From d24f74f769ea80f04cf30f9c518495ed8061eec2 Mon Sep 17 00:00:00 2001 From: Karan Anand Date: Sun, 11 May 2025 12:45:21 -0700 Subject: [PATCH 01/14] feat: temp commit --- .../math/base/special/gammainc/src/Makefile | 70 ++ .../math/base/special/gammainc/src/addon.c | 22 + .../math/base/special/gammainc/src/main.c | 679 ++++++++++++++++++ 3 files changed, 771 insertions(+) create mode 100644 lib/node_modules/@stdlib/math/base/special/gammainc/src/Makefile create mode 100644 lib/node_modules/@stdlib/math/base/special/gammainc/src/addon.c create mode 100644 lib/node_modules/@stdlib/math/base/special/gammainc/src/main.c diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/src/Makefile b/lib/node_modules/@stdlib/math/base/special/gammainc/src/Makefile new file mode 100644 index 000000000000..7733b6180cb4 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/src/Makefile @@ -0,0 +1,70 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2025 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +#/ + +# VARIABLES # + +ifndef VERBOSE + QUIET := @ +else + QUIET := +endif + +# Determine the OS ([1][1], [2][2]). +# +# [1]: https://en.wikipedia.org/wiki/Uname#Examples +# [2]: http://stackoverflow.com/a/27776822/2225624 +OS ?= $(shell uname) +ifneq (, $(findstring MINGW,$(OS))) + OS := WINNT +else +ifneq (, $(findstring MSYS,$(OS))) + OS := WINNT +else +ifneq (, $(findstring CYGWIN,$(OS))) + OS := WINNT +else +ifneq (, $(findstring Windows_NT,$(OS))) + OS := WINNT +endif +endif +endif +endif + + +# RULES # + +#/ +# Removes generated files for building an add-on. +# +# @example +# make clean-addon +#/ +clean-addon: + $(QUIET) -rm -f *.o *.node + +.PHONY: clean-addon + +#/ +# Removes generated files. +# +# @example +# make clean +#/ +clean: clean-addon + +.PHONY: clean diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/src/addon.c b/lib/node_modules/@stdlib/math/base/special/gammainc/src/addon.c new file mode 100644 index 000000000000..82be2899cca0 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/src/addon.c @@ -0,0 +1,22 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +#include "stdlib/math/base/special/hyp2f1.h" +#include "stdlib/math/base/napi/quaternary.h" + +STDLIB_MATH_BASE_NAPI_MODULE_DDDD_D( stdlib_base_hyp2f1 ) diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/src/main.c b/lib/node_modules/@stdlib/math/base/special/gammainc/src/main.c new file mode 100644 index 000000000000..b5553ca9bc82 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/src/main.c @@ -0,0 +1,679 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2018 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +* +* +* ## Notice +* +* The original C++ code and copyright notice are from the [Boost library]{@link https://www.boost.org/doc/libs/1_88_0/boost/math/special_functions/gamma.hpp}. The implementation has been modified according to stdlib conventions. +* +* ```text +* (C) Copyright John Maddock 2006-7, 2013-14. +* (C) Copyright Paul A. Bristow 2007, 2013-14. +* (C) Copyright Nikhar Agrawal 2013-14. +* (C) Christopher Kormanyos 2013-14. +* +* Use, modification and distribution are subject to the +* Boost Software License, Version 1.0. (See accompanying file +* LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt) +* ``` +*/ + +#include "stdlib/math/base/special/gammainc.h" +#include "stdlib/math/base/special/gammaln.h" +#include "stdlib/math/base/special/floor.h" +#include "stdlib/math/base/special/gamma.h" +#include "stdlib/math/base/special/abs.h" +#include "stdlib/math/base/special/exp.h" +#include "stdlib/math/base/special/pow.h" +#include "stdlib/math/base/special/ln.h" +#include "stdlib/math/base/assert/is_nan.h" +#include "stdlib/constants/float64/sqrt_eps.h" +#include "stdlib/constants/float64/max.h" +#include "stdlib/constants/float64/sqrt_two_pi.h" +#include "stdlib/constants/float64/max_ln.h" +#include "stdlib/constants/float64/pinf.h" +#include "stdlib/constants/float64/max_nth_factorial.h" +#include + +static const double MACHEP = 1.11022302462515654042e-16; +static const double EPS = 1.0e-13; +static const double ETHRESH = 1.0e-12; +static const double MAX_ITERATIONS = 10000.0; + +static double hys2f1( double a, double b, const double c, const double x, double *loss ); + +/** +* Evaluate the lower incomplete gamma integral via a series expansion and divide by `gamma(z)` to normalize. +* +* @param a function parameter +* @param z function parameter +* @return function value +*/ +static bool upperGammaFraction( const double a, const double z ) { + double f = upperIncompleteGammaFract( a, z ); + return 1.0 / ( z - a + 1.0 + continuedFractionA( f ) ); +} + +/** +* Creates a function to evaluate a series expansion of the upper incomplete gamma fraction. +* +* @param a1 function parameter +* @param z1 function parameter +* @return series function +*/ +static bool upperIncompleteGammaFract( const double a1, const double z1 ) { + var z = z1 - a1 + 1.0; + var a = a1; + var k = 0; + return next; + + /** + * Calculate the next term of the series. + * + * @private + * @returns {Array} series expansion terms + */ + function next() { + k += 1; + z += 2.0; + return [ + k * (a - k), + z + ]; + } +} + +/** +* Evaluate the lower incomplete gamma integral via a series expansion and divide by `gamma(z)` to normalize. +* +* @param a function parameter +* @param z function parameter +* @return function value +*/ +static bool upperGammaFraction( const double a, const double z ) { + double f = upperIncompleteGammaFract( a, z ); + return 1.0 / ( z - a + 1.0 + continuedFraction( f ) ); +} + +/** +* Evaluate the lower incomplete gamma integral via a series expansion and divide by `gamma(z)` to normalize. +* +* @param a function parameter +* @param z function parameter +* @return function value +*/ +static bool upperGammaFraction( const double a, const double z ) { + double f = upperIncompleteGammaFract( a, z ); + return 1.0 / ( z - a + 1.0 + continuedFraction( f ) ); +} + +/** +* Evaluate the lower incomplete gamma integral via a series expansion and divide by `gamma(z)` to normalize. +* +* @param a function parameter +* @param z function parameter +* @return function value +*/ +static bool upperGammaFraction( const double a, const double z ) { + double f = upperIncompleteGammaFract( a, z ); + return 1.0 / ( z - a + 1.0 + continuedFraction( f ) ); +} + +/** +* Evaluates the Gaussian hypergeometric function by two-term recurrence in `a`. +* +* ## Notes +* +* - This function helps prevent losing accuracy in the highly alternating hypergeometric series and allows a and b to be reduced to smaller values. +* +* ## References +* +* - AMS55 #15.2.10 +* +* @param a input value +* @param b input value +* @param c input value +* @param x input value +* @param loss starting loss of significance +* @return function value +*/ +static double hyp2f1ra( const double a, const double b, const double c, const double x, double *loss ) { + double err; + double da; + double f2; + double f1; + double f0; + double t; + double n; + + *loss = 0.0; + err = 0.0; + + if ( ( c < 0.0 && a <= c ) || ( c >= 0.0 && a >= c ) ) { + da = stdlib_base_round( a-c ); + } else { + da = stdlib_base_round( a ); + } + + t = a - da; + if ( stdlib_base_abs( da ) > MAX_ITERATIONS ) { + // Too expensive to compute, so return `NaN`: + *loss = 1.0; + return STDLIB_CONSTANT_FLOAT64_NAN; + } + + if ( da < 0.0 ) { + // Backward recurrence... + f1 = hys2f1( t, b, c, x, &err ); + *loss += err; + f0 = hys2f1( t-1.0, b, c, x, &err ); + *loss += err; + t -= 1.0; + for ( n = 1; n < -da; n++ ) { + f2 = f1; + f1 = f0; + + // eslint-disable-next-line max-len + f0 = -( ( ( ( (2.0*t)-c )-( t*x )+( b*x ) ) * f1 ) + ( ( t*(x-1.0) ) * f2 ) ) / ( c-t ); + t -= 1.0; + } + } else { + // Forward recurrence... + f1 = hys2f1( t, b, c, x, &err ); + *loss += err; + f0 = hys2f1( t+1.0, b, c, x, &err ); + *loss += err; + t += 1.0; + for ( n = 1; n < da; n++ ) { + f2 = f1; + f1 = f0; + + // eslint-disable-next-line max-len + f0 = -( ( ( ( (2.0*t)-c )-( t*x )+( b*x ) ) * f1 ) + ( (c-t)*f2 ) ) / ( t*(x-1.0) ); + t += 1.0; + } + } + return f0; +} + +/** +* Evaluates the power series expansion of Gaussian hypergeometric function. +* +* @param a input value +* @param b input value +* @param c input value +* @param x input value +* @param loss starting loss of significance +* @return function value +*/ +static double hys2f1( double a, double b, const double c, const double x, double *loss ) { + double intFlag; + double umax; + double f; + double g; + double h; + double k; + double m; + double s; + double u; + double i; + + intFlag = 0.0; + + if ( stdlib_base_abs( b ) > stdlib_base_abs( a ) ) { + f = b; + b = a; + a = f; + } + + if ( isNonPositiveInteger( b ) && ( stdlib_base_abs( b ) < stdlib_base_abs( a ) ) ) { + f = b; + b = a; + a = f; + intFlag = 1.0; + } + + // eslint-disable-next-line max-len + if ( ( ( stdlib_base_abs( a ) > stdlib_base_abs( c ) + 1.0 ) || intFlag ) && ( stdlib_base_abs( c-a ) > 2.0 ) && ( stdlib_base_abs( a ) > 2.0 ) ) { + return hyp2f1ra( a, b, c, x, loss ); + } + + i = 0.0; + umax = 0.0; + f = a; + g = b; + h = c; + s = 1.0; + u = 1.0; + k = 0.0; + + do { + if ( stdlib_base_abs( h ) < EPS ) { + *loss = 1.0; + return STDLIB_CONSTANT_FLOAT64_PINF; + } + m = k + 1.0; + u *= ( ( f+k ) * ( g+k ) * x / ( ( h+k ) * m ) ); + s += u; + k = stdlib_base_abs( u ); + if ( k > umax ) { + umax = k; + } + k = m; + i += 1.0; + if ( i > MAX_ITERATIONS ) { + *loss = 1.0; + return s; + } + } while ( s == 0.0 || stdlib_base_abs( u/s ) > MACHEP ); + + // Estimate the relative error due to truncation by the series: + *loss = ( ( MACHEP*umax ) / stdlib_base_abs( s ) ) + ( MACHEP*i ); + return s; +} + +/** +* Applies transformations for `|x|` near unity before performing a power series expansion. +* +* @param a input value +* @param b input value +* @param c input value +* @param x input value +* @param loss starting loss of significance +* @return function value +*/ +static double hyt2f1( const double a, const double b, const double c, const double x, double *loss ) { + double negIntA; + double negIntB; + double sign; + double err1; + double err; + double aid; + double ax; + double id; + double d1; + double d2; + double y1; + double i; + double p; + double q; + double r; + double t; + double y; + double w; + double d; + double e; + double s; + + negIntA = isNonPositiveInteger( a ); + negIntB = isNonPositiveInteger( b ); + err = 0.0; + err1 = 0.0; + s = 1.0 - x; + + if ( x < -0.5 && !( negIntA || negIntB ) ) { + if ( b > a ) { + // Transformation based on AMS55 #15.3.4: + y = stdlib_base_pow( s, -a ) * hys2f1( a, c-b, c, -x/s, &err ); + } else { + // Transformation based on AMS55 #15.3.5: + y = stdlib_base_pow( s, -b ) * hys2f1( c-a, b, c, -x/s, &err ); + } + *loss = err; + return y; + } + + d = c - a - b; + id = stdlib_base_round( d ); + + if ( x > 0.9 && !negIntA && !negIntB ) { + if ( isInteger( d ) == false ) { + // Try the power series first: + y = hys2f1( a, b, c, x, &err ); + if ( err < ETHRESH ) { + *loss = err; + return y; + } + // If the power series fails, then apply AMS55 #15.3.6... + q = hys2f1( a, b, 1.0-d, s, &err ); + sign = 1.0; + w = stdlib_base_gammaln( d ); + sign *= stdlib_base_gammasgn( d ); + w -= stdlib_base_gammaln( c-a ); + sign *= stdlib_base_gammasgn( c-a ); + w -= stdlib_base_gammaln( c-b ); + sign *= stdlib_base_gammasgn( c-b ); + q *= sign * stdlib_base_exp( w ); + + r = stdlib_base_pow( s, d ) * hys2f1( c-a, c-b, d+1.0, s, &err1 ); + sign = 1.0; + w = stdlib_base_gammaln( -d ); + sign *= stdlib_base_gammasgn( -d ); + w -= stdlib_base_gammaln( a ); + sign *= stdlib_base_gammasgn( a ); + w -= stdlib_base_gammaln( b ); + sign *= stdlib_base_gammasgn( b ); + r *= sign * stdlib_base_exp( w ); + + y = q + r; + q = stdlib_base_abs( q ); + r = stdlib_base_abs( r ); + if ( q > r ) { + r = q; + } + err += err1 + ( ( MACHEP*r ) / y ); + y *= stdlib_base_gamma( c ); + } else { + // Psi function expansion, AMS55 #15.3.10, #15.3.11, #15.3.12... + if ( id >= 0.0 ) { + e = d; + d1 = d; + d2 = 0.0; + aid = id; + } else { + e = -d; + d1 = 0.0; + d2 = d; + aid = -id; + } + ax = stdlib_base_ln( s ); + + // eslint-disable-next-line max-len + y = stdlib_base_digamma( 1.0 ) + stdlib_base_digamma( 1.0+e ) - stdlib_base_digamma( a+d1 ) - stdlib_base_digamma( b+d1 ) - ax; + y /= stdlib_base_gamma( e+1.0 ); + p = ( a+d1 ) * ( b+d1 ) * s / stdlib_base_gamma( e+2.0 ); + t = 1.0; + do { + // eslint-disable-next-line max-len + r = stdlib_base_digamma( 1.0+t ) + stdlib_base_digamma( 1.0+t+e ) - stdlib_base_digamma( a+t+d1 ) - stdlib_base_digamma( b+t+d1 ) - ax; + q = p * r; + y += q; + p *= s * ( a+t+d1 ) / ( t+1.0 ); + p *= ( b+t+d1 ) / ( t+1.0+e ); + t += 1.0; + if ( t > MAX_ITERATIONS ) { + *loss = 1.0; + return STDLIB_CONSTANT_FLOAT64_NAN; + } + } while ( y == 0.0 || stdlib_base_abs( q/y ) > EPS ); + + if ( id == 0.0 ) { + y *= stdlib_base_gamma( c ) / ( stdlib_base_gamma( a ) * stdlib_base_gamma( b ) ); + *loss = err; + return y; + } + + y1 = 1.0; + if ( aid != 1.0 ) { + t = 0.0; + p = 1.0; + for ( i = 1; i < aid; i++ ) { + r = 1.0 - e + t; + p *= s * ( a+t+d2 ) * ( b+t+d2 ) / r; + t += 1.0; + p /= t; + y1 += p; + } + } + + p = stdlib_base_gamma( c ); + y1 *= stdlib_base_gamma( e ) * p / ( stdlib_base_gamma( a+d1 ) * stdlib_base_gamma( b+d1 ) ); + y *= p / ( stdlib_base_gamma( a+d2 ) * stdlib_base_gamma( b+d2 ) ); + if ( ( (int)aid & 1 ) != 0 ) { + y = -y; + } + q = stdlib_base_pow( s, id ); + y = ( id > 0.0 ) ? y*q : y1*q; + y += y1; + } + *loss = err; + return y; + } + // Perform power series if no special cases: + y = hys2f1( a, b, c, x, &err ); + *loss = err; + return y; +} + +/** +* Computes the regularized incomplete gamma function. The upper tail is calculated via the modified Lentz's method for computing continued fractions, the lower tail using a power expansion. +* +* ## Notes +* +* - When `a >= FLOAT64_MAX_NTH_FACTORIAL` and computing the non-regularized incomplete gamma, result is rather hard to compute unless we use logs. There are really two options a) if `x` is a long way from `a` in value then we can reliably use methods 2 and 4 below in logarithmic form and go straight to the result. Otherwise we let the regularized gamma take the strain (the result is unlikely to underflow in the central region anyway) and combine with `lgamma` in the hopes that we get a finite result. +* +* @param x input value +* @param a input value +* @param regularized input value +* @param upper input value +* @return function value +* +* @example +* double v = stdlib_base_gamma( 1.0, 1.0, 1.0, 0.0 ); +* // returns 1.0 +*/ +double stdlib_base_gammainc( const double x, const double a, const bool regularized, const bool upper ) { + double optimisedInvert; + double evalMethod; + double initValue; + double isHalfInt; + double useTemme; + double isSmallA; + double invert; + double result; + double isInt; + double sigma; + double gam; + double res; + double fa; + double g; + + if ( x < 0.0 || a <= 0.0 ) { + return 0.0 / 0.0; // NaN + } + invert = upper; + result = 0.0; + if ( a >= STDLIB_CONSTANT_FLOAT64_MAX_NTH_FACTORIAL && !regularized ) { + if ( invert && ( a * 4.0 < x ) ) { + // This is method 4 below, done in logs: + result = ( a * stdlib_base_ln(x) ) - x; + result += ln( upperGammaFraction( a, x ) ); + } else if ( !invert && ( a > 4.0 * x ) ) { + // This is method 2 below, done in logs: + result = ( a * ln(x) ) - x; + initValue = 0; + result += ln( lowerGammaSeries( a, x, initValue ) / a ); + } else { + result = igammaFinal( a, x, true, invert ); + if ( result == 0.0 ) { + if ( invert ) { + // Try http://functions.wolfram.com/06.06.06.0039.01: + result = 1.0 + ( 1.0 / (12.0*a) ) + ( 1.0 / (288.0*a*a) ); + result = ln( result ) - a + ( ( a-0.5 ) * ln(a) ); + result += ln( STDLIB_CONSTANT_FLOAT64_SQRT_TWO_PI ); + } else { + // This is method 2 below, done in logs, we're really outside the range of this method, but since the result is almost certainly infinite, we should probably be OK: + result = ( a * ln( x ) ) - x; + initValue = 0.0; + result += ln( lowerGammaSeries( a, x, initValue ) / a ); + } + } else { + result = ln( result ) + gammaln( a ); + } + } + if ( result > STDLIB_CONSTANT_FLOAT64_MAX_LN ) { + return STDLIB_CONSTANT_FLOAT64_PINF; + } + return exp( result ); + } + // If no special handling is required then we proceeds as normal: + return igammaFinal( a, x, regularized, invert ); + + // isSmallA = ( a < 30 ) && ( a <= x + 1.0 ) && ( x < MAX_LN ); + // if ( isSmallA ) { + // fa = floor( a ); + // isInt = ( fa == a ); + // isHalfInt = ( isInt ) ? false : ( abs( fa - a ) == 0.5 ); + // } else { + // isInt = isHalfInt = false; + // } + // if ( isInt && x > 0.6 ) { + // // Calculate Q via finite sum: + // invert = !invert; + // evalMethod = 0; + // } else if ( isHalfInt && x > 0.2 ) { + // // Calculate Q via finite sum for half integer a: + // invert = !invert; + // evalMethod = 1; + // } else if ( x < SQRT_EPSILON && a > 1.0 ) { + // evalMethod = 6; + // } else if ( x < 0.5 ) { + // // Changeover criterion chosen to give a changeover at Q ~ 0.33: + // if ( -0.4 / ln( x ) < a ) { + // evalMethod = 2; + // } else { + // evalMethod = 3; + // } + // } else if ( x < 1.1 ) { + // // Changeover here occurs when P ~ 0.75 or Q ~ 0.25: + // if ( x * 0.75 < a ) { + // evalMethod = 2; + // } else { + // evalMethod = 3; + // } + // } else { + // // Begin by testing whether we're in the "bad" zone where the result will be near 0.5 and the usual series and continued fractions are slow to converge: + // useTemme = false; + // if ( regularized && a > 20 ) { + // sigma = abs( (x-a)/a ); + // if ( a > 200 ) { + // // Limit chosen so that we use Temme's expansion only if the result would be larger than about 10^-6. Below that the regular series and continued fractions converge OK, and if we use Temme's method we get increasing errors from the dominant erfc term as it's (inexact) argument increases in magnitude. + // if ( 20 / a > sigma * sigma ) { + // useTemme = true; + // } + // } else if ( sigma < 0.4 ) { + // useTemme = true; + // } + // } + // if ( useTemme ) { + // evalMethod = 5; + // } + // // Regular case where the result will not be too close to 0.5: Changeover occurs at P ~ Q ~ 0.5. Note that series computation of P is about x2 faster than continued fraction calculation of Q, so try and use the CF only when really necessary, especially for small x. + // else if ( x - ( 1.0 / (3.0 * x) ) < a ) { + // evalMethod = 2; + // } else { + // evalMethod = 4; + // invert = !invert; + // } + // } + + // /* eslint-disable default-case */ + // switch ( evalMethod ) { + // case 0: + // result = finiteGammaQ( a, x ); + // if (regularized == false ) { + // result *= gamma( a ); + // } + // break; + // case 1: + // result = finiteHalfGammaQ( a, x ); + // if ( regularized == false ) { + // result *= gamma( a ); + // } + // break; + // case 2: + // // Compute P: + // result = ( regularized ) ? + // regularisedGammaPrefix( a, x ) : + // fullIGammaPrefix( a, x ); + // if ( result !== 0.0 ) { + // initValue = 0.0; + // optimisedInvert = false; + // if ( invert ) { + // initValue = ( regularized ) ? 1.0 : gamma( a ); + // if ( + // regularized || + // result >= 1.0 || + // FLOAT64_MAX * result > initValue + // ) { + // initValue /= result; + // if ( + // regularized || + // a < 1.0 || + // ( FLOAT64_MAX / a > initValue ) + // ) { + // initValue *= -a; + // optimisedInvert = true; + // } + // else { + // initValue = 0.0; + // } + // } + // else { + // initValue = 0.0; + // } + // } + // } + // result *= lowerGammaSeries( a, x, initValue ) / a; + // if ( optimisedInvert ) { + // invert = false; + // result = -result; + // } + // break; + // case 3: + // // Compute Q: + // invert = !invert; + // res = tgammaSmallUpperPart( a, x, invert ); + // result = res[ 0 ]; + // g = res[ 1 ]; + // invert = false; + // if ( regularized ) { + // result /= g; + // } + // break; + // case 4: + // // Compute Q: + // result = ( regularized ) ? + // regularisedGammaPrefix( a, x ) : + // fullIGammaPrefix( a, x ); + // if ( result !== 0 ) { + // result *= upperGammaFraction( a, x ); + // } + // break; + // case 5: + // result = igammaTemmeLarge( a, x ); + // if ( x >= a ) { + // invert = !invert; + // } + // break; + // case 6: + // // Since x is so small that P is necessarily very small too, use http://functions.wolfram.com/GammaBetaErf/GammaRegularized/06/01/05/01/01/ + // result = ( regularized ) ? + // pow(x, a) / gamma( a + 1.0 ) : + // pow( x, a ) / a; + // result *= 1.0 - ( a * x / ( a + 1.0 ) ); + // break; + // } + // if ( regularized && result > 1.0 ) { + // result = 1.0; + // } + // if ( invert ) { + // gam = ( regularized ) ? 1.0 : gamma( a ); + // result = gam - result; + // } + // return result; +} From a225e46a4c3a11bef4c15f46ead4344264bd6427 Mon Sep 17 00:00:00 2001 From: Karan Anand Date: Wed, 18 Jun 2025 15:57:22 -0700 Subject: [PATCH 02/14] feat: temp commit --- .../base/special/gammainc/scripts/evalpoly.js | 79 + .../math/base/special/gammainc/src/main.c | 1389 +++++++++++------ 2 files changed, 964 insertions(+), 504 deletions(-) diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/scripts/evalpoly.js b/lib/node_modules/@stdlib/math/base/special/gammainc/scripts/evalpoly.js index c262caea673b..41613da2042b 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/scripts/evalpoly.js +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/scripts/evalpoly.js @@ -24,10 +24,15 @@ // MODULES // var resolve = require( 'path' ).resolve; +var readFileSync = require( '@stdlib/fs/read-file' ).sync; var writeFileSync = require( '@stdlib/fs/write-file' ).sync; var currentYear = require( '@stdlib/time/current-year' ); var licenseHeader = require( '@stdlib/_tools/licenses/header' ); var compile = require( '@stdlib/math/base/tools/evalpoly-compile' ); +var compileC = require( '@stdlib/math/base/tools/evalpoly-compile-c' ); +var substringBefore = require( '@stdlib/string/substring-before' ); +var substringAfter = require( '@stdlib/string/substring-after' ); +var format = require( '@stdlib/string/format' ); // VARIABLES // @@ -139,6 +144,33 @@ var header = licenseHeader( 'Apache-2.0', 'js', { header += '\n/* This is a generated file. Do not edit directly. */\n'; +// FUNCTIONS // + +/** +* Inserts a compiled function into file content. +* +* @private +* @param {string} text - source content +* @param {string} id - function identifier +* @param {string} str - function string +* @returns {string} updated content +*/ +function insert( text, id, str ) { + var before; + var after; + var begin; + var end; + + begin = '// BEGIN: '+id; + end = '// END: '+id; + + before = substringBefore( text, begin ); + after = substringAfter( text, end ); + + return format( '%s// BEGIN: %s\n\n%s\n%s%s', before, id, str, end, after ); +} + + // MAIN // /** @@ -148,7 +180,9 @@ header += '\n/* This is a generated file. Do not edit directly. */\n'; */ function main() { var fpath; + var copts; var opts; + var file; var str; opts = { @@ -190,6 +224,51 @@ function main() { fpath = resolve( __dirname, '..', 'lib', 'polyval_c8.js' ); str = header + compile( C8 ); writeFileSync( fpath, str, opts ); + + copts = { + 'dtype': 'double', + 'name': '' + }; + fpath = resolve( __dirname, '..', 'src', 'main.c' ); + file = readFileSync( fpath, opts ); + + copts.name = 'polyval_c0'; + str = compileC( C0, copts ); + file = insert( file, copts.name, str ); + + copts.name = 'polyval_c1'; + str = compileC( C1, copts ); + file = insert( file, copts.name, str ); + + copts.name = 'polyval_c2'; + str = compileC( C2, copts ); + file = insert( file, copts.name, str ); + + copts.name = 'polyval_c3'; + str = compileC( C3, copts ); + file = insert( file, copts.name, str ); + + copts.name = 'polyval_c4'; + str = compileC( C4, copts ); + file = insert( file, copts.name, str ); + + copts.name = 'polyval_c5'; + str = compileC( C5, copts ); + file = insert( file, copts.name, str ); + + copts.name = 'polyval_c6'; + str = compileC( C6, copts ); + file = insert( file, copts.name, str ); + + copts.name = 'polyval_c7'; + str = compileC( C7, copts ); + file = insert( file, copts.name, str ); + + copts.name = 'polyval_c8'; + str = compileC( C8, copts ); + file = insert( file, copts.name, str ); + + writeFileSync( fpath, file, opts ); } main(); diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/src/main.c b/lib/node_modules/@stdlib/math/base/special/gammainc/src/main.c index b5553ca9bc82..c54547b0abe2 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/src/main.c +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/src/main.c @@ -18,7 +18,7 @@ * * ## Notice * -* The original C++ code and copyright notice are from the [Boost library]{@link https://www.boost.org/doc/libs/1_88_0/boost/math/special_functions/gamma.hpp}. The implementation has been modified according to stdlib conventions. +* The original C++ code and copyright notice are from the [Boost library]{@link https://www.boost.org/doc/libs/1_88_0/boost/math/special_functions/stdlib_base_gamma.hpp}. The implementation has been modified according to stdlib conventions. * * ```text * (C) Copyright John Maddock 2006-7, 2013-14. @@ -33,428 +33,974 @@ */ #include "stdlib/math/base/special/gammainc.h" -#include "stdlib/math/base/special/gammaln.h" -#include "stdlib/math/base/special/floor.h" -#include "stdlib/math/base/special/gamma.h" -#include "stdlib/math/base/special/abs.h" -#include "stdlib/math/base/special/exp.h" -#include "stdlib/math/base/special/pow.h" -#include "stdlib/math/base/special/ln.h" +#include "stdlib/math/base/special/stdlib_base_gammaln.h" +#include "stdlib/math/base/special/stdlib_base_floor.h" +#include "stdlib/math/base/special/stdlib_base_gamma.h" +#include "stdlib/math/base/special/stdlib_base_abs.h" +#include "stdlib/math/base/special/stdlib_base_exp.h" +#include "stdlib/math/base/special/stdlib_base_pow.h" +#include "stdlib/math/base/special/stdlib_base_ln.h" #include "stdlib/math/base/assert/is_nan.h" #include "stdlib/constants/float64/sqrt_eps.h" #include "stdlib/constants/float64/max.h" #include "stdlib/constants/float64/sqrt_two_pi.h" #include "stdlib/constants/float64/max_ln.h" #include "stdlib/constants/float64/pinf.h" +#include "stdlib/constants/float64/eps.h" +#include "stdlib/constants/float32/smallest_normal.h" #include "stdlib/constants/float64/max_nth_factorial.h" +#include #include -static const double MACHEP = 1.11022302462515654042e-16; -static const double EPS = 1.0e-13; -static const double ETHRESH = 1.0e-12; -static const double MAX_ITERATIONS = 10000.0; +static const int32_t MAX_ITERATIONS = 1000000; static double hys2f1( double a, double b, const double c, const double x, double *loss ); +/* Begin auto-generated functions. The following functions are auto-generated. Do not edit directly. */ + +// BEGIN: polyval_c0 + /** -* Evaluate the lower incomplete gamma integral via a series expansion and divide by `gamma(z)` to normalize. +* Evaluates a polynomial. * -* @param a function parameter -* @param z function parameter -* @return function value +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_c0( const double x ) { + return -0.3333333333333333 + (x * (0.08333333333333333 + (x * (-0.014814814814814815 + (x * (0.0011574074074074073 + (x * (0.0003527336860670194 + (x * (-0.0001787551440329218 + (x * (0.00003919263178522438 + (x * (-0.0000021854485106799924 + (x * (-0.00000185406221071516 + (x * (8.296711340953087e-7 + (x * (-1.7665952736826078e-7 + (x * (6.707853543401498e-9 + (x * (1.0261809784240309e-8 + (x * (-4.382036018453353e-9 + (x * 9.14769958223679e-10))))))))))))))))))))))))))); +} + +// END: polyval_c0// BEGIN: polyval_c1 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_c1( const double x ) { + return -0.001851851851851852 + (x * (-0.003472222222222222 + (x * (0.0026455026455026454 + (x * (-0.0009902263374485596 + (x * (0.00020576131687242798 + (x * (-4.018775720164609e-7 + (x * (-0.000018098550334489977 + (x * (0.00000764916091608111 + (x * (-0.0000016120900894563446 + (x * (4.647127802807434e-9 + (x * (1.378633446915721e-7 + (x * (-5.752545603517705e-8 + (x * 1.1951628599778148e-8))))))))))))))))))))))); +} + +// END: polyval_c1// BEGIN: polyval_c2 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_c2( const double x ) { + return 0.004133597883597883 + (x * (-0.0026813271604938273 + (x * (0.0007716049382716049 + (x * (0.0000020093878600823047 + (x * (-0.00010736653226365161 + (x * (0.000052923448829120125 + (x * (-0.000012760635188618728 + (x * (3.423578734096138e-8 + (x * (0.0000013721957309062932 + (x * (-6.298992138380055e-7 + (x * 1.4280614206064242e-7))))))))))))))))))); +} + +// END: polyval_c2// BEGIN: polyval_c3 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_c3( const double x ) { + return 0.0006494341563786008 + (x * (0.00022947209362139917 + (x * (-0.0004691894943952557 + (x * (0.00026772063206283885 + (x * (-0.00007561801671883977 + (x * (-2.396505113867297e-7 + (x * (0.000011082654115347302 + (x * (-0.0000056749528269915965 + (x * 0.0000014230900732435883))))))))))))))); +} + +// END: polyval_c3// BEGIN: polyval_c4 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_c4( const double x ) { + return -0.0008618882909167117 + (x * (0.0007840392217200666 + (x * (-0.0002990724803031902 + (x * (-0.0000014638452578843418 + (x * (0.00006641498215465122 + (x * (-0.00003968365047179435 + (x * 0.000011375726970678419))))))))))); +} + +// END: polyval_c4// BEGIN: polyval_c5 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_c5( const double x ) { + return -0.00033679855336635813 + (x * (-0.00006972813758365858 + (x * (0.0002772753244959392 + (x * (-0.00019932570516188847 + (x * (0.00006797780477937208 + (x * (1.419062920643967e-7 + (x * (-0.000013594048189768693 + (x * (0.000008018470256334202 + (x * -0.000002291481176508095))))))))))))))); +} + +// END: polyval_c5// BEGIN: polyval_c6 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_c6( const double x ) { + return 0.0005313079364639922 + (x * (-0.0005921664373536939 + (x * (0.0002708782096718045 + (x * (7.902353232660328e-7 + (x * (-0.00008153969367561969 + (x * (0.0000561168275310625 + (x * -0.000018329116582843375))))))))))); +} + +// END: polyval_c6// BEGIN: polyval_c7 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_c7( const double x ) { + return 0.00034436760689237765 + (x * (0.00005171790908260592 + (x * (-0.00033493161081142234 + (x * (0.0002812695154763237 + (x * -0.00010976582244684731))))))); +} + +// END: polyval_c7// BEGIN: polyval_c8 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial */ -static bool upperGammaFraction( const double a, const double z ) { - double f = upperIncompleteGammaFract( a, z ); - return 1.0 / ( z - a + 1.0 + continuedFractionA( f ) ); +static double polyval_c8( const double x ) { + return -0.0006526239185953094 + (x * (0.0008394987206720873 + (x * -0.000438297098541721))); } +// END: polyval_c8 + +/* End auto-generated functions. */ + /** -* Creates a function to evaluate a series expansion of the upper incomplete gamma fraction. +* Creates a function to evaluate a series expansion of the upper incomplete stdlib_base_gamma fraction. * * @param a1 function parameter * @param z1 function parameter * @return series function */ -static bool upperIncompleteGammaFract( const double a1, const double z1 ) { - var z = z1 - a1 + 1.0; - var a = a1; - var k = 0; - return next; - - /** - * Calculate the next term of the series. - * - * @private - * @returns {Array} series expansion terms - */ - function next() { - k += 1; - z += 2.0; - return [ - k * (a - k), - z - ]; +static void upperIncompleteGammaFract( const double a, double* z, double* k, double *out ) { + *z += 2.0; + *k += 1.0; + out[ 0 ] = ( *k ) * ( a - (*k) ); + out[ 1 ] = *z; + return; +} + +/** +* Evaluates a continued fraction expansion. +* +* ```text +* a1 +* --------------- +* b1 + a2 +* ---------- +* b2 + a3 +* ----- +* b3 + ... +* ``` +* +* @private +* @param {Function} gen - function giving terms of continued fraction expansion +* @param {PositiveNumber} factor - further terms are only added as long as factor*result is smaller than the next term +* @param {PositiveInteger} maxIter - maximum number of iterations +* @returns {number} evaluated expansion +*/ +static double continuedFractionA( const double a, const double z, const double factor, const int32_t maxIter ) { + int32_t maxIterC; + double out[ 2 ]; + double delta; + double zc; + double a0; + double C; + double D; + double f; + double k; + + zc = z; + k = 0.0; + upperIncompleteGammaFract( a, &zc, &k, out ); + + f = out[ 1 ]; + a0 = out[ 0 ]; + if ( f == 0.0 ) { + f = STDLIB_CONSTANT_FLOAT32_SMALLEST_NORMAL; } + C = f; + D = 0.0; + maxIterC = maxIter; + + do { + upperIncompleteGammaFract( a, &zc, &k, out ); + D = out[ 1 ] + ( out[ 0 ] * D ); + if ( D == 0.0 ) { + D = STDLIB_CONSTANT_FLOAT32_SMALLEST_NORMAL; + } + C = out[ 1 ] + ( out[ 0 ] / C ); + if ( C == 0.0 ) { + C = STDLIB_CONSTANT_FLOAT32_SMALLEST_NORMAL; + } + D = 1.0 / D; + delta = C * D; + f *= delta; + } while ( out && ( stdlib_base_abs( delta - 1.0 ) > factor ) && --maxIterC ); + + return a0 / f; } /** -* Evaluate the lower incomplete gamma integral via a series expansion and divide by `gamma(z)` to normalize. +* Evaluate the lower incomplete stdlib_base_gamma integral via a series expansion and divide by `stdlib_base_gamma(z)` to normalize. * * @param a function parameter * @param z function parameter * @return function value */ -static bool upperGammaFraction( const double a, const double z ) { - double f = upperIncompleteGammaFract( a, z ); - return 1.0 / ( z - a + 1.0 + continuedFraction( f ) ); +static double upperGammaFraction( const double a, const double z ) { + double f; + + f = z - a + 1.0; + return 1.0 / ( f + continuedFractionA( a, f, STDLIB_CONSTANT_FLOAT64_EPS, MAX_ITERATIONS ) ); } /** -* Evaluate the lower incomplete gamma integral via a series expansion and divide by `gamma(z)` to normalize. +* Creates a function to evaluate a series expansion of the upper incomplete stdlib_base_gamma fraction. * -* @param a function parameter -* @param z function parameter -* @return function value +* @param a1 function parameter +* @param z1 function parameter +* @return series function +*/ +static double lowerIncompleteGammaSeries( double* a, const double z, double* result ) { + double r; + + r = *result; + *a += 1.0; + *result *= z / ( *a ); + return r; +} + +/** +* Evaluates a continued fraction expansion. +* +* ```text +* a1 +* --------------- +* b1 + a2 +* ---------- +* b2 + a3 +* ----- +* b3 + ... +* ``` +* +* @private +* @param {Function} gen - function giving terms of continued fraction expansion +* @param {PositiveNumber} factor - further terms are only added as long as factor*result is smaller than the next term +* @param {PositiveInteger} maxIter - maximum number of iterations +* @returns {number} evaluated expansion */ -static bool upperGammaFraction( const double a, const double z ) { - double f = upperIncompleteGammaFract( a, z ); - return 1.0 / ( z - a + 1.0 + continuedFraction( f ) ); +static double sumSeries( const double a, const double z, const double initialValue ) { + int32_t counter; + double nextTerm; + double result; + double sum; + double ac; + + ac = a; + result = 1.0; + sum = initialValue; + counter = MAX_ITERATIONS; + + // Repeatedly call function... + do { + nextTerm = lowerIncompleteGammaSeries( &ac, z, &result ); + sum += nextTerm; + } + while ( ( stdlib_base_abs(STDLIB_CONSTANT_FLOAT64_EPS * sum) < stdlib_base_abs(nextTerm) ) && --counter ); + + return sum; } /** -* Evaluate the lower incomplete gamma integral via a series expansion and divide by `gamma(z)` to normalize. +* Evaluate the lower incomplete stdlib_base_gamma integral via a series expansion and divide by `stdlib_base_gamma(z)` to normalize. * * @param a function parameter * @param z function parameter * @return function value */ -static bool upperGammaFraction( const double a, const double z ) { - double f = upperIncompleteGammaFract( a, z ); - return 1.0 / ( z - a + 1.0 + continuedFraction( f ) ); +static double lowerGammaSeries( const double a, const double z, const double initValue ) { + return sumSeries( a, z, initValue ); } /** -* Evaluates the Gaussian hypergeometric function by two-term recurrence in `a`. -* -* ## Notes +* Calculates normalized Q when a is an integer. * -* - This function helps prevent losing accuracy in the highly alternating hypergeometric series and allows a and b to be reduced to smaller values. -* -* ## References -* -* - AMS55 #15.2.10 -* -* @param a input value -* @param b input value -* @param c input value -* @param x input value -* @param loss starting loss of significance -* @return function value +* @private +* @param {integer} a - function parameter +* @param {number} x - function parameter +* @returns {number} upper stdlib_base_gamma fraction */ -static double hyp2f1ra( const double a, const double b, const double c, const double x, double *loss ) { - double err; - double da; - double f2; - double f1; - double f0; - double t; +static double finiteGammaQ( const double a, const double x ) { + double term; + double sum; + double e; double n; - *loss = 0.0; - err = 0.0; + e = stdlib_base_exp( -x ); + sum = e; + if ( sum != 0.0 ) { + term = sum; + for ( n = 1; n < a; ++n ) { + term /= n; + term *= x; + sum += term; + } + } + return sum; +} + +/** +* Calculates normalized Q when a is a half-integer. +* +* @private +* @param {number} a - function parameter +* @param {number} x - function parameter +* @returns {number} upper stdlib_base_gamma fraction +*/ +static double finiteHalfGammaQ( const double a, const double x ) { + double half; + double term; + double sum; + double e; + double n; - if ( ( c < 0.0 && a <= c ) || ( c >= 0.0 && a >= c ) ) { - da = stdlib_base_round( a-c ); - } else { - da = stdlib_base_round( a ); + e = stdlib_base_erfc( stdlib_base_sqrt(x) ); + if ( e != 0 && a > 1.0 ) { + term = stdlib_base_exp( -x ) / stdlib_base_sqrt( PI * x ); + term *= x; + half = 0.5; + term /= half; + sum = term; + for ( n = 2; n < a; ++n ) { + term /= n - half; + term *= x; + sum += term; + } + e += sum; } + return e; +} + +/** +* Computes `(z^a)*(e^-z) / stdlib_base_gamma(a)`. +* +* @private +* @param {number} a - input value +* @param {number} z - input value +* @returns {number} function value +*/ +static double regularisedGammaPrefix( const double a, const double z ) { + // TODO: NEEDS TO BE CHANGED (to be continued here) + double prefix; + double amza; + double agh; + double alz; + double amz; + double sq; + double d; - t = a - da; - if ( stdlib_base_abs( da ) > MAX_ITERATIONS ) { - // Too expensive to compute, so return `NaN`: - *loss = 1.0; - return STDLIB_CONSTANT_FLOAT64_NAN; + agh = a + G - 0.5; + d = ( (z - a) - G + 0.5 ) / agh; + if ( a < 1.0 ) { + // Treat a < 1 as a special case because our Lanczos approximations are optimized against the factorials with a > 1, and for high precision types very small values of `a` can give rather erroneous results for stdlib_base_gamma: + if ( z <= STDLIB_CONSTANT_FLOAT64_MIN_LN ) { + // Use logs, so should be free of cancellation errors: + return stdlib_base_exp( ( a * stdlib_base_ln(z) ) - z - stdlib_base_gammaln( a ) ); + } + // No danger of overflow as stdlib_base_gamma(a) < 1/a for small a, so direct calculation: + return stdlib_base_pow( z, a ) * stdlib_base_exp( -z ) / stdlib_base_gamma( a ); + } + if ( stdlib_base_abs(d*d*a) <= 100.0 && a > 150.0 ) { + // Special case for large a and a ~ z: + prefix = ( a * ( log1p( d ) - d ) ) + ( z * ( 0.5-G ) / agh ); + prefix = stdlib_base_exp( prefix ); } + else { + // General case. Direct computation is most accurate, but use various fallbacks for different parts of the problem domain: + alz = a * stdlib_base_ln(z / agh); + amz = a - z; + if ( + min(alz, amz) <= STDLIB_CONSTANT_FLOAT64_MIN_LN || + max(alz, amz) >= STDLIB_CONSTANT_FLOAT64_MAX_LN + ) { + amza = amz / a; + if ( + min(alz, amz)/2.0 > STDLIB_CONSTANT_FLOAT64_MIN_LN && + max(alz, amz)/2.0 < STDLIB_CONSTANT_FLOAT64_MAX_LN + ) { + // Compute square root of the result and then square it: + sq = stdlib_base_pow( z / agh, a / 2.0 ) * stdlib_base_exp( amz / 2.0 ); + prefix = sq * sq; + } + else if ( + min(alz, amz)/4.0 > STDLIB_CONSTANT_FLOAT64_MIN_LN && + max(alz, amz)/4.0 < STDLIB_CONSTANT_FLOAT64_MAX_LN && + z > a + ) { + // Compute the 4th root of the result then square it twice: + sq = stdlib_base_pow( z / agh, a / 4.0 ) * stdlib_base_exp( amz / 4.0 ); + prefix = sq * sq; + prefix *= prefix; + } + else if ( + amza > STDLIB_CONSTANT_FLOAT64_MIN_LN && + amza < STDLIB_CONSTANT_FLOAT64_MAX_LN + ) { + prefix = stdlib_base_pow( (z * stdlib_base_exp(amza)) / agh, a ); + } + else { + prefix = stdlib_base_exp( alz + amz ); + } + } + else + { + prefix = stdlib_base_pow( z / agh, a ) * stdlib_base_exp( amz ); + } + } + prefix *= stdlib_base_sqrt( agh / E ) / lanczosSumExpGScaled( a ); + return prefix; +} + +/** +* Calculates the power term prefix `(z^a)(e^-z)` used in the non-normalized incomplete gammas. +* +* @private +* @param {number} a - function parameter +* @param {number} z - function parameter +* @returns {number} power term prefix +*/ +static double fullIGammaPrefix( a, z ) { + double prefix; + double alz; - if ( da < 0.0 ) { - // Backward recurrence... - f1 = hys2f1( t, b, c, x, &err ); - *loss += err; - f0 = hys2f1( t-1.0, b, c, x, &err ); - *loss += err; - t -= 1.0; - for ( n = 1; n < -da; n++ ) { - f2 = f1; - f1 = f0; - - // eslint-disable-next-line max-len - f0 = -( ( ( ( (2.0*t)-c )-( t*x )+( b*x ) ) * f1 ) + ( ( t*(x-1.0) ) * f2 ) ) / ( c-t ); - t -= 1.0; + alz = a * stdlib_base_ln( z ); + if ( z >= 1.0 ) { + if ( ( alz < STDLIB_CONSTANT_FLOAT64_MAX_LN ) && ( -z > STDLIB_CONSTANT_FLOAT64_MIN_LN) ) { + prefix = stdlib_base_pow( z, a ) * stdlib_base_exp( -z ); + } else if ( a >= 1.0 ) { + prefix = stdlib_base_pow( z / stdlib_base_exp(z/a), a ); } - } else { - // Forward recurrence... - f1 = hys2f1( t, b, c, x, &err ); - *loss += err; - f0 = hys2f1( t+1.0, b, c, x, &err ); - *loss += err; - t += 1.0; - for ( n = 1; n < da; n++ ) { - f2 = f1; - f1 = f0; - - // eslint-disable-next-line max-len - f0 = -( ( ( ( (2.0*t)-c )-( t*x )+( b*x ) ) * f1 ) + ( (c-t)*f2 ) ) / ( t*(x-1.0) ); - t += 1.0; + else { + prefix = stdlib_base_exp( alz - z ); } } - return f0; + else { + if ( alz > STDLIB_CONSTANT_FLOAT64_MIN_LN ) { + prefix = stdlib_base_pow( z, a ) * stdlib_base_exp( -z ); + } else if ( z/a < STDLIB_CONSTANT_FLOAT64_MAX_LN ) { + prefix = stdlib_base_pow( z / stdlib_base_exp(z/a), a ); + } else { + prefix = stdlib_base_exp( alz - z ); + } + } + return prefix; } /** -* Evaluates the power series expansion of Gaussian hypergeometric function. -* -* @param a input value -* @param b input value -* @param c input value -* @param x input value -* @param loss starting loss of significance -* @return function value +* Creates a function to evaluate a series expansion of the upper incomplete stdlib_base_gamma fraction. +* +* @param a1 function parameter +* @param z1 function parameter +* @return series function */ -static double hys2f1( double a, double b, const double c, const double x, double *loss ) { - double intFlag; - double umax; - double f; - double g; - double h; - double k; - double m; - double s; - double u; - double i; +static double smallGamma2Series( double* a, double* x, int32_t* n, double* result ) { + double r; - intFlag = 0.0; + r = ( *result ) / ( *a ); + *result *= ( *x ); + *n += 1; + *result /= ( *n ); + *a += 1.0; + return r; +} - if ( stdlib_base_abs( b ) > stdlib_base_abs( a ) ) { - f = b; - b = a; - a = f; - } +/** +* Evaluates a continued fraction expansion. +* +* ```text +* a1 +* --------------- +* b1 + a2 +* ---------- +* b2 + a3 +* ----- +* b3 + ... +* ``` +* +* @private +* @param {Function} gen - function giving terms of continued fraction expansion +* @param {PositiveNumber} factor - further terms are only added as long as factor*result is smaller than the next term +* @param {PositiveInteger} maxIter - maximum number of iterations +* @returns {number} evaluated expansion +*/ +static double sumSeries2( const double a, const double x, const double initialValue ) { + int32_t counter; + double nextTerm; + double result; + double sum; + int32_t n; + double ac; + double xc; + + xc = -x; + ac = a + 1.0; + result = -x; + n = 1; + sum = initialValue; + counter = MAX_ITERATIONS; - if ( isNonPositiveInteger( b ) && ( stdlib_base_abs( b ) < stdlib_base_abs( a ) ) ) { - f = b; - b = a; - a = f; - intFlag = 1.0; + // Repeatedly call function... + do { + nextTerm = smallGamma2Series( &ac, &xc, &n, &result ); + sum += nextTerm; } + while ( ( stdlib_base_abs(STDLIB_CONSTANT_FLOAT64_EPS * sum) < stdlib_base_abs(nextTerm) ) && --counter ); + + return sum; +} + +/** +* Evaluate the lower incomplete stdlib_base_gamma integral via a series expansion and divide by `stdlib_base_gamma(z)` to normalize. +* +* @param a function parameter +* @param z function parameter +* @return function value +*/ +static void tgammaSmallUpperPart( const double a, const double x, const bool invert, double* out ) { + double initialValue; + double result; + double pgam; + double p; - // eslint-disable-next-line max-len - if ( ( ( stdlib_base_abs( a ) > stdlib_base_abs( c ) + 1.0 ) || intFlag ) && ( stdlib_base_abs( c-a ) > 2.0 ) && ( stdlib_base_abs( a ) > 2.0 ) ) { - return hyp2f1ra( a, b, c, x, loss ); + result = stdlib_base_gamma1pm1( a ); + pgam = ( result + 1.0 ) / a; + p = stdlib_base_powm1( x, a ); + result -= p; + result /= a; + p += 1.0; + initialValue = ( invert ) ? pgam : 0.0; + result = -p * sumSeries2( a, x, ( initialValue-result ) / p ); + if ( invert ) { + result = -result; } + out[ 0 ] = result; + out[ 1 ] = pgam; +} - i = 0.0; - umax = 0.0; - f = a; - g = b; - h = c; - s = 1.0; - u = 1.0; - k = 0.0; +/** +* Creates a function to evaluate a series expansion of the upper incomplete stdlib_base_gamma fraction. +* +* @param a1 function parameter +* @param z1 function parameter +* @return series function +*/ +static double tgammaILargeXSeries( double* a, const double z, double* result ) { + double r; + + r = *result; + *result *= ( *a ) / z; + *a -= 1.0; + return r; +} + +/** +* Evaluates a continued fraction expansion. +* +* ```text +* a1 +* --------------- +* b1 + a2 +* ---------- +* b2 + a3 +* ----- +* b3 + ... +* ``` +* +* @private +* @param {Function} gen - function giving terms of continued fraction expansion +* @param {PositiveNumber} factor - further terms are only added as long as factor*result is smaller than the next term +* @param {PositiveInteger} maxIter - maximum number of iterations +* @returns {number} evaluated expansion +*/ +static double sumSeries3( const double a, const double z ) { + int32_t counter; + double nextTerm; + double result; + double sum; + double ac; + ac = a; + sum = 0.0; + result = 1.0; + counter = MAX_ITERATIONS; + + // Repeatedly call function... do { - if ( stdlib_base_abs( h ) < EPS ) { - *loss = 1.0; - return STDLIB_CONSTANT_FLOAT64_PINF; - } - m = k + 1.0; - u *= ( ( f+k ) * ( g+k ) * x / ( ( h+k ) * m ) ); - s += u; - k = stdlib_base_abs( u ); - if ( k > umax ) { - umax = k; - } - k = m; - i += 1.0; - if ( i > MAX_ITERATIONS ) { - *loss = 1.0; - return s; - } - } while ( s == 0.0 || stdlib_base_abs( u/s ) > MACHEP ); + nextTerm = tgammaILargeXSeries( &ac, z, &result ); + sum += nextTerm; + } + while ( ( stdlib_base_abs(STDLIB_CONSTANT_FLOAT64_EPS * sum) < stdlib_base_abs(nextTerm) ) && --counter ); - // Estimate the relative error due to truncation by the series: - *loss = ( ( MACHEP*umax ) / stdlib_base_abs( s ) ) + ( MACHEP*i ); - return s; + return sum; } /** -* Applies transformations for `|x|` near unity before performing a power series expansion. -* -* @param a input value -* @param b input value -* @param c input value -* @param x input value -* @param loss starting loss of significance -* @return function value +* Evaluate the lower incomplete stdlib_base_gamma integral via a series expansion and divide by `stdlib_base_gamma(z)` to normalize. +* +* @param a function parameter +* @param z function parameter +* @return function value */ -static double hyt2f1( const double a, const double b, const double c, const double x, double *loss ) { - double negIntA; - double negIntB; - double sign; - double err1; - double err; - double aid; - double ax; - double id; - double d1; - double d2; - double y1; - double i; +static double tgammaILargeX( const double a, const double x ) { + return sumSeries3( a, x ); +} + +/** +* Evaluates a polynomial using double-precision floating-point arithmetic. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param c - polynomial coefficients sorted in ascending degree +* @param x - value at which to evaluate the polynomial +* @returns evaluated polynomial +*/ +static double evalpoly( double *c, const double x ){ + int32_t i; double p; - double q; - double r; - double t; + + i = 10; + if ( x == 0.0 ) { + return c[ 0 ]; + } + i -= 1; + p = ( c[ i ] * x ) + c[ i-1 ]; + i -= 2; + while ( i >= 0 ) { + p = ( p * x ) + c[ i ]; + i -= 1; + } + return p; +} + +/** +* Asymptotic expansions of the incomplete stdlib_base_gamma functions when `a` is large and `x ~ a` (IEEE double precision or 10^-17). +* +* @private +* @param {number} a - function parameter +* @param {number} x - function parameter +* @returns {number} value of asymptotic expansion +*/ +static double igammaTemmeLarge( const double a, const double x ) { + double workspace[ 10 ]; + double result; + double sigma; + double phi; double y; - double w; - double d; - double e; - double s; - - negIntA = isNonPositiveInteger( a ); - negIntB = isNonPositiveInteger( b ); - err = 0.0; - err1 = 0.0; - s = 1.0 - x; - - if ( x < -0.5 && !( negIntA || negIntB ) ) { - if ( b > a ) { - // Transformation based on AMS55 #15.3.4: - y = stdlib_base_pow( s, -a ) * hys2f1( a, c-b, c, -x/s, &err ); - } else { - // Transformation based on AMS55 #15.3.5: - y = stdlib_base_pow( s, -b ) * hys2f1( c-a, b, c, -x/s, &err ); - } - *loss = err; - return y; + double z; + + sigma = ( x-a ) / a; + phi = -stdlib_base_log1pmx( sigma ); + y = a * phi; + z = stdlib_base_sqrt( 2.0 * phi ); + if ( x < a ) { + z = -z; } + workspace[ 0 ] = polyvalC0( z ); + workspace[ 1 ] = polyvalC1( z ); + workspace[ 2 ] = polyvalC2( z ); + workspace[ 3 ] = polyvalC3( z ); + workspace[ 4 ] = polyvalC4( z ); + workspace[ 5 ] = polyvalC5( z ); + workspace[ 6 ] = polyvalC6( z ); + workspace[ 7 ] = polyvalC7( z ); + workspace[ 8 ] = polyvalC8( z ); + workspace[ 9 ] = -0.00059676129019274625; + result = evalpoly( workspace, 1.0/a ); + result *= stdlib_base_exp( -y ) / stdlib_base_sqrt( STDLIB_CONSTANT_FLOAT64_TWO_PI * a ); + if ( x < a ) { + result = -result; + } + result += stdlib_base_erfc( stdlib_base_sqrt(y) ) / 2.0; + return result; +} - d = c - a - b; - id = stdlib_base_round( d ); +/** +* Computes the regularized incomplete stdlib_base_gamma function. The upper tail is calculated via the modified Lentz's method for computing continued fractions, the lower tail using a power expansion. +* +* ## Notes +* +* - When `a >= FLOAT64_MAX_NTH_FACTORIAL` and computing the non-regularized incomplete stdlib_base_gamma, result is rather hard to compute unless we use logs. There are really two options a) if `x` is a long way from `a` in value then we can reliably use methods 2 and 4 below in logarithmic form and go straight to the result. Otherwise we let the regularized stdlib_base_gamma take the strain (the result is unlikely to underflow in the central region anyway) and combine with `lgamma` in the hopes that we get a finite result. +* +* @param x input value +* @param a input value +* @param regularized input value +* @param upper input value +* @return function value +* +* @example +* double v = stdlib_base_gammainc( 1.0, 1.0, 1.0, 0.0 ); +* // returns 1.0 +*/ +double igammaFinal( const double a, const double x, const bool regularized, const bool upper ) { + bool optimisedInvert; + int32_t evalMethod; + double initValue; + double out[ 2 ]; + bool isHalfInt; + bool useTemme; + bool isSmallA; + double result; + double sigma; + bool invert; + bool isInt; + double gam; + double fa; + double g; - if ( x > 0.9 && !negIntA && !negIntB ) { - if ( isInteger( d ) == false ) { - // Try the power series first: - y = hys2f1( a, b, c, x, &err ); - if ( err < ETHRESH ) { - *loss = err; - return y; - } - // If the power series fails, then apply AMS55 #15.3.6... - q = hys2f1( a, b, 1.0-d, s, &err ); - sign = 1.0; - w = stdlib_base_gammaln( d ); - sign *= stdlib_base_gammasgn( d ); - w -= stdlib_base_gammaln( c-a ); - sign *= stdlib_base_gammasgn( c-a ); - w -= stdlib_base_gammaln( c-b ); - sign *= stdlib_base_gammasgn( c-b ); - q *= sign * stdlib_base_exp( w ); - - r = stdlib_base_pow( s, d ) * hys2f1( c-a, c-b, d+1.0, s, &err1 ); - sign = 1.0; - w = stdlib_base_gammaln( -d ); - sign *= stdlib_base_gammasgn( -d ); - w -= stdlib_base_gammaln( a ); - sign *= stdlib_base_gammasgn( a ); - w -= stdlib_base_gammaln( b ); - sign *= stdlib_base_gammasgn( b ); - r *= sign * stdlib_base_exp( w ); - - y = q + r; - q = stdlib_base_abs( q ); - r = stdlib_base_abs( r ); - if ( q > r ) { - r = q; - } - err += err1 + ( ( MACHEP*r ) / y ); - y *= stdlib_base_gamma( c ); + result = 0.0; + invert = upper; + isSmallA = ( a < 30 ) && ( a <= x + 1.0 ) && ( x < STDLIB_CONSTANT_FLOAT64_MAX_LN ); + if ( isSmallA ) { + fa = stdlib_base_floor( a ); + isInt = ( fa == a ); + isHalfInt = ( isInt ) ? false : ( stdlib_base_abs( fa - a ) == 0.5 ); + } else { + isInt = false; + isHalfInt = false; + } + if ( isInt && x > 0.6 ) { + // Calculate Q via finite sum: + invert = !invert; + evalMethod = 0; + } else if ( isHalfInt && x > 0.2 ) { + // Calculate Q via finite sum for half integer a: + invert = !invert; + evalMethod = 1; + } else if ( x < STDLIB_CONSTANT_FLOAT64_SQRT_EPS && a > 1.0 ) { + evalMethod = 6; + } else if ( ( x > 1000.0 ) && ( ( a < x ) || ( stdlib_base_abs( a - 50.0 ) / x < 1.0 ) ) ) { + // calculate Q via asymptotic approximation: + invert = !invert; + evalMethod = 7; + } else if ( x < 0.5 ) { + // Changeover criterion chosen to give a changeover at Q ~ 0.33: + if ( -0.4 / stdlib_base_ln( x ) < a ) { + evalMethod = 2; } else { - // Psi function expansion, AMS55 #15.3.10, #15.3.11, #15.3.12... - if ( id >= 0.0 ) { - e = d; - d1 = d; - d2 = 0.0; - aid = id; - } else { - e = -d; - d1 = 0.0; - d2 = d; - aid = -id; - } - ax = stdlib_base_ln( s ); - - // eslint-disable-next-line max-len - y = stdlib_base_digamma( 1.0 ) + stdlib_base_digamma( 1.0+e ) - stdlib_base_digamma( a+d1 ) - stdlib_base_digamma( b+d1 ) - ax; - y /= stdlib_base_gamma( e+1.0 ); - p = ( a+d1 ) * ( b+d1 ) * s / stdlib_base_gamma( e+2.0 ); - t = 1.0; - do { - // eslint-disable-next-line max-len - r = stdlib_base_digamma( 1.0+t ) + stdlib_base_digamma( 1.0+t+e ) - stdlib_base_digamma( a+t+d1 ) - stdlib_base_digamma( b+t+d1 ) - ax; - q = p * r; - y += q; - p *= s * ( a+t+d1 ) / ( t+1.0 ); - p *= ( b+t+d1 ) / ( t+1.0+e ); - t += 1.0; - if ( t > MAX_ITERATIONS ) { - *loss = 1.0; - return STDLIB_CONSTANT_FLOAT64_NAN; + evalMethod = 3; + } + } else if ( x < 1.1 ) { + // Changeover here occurs when P ~ 0.75 or Q ~ 0.25: + if ( x * 0.75 < a ) { + evalMethod = 2; + } else { + evalMethod = 3; + } + } else { + // Begin by testing whether we're in the "bad" zone where the result will be near 0.5 and the usual series and continued fractions are slow to converge: + useTemme = false; + if ( regularized && a > 20.0 ) { + sigma = stdlib_base_abs( (x-a)/a ); + if ( a > 200 ) { + // Limit chosen so that we use Temme's expansion only if the result would be larger than about 10^-6. Below that the regular series and continued fractions converge OK, and if we use Temme's method we get increasing errors from the dominant stdlib_base_erfc term as it's (inexact) argument increases in magnitude. + if ( 20 / a > sigma * sigma ) { + useTemme = true; } - } while ( y == 0.0 || stdlib_base_abs( q/y ) > EPS ); - - if ( id == 0.0 ) { - y *= stdlib_base_gamma( c ) / ( stdlib_base_gamma( a ) * stdlib_base_gamma( b ) ); - *loss = err; - return y; + } else if ( sigma < 0.4 ) { + useTemme = true; } + } + if ( useTemme ) { + evalMethod = 5; + } + // Regular case where the result will not be too close to 0.5: Changeover occurs at P ~ Q ~ 0.5. Note that series computation of P is about x2 faster than continued fraction calculation of Q, so try and use the CF only when really necessary, especially for small x. + else if ( x - ( 1.0 / (3.0 * x) ) < a ) { + evalMethod = 2; + } else { + evalMethod = 4; + invert = !invert; + } + } - y1 = 1.0; - if ( aid != 1.0 ) { - t = 0.0; - p = 1.0; - for ( i = 1; i < aid; i++ ) { - r = 1.0 - e + t; - p *= s * ( a+t+d2 ) * ( b+t+d2 ) / r; - t += 1.0; - p /= t; - y1 += p; + switch ( evalMethod ) { + case 0: + result = finiteGammaQ( a, x ); + if ( regularized == false ) { + result *= stdlib_base_gamma( a ); + } + break; + case 1: + result = finiteHalfGammaQ( a, x ); + if ( regularized == false ) { + result *= stdlib_base_gamma( a ); + } + break; + case 2: + // Compute P: + result = ( regularized ) ? + regularisedGammaPrefix( a, x ) : + fullIGammaPrefix( a, x ); + if ( result != 0.0 ) { + initValue = 0.0; + optimisedInvert = false; + if ( invert ) { + initValue = ( regularized ) ? 1.0 : stdlib_base_gamma( a ); + if ( + regularized || + result >= 1.0 || + STDLIB_CONSTANT_FLOAT64_MAX * result > initValue + ) { + initValue /= result; + if ( + regularized || + a < 1.0 || + ( STDLIB_CONSTANT_FLOAT64_MAX / a > initValue ) + ) { + initValue *= -a; + optimisedInvert = true; + } + else { + initValue = 0.0; + } + } + else { + initValue = 0.0; } } - - p = stdlib_base_gamma( c ); - y1 *= stdlib_base_gamma( e ) * p / ( stdlib_base_gamma( a+d1 ) * stdlib_base_gamma( b+d1 ) ); - y *= p / ( stdlib_base_gamma( a+d2 ) * stdlib_base_gamma( b+d2 ) ); - if ( ( (int)aid & 1 ) != 0 ) { - y = -y; - } - q = stdlib_base_pow( s, id ); - y = ( id > 0.0 ) ? y*q : y1*q; - y += y1; } - *loss = err; - return y; + result *= lowerGammaSeries( a, x, initValue ) / a; + if ( optimisedInvert ) { + invert = false; + result = -result; + } + break; + case 3: + // Compute Q: + invert = !invert; + // it can be changed to return result and option to store g: + tgammaSmallUpperPart( a, x, invert, out ); + result = out[ 0 ]; + g = out[ 1 ]; + invert = false; + if ( regularized ) { + result /= g; + } + break; + case 4: + // Compute Q: + result = ( regularized ) ? + regularisedGammaPrefix( a, x ) : + fullIGammaPrefix( a, x ); + if ( result != 0 ) { + result *= upperGammaFraction( a, x ); + } + break; + case 5: + result = igammaTemmeLarge( a, x ); + if ( x >= a ) { + invert = !invert; + } + break; + case 6: + // Since x is so small that P is necessarily very small too, use http://functions.wolfram.com/GammaBetaErf/GammaRegularized/06/01/05/01/01/ + result = ( regularized ) ? + stdlib_base_pow(x, a) / stdlib_base_gamma( a + 1.0 ) : + stdlib_base_pow( x, a ) / a; + result *= 1.0 - ( a * x / ( a + 1.0 ) ); + break; + case 7: + // x is large, so compute Q: + result = ( regularized ) ? + regularisedGammaPrefix( a, x ) : + fullIGammaPrefix( a, x ); + result /= x; + if ( result != 0.0 ) { + result *= tgammaILargeX( a, x ); + } + break; + } + if ( regularized && result > 1.0 ) { + result = 1.0; } - // Perform power series if no special cases: - y = hys2f1( a, b, c, x, &err ); - *loss = err; - return y; + if ( invert ) { + gam = ( regularized ) ? 1.0 : stdlib_base_gamma( a ); + result = gam - result; + } + return result; } + + /** -* Computes the regularized incomplete gamma function. The upper tail is calculated via the modified Lentz's method for computing continued fractions, the lower tail using a power expansion. +* Computes the regularized incomplete stdlib_base_gamma function. The upper tail is calculated via the modified Lentz's method for computing continued fractions, the lower tail using a power expansion. * * ## Notes * -* - When `a >= FLOAT64_MAX_NTH_FACTORIAL` and computing the non-regularized incomplete gamma, result is rather hard to compute unless we use logs. There are really two options a) if `x` is a long way from `a` in value then we can reliably use methods 2 and 4 below in logarithmic form and go straight to the result. Otherwise we let the regularized gamma take the strain (the result is unlikely to underflow in the central region anyway) and combine with `lgamma` in the hopes that we get a finite result. +* - When `a >= FLOAT64_MAX_NTH_FACTORIAL` and computing the non-regularized incomplete stdlib_base_gamma, result is rather hard to compute unless we use logs. There are really two options a) if `x` is a long way from `a` in value then we can reliably use methods 2 and 4 below in logarithmic form and go straight to the result. Otherwise we let the regularized stdlib_base_gamma take the strain (the result is unlikely to underflow in the central region anyway) and combine with `lgamma` in the hopes that we get a finite result. * * @param x input value * @param a input value @@ -463,24 +1009,13 @@ static double hyt2f1( const double a, const double b, const double c, const doub * @return function value * * @example -* double v = stdlib_base_gamma( 1.0, 1.0, 1.0, 0.0 ); +* double v = stdlib_base_gammainc( 1.0, 1.0, 1.0, 0.0 ); * // returns 1.0 */ double stdlib_base_gammainc( const double x, const double a, const bool regularized, const bool upper ) { - double optimisedInvert; - double evalMethod; double initValue; - double isHalfInt; - double useTemme; - double isSmallA; - double invert; double result; - double isInt; - double sigma; - double gam; - double res; - double fa; - double g; + bool invert; if ( x < 0.0 || a <= 0.0 ) { return 0.0 / 0.0; // NaN @@ -491,189 +1026,35 @@ double stdlib_base_gammainc( const double x, const double a, const bool regulari if ( invert && ( a * 4.0 < x ) ) { // This is method 4 below, done in logs: result = ( a * stdlib_base_ln(x) ) - x; - result += ln( upperGammaFraction( a, x ) ); + result += stdlib_base_ln( upperGammaFraction( a, x ) ); } else if ( !invert && ( a > 4.0 * x ) ) { // This is method 2 below, done in logs: - result = ( a * ln(x) ) - x; - initValue = 0; - result += ln( lowerGammaSeries( a, x, initValue ) / a ); + result = ( a * stdlib_base_ln(x) ) - x; + initValue = 0.0; + result += stdlib_base_ln( lowerGammaSeries( a, x, initValue ) / a ); } else { result = igammaFinal( a, x, true, invert ); if ( result == 0.0 ) { if ( invert ) { // Try http://functions.wolfram.com/06.06.06.0039.01: result = 1.0 + ( 1.0 / (12.0*a) ) + ( 1.0 / (288.0*a*a) ); - result = ln( result ) - a + ( ( a-0.5 ) * ln(a) ); - result += ln( STDLIB_CONSTANT_FLOAT64_SQRT_TWO_PI ); + result = stdlib_base_ln( result ) - a + ( ( a-0.5 ) * stdlib_base_ln(a) ); + result += stdlib_base_ln( STDLIB_CONSTANT_FLOAT64_SQRT_TWO_PI ); } else { // This is method 2 below, done in logs, we're really outside the range of this method, but since the result is almost certainly infinite, we should probably be OK: - result = ( a * ln( x ) ) - x; + result = ( a * stdlib_base_ln( x ) ) - x; initValue = 0.0; - result += ln( lowerGammaSeries( a, x, initValue ) / a ); + result += stdlib_base_ln( lowerGammaSeries( a, x, initValue ) / a ); } } else { - result = ln( result ) + gammaln( a ); + result = stdlib_base_ln( result ) + stdlib_base_gammaln( a ); } } if ( result > STDLIB_CONSTANT_FLOAT64_MAX_LN ) { return STDLIB_CONSTANT_FLOAT64_PINF; } - return exp( result ); + return stdlib_base_exp( result ); } - // If no special handling is required then we proceeds as normal: + // If no special handling is required then we proceed as normal: return igammaFinal( a, x, regularized, invert ); - - // isSmallA = ( a < 30 ) && ( a <= x + 1.0 ) && ( x < MAX_LN ); - // if ( isSmallA ) { - // fa = floor( a ); - // isInt = ( fa == a ); - // isHalfInt = ( isInt ) ? false : ( abs( fa - a ) == 0.5 ); - // } else { - // isInt = isHalfInt = false; - // } - // if ( isInt && x > 0.6 ) { - // // Calculate Q via finite sum: - // invert = !invert; - // evalMethod = 0; - // } else if ( isHalfInt && x > 0.2 ) { - // // Calculate Q via finite sum for half integer a: - // invert = !invert; - // evalMethod = 1; - // } else if ( x < SQRT_EPSILON && a > 1.0 ) { - // evalMethod = 6; - // } else if ( x < 0.5 ) { - // // Changeover criterion chosen to give a changeover at Q ~ 0.33: - // if ( -0.4 / ln( x ) < a ) { - // evalMethod = 2; - // } else { - // evalMethod = 3; - // } - // } else if ( x < 1.1 ) { - // // Changeover here occurs when P ~ 0.75 or Q ~ 0.25: - // if ( x * 0.75 < a ) { - // evalMethod = 2; - // } else { - // evalMethod = 3; - // } - // } else { - // // Begin by testing whether we're in the "bad" zone where the result will be near 0.5 and the usual series and continued fractions are slow to converge: - // useTemme = false; - // if ( regularized && a > 20 ) { - // sigma = abs( (x-a)/a ); - // if ( a > 200 ) { - // // Limit chosen so that we use Temme's expansion only if the result would be larger than about 10^-6. Below that the regular series and continued fractions converge OK, and if we use Temme's method we get increasing errors from the dominant erfc term as it's (inexact) argument increases in magnitude. - // if ( 20 / a > sigma * sigma ) { - // useTemme = true; - // } - // } else if ( sigma < 0.4 ) { - // useTemme = true; - // } - // } - // if ( useTemme ) { - // evalMethod = 5; - // } - // // Regular case where the result will not be too close to 0.5: Changeover occurs at P ~ Q ~ 0.5. Note that series computation of P is about x2 faster than continued fraction calculation of Q, so try and use the CF only when really necessary, especially for small x. - // else if ( x - ( 1.0 / (3.0 * x) ) < a ) { - // evalMethod = 2; - // } else { - // evalMethod = 4; - // invert = !invert; - // } - // } - - // /* eslint-disable default-case */ - // switch ( evalMethod ) { - // case 0: - // result = finiteGammaQ( a, x ); - // if (regularized == false ) { - // result *= gamma( a ); - // } - // break; - // case 1: - // result = finiteHalfGammaQ( a, x ); - // if ( regularized == false ) { - // result *= gamma( a ); - // } - // break; - // case 2: - // // Compute P: - // result = ( regularized ) ? - // regularisedGammaPrefix( a, x ) : - // fullIGammaPrefix( a, x ); - // if ( result !== 0.0 ) { - // initValue = 0.0; - // optimisedInvert = false; - // if ( invert ) { - // initValue = ( regularized ) ? 1.0 : gamma( a ); - // if ( - // regularized || - // result >= 1.0 || - // FLOAT64_MAX * result > initValue - // ) { - // initValue /= result; - // if ( - // regularized || - // a < 1.0 || - // ( FLOAT64_MAX / a > initValue ) - // ) { - // initValue *= -a; - // optimisedInvert = true; - // } - // else { - // initValue = 0.0; - // } - // } - // else { - // initValue = 0.0; - // } - // } - // } - // result *= lowerGammaSeries( a, x, initValue ) / a; - // if ( optimisedInvert ) { - // invert = false; - // result = -result; - // } - // break; - // case 3: - // // Compute Q: - // invert = !invert; - // res = tgammaSmallUpperPart( a, x, invert ); - // result = res[ 0 ]; - // g = res[ 1 ]; - // invert = false; - // if ( regularized ) { - // result /= g; - // } - // break; - // case 4: - // // Compute Q: - // result = ( regularized ) ? - // regularisedGammaPrefix( a, x ) : - // fullIGammaPrefix( a, x ); - // if ( result !== 0 ) { - // result *= upperGammaFraction( a, x ); - // } - // break; - // case 5: - // result = igammaTemmeLarge( a, x ); - // if ( x >= a ) { - // invert = !invert; - // } - // break; - // case 6: - // // Since x is so small that P is necessarily very small too, use http://functions.wolfram.com/GammaBetaErf/GammaRegularized/06/01/05/01/01/ - // result = ( regularized ) ? - // pow(x, a) / gamma( a + 1.0 ) : - // pow( x, a ) / a; - // result *= 1.0 - ( a * x / ( a + 1.0 ) ); - // break; - // } - // if ( regularized && result > 1.0 ) { - // result = 1.0; - // } - // if ( invert ) { - // gam = ( regularized ) ? 1.0 : gamma( a ); - // result = gam - result; - // } - // return result; } From 8cc8e26dab3e20820e6f6c581a8a7a183b3de0d3 Mon Sep 17 00:00:00 2001 From: Karan Anand Date: Thu, 19 Jun 2025 00:12:38 -0700 Subject: [PATCH 03/14] feat: add C implementation for `math/base/special/gammainc` --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown status: passed - task: lint_package_json status: passed - task: lint_repl_help status: na - task: lint_javascript_src status: passed - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: passed - task: lint_javascript_benchmarks status: passed - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: passed - task: lint_c_examples status: passed - task: lint_c_benchmarks status: passed - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: na - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../math/base/special/gammainc/README.md | 100 +++++ .../gammainc/benchmark/benchmark.native.js | 135 ++++++ .../gammainc/benchmark/c/native/Makefile | 146 ++++++ .../gammainc/benchmark/c/native/benchmark.c | 140 ++++++ .../math/base/special/gammainc/binding.gyp | 170 +++++++ .../base/special/gammainc/examples/c/Makefile | 146 ++++++ .../special/gammainc/examples/c/example.c | 40 ++ .../math/base/special/gammainc/include.gypi | 53 +++ .../stdlib/math/base/special/gammainc.h | 40 ++ .../math/base/special/gammainc/lib/native.js | 69 +++ .../math/base/special/gammainc/manifest.json | 160 +++++++ .../math/base/special/gammainc/package.json | 4 +- .../math/base/special/gammainc/src/addon.c | 30 +- .../math/base/special/gammainc/src/main.c | 422 +++++++++--------- .../base/special/gammainc/test/test.native.js | 201 +++++++++ 15 files changed, 1634 insertions(+), 222 deletions(-) create mode 100644 lib/node_modules/@stdlib/math/base/special/gammainc/benchmark/benchmark.native.js create mode 100644 lib/node_modules/@stdlib/math/base/special/gammainc/benchmark/c/native/Makefile create mode 100644 lib/node_modules/@stdlib/math/base/special/gammainc/benchmark/c/native/benchmark.c create mode 100644 lib/node_modules/@stdlib/math/base/special/gammainc/binding.gyp create mode 100644 lib/node_modules/@stdlib/math/base/special/gammainc/examples/c/Makefile create mode 100644 lib/node_modules/@stdlib/math/base/special/gammainc/examples/c/example.c create mode 100644 lib/node_modules/@stdlib/math/base/special/gammainc/include.gypi create mode 100644 lib/node_modules/@stdlib/math/base/special/gammainc/include/stdlib/math/base/special/gammainc.h create mode 100644 lib/node_modules/@stdlib/math/base/special/gammainc/lib/native.js create mode 100644 lib/node_modules/@stdlib/math/base/special/gammainc/manifest.json create mode 100644 lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/README.md b/lib/node_modules/@stdlib/math/base/special/gammainc/README.md index 6abe4afc36b1..476abde9bce5 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/README.md +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/README.md @@ -173,6 +173,106 @@ logEachMap( 'x: %0.4f, \t s: %0.4f, \t f(x,s): %0.4f', x, s, gammainc ); + + +* * * + +
+ +## C APIs + + + +
+ +
+ + + + + +
+ +### Usage + +```c +#include "stdlib/math/base/special/gammainc.h" +``` + +#### stdlib_base_gammainc( x, a, regularized, upper ) + +Evaluates the [incomplete gamma function][incomplete-gamma-function] for inputs `x` and `a`. The third and fourth parameters of the function can be used to specify whether instead to evaluate the non-regularized and/or upper incomplete gamma functions, respectively. + +```c +double out = stdlib_base_gammainc( 0.0, 1.0, true, false ); +// returns 0.0 + +out = stdlib_base_gammainc( 6.0, 2.0, true, false ); +// returns ~0.9826 +``` + +The function accepts the following arguments: + +- **x**: `[in] double` input value. +- **a**: `[in] double` input value. +- **regularized**: `[in] bool` input value. +- **upper**: `[in] bool` input value. + +```c +double stdlib_base_gammainc( const double x, const double a, const bool regularized, const bool upper ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +### Examples + +```c +#include "stdlib/math/base/special/gammainc.h" +#include +#include + +static double random_uniform( const double min, const double max ) { + double v = (double)rand() / ( (double)RAND_MAX + 1.0 ); + return min + ( v*(max-min) ); +} + +int main( void ) { + double x; + double a; + double y; + int i; + + for ( i = 0; i < 10; i++ ) { + x = random_uniform( 0.0, 1000.0 ); + a = random_uniform( 1.0, 1000.0 ); + y = stdlib_base_gammainc( x, a, true, false ); + printf( "x: %lf, s: %lf, f(x,s): %lf\n", x, a, y ); + } +} +``` + +
+ + + +
+ + +
diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/benchmark/benchmark.native.js b/lib/node_modules/@stdlib/math/base/special/gammainc/benchmark/benchmark.native.js new file mode 100644 index 000000000000..279efaa72338 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/benchmark/benchmark.native.js @@ -0,0 +1,135 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var resolve = require( 'path' ).resolve; +var bench = require( '@stdlib/bench' ); +var uniform = require( '@stdlib/random/array/uniform' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var tryRequire = require( '@stdlib/utils/try-require' ); +var pkg = require( './../package.json' ).name; + + +// VARIABLES // + +var gammainc = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( gammainc instanceof Error ) +}; + + +// MAIN // + +bench( pkg+'::native:regularized=true,upper=true', opts, function benchmark( b ) { + var x; + var y; + var z; + var i; + + x = uniform( 100, 0.0, 1000.0 ); + y = uniform( 100, 1.0, 1000.0 ); + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + z = gammainc( x[ i%x.length ], y[ i%y.length ], true, true ); + if ( isnan( z ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( z ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); + +bench( pkg+'::native:regularized=true,upper=false', opts, function benchmark( b ) { + var x; + var y; + var z; + var i; + + x = uniform( 100, 0.0, 1000.0 ); + y = uniform( 100, 1.0, 1000.0 ); + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + z = gammainc( x[ i%x.length ], y[ i%y.length ], true, false ); + if ( isnan( z ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( z ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); + +bench( pkg+'::native:regularized=false,upper=true', opts, function benchmark( b ) { + var x; + var y; + var z; + var i; + + x = uniform( 100, 0.0, 1000.0 ); + y = uniform( 100, 1.0, 1000.0 ); + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + z = gammainc( x[ i%x.length ], y[ i%y.length ], false, true ); + if ( isnan( z ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( z ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); + +bench( pkg+'::native:regularized=false,upper=false', opts, function benchmark( b ) { + var x; + var y; + var z; + var i; + + x = uniform( 100, 0.0, 1000.0 ); + y = uniform( 100, 1.0, 1000.0 ); + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + z = gammainc( x[ i%x.length ], y[ i%y.length ], false, false ); + if ( isnan( z ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( z ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/benchmark/c/native/Makefile b/lib/node_modules/@stdlib/math/base/special/gammainc/benchmark/c/native/Makefile new file mode 100644 index 000000000000..a4bd7b38fd74 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/benchmark/c/native/Makefile @@ -0,0 +1,146 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2025 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +#/ + +# VARIABLES # + +ifndef VERBOSE + QUIET := @ +else + QUIET := +endif + +# Determine the OS ([1][1], [2][2]). +# +# [1]: https://en.wikipedia.org/wiki/Uname#Examples +# [2]: http://stackoverflow.com/a/27776822/2225624 +OS ?= $(shell uname) +ifneq (, $(findstring MINGW,$(OS))) + OS := WINNT +else +ifneq (, $(findstring MSYS,$(OS))) + OS := WINNT +else +ifneq (, $(findstring CYGWIN,$(OS))) + OS := WINNT +else +ifneq (, $(findstring Windows_NT,$(OS))) + OS := WINNT +endif +endif +endif +endif + +# Define the program used for compiling C source files: +ifdef C_COMPILER + CC := $(C_COMPILER) +else + CC := gcc +endif + +# Define the command-line options when compiling C files: +CFLAGS ?= \ + -std=c99 \ + -O3 \ + -Wall \ + -pedantic + +# Determine whether to generate position independent code ([1][1], [2][2]). +# +# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options +# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option +ifeq ($(OS), WINNT) + fPIC ?= +else + fPIC ?= -fPIC +endif + +# List of includes (e.g., `-I /foo/bar -I /beep/boop/include`): +INCLUDE ?= + +# List of source files: +SOURCE_FILES ?= + +# List of libraries (e.g., `-lopenblas -lpthread`): +LIBRARIES ?= + +# List of library paths (e.g., `-L /foo/bar -L /beep/boop`): +LIBPATH ?= + +# List of C targets: +c_targets := benchmark.out + + +# RULES # + +#/ +# Compiles source files. +# +# @param {string} [C_COMPILER] - C compiler (e.g., `gcc`) +# @param {string} [CFLAGS] - C compiler options +# @param {(string|void)} [fPIC] - compiler flag determining whether to generate position independent code (e.g., `-fPIC`) +# @param {string} [INCLUDE] - list of includes (e.g., `-I /foo/bar -I /beep/boop/include`) +# @param {string} [SOURCE_FILES] - list of source files +# @param {string} [LIBPATH] - list of library paths (e.g., `-L /foo/bar -L /beep/boop`) +# @param {string} [LIBRARIES] - list of libraries (e.g., `-lopenblas -lpthread`) +# +# @example +# make +# +# @example +# make all +#/ +all: $(c_targets) + +.PHONY: all + +#/ +# Compiles C source files. +# +# @private +# @param {string} CC - C compiler (e.g., `gcc`) +# @param {string} CFLAGS - C compiler options +# @param {(string|void)} fPIC - compiler flag determining whether to generate position independent code (e.g., `-fPIC`) +# @param {string} INCLUDE - list of includes (e.g., `-I /foo/bar`) +# @param {string} SOURCE_FILES - list of source files +# @param {string} LIBPATH - list of library paths (e.g., `-L /foo/bar`) +# @param {string} LIBRARIES - list of libraries (e.g., `-lopenblas`) +#/ +$(c_targets): %.out: %.c + $(QUIET) $(CC) $(CFLAGS) $(fPIC) $(INCLUDE) -o $@ $(SOURCE_FILES) $< $(LIBPATH) -lm $(LIBRARIES) + +#/ +# Runs compiled benchmarks. +# +# @example +# make run +#/ +run: $(c_targets) + $(QUIET) ./$< + +.PHONY: run + +#/ +# Removes generated files. +# +# @example +# make clean +#/ +clean: + $(QUIET) -rm -f *.o *.out + +.PHONY: clean diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/benchmark/c/native/benchmark.c b/lib/node_modules/@stdlib/math/base/special/gammainc/benchmark/c/native/benchmark.c new file mode 100644 index 000000000000..7e9ec6c656cf --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/benchmark/c/native/benchmark.c @@ -0,0 +1,140 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +#include "stdlib/math/base/special/gammainc.h" +#include +#include +#include +#include +#include + +#define NAME "gammainc" +#define ITERATIONS 1000000 +#define REPEATS 3 + +/** +* Prints the TAP version. +*/ +static void print_version( void ) { + printf( "TAP version 13\n" ); +} + +/** +* Prints the TAP summary. +* +* @param total total number of tests +* @param passing total number of passing tests +*/ +static void print_summary( int total, int passing ) { + printf( "#\n" ); + printf( "1..%d\n", total ); // TAP plan + printf( "# total %d\n", total ); + printf( "# pass %d\n", passing ); + printf( "#\n" ); + printf( "# ok\n" ); +} + +/** +* Prints benchmarks results. +* +* @param elapsed elapsed time in seconds +*/ +static void print_results( double elapsed ) { + double rate = (double)ITERATIONS / elapsed; + printf( " ---\n" ); + printf( " iterations: %d\n", ITERATIONS ); + printf( " elapsed: %0.9f\n", elapsed ); + printf( " rate: %0.9f\n", rate ); + printf( " ...\n" ); +} + +/** +* Returns a clock time. +* +* @return clock time +*/ +static double tic( void ) { + struct timeval now; + gettimeofday( &now, NULL ); + return (double)now.tv_sec + (double)now.tv_usec / 1.0e6; +} + +/** +* Generates a random number on the interval [min,max). +* +* @param min minimum value (inclusive) +* @param max maximum value (exclusive) +* @return random number +*/ +static double random_uniform( const double min, const double max ) { + double v = (double)rand() / ( (double)RAND_MAX + 1.0 ); + return min + ( v*(max-min) ); +} + +/** +* Runs a benchmark. +* +* @return elapsed time in seconds +*/ +static double benchmark( void ) { + double x[ 100 ]; + double a[ 100 ]; + double elapsed; + double y; + double t; + int i; + + for ( i = 0; i < 100; i++ ) { + x[ i ] = random_uniform( 0.0, 1000.0 ); + a[ i ] = random_uniform( 1.0, 1000.0 ); + } + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + y = stdlib_base_gammainc( x[ i%100 ], a[ i%100 ], true, false ); + if ( y != y ) { + printf( "should not return NaN\n" ); + break; + } + } + elapsed = tic() - t; + if ( y != y ) { + printf( "should not return NaN\n" ); + } + return elapsed; +} + +/** +* Main execution sequence. +*/ +int main( void ) { + double elapsed; + int i; + + // Use the current time to seed the random number generator: + srand( time( NULL ) ); + + print_version(); + for ( i = 0; i < REPEATS; i++ ) { + printf( "# c::native::%s\n", NAME ); + elapsed = benchmark(); + print_results( elapsed ); + printf( "ok %d benchmark finished\n", i+1 ); + } + print_summary( REPEATS, REPEATS ); +} diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/binding.gyp b/lib/node_modules/@stdlib/math/base/special/gammainc/binding.gyp new file mode 100644 index 000000000000..68a1ca11d160 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/binding.gyp @@ -0,0 +1,170 @@ +# @license Apache-2.0 +# +# Copyright (c) 2025 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +# A `.gyp` file for building a Node.js native add-on. +# +# [1]: https://gyp.gsrc.io/docs/InputFormatReference.md +# [2]: https://gyp.gsrc.io/docs/UserDocumentation.md +{ + # List of files to include in this file: + 'includes': [ + './include.gypi', + ], + + # Define variables to be used throughout the configuration for all targets: + 'variables': { + # Target name should match the add-on export name: + 'addon_target_name%': 'addon', + + # Set variables based on the host OS: + 'conditions': [ + [ + 'OS=="win"', + { + # Define the object file suffix: + 'obj': 'obj', + }, + { + # Define the object file suffix: + 'obj': 'o', + } + ], # end condition (OS=="win") + ], # end conditions + }, # end variables + + # Define compile targets: + 'targets': [ + + # Target to generate an add-on: + { + # The target name should match the add-on export name: + 'target_name': '<(addon_target_name)', + + # Define dependencies: + 'dependencies': [], + + # Define directories which contain relevant include headers: + 'include_dirs': [ + # Local include directory: + '<@(include_dirs)', + ], + + # List of source files: + 'sources': [ + '<@(src_files)', + ], + + # Settings which should be applied when a target's object files are used as linker input: + 'link_settings': { + # Define libraries: + 'libraries': [ + '<@(libraries)', + ], + + # Define library directories: + 'library_dirs': [ + '<@(library_dirs)', + ], + }, + + # C/C++ compiler flags: + 'cflags': [ + # Enable commonly used warning options: + '-Wall', + + # Aggressive optimization: + '-O3', + ], + + # C specific compiler flags: + 'cflags_c': [ + # Specify the C standard to which a program is expected to conform: + '-std=c99', + ], + + # C++ specific compiler flags: + 'cflags_cpp': [ + # Specify the C++ standard to which a program is expected to conform: + '-std=c++11', + ], + + # Linker flags: + 'ldflags': [], + + # Apply conditions based on the host OS: + 'conditions': [ + [ + 'OS=="mac"', + { + # Linker flags: + 'ldflags': [ + '-undefined dynamic_lookup', + '-Wl,-no-pie', + '-Wl,-search_paths_first', + ], + }, + ], # end condition (OS=="mac") + [ + 'OS!="win"', + { + # C/C++ flags: + 'cflags': [ + # Generate platform-independent code: + '-fPIC', + ], + }, + ], # end condition (OS!="win") + ], # end conditions + }, # end target <(addon_target_name) + + # Target to copy a generated add-on to a standard location: + { + 'target_name': 'copy_addon', + + # Declare that the output of this target is not linked: + 'type': 'none', + + # Define dependencies: + 'dependencies': [ + # Require that the add-on be generated before building this target: + '<(addon_target_name)', + ], + + # Define a list of actions: + 'actions': [ + { + 'action_name': 'copy_addon', + 'message': 'Copying addon...', + + # Explicitly list the inputs in the command-line invocation below: + 'inputs': [], + + # Declare the expected outputs: + 'outputs': [ + '<(addon_output_dir)/<(addon_target_name).node', + ], + + # Define the command-line invocation: + 'action': [ + 'cp', + '<(PRODUCT_DIR)/<(addon_target_name).node', + '<(addon_output_dir)/<(addon_target_name).node', + ], + }, + ], # end actions + }, # end target copy_addon + ], # end targets +} diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/examples/c/Makefile b/lib/node_modules/@stdlib/math/base/special/gammainc/examples/c/Makefile new file mode 100644 index 000000000000..25ced822f96a --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/examples/c/Makefile @@ -0,0 +1,146 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2025 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +#/ + +# VARIABLES # + +ifndef VERBOSE + QUIET := @ +else + QUIET := +endif + +# Determine the OS ([1][1], [2][2]). +# +# [1]: https://en.wikipedia.org/wiki/Uname#Examples +# [2]: http://stackoverflow.com/a/27776822/2225624 +OS ?= $(shell uname) +ifneq (, $(findstring MINGW,$(OS))) + OS := WINNT +else +ifneq (, $(findstring MSYS,$(OS))) + OS := WINNT +else +ifneq (, $(findstring CYGWIN,$(OS))) + OS := WINNT +else +ifneq (, $(findstring Windows_NT,$(OS))) + OS := WINNT +endif +endif +endif +endif + +# Define the program used for compiling C source files: +ifdef C_COMPILER + CC := $(C_COMPILER) +else + CC := gcc +endif + +# Define the command-line options when compiling C files: +CFLAGS ?= \ + -std=c99 \ + -O3 \ + -Wall \ + -pedantic + +# Determine whether to generate position independent code ([1][1], [2][2]). +# +# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options +# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option +ifeq ($(OS), WINNT) + fPIC ?= +else + fPIC ?= -fPIC +endif + +# List of includes (e.g., `-I /foo/bar -I /beep/boop/include`): +INCLUDE ?= + +# List of source files: +SOURCE_FILES ?= + +# List of libraries (e.g., `-lopenblas -lpthread`): +LIBRARIES ?= + +# List of library paths (e.g., `-L /foo/bar -L /beep/boop`): +LIBPATH ?= + +# List of C targets: +c_targets := example.out + + +# RULES # + +#/ +# Compiles source files. +# +# @param {string} [C_COMPILER] - C compiler (e.g., `gcc`) +# @param {string} [CFLAGS] - C compiler options +# @param {(string|void)} [fPIC] - compiler flag determining whether to generate position independent code (e.g., `-fPIC`) +# @param {string} [INCLUDE] - list of includes (e.g., `-I /foo/bar -I /beep/boop/include`) +# @param {string} [SOURCE_FILES] - list of source files +# @param {string} [LIBPATH] - list of library paths (e.g., `-L /foo/bar -L /beep/boop`) +# @param {string} [LIBRARIES] - list of libraries (e.g., `-lopenblas -lpthread`) +# +# @example +# make +# +# @example +# make all +#/ +all: $(c_targets) + +.PHONY: all + +#/ +# Compiles C source files. +# +# @private +# @param {string} CC - C compiler (e.g., `gcc`) +# @param {string} CFLAGS - C compiler options +# @param {(string|void)} fPIC - compiler flag determining whether to generate position independent code (e.g., `-fPIC`) +# @param {string} INCLUDE - list of includes (e.g., `-I /foo/bar`) +# @param {string} SOURCE_FILES - list of source files +# @param {string} LIBPATH - list of library paths (e.g., `-L /foo/bar`) +# @param {string} LIBRARIES - list of libraries (e.g., `-lopenblas`) +#/ +$(c_targets): %.out: %.c + $(QUIET) $(CC) $(CFLAGS) $(fPIC) $(INCLUDE) -o $@ $(SOURCE_FILES) $< $(LIBPATH) -lm $(LIBRARIES) + +#/ +# Runs compiled examples. +# +# @example +# make run +#/ +run: $(c_targets) + $(QUIET) ./$< + +.PHONY: run + +#/ +# Removes generated files. +# +# @example +# make clean +#/ +clean: + $(QUIET) -rm -f *.o *.out + +.PHONY: clean diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/examples/c/example.c b/lib/node_modules/@stdlib/math/base/special/gammainc/examples/c/example.c new file mode 100644 index 000000000000..34f902d5ce46 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/examples/c/example.c @@ -0,0 +1,40 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +#include "stdlib/math/base/special/gammainc.h" +#include +#include + +static double random_uniform( const double min, const double max ) { + double v = (double)rand() / ( (double)RAND_MAX + 1.0 ); + return min + ( v*(max-min) ); +} + +int main( void ) { + double x; + double a; + double y; + int i; + + for ( i = 0; i < 10; i++ ) { + x = random_uniform( 0.0, 1000.0 ); + a = random_uniform( 1.0, 1000.0 ); + y = stdlib_base_gammainc( x, a, true, false ); + printf( "x: %lf, s: %lf, f(x,s): %lf\n", x, a, y ); + } +} diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/include.gypi b/lib/node_modules/@stdlib/math/base/special/gammainc/include.gypi new file mode 100644 index 000000000000..ecfaf82a3279 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/include.gypi @@ -0,0 +1,53 @@ +# @license Apache-2.0 +# +# Copyright (c) 2025 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +# A GYP include file for building a Node.js native add-on. +# +# Main documentation: +# +# [1]: https://gyp.gsrc.io/docs/InputFormatReference.md +# [2]: https://gyp.gsrc.io/docs/UserDocumentation.md +{ + # Define variables to be used throughout the configuration for all targets: + 'variables': { + # Source directory: + 'src_dir': './src', + + # Include directories: + 'include_dirs': [ + ' + +/* +* If C++, prevent name mangling so that the compiler emits a binary file having undecorated names, thus mirroring the behavior of a C compiler. +*/ +#ifdef __cplusplus +extern "C" { +#endif + +/** +* Computes the incomplete gamma function. The upper tail is calculated via the modified Lentz's method for computing continued fractions, the lower tail using a power expansion. +*/ +double stdlib_base_gammainc( const double x, const double a, const bool regularized, const bool upper ); + +#ifdef __cplusplus +} +#endif + +#endif // !STDLIB_MATH_BASE_SPECIAL_GAMMAINC_H diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/lib/native.js b/lib/node_modules/@stdlib/math/base/special/gammainc/lib/native.js new file mode 100644 index 000000000000..302f7d98c98f --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/lib/native.js @@ -0,0 +1,69 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var addon = require( './../src/addon.node' ); + + +// MAIN // + +/** +* Computes the incomplete gamma function. The upper tail is calculated via the modified Lentz's method for computing continued fractions, the lower tail using a power expansion. +* +* @private +* @param {NonNegativeNumber} x - function parameter +* @param {PositiveNumber} a - function parameter +* @param {boolean} regularized - boolean indicating if the function should evaluate the regularized or non-regularized incomplete gamma functions +* @param {boolean} upper - boolean indicating if the function should return the upper tail of the incomplete gamma function +* @returns {number} function value +* +* @example +* var v = gammainc( 6.0, 2.0, true, false ); +* // returns ~0.9826 +* +* @example +* var v = gammainc( 1.0, 2.0, true, true ); +* // returns ~0.7358 +* +* @example +* var v = gammainc( 7.0, 5.0, true, false ); +* // returns ~0.8270 +* +* @example +* var v = gammainc( 7.0, 5.0, false, false ); +* // returns ~19.8482 +* +* @example +* var v = gammainc( NaN, 3.0, true, false ); +* // returns NaN +* +* @example +* var v = gammainc( 1.0, NaN, true, false ); +* // returns NaN +*/ +function gammainc( x, a, regularized, upper ) { + return addon( x, a, regularized, upper ); +} + + +// EXPORTS // + +module.exports = gammainc; diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/manifest.json b/lib/node_modules/@stdlib/math/base/special/gammainc/manifest.json new file mode 100644 index 000000000000..d38ecfe1028a --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/manifest.json @@ -0,0 +1,160 @@ +{ + "options": { + "task": "build" + }, + "fields": [ + { + "field": "src", + "resolve": true, + "relative": true + }, + { + "field": "include", + "resolve": true, + "relative": true + }, + { + "field": "libraries", + "resolve": false, + "relative": false + }, + { + "field": "libpath", + "resolve": true, + "relative": false + } + ], + "confs": [ + { + "task": "build", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/napi/export", + "@stdlib/napi/argv", + "@stdlib/napi/argv-double", + "@stdlib/napi/argv-bool", + "@stdlib/napi/create-double", + "@stdlib/math/base/assert/is-nan", + "@stdlib/math/base/special/gammaln", + "@stdlib/math/base/special/floor", + "@stdlib/math/base/special/gamma", + "@stdlib/math/base/special/abs", + "@stdlib/math/base/special/exp", + "@stdlib/math/base/special/pow", + "@stdlib/math/base/special/ln", + "@stdlib/math/base/special/erfc", + "@stdlib/math/base/special/log1pmx", + "@stdlib/math/base/special/min", + "@stdlib/math/base/special/max", + "@stdlib/math/base/special/sqrt", + "@stdlib/math/base/special/gamma1pm1", + "@stdlib/math/base/special/powm1", + "@stdlib/math/base/special/gamma-lanczos-sum-expg-scaled", + "@stdlib/constants/float64/sqrt-eps", + "@stdlib/constants/float64/max", + "@stdlib/constants/float64/two-pi", + "@stdlib/constants/float64/sqrt-two-pi", + "@stdlib/constants/float64/max-ln", + "@stdlib/constants/float64/min-ln", + "@stdlib/constants/float64/pinf", + "@stdlib/constants/float64/pi", + "@stdlib/constants/float64/eps", + "@stdlib/constants/float64/e", + "@stdlib/constants/float64/gamma-lanczos-g", + "@stdlib/constants/float32/smallest-normal", + "@stdlib/constants/float64/max-nth-factorial" + ] + }, + { + "task": "benchmark", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/math/base/assert/is-nan", + "@stdlib/math/base/special/gammaln", + "@stdlib/math/base/special/floor", + "@stdlib/math/base/special/gamma", + "@stdlib/math/base/special/abs", + "@stdlib/math/base/special/exp", + "@stdlib/math/base/special/pow", + "@stdlib/math/base/special/ln", + "@stdlib/math/base/special/erfc", + "@stdlib/math/base/special/log1pmx", + "@stdlib/math/base/special/min", + "@stdlib/math/base/special/max", + "@stdlib/math/base/special/sqrt", + "@stdlib/math/base/special/gamma1pm1", + "@stdlib/math/base/special/powm1", + "@stdlib/math/base/special/gamma-lanczos-sum-expg-scaled", + "@stdlib/constants/float64/sqrt-eps", + "@stdlib/constants/float64/max", + "@stdlib/constants/float64/two-pi", + "@stdlib/constants/float64/sqrt-two-pi", + "@stdlib/constants/float64/max-ln", + "@stdlib/constants/float64/min-ln", + "@stdlib/constants/float64/pinf", + "@stdlib/constants/float64/pi", + "@stdlib/constants/float64/eps", + "@stdlib/constants/float64/e", + "@stdlib/constants/float64/gamma-lanczos-g", + "@stdlib/constants/float32/smallest-normal", + "@stdlib/constants/float64/max-nth-factorial" + ] + }, + { + "task": "examples", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/math/base/assert/is-nan", + "@stdlib/math/base/special/gammaln", + "@stdlib/math/base/special/floor", + "@stdlib/math/base/special/gamma", + "@stdlib/math/base/special/abs", + "@stdlib/math/base/special/exp", + "@stdlib/math/base/special/pow", + "@stdlib/math/base/special/ln", + "@stdlib/math/base/special/erfc", + "@stdlib/math/base/special/log1pmx", + "@stdlib/math/base/special/min", + "@stdlib/math/base/special/max", + "@stdlib/math/base/special/sqrt", + "@stdlib/math/base/special/gamma1pm1", + "@stdlib/math/base/special/powm1", + "@stdlib/math/base/special/gamma-lanczos-sum-expg-scaled", + "@stdlib/constants/float64/sqrt-eps", + "@stdlib/constants/float64/max", + "@stdlib/constants/float64/two-pi", + "@stdlib/constants/float64/sqrt-two-pi", + "@stdlib/constants/float64/max-ln", + "@stdlib/constants/float64/min-ln", + "@stdlib/constants/float64/pinf", + "@stdlib/constants/float64/pi", + "@stdlib/constants/float64/eps", + "@stdlib/constants/float64/e", + "@stdlib/constants/float64/gamma-lanczos-g", + "@stdlib/constants/float32/smallest-normal", + "@stdlib/constants/float64/max-nth-factorial" + ] + } + ] +} diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/package.json b/lib/node_modules/@stdlib/math/base/special/gammainc/package.json index 522e768ec09d..1ebd756bd644 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/package.json +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/package.json @@ -14,12 +14,14 @@ } ], "main": "./lib", + "gypfile": true, "directories": { "benchmark": "./benchmark", "doc": "./docs", "example": "./examples", + "include": "./include", "lib": "./lib", - "scripts": "./scripts", + "src": "./src", "test": "./test" }, "types": "./docs/types", diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/src/addon.c b/lib/node_modules/@stdlib/math/base/special/gammainc/src/addon.c index 82be2899cca0..6953da628e31 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/src/addon.c +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/src/addon.c @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2025 The Stdlib Authors. +* Copyright (c) 2024 The Stdlib Authors. * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. @@ -16,7 +16,29 @@ * limitations under the License. */ -#include "stdlib/math/base/special/hyp2f1.h" -#include "stdlib/math/base/napi/quaternary.h" +#include "stdlib/math/base/special/gammainc.h" +#include "stdlib/napi/argv.h" +#include "stdlib/napi/argv_double.h" +#include "stdlib/napi/argv_bool.h" +#include "stdlib/napi/create_double.h" +#include "stdlib/napi/export.h" +#include -STDLIB_MATH_BASE_NAPI_MODULE_DDDD_D( stdlib_base_hyp2f1 ) +/** +* Receives JavaScript callback invocation data. +* +* @param env environment under which the function is invoked +* @param info callback data +* @return Node-API value +*/ +static napi_value addon( napi_env env, napi_callback_info info ) { + STDLIB_NAPI_ARGV( env, info, argv, argc, 4 ); + STDLIB_NAPI_ARGV_DOUBLE( env, x, argv, 0 ); + STDLIB_NAPI_ARGV_DOUBLE( env, a, argv, 1 ); + STDLIB_NAPI_ARGV_BOOL( env, regularized, argv, 2 ); + STDLIB_NAPI_ARGV_BOOL( env, upper, argv, 3 ); + STDLIB_NAPI_CREATE_DOUBLE( env, stdlib_base_gammainc( x, a, regularized, upper ), out ); + return out; +} + +STDLIB_NAPI_MODULE_EXPORT_FCN( addon ) diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/src/main.c b/lib/node_modules/@stdlib/math/base/special/gammainc/src/main.c index c54547b0abe2..2a2647b32ed7 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/src/main.c +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/src/main.c @@ -18,7 +18,7 @@ * * ## Notice * -* The original C++ code and copyright notice are from the [Boost library]{@link https://www.boost.org/doc/libs/1_88_0/boost/math/special_functions/stdlib_base_gamma.hpp}. The implementation has been modified according to stdlib conventions. +* The original C++ code and copyright notice are from the [Boost library]{@link https://www.boost.org/doc/libs/1_88_0/boost/math/special_functions/gamma.hpp}. The implementation has been modified according to stdlib conventions. * * ```text * (C) Copyright John Maddock 2006-7, 2013-14. @@ -33,28 +33,52 @@ */ #include "stdlib/math/base/special/gammainc.h" -#include "stdlib/math/base/special/stdlib_base_gammaln.h" -#include "stdlib/math/base/special/stdlib_base_floor.h" -#include "stdlib/math/base/special/stdlib_base_gamma.h" -#include "stdlib/math/base/special/stdlib_base_abs.h" -#include "stdlib/math/base/special/stdlib_base_exp.h" -#include "stdlib/math/base/special/stdlib_base_pow.h" -#include "stdlib/math/base/special/stdlib_base_ln.h" #include "stdlib/math/base/assert/is_nan.h" -#include "stdlib/constants/float64/sqrt_eps.h" -#include "stdlib/constants/float64/max.h" +#include "stdlib/math/base/special/gamma_lanczos_sum_expg_scaled.h" +#include "stdlib/math/base/special/gamma1pm1.h" +#include "stdlib/math/base/special/log1pmx.h" +#include "stdlib/math/base/special/gammaln.h" +#include "stdlib/math/base/special/floor.h" +#include "stdlib/math/base/special/powm1.h" +#include "stdlib/math/base/special/gamma.h" +#include "stdlib/math/base/special/erfc.h" +#include "stdlib/math/base/special/sqrt.h" +#include "stdlib/math/base/special/abs.h" +#include "stdlib/math/base/special/exp.h" +#include "stdlib/math/base/special/pow.h" +#include "stdlib/math/base/special/min.h" +#include "stdlib/math/base/special/max.h" +#include "stdlib/math/base/special/ln.h" +#include "stdlib/constants/float32/smallest_normal.h" +#include "stdlib/constants/float64/max_nth_factorial.h" +#include "stdlib/constants/float64/gamma_lanczos_g.h" #include "stdlib/constants/float64/sqrt_two_pi.h" +#include "stdlib/constants/float64/sqrt_eps.h" +#include "stdlib/constants/float64/two_pi.h" #include "stdlib/constants/float64/max_ln.h" +#include "stdlib/constants/float64/min_ln.h" #include "stdlib/constants/float64/pinf.h" #include "stdlib/constants/float64/eps.h" -#include "stdlib/constants/float32/smallest_normal.h" -#include "stdlib/constants/float64/max_nth_factorial.h" -#include +#include "stdlib/constants/float64/max.h" +#include "stdlib/constants/float64/pi.h" +#include "stdlib/constants/float64/e.h" #include +#include static const int32_t MAX_ITERATIONS = 1000000; - -static double hys2f1( double a, double b, const double c, const double x, double *loss ); +static const double E = STDLIB_CONSTANT_FLOAT64_E; +static const double PI = STDLIB_CONSTANT_FLOAT64_PI; +static const double EPS = STDLIB_CONSTANT_FLOAT64_EPS; +static const double MAX = STDLIB_CONSTANT_FLOAT64_MAX; +static const double PINF = STDLIB_CONSTANT_FLOAT64_PINF; +static const double TWO_PI = STDLIB_CONSTANT_FLOAT64_TWO_PI; +static const double MAX_LN = STDLIB_CONSTANT_FLOAT64_MAX_LN; +static const double MIN_LN = STDLIB_CONSTANT_FLOAT64_MIN_LN; +static const double SQRT_EPS = STDLIB_CONSTANT_FLOAT64_SQRT_EPS; +static const double SQRT_TWO_PI = STDLIB_CONSTANT_FLOAT64_SQRT_TWO_PI; +static const double GAMMA_LANCZOS_G = STDLIB_CONSTANT_FLOAT64_GAMMA_LANCZOS_G; +static const double MAX_NTH_FACTORIAL = STDLIB_CONSTANT_FLOAT64_MAX_NTH_FACTORIAL; +static const float SMALLEST_NORMAL = STDLIB_CONSTANT_FLOAT32_SMALLEST_NORMAL; /* Begin auto-generated functions. The following functions are auto-generated. Do not edit directly. */ @@ -225,11 +249,12 @@ static double polyval_c8( const double x ) { /* End auto-generated functions. */ /** -* Creates a function to evaluate a series expansion of the upper incomplete stdlib_base_gamma fraction. +* Evaluates a series expansion of the upper incomplete gamma fraction and stores the numerator and denominator in an output array. * -* @param a1 function parameter -* @param z1 function parameter -* @return series function +* @param a function parameter +* @param z pointer to function parameter +* @param k pointer to function parameter +* @param out destination array for storing the numerator and denominator */ static void upperIncompleteGammaFract( const double a, double* z, double* k, double *out ) { *z += 2.0; @@ -240,7 +265,7 @@ static void upperIncompleteGammaFract( const double a, double* z, double* k, dou } /** -* Evaluates a continued fraction expansion. +* Evaluates a continued fraction expansion of the lower incomplete gamma integral. * * ```text * a1 @@ -252,11 +277,11 @@ static void upperIncompleteGammaFract( const double a, double* z, double* k, dou * b3 + ... * ``` * -* @private -* @param {Function} gen - function giving terms of continued fraction expansion -* @param {PositiveNumber} factor - further terms are only added as long as factor*result is smaller than the next term -* @param {PositiveInteger} maxIter - maximum number of iterations -* @returns {number} evaluated expansion +* @param a function parameter +* @param z function parameter +* @param factor further terms are only added as long as factor*result is smaller than the next term +* @param maxIter maximum number of iterations +* @returns evaluated expansion */ static double continuedFractionA( const double a, const double z, const double factor, const int32_t maxIter ) { int32_t maxIterC; @@ -276,7 +301,7 @@ static double continuedFractionA( const double a, const double z, const double f f = out[ 1 ]; a0 = out[ 0 ]; if ( f == 0.0 ) { - f = STDLIB_CONSTANT_FLOAT32_SMALLEST_NORMAL; + f = SMALLEST_NORMAL; } C = f; D = 0.0; @@ -286,40 +311,46 @@ static double continuedFractionA( const double a, const double z, const double f upperIncompleteGammaFract( a, &zc, &k, out ); D = out[ 1 ] + ( out[ 0 ] * D ); if ( D == 0.0 ) { - D = STDLIB_CONSTANT_FLOAT32_SMALLEST_NORMAL; + D = SMALLEST_NORMAL; } C = out[ 1 ] + ( out[ 0 ] / C ); if ( C == 0.0 ) { - C = STDLIB_CONSTANT_FLOAT32_SMALLEST_NORMAL; + C = SMALLEST_NORMAL; } D = 1.0 / D; delta = C * D; f *= delta; - } while ( out && ( stdlib_base_abs( delta - 1.0 ) > factor ) && --maxIterC ); + } while ( ( stdlib_base_abs( delta - 1.0 ) > factor ) && --maxIterC ); return a0 / f; } /** -* Evaluate the lower incomplete stdlib_base_gamma integral via a series expansion and divide by `stdlib_base_gamma(z)` to normalize. +* Evaluates the upper incomplete gamma integral via a series expansion and divide by `gamma(z)` to normalize. * -* @param a function parameter -* @param z function parameter -* @return function value +* ## Method +* +* - Multiply result by `(z^a) * (e^-z)` to get the full upper incomplete integral. +* - Divide by `gamma(z)` to get the normalized value. +* +* @param a function parameter +* @param z function parameter +* @returns function value */ static double upperGammaFraction( const double a, const double z ) { double f; f = z - a + 1.0; - return 1.0 / ( f + continuedFractionA( a, f, STDLIB_CONSTANT_FLOAT64_EPS, MAX_ITERATIONS ) ); + return 1.0 / ( f + continuedFractionA( a, f, EPS, MAX_ITERATIONS ) ); } /** -* Creates a function to evaluate a series expansion of the upper incomplete stdlib_base_gamma fraction. +* Computes the next term in the series expansion of the lower incomplete gamma function. * -* @param a1 function parameter -* @param z1 function parameter -* @return series function +* @param a pointer to function parameter +* @param x pointer to function parameter +* @param result pointer to result so far in series +* @return next term in series */ static double lowerIncompleteGammaSeries( double* a, const double z, double* result ) { double r; @@ -331,25 +362,14 @@ static double lowerIncompleteGammaSeries( double* a, const double z, double* res } /** -* Evaluates a continued fraction expansion. +* Helper function to sum the elements of the series expansion of the lower incomplete gamma function. * -* ```text -* a1 -* --------------- -* b1 + a2 -* ---------- -* b2 + a3 -* ----- -* b3 + ... -* ``` -* -* @private -* @param {Function} gen - function giving terms of continued fraction expansion -* @param {PositiveNumber} factor - further terms are only added as long as factor*result is smaller than the next term -* @param {PositiveInteger} maxIter - maximum number of iterations -* @returns {number} evaluated expansion +* @param a function parameter +* @param z function parameter +* @param initialValue initial value for the series +* @return sum of series */ -static double sumSeries( const double a, const double z, const double initialValue ) { +static double sumSeries1( const double a, const double z, const double initialValue ) { int32_t counter; double nextTerm; double result; @@ -366,35 +386,40 @@ static double sumSeries( const double a, const double z, const double initialVal nextTerm = lowerIncompleteGammaSeries( &ac, z, &result ); sum += nextTerm; } - while ( ( stdlib_base_abs(STDLIB_CONSTANT_FLOAT64_EPS * sum) < stdlib_base_abs(nextTerm) ) && --counter ); + while ( ( stdlib_base_abs(EPS * sum) < stdlib_base_abs(nextTerm) ) && --counter ); return sum; } /** -* Evaluate the lower incomplete stdlib_base_gamma integral via a series expansion and divide by `stdlib_base_gamma(z)` to normalize. +* Sums elements of the series expansion of the lower incomplete gamma function. * -* @param a function parameter -* @param z function parameter -* @return function value +* ## Method +* +* - Multiply result by `((z^a) * (e^-z) / a)` to get the full lower incomplete integral. +* - Divide by `gamma(a)` to get the normalized value. +* +* @param a function parameter +* @param z function parameter +* @param initialValue initial value of the resulting sum +* @returns sum of terms of lower gamma series */ static double lowerGammaSeries( const double a, const double z, const double initValue ) { - return sumSeries( a, z, initValue ); + return sumSeries1( a, z, initValue ); } /** * Calculates normalized Q when a is an integer. * -* @private -* @param {integer} a - function parameter -* @param {number} x - function parameter -* @returns {number} upper stdlib_base_gamma fraction +* @param a function parameter +* @param x function parameter +* @returns upper gamma fraction */ static double finiteGammaQ( const double a, const double x ) { double term; double sum; double e; - double n; + int32_t n; e = stdlib_base_exp( -x ); sum = e; @@ -412,17 +437,16 @@ static double finiteGammaQ( const double a, const double x ) { /** * Calculates normalized Q when a is a half-integer. * -* @private -* @param {number} a - function parameter -* @param {number} x - function parameter -* @returns {number} upper stdlib_base_gamma fraction +* @param a function parameter +* @param x function parameter +* @returns upper gamma fraction */ static double finiteHalfGammaQ( const double a, const double x ) { double half; double term; double sum; double e; - double n; + int32_t n; e = stdlib_base_erfc( stdlib_base_sqrt(x) ); if ( e != 0 && a > 1.0 ) { @@ -442,15 +466,13 @@ static double finiteHalfGammaQ( const double a, const double x ) { } /** -* Computes `(z^a)*(e^-z) / stdlib_base_gamma(a)`. +* Computes `(z^a)*(e^-z) / gamma(a)`. * -* @private -* @param {number} a - input value -* @param {number} z - input value -* @returns {number} function value +* @param a input value +* @param z input value +* @returns function value */ static double regularisedGammaPrefix( const double a, const double z ) { - // TODO: NEEDS TO BE CHANGED (to be continued here) double prefix; double amza; double agh; @@ -459,42 +481,42 @@ static double regularisedGammaPrefix( const double a, const double z ) { double sq; double d; - agh = a + G - 0.5; - d = ( (z - a) - G + 0.5 ) / agh; + agh = a + GAMMA_LANCZOS_G - 0.5; + d = ( (z - a) - GAMMA_LANCZOS_G + 0.5 ) / agh; if ( a < 1.0 ) { - // Treat a < 1 as a special case because our Lanczos approximations are optimized against the factorials with a > 1, and for high precision types very small values of `a` can give rather erroneous results for stdlib_base_gamma: - if ( z <= STDLIB_CONSTANT_FLOAT64_MIN_LN ) { + // Treat a < 1.0 as a special case because our Lanczos approximations are optimized against the factorials with a > 1.0, and for high precision types very small values of `a` can give rather erroneous results for gamma: + if ( z <= MIN_LN || a < 1.0 / MAX ) { // Use logs, so should be free of cancellation errors: return stdlib_base_exp( ( a * stdlib_base_ln(z) ) - z - stdlib_base_gammaln( a ) ); } - // No danger of overflow as stdlib_base_gamma(a) < 1/a for small a, so direct calculation: + // No danger of overflow as gamma(a) < 1/a for small a, so direct calculation: return stdlib_base_pow( z, a ) * stdlib_base_exp( -z ) / stdlib_base_gamma( a ); } if ( stdlib_base_abs(d*d*a) <= 100.0 && a > 150.0 ) { // Special case for large a and a ~ z: - prefix = ( a * ( log1p( d ) - d ) ) + ( z * ( 0.5-G ) / agh ); + prefix = ( a * ( stdlib_base_log1pmx( d ) - d ) ) + ( z * ( 0.5-GAMMA_LANCZOS_G ) / agh ); prefix = stdlib_base_exp( prefix ); } else { // General case. Direct computation is most accurate, but use various fallbacks for different parts of the problem domain: - alz = a * stdlib_base_ln(z / agh); + alz = a * stdlib_base_ln( z / agh ); amz = a - z; if ( - min(alz, amz) <= STDLIB_CONSTANT_FLOAT64_MIN_LN || - max(alz, amz) >= STDLIB_CONSTANT_FLOAT64_MAX_LN + stdlib_base_min(alz, amz) <= MIN_LN || + stdlib_base_max(alz, amz) >= MAX_LN ) { amza = amz / a; if ( - min(alz, amz)/2.0 > STDLIB_CONSTANT_FLOAT64_MIN_LN && - max(alz, amz)/2.0 < STDLIB_CONSTANT_FLOAT64_MAX_LN + stdlib_base_min(alz, amz)/2.0 > MIN_LN && + stdlib_base_max(alz, amz)/2.0 < MAX_LN ) { // Compute square root of the result and then square it: sq = stdlib_base_pow( z / agh, a / 2.0 ) * stdlib_base_exp( amz / 2.0 ); prefix = sq * sq; } else if ( - min(alz, amz)/4.0 > STDLIB_CONSTANT_FLOAT64_MIN_LN && - max(alz, amz)/4.0 < STDLIB_CONSTANT_FLOAT64_MAX_LN && + stdlib_base_min(alz, amz)/4.0 > MIN_LN && + stdlib_base_max(alz, amz)/4.0 < MAX_LN && z > a ) { // Compute the 4th root of the result then square it twice: @@ -503,8 +525,8 @@ static double regularisedGammaPrefix( const double a, const double z ) { prefix *= prefix; } else if ( - amza > STDLIB_CONSTANT_FLOAT64_MIN_LN && - amza < STDLIB_CONSTANT_FLOAT64_MAX_LN + amza > MIN_LN && + amza < MAX_LN ) { prefix = stdlib_base_pow( (z * stdlib_base_exp(amza)) / agh, a ); } @@ -517,25 +539,24 @@ static double regularisedGammaPrefix( const double a, const double z ) { prefix = stdlib_base_pow( z / agh, a ) * stdlib_base_exp( amz ); } } - prefix *= stdlib_base_sqrt( agh / E ) / lanczosSumExpGScaled( a ); + prefix *= stdlib_base_sqrt( agh / E ) / stdlib_base_gamma_lanczos_sum_expg_scaled( a ); return prefix; } /** * Calculates the power term prefix `(z^a)(e^-z)` used in the non-normalized incomplete gammas. * -* @private -* @param {number} a - function parameter -* @param {number} z - function parameter -* @returns {number} power term prefix +* @param a function parameter +* @param z function parameter +* @returns power term prefix */ -static double fullIGammaPrefix( a, z ) { +static double fullIGammaPrefix( const double a, const double z ) { double prefix; double alz; alz = a * stdlib_base_ln( z ); if ( z >= 1.0 ) { - if ( ( alz < STDLIB_CONSTANT_FLOAT64_MAX_LN ) && ( -z > STDLIB_CONSTANT_FLOAT64_MIN_LN) ) { + if ( ( alz < MAX_LN ) && ( -z > MIN_LN) ) { prefix = stdlib_base_pow( z, a ) * stdlib_base_exp( -z ); } else if ( a >= 1.0 ) { prefix = stdlib_base_pow( z / stdlib_base_exp(z/a), a ); @@ -545,9 +566,9 @@ static double fullIGammaPrefix( a, z ) { } } else { - if ( alz > STDLIB_CONSTANT_FLOAT64_MIN_LN ) { + if ( alz > MIN_LN ) { prefix = stdlib_base_pow( z, a ) * stdlib_base_exp( -z ); - } else if ( z/a < STDLIB_CONSTANT_FLOAT64_MAX_LN ) { + } else if ( z/a < MAX_LN ) { prefix = stdlib_base_pow( z / stdlib_base_exp(z/a), a ); } else { prefix = stdlib_base_exp( alz - z ); @@ -557,17 +578,18 @@ static double fullIGammaPrefix( a, z ) { } /** -* Creates a function to evaluate a series expansion of the upper incomplete stdlib_base_gamma fraction. +* Computes the next term in the series for the full upper fraction (Q) when `a` is very small. * -* @param a1 function parameter -* @param z1 function parameter -* @return series function +* @param a pointer to function parameter +* @param x function parameter +* @param result pointer to result so far in series +* @return next term in series */ -static double smallGamma2Series( double* a, double* x, int32_t* n, double* result ) { +static double smallGamma2Series( double* a, const double x, int32_t* n, double* result ) { double r; r = ( *result ) / ( *a ); - *result *= ( *x ); + *result *= x; *n += 1; *result /= ( *n ); *a += 1.0; @@ -575,23 +597,12 @@ static double smallGamma2Series( double* a, double* x, int32_t* n, double* resul } /** -* Evaluates a continued fraction expansion. -* -* ```text -* a1 -* --------------- -* b1 + a2 -* ---------- -* b2 + a3 -* ----- -* b3 + ... -* ``` +* Sums the elements of the series given by the full upper fraction (Q) when `a` is very small. * -* @private -* @param {Function} gen - function giving terms of continued fraction expansion -* @param {PositiveNumber} factor - further terms are only added as long as factor*result is smaller than the next term -* @param {PositiveInteger} maxIter - maximum number of iterations -* @returns {number} evaluated expansion +* @param a function parameter +* @param x function parameter +* @param initialValue initial value for the series +* @return sum of series */ static double sumSeries2( const double a, const double x, const double initialValue ) { int32_t counter; @@ -611,20 +622,21 @@ static double sumSeries2( const double a, const double x, const double initialVa // Repeatedly call function... do { - nextTerm = smallGamma2Series( &ac, &xc, &n, &result ); + nextTerm = smallGamma2Series( &ac, xc, &n, &result ); sum += nextTerm; } - while ( ( stdlib_base_abs(STDLIB_CONSTANT_FLOAT64_EPS * sum) < stdlib_base_abs(nextTerm) ) && --counter ); + while ( ( stdlib_base_abs(EPS * sum) < stdlib_base_abs(nextTerm) ) && --counter ); return sum; } /** -* Evaluate the lower incomplete stdlib_base_gamma integral via a series expansion and divide by `stdlib_base_gamma(z)` to normalize. +* Compute the full upper fraction (Q) when `a` is very small. * -* @param a function parameter -* @param z function parameter -* @return function value +* @param a function parameter +* @param x function parameter +* @param invert boolean indicating if the upper tail of the incomplete gamma function should be evaluated +* @param out destination array for storing the full upper fraction (Q) and pgam */ static void tgammaSmallUpperPart( const double a, const double x, const bool invert, double* out ) { double initialValue; @@ -648,41 +660,30 @@ static void tgammaSmallUpperPart( const double a, const double x, const bool inv } /** -* Creates a function to evaluate a series expansion of the upper incomplete stdlib_base_gamma fraction. +* Computes the next term in the series for the full upper fraction (Q) when `x` is large. * -* @param a1 function parameter -* @param z1 function parameter -* @return series function +* @param a pointer to function parameter +* @param x function parameter +* @param result pointer to result so far in series +* @return next term in series */ -static double tgammaILargeXSeries( double* a, const double z, double* result ) { +static double tgammaILargeXSeries( double* a, const double x, double* result ) { double r; r = *result; - *result *= ( *a ) / z; + *result *= ( *a ) / x; *a -= 1.0; return r; } /** -* Evaluates a continued fraction expansion. +* Sums the elements of the series given by the full upper fraction (Q) when `x` is large. * -* ```text -* a1 -* --------------- -* b1 + a2 -* ---------- -* b2 + a3 -* ----- -* b3 + ... -* ``` -* -* @private -* @param {Function} gen - function giving terms of continued fraction expansion -* @param {PositiveNumber} factor - further terms are only added as long as factor*result is smaller than the next term -* @param {PositiveInteger} maxIter - maximum number of iterations -* @returns {number} evaluated expansion +* @param a function parameter +* @param x function parameter +* @return sum of series */ -static double sumSeries3( const double a, const double z ) { +static double sumSeries3( const double a, const double x ) { int32_t counter; double nextTerm; double result; @@ -696,19 +697,19 @@ static double sumSeries3( const double a, const double z ) { // Repeatedly call function... do { - nextTerm = tgammaILargeXSeries( &ac, z, &result ); + nextTerm = tgammaILargeXSeries( &ac, x, &result ); sum += nextTerm; } - while ( ( stdlib_base_abs(STDLIB_CONSTANT_FLOAT64_EPS * sum) < stdlib_base_abs(nextTerm) ) && --counter ); + while ( ( stdlib_base_abs(EPS * sum) < stdlib_base_abs(nextTerm) ) && --counter ); return sum; } /** -* Evaluate the lower incomplete stdlib_base_gamma integral via a series expansion and divide by `stdlib_base_gamma(z)` to normalize. +* Computes the asymptotic expansion of the full upper fraction (Q) when `x` is large. * * @param a function parameter -* @param z function parameter +* @param x function parameter * @return function value */ static double tgammaILargeX( const double a, const double x ) { @@ -724,9 +725,9 @@ static double tgammaILargeX( const double a, const double x ) { * * [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method * -* @param c - polynomial coefficients sorted in ascending degree -* @param x - value at which to evaluate the polynomial -* @returns evaluated polynomial +* @param c pointer to polynomial coefficients sorted in ascending degree +* @param x value at which to evaluate the polynomial +* @returns evaluated polynomial */ static double evalpoly( double *c, const double x ){ int32_t i; @@ -747,12 +748,11 @@ static double evalpoly( double *c, const double x ){ } /** -* Asymptotic expansions of the incomplete stdlib_base_gamma functions when `a` is large and `x ~ a` (IEEE double precision or 10^-17). +* Asymptotic expansions of the incomplete gamma functions when `a` is large and `x ~ a` (IEEE double precision or 10^-17). * -* @private -* @param {number} a - function parameter -* @param {number} x - function parameter -* @returns {number} value of asymptotic expansion +* @param a function parameter +* @param x function parameter +* @returns value of asymptotic expansion */ static double igammaTemmeLarge( const double a, const double x ) { double workspace[ 10 ]; @@ -769,18 +769,18 @@ static double igammaTemmeLarge( const double a, const double x ) { if ( x < a ) { z = -z; } - workspace[ 0 ] = polyvalC0( z ); - workspace[ 1 ] = polyvalC1( z ); - workspace[ 2 ] = polyvalC2( z ); - workspace[ 3 ] = polyvalC3( z ); - workspace[ 4 ] = polyvalC4( z ); - workspace[ 5 ] = polyvalC5( z ); - workspace[ 6 ] = polyvalC6( z ); - workspace[ 7 ] = polyvalC7( z ); - workspace[ 8 ] = polyvalC8( z ); + workspace[ 0 ] = polyval_c0( z ); + workspace[ 1 ] = polyval_c1( z ); + workspace[ 2 ] = polyval_c2( z ); + workspace[ 3 ] = polyval_c3( z ); + workspace[ 4 ] = polyval_c4( z ); + workspace[ 5 ] = polyval_c5( z ); + workspace[ 6 ] = polyval_c6( z ); + workspace[ 7 ] = polyval_c7( z ); + workspace[ 8 ] = polyval_c8( z ); workspace[ 9 ] = -0.00059676129019274625; result = evalpoly( workspace, 1.0/a ); - result *= stdlib_base_exp( -y ) / stdlib_base_sqrt( STDLIB_CONSTANT_FLOAT64_TWO_PI * a ); + result *= stdlib_base_exp( -y ) / stdlib_base_sqrt( TWO_PI * a ); if ( x < a ) { result = -result; } @@ -789,21 +789,13 @@ static double igammaTemmeLarge( const double a, const double x ) { } /** -* Computes the regularized incomplete stdlib_base_gamma function. The upper tail is calculated via the modified Lentz's method for computing continued fractions, the lower tail using a power expansion. +* Main entry point for evaluating all the four incomplete gamma functions (lower, upper, regularized lower, and regularized upper). * -* ## Notes -* -* - When `a >= FLOAT64_MAX_NTH_FACTORIAL` and computing the non-regularized incomplete stdlib_base_gamma, result is rather hard to compute unless we use logs. There are really two options a) if `x` is a long way from `a` in value then we can reliably use methods 2 and 4 below in logarithmic form and go straight to the result. Otherwise we let the regularized stdlib_base_gamma take the strain (the result is unlikely to underflow in the central region anyway) and combine with `lgamma` in the hopes that we get a finite result. -* -* @param x input value -* @param a input value -* @param regularized input value -* @param upper input value +* @param x function parameter +* @param a function parameter +* @param regularized boolean indicating if the function should evaluate the regularized or non-regularized incomplete gamma functions +* @param upper boolean indicating if the function should return the upper tail of the incomplete gamma function * @return function value -* -* @example -* double v = stdlib_base_gammainc( 1.0, 1.0, 1.0, 0.0 ); -* // returns 1.0 */ double igammaFinal( const double a, const double x, const bool regularized, const bool upper ) { bool optimisedInvert; @@ -823,7 +815,7 @@ double igammaFinal( const double a, const double x, const bool regularized, cons result = 0.0; invert = upper; - isSmallA = ( a < 30 ) && ( a <= x + 1.0 ) && ( x < STDLIB_CONSTANT_FLOAT64_MAX_LN ); + isSmallA = ( a < 30 ) && ( a <= x + 1.0 ) && ( x < MAX_LN ); if ( isSmallA ) { fa = stdlib_base_floor( a ); isInt = ( fa == a ); @@ -840,7 +832,7 @@ double igammaFinal( const double a, const double x, const bool regularized, cons // Calculate Q via finite sum for half integer a: invert = !invert; evalMethod = 1; - } else if ( x < STDLIB_CONSTANT_FLOAT64_SQRT_EPS && a > 1.0 ) { + } else if ( x < SQRT_EPS && a > 1.0 ) { evalMethod = 6; } else if ( ( x > 1000.0 ) && ( ( a < x ) || ( stdlib_base_abs( a - 50.0 ) / x < 1.0 ) ) ) { // calculate Q via asymptotic approximation: @@ -905,6 +897,7 @@ double igammaFinal( const double a, const double x, const bool regularized, cons regularisedGammaPrefix( a, x ) : fullIGammaPrefix( a, x ); if ( result != 0.0 ) { + // If the result will be inverted, we can potentially save computation by initializing the series sum closer to the final result. This reduces the number of iterations needed in the series evaluation. However, care must be taken to avoid spurious numeric overflows. In practice, the more expensive overflow checks below are typically bypassed for well-behaved input values. initValue = 0.0; optimisedInvert = false; if ( invert ) { @@ -912,13 +905,13 @@ double igammaFinal( const double a, const double x, const bool regularized, cons if ( regularized || result >= 1.0 || - STDLIB_CONSTANT_FLOAT64_MAX * result > initValue + MAX * result > initValue ) { initValue /= result; if ( regularized || a < 1.0 || - ( STDLIB_CONSTANT_FLOAT64_MAX / a > initValue ) + ( MAX / a > initValue ) ) { initValue *= -a; optimisedInvert = true; @@ -926,22 +919,20 @@ double igammaFinal( const double a, const double x, const bool regularized, cons else { initValue = 0.0; } - } - else { + } else { initValue = 0.0; } } - } - result *= lowerGammaSeries( a, x, initValue ) / a; - if ( optimisedInvert ) { - invert = false; - result = -result; + result *= lowerGammaSeries( a, x, initValue ) / a; + if ( optimisedInvert ) { + invert = false; + result = -result; + } } break; case 3: // Compute Q: invert = !invert; - // it can be changed to return result and option to store g: tgammaSmallUpperPart( a, x, invert, out ); result = out[ 0 ]; g = out[ 1 ]; @@ -993,24 +984,22 @@ double igammaFinal( const double a, const double x, const bool regularized, cons return result; } - - /** -* Computes the regularized incomplete stdlib_base_gamma function. The upper tail is calculated via the modified Lentz's method for computing continued fractions, the lower tail using a power expansion. +* Computes the incomplete gamma function. The upper tail is calculated via the modified Lentz's method for computing continued fractions, the lower tail using a power expansion. * * ## Notes * -* - When `a >= FLOAT64_MAX_NTH_FACTORIAL` and computing the non-regularized incomplete stdlib_base_gamma, result is rather hard to compute unless we use logs. There are really two options a) if `x` is a long way from `a` in value then we can reliably use methods 2 and 4 below in logarithmic form and go straight to the result. Otherwise we let the regularized stdlib_base_gamma take the strain (the result is unlikely to underflow in the central region anyway) and combine with `lgamma` in the hopes that we get a finite result. +* - When `a >= FLOAT64_MAX_NTH_FACTORIAL` and computing the non-normalized incomplete gamma, result is rather hard to compute unless we use logs. There are really two options a) if `x` is a long way from `a` in value then we can reliably use methods 2 and 4 below in logarithmic form and go straight to the result. Otherwise we let the regularized gamma take the strain (the result is unlikely to underflow in the central region anyway) and combine with `lgamma` in the hopes that we get a finite result. * -* @param x input value -* @param a input value -* @param regularized input value -* @param upper input value +* @param x function parameter +* @param a function parameter +* @param regularized boolean indicating if the function should evaluate the regularized or non-regularized incomplete gamma functions +* @param upper boolean indicating if the function should return the upper tail of the incomplete gamma function * @return function value * * @example -* double v = stdlib_base_gammainc( 1.0, 1.0, 1.0, 0.0 ); -* // returns 1.0 +* double v = stdlib_base_gammainc( 0.0, 1.0, true, false ); +* // returns 0.0 */ double stdlib_base_gammainc( const double x, const double a, const bool regularized, const bool upper ) { double initValue; @@ -1021,14 +1010,13 @@ double stdlib_base_gammainc( const double x, const double a, const bool regulari return 0.0 / 0.0; // NaN } invert = upper; - result = 0.0; - if ( a >= STDLIB_CONSTANT_FLOAT64_MAX_NTH_FACTORIAL && !regularized ) { + if ( a >= MAX_NTH_FACTORIAL && !regularized ) { if ( invert && ( a * 4.0 < x ) ) { - // This is method 4 below, done in logs: + // This is method 4 in `igammaFinal`, done in logs: result = ( a * stdlib_base_ln(x) ) - x; result += stdlib_base_ln( upperGammaFraction( a, x ) ); } else if ( !invert && ( a > 4.0 * x ) ) { - // This is method 2 below, done in logs: + // This is method 2 in `igammaFinal`, done in logs: result = ( a * stdlib_base_ln(x) ) - x; initValue = 0.0; result += stdlib_base_ln( lowerGammaSeries( a, x, initValue ) / a ); @@ -1039,9 +1027,9 @@ double stdlib_base_gammainc( const double x, const double a, const bool regulari // Try http://functions.wolfram.com/06.06.06.0039.01: result = 1.0 + ( 1.0 / (12.0*a) ) + ( 1.0 / (288.0*a*a) ); result = stdlib_base_ln( result ) - a + ( ( a-0.5 ) * stdlib_base_ln(a) ); - result += stdlib_base_ln( STDLIB_CONSTANT_FLOAT64_SQRT_TWO_PI ); + result += stdlib_base_ln( SQRT_TWO_PI ); } else { - // This is method 2 below, done in logs, we're really outside the range of this method, but since the result is almost certainly infinite, we should probably be OK: + // This is method 2 in `igammaFinal`, done in logs, we're really outside the range of this method, but since the result is almost certainly infinite, we should probably be OK: result = ( a * stdlib_base_ln( x ) ) - x; initValue = 0.0; result += stdlib_base_ln( lowerGammaSeries( a, x, initValue ) / a ); @@ -1050,8 +1038,8 @@ double stdlib_base_gammainc( const double x, const double a, const bool regulari result = stdlib_base_ln( result ) + stdlib_base_gammaln( a ); } } - if ( result > STDLIB_CONSTANT_FLOAT64_MAX_LN ) { - return STDLIB_CONSTANT_FLOAT64_PINF; + if ( result > MAX_LN ) { + return PINF; } return stdlib_base_exp( result ); } diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js new file mode 100644 index 000000000000..eabb7013002c --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js @@ -0,0 +1,201 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var resolve = require( 'path' ).resolve; +var tape = require( 'tape' ); +var isfinite = require( '@stdlib/math/base/assert/is-finite' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var abs = require( '@stdlib/math/base/special/abs' ); +var EPS = require( '@stdlib/constants/float64/eps' ); +var tryRequire = require( '@stdlib/utils/try-require' ); + + +// VARIABLES // + +var gammainc = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( gammainc instanceof Error ) +}; + + +// FIXTURES // + +var fixtures = require( './fixtures/cpp/output.json' ); +var expected1 = fixtures.lower_regularized; +var expected2 = fixtures.upper_regularized; +var expected3 = fixtures.lower_unregularized; +var expected4 = fixtures.upper_unregularized; +var x = fixtures.x; +var s = fixtures.s; + + +// TESTS // + +tape( 'main export is a function', opts, function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof gammainc, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function returns `NaN` if provided a `NaN`', opts, function test( t ) { + var val; + + val = gammainc( NaN, 2, true, false ); + t.strictEqual( isnan( val ), true, 'returns expected value' ); + + val = gammainc( 4, NaN, true, false ); + t.strictEqual( isnan( val ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns NaN if provided x < 0 or s <= 0', opts, function test( t ) { + var val; + + // Case: x < 0 + val = gammainc( -0.1, 2, true, false ); + t.strictEqual( isnan( val ), true, 'returns expected value' ); + + // Case: s = 0 + val = gammainc( 0.1, 0, true, false ); + t.strictEqual( isnan( val ), true, 'returns expected value' ); + + // Case: s < 0 + val = gammainc( 0.1, -2, true, false ); + t.strictEqual( isnan( val ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns 0 for the lower incomplete gamma function when the first argument is zero', opts, function test( t ) { + var val; + var s; + for ( s = 1; s < 10; s++ ) { + val = gammainc( 0, s, true, false ); + t.strictEqual( val, 0, 'returns expected value' ); + } + t.end(); +}); + +tape.only( 'the function correctly evaluates the lower incomplete gamma function', opts, function test( t ) { + var actual; + var delta; + var tol; + var b1; + var b2; + var i; + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], true, false ); + + b1 = isfinite( actual ); + b2 = isfinite( expected1[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected1[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + delta = abs( actual - expected1[ i ] ); + tol = 80.0 * EPS * abs( expected1[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected1[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + } + t.end(); +}); + +tape( 'the function correctly evaluates the upper incomplete gamma function', opts, function test( t ) { + var actual; + var delta; + var tol; + var b1; + var b2; + var i; + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], true, true ); + + b1 = isfinite( actual ); + b2 = isfinite( expected2[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected2[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + delta = abs( actual - expected2[ i ] ); + tol = 20.0 * EPS * abs( expected2[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected2[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + } + t.end(); +}); + +tape( 'the function correctly evaluates the unregularized lower incomplete gamma function', opts, function test( t ) { + var actual; + var delta; + var tol; + var b1; + var b2; + var i; + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], false, false ); + + b1 = isfinite( actual ); + b2 = isfinite( expected3[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected3[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + delta = abs( actual - expected3[ i ] ); + tol = 10.0 * EPS * abs( expected3[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected3[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + } + t.end(); +}); + +tape( 'the function correctly evaluates the unregularized upper incomplete gamma function', opts, function test( t ) { + var actual; + var delta; + var tol; + var b1; + var b2; + var i; + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], false, true ); + + b1 = isfinite( actual ); + b2 = isfinite( expected4[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected4[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + delta = abs( actual - expected4[ i ] ); + tol = 10.0 * EPS * abs( expected4[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected4[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + } + t.end(); +}); From 02b8dd180980323320b42cb17143f71084e56806 Mon Sep 17 00:00:00 2001 From: stdlib-bot <82920195+stdlib-bot@users.noreply.github.com> Date: Thu, 19 Jun 2025 07:23:10 +0000 Subject: [PATCH 04/14] chore: update copyright years --- lib/node_modules/@stdlib/math/base/special/gammainc/src/addon.c | 2 +- lib/node_modules/@stdlib/math/base/special/gammainc/src/main.c | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/src/addon.c b/lib/node_modules/@stdlib/math/base/special/gammainc/src/addon.c index 6953da628e31..082ef4c69653 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/src/addon.c +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/src/addon.c @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2024 The Stdlib Authors. +* Copyright (c) 2025 The Stdlib Authors. * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/src/main.c b/lib/node_modules/@stdlib/math/base/special/gammainc/src/main.c index 2a2647b32ed7..bd9c17f77338 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/src/main.c +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/src/main.c @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2018 The Stdlib Authors. +* Copyright (c) 2025 The Stdlib Authors. * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. From cc286561c0838e87b6a17e79ece6ccb62f2dcbcf Mon Sep 17 00:00:00 2001 From: Karan Anand Date: Thu, 19 Jun 2025 00:28:24 -0700 Subject: [PATCH 05/14] bench: shorten the interval for input values --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: na - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: passed - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: na - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../gammainc/benchmark/benchmark.native.js | 16 ++++++++-------- 1 file changed, 8 insertions(+), 8 deletions(-) diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/benchmark/benchmark.native.js b/lib/node_modules/@stdlib/math/base/special/gammainc/benchmark/benchmark.native.js index 279efaa72338..f0d87333d6ea 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/benchmark/benchmark.native.js +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/benchmark/benchmark.native.js @@ -44,8 +44,8 @@ bench( pkg+'::native:regularized=true,upper=true', opts, function benchmark( b ) var z; var i; - x = uniform( 100, 0.0, 1000.0 ); - y = uniform( 100, 1.0, 1000.0 ); + x = uniform( 100, 0.0, 100.0 ); + y = uniform( 100, 1.0, 100.0 ); b.tic(); for ( i = 0; i < b.iterations; i++ ) { @@ -68,8 +68,8 @@ bench( pkg+'::native:regularized=true,upper=false', opts, function benchmark( b var z; var i; - x = uniform( 100, 0.0, 1000.0 ); - y = uniform( 100, 1.0, 1000.0 ); + x = uniform( 100, 0.0, 100.0 ); + y = uniform( 100, 1.0, 100.0 ); b.tic(); for ( i = 0; i < b.iterations; i++ ) { @@ -92,8 +92,8 @@ bench( pkg+'::native:regularized=false,upper=true', opts, function benchmark( b var z; var i; - x = uniform( 100, 0.0, 1000.0 ); - y = uniform( 100, 1.0, 1000.0 ); + x = uniform( 100, 0.0, 100.0 ); + y = uniform( 100, 1.0, 100.0 ); b.tic(); for ( i = 0; i < b.iterations; i++ ) { @@ -116,8 +116,8 @@ bench( pkg+'::native:regularized=false,upper=false', opts, function benchmark( b var z; var i; - x = uniform( 100, 0.0, 1000.0 ); - y = uniform( 100, 1.0, 1000.0 ); + x = uniform( 100, 0.0, 100.0 ); + y = uniform( 100, 1.0, 100.0 ); b.tic(); for ( i = 0; i < b.iterations; i++ ) { From f0528170e0147dfbf3d5da14001f4ee07c6482dc Mon Sep 17 00:00:00 2001 From: Karan Anand Date: Thu, 19 Jun 2025 00:36:26 -0700 Subject: [PATCH 06/14] chore: add scripts --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown status: na - task: lint_package_json status: passed - task: lint_repl_help status: na - task: lint_javascript_src status: na - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: na - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- lib/node_modules/@stdlib/math/base/special/gammainc/package.json | 1 + 1 file changed, 1 insertion(+) diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/package.json b/lib/node_modules/@stdlib/math/base/special/gammainc/package.json index 1ebd756bd644..3c48218c3c55 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/package.json +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/package.json @@ -21,6 +21,7 @@ "example": "./examples", "include": "./include", "lib": "./lib", + "scripts": "./scripts", "src": "./src", "test": "./test" }, From 474b103df845318594bb9d23855ebb97d714bfe7 Mon Sep 17 00:00:00 2001 From: Karan Anand Date: Fri, 20 Jun 2025 17:49:09 -0700 Subject: [PATCH 07/14] fix: use correct equation --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: na - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: passed - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: na - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- lib/node_modules/@stdlib/math/base/special/gammainc/src/main.c | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/src/main.c b/lib/node_modules/@stdlib/math/base/special/gammainc/src/main.c index bd9c17f77338..543a6d1e1461 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/src/main.c +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/src/main.c @@ -494,7 +494,7 @@ static double regularisedGammaPrefix( const double a, const double z ) { } if ( stdlib_base_abs(d*d*a) <= 100.0 && a > 150.0 ) { // Special case for large a and a ~ z: - prefix = ( a * ( stdlib_base_log1pmx( d ) - d ) ) + ( z * ( 0.5-GAMMA_LANCZOS_G ) / agh ); + prefix = ( a * stdlib_base_log1pmx( d ) ) + ( z * ( 0.5-GAMMA_LANCZOS_G ) / agh ); prefix = stdlib_base_exp( prefix ); } else { From d79211e074b98988f21bf5253e652930a8811531 Mon Sep 17 00:00:00 2001 From: Karan Anand Date: Fri, 20 Jun 2025 19:59:06 -0700 Subject: [PATCH 08/14] test: add more tests --- .../gammainc/test/fixtures/cpp/huge.json | 1 + .../gammainc/test/fixtures/cpp/large.json | 1 + .../gammainc/test/fixtures/cpp/medium.json | 1 + .../gammainc/test/fixtures/cpp/runner.cpp | 19 +- .../gammainc/test/fixtures/cpp/small.json | 1 + .../base/special/gammainc/test/test.native.js | 500 ++++++++++++++++-- 6 files changed, 490 insertions(+), 33 deletions(-) create mode 100644 lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/huge.json create mode 100644 lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/large.json create mode 100644 lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/medium.json create mode 100644 lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/small.json diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/huge.json b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/huge.json new file mode 100644 index 000000000000..ceb786d7e597 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/huge.json @@ -0,0 +1 @@ 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\ No newline at end of file diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/runner.cpp b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/runner.cpp index 48ba6d3685a9..7901ed6eb787 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/runner.cpp +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/runner.cpp @@ -341,10 +341,25 @@ int main( void ) { exit( 1 ); } - // Generate fixture data: + // Small x and s: rand_array_f64( x, len, 1.0, 40.0 ); rand_array_f64( s, len, 1.0, 40.0 ); - generate( x, s, len, "output.json" ); + generate( x, s, len, "small.json" ); + + // Medium x and s: + rand_array_f64( x, len, 40.0, 100.0 ); + rand_array_f64( s, len, 40.0, 100.0 ); + generate( x, s, len, "medium.json" ); + + // Large x and small s: + rand_array_f64( x, len, 100.0, 1000.0 ); + rand_array_f64( s, len, 1.0, 50.0 ); + generate( x, s, len, "large.json" ); + + // Large x and medium s: + rand_array_f64( x, len, 100.0, 1000.0 ); + rand_array_f64( s, len, 50.0, 100.0 ); + generate( x, s, len, "huge.json" ); // Free allocated memory: free( x ); diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/small.json b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/small.json new file mode 100644 index 000000000000..6116cd5c2e62 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/small.json @@ -0,0 +1 @@ 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\ No newline at end of file diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js index eabb7013002c..249745d81e37 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js @@ -25,6 +25,8 @@ var tape = require( 'tape' ); var isfinite = require( '@stdlib/math/base/assert/is-finite' ); var isnan = require( '@stdlib/math/base/assert/is-nan' ); var abs = require( '@stdlib/math/base/special/abs' ); +var epsdiff = require( '@stdlib/math/base/utils/float64-epsilon-difference' ); +var toBinaryString = require( '@stdlib/number/float64/base/to-binary-string' ); var EPS = require( '@stdlib/constants/float64/eps' ); var tryRequire = require( '@stdlib/utils/try-require' ); @@ -39,13 +41,10 @@ var opts = { // FIXTURES // -var fixtures = require( './fixtures/cpp/output.json' ); -var expected1 = fixtures.lower_regularized; -var expected2 = fixtures.upper_regularized; -var expected3 = fixtures.lower_unregularized; -var expected4 = fixtures.upper_unregularized; -var x = fixtures.x; -var s = fixtures.s; +var small = require( './fixtures/cpp/small.json' ); +var medium = require( './fixtures/cpp/medium.json' ); +var large = require( './fixtures/cpp/large.json' ); +var huge = require( './fixtures/cpp/huge.json' ); // TESTS // @@ -96,105 +95,544 @@ tape( 'the function returns 0 for the lower incomplete gamma function when the f t.end(); }); -tape.only( 'the function correctly evaluates the lower incomplete gamma function', opts, function test( t ) { +tape( 'the function correctly evaluates the lower incomplete gamma function for small `x` and small `s`', opts, function test( t ) { + var expected; var actual; var delta; var tol; var b1; var b2; + var x; + var s; + var i; + + expected = small.lower_regularized; + x = small.x; + s = small.s; + + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], true, false ); + + b1 = isfinite( actual ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + delta = abs( actual - expected[ i ] ); + tol = 80.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + } + t.end(); +}); + +tape( 'the function correctly evaluates the upper incomplete gamma function for small `x` and small `s`', opts, function test( t ) { + var expected; + var actual; + var delta; + var tol; + var b1; + var b2; + var x; + var s; + var i; + + expected = small.upper_regularized; + x = small.x; + s = small.s; + + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], true, true ); + + b1 = isfinite( actual ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + delta = abs( actual - expected[ i ] ); + tol = 20.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + } + t.end(); +}); + +tape( 'the function correctly evaluates the unregularized lower incomplete gamma function for small `x` and small `s`', opts, function test( t ) { + var expected; + var actual; + var delta; + var tol; + var b1; + var b2; + var x; + var s; + var i; + + expected = small.lower_unregularized; + x = small.x; + s = small.s; + + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], false, false ); + + b1 = isfinite( actual ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + delta = abs( actual - expected[ i ] ); + tol = 10.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + } + t.end(); +}); + +tape( 'the function correctly evaluates the unregularized upper incomplete gamma function for small `x` and small `s`', opts, function test( t ) { + var expected; + var actual; + var delta; + var tol; + var b1; + var b2; + var x; + var s; + var i; + + expected = small.upper_unregularized; + x = small.x; + s = small.s; + + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], false, true ); + + b1 = isfinite( actual ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + delta = abs( actual - expected[ i ] ); + tol = 10.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + } + t.end(); +}); + +tape( 'the function correctly evaluates the lower incomplete gamma function for medium `x` and medium `s`', opts, function test( t ) { + var expected; + var actual; + var delta; + var tol; + var b1; + var b2; + var x; + var s; + var i; + + expected = medium.lower_regularized; + x = medium.x; + s = medium.s; + + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], true, false ); + + b1 = isfinite( actual ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + delta = abs( actual - expected[ i ] ); + tol = 65.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + } + t.end(); +}); + +tape( 'the function correctly evaluates the upper incomplete gamma function for medium `x` and medium `s`', opts, function test( t ) { + var expected; + var actual; + var delta; + var tol; + var b1; + var b2; + var x; + var s; + var i; + + expected = medium.upper_regularized; + x = medium.x; + s = medium.s; + + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], true, true ); + + b1 = isfinite( actual ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + delta = abs( actual - expected[ i ] ); + tol = 55.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + } + t.end(); +}); + +tape( 'the function correctly evaluates the unregularized lower incomplete gamma function for medium `x` and medium `s`', opts, function test( t ) { + var expected; + var actual; + var delta; + var tol; + var b1; + var b2; + var x; + var s; + var i; + + expected = medium.lower_unregularized; + x = medium.x; + s = medium.s; + + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], false, false ); + + b1 = isfinite( actual ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + delta = abs( actual - expected[ i ] ); + tol = 5.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + } + t.end(); +}); + +tape( 'the function correctly evaluates the unregularized upper incomplete gamma function for medium `x` and medium `s`', opts, function test( t ) { + var expected; + var actual; + var delta; + var tol; + var b1; + var b2; + var x; + var s; var i; + + expected = medium.upper_unregularized; + x = medium.x; + s = medium.s; + + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], false, true ); + + b1 = isfinite( actual ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + delta = abs( actual - expected[ i ] ); + tol = 5.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + } + t.end(); +}); + +tape( 'the function correctly evaluates the lower incomplete gamma function for large `x` and small `s`', opts, function test( t ) { + var expected; + var actual; + var b1; + var b2; + var x; + var s; + var i; + + expected = large.lower_regularized; + x = large.x; + s = large.s; + for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], true, false ); b1 = isfinite( actual ); - b2 = isfinite( expected1[ i ] ); + b2 = isfinite( expected[ i ] ); t.strictEqual( b1, b2, 'returns expected value' ); b1 = isnan( actual ); - b2 = isnan( expected1[ i ] ); + b2 = isnan( expected[ i ] ); t.strictEqual( b1, b2, 'returns expected value' ); if ( !b1 || !b2 ) { - delta = abs( actual - expected1[ i ] ); - tol = 80.0 * EPS * abs( expected1[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected1[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + t.strictEqual( actual, expected[ i ], 'returns expected value' ); } } t.end(); }); -tape( 'the function correctly evaluates the upper incomplete gamma function', opts, function test( t ) { +tape( 'the function correctly evaluates the upper incomplete gamma function for large `x` and small `s`', opts, function test( t ) { + var expected; + var actual; + var s1; + var s2; + var b1; + var b2; + var x; + var s; + var i; + + expected = large.upper_regularized; + x = large.x; + s = large.s; + + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], true, true ); + + b1 = isfinite( actual ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + // We use bit string comparison for extremely small expected values, as the tolerance becomes smaller than the minimum representable double-precision floating-point value. Out of the 500 values tested, only 16 faced this issue. If those values are excluded, the test passes with a tolerance of `30.0 * EPS`. + s1 = toBinaryString( actual ); + s2 = toBinaryString( expected[ i ] ); + t.strictEqual( s1.substring( 0, s1.length-12 ), s2.substring( 0, s2.length-12 ), 'returns expected value' ); + } + } + t.end(); +}); + +tape( 'the function correctly evaluates the unregularized lower incomplete gamma function for large `x` and small `s`', opts, function test( t ) { + var expected; var actual; var delta; var tol; var b1; var b2; + var x; + var s; var i; + + expected = large.lower_unregularized; + x = large.x; + s = large.s; + + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], false, false ); + + b1 = isfinite( actual ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + delta = abs( actual - expected[ i ] ); + tol = 5.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + } + t.end(); +}); + +tape( 'the function correctly evaluates the unregularized upper incomplete gamma function for large `x` and small `s`', opts, function test( t ) { + var expected; + var actual; + var delta; + var tol; + var b1; + var b2; + var x; + var s; + var i; + + expected = large.upper_unregularized; + x = large.x; + s = large.s; + + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], false, true ); + + b1 = isfinite( actual ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + delta = abs( actual - expected[ i ] ); + tol = 40.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + } + t.end(); +}); + +tape( 'the function correctly evaluates the lower incomplete gamma function for large `x` and medium `s`', opts, function test( t ) { + var expected; + var actual; + var delta; + var tol; + var b1; + var b2; + var x; + var s; + var i; + + expected = huge.lower_regularized; + x = huge.x; + s = huge.s; + + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], true, false ); + + b1 = isfinite( actual ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + delta = abs( actual - expected[ i ] ); + tol = EPS * abs( expected[ i ] ); + // Only 1 value in the test suite is not exactly equal to the expected value. If we exclude that value, we can use exact equality for the rest of the values. + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + } + t.end(); +}); + +tape( 'the function correctly evaluates the upper incomplete gamma function for large `x` and medium `s`', opts, function test( t ) { + var expected; + var actual; + var s1; + var s2; + var b1; + var b2; + var x; + var s; + var i; + + expected = huge.upper_regularized; + x = huge.x; + s = huge.s; + for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], true, true ); b1 = isfinite( actual ); - b2 = isfinite( expected2[ i ] ); + b2 = isfinite( expected[ i ] ); t.strictEqual( b1, b2, 'returns expected value' ); b1 = isnan( actual ); - b2 = isnan( expected2[ i ] ); + b2 = isnan( expected[ i ] ); t.strictEqual( b1, b2, 'returns expected value' ); if ( !b1 || !b2 ) { - delta = abs( actual - expected2[ i ] ); - tol = 20.0 * EPS * abs( expected2[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected2[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + // We use bit string comparison for extremely small expected values, as the tolerance becomes smaller than the minimum representable double-precision floating-point value. Out of the 500 values tested, only 10 faced this issue. If those values are excluded, the test passes with a tolerance of `100.0 * EPS`. + s1 = toBinaryString( actual ); + s2 = toBinaryString( expected[ i ] ); + t.strictEqual( s1.substring( 0, s1.length-16 ), s2.substring( 0, s2.length-16 ), 'returns expected value' ); } } t.end(); }); -tape( 'the function correctly evaluates the unregularized lower incomplete gamma function', opts, function test( t ) { +tape( 'the function correctly evaluates the unregularized lower incomplete gamma function for large `x` and medium `s`', opts, function test( t ) { + var expected; var actual; var delta; var tol; var b1; var b2; + var x; + var s; var i; + + expected = huge.lower_unregularized; + x = huge.x; + s = huge.s; + for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, false ); b1 = isfinite( actual ); - b2 = isfinite( expected3[ i ] ); + b2 = isfinite( expected[ i ] ); t.strictEqual( b1, b2, 'returns expected value' ); b1 = isnan( actual ); - b2 = isnan( expected3[ i ] ); + b2 = isnan( expected[ i ] ); t.strictEqual( b1, b2, 'returns expected value' ); if ( !b1 || !b2 ) { - delta = abs( actual - expected3[ i ] ); - tol = 10.0 * EPS * abs( expected3[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected3[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + delta = abs( actual - expected[ i ] ); + tol = 5.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); } } t.end(); }); -tape( 'the function correctly evaluates the unregularized upper incomplete gamma function', opts, function test( t ) { +tape( 'the function correctly evaluates the unregularized upper incomplete gamma function for large `x` and medium `s`', opts, function test( t ) { + var expected; var actual; var delta; var tol; var b1; var b2; + var x; + var s; var i; + + expected = huge.upper_unregularized; + x = huge.x; + s = huge.s; + for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, true ); b1 = isfinite( actual ); - b2 = isfinite( expected4[ i ] ); + b2 = isfinite( expected[ i ] ); t.strictEqual( b1, b2, 'returns expected value' ); b1 = isnan( actual ); - b2 = isnan( expected4[ i ] ); + b2 = isnan( expected[ i ] ); t.strictEqual( b1, b2, 'returns expected value' ); if ( !b1 || !b2 ) { - delta = abs( actual - expected4[ i ] ); - tol = 10.0 * EPS * abs( expected4[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected4[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + delta = abs( actual - expected[ i ] ); + tol = 90.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); } } t.end(); From bf5c3bcf35e6f936dd1ddccbcfbc2fbe8e3fa741 Mon Sep 17 00:00:00 2001 From: Karan Anand Date: Fri, 20 Jun 2025 21:47:49 -0700 Subject: [PATCH 09/14] test: use `ulpdiff` for tests --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: na - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: passed - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: na - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../math/base/special/gammainc/test/test.js | 499 +++++++++++++++--- .../base/special/gammainc/test/test.native.js | 111 +--- 2 files changed, 460 insertions(+), 150 deletions(-) diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.js b/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.js index a9ac362f35b1..59c76b1bd73b 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.js +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.js @@ -23,20 +23,17 @@ var tape = require( 'tape' ); var isfinite = require( '@stdlib/math/base/assert/is-finite' ); var isnan = require( '@stdlib/math/base/assert/is-nan' ); -var abs = require( '@stdlib/math/base/special/abs' ); -var EPS = require( '@stdlib/constants/float64/eps' ); +var isSameValue = require( '@stdlib/assert/is-same-value' ); +var ulpdiff = require( '@stdlib/number/float64/base/ulp-difference' ); var gammainc = require( './../lib' ); // FIXTURES // -var fixtures = require( './fixtures/cpp/output.json' ); -var expected1 = fixtures.lower_regularized; -var expected2 = fixtures.upper_regularized; -var expected3 = fixtures.lower_unregularized; -var expected4 = fixtures.upper_unregularized; -var x = fixtures.x; -var s = fixtures.s; +var small = require( './fixtures/cpp/small.json' ); +var medium = require( './fixtures/cpp/medium.json' ); +var large = require( './fixtures/cpp/large.json' ); +var huge = require( './fixtures/cpp/huge.json' ); // TESTS // @@ -50,11 +47,11 @@ tape( 'main export is a function', function test( t ) { tape( 'the function returns `NaN` if provided a `NaN`', function test( t ) { var val; - val = gammainc( NaN, 2 ); - t.strictEqual( isnan( val ), true, 'returns expected value' ); + val = gammainc( NaN, 2, true, false ); + t.strictEqual( isSameValue( val, NaN ), true, 'returns expected value' ); - val = gammainc( 4, NaN ); - t.strictEqual( isnan( val ), true, 'returns expected value' ); + val = gammainc( 4, NaN, true, false ); + t.strictEqual( isSameValue( val, NaN ), true, 'returns expected value' ); t.end(); }); @@ -63,16 +60,16 @@ tape( 'the function returns NaN if provided x < 0 or s <= 0', function test( t ) var val; // Case: x < 0 - val = gammainc( -0.1, 2 ); - t.strictEqual( isnan( val ), true, 'returns expected value' ); + val = gammainc( -0.1, 2, true, false ); + t.strictEqual( isSameValue( val, NaN ), true, 'returns expected value' ); // Case: s = 0 - val = gammainc( 0.1, 0 ); - t.strictEqual( isnan( val ), true, 'returns expected value' ); + val = gammainc( 0.1, 0, true, false ); + t.strictEqual( isSameValue( val, NaN ), true, 'returns expected value' ); // Case: s < 0 - val = gammainc( 0.1, -2 ); - t.strictEqual( isnan( val ), true, 'returns expected value' ); + val = gammainc( 0.1, -2, true, false ); + t.strictEqual( isSameValue( val, NaN ), true, 'returns expected value' ); t.end(); }); @@ -81,111 +78,489 @@ tape( 'the function returns 0 for the lower incomplete gamma function when the f var val; var s; for ( s = 1; s < 10; s++ ) { - val = gammainc( 0, s ); - t.ok( val === 0, 'returns expected value' ); + val = gammainc( 0, s, true, false ); + t.strictEqual( isSameValue( val, 0.0 ), true, 'returns expected value' ); } t.end(); }); -tape( 'the function correctly evaluates the lower incomplete gamma function', function test( t ) { +tape( 'the function correctly evaluates the lower incomplete gamma function for small `x` and small `s`', function test( t ) { + var expected; var actual; - var delta; - var tol; var b1; var b2; + var x; + var s; var i; + + expected = small.lower_regularized; + x = small.x; + s = small.s; + for ( i = 0; i < x.length; i++ ) { - actual = gammainc( x[ i ], s[ i ] ); + actual = gammainc( x[ i ], s[ i ], true, false ); b1 = isfinite( actual ); - b2 = isfinite( expected1[ i ] ); - t.strictEqual( b1, b2, 'returned result is ' + ( (b2) ? 'finite' : 'not finite' ) ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); b1 = isnan( actual ); - b2 = isnan( expected1[ i ] ); - t.strictEqual( b1, b2, 'returned result is ' + ( (b1) ? '' : 'not' ) + ' NaN' ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); if ( !b1 || !b2 ) { - delta = abs( actual - expected1[ i ] ); - tol = 300.0 * EPS * abs( expected1[i] ); - t.ok( delta <= tol, 'returned result is within tolerance. x: '+x[i]+', s: '+s[i]+' actual: ' + actual + '; expected: ' + expected1[ i ] + '.' ); + // TODO: The difference is larger here as compared to the native tests. This is likely because the C implementation follows the latest Boost implementation, unlike the JS implementation. + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 45, true, 'returns expected value within 45 ulp' ); } } t.end(); }); -tape( 'the function correctly evaluates the upper incomplete gamma function', function test( t ) { +tape( 'the function correctly evaluates the upper incomplete gamma function for small `x` and small `s`', function test( t ) { + var expected; var actual; - var delta; - var tol; var b1; var b2; + var x; + var s; var i; + + expected = small.upper_regularized; + x = small.x; + s = small.s; + for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], true, true ); b1 = isfinite( actual ); - b2 = isfinite( expected2[ i ] ); - t.strictEqual( b1, b2, 'returned result is ' + ( (b2) ? 'finite' : 'not finite' ) ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); b1 = isnan( actual ); - b2 = isnan( expected2[ i ] ); - t.strictEqual( b1, b2, 'returned result is ' + ( (b1) ? '' : 'not' ) + ' NaN' ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); if ( !b1 || !b2 ) { - delta = abs( actual - expected2[ i ] ); - tol = 350.0 * EPS * abs( expected2[i] ); - t.ok( delta <= tol, 'within tolerance. x: '+x[i]+', s: '+s[i]+' actual: ' + actual + '; expected: ' + expected2[ i ] + '.' ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 33, true, 'returns expected value within 33 ulp' ); } } t.end(); }); -tape( 'the function correctly evaluates the unregularized lower incomplete gamma function', function test( t ) { +tape( 'the function correctly evaluates the unregularized lower incomplete gamma function for small `x` and small `s`', function test( t ) { + var expected; var actual; - var delta; - var tol; var b1; var b2; + var x; + var s; var i; + + expected = small.lower_unregularized; + x = small.x; + s = small.s; + for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, false ); b1 = isfinite( actual ); - b2 = isfinite( expected3[ i ] ); - t.strictEqual( b1, b2, 'returned result is ' + ( (b2) ? 'finite' : 'not finite' ) ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 6, true, 'returns expected value within 6 ulp' ); + } + } + t.end(); +}); + +tape( 'the function correctly evaluates the unregularized upper incomplete gamma function for small `x` and small `s`', function test( t ) { + var expected; + var actual; + var b1; + var b2; + var x; + var s; + var i; + + expected = small.upper_unregularized; + x = small.x; + s = small.s; + + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], false, true ); + + b1 = isfinite( actual ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 9, true, 'returns expected value within 9 ulp' ); + } + } + t.end(); +}); + +tape( 'the function correctly evaluates the lower incomplete gamma function for medium `x` and medium `s`', function test( t ) { + var expected; + var actual; + var b1; + var b2; + var x; + var s; + var i; + + expected = medium.lower_regularized; + x = medium.x; + s = medium.s; + + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], true, false ); + + b1 = isfinite( actual ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); b1 = isnan( actual ); - b2 = isnan( expected3[ i ] ); - t.strictEqual( b1, b2, 'returned result is ' + ( (b1) ? '' : 'not' ) + ' NaN' ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); if ( !b1 || !b2 ) { - delta = abs( actual - expected3[ i ] ); - tol = 10.0 * EPS * abs( expected3[i] ); - t.ok( delta <= tol, 'within tolerance. x: '+x[i]+', s: '+s[i]+' actual: ' + actual + '; expected: ' + expected3[ i ] + '.' ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 98, true, 'returns expected value within 98 ulp' ); } } t.end(); }); -tape( 'the function correctly evaluates the unregularized upper incomplete gamma function', function test( t ) { +tape( 'the function correctly evaluates the upper incomplete gamma function for medium `x` and medium `s`', function test( t ) { + var expected; var actual; - var delta; - var tol; var b1; var b2; + var x; + var s; var i; + + expected = medium.upper_regularized; + x = medium.x; + s = medium.s; + + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], true, true ); + + b1 = isfinite( actual ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 84, true, 'returns expected value within 84 ulp' ); + } + } + t.end(); +}); + +tape( 'the function correctly evaluates the unregularized lower incomplete gamma function for medium `x` and medium `s`', function test( t ) { + var expected; + var actual; + var b1; + var b2; + var x; + var s; + var i; + + expected = medium.lower_unregularized; + x = medium.x; + s = medium.s; + + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], false, false ); + + b1 = isfinite( actual ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 6, true, 'returns expected value within 6 ulp' ); + } + } + t.end(); +}); + +tape( 'the function correctly evaluates the unregularized upper incomplete gamma function for medium `x` and medium `s`', function test( t ) { + var expected; + var actual; + var b1; + var b2; + var x; + var s; + var i; + + expected = medium.upper_unregularized; + x = medium.x; + s = medium.s; + + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], false, true ); + + b1 = isfinite( actual ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 9, true, 'returns expected value within 9 ulp' ); + } + } + t.end(); +}); + +tape( 'the function correctly evaluates the lower incomplete gamma function for large `x` and small `s`', function test( t ) { + var expected; + var actual; + var b1; + var b2; + var x; + var s; + var i; + + expected = large.lower_regularized; + x = large.x; + s = large.s; + + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], true, false ); + + b1 = isfinite( actual ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + t.strictEqual( actual, expected[ i ], 'returns expected value' ); + } + } + t.end(); +}); + +tape( 'the function correctly evaluates the upper incomplete gamma function for large `x` and small `s`', function test( t ) { + var expected; + var actual; + var b1; + var b2; + var x; + var s; + var i; + + expected = large.upper_regularized; + x = large.x; + s = large.s; + + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], true, true ); + + b1 = isfinite( actual ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 61, true, 'returns expected value within 61 ulp' ); + } + } + t.end(); +}); + +tape( 'the function correctly evaluates the unregularized lower incomplete gamma function for large `x` and small `s`', function test( t ) { + var expected; + var actual; + var b1; + var b2; + var x; + var s; + var i; + + expected = large.lower_unregularized; + x = large.x; + s = large.s; + + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], false, false ); + + b1 = isfinite( actual ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 6, true, 'returns expected value within 6 ulp' ); + } + } + t.end(); +}); + +tape( 'the function correctly evaluates the unregularized upper incomplete gamma function for large `x` and small `s`', function test( t ) { + var expected; + var actual; + var b1; + var b2; + var x; + var s; + var i; + + expected = large.upper_unregularized; + x = large.x; + s = large.s; + + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], false, true ); + + b1 = isfinite( actual ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 56, true, 'returns expected value within 56 ulp' ); + } + } + t.end(); +}); + +tape( 'the function correctly evaluates the lower incomplete gamma function for large `x` and medium `s`', function test( t ) { + var expected; + var actual; + var b1; + var b2; + var x; + var s; + var i; + + expected = huge.lower_regularized; + x = huge.x; + s = huge.s; + + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], true, false ); + + b1 = isfinite( actual ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 1, true, 'returns expected value within 4 ulp' ); + } + } + t.end(); +}); + +tape( 'the function correctly evaluates the upper incomplete gamma function for large `x` and medium `s`', function test( t ) { + var expected; + var actual; + var b1; + var b2; + var x; + var s; + var i; + + expected = huge.upper_regularized; + x = huge.x; + s = huge.s; + + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], true, true ); + + b1 = isfinite( actual ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + // TODO: The difference is larger here as compared to the native tests. This is likely because the C implementation follows the latest Boost implementation, unlike the JS implementation. + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 134, true, 'returns expected value within 131 ulp' ); + } + } + t.end(); +}); + +tape( 'the function correctly evaluates the unregularized lower incomplete gamma function for large `x` and medium `s`', function test( t ) { + var expected; + var actual; + var b1; + var b2; + var x; + var s; + var i; + + expected = huge.lower_unregularized; + x = huge.x; + s = huge.s; + + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], false, false ); + + b1 = isfinite( actual ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + + b1 = isnan( actual ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); + if ( !b1 || !b2 ) { + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 5, true, 'returns expected value within 5 ulp' ); + } + } + t.end(); +}); + +tape( 'the function correctly evaluates the unregularized upper incomplete gamma function for large `x` and medium `s`', function test( t ) { + var expected; + var actual; + var b1; + var b2; + var x; + var s; + var i; + + expected = huge.upper_unregularized; + x = huge.x; + s = huge.s; + for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, true ); b1 = isfinite( actual ); - b2 = isfinite( expected4[ i ] ); - t.strictEqual( b1, b2, 'returned result is ' + ( (b2) ? 'finite' : 'not finite' ) ); + b2 = isfinite( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); b1 = isnan( actual ); - b2 = isnan( expected4[ i ] ); - t.strictEqual( b1, b2, 'returned result is ' + ( (b1) ? '' : 'not' ) + ' NaN' ); + b2 = isnan( expected[ i ] ); + t.strictEqual( b1, b2, 'returns expected value' ); if ( !b1 || !b2 ) { - delta = abs( actual - expected4[ i ] ); - tol = 10.0 * EPS * abs( expected4[i] ); - t.ok( delta <= tol, 'within tolerance. x: '+x[i]+', s: '+s[i]+' actual: ' + actual + '; expected: ' + expected4[ i ] + '.' ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 160, true, 'returns expected value within 160 ulp' ); } } t.end(); diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js index 249745d81e37..452f72178ee3 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js @@ -24,10 +24,8 @@ var resolve = require( 'path' ).resolve; var tape = require( 'tape' ); var isfinite = require( '@stdlib/math/base/assert/is-finite' ); var isnan = require( '@stdlib/math/base/assert/is-nan' ); -var abs = require( '@stdlib/math/base/special/abs' ); -var epsdiff = require( '@stdlib/math/base/utils/float64-epsilon-difference' ); -var toBinaryString = require( '@stdlib/number/float64/base/to-binary-string' ); -var EPS = require( '@stdlib/constants/float64/eps' ); +var isSameValue = require( '@stdlib/assert/is-same-value' ); +var ulpdiff = require( '@stdlib/number/float64/base/ulp-difference' ); var tryRequire = require( '@stdlib/utils/try-require' ); @@ -59,10 +57,10 @@ tape( 'the function returns `NaN` if provided a `NaN`', opts, function test( t ) var val; val = gammainc( NaN, 2, true, false ); - t.strictEqual( isnan( val ), true, 'returns expected value' ); + t.strictEqual( isSameValue( val, NaN ), true, 'returns expected value' ); val = gammainc( 4, NaN, true, false ); - t.strictEqual( isnan( val ), true, 'returns expected value' ); + t.strictEqual( isSameValue( val, NaN ), true, 'returns expected value' ); t.end(); }); @@ -72,15 +70,15 @@ tape( 'the function returns NaN if provided x < 0 or s <= 0', opts, function tes // Case: x < 0 val = gammainc( -0.1, 2, true, false ); - t.strictEqual( isnan( val ), true, 'returns expected value' ); + t.strictEqual( isSameValue( val, NaN ), true, 'returns expected value' ); // Case: s = 0 val = gammainc( 0.1, 0, true, false ); - t.strictEqual( isnan( val ), true, 'returns expected value' ); + t.strictEqual( isSameValue( val, NaN ), true, 'returns expected value' ); // Case: s < 0 val = gammainc( 0.1, -2, true, false ); - t.strictEqual( isnan( val ), true, 'returns expected value' ); + t.strictEqual( isSameValue( val, NaN ), true, 'returns expected value' ); t.end(); }); @@ -90,7 +88,7 @@ tape( 'the function returns 0 for the lower incomplete gamma function when the f var s; for ( s = 1; s < 10; s++ ) { val = gammainc( 0, s, true, false ); - t.strictEqual( val, 0, 'returns expected value' ); + t.strictEqual( isSameValue( val, 0.0 ), true, 'returns expected value' ); } t.end(); }); @@ -98,8 +96,6 @@ tape( 'the function returns 0 for the lower incomplete gamma function when the f tape( 'the function correctly evaluates the lower incomplete gamma function for small `x` and small `s`', opts, function test( t ) { var expected; var actual; - var delta; - var tol; var b1; var b2; var x; @@ -121,9 +117,7 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for b2 = isnan( expected[ i ] ); t.strictEqual( b1, b2, 'returns expected value' ); if ( !b1 || !b2 ) { - delta = abs( actual - expected[ i ] ); - tol = 80.0 * EPS * abs( expected[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 44, true, 'returns expected value within 44 ulp' ); } } t.end(); @@ -132,8 +126,6 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for tape( 'the function correctly evaluates the upper incomplete gamma function for small `x` and small `s`', opts, function test( t ) { var expected; var actual; - var delta; - var tol; var b1; var b2; var x; @@ -155,9 +147,7 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for b2 = isnan( expected[ i ] ); t.strictEqual( b1, b2, 'returns expected value' ); if ( !b1 || !b2 ) { - delta = abs( actual - expected[ i ] ); - tol = 20.0 * EPS * abs( expected[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 33, true, 'returns expected value within 33 ulp' ); } } t.end(); @@ -166,8 +156,6 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for tape( 'the function correctly evaluates the unregularized lower incomplete gamma function for small `x` and small `s`', opts, function test( t ) { var expected; var actual; - var delta; - var tol; var b1; var b2; var x; @@ -189,9 +177,7 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma b2 = isnan( expected[ i ] ); t.strictEqual( b1, b2, 'returns expected value' ); if ( !b1 || !b2 ) { - delta = abs( actual - expected[ i ] ); - tol = 10.0 * EPS * abs( expected[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 6, true, 'returns expected value within 6 ulp' ); } } t.end(); @@ -200,8 +186,6 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma tape( 'the function correctly evaluates the unregularized upper incomplete gamma function for small `x` and small `s`', opts, function test( t ) { var expected; var actual; - var delta; - var tol; var b1; var b2; var x; @@ -223,9 +207,7 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma b2 = isnan( expected[ i ] ); t.strictEqual( b1, b2, 'returns expected value' ); if ( !b1 || !b2 ) { - delta = abs( actual - expected[ i ] ); - tol = 10.0 * EPS * abs( expected[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 9, true, 'returns expected value within 9 ulp' ); } } t.end(); @@ -234,8 +216,6 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma tape( 'the function correctly evaluates the lower incomplete gamma function for medium `x` and medium `s`', opts, function test( t ) { var expected; var actual; - var delta; - var tol; var b1; var b2; var x; @@ -257,9 +237,7 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for b2 = isnan( expected[ i ] ); t.strictEqual( b1, b2, 'returns expected value' ); if ( !b1 || !b2 ) { - delta = abs( actual - expected[ i ] ); - tol = 65.0 * EPS * abs( expected[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 98, true, 'returns expected value within 98 ulp' ); } } t.end(); @@ -268,8 +246,6 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for tape( 'the function correctly evaluates the upper incomplete gamma function for medium `x` and medium `s`', opts, function test( t ) { var expected; var actual; - var delta; - var tol; var b1; var b2; var x; @@ -291,9 +267,7 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for b2 = isnan( expected[ i ] ); t.strictEqual( b1, b2, 'returns expected value' ); if ( !b1 || !b2 ) { - delta = abs( actual - expected[ i ] ); - tol = 55.0 * EPS * abs( expected[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 84, true, 'returns expected value within 84 ulp' ); } } t.end(); @@ -302,8 +276,6 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for tape( 'the function correctly evaluates the unregularized lower incomplete gamma function for medium `x` and medium `s`', opts, function test( t ) { var expected; var actual; - var delta; - var tol; var b1; var b2; var x; @@ -325,9 +297,7 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma b2 = isnan( expected[ i ] ); t.strictEqual( b1, b2, 'returns expected value' ); if ( !b1 || !b2 ) { - delta = abs( actual - expected[ i ] ); - tol = 5.0 * EPS * abs( expected[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 6, true, 'returns expected value within 6 ulp' ); } } t.end(); @@ -336,8 +306,6 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma tape( 'the function correctly evaluates the unregularized upper incomplete gamma function for medium `x` and medium `s`', opts, function test( t ) { var expected; var actual; - var delta; - var tol; var b1; var b2; var x; @@ -359,9 +327,7 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma b2 = isnan( expected[ i ] ); t.strictEqual( b1, b2, 'returns expected value' ); if ( !b1 || !b2 ) { - delta = abs( actual - expected[ i ] ); - tol = 5.0 * EPS * abs( expected[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 9, true, 'returns expected value within 9 ulp' ); } } t.end(); @@ -400,8 +366,6 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for tape( 'the function correctly evaluates the upper incomplete gamma function for large `x` and small `s`', opts, function test( t ) { var expected; var actual; - var s1; - var s2; var b1; var b2; var x; @@ -423,10 +387,7 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for b2 = isnan( expected[ i ] ); t.strictEqual( b1, b2, 'returns expected value' ); if ( !b1 || !b2 ) { - // We use bit string comparison for extremely small expected values, as the tolerance becomes smaller than the minimum representable double-precision floating-point value. Out of the 500 values tested, only 16 faced this issue. If those values are excluded, the test passes with a tolerance of `30.0 * EPS`. - s1 = toBinaryString( actual ); - s2 = toBinaryString( expected[ i ] ); - t.strictEqual( s1.substring( 0, s1.length-12 ), s2.substring( 0, s2.length-12 ), 'returns expected value' ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 61, true, 'returns expected value within 61 ulp' ); } } t.end(); @@ -435,8 +396,6 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for tape( 'the function correctly evaluates the unregularized lower incomplete gamma function for large `x` and small `s`', opts, function test( t ) { var expected; var actual; - var delta; - var tol; var b1; var b2; var x; @@ -458,9 +417,7 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma b2 = isnan( expected[ i ] ); t.strictEqual( b1, b2, 'returns expected value' ); if ( !b1 || !b2 ) { - delta = abs( actual - expected[ i ] ); - tol = 5.0 * EPS * abs( expected[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 6, true, 'returns expected value within 6 ulp' ); } } t.end(); @@ -469,8 +426,6 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma tape( 'the function correctly evaluates the unregularized upper incomplete gamma function for large `x` and small `s`', opts, function test( t ) { var expected; var actual; - var delta; - var tol; var b1; var b2; var x; @@ -492,9 +447,7 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma b2 = isnan( expected[ i ] ); t.strictEqual( b1, b2, 'returns expected value' ); if ( !b1 || !b2 ) { - delta = abs( actual - expected[ i ] ); - tol = 40.0 * EPS * abs( expected[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 56, true, 'returns expected value within 56 ulp' ); } } t.end(); @@ -503,8 +456,6 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma tape( 'the function correctly evaluates the lower incomplete gamma function for large `x` and medium `s`', opts, function test( t ) { var expected; var actual; - var delta; - var tol; var b1; var b2; var x; @@ -526,10 +477,7 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for b2 = isnan( expected[ i ] ); t.strictEqual( b1, b2, 'returns expected value' ); if ( !b1 || !b2 ) { - delta = abs( actual - expected[ i ] ); - tol = EPS * abs( expected[ i ] ); - // Only 1 value in the test suite is not exactly equal to the expected value. If we exclude that value, we can use exact equality for the rest of the values. - t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 1, true, 'returns expected value within 4 ulp' ); } } t.end(); @@ -538,8 +486,6 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for tape( 'the function correctly evaluates the upper incomplete gamma function for large `x` and medium `s`', opts, function test( t ) { var expected; var actual; - var s1; - var s2; var b1; var b2; var x; @@ -561,10 +507,7 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for b2 = isnan( expected[ i ] ); t.strictEqual( b1, b2, 'returns expected value' ); if ( !b1 || !b2 ) { - // We use bit string comparison for extremely small expected values, as the tolerance becomes smaller than the minimum representable double-precision floating-point value. Out of the 500 values tested, only 10 faced this issue. If those values are excluded, the test passes with a tolerance of `100.0 * EPS`. - s1 = toBinaryString( actual ); - s2 = toBinaryString( expected[ i ] ); - t.strictEqual( s1.substring( 0, s1.length-16 ), s2.substring( 0, s2.length-16 ), 'returns expected value' ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 130, true, 'returns expected value within 130 ulp' ); } } t.end(); @@ -573,8 +516,6 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for tape( 'the function correctly evaluates the unregularized lower incomplete gamma function for large `x` and medium `s`', opts, function test( t ) { var expected; var actual; - var delta; - var tol; var b1; var b2; var x; @@ -596,9 +537,7 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma b2 = isnan( expected[ i ] ); t.strictEqual( b1, b2, 'returns expected value' ); if ( !b1 || !b2 ) { - delta = abs( actual - expected[ i ] ); - tol = 5.0 * EPS * abs( expected[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 5, true, 'returns expected value within 5 ulp' ); } } t.end(); @@ -607,8 +546,6 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma tape( 'the function correctly evaluates the unregularized upper incomplete gamma function for large `x` and medium `s`', opts, function test( t ) { var expected; var actual; - var delta; - var tol; var b1; var b2; var x; @@ -630,9 +567,7 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma b2 = isnan( expected[ i ] ); t.strictEqual( b1, b2, 'returns expected value' ); if ( !b1 || !b2 ) { - delta = abs( actual - expected[ i ] ); - tol = 90.0 * EPS * abs( expected[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + ' s: ' + s[ i ] + '. Actual: ' + actual + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 160, true, 'returns expected value within 160 ulp' ); } } t.end(); From d27d06c4f2522215d309c81e8f5727284d8da337 Mon Sep 17 00:00:00 2001 From: Karan Anand Date: Fri, 20 Jun 2025 21:52:35 -0700 Subject: [PATCH 10/14] test: fix ulp difference --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: na - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: passed - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: na - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../@stdlib/math/base/special/gammainc/test/test.js | 2 -- .../@stdlib/math/base/special/gammainc/test/test.native.js | 4 ++-- 2 files changed, 2 insertions(+), 4 deletions(-) diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.js b/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.js index 59c76b1bd73b..59c429aac45a 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.js +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.js @@ -108,7 +108,6 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for b2 = isnan( expected[ i ] ); t.strictEqual( b1, b2, 'returns expected value' ); if ( !b1 || !b2 ) { - // TODO: The difference is larger here as compared to the native tests. This is likely because the C implementation follows the latest Boost implementation, unlike the JS implementation. t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 45, true, 'returns expected value within 45 ulp' ); } } @@ -499,7 +498,6 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for b2 = isnan( expected[ i ] ); t.strictEqual( b1, b2, 'returns expected value' ); if ( !b1 || !b2 ) { - // TODO: The difference is larger here as compared to the native tests. This is likely because the C implementation follows the latest Boost implementation, unlike the JS implementation. t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 134, true, 'returns expected value within 131 ulp' ); } } diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js index 452f72178ee3..9204ff4f94cc 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js @@ -117,7 +117,7 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for b2 = isnan( expected[ i ] ); t.strictEqual( b1, b2, 'returns expected value' ); if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 44, true, 'returns expected value within 44 ulp' ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 45, true, 'returns expected value within 45 ulp' ); } } t.end(); @@ -507,7 +507,7 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for b2 = isnan( expected[ i ] ); t.strictEqual( b1, b2, 'returns expected value' ); if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 130, true, 'returns expected value within 130 ulp' ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 134, true, 'returns expected value within 131 ulp' ); } } t.end(); From c9f071c8710f75b477e37e1d358d97bf92c98b4c Mon Sep 17 00:00:00 2001 From: Karan Anand Date: Fri, 20 Jun 2025 22:27:04 -0700 Subject: [PATCH 11/14] test: use appropriate filenames for clarity --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: na - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: passed - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: na - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../gammainc/test/fixtures/cpp/huge.json | 2 +- .../gammainc/test/fixtures/cpp/large.json | 2 +- .../test/fixtures/cpp/large_x_medium_s.json | 1 + .../test/fixtures/cpp/large_x_small_s.json | 1 + .../gammainc/test/fixtures/cpp/medium.json | 2 +- .../gammainc/test/fixtures/cpp/output.json | 1 - .../gammainc/test/fixtures/cpp/runner.cpp | 4 +- .../gammainc/test/fixtures/cpp/small.json | 2 +- .../math/base/special/gammainc/test/test.js | 52 +++++++++---------- .../base/special/gammainc/test/test.native.js | 52 +++++++++---------- 10 files changed, 60 insertions(+), 59 deletions(-) create mode 100644 lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/large_x_medium_s.json create mode 100644 lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/large_x_small_s.json delete mode 100644 lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/output.json diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/huge.json b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/huge.json index ceb786d7e597..2cf85093302e 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/huge.json +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/huge.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/large.json b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/large.json index dbd1b41230ea..1de0eadb306e 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/large.json +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/large.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/large_x_medium_s.json b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/large_x_medium_s.json new file mode 100644 index 000000000000..2cf85093302e --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/large_x_medium_s.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/large_x_small_s.json b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/large_x_small_s.json new file mode 100644 index 000000000000..1de0eadb306e --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/large_x_small_s.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/medium.json b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/medium.json index fba9fc49c315..93d20a45efe7 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/medium.json +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/medium.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/output.json b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/output.json deleted file mode 100644 index 44c971424c7c..000000000000 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/output.json +++ /dev/null @@ -1 +0,0 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/runner.cpp b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/runner.cpp index 7901ed6eb787..10a9dbe39a37 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/runner.cpp +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/runner.cpp @@ -354,12 +354,12 @@ int main( void ) { // Large x and small s: rand_array_f64( x, len, 100.0, 1000.0 ); rand_array_f64( s, len, 1.0, 50.0 ); - generate( x, s, len, "large.json" ); + generate( x, s, len, "large_x_small_s.json" ); // Large x and medium s: rand_array_f64( x, len, 100.0, 1000.0 ); rand_array_f64( s, len, 50.0, 100.0 ); - generate( x, s, len, "huge.json" ); + generate( x, s, len, "large_x_medium_s.json" ); // Free allocated memory: free( x ); diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/small.json b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/small.json index 6116cd5c2e62..9645e723e164 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/small.json +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/small.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.js b/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.js index 59c429aac45a..0d93d81b9d53 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.js +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.js @@ -32,8 +32,8 @@ var gammainc = require( './../lib' ); var small = require( './fixtures/cpp/small.json' ); var medium = require( './fixtures/cpp/medium.json' ); -var large = require( './fixtures/cpp/large.json' ); -var huge = require( './fixtures/cpp/huge.json' ); +var largeXSmallS = require( './fixtures/cpp/large_x_small_s.json' ); +var largeXMediumS = require( './fixtures/cpp/large_x_medium_s.json' ); // TESTS // @@ -333,9 +333,9 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for var s; var i; - expected = large.lower_regularized; - x = large.x; - s = large.s; + expected = largeXSmallS.lower_regularized; + x = largeXSmallS.x; + s = largeXSmallS.s; for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], true, false ); @@ -363,9 +363,9 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for var s; var i; - expected = large.upper_regularized; - x = large.x; - s = large.s; + expected = largeXSmallS.upper_regularized; + x = largeXSmallS.x; + s = largeXSmallS.s; for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], true, true ); @@ -393,9 +393,9 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma var s; var i; - expected = large.lower_unregularized; - x = large.x; - s = large.s; + expected = largeXSmallS.lower_unregularized; + x = largeXSmallS.x; + s = largeXSmallS.s; for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, false ); @@ -423,9 +423,9 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma var s; var i; - expected = large.upper_unregularized; - x = large.x; - s = large.s; + expected = largeXSmallS.upper_unregularized; + x = largeXSmallS.x; + s = largeXSmallS.s; for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, true ); @@ -453,9 +453,9 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for var s; var i; - expected = huge.lower_regularized; - x = huge.x; - s = huge.s; + expected = largeXMediumS.lower_regularized; + x = largeXMediumS.x; + s = largeXMediumS.s; for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], true, false ); @@ -483,9 +483,9 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for var s; var i; - expected = huge.upper_regularized; - x = huge.x; - s = huge.s; + expected = largeXMediumS.upper_regularized; + x = largeXMediumS.x; + s = largeXMediumS.s; for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], true, true ); @@ -513,9 +513,9 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma var s; var i; - expected = huge.lower_unregularized; - x = huge.x; - s = huge.s; + expected = largeXMediumS.lower_unregularized; + x = largeXMediumS.x; + s = largeXMediumS.s; for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, false ); @@ -543,9 +543,9 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma var s; var i; - expected = huge.upper_unregularized; - x = huge.x; - s = huge.s; + expected = largeXMediumS.upper_unregularized; + x = largeXMediumS.x; + s = largeXMediumS.s; for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, true ); diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js index 9204ff4f94cc..e584fba8067e 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js @@ -41,8 +41,8 @@ var opts = { var small = require( './fixtures/cpp/small.json' ); var medium = require( './fixtures/cpp/medium.json' ); -var large = require( './fixtures/cpp/large.json' ); -var huge = require( './fixtures/cpp/huge.json' ); +var largeXSmallS = require( './fixtures/cpp/large_x_small_s.json' ); +var largeXMediumS = require( './fixtures/cpp/large_x_medium_s.json' ); // TESTS // @@ -342,9 +342,9 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for var s; var i; - expected = large.lower_regularized; - x = large.x; - s = large.s; + expected = largeXSmallS.lower_regularized; + x = largeXSmallS.x; + s = largeXSmallS.s; for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], true, false ); @@ -372,9 +372,9 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for var s; var i; - expected = large.upper_regularized; - x = large.x; - s = large.s; + expected = largeXSmallS.upper_regularized; + x = largeXSmallS.x; + s = largeXSmallS.s; for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], true, true ); @@ -402,9 +402,9 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma var s; var i; - expected = large.lower_unregularized; - x = large.x; - s = large.s; + expected = largeXSmallS.lower_unregularized; + x = largeXSmallS.x; + s = largeXSmallS.s; for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, false ); @@ -432,9 +432,9 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma var s; var i; - expected = large.upper_unregularized; - x = large.x; - s = large.s; + expected = largeXSmallS.upper_unregularized; + x = largeXSmallS.x; + s = largeXSmallS.s; for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, true ); @@ -462,9 +462,9 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for var s; var i; - expected = huge.lower_regularized; - x = huge.x; - s = huge.s; + expected = largeXMediumS.lower_regularized; + x = largeXMediumS.x; + s = largeXMediumS.s; for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], true, false ); @@ -492,9 +492,9 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for var s; var i; - expected = huge.upper_regularized; - x = huge.x; - s = huge.s; + expected = largeXMediumS.upper_regularized; + x = largeXMediumS.x; + s = largeXMediumS.s; for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], true, true ); @@ -522,9 +522,9 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma var s; var i; - expected = huge.lower_unregularized; - x = huge.x; - s = huge.s; + expected = largeXMediumS.lower_unregularized; + x = largeXMediumS.x; + s = largeXMediumS.s; for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, false ); @@ -552,9 +552,9 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma var s; var i; - expected = huge.upper_unregularized; - x = huge.x; - s = huge.s; + expected = largeXMediumS.upper_unregularized; + x = largeXMediumS.x; + s = largeXMediumS.s; for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, true ); From effeccacf7b5d53103ed3443e7dd3786482b4257 Mon Sep 17 00:00:00 2001 From: Karan Anand Date: Fri, 20 Jun 2025 23:51:06 -0700 Subject: [PATCH 12/14] test: add more tests --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: na - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: passed - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: na - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../test/fixtures/cpp/large_x_large_s.json | 1 + .../gammainc/test/fixtures/cpp/runner.cpp | 7 + .../math/base/special/gammainc/test/test.js | 226 +------------ .../base/special/gammainc/test/test.native.js | 313 ++++++------------ 4 files changed, 130 insertions(+), 417 deletions(-) create mode 100644 lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/large_x_large_s.json diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/large_x_large_s.json b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/large_x_large_s.json new file mode 100644 index 000000000000..463828e23190 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/large_x_large_s.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/runner.cpp b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/runner.cpp index 10a9dbe39a37..a05db97eede2 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/runner.cpp +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/runner.cpp @@ -361,6 +361,13 @@ int main( void ) { rand_array_f64( s, len, 50.0, 100.0 ); generate( x, s, len, "large_x_medium_s.json" ); + // Large x and large s: + + // NOTE: The following fixture generation is commented out as its generation was handled manually to avoid the overflowing of the gamma function for large values of `x` and `s`. If you wish to generate this fixture, you can uncomment the following lines and need to ensure proper exception handling in the `generate` function to handle potential overflow errors. + // rand_array_f64( x, len, 100.0, 1000.0 ); + // rand_array_f64( s, len, 100.0, 1000.0 ); + // generate( x, s, len, "large_x_large_s.json" ); + // Free allocated memory: free( x ); free( s ); diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.js b/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.js index 0d93d81b9d53..b7fce2ab6a6c 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.js +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.js @@ -21,8 +21,6 @@ // MODULES // var tape = require( 'tape' ); -var isfinite = require( '@stdlib/math/base/assert/is-finite' ); -var isnan = require( '@stdlib/math/base/assert/is-nan' ); var isSameValue = require( '@stdlib/assert/is-same-value' ); var ulpdiff = require( '@stdlib/number/float64/base/ulp-difference' ); var gammainc = require( './../lib' ); @@ -87,8 +85,6 @@ tape( 'the function returns 0 for the lower incomplete gamma function when the f tape( 'the function correctly evaluates the lower incomplete gamma function for small `x` and small `s`', function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -99,17 +95,7 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], true, false ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 45, true, 'returns expected value within 45 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 45, true, 'returns expected value within 45 ulp' ); } t.end(); }); @@ -117,8 +103,6 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for tape( 'the function correctly evaluates the upper incomplete gamma function for small `x` and small `s`', function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -129,17 +113,7 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], true, true ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 33, true, 'returns expected value within 33 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 33, true, 'returns expected value within 33 ulp' ); } t.end(); }); @@ -147,8 +121,6 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for tape( 'the function correctly evaluates the unregularized lower incomplete gamma function for small `x` and small `s`', function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -159,17 +131,7 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, false ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 6, true, 'returns expected value within 6 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 6, true, 'returns expected value within 6 ulp' ); } t.end(); }); @@ -177,8 +139,6 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma tape( 'the function correctly evaluates the unregularized upper incomplete gamma function for small `x` and small `s`', function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -189,17 +149,7 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, true ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 9, true, 'returns expected value within 9 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 9, true, 'returns expected value within 9 ulp' ); } t.end(); }); @@ -207,8 +157,6 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma tape( 'the function correctly evaluates the lower incomplete gamma function for medium `x` and medium `s`', function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -219,17 +167,7 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], true, false ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 98, true, 'returns expected value within 98 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 98, true, 'returns expected value within 98 ulp' ); } t.end(); }); @@ -237,8 +175,6 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for tape( 'the function correctly evaluates the upper incomplete gamma function for medium `x` and medium `s`', function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -249,17 +185,7 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], true, true ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 84, true, 'returns expected value within 84 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 84, true, 'returns expected value within 84 ulp' ); } t.end(); }); @@ -267,8 +193,6 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for tape( 'the function correctly evaluates the unregularized lower incomplete gamma function for medium `x` and medium `s`', function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -279,17 +203,7 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, false ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 6, true, 'returns expected value within 6 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 6, true, 'returns expected value within 6 ulp' ); } t.end(); }); @@ -297,8 +211,6 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma tape( 'the function correctly evaluates the unregularized upper incomplete gamma function for medium `x` and medium `s`', function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -309,17 +221,7 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, true ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 9, true, 'returns expected value within 9 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 9, true, 'returns expected value within 9 ulp' ); } t.end(); }); @@ -327,8 +229,6 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma tape( 'the function correctly evaluates the lower incomplete gamma function for large `x` and small `s`', function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -339,17 +239,7 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], true, false ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( actual, expected[ i ], 'returns expected value' ); - } + t.strictEqual( actual, expected[ i ], 'returns expected value' ); } t.end(); }); @@ -357,8 +247,6 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for tape( 'the function correctly evaluates the upper incomplete gamma function for large `x` and small `s`', function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -369,17 +257,7 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], true, true ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 61, true, 'returns expected value within 61 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 61, true, 'returns expected value within 61 ulp' ); } t.end(); }); @@ -387,8 +265,6 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for tape( 'the function correctly evaluates the unregularized lower incomplete gamma function for large `x` and small `s`', function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -399,17 +275,7 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, false ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 6, true, 'returns expected value within 6 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 6, true, 'returns expected value within 6 ulp' ); } t.end(); }); @@ -417,8 +283,6 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma tape( 'the function correctly evaluates the unregularized upper incomplete gamma function for large `x` and small `s`', function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -429,17 +293,7 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, true ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 56, true, 'returns expected value within 56 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 56, true, 'returns expected value within 56 ulp' ); } t.end(); }); @@ -447,8 +301,6 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma tape( 'the function correctly evaluates the lower incomplete gamma function for large `x` and medium `s`', function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -459,17 +311,7 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], true, false ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 1, true, 'returns expected value within 4 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 1, true, 'returns expected value within 1 ulp' ); } t.end(); }); @@ -477,8 +319,6 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for tape( 'the function correctly evaluates the upper incomplete gamma function for large `x` and medium `s`', function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -489,17 +329,7 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], true, true ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 134, true, 'returns expected value within 131 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 134, true, 'returns expected value within 134 ulp' ); } t.end(); }); @@ -507,8 +337,6 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for tape( 'the function correctly evaluates the unregularized lower incomplete gamma function for large `x` and medium `s`', function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -519,17 +347,7 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, false ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 5, true, 'returns expected value within 5 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 5, true, 'returns expected value within 5 ulp' ); } t.end(); }); @@ -537,8 +355,6 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma tape( 'the function correctly evaluates the unregularized upper incomplete gamma function for large `x` and medium `s`', function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -549,17 +365,7 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, true ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 160, true, 'returns expected value within 160 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 160, true, 'returns expected value within 160 ulp' ); } t.end(); }); diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js index e584fba8067e..31350da33936 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js @@ -22,10 +22,9 @@ var resolve = require( 'path' ).resolve; var tape = require( 'tape' ); -var isfinite = require( '@stdlib/math/base/assert/is-finite' ); -var isnan = require( '@stdlib/math/base/assert/is-nan' ); var isSameValue = require( '@stdlib/assert/is-same-value' ); var ulpdiff = require( '@stdlib/number/float64/base/ulp-difference' ); +var PINF = require( '@stdlib/constants/float64/pinf' ); var tryRequire = require( '@stdlib/utils/try-require' ); @@ -44,6 +43,9 @@ var medium = require( './fixtures/cpp/medium.json' ); var largeXSmallS = require( './fixtures/cpp/large_x_small_s.json' ); var largeXMediumS = require( './fixtures/cpp/large_x_medium_s.json' ); +// TODO: Add this to `test.js` once the JS implementation matches the latest Boost C++ implementation. +var largeXLargeS = require( './fixtures/cpp/large_x_large_s.json' ); + // TESTS // @@ -96,8 +98,6 @@ tape( 'the function returns 0 for the lower incomplete gamma function when the f tape( 'the function correctly evaluates the lower incomplete gamma function for small `x` and small `s`', opts, function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -108,17 +108,7 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], true, false ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 45, true, 'returns expected value within 45 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 45, true, 'returns expected value within 45 ulp' ); } t.end(); }); @@ -126,8 +116,6 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for tape( 'the function correctly evaluates the upper incomplete gamma function for small `x` and small `s`', opts, function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -138,17 +126,7 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], true, true ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 33, true, 'returns expected value within 33 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 33, true, 'returns expected value within 33 ulp' ); } t.end(); }); @@ -156,8 +134,6 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for tape( 'the function correctly evaluates the unregularized lower incomplete gamma function for small `x` and small `s`', opts, function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -168,17 +144,7 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, false ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 6, true, 'returns expected value within 6 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 6, true, 'returns expected value within 6 ulp' ); } t.end(); }); @@ -186,8 +152,6 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma tape( 'the function correctly evaluates the unregularized upper incomplete gamma function for small `x` and small `s`', opts, function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -198,17 +162,7 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, true ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 9, true, 'returns expected value within 9 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 9, true, 'returns expected value within 9 ulp' ); } t.end(); }); @@ -216,8 +170,6 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma tape( 'the function correctly evaluates the lower incomplete gamma function for medium `x` and medium `s`', opts, function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -228,17 +180,7 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], true, false ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 98, true, 'returns expected value within 98 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 98, true, 'returns expected value within 98 ulp' ); } t.end(); }); @@ -246,8 +188,6 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for tape( 'the function correctly evaluates the upper incomplete gamma function for medium `x` and medium `s`', opts, function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -258,17 +198,7 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], true, true ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 84, true, 'returns expected value within 84 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 84, true, 'returns expected value within 84 ulp' ); } t.end(); }); @@ -276,8 +206,6 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for tape( 'the function correctly evaluates the unregularized lower incomplete gamma function for medium `x` and medium `s`', opts, function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -288,17 +216,7 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, false ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 6, true, 'returns expected value within 6 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 6, true, 'returns expected value within 6 ulp' ); } t.end(); }); @@ -306,8 +224,6 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma tape( 'the function correctly evaluates the unregularized upper incomplete gamma function for medium `x` and medium `s`', opts, function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -318,17 +234,7 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, true ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 9, true, 'returns expected value within 9 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 9, true, 'returns expected value within 9 ulp' ); } t.end(); }); @@ -336,8 +242,6 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma tape( 'the function correctly evaluates the lower incomplete gamma function for large `x` and small `s`', opts, function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -348,17 +252,7 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], true, false ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( actual, expected[ i ], 'returns expected value' ); - } + t.strictEqual( actual, expected[ i ], 'returns expected value' ); } t.end(); }); @@ -366,8 +260,6 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for tape( 'the function correctly evaluates the upper incomplete gamma function for large `x` and small `s`', opts, function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -378,17 +270,7 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], true, true ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 61, true, 'returns expected value within 61 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 61, true, 'returns expected value within 61 ulp' ); } t.end(); }); @@ -396,8 +278,6 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for tape( 'the function correctly evaluates the unregularized lower incomplete gamma function for large `x` and small `s`', opts, function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -408,17 +288,7 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, false ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 6, true, 'returns expected value within 6 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 6, true, 'returns expected value within 6 ulp' ); } t.end(); }); @@ -426,8 +296,6 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma tape( 'the function correctly evaluates the unregularized upper incomplete gamma function for large `x` and small `s`', opts, function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -438,17 +306,7 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, true ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 56, true, 'returns expected value within 56 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 56, true, 'returns expected value within 56 ulp' ); } t.end(); }); @@ -456,8 +314,6 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma tape( 'the function correctly evaluates the lower incomplete gamma function for large `x` and medium `s`', opts, function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -468,17 +324,7 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], true, false ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 1, true, 'returns expected value within 4 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 1, true, 'returns expected value within 1 ulp' ); } t.end(); }); @@ -486,8 +332,6 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for tape( 'the function correctly evaluates the upper incomplete gamma function for large `x` and medium `s`', opts, function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -498,17 +342,7 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], true, true ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 134, true, 'returns expected value within 131 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 134, true, 'returns expected value within 134 ulp' ); } t.end(); }); @@ -516,8 +350,6 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for tape( 'the function correctly evaluates the unregularized lower incomplete gamma function for large `x` and medium `s`', opts, function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -528,17 +360,7 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, false ); - - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 5, true, 'returns expected value within 5 ulp' ); - } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 5, true, 'returns expected value within 5 ulp' ); } t.end(); }); @@ -546,8 +368,6 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma tape( 'the function correctly evaluates the unregularized upper incomplete gamma function for large `x` and medium `s`', opts, function test( t ) { var expected; var actual; - var b1; - var b2; var x; var s; var i; @@ -558,17 +378,96 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma for ( i = 0; i < x.length; i++ ) { actual = gammainc( x[ i ], s[ i ], false, true ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 160, true, 'returns expected value within 160 ulp' ); + } + t.end(); +}); + +tape( 'the function correctly evaluates the lower incomplete gamma function for large `x` and large `s`', opts, function test( t ) { + var expected; + var actual; + var x; + var s; + var i; + + expected = largeXLargeS.lower_regularized; + x = largeXLargeS.x; + s = largeXLargeS.s; + + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], true, false ); + + if ( expected[ i ] === 'PINF' ) { + t.strictEqual( isSameValue( actual, PINF ), true, 'returns expected value' ); + continue; + } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 1370, true, 'returns expected value within 1370 ulp' ); + } + t.end(); +}); + +tape( 'the function correctly evaluates the upper incomplete gamma function for large `x` and large `s`', opts, function test( t ) { + var expected; + var actual; + var x; + var s; + var i; + + expected = largeXLargeS.upper_regularized; + x = largeXLargeS.x; + s = largeXLargeS.s; + + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], true, true ); + if ( expected[ i ] === 'PINF' ) { + t.strictEqual( isSameValue( actual, PINF ), true, 'returns expected value' ); + continue; + } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 658, true, 'returns expected value within 658 ulp' ); + } + t.end(); +}); - b1 = isfinite( actual ); - b2 = isfinite( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); +tape( 'the function correctly evaluates the unregularized lower incomplete gamma function for large `x` and large `s`', opts, function test( t ) { + var expected; + var actual; + var x; + var s; + var i; + + expected = largeXLargeS.lower_unregularized; + x = largeXLargeS.x; + s = largeXLargeS.s; - b1 = isnan( actual ); - b2 = isnan( expected[ i ] ); - t.strictEqual( b1, b2, 'returns expected value' ); - if ( !b1 || !b2 ) { - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 160, true, 'returns expected value within 160 ulp' ); + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], false, false ); + if ( expected[ i ] === 'PINF' ) { + t.strictEqual( isSameValue( actual, PINF ), true, 'returns expected value' ); + continue; + } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 534, true, 'returns expected value within 534 ulp' ); + } + t.end(); +}); + +tape( 'the function correctly evaluates the unregularized upper incomplete gamma function for large `x` and large `s`', opts, function test( t ) { + var expected; + var actual; + var x; + var s; + var i; + + expected = largeXLargeS.upper_unregularized; + x = largeXLargeS.x; + s = largeXLargeS.s; + + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], false, true ); + if ( expected[ i ] === 'PINF' ) { + t.strictEqual( isSameValue( actual, PINF ), true, 'returns expected value' ); + continue; } + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 969, true, 'returns expected value within 969 ulp' ); } t.end(); }); From 24a88abe53c98db7c2821c891b52390d6876cffa Mon Sep 17 00:00:00 2001 From: Karan Anand Date: Sat, 21 Jun 2025 00:07:05 -0700 Subject: [PATCH 13/14] test: add comment explaining large differences --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: na - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: passed - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: na - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../@stdlib/math/base/special/gammainc/test/test.native.js | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js index 31350da33936..b4ad79448f0c 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js @@ -401,6 +401,7 @@ tape( 'the function correctly evaluates the lower incomplete gamma function for t.strictEqual( isSameValue( actual, PINF ), true, 'returns expected value' ); continue; } + // NOTE: The difference is high because some of the expected values are very small. t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 1370, true, 'returns expected value within 1370 ulp' ); } t.end(); @@ -423,6 +424,7 @@ tape( 'the function correctly evaluates the upper incomplete gamma function for t.strictEqual( isSameValue( actual, PINF ), true, 'returns expected value' ); continue; } + // NOTE: The difference is high because some of the expected values are very large. t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 658, true, 'returns expected value within 658 ulp' ); } t.end(); @@ -445,6 +447,7 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma t.strictEqual( isSameValue( actual, PINF ), true, 'returns expected value' ); continue; } + // NOTE: The difference is high because some of the expected values are very large. t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 534, true, 'returns expected value within 534 ulp' ); } t.end(); @@ -467,6 +470,7 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma t.strictEqual( isSameValue( actual, PINF ), true, 'returns expected value' ); continue; } + // NOTE: The difference is high because some of the expected values are very large. t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 969, true, 'returns expected value within 969 ulp' ); } t.end(); From dbb1de655f6b749fd3b9fb64e3f2217cf810fb5f Mon Sep 17 00:00:00 2001 From: Karan Anand Date: Fri, 27 Jun 2025 14:39:09 -0700 Subject: [PATCH 14/14] test: increase the tolerance threshold to account for compiler optimisations --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: na - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: passed - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: na - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../math/base/special/gammainc/test/test.native.js | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js index b4ad79448f0c..f9af56aede7e 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js @@ -447,8 +447,8 @@ tape( 'the function correctly evaluates the unregularized lower incomplete gamma t.strictEqual( isSameValue( actual, PINF ), true, 'returns expected value' ); continue; } - // NOTE: The difference is high because some of the expected values are very large. - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 534, true, 'returns expected value within 534 ulp' ); + // NOTE: The difference is high because some of the expected values are very large and the compiler optimizations have been disabled. + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 947, true, 'returns expected value within 947 ulp' ); } t.end(); }); @@ -470,8 +470,8 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma t.strictEqual( isSameValue( actual, PINF ), true, 'returns expected value' ); continue; } - // NOTE: The difference is high because some of the expected values are very large. - t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 969, true, 'returns expected value within 969 ulp' ); + // NOTE: The difference is high because some of the expected values are very large and the compiler optimizations have been disabled. + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 1544, true, 'returns expected value within 1544 ulp' ); } t.end(); });