void test_digamma(T, const char* name)
{
//
// The actual test data is rather verbose, so it's in a separate file
//
// The contents are as follows, each row of data contains
// three items, input value a, input value b and erf(a, b):
//
# include "digamma_data.ipp"
do_test_digamma<T>(digamma_data, name, "Digamma Function: Large Values");
# include "digamma_root_data.ipp"
do_test_digamma<T>(digamma_root_data, name, "Digamma Function: Near the Positive Root");
# include "digamma_small_data.ipp"
do_test_digamma<T>(digamma_small_data, name, "Digamma Function: Near Zero");
# include "digamma_neg_data.ipp"
do_test_digamma<T>(digamma_neg_data, name, "Digamma Function: Negative Values");
static const boost::array<boost::array<T, 2>, 5> digamma_bugs = {{
// Test cases from Rocco Romeo:
{{ static_cast<T>(std::ldexp(1.0, -100)), SC_(-1.26765060022822940149670320537657721566490153286060651209008e30) }},
{{ static_cast<T>(-std::ldexp(1.0, -100)), SC_(1.26765060022822940149670320537542278433509846713939348790992e30) }},
{{ static_cast<T>(1), SC_(-0.577215664901532860606512090082402431042159335939923598805767) }},
{{ static_cast<T>(-1) + static_cast<T>(std::ldexp(1.0, -20)), SC_(-1.04857557721314249602848739817764518743062133735858753112190e6) }},
{{ static_cast<T>(-1) - static_cast<T>(std::ldexp(1.0, -20)), SC_(1.04857642278181269259522681939281063878220298942888100442172e6) }},
}
};
do_test_digamma<T>(digamma_bugs, name, "Digamma Function: Values near 0");
static const boost::array<boost::array<T, 2>, 40> digamma_integers = { {
{ 1, SC_(-0.57721566490153286060651209008240243) }, { 2, SC_(0.42278433509846713939348790991759757) }, { 3, SC_(0.92278433509846713939348790991759757) }, { 4, SC_(1.2561176684318004727268212432509309) }, { 5, SC_(1.5061176684318004727268212432509309) }, { 6, SC_(1.7061176684318004727268212432509309) }, { 7, SC_(1.8727843350984671393934879099175976) }, { 8, SC_(2.0156414779556099965363450527747404) }, { 9, SC_(2.1406414779556099965363450527747404) }, { SC_(10.0), SC_(2.2517525890667211076474561638858515) }, { SC_(11.0), SC_(2.3517525890667211076474561638858515) }, { SC_(12.0), SC_(2.4426616799758120167383652547949424) }, { SC_(13.0), SC_(2.5259950133091453500716985881282758) }, { SC_(14.0), SC_(2.6029180902322222731486216650513527) }, { SC_(15.0), SC_(2.6743466616607937017200502364799241) }, { SC_(16.0), SC_(2.7410133283274603683867169031465908) }, { SC_(17.0), SC_(2.8035133283274603683867169031465908) }, { SC_(18.0), SC_(2.8623368577392250742690698443230614) }, { SC_(19.0), SC_(2.9178924132947806298246253998786169) }, { SC_(20.0), SC_(2.9705239922421490508772569788259854) }, { SC_(21.0), SC_(3.0205239922421490508772569788259854) }, { SC_(22.0), SC_(3.0681430398611966699248760264450330) }, { SC_(23.0), SC_(3.1135975853157421244703305718995784) }, { SC_(24.0), SC_(3.1570758461853073418616349197256654) }, { SC_(25.0), SC_(3.1987425128519740085283015863923321) }, { SC_(26.0), SC_(3.2387425128519740085283015863923321) }, { SC_(27.0), SC_(3.2772040513135124700667631248538705) }, { SC_(28.0), SC_(3.3142410883505495071038001618909076) }, { SC_(29.0), SC_(3.3499553740648352213895144476051933) }, { SC_(30.0), SC_(3.3844381326855248765619282407086415) }, { SC_(31.0), SC_(3.4177714660188582098952615740419749) }, { SC_(32.0), SC_(3.4500295305349872421533260901710071) }, { SC_(33.0), SC_(3.4812795305349872421533260901710071) }, { SC_(34.0), SC_(3.5115825608380175451836291204740374) }, { SC_(35.0), SC_(3.5409943255438998981248055910622727) }, { SC_(36.0), SC_(3.5695657541153284695533770196337013) }, { SC_(37.0), SC_(3.5973435318931062473311547974114791) }, { SC_(38.0), SC_(3.6243705589201332743581818244385061) }, { SC_(39.0), SC_(3.6506863483938174848844976139121903) }, { SC_(40.0), SC_(3.6763273740348431259101386395532160) }
}
};
do_test_digamma<T>(digamma_integers, name, "Digamma Function: Integer arguments");
static const boost::array<boost::array<T, 2>, 41> digamma_half_integers = { {
{ SC_(0.5), SC_(-1.9635100260214234794409763329987556) }, { SC_(1.5), SC_(0.036489973978576520559023667001244433) }, { SC_(2.5), SC_(0.70315664064524318722569033366791110) }, { SC_(3.5), SC_(1.1031566406452431872256903336679111) }, { SC_(4.5), SC_(1.3888709263595289015114046193821968) }, { SC_(5.5), SC_(1.6110931485817511237336268416044190) }, { SC_(6.5), SC_(1.7929113303999329419154450234226009) }, { SC_(7.5), SC_(1.9467574842460867880692911772687547) }, { SC_(8.5), SC_(2.0800908175794201214026245106020880) }, { SC_(9.5), SC_(2.1977378764029495331673303929550292) }, { SC_(10.5), SC_(2.3030010342976863752725935508497661) }, { SC_(11.5), SC_(2.3982391295357816133678316460878613) }, { SC_(12.5), SC_(2.4851956512749120481504403417400352) }, { SC_(13.5), SC_(2.5651956512749120481504403417400352) }, { SC_(14.5), SC_(2.6392697253489861222245144158141093) }, { SC_(15.5), SC_(2.7082352425903654325693420020210058) }, { SC_(16.5), SC_(2.7727513716226234970854710342790703) }, { SC_(17.5), SC_(2.8333574322286841031460770948851310) }, { SC_(18.5), SC_(2.8905002893715412460032199520279881) }, { SC_(19.5), SC_(2.9445543434255953000572740060820421) }, { SC_(20.5), SC_(2.9958363947076465821085560573640934) }, { SC_(21.5), SC_(3.0446168825125246308890438622421422) }, { SC_(22.5), SC_(3.0911285104195013750750903738700492) }, { SC_(23.5), SC_(3.1355729548639458195195348183144936) }, { SC_(24.5), SC_(3.1781261463533075216471943927825787) }, { SC_(25.5), SC_(3.2189424728839197665451535764560481) }, { SC_(26.5), SC_(3.2581581591584295704667222039070285) }, { SC_(27.5), SC_(3.2958940082150333440516278642843870) }, { SC_(28.5), SC_(3.3322576445786697076879915006480234) }, { SC_(29.5), SC_(3.3673453638769153217230792199462690) }, { SC_(30.5), SC_(3.4012436689616610844349436267259300) }, { SC_(31.5), SC_(3.4340305542075627237792059218078972) }, { SC_(32.5), SC_(3.4657765859535944698109519535539290) }, { SC_(33.5), SC_(3.4965458167228252390417211843231597) }, { SC_(34.5), SC_(3.5263965629914819554596316320843538) }, { SC_(35.5), SC_(3.5553820702378587670538345306350784) }, { SC_(36.5), SC_(3.5835510843223658093073556573956418) }, { SC_(37.5), SC_(3.6109483445963384120470816847929021) }, { SC_(38.5), SC_(3.6376150112630050787137483514595687) }, { SC_(39.5), SC_(3.6635890372370310527397223774335947) }, { SC_(40.5), SC_(3.6889054929332335843852919976867593) }
}
};
do_test_digamma<T>(digamma_half_integers, name, "Digamma Function: Half integer arguments");
BOOST_MATH_CHECK_THROW(boost::math::digamma(T(0)), std::domain_error);
BOOST_MATH_CHECK_THROW(boost::math::digamma(T(-1)), std::domain_error);
BOOST_MATH_CHECK_THROW(boost::math::digamma(T(-2)), std::domain_error);
}
void test_spots(T, const char* type_name)
{
BOOST_MATH_STD_USING
// Function values calculated on http://functions.wolfram.com/
// Note that Mathematica's EllipticE accepts k^2 as the second parameter.
static const boost::array<boost::array<T, 3>, 10> data1 = {{
{ { SC_(0.5), SC_(0.5), SC_(0.040348098248931543984282958654503585) } },
{{ SC_(0), SC_(0.5), SC_(0) }},
{ { SC_(1), SC_(0.5), SC_(0.28991866293419922467977188008516755) } },
{ { SC_(1), T(1), SC_(0.38472018607562056416055864584160775) } },
{ { SC_(-1), T(1), SC_(-0.38472018607562056416055864584160775) } },
{ { SC_(-1), T(0.5), SC_(-0.28991866293419922467977188008516755) } },
{ { SC_(-10), T(0.5), SC_(-5.2996914501577855803123384771117708) } },
{ { SC_(10), SC_(-0.5), SC_(5.2996914501577855803123384771117708) } },
}};
do_test_ellint_d2<T>(data1, type_name, "Elliptic Integral E: Mathworld Data");
#include "ellint_d2_data.ipp"
do_test_ellint_d2<T>(ellint_d2_data, type_name, "Elliptic Integral D: Random Data");
// Function values calculated on http://functions.wolfram.com/
// Note that Mathematica's EllipticE accepts k^2 as the second parameter.
static const boost::array<boost::array<T, 2>, 3> data2 = {{
{ { SC_(0.5), SC_(0.87315258189267554964563356323264341) } },
{ { SC_(1.0) / 1024, SC_(0.78539844427788694671464428063604776) } },
{ { boost::math::tools::root_epsilon<T>(), SC_(0.78539816339744830961566084581987572) } }
}};
do_test_ellint_d1<T>(data2, type_name, "Elliptic Integral E: Mathworld Data");
#include "ellint_d_data.ipp"
do_test_ellint_d1<T>(ellint_d_data, type_name, "Elliptic Integral D: Random Data");
BOOST_MATH_CHECK_THROW(boost::math::ellint_d(T(1)), std::domain_error);
BOOST_MATH_CHECK_THROW(boost::math::ellint_d(T(-1)), std::domain_error);
BOOST_MATH_CHECK_THROW(boost::math::ellint_d(T(1.5)), std::domain_error);
BOOST_MATH_CHECK_THROW(boost::math::ellint_d(T(-1.5)), std::domain_error);
}
void test_spots(T, const char*)
{
#ifdef _MSC_VER
# pragma warning(push)
# pragma warning(disable:4127 4756)
#endif
//
// A few special spot tests:
//
BOOST_MATH_STD_USING
T tol = boost::math::tools::epsilon<T>() * 20;
if(std::numeric_limits<T>::max_exponent > 200)
{
BOOST_CHECK_CLOSE_FRACTION(boost::math::tgamma_ratio(T(ldexp(T(1), -500)), T(180.25)), T(8.0113754557649679470816892372669519037339812035512e-178L), 3 * tol);
BOOST_CHECK_CLOSE_FRACTION(boost::math::tgamma_ratio(T(ldexp(T(1), -525)), T(192.25)), T(1.5966560279353205461166489184101261541784867035063e-197L), 3 * tol);
BOOST_CHECK_CLOSE_FRACTION(boost::math::tgamma_ratio(T(182.25), T(ldexp(T(1), -500))), T(4.077990437521002194346763299159975185747917450788e+181L), 3 * tol);
BOOST_CHECK_CLOSE_FRACTION(boost::math::tgamma_ratio(T(193.25), T(ldexp(T(1), -525))), T(1.2040790040958522422697601672703926839178050326148e+199L), 3 * tol);
BOOST_CHECK_CLOSE_FRACTION(boost::math::tgamma_ratio(T(193.25), T(194.75)), T(0.00037151765099653237632823607820104961270831942138159L), 3 * tol);
}
BOOST_MATH_CHECK_THROW(boost::math::tgamma_ratio(T(0), T(2)), std::domain_error);
BOOST_MATH_CHECK_THROW(boost::math::tgamma_ratio(T(2), T(0)), std::domain_error);
BOOST_MATH_CHECK_THROW(boost::math::tgamma_ratio(T(-1), T(2)), std::domain_error);
BOOST_MATH_CHECK_THROW(boost::math::tgamma_ratio(T(2), T(-1)), std::domain_error);
if(std::numeric_limits<T>::has_infinity)
{
BOOST_MATH_CHECK_THROW(boost::math::tgamma_ratio(std::numeric_limits<T>::infinity(), T(2)), std::domain_error);
BOOST_MATH_CHECK_THROW(boost::math::tgamma_ratio(T(2), std::numeric_limits<T>::infinity()), std::domain_error);
}
//
// Some bug cases from Rocco Romeo:
//
if(std::numeric_limits<T>::min_exponent < -1020)
{
BOOST_CHECK_CLOSE_FRACTION(boost::math::tgamma_ratio(T(ldexp(T(1), -1020)), T(100)), T(1.20390418056093374068585549133304106854441830616070800417660e151L), tol);
BOOST_CHECK_CLOSE_FRACTION(boost::math::tgamma_ratio(T(ldexp(T(1), -1020)), T(150)), T(2.94980580122226729924781231239336413648584663386992050529324e46L), tol);
BOOST_CHECK_CLOSE_FRACTION(boost::math::tgamma_ratio(T(ldexp(T(1), -1020)), T(180)), T(1.00669209319561468911303652019446665496398881230516805140750e-20L), tol);
BOOST_CHECK_CLOSE_FRACTION(boost::math::tgamma_ratio(T(ldexp(T(1), -1020)), T(220)), T(1.08230263539550701700187215488533416834407799907721731317227e-112L), tol);
BOOST_CHECK_CLOSE_FRACTION(boost::math::tgamma_ratio(T(ldexp(T(1), -1020)), T(260)), T(7.62689807594728483940172477902929825624752380292252137809206e-208L), tol);
BOOST_CHECK_CLOSE_FRACTION(boost::math::tgamma_ratio(T(ldexp(T(1), -1020)), T(290)), T(5.40206998243175672775582485422795773284966068149812072521290e-281L), tol);
BOOST_CHECK_CLOSE_FRACTION(boost::math::tgamma_delta_ratio(T(ldexp(T(1), -1020)), T(ldexp(T(1), -1020))), T(2), tol);
if(0 != ldexp(T(1), -1074))
{
// This is denorm_min at double precision:
BOOST_CHECK_CLOSE_FRACTION(boost::math::tgamma_ratio(T(ldexp(T(1), -1074)), T(200)), T(5.13282785052571536804189023927976812551830809667482691717029e-50), tol * 50);
BOOST_CHECK_CLOSE_FRACTION(boost::math::tgamma_ratio(T(200), T(ldexp(T(1), -1074))), T(1.94824379293682687942882944294875087145333536754699303593931e49), tol * 10);
BOOST_CHECK_CLOSE_FRACTION(boost::math::tgamma_delta_ratio(T(ldexp(T(1), -1074)), T(200)), T(5.13282785052571536804189023927976812551830809667482691717029e-50), tol * 10);
BOOST_CHECK_CLOSE_FRACTION(boost::math::tgamma_delta_ratio(T(200), T(ldexp(T(1), -1074))), T(1), tol);
}
}
}
