594194718369731136519624e94) }, { SC_(35.0), SC_(0.01562500000), SC_(1.0882074924904162473416628106826351e105) }, { SC_(35.0), SC_(0.007812500000), SC_(7.4781049464136054012151819362261716e115) }, { SC_(35.0), SC_(0.003906250000), SC_(5.1389145889443628300269064119650184e126) }, { SC_(35.0), SC_(0.001953125000), SC_(3.5314352154325314429637711743107931e137) }, { SC_(35.0), SC_(0.0009765625000), SC_(2.4267838013160699267233738410387795e148) }
} };
do_test_polygamma<T>(small_data, name, "Mathematica Data - small arguments");
}
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