test_tr1.cpp

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   BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(1, static_cast<float>(-0.5L)), static_cast<float>(1.5L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(4, static_cast<float>(-0.5L)), static_cast<float>(3.835937500000000000000000000000000000000L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(7, static_cast<float>(-0.5L)), static_cast<float>(7.950934709821428571428571428571428571429L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(20, static_cast<float>(-0.5L)), static_cast<float>(76.12915699869631476833699787070874048223L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(50, static_cast<float>(-0.5L)), static_cast<float>(2307.428631277506570629232863491518399720L), eps * 100);

   BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(1, static_cast<float>(4.5L)), static_cast<float>(-3.500000000000000000000000000000000000000L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(4, static_cast<float>(4.5L)), static_cast<float>(0.08593750000000000000000000000000000000000L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(7, static_cast<float>(4.5L)), static_cast<float>(-1.036928013392857142857142857142857142857L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(20, static_cast<float>(4.5L)), static_cast<float>(1.437239150257817378525582974722170737587L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(50, static_cast<float>(4.5L)), static_cast<float>(-0.7795068145562651416494321484050019245248L), eps * 100);

   BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(4, 2, static_cast<float>(0.5L)), static_cast<float>(4.218750000000000000000000000000000000000L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(7, 5, static_cast<float>(0.5L)), static_cast<float>(5696.789530152175143607977274672800795328L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(4, 2, static_cast<float>(-0.5L)), static_cast<float>(4.218750000000000000000000000000000000000L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(7, 5, static_cast<float>(-0.5L)), static_cast<float>(5696.789530152175143607977274672800795328L), eps * 100);

   BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(1, static_cast<float>(0.5L)), static_cast<float>(0.5L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(4, static_cast<float>(0.5L)), static_cast<float>(-0.2890625000000000000000000000000000000000L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(7, static_cast<float>(0.5L)), static_cast<float>(0.2231445312500000000000000000000000000000L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(40, static_cast<float>(0.5L)), static_cast<float>(-0.09542943523261546936538467572384923220258L), eps * 100);

   BOOST_CHECK_CLOSE(tr1::beta(static_cast<float>(1), static_cast<float>(1)), static_cast<float>(1), eps * 20 * 100);
   BOOST_CHECK_CLOSE(tr1::beta(static_cast<float>(1), static_cast<float>(4)), static_cast<float>(0.25), eps * 20 * 100);
   BOOST_CHECK_CLOSE(tr1::beta(static_cast<float>(4), static_cast<float>(1)), static_cast<float>(0.25), eps * 20 * 100);
   BOOST_CHECK_CLOSE(tr1::beta(sv, static_cast<float>(4)), 1/sv, eps * 20 * 100);
   BOOST_CHECK_CLOSE(tr1::beta(static_cast<float>(4), sv), 1/sv, eps * 20 * 100);
   BOOST_CHECK_CLOSE(tr1::beta(static_cast<float>(4), static_cast<float>(20)), static_cast<float>(0.00002823263692828910220214568040654997176736L), eps * 20 * 100);
   BOOST_CHECK_CLOSE(tr1::beta(static_cast<float>(0.0125L), static_cast<float>(0.000023L)), static_cast<float>(43558.24045647538375006349016083320744662L), eps * 20 * 100);

   BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<float>(0)), static_cast<float>(1.5707963267948966192313216916397514420985846996876), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<float>(0.125)), static_cast<float>(1.5769867712158131421244030532288080803822271060839), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<float>(0.25)), static_cast<float>(1.5962422221317835101489690714979498795055744578951), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<float>(300)/1024), static_cast<float>(1.6062331054696636704261124078746600894998873503208), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<float>(400)/1024), static_cast<float>(1.6364782007562008756208066125715722889067992997614), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<float>(-0.5)), static_cast<float>(1.6857503548125960428712036577990769895008008941411), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<float>(-0.75)), static_cast<float>(1.9109897807518291965531482187613425592531451316788), eps * 5000);

   BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(-1)), static_cast<float>(1), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(0)), static_cast<float>(1.5707963267948966192313216916397514420985846996876), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(100) / 1024), static_cast<float>(1.5670445330545086723323795143598956428788609133377), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(200) / 1024), static_cast<float>(1.5557071588766556854463404816624361127847775545087), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(300) / 1024), static_cast<float>(1.5365278991162754883035625322482669608948678755743), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(400) / 1024), static_cast<float>(1.5090417763083482272165682786143770446401437564021), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(-0.5)), static_cast<float>(1.4674622093394271554597952669909161360253617523272), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(-600) / 1024), static_cast<float>(1.4257538571071297192428217218834579920545946473778), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(-800) / 1024), static_cast<float>(1.2927868476159125056958680222998765985004489572909), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(-900) / 1024), static_cast<float>(1.1966864890248739524112920627353824133420353430982), eps * 5000);

   BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<float>(0.2), static_cast<float>(0)), static_cast<float>(1.586867847454166237308008033828114192951), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<float>(0.4), static_cast<float>(0)), static_cast<float>(1.639999865864511206865258329748601457626), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<float>(0), static_cast<float>(0)), static_cast<float>(1.57079632679489661923132169163975144209858469968755291048747), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<float>(0), static_cast<float>(0.5)), static_cast<float>(2.221441469079183123507940495030346849307), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<float>(0.3), static_cast<float>(-4)), static_cast<float>(0.712708870925620061597924858162260293305195624270730660081949), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<float>(-0.5), static_cast<float>(-1e+05)), static_cast<float>(0.00496944596485066055800109163256108604615568144080386919012831), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<float>(-0.75), static_cast<float>(-1e+10)), static_cast<float>(0.0000157080225184890546939710019277357161497407143903832703317801), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<float>(-0.875), static_cast<float>(1) / 1024), static_cast<float>(2.18674503176462374414944618968850352696579451638002110619287), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<float>(-0.875), static_cast<float>(1023)/1024), static_cast<float>(101.045289804941384100960063898569538919135722087486350366997), eps * 5000);

   BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<float>(2.25), static_cast<float>(1)/(1024*1024)), static_cast<float>(2.34379212133481347189068464680335815256364262507955635911656e-15), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<float>(5.5), static_cast<float>(3.125)), static_cast<float>(0.0583514045989371500460946536220735787163510569634133670181210), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<float>(-5) + static_cast<float>(1)/1024, static_cast<float>(2.125)), static_cast<float>(0.0267920938009571023702933210070984416052633027166975342895062), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<float>(-5.5), static_cast<float>(10)), static_cast<float>(597.577606961369169607937419869926705730305175364662688426534), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<float>(-10486074)/(1024*1024), static_cast<float>(1)/1024), static_cast<float>(1.41474005665181350367684623930576333542989766867888186478185e35), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<float>(-10486074)/(1024*1024), static_cast<float>(50)), static_cast<float>(1.07153277202900671531087024688681954238311679648319534644743e20), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<float>(144794)/1024, static_cast<float>(100)), static_cast<float>(2066.27694757392660413922181531984160871678224178890247540320), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<float>(-144794)/1024, static_cast<float>(100)), static_cast<float>(2066.27694672763190927440969155740243346136463461655104698748), eps * 5000);

   BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(2457)/1024, static_cast<float>(1)/1024), static_cast<float>(3.80739920118603335646474073457326714709615200130620574875292e-9), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(5.5), static_cast<float>(3217)/1024), static_cast<float>(0.0281933076257506091621579544064767140470089107926550720453038), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(-5.5), static_cast<float>(3217)/1024), static_cast<float>(-2.55820064470647911823175836997490971806135336759164272675969), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(-5.5), static_cast<float>(1e+04)), static_cast<float>(2.449843111985605522111159013846599118397e-03), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(5.5), static_cast<float>(1e+04)), static_cast<float>(0.00759343502722670361395585198154817047185480147294665270646578), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(5.5), static_cast<float>(1e+06)), static_cast<float>(-0.000747424248595630177396350688505919533097973148718960064663632), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(5.125), static_cast<float>(1e+06)), static_cast<float>(-0.000776600124835704280633640911329691642748783663198207360238214), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(5.875), static_cast<float>(1e+06)), static_cast<float>(-0.000466322721115193071631008581529503095819705088484386434589780), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(0.5), static_cast<float>(101)), static_cast<float>(0.0358874487875643822020496677692429287863419555699447066226409), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(-5.5), static_cast<float>(1e+04)), static_cast<float>(0.00244984311198560552211115901384659911839737686676766460822577), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(-5.5), static_cast<float>(1e+06)), static_cast<float>(0.000279243200433579511095229508894156656558211060453622750659554), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(-0.5), static_cast<float>(101)), static_cast<float>(0.0708184798097594268482290389188138201440114881159344944791454), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(-10486074) / (1024*1024), static_cast<float>(1)/1024), static_cast<float>(1.41474013160494695750009004222225969090304185981836460288562e35), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(-10486074) / (1024*1024), static_cast<float>(15)), static_cast<float>(-0.0902239288885423309568944543848111461724911781719692852541489), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(10486074) / (1024*1024), static_cast<float>(1e+02)), static_cast<float>(-0.0547064914615137807616774867984047583596945624129838091326863), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(10486074) / (1024*1024), static_cast<float>(2e+04)), static_cast<float>(-0.00556783614400875611650958980796060611309029233226596737701688), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(-10486074) / (1024*1024), static_cast<float>(1e+02)), static_cast<float>(-0.0547613660316806551338637153942604550779513947674222863858713), eps * 5000);

   BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(0.5), static_cast<float>(0.875)), static_cast<float>(0.558532231646608646115729767013630967055657943463362504577189), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(0.5), static_cast<float>(1.125)), static_cast<float>(0.383621010650189547146769320487006220295290256657827220786527), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(2.25), static_cast<float>(std::ldexp(1.0, -30))), static_cast<float>(5.62397392719283271332307799146649700147907612095185712015604e20), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(5.5), static_cast<float>(3217)/1024), static_cast<float>(1.30623288775012596319554857587765179889689223531159532808379), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(-5.5), static_cast<float>(10)), static_cast<float>(0.0000733045300798502164644836879577484533096239574909573072142667), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(-5.5), static_cast<float>(100)), static_cast<float>(5.41274555306792267322084448693957747924412508020839543293369e-45), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(10240)/1024, static_cast<float>(1)/1024), static_cast<float>(2.35522579263922076203415803966825431039900000000993410734978e38), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(10240)/1024, static_cast<float>(10)), static_cast<float>(0.00161425530039067002345725193091329085443750382929208307802221), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(144793)/1024, static_cast<float>(100)), static_cast<float>(1.39565245860302528069481472855619216759142225046370312329416e-6), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(144793)/1024, static_cast<float>(200)), static_cast<float>(9.11950412043225432171915100042647230802198254567007382956336e-68), eps * 5000);

   BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<float>(0.5), static_cast<float>(1) / (1024*1024)), static_cast<float>(-817.033790261762580469303126467917092806755460418223776544122), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<float>(5.5), static_cast<float>(3.125)), static_cast<float>(-2.61489440328417468776474188539366752698192046890955453259866), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<float>(-5.5), static_cast<float>(3.125)), static_cast<float>(-0.0274994493896489729948109971802244976377957234563871795364056), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<float>(-5.5), static_cast<float>(1e+04)), static_cast<float>(-0.0075934350272267036139558519815481704718548