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Fixes for #1198.

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Use asymptotic expansion for very large a,b and add test cases.
Add some corrections to improve numeric stability.
Add better error handling of cases that explode so we get evaluation_error's.
This commit is contained in:
jzmaddock
2025-04-10 18:52:35 +01:00
parent 4d58e93b5d
commit dd59c01ac8
7 changed files with 1539 additions and 30 deletions
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105
include/boost/math/special_functions/beta.hpp
View File

@@ -240,21 +240,25 @@ BOOST_MATH_GPU_ENABLED T ibeta_power_terms(T a,
T c = a + b;
// combine power terms with Lanczos approximation:
T agh = static_cast<T>(a + Lanczos::g() - 0.5f);
T bgh = static_cast<T>(b + Lanczos::g() - 0.5f);
T cgh = static_cast<T>(c + Lanczos::g() - 0.5f);
T gh = Lanczos::g() - 0.5f;
T agh = static_cast<T>(a + gh);
T bgh = static_cast<T>(b + gh);
T cgh = static_cast<T>(c + gh);
if ((a < tools::min_value<T>()) || (b < tools::min_value<T>()))
result = 0; // denominator overflows in this case
else
result = Lanczos::lanczos_sum_expG_scaled(c) / (Lanczos::lanczos_sum_expG_scaled(a) * Lanczos::lanczos_sum_expG_scaled(b));
BOOST_MATH_INSTRUMENT_VARIABLE(result);
result *= prefix;
BOOST_MATH_INSTRUMENT_VARIABLE(result);
// combine with the leftover terms from the Lanczos approximation:
result *= sqrt(bgh / boost::math::constants::e<T>());
result *= sqrt(agh / cgh);
BOOST_MATH_INSTRUMENT_VARIABLE(result);
// l1 and l2 are the base of the exponents minus one:
T l1 = (x * b - y * agh) / agh;
T l2 = (y * a - x * bgh) / bgh;
T l1 = ((x * b - y * a) - y * gh) / agh;
T l2 = ((y * a - x * b) - x * gh) / bgh;
if((BOOST_MATH_GPU_SAFE_MIN(fabs(l1), fabs(l2)) < 0.2))
{
// when the base of the exponent is very near 1 we get really
@@ -809,9 +813,8 @@ struct ibeta_fraction2_t
BOOST_MATH_GPU_ENABLED result_type operator()()
{
T aN = (a + m - 1) * (a + b + m - 1) * m * (b - m) * x * x;
T denom = (a + 2 * m - 1);
aN /= denom * denom;
T aN = (m * (a + m - 1) / denom) * ((a + b + m - 1) / denom) * (b - m) * x * x;
T bN = static_cast<T>(m);
bN += (m * (b - m) * x) / (a + 2*m - 1);
@@ -844,7 +847,9 @@ BOOST_MATH_GPU_ENABLED inline T ibeta_fraction2(T a, T b, T x, T y, const Policy
return result;
ibeta_fraction2_t<T> f(a, b, x, y);
T fract = boost::math::tools::continued_fraction_b(f, boost::math::policies::get_epsilon<T, Policy>());
boost::uintmax_t max_terms = boost::math::policies::get_max_series_iterations<Policy>();
T fract = boost::math::tools::continued_fraction_b(f, boost::math::policies::get_epsilon<T, Policy>(), max_terms);
boost::math::policies::check_series_iterations<T>("boost::math::ibeta", max_terms, pol);
BOOST_MATH_INSTRUMENT_VARIABLE(fract);
BOOST_MATH_INSTRUMENT_VARIABLE(result);
return result / fract;
@@ -1118,6 +1123,60 @@ BOOST_MATH_GPU_ENABLED T binomial_ccdf(T n, T k, T x, T y, const Policy& pol)
return result;
}
template <class T, class Policy>
T ibeta_large_ab(T a, T b, T x, T y, bool invert, bool normalised, const Policy& pol)
{
//
// Large arguments, symetric case, see https://dlmf.nist.gov/8.18
//
BOOST_MATH_STD_USING
T x0 = a / (a + b);
T y0 = b / (a + b);
T nu = x0 * log(x / x0) + y0 * log(y / y0);
//
// Above compution is unstable, force nu to zero if
// something went wrong:
//
if ((nu > 0) || (x == x0) || (y == y0))
nu = 0;
nu = sqrt(-2 * nu);
//
// As per https://dlmf.nist.gov/8.18#E10 we need to make sure we have the correct root:
//
if ((nu != 0) && (nu / (x - x0) < 0))
nu = -nu;
//
// The correction term in https://dlmf.nist.gov/8.18#E9 is badly unstable, and often
// makes the compution worse not better, we exclude it for now:
/*
T c0 = 0;
if (nu != 0)
{
c0 = 1 / nu;
T lim = fabs(10 * tools::epsilon<T>() * c0);
c0 -= sqrt(x0 * y0) / (x - x0);
if(fabs(c0) < lim)
c0 = (1 - 2 * x0) / (3 * sqrt(x0 * y0));
else
c0 *= exp(a * log(x / x0) + b * log(y / y0));
c0 /= sqrt(constants::two_pi<T>() * (a + b));
}
else
{
c0 = (1 - 2 * x0) / (3 * sqrt(x0 * y0));
c0 /= sqrt(constants::two_pi<T>() * (a + b));
}
*/
T mul = 1;
if (!normalised)
mul = beta(a, b, pol);
return mul * ((invert ? (1 + boost::math::erf(-nu * sqrt((a + b) / 2), pol)) / 2 : boost::math::erfc(-nu * sqrt((a + b) / 2), pol) / 2));
}
//
// The incomplete beta function implementation:
@@ -1502,7 +1561,37 @@ BOOST_MATH_GPU_ENABLED T ibeta_imp(T a, T b, T x, const Policy& pol, bool inv, b
}
else
{
// a and b both large:
bool use_asym = false;
T ma = (std::max)(a, b);
T xa = ma == a ? x : y;
T saddle = ma / (a + b);
T powers = 0;
if ((ma > 1e-5f / tools::epsilon<T>()) && (ma / (std::min)(a, b) < (xa < saddle ? 2 : 15)))
{
if (a == b)
use_asym = true;
else
{
powers = exp(log(x / (a / (a + b))) * a + log(y / (b / (a + b))) * b);
if (powers < tools::epsilon<T>())
use_asym = true;
}
}
if(use_asym)
{
fract = ibeta_large_ab(a, b, x, y, invert, normalised, pol);
if (fract * tools::epsilon<T>() < powers)
{
// Erf approximation failed, correction term is too large, fall back:
fract = ibeta_fraction2(a, b, x, y, pol, normalised, p_derivative);
}
else
invert = false;
}
else
fract = ibeta_fraction2(a, b, x, y, pol, normalised, p_derivative);
BOOST_MATH_INSTRUMENT_VARIABLE(fract);
}
}

7
test/Jamfile.v2
View File

@@ -260,6 +260,7 @@ test-suite special_fun :
: # requirements
<define>TEST_FLOAT
<toolset>intel:<pch>off
<toolset>gcc:<cxxflags>-Wno-overflow
: test_ibeta_float ]
[ run test_ibeta.cpp test_instances//test_instances pch_light /boost/test//boost_unit_test_framework
: # command line
@@ -267,6 +268,7 @@ test-suite special_fun :
: # requirements
<define>TEST_DOUBLE
<toolset>intel:<pch>off
<toolset>gcc:<cxxflags>-Wno-overflow
: test_ibeta_double ]
[ run test_ibeta.cpp test_instances//test_instances pch_light /boost/test//boost_unit_test_framework
: # command line
@@ -274,6 +276,7 @@ test-suite special_fun :
: # requirements
<define>TEST_LDOUBLE
<toolset>intel:<pch>off
<toolset>gcc:<cxxflags>-Wno-overflow
: test_ibeta_long_double ]
[ run test_ibeta.cpp test_instances//test_instances pch_light /boost/test//boost_unit_test_framework
: # command line
@@ -282,6 +285,7 @@ test-suite special_fun :
<define>TEST_REAL_CONCEPT
<define>TEST_DATA=1
<toolset>intel:<pch>off
<toolset>gcc:<cxxflags>-Wno-overflow
: test_ibeta_real_concept1 ]
[ run test_ibeta.cpp test_instances//test_instances pch_light /boost/test//boost_unit_test_framework
: # command line
@@ -290,6 +294,7 @@ test-suite special_fun :
<define>TEST_REAL_CONCEPT
<define>TEST_DATA=2
<toolset>intel:<pch>off
<toolset>gcc:<cxxflags>-Wno-overflow
: test_ibeta_real_concept2 ]
[ run test_ibeta.cpp test_instances//test_instances pch_light /boost/test//boost_unit_test_framework
: # command line
@@ -298,6 +303,7 @@ test-suite special_fun :
<define>TEST_REAL_CONCEPT
<define>TEST_DATA=3
<toolset>intel:<pch>off
<toolset>gcc:<cxxflags>-Wno-overflow
: test_ibeta_real_concept3 ]
[ run test_ibeta.cpp test_instances//test_instances pch_light /boost/test//boost_unit_test_framework
: # command line
@@ -306,6 +312,7 @@ test-suite special_fun :
<define>TEST_REAL_CONCEPT
<define>TEST_DATA=4
<toolset>intel:<pch>off
<toolset>gcc:<cxxflags>-Wno-overflow
: test_ibeta_real_concept4 ]
[ run test_ibeta_derivative.cpp test_instances//test_instances pch_light /boost/test//boost_unit_test_framework

1046
test/ibeta_asym.ipp Normal file
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File diff suppressed because it is too large Load Diff

223
test/ibeta_large_asym_data.ipp Normal file
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@@ -0,0 +1,223 @@
#ifndef SC_
# define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
#endif
static const std::array<std::array<T, 7>, 216> ibeta_large_asym_data = {{
{ SC_(1.9028755000000000000000000000000000000000e+06), SC_(1.9028755000000000000000000000000000000000e+06), SC_(4.4999998807907104492187500000000000000000e-01), SC_(6.7345257302164224681015863169909954819429e-1153957), SC_(1.5954073231380415067243088463626848362274e-1145648), SC_(4.2211951973306332397251065526138530932813e-8309), SC_(1.0000000000000000000000000000000000000000e+00) },
{ SC_(1.9028755000000000000000000000000000000000e+06), SC_(2.3812680000000000000000000000000000000000e+06), SC_(4.3972539901733398437500000000000000000000e-01), SC_(6.8182153543183326515176359239213424241007e-1278111), SC_(8.7872964934870212072663237910183403621465e-1278035), SC_(7.7591729826936709829482073357324976283268e-77), SC_(1.0000000000000000000000000000000000000000e+00) },
{ SC_(1.9028755000000000000000000000000000000000e+06), SC_(7.9934700000000000000000000000000000000000e+06), SC_(1.9226138293743133544921875000000000000000e-01), SC_(9.9067809076337205020226204324704297621190e-2103896), SC_(1.2658599881338445200823176947439963560657e-2103895), SC_(4.3902564730816430949562878362500765540572e-01), SC_(5.6097435269183569050437121637499234459428e-01) },
{ SC_(1.9028755000000000000000000000000000000000e+06), SC_(1.5393168000000000000000000000000000000000e+07), SC_(1.1001686006784439086914062500000000000000e-01), SC_(3.0709384592321328069793224227070303132484e-2603162), SC_(3.1427207567895459654869249145913055789048e-2603162), SC_(4.9422383051098736680545332614875134887372e-01), SC_(5.0577616948901263319454667385124865112628e-01) },
{ SC_(1.9028755000000000000000000000000000000000e+06), SC_(1.8907696000000000000000000000000000000000e+07), SC_(9.1437831521034240722656250000000000000000e-02), SC_(2.0420460469102022545138913384686152410490e-2764269), SC_(2.0462559304440475118318579715281013896173e-2764269), SC_(4.9948513055577052930631242831720019446330e-01), SC_(5.0051486944422947069368757168279980553670e-01) },
{ SC_(1.9028755000000000000000000000000000000000e+06), SC_(6.6064240000000000000000000000000000000000e+07), SC_(2.7997003868222236633300781250000000000000e-02), SC_(1.5774679601689457701293713337946112843357e-3769687), SC_(1.5767088254989601689348312809270469665752e-3769687), SC_(5.0012033800284039124664276046170731990251e-01), SC_(4.9987966199715960875335723953829268009749e-01) },
{ SC_(1.9028755000000000000000000000000000000000e+06), SC_(1.2840448000000000000000000000000000000000e+08), SC_(1.4617582783102989196777343750000000000000e-02), SC_(1.2272989543515196592379719361127742228658e-4313187), SC_(1.1011430443339915966266513371237709561213e-4313188), SC_(9.1766620847363110463334708486842706468688e-01), SC_(8.2333791526368895366652915131572935313120e-02) },
{ SC_(1.9028755000000000000000000000000000000000e+06), SC_(1.6388441600000000000000000000000000000000e+08), SC_(1.2625593692064285278320312500000000000000e-02), SC_(2.2379905591363438077718248053802504138894e-4513497), SC_(1.2306617078599706585561478539321573698236e-4517423), SC_(1.0000000000000000000000000000000000000000e+00), SC_(5.4989584421432573401578165749458187966298e-3927) },
{ SC_(1.9028755000000000000000000000000000000000e+06), SC_(4.3818304000000000000000000000000000000000e+08), SC_(4.3239160440862178802490234375000000000000e-03), SC_(2.1351052162080738377752158329364831082938e-5323262), SC_(2.0876657782441229043598198786249387838491e-5323262), SC_(5.0561709811238592429363082896628831418203e-01), SC_(4.9438290188761407570636917103371168581797e-01) },
{ SC_(1.9028755000000000000000000000000000000000e+06), SC_(7.0231680000000000000000000000000000000000e+08), SC_(2.7021053247153759002685546875000000000000e-03), SC_(1.7171753658340205536597508835090813960451e-5712445), SC_(1.7160489432345209932774457020612746553550e-5712445), SC_(5.0016404733540482924881125749617034624668e-01), SC_(4.9983595266459517075118874250382965375332e-01) },
{ SC_(1.9028755000000000000000000000000000000000e+06), SC_(1.1784750080000000000000000000000000000000e+09), SC_(1.6120901564136147499084472656250000000000e-03), SC_(4.4528130280243712434575052875990444930800e-6139736), SC_(4.4507560572119092841812213188918101812581e-6139736), SC_(5.0011551383455162868187758358483146394170e-01), SC_(4.9988448616544837131812241641516853605830e-01) },
{ SC_(1.9028755000000000000000000000000000000000e+06), SC_(3.3226301440000000000000000000000000000000e+09), SC_(5.1513640210032463073730468750000000000000e-04), SC_(6.1227243528801362601263162508127393370932e-7000342), SC_(4.6306591220351569534527518404998617242648e-6995907), SC_(1.3222144389218661275155255990656824473730e-4435), SC_(1.0000000000000000000000000000000000000000e+00) },
{ SC_(1.9028755000000000000000000000000000000000e+06), SC_(5.4911078400000000000000000000000000000000e+09), SC_(3.4295339719392359256744384765625000000000e-04), SC_(2.6149108484367269736237820382089470752852e-7411022), SC_(3.7248296633465956938312661632485346466848e-7410979), SC_(7.0202159152892498671644211451960469438267e-44), SC_(1.0000000000000000000000000000000000000000e+00) },
{ SC_(1.9028755000000000000000000000000000000000e+06), SC_(1.0208120832000000000000000000000000000000e+10), SC_(1.8635463493410497903823852539062500000000e-04), SC_(9.2748555649264491893525898280981783335603e-7923331), SC_(1.1556342762635367611762646503508689369005e-7923330), SC_(4.4523869530130975886731984520101623889977e-01), SC_(5.5476130469869024113268015479898376110023e-01) },
{ SC_(1.9028755000000000000000000000000000000000e+06), SC_(2.6575216640000000000000000000000000000000e+10), SC_(7.1597540227230638265609741210937500000000e-05), SC_(4.6276736624195611675530268686084230968335e-8713987), SC_(4.7293318011006872829167186573859413979977e-8713987), SC_(4.9456780595686000753719434572816230736847e-01), SC_(5.0543219404313999246280565427183769263153e-01) },
{ SC_(1.9028755000000000000000000000000000000000e+06), SC_(6.8474880000000000000000000000000000000000e+10), SC_(2.7788595616584643721580505371093750000000e-05), SC_(1.9961080344733652118397772544625551064161e-9496154), SC_(1.9996632325188685070655211837751330538841e-9496154), SC_(4.9955512993513021760290705811696850552580e-01), SC_(5.0044487006486978239709294188303149447420e-01) },
{ SC_(1.9028755000000000000000000000000000000000e+06), SC_(1.3451883315200000000000000000000000000000e+11), SC_(1.4145593013381585478782653808593750000000e-05), SC_(1.7802207917710567492358760459317641530120e-10054170), SC_(1.7793621662538154355941990724670419045647e-10054170), SC_(5.0012060760029564593906902888483559886994e-01), SC_(4.9987939239970435406093097111516440113006e-01) },
{ SC_(1.9028755000000000000000000000000000000000e+06), SC_(2.7439156428800000000000000000000000000000e+11), SC_(6.9417778831848409026861190795898437500000e-06), SC_(5.1498173848455335180334842326780925784369e-10643274), SC_(4.7162291027388222554886517100796076759608e-10643275), SC_(9.1610283387989561791260098861862134587185e-01), SC_(8.3897166120104382087399011381378654128150e-02) },
{ SC_(1.9028755000000000000000000000000000000000e+06), SC_(5.4010445824000000000000000000000000000000e+11), SC_(3.8754646993766073137521743774414062500000e-06), SC_(1.3881076254193924371200087146474294833952e-11202921), SC_(7.5711059271845288998190054758937238577325e-11206800), SC_(1.0000000000000000000000000000000000000000e+00), SC_(5.4542643441621118418855248447818265689195e-3879) },
{ SC_(1.9028755000000000000000000000000000000000e+06), SC_(1.0817516339200000000000000000000000000000e+12), SC_(1.7590832612768281251192092895507812500000e-06), SC_(3.6772333809533645557755250995091540910167e-11776923), SC_(3.5957399673152117619500596891305185785393e-11776923), SC_(5.0560248262545560791996817742161318129120e-01), SC_(4.9439751737454439208003182257838681870880e-01) },
{ SC_(1.9028755000000000000000000000000000000000e+06), SC_(1.2728087347200000000000000000000000000000e+12), SC_(1.4950186368878348730504512786865234375000e-06), SC_(8.7426884581369101298023785104687130896670e-11911334), SC_(8.7380599673087001814241395987917522701361e-11911334), SC_(5.0013238823406074964018234911849650065137e-01), SC_(4.9986761176593925035981765088150349934863e-01) },
{ SC_(2.3812680000000000000000000000000000000000e+06), SC_(1.9028755000000000000000000000000000000000e+06), SC_(5.5583292245864868164062500000000000000000e-01), SC_(4.3935276310388312510238078544989597454643e-1278035), SC_(4.3937688624481899562425159365193806166822e-1278035), SC_(4.9998627385513067065623722003879892278745e-01), SC_(5.0001372614486932934376277996120107721255e-01) },
{ SC_(2.3812680000000000000000000000000000000000e+06), SC_(2.3812680000000000000000000000000000000000e+06), SC_(4.4999998807907104492187500000000000000000e-01), SC_(4.5221069700471147968135939224937236509789e-1444066), SC_(1.4783295654065370262831934073840562017973e-1433669), SC_(3.0589302114130054654341777662643761052713e-10397), SC_(1.0000000000000000000000000000000000000000e+00) },
{ SC_(2.3812680000000000000000000000000000000000e+06), SC_(7.9934700000000000000000000000000000000000e+06), SC_(2.2723035514354705810546875000000000000000e-01), SC_(9.8761355384028798154568169931415324504496e-2427300), SC_(1.1724212308990434807444743750283216404172e-2427230), SC_(8.4237092250791116712910030639025307589294e-70), SC_(1.0000000000000000000000000000000000000000e+00) },
{ SC_(2.3812680000000000000000000000000000000000e+06), SC_(1.5393168000000000000000000000000000000000e+07), SC_(1.3395811617374420166015625000000000000000e-01), SC_(8.1371310060783079316903184433500805998719e-3040399), SC_(1.0601714062504520983057644616907686491967e-3040398), SC_(4.3423866179036072297694471386694200205101e-01), SC_(5.6576133820963927702305528613305799794899e-01) },
{ SC_(2.3812680000000000000000000000000000000000e+06), SC_(1.8907696000000000000000000000000000000000e+07), SC_(1.1185345798730850219726562500000000000000e-01), SC_(1.7987736724254806309946776808865846376324e-3239461), SC_(1.8457633578563132960515199026525442649307e-3239461), SC_(4.9355340815028027796029154913140179427153e-01), SC_(5.0644659184971972203970845086859820572847e-01) },
{ SC_(2.3812680000000000000000000000000000000000e+06), SC_(6.6064240000000000000000000000000000000000e+07), SC_(3.4790679812431335449218750000000000000000e-02), SC_(5.8610359800492490130189506957543215537233e-4489140), SC_(5.8729944316146225646673601843131502231818e-4489140), SC_(4.9949043716669224750127278155856984273401e-01), SC_(5.0050956283330775249872721844143015726599e-01) },
{ SC_(2.3812680000000000000000000000000000000000e+06), SC_(1.2840448000000000000000000000000000000000e+08), SC_(1.8207397311925888061523437500000000000000e-02), SC_(5.0425212280790481304249820816925099781849e-5167519), SC_(5.0404283496123721648252818294024846307457e-5167519), SC_(5.0010378304733896866680889921830851784316e-01), SC_(4.9989621695266103133319110078169148215684e-01) },
{ SC_(2.3812680000000000000000000000000000000000e+06), SC_(1.6388441600000000000000000000000000000000e+08), SC_(1.4336388558149337768554687500000000000000e-02), SC_(1.7767528734811402715695898442966249753902e-5417778), SC_(1.1356498789439435786130694695684836764265e-5417779), SC_(9.3992280863719073113829860025252510538100e-01), SC_(6.0077191362809268861701399747474894618996e-02) },
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{ SC_(5.4911078400000000000000000000000000000000e+09), SC_(7.9934700000000000000000000000000000000000e+06), SC_(8.9869177341461181640625000000000000000000e-01), SC_(4.7008172934117010744268608837489606361011e-262676644), SC_(4.2099445612168176222312446731296295994010e-26150921), SC_(1.1165983839114984649414055074581842219116e-236525723), SC_(1.0000000000000000000000000000000000000000e+00) },
{ SC_(5.4911078400000000000000000000000000000000e+09), SC_(1.5393168000000000000000000000000000000000e+07), SC_(9.8723250627517700195312500000000000000000e-01), SC_(8.7696664459171685513222307445519816724999e-59796462), SC_(4.8704394498414282387240246481462481071204e-45983008), SC_(1.8005903853712197038127909088061405658382e-13813454), SC_(1.0000000000000000000000000000000000000000e+00) },
{ SC_(5.4911078400000000000000000000000000000000e+09), SC_(1.8907696000000000000000000000000000000000e+07), SC_(9.9646884202957153320312500000000000000000e-01), SC_(3.2393581388032644259773207088889754299989e-54799103), SC_(2.0170281900044893609559639027931345809476e-54795692), SC_(1.6060053869629132392532509459281957661979e-3411), SC_(1.0000000000000000000000000000000000000000e+00) },
{ SC_(5.4911078400000000000000000000000000000000e+09), SC_(6.6064240000000000000000000000000000000000e+07), SC_(9.8810195922851562500000000000000000000000e-01), SC_(3.8337503525777798567498581452972813212339e-155686351), SC_(9.2019309889757544287651407541317351232536e-155686340), SC_(4.1662454947279857412631515454515646519085e-12), SC_(9.9999999999583375450527201425873684845455e-01) },
{ SC_(5.4911078400000000000000000000000000000000e+09), SC_(1.2840448000000000000000000000000000000000e+08), SC_(9.7714924812316894531250000000000000000000e-01), SC_(3.7940599521723360006713238961938756799799e-265850302), SC_(8.5044232555380600016370205623037074278942e-265850302), SC_(3.0849820161511402481070471077236571081517e-01), SC_(6.9150179838488597518929528922763428918483e-01) },
{ SC_(5.4911078400000000000000000000000000000000e+09), SC_(1.6388441600000000000000000000000000000000e+08), SC_(9.7101950645446777343750000000000000000000e-01), SC_(3.9764175280848910737775000867174136318920e-322169581), SC_(4.0020979714725228373550753013921756958625e-322169581), SC_(4.9839065027892367225614105030689706564896e-01), SC_(5.0160934972107632774385894969310293435104e-01) },
{ SC_(1.0208120832000000000000000000000000000000e+10), SC_(1.9028755000000000000000000000000000000000e+06), SC_(9.9982368946075439453125000000000000000000e-01), SC_(2.0831198327561816801115236331606867702565e-7923330), SC_(1.1690566962073294390040411611762303251245e-7924582), SC_(1.0000000000000000000000000000000000000000e+00), SC_(5.6120472659537173757780473685839358681957e-1253) },
{ SC_(1.0208120832000000000000000000000000000000e+10), SC_(2.3812680000000000000000000000000000000000e+06), SC_(9.9976694583892822265625000000000000000000e-01), SC_(1.3121290802946075554175857984811456035977e-9683388), SC_(2.1330308954451816390308180020820834213545e-9683389), SC_(8.6016874839671604937946808127838684560430e-01), SC_(1.3983125160328395062053191872161315439570e-01) },
{ SC_(1.0208120832000000000000000000000000000000e+10), SC_(7.9934700000000000000000000000000000000000e+06), SC_(9.9921756982803344726562500000000000000000e-01), SC_(6.9766830624800081791017804293838607464749e-28302283), SC_(6.6926926551992406604565490702529843120478e-28302283), SC_(5.1038783383916609007798460281959528100871e-01), SC_(4.8961216616083390992201539718040471899129e-01) },
{ SC_(1.0208120832000000000000000000000000000000e+10), SC_(1.8907696000000000000000000000000000000000e+07), SC_(9.8816967010498046875000000000000000000000e-01), SC_(3.4137381383370857347172608963535683079741e-89195667), SC_(8.0016560944402144898752152123077406806487e-59880746), SC_(4.2662895006310645985871232086823001047668e-29314922), SC_(1.0000000000000000000000000000000000000000e+00) },
{ SC_(1.0208120832000000000000000000000000000000e+10), SC_(6.6064240000000000000000000000000000000000e+07), SC_(9.9347048997879028320312500000000000000000e-01), SC_(9.3580886115766235922264720015954794750574e-173400656), SC_(1.5349949874122546472219873459503901279923e-173397238), SC_(6.0964945738049601672163298413239264409616e-3418), SC_(1.0000000000000000000000000000000000000000e+00) },
{ SC_(1.0208120832000000000000000000000000000000e+10), SC_(1.2840448000000000000000000000000000000000e+08), SC_(9.8756772279739379882812500000000000000000e-01), SC_(5.1820196848058693175449285859650984576576e-300130106), SC_(8.0572302855350165615268641121218750367142e-300130087), SC_(6.4315149265486987592915343059237609231928e-20), SC_(9.9999999999999999993568485073451301240708e-01) },
{ SC_(1.3451883315200000000000000000000000000000e+11), SC_(1.9028755000000000000000000000000000000000e+06), SC_(9.9998486042022705078125000000000000000000e-01), SC_(4.9051680773388075190719347586453139472071e-10056122), SC_(3.5595829580248721848300751183988060575767e-10054170), SC_(1.3780176316105773450102617650129773815088e-1952), SC_(1.0000000000000000000000000000000000000000e+00) },
{ SC_(1.3451883315200000000000000000000000000000e+11), SC_(2.3812680000000000000000000000000000000000e+06), SC_(9.9998229742050170898437500000000000000000e-01), SC_(4.1156386876989822922772865888407071090856e-12349910), SC_(4.5869595210638883658221978499220925609089e-12349910), SC_(4.7292068287776856303434958063406477318607e-01), SC_(5.2707931712223143696565041936593522681393e-01) },
{ SC_(2.7439156428800000000000000000000000000000e+11), SC_(1.9028755000000000000000000000000000000000e+06), SC_(9.9998307228088378906250000000000000000000e-01), SC_(1.6829996164229106165276721752391297776754e-11096628), SC_(5.6214402951194157435823494036860533460330e-10643274), SC_(2.9938939632323513081891806297480617610184e-453355), SC_(1.0000000000000000000000000000000000000000e+00) },
{ SC_(2.7439156428800000000000000000000000000000e+11), SC_(2.3812680000000000000000000000000000000000e+06), SC_(9.9999034404754638671875000000000000000000e-01), SC_(5.2631814242827204795656447953582228243431e-13093227), SC_(2.5583815798952895536761257087421433721540e-13087116), SC_(2.0572308156229509893753815776204759364258e-6111), SC_(1.0000000000000000000000000000000000000000e+00) },
{ SC_(2.7439156428800000000000000000000000000000e+11), SC_(7.9934700000000000000000000000000000000000e+06), SC_(9.9997085332870483398437500000000000000000e-01), SC_(5.1048234014001975179816586694675258925023e-39727041), SC_(7.8063302663582094143028915587948982826828e-39727040), SC_(6.1379565020036795368260014426378256132886e-02), SC_(9.3862043497996320463173998557362174386711e-01) },
{ SC_(5.4010445824000000000000000000000000000000e+11), SC_(1.9028755000000000000000000000000000000000e+06), SC_(9.9989646673202514648437500000000000000000e-01), SC_(6.4969552030046504582592323046747707632721e-31869290), SC_(1.3881076254193924371200087146474294833952e-11202921), SC_(4.6804405393578247174189149262151496011253e-20666369), SC_(1.0000000000000000000000000000000000000000e+00) },
{ SC_(5.4010445824000000000000000000000000000000e+11), SC_(2.3812680000000000000000000000000000000000e+06), SC_(9.9998557567596435546875000000000000000000e-01), SC_(1.2810764791330623823942182869157436560355e-14910955), SC_(1.0288081627421349708687968862886394486490e-13787461), SC_(1.2452044273429399863007391374119654114562e-1123494), SC_(1.0000000000000000000000000000000000000000e+00) },
{ SC_(5.4010445824000000000000000000000000000000e+11), SC_(7.9934700000000000000000000000000000000000e+06), SC_(9.9998420476913452148437500000000000000000e-01), SC_(6.7651429999074967322095576365358877350799e-42085473), SC_(1.8296260828558949392932305747296630752961e-42077950), SC_(3.6975549612561645549999484238750497415660e-7523), SC_(1.0000000000000000000000000000000000000000e+00) },
{ SC_(5.4010445824000000000000000000000000000000e+11), SC_(1.5393168000000000000000000000000000000000e+07), SC_(9.9997150897979736328125000000000000000000e-01), SC_(6.8111367048550008031889878844483519560298e-76649521), SC_(9.3209944366439402355548780229705257402903e-76649522), SC_(8.7962404532339837203786730721507019671755e-01), SC_(1.2037595467660162796213269278492980328245e-01) },
{ SC_(1.0817516339200000000000000000000000000000e+12), SC_(1.9028755000000000000000000000000000000000e+06), SC_(9.9989825487136840820312500000000000000000e-01), SC_(6.0589317120723252541113349946179268351405e-55399381), SC_(7.2729733482685763177255847886396726695559e-11776923), SC_(8.3307492299758404929371656193733935608539e-43622459), SC_(1.0000000000000000000000000000000000000000e+00) },
{ SC_(1.0817516339200000000000000000000000000000e+12), SC_(2.3812680000000000000000000000000000000000e+06), SC_(9.9998778104782104492187500000000000000000e-01), SC_(2.7642009221596932108111810135428562127092e-17439580), SC_(1.3910953068816099436510223376105936614661e-14505769), SC_(1.9870679661454298179818292548319975722198e-2933811), SC_(1.0000000000000000000000000000000000000000e+00) },
{ SC_(1.0817516339200000000000000000000000000000e+12), SC_(7.9934700000000000000000000000000000000000e+06), SC_(9.9999159574508666992187500000000000000000e-01), SC_(3.4634825991925741776506724573595062163831e-44519195), SC_(3.2854376809849461544249645186823389479535e-44489166), SC_(1.0541921459165378773841716614592790604618e-30029), SC_(1.0000000000000000000000000000000000000000e+00) },
{ SC_(1.0817516339200000000000000000000000000000e+12), SC_(1.5393168000000000000000000000000000000000e+07), SC_(9.9998575448989868164062500000000000000000e-01), SC_(2.3257807249496668414319408874823334548697e-81292824), SC_(3.7608068638403042310159899282597120402851e-81292819), SC_(6.1842217003164798358762899509760774024875e-06), SC_(9.9999381577829968352016412371004902392260e-01) },
{ SC_(1.2728087347200000000000000000000000000000e+12), SC_(2.3812680000000000000000000000000000000000e+06), SC_(9.9989813566207885742187500000000000000000e-01), SC_(3.6948900225630247813534401741275619090862e-65816784), SC_(1.1241495287185133368978736390114774726005e-14673971), SC_(3.2868314473921057860079183641046716367451e-51142813), SC_(1.0000000000000000000000000000000000000000e+00) },
{ SC_(1.2728087347200000000000000000000000000000e+12), SC_(7.9934700000000000000000000000000000000000e+06), SC_(9.9998372793197631835937500000000000000000e-01), SC_(9.1736557910826772467040055287472354213489e-47272043), SC_(9.8830085864725315646649020107298097777291e-45053788), SC_(9.2822501476313719233238340353518419973114e-2218256), SC_(1.0000000000000000000000000000000000000000e+00) },
{ SC_(1.2728087347200000000000000000000000000000e+12), SC_(1.5393168000000000000000000000000000000000e+07), SC_(9.9998694658279418945312500000000000000000e-01), SC_(9.9871617076394215343482999901350101596173e-82400119), SC_(1.7982567628805513164721163082264438987906e-82380117), SC_(5.5538018339724802981269582109648165246413e-20002), SC_(1.0000000000000000000000000000000000000000e+00) },
{ SC_(1.2728087347200000000000000000000000000000e+12), SC_(1.8907696000000000000000000000000000000000e+07), SC_(9.9998515844345092773437500000000000000000e-01), SC_(5.6911712371451191546793733229095185848466e-99500284), SC_(2.7398036679964406630476792082766168887765e-99500288), SC_(9.9995186102012250980477933663466132120549e-01), SC_(4.8138979877490195220663365338678794509716e-05) }
}};
//#undef SC_

49
test/test_ibeta.cpp
View File

@@ -97,6 +97,23 @@ void expected_results()
largest_type, // test type(s)
"(?i).*medium.*", // test data group
".*", 300, 80); // test function
if (std::numeric_limits<double>::max_exponent < std::numeric_limits<long double>::max_exponent)
{
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"[^|]*", // platform
largest_type, // test type(s)
"(?i).*Very Large.*", // test data group
".*", 2000000, 200000); // test function
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
".*", // platform
largest_type, // test type(s)
"(?i).*Asymptotically.*", // test data group
".*", 900000000, 90000000); // test function
}
//
// Deficiencies in pow function really kick in here for
// large arguments. Note also that the tests here get
@@ -110,15 +127,25 @@ void expected_results()
largest_type, // test type(s)
"(?i).*large.*", // test data group
".*", 200000, 10000); // test function
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
if (std::numeric_limits<long double>::digits == 64)
{
// 80-bit long double, errors spill over:
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"linux|Mac OS|Sun.*", // platform
".*", // platform
"double", // test type(s)
"(?i).*Asymptotically.*", // test data group
".*", 500000, 50000); // test function
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
".*", // platform
"double", // test type(s)
"(?i).*large.*", // test data group
".*", 40, 20); // test function
#endif
".*", 200, 20); // test function
}
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
@@ -267,6 +294,20 @@ void expected_results()
largest_type, // test type(s)
"(?i).*medium.*", // test data group
".*", 350, 50); // test function
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"[^|]*", // platform
largest_type, // test type(s)
"(?i).*Very Large.*", // test data group
".*", 200000, 20000); // test function
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"[^|]*", // platform
largest_type, // test type(s)
"(?i).*Asymptotically Large.*", // test data group
".*", 900000000, 80000000); // test function
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib

13
test/test_ibeta.hpp
View File

@@ -131,6 +131,19 @@ void test_beta(T, const char* name)
do_test_beta<T>(ibeta_int_data, name, "Incomplete Beta Function: Small Integer Values");
#endif
#if !defined(TEST_DATA) || (TEST_DATA == 5)
if (std::numeric_limits<T>::is_specialized)
{
# include "ibeta_large_asym_data.ipp"
do_test_beta<T>(ibeta_large_asym_data, name, "Incomplete Beta Function: Very Large a,b Values");
# include "ibeta_asym.ipp"
do_test_beta<T>(ibeta_asym, name, "Incomplete Beta Function: Asymptotically Large a,b Values");
}
#endif
}
template <class T>

114
tools/ibeta_data.cpp
View File

@@ -79,16 +79,22 @@ T get_beta(T a, T b)
// compute the continued fraction:
//
template <class T>
T get_ibeta_fraction1(T a, T b, T x)
T get_ibeta_fraction1(T a, T b, T x, T log_scaling = 0)
{
using std::isnormal;
ibeta_fraction1_t<T> f(a, b, x);
T fract = boost::math::tools::continued_fraction_a(f, boost::math::policies::digits<T, boost::math::policies::policy<> >());
T denom = (a * (fract + 1));
T num = pow(x, a) * pow(1 - x, b);
if(num == 0)
return 0;
else if(denom == 0)
if(denom == 0)
return -1;
else if (!isnormal(num) || log_scaling)
{
return exp(a * log(x) + b * log(1 - x) - log(denom) - log_scaling);
}
else if (num == 0)
return 0;
return num / denom;
}
//
@@ -100,7 +106,7 @@ std::pair<T,T> ibeta_fraction1(T a, T b, T x)
T bet = get_beta(a, b);
if(x > ((a+1)/(a+b+2)))
{
T fract = get_ibeta_fraction1(b, a, 1-x);
T fract = get_ibeta_fraction1(b, a, T(1-x));
if(fract/bet > 0.75)
{
fract = get_ibeta_fraction1(a, b, x);
@@ -111,7 +117,7 @@ std::pair<T,T> ibeta_fraction1(T a, T b, T x)
T fract = get_ibeta_fraction1(a, b, x);
if(fract/bet > 0.75)
{
fract = get_ibeta_fraction1(b, a, 1-x);
fract = get_ibeta_fraction1(b, a, T(1-x));
return std::make_pair(bet - fract, fract);
}
return std::make_pair(fract, bet - fract);
@@ -124,24 +130,30 @@ template <class T>
std::pair<T,T> ibeta_fraction1_regular(T a, T b, T x)
{
T bet = get_beta(a, b);
T log_scaling = 0;
if (bet == 0)
{
log_scaling = boost::math::lgamma(a) + boost::math::lgamma(b) - boost::math::lgamma(a + b);
bet = 1;
}
if(x > ((a+1)/(a+b+2)))
{
T fract = get_ibeta_fraction1(b, a, 1-x);
T fract = get_ibeta_fraction1(b, a, T(1-x), log_scaling);
if(fract == 0)
bet = 1; // normalise so we don't get 0/0
else if(bet == 0)
return std::make_pair(T(-1), T(-1)); // Yikes!!
if(fract / bet > 0.75)
{
fract = get_ibeta_fraction1(a, b, x);
fract = get_ibeta_fraction1(a, b, x, log_scaling);
return std::make_pair(fract / bet, 1 - (fract / bet));
}
return std::make_pair(1 - (fract / bet), fract / bet);
}
T fract = get_ibeta_fraction1(a, b, x);
T fract = get_ibeta_fraction1(a, b, x, log_scaling);
if(fract / bet > 0.75)
{
fract = get_ibeta_fraction1(b, a, 1-x);
fract = get_ibeta_fraction1(b, a, T(1-x), log_scaling);
return std::make_pair(1 - (fract / bet), fract / bet);
}
return std::make_pair(fract / bet, 1 - (fract / bet));
@@ -237,9 +249,70 @@ struct beta_data_generator_int
}
};
template <class T>
bool is_01(const T& x)
{
return (x >= 0) && (x <= 1);
}
template <class T>
bool is_interesting(const T& x)
{
return (x > 0) && (x < 1);
}
struct beta_data_generator_asym
{
boost::math::tuple<mp_t, mp_t, mp_t, mp_t, mp_t, mp_t, mp_t> operator()(mp_t a_, mp_t b_)
{
float a = truncate_to_float(a_);
float b = truncate_to_float(b_);
float x0 = a / (a + b);
static const float mul[] = { 0.9, 0.99, 0.9999, 0.99999, 0.999999, 0.99999999, 1.001, 1.1, 1.00001, 1.0000001, 1.000000001 };
static int index = 0;
float x = truncate_to_float(real_cast<float>(x0 * mul[index]));
if (x >= 1)
throw std::domain_error("");
index = index == 10 ? 0 : ++index;
std::pair<mp_t, mp_t> ib_full = ibeta_fraction1(mp_t(a), mp_t(b), mp_t(x));
std::pair<mp_t, mp_t> ib_reg = ibeta_fraction1_regular(mp_t(a), mp_t(b), mp_t(x));
if (!isnormal(ib_full.first) || !isnormal(ib_reg.first) || !isnormal(ib_reg.second) || !isnormal(ib_full.second) || !is_01(ib_reg.first) || !is_01(ib_reg.second))
throw std::domain_error("");
std::cout << a << " " << b << " " << x << " " << ib_full.first << " " << ib_reg.first << " " << ib_reg.second << std::endl;
return boost::math::make_tuple(a, b, x, ib_full.first, ib_full.second, ib_reg.first, ib_reg.second);
}
};
struct beta_data_generator_asym2
{
boost::math::tuple<mp_t, mp_t, mp_t, mp_t, mp_t, mp_t, mp_t> operator()(mp_t a_power, mp_t _b_mul, mp_t _x_mul)
{
float b_mul = truncate_to_float(_b_mul);
float x_mul = truncate_to_float(_x_mul);
float a = truncate_to_float(pow(mp_t(10), a_power));
float b = truncate_to_float(a * b_mul);
float x0 = a / (a + b);
std::cout << a << " " << b_mul << " " << x_mul << std::endl;
float x = truncate_to_float(x0 * x_mul);
if (x >= 1)
throw std::domain_error("");
if(std::isinf(a))
throw std::domain_error("");
std::pair<mp_t, mp_t> ib_full = ibeta_fraction1(mp_t(a), mp_t(b), mp_t(x));
std::pair<mp_t, mp_t> ib_reg = ibeta_fraction1_regular(mp_t(a), mp_t(b), mp_t(x));
if (isnan(ib_full.first) || !isnormal(ib_reg.first) || !isnormal(ib_reg.second) || isnan(ib_full.second) || !is_01(ib_reg.first) || !is_01(ib_reg.second) || !(is_interesting(ib_reg.first) || is_interesting(ib_reg.second)))
throw std::domain_error("");
std::cout << a << " " << b << " " << x << " " << ib_full.first << " " << ib_reg.first << " " << ib_reg.second << std::endl;
return boost::math::make_tuple(a, b, x, ib_full.first, ib_full.second, ib_reg.first, ib_reg.second);
}
};
int main(int, char* [])
{
parameter_info<mp_t> arg1, arg2, arg3, arg4, arg5;
parameter_info<mp_t> arg1, arg2, arg3, arg4, arg5, arg6, arg7, arg8, arg9, arg10, arg11, arg12;
test_data<mp_t> data;
std::cout << "Welcome.\n"
@@ -252,19 +325,36 @@ int main(int, char* [])
arg3 = make_random_param(mp_t(0.0001), mp_t(1), 10);
arg4 = make_random_param(mp_t(0.0001), mp_t(1), 100 /*500*/);
arg5 = make_periodic_param(mp_t(1), mp_t(41), 10);
arg6 = make_power_param(mp_t(0), 20, 40);
arg7 = make_power_param(mp_t(0), 20, 40);
arg8 = make_power_param(mp_t(0), 50, 70);
arg9 = make_power_param(mp_t(0), 50, 70);
arg10 = make_periodic_param(mp_t(10), mp_t(18), 4);
arg11 = make_periodic_param(mp_t(1) - 10 * mp_t(1)/2048, mp_t(1) + 10 * mp_t(1) / 2048, 20);
arg12 = make_periodic_param(mp_t(1) - 10 * mp_t(1)/2048, mp_t(1) + 10 * mp_t(1) / 2048, 20);
arg1.type |= dummy_param;
arg2.type |= dummy_param;
arg3.type |= dummy_param;
arg4.type |= dummy_param;
arg5.type |= dummy_param;
arg6.type |= dummy_param;
arg7.type |= dummy_param;
arg8.type |= dummy_param;
arg9.type |= dummy_param;
arg10.type |= dummy_param;
arg11.type |= dummy_param;
arg12.type |= dummy_param;
// comment out all but one of the following when running
// or this program will take forever to complete!
//data.insert(beta_data_generator(), arg1, arg2, arg3);
//data.insert(beta_data_generator_medium(), arg4);
//data.insert(beta_data_generator_small(), arg4);
data.insert(beta_data_generator_int(), arg5, arg5, arg3);
//data.insert(beta_data_generator_int(), arg5, arg5, arg3);
//data.insert(beta_data_generator_asym(), arg6, arg7);
//data.insert(beta_data_generator_asym(), arg8, arg9);
data.insert(beta_data_generator_asym2(), arg10, arg11, arg12);
test_data<mp_t>::const_iterator i, j;
i = data.begin();