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 42fa8cba2e7d..e743844dd825 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/README.md +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/README.md @@ -174,6 +174,98 @@ for ( i = 0; i < 100; i++ ) { + + +* * * + +
+ +## C APIs + + + +
+ +
+ + + + + +
+ +### Usage + +```c +#include "stdlib/math/base/special/gammainc.h" +``` + +#### stdlib_base_gammainc( x, s, regularized, upper ) + +Computes the regularized lower [incomplete gamma function][incomplete-gamma-function] for inputs `x` and `s`. . + +```c +double out = stdlib_base_gammainc( 1.0, 2.0, true, true ); +// returns ~0.7358 +``` + +The function accepts the following arguments: + +- **x**: `[in] double` input value. +- **s**: `[in] double` input value. +- **regularized**: `[in] bool` indicating if the function should evaluate the regularized or non-regularized incomplete gamma functions. +- **upper**: `[in] bool` indicating if the function should return the upper tail of the incomplete gamma function + +```c +double stdlib_base_gammainc( double x, double a, bool regularized, bool upper ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +### Examples + +```c +#include "stdlib/math/base/special/gammainc.h" +#include +#include + +int main( void ) { + const double x[] = { 6.0, 1.0, 7.0, 7.0, 0.0/0.0, 6.0 }; + const double a[] = { 2.0, 2.0, 5.0, 5.0, 2.0, 0.0/0.0 }; + const bool regularized[] = { true, true, true, false, true, true }; + const bool upper[] = { false, true, false, false, false, false }; + + double y; + int i; + for ( i = 0; i <6; i++ ) { + y = stdlib_base_gammainc( x[ i ], a[ i ], regularized[ i ], upper[ i ] ); + printf( "gammainc( %lf, %lf, %s, %s ) = %lf\n", x[ i ], a[ i ], regularized[ i ] ? "true" : "false", upper[ i ] ? "true" : "false", y ); + } +} +``` + +
+ + + +
+ + +
diff --git a/lib/node_modules/@stdlib/math/base/special/gammainc/benchmark/benchmark.js b/lib/node_modules/@stdlib/math/base/special/gammainc/benchmark/benchmark.js index 84a867ba14f0..aec9053055da 100644 --- a/lib/node_modules/@stdlib/math/base/special/gammainc/benchmark/benchmark.js +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/benchmark/benchmark.js @@ -21,13 +21,20 @@ // MODULES // var bench = require( '@stdlib/bench' ); -var randu = require( '@stdlib/random/base/randu' ); +var uniform = require( '@stdlib/random/array/uniform' ); var isnan = require( '@stdlib/math/base/assert/is-nan' ); var EPS = require( '@stdlib/constants/float64/eps' ); var pkg = require( './../package.json' ).name; var gammainc = require( './../lib' ); +// VARIABLES // + +var options = { + 'dtype': 'float64' +}; + + // MAIN // bench( pkg, function benchmark( b ) { @@ -36,11 +43,12 @@ bench( pkg, function benchmark( b ) { var z; var i; + x = uniform( b.iterations, 10, 1000, options ); + y = uniform( b.iterations, EPS, 1000, options ); + b.tic(); for ( i = 0; i < b.iterations; i++ ) { - x = ( randu()*1000.0 ) - 0.0; - y = ( randu()*1000.0 ) + EPS; - z = gammainc( x, y ); + z = gammainc( x[ i ], y[ i ] ); if ( isnan( z ) ) { b.fail( 'should not return NaN' ); } @@ -59,11 +67,12 @@ bench( pkg+':regularized=true', function benchmark( b ) { var z; var i; + x = uniform( b.iterations, 0, 1000, options ); + y = uniform( b.iterations, EPS, 1000, options ); + b.tic(); for ( i = 0; i < b.iterations; i++ ) { - x = ( randu()*1000.0 ) - 0.0; - y = ( randu()*1000.0 ) + EPS; - z = gammainc( x, y, true ); + z = gammainc( x[ i ], y[ i ], true ); if ( isnan( z ) ) { b.fail( 'should not return NaN' ); } @@ -82,11 +91,12 @@ bench( pkg+':regularized=false', function benchmark( b ) { var z; var i; + x = uniform( b.iterations, 0, 1000, options ); + y = uniform( b.iterations, EPS, 1000, options ); + b.tic(); for ( i = 0; i < b.iterations; i++ ) { - x = ( randu()*1000.0 ) - 0.0; - y = ( randu()*1000.0 ) + EPS; - z = gammainc( x, y, false ); + z = gammainc( x[ i ], y[ i ], false ); if ( isnan( z ) ) { b.fail( 'should not return NaN' ); } @@ -105,11 +115,12 @@ bench( pkg+':regularized=true,upper=true', function benchmark( b ) { var z; var i; + x = uniform( b.iterations, 0, 1000, options ); + y = uniform( b.iterations, EPS, 1000, options ); + b.tic(); for ( i = 0; i < b.iterations; i++ ) { - x = ( randu()*1000.0 ) - 0.0; - y = ( randu()*1000.0 ) + EPS; - z = gammainc( x, y, true, true ); + z = gammainc( x[ i ], y[ i ], true, true ); if ( isnan( z ) ) { b.fail( 'should not return NaN' ); } @@ -128,11 +139,12 @@ bench( pkg+':regularized=true,upper=false', function benchmark( b ) { var z; var i; + x = uniform( b.iterations, 0, 1000, options ); + y = uniform( b.iterations, EPS, 1000, options ); + b.tic(); for ( i = 0; i < b.iterations; i++ ) { - x = ( randu()*1000.0 ) - 0.0; - y = ( randu()*1000.0 ) + EPS; - z = gammainc( x, y, true, false ); + z = gammainc( x[ i ], y[ i ], true, false ); if ( isnan( z ) ) { b.fail( 'should not return NaN' ); } @@ -151,11 +163,12 @@ bench( pkg+':regularized=false,upper=true', function benchmark( b ) { var z; var i; + x = uniform( b.iterations, 0, 1000, options ); + y = uniform( b.iterations, EPS, 1000, options ); + b.tic(); for ( i = 0; i < b.iterations; i++ ) { - x = ( randu()*1000.0 ) - 0.0; - y = ( randu()*1000.0 ) + EPS; - z = gammainc( x, y, false, true ); + z = gammainc( x[ i ], y[ i ], false, true ); if ( isnan( z ) ) { b.fail( 'should not return NaN' ); } @@ -174,11 +187,12 @@ bench( pkg+':regularized=false,upper=false', function benchmark( b ) { var z; var i; + x = uniform( b.iterations, 0, 1000, options ); + y = uniform( b.iterations, EPS, 1000, options ); + b.tic(); for ( i = 0; i < b.iterations; i++ ) { - x = ( randu()*1000.0 ) - 0.0; - y = ( randu()*1000.0 ) + EPS; - z = gammainc( x, y, false, false ); + z = gammainc( x[ i ], y[ i ], false, false ); if ( isnan( z ) ) { b.fail( 'should not return NaN' ); } 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..01f8943ea965 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/benchmark/benchmark.native.js @@ -0,0 +1,211 @@ +/** +* @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 EPS = require( '@stdlib/constants/float64/eps' ); +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 ) +}; +var options = { + 'dtype': 'float64' +}; + + +// MAIN // + +bench( pkg+'::native', opts, function benchmark( b ) { + var x; + var y; + var z; + var i; + + x = uniform( b.iterations, 0, 1000, options ); + y = uniform( b.iterations, EPS, 1000, options ); + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + z = gammainc( x[ i ], y[ i ], 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=true', opts, function benchmark( b ) { + var x; + var y; + var z; + var i; + + x = uniform( b.iterations, 0, 1000, options ); + y = uniform( b.iterations, EPS, 1000, options ); + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + z = gammainc( x[ i ], y[ i ], 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', opts, function benchmark( b ) { + var x; + var y; + var z; + var i; + + x = uniform( b.iterations, 0, 1000, options ); + y = uniform( b.iterations, EPS, 1000, options ); + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + z = gammainc( x[ i ], y[ i ], 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(); +}); + +bench( pkg+'::native:regularized=true,upper=true', opts, function benchmark( b ) { + var x; + var y; + var z; + var i; + + x = uniform( b.iterations, 0, 1000, options ); + y = uniform( b.iterations, EPS, 1000, options ); + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + z = gammainc( x[ i ], y[ i ], 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( b.iterations, 0, 1000, options ); + y = uniform( b.iterations, EPS, 1000, options ); + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + z = gammainc( x[ i ], y[ i ], 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( b.iterations, 0, 1000, options ); + y = uniform( b.iterations, EPS, 1000, options ); + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + z = gammainc( x[ i ], y[ i ], 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( b.iterations, 0, 1000, options ); + y = uniform( b.iterations, EPS, 1000, options ); + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + z = gammainc( x[ i ], y[ i ], 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..af5a2688781a --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/benchmark/c/native/benchmark.c @@ -0,0 +1,253 @@ +/** +* @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 "stdlib/constants/float64/eps.h" +#include +#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 [0,1). +* +* @return random number +*/ +static double rand_double( void ) { + int r = rand(); + return (double)r / ( (double)RAND_MAX + 1.0 ); +} + +/** +* Runs a benchmark. +* +* @return elapsed time in seconds +*/ +static double benchmark1( void ) { + double elapsed; + double x[ 10 ]; + double a[ 10 ]; + double y; + double t; + int i; + + for( i = 0; i < 10 ; i++ ){ + x[ i ] = ( 1000.0 * rand_double() ); + a[ i ] = ( 1000.0 * rand_double() ) + STDLIB_CONSTANT_FLOAT64_EPS; + } + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + y = stdlib_base_gammainc( x[ i % 10 ], a[ i % 10 ], 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; +} +/** +* Runs a benchmark. +* +* @return elapsed time in seconds +*/ +static double benchmark2( void ) { + double elapsed; + double x[ 10 ]; + double a[ 10 ]; + double y; + double t; + int i; + + for( i = 0; i < 10 ; i++ ){ + x[ i ] = ( 1000.0 * rand_double() ); + a[ i ] = ( 1000.0 * rand_double() ) + STDLIB_CONSTANT_FLOAT64_EPS; + } + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + y = stdlib_base_gammainc( x[ i % 10 ], a[ i % 10 ], true, true ); + if ( y != y ) { + printf( "should not return NaN\n" ); + break; + } + } + elapsed = tic() - t; + if ( y != y ) { + printf( "should not return NaN\n" ); + } + return elapsed; +} +/** +* Runs a benchmark. +* +* @return elapsed time in seconds +*/ +static double benchmark3( void ) { + double elapsed; + double x[ 10 ]; + double a[ 10 ]; + double y; + double t; + int i; + + for( i = 0; i < 10 ; i++ ){ + x[ i ] = ( 1000.0 * rand_double() ); + a[ i ] = ( 1000.0 * rand_double() ) + STDLIB_CONSTANT_FLOAT64_EPS; + } + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + y = stdlib_base_gammainc( x[ i % 10 ], a[ i % 10 ], false, 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; +} +/** +* Runs a benchmark. +* +* @return elapsed time in seconds +*/ +static double benchmark4( void ) { + double elapsed; + double x[ 10 ]; + double a[ 10 ]; + double y; + double t; + int i; + + for( i = 0; i < 10 ; i++ ){ + x[ i ] = ( 1000.0 * rand_double() ); + a[ i ] = ( 1000.0 * rand_double() ) + STDLIB_CONSTANT_FLOAT64_EPS; + } + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + y = stdlib_base_gammainc( x[ i % 10 ], a[ i % 10 ], false, true ); + 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:regularized=true,upper=false::%s\n", NAME ); + elapsed = benchmark1(); + print_results( elapsed ); + printf( "ok %d benchmark finished\n", i+1 ); + } + for ( i = 0; i < REPEATS; i++ ) { + printf( "# c::native:regularized=true,upper=true::%s\n", NAME ); + elapsed = benchmark2(); + print_results( elapsed ); + printf( "ok %d benchmark finished\n", i+1 ); + } + for ( i = 0; i < REPEATS; i++ ) { + printf( "# c::native:regularized=false,upper=false::%s\n", NAME ); + elapsed = benchmark3(); + print_results( elapsed ); + printf( "ok %d benchmark finished\n", i+1 ); + } + for ( i = 0; i < REPEATS; i++ ) { + printf( "# c::native:regularized=false,upper=true::%s\n", NAME ); + elapsed = benchmark4(); + 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..c2f4f0f8d774 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/examples/c/example.c @@ -0,0 +1,35 @@ +/** +* @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 + +int main( void ) { + const double x[] = { 6.0, 1.0, 7.0, 7.0, 0.0/0.0, 6.0 }; + const double a[] = { 2.0, 2.0, 5.0, 5.0, 2.0, 0.0/0.0 }; + const bool regularized[] = { true, true, true, false, true, true }; + const bool upper[] = { false, true, false, false, false, false }; + + double y; + int i; + for ( i = 0; i <6; i++ ) { + y = stdlib_base_gammainc( x[ i ], a[ i ], regularized[ i ], upper[ i ] ); + printf( "gammainc( %lf, %lf, %s, %s ) = %lf\n", x[ i ], a[ i ], regularized[ i ] ? "true" : "false", upper[ i ] ? "true" : "false", 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 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. +*/ +double API_SUFFIX(stdlib_base_gammainc)( double x, double a, bool regularized, 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..d3d629cd33e6 --- /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 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 >= MAX_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 {NonNegativeNumber} x - function parameter +* @param {PositiveNumber} a - function parameter +* @param {boolean} [regularized=true] - boolean indicating if the function should evaluate the regularized or non-regularized incomplete gamma functions +* @param {boolean} [upper=false] - boolean indicating if the function should return the upper tail of the incomplete gamma function +* @returns {number} function value +* +* @example +* var gammainc = require( '@stdlib/math/base/special/gammainc' ); +* +* var v = gammainc( 6.0, 2.0, true, false ); +* //returns ~0.9826 +* +* v = gammainc( 1.0, 2.0, true, true ); +* //returns ~0.7358 +* +* v = gammainc( 7.0, 5.0, true, false ); +* //returns ~0.8270 +* +* v = gammainc( 7.0, 5.0, false, false ); +* //returns ~19.8482 +* +* v = gammainc( NaN, 2.0, true, false ); +* //returns NaN +* +* v = gammainc( 6.0, 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..48648c866898 --- /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/argv", + "@stdlib/blas/base/shared", + "@stdlib/napi/argv-double", + "@stdlib/napi/argv-bool", + "@stdlib/napi/create-double", + "@stdlib/napi/export", + "@stdlib/math/base/special/gamma-lanczos-sum-expg-scaled", + "@stdlib/math/base/special/gammaln", + "@stdlib/math/base/special/gamma", + "@stdlib/math/base/special/floor", + "@stdlib/math/base/special/log1pmx", + "@stdlib/math/base/special/log1p", + "@stdlib/math/base/special/sqrt", + "@stdlib/math/base/special/erfc", + "@stdlib/math/base/special/abs", + "@stdlib/math/base/special/exp", + "@stdlib/math/base/special/pow", + "@stdlib/math/base/special/max", + "@stdlib/math/base/special/min", + "@stdlib/math/base/special/ln", + "@stdlib/constants/float32/smallest-normal", + "@stdlib/constants/float64/eps", + "@stdlib/constants/float64/sqrt-eps", + "@stdlib/constants/float64/max", + "@stdlib/constants/float64/two-pi", + "@stdlib/math/base/special/powm1", + "@stdlib/math/base/special/gamma1pm1", + "@stdlib/constants/float64/pinf", + "@stdlib/constants/float64/sqrt-two-pi", + "@stdlib/constants/float64/pi", + "@stdlib/constants/float64/max-ln", + "@stdlib/constants/float64/min-ln", + "@stdlib/constants/float64/gamma-lanczos-g", + "@stdlib/constants/float64/e" + ] + }, + { + "task": "benchmark", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/blas/base/shared", + "@stdlib/math/base/special/gamma-lanczos-sum-expg-scaled", + "@stdlib/math/base/special/gammaln", + "@stdlib/math/base/special/gamma", + "@stdlib/math/base/special/floor", + "@stdlib/math/base/special/log1pmx", + "@stdlib/math/base/special/log1p", + "@stdlib/math/base/special/sqrt", + "@stdlib/math/base/special/erfc", + "@stdlib/math/base/special/abs", + "@stdlib/math/base/special/exp", + "@stdlib/math/base/special/powm1", + "@stdlib/math/base/special/gamma1pm1", + "@stdlib/math/base/special/pow", + "@stdlib/math/base/special/max", + "@stdlib/math/base/special/min", + "@stdlib/math/base/special/ln", + "@stdlib/constants/float32/smallest-normal", + "@stdlib/constants/float64/eps", + "@stdlib/constants/float64/sqrt-eps", + "@stdlib/constants/float64/max", + "@stdlib/constants/float64/two-pi", + "@stdlib/constants/float64/pinf", + "@stdlib/constants/float64/sqrt-two-pi", + "@stdlib/constants/float64/pi", + "@stdlib/constants/float64/max-ln", + "@stdlib/constants/float64/min-ln", + "@stdlib/constants/float64/gamma-lanczos-g", + "@stdlib/constants/float64/e" + ] + }, + { + "task": "examples", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/blas/base/shared", + "@stdlib/math/base/special/gamma-lanczos-sum-expg-scaled", + "@stdlib/math/base/special/gammaln", + "@stdlib/math/base/special/gamma", + "@stdlib/math/base/special/floor", + "@stdlib/math/base/special/powm1", + "@stdlib/math/base/special/gamma1pm1", + "@stdlib/math/base/special/log1pmx", + "@stdlib/math/base/special/log1p", + "@stdlib/math/base/special/sqrt", + "@stdlib/math/base/special/erfc", + "@stdlib/math/base/special/abs", + "@stdlib/math/base/special/exp", + "@stdlib/math/base/special/pow", + "@stdlib/math/base/special/max", + "@stdlib/math/base/special/min", + "@stdlib/math/base/special/ln", + "@stdlib/constants/float32/smallest-normal", + "@stdlib/constants/float64/eps", + "@stdlib/constants/float64/sqrt-eps", + "@stdlib/constants/float64/max", + "@stdlib/constants/float64/two-pi", + "@stdlib/constants/float64/pinf", + "@stdlib/constants/float64/sqrt-two-pi", + "@stdlib/constants/float64/pi", + "@stdlib/constants/float64/max-ln", + "@stdlib/constants/float64/min-ln", + "@stdlib/constants/float64/gamma-lanczos-g", + "@stdlib/constants/float64/e" + ] + } + ] +} 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..3c48218c3c55 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 +14,15 @@ } ], "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/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..58e0b02f5134 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/src/addon.c @@ -0,0 +1,45 @@ +/** +* @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 "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 +#include + +/** +* 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 new file mode 100644 index 000000000000..8760468b2e0f --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/src/main.c @@ -0,0 +1,946 @@ +/** +* @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. +* +* +* ## Notice +* +* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_62_0/boost/math/special_functions/gamma.hpp}. The implementation has been modified for JavaScript. +* +* ```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/gamma_lanczos_sum_expg_scaled.h" +#include "stdlib/math/base/special/gammaln.h" +#include "stdlib/math/base/special/gamma.h" +#include "stdlib/math/base/special/powm1.h" +#include "stdlib/math/base/special/gamma1pm1.h" +#include "stdlib/math/base/special/floor.h" +#include "stdlib/math/base/special/log1pmx.h" +#include "stdlib/math/base/special/log1p.h" +#include "stdlib/math/base/special/sqrt.h" +#include "stdlib/math/base/special/erfc.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/max.h" +#include "stdlib/math/base/special/min.h" +#include "stdlib/math/base/special/ln.h" +#include "stdlib/constants/float32/smallest_normal.h" +#include "stdlib/constants/float64/eps.h" +#include "stdlib/constants/float64/sqrt_eps.h" +#include "stdlib/constants/float64/max.h" +#include "stdlib/constants/float64/two_pi.h" +#include "stdlib/constants/float64/pinf.h" +#include "stdlib/constants/float64/sqrt_two_pi.h" +#include "stdlib/constants/float64/pi.h" +#include "stdlib/constants/float64/max_ln.h" +#include "stdlib/constants/float64/min_ln.h" +#include "stdlib/constants/float64/gamma_lanczos_g.h" +#include "stdlib/constants/float64/e.h" +#include "stdlib/blas/base/shared.h" +#include + +static const int MAX_TERMS = 1000000; +static const int MAX_FACTORIAL = 170; // TODO: consider extracting as a constant + +/** +* 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 +* +* @private +* @param x - value at which to evaluate the polynomial +* @returns evaluated polynomial +*/ +static double polyval_c0( const double x ) { + if ( x == 0.0 ) { + return -0.3333333333333333; + } + 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))))))))))))))))))))))))))); // eslint-disable-line max-len +} + +/** +* 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 +* +* @private +* @param x - value at which to evaluate the polynomial +* @returns evaluated polynomial +*/ +static double polyval_c1( const double x ) { + if ( x == 0.0 ) { + return -0.001851851851851852; + } + 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))))))))))))))))))))))); // eslint-disable-line max-len +} + +/** +* 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 +* +* @private +* @param x - value at which to evaluate the polynomial +* @returns evaluated polynomial +*/ +static double polyval_c2( const double x ) { + if ( x == 0.0 ) { + return 0.004133597883597883; + } + 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))))))))))))))))))); // eslint-disable-line max-len +} + +/** +* 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 +* +* @private +* @param x - value at which to evaluate the polynomial +* @returns evaluated polynomial +*/ +static double polyval_c3( const double x ) { + if ( x == 0.0 ) { + return 0.0006494341563786008; + } + 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))))))))))))))); // eslint-disable-line max-len +} + +/** +* 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 +* +* @private +* @param x - value at which to evaluate the polynomial +* @returns evaluated polynomial +*/ +static double polyval_c4( const double x ) { + if ( x == 0.0 ) { + return -0.0008618882909167117; + } + return -0.0008618882909167117 + (x * (0.0007840392217200666 + (x * (-0.0002990724803031902 + (x * (-0.0000014638452578843418 + (x * (0.00006641498215465122 + (x * (-0.00003968365047179435 + (x * 0.000011375726970678419))))))))))); // eslint-disable-line max-len +} + +/** +* 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 +* +* @private +* @param x - value at which to evaluate the polynomial +* @returns evaluated polynomial +*/ +static double polyval_c5( const double x ) { + if ( x == 0.0 ) { + return -0.00033679855336635813; + } + 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))))))))))))))); // eslint-disable-line max-len +} + +/** +* 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 +* +* @private +* @param x - value at which to evaluate the polynomial +* @returns evaluated polynomial +*/ +static double polyval_c6( const double x ) { + if ( x == 0.0 ) { + return 0.0005313079364639922; + } + return 0.0005313079364639922 + (x * (-0.0005921664373536939 + (x * (0.0002708782096718045 + (x * (7.902353232660328e-7 + (x * (-0.00008153969367561969 + (x * (0.0000561168275310625 + (x * -0.000018329116582843375))))))))))); // eslint-disable-line max-len +} + +/** +* 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 +* +* @private +* @param x - value at which to evaluate the polynomial +* @returns evaluated polynomial +*/ +static double polyval_c7( const double x ) { + if ( x == 0.0 ) { + return 0.00034436760689237765; + } + return 0.00034436760689237765 + (x * (0.00005171790908260592 + (x * (-0.00033493161081142234 + (x * (0.0002812695154763237 + (x * -0.00010976582244684731))))))); // eslint-disable-line max-len +} + +/** +* 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 +* +* @private +* @param x - value at which to evaluate the polynomial +* @returns evaluated polynomial +*/ +static double polyval_c8( const double x ) { + if ( x == 0.0 ) { + return -0.0006526239185953094; + } + return -0.0006526239185953094 + (x * (0.0008394987206720873 + (x * -0.000438297098541721))); // eslint-disable-line max-len +} + +/** +* Computes `(z^a)*(e^-z) / stdlib_base_gamma(a)`. +* +* @private +* @param a - input value +* @param z - input value +* @returns function value +*/ +static double regularisedGammaPrefix( double a, double z ) { + double prefix; + double amza; + double agh; + double alz; + double amz; + double sq; + double d; + + agh = a + STDLIB_CONSTANT_FLOAT64_GAMMA_LANCZOS_G - 0.5; + d = ( (z - a) - STDLIB_CONSTANT_FLOAT64_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 ) { + // 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 * ( stdlib_base_log1p( d ) - d ) ) + ( z * ( 0.5-STDLIB_CONSTANT_FLOAT64_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); + amz = a - z; + if ( + stdlib_base_min(alz, amz) <= STDLIB_CONSTANT_FLOAT64_MIN_LN || + stdlib_base_max(alz, amz) >= STDLIB_CONSTANT_FLOAT64_MAX_LN + ) { + amza = amz / a; + if ( + stdlib_base_min(alz, amz)/2.0 > STDLIB_CONSTANT_FLOAT64_MIN_LN && + stdlib_base_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 ( + stdlib_base_min(alz, amz)/4.0 > STDLIB_CONSTANT_FLOAT64_MIN_LN && + stdlib_base_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 / STDLIB_CONSTANT_FLOAT64_E ) / stdlib_base_gamma_lanczos_sum_expg_scaled( a ); + return prefix; +} + +/** +* Computes the sum-series with initial value `z` +* +* @private +* @param a - input value +* @param z - input value +* @returns function value +*/ +static double sumseries1( double a, double x, double s ){ + double result; + double sum; + double apn; + double n; + int i; + + sum = s; + result = -x; + x = -x; + apn = a + 1.0; + n = 1; + + for( i = 0; i < MAX_TERMS; i++ ){ + sum += result / apn; + result *= x; + n += 1; + result /= n; + apn += 1.0; + } + + return sum; +} + +/** +* Compute the full upper fraction (Q) when `a` is very small. +* +* @private +* @param a - function parameter +* @param x - function parameter +* @param invert - boolean indicating if the upper tail of the incomplete gamma function should be evaluated +* @returns full upper fraction (Q) and pgam +*/ +static void tgammaSmallUpperPart( const double a, const double x, const bool invert, double *Out ) { + double initialValue; + double result; + double pgam; + double p; + + 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 * sumseries1( a, x, (initialValue - result) / p ); + if ( invert ) { + result = -result; + } + Out[ 0 ] = result; + Out[ 1 ] = pgam; + return; +} +/** +* Creates a function to evaluate a series expansion of the upper incomplete gamma fraction. +* +* @private +* @param z - function parameter +* @param a - function parameter +* @param k - function parameter +* @param Out - function parameter +*/ +static void upperIncompleteGammaFract( double* z, const double a, double* k, double* Out ) { + *z += 2.0; + *k += 1; + Out[0] = *k * (a - *k); + Out[1] = *z; + return; +} + +/** +* Evaluates a continued fraction expansion. +* +* ```text +* a1 +* --------------- +* b1 + a2 +* ---------- +* b2 + a3 +* ----- +* b3 + ... +* ``` +* +* @private +* @param a - function parameter +* @param z - function parameter +* @returns evaluated expansion +*/ +static double continuedFraction( double a, double z ){ + double factor = STDLIB_CONSTANT_FLOAT64_EPS; + double maxIter = MAX_TERMS; + double delta; + double a0; + double f; + double C; + double D; + double v[ 2 ]; + double zz = z - a + 1.0; + double aa = a; + double k = 0; + upperIncompleteGammaFract( &zz, aa, &k, v ); + f = v[ 1 ]; + a0 = v[ 0 ]; + if ( f == 0.0 ) { + f = STDLIB_CONSTANT_FLOAT32_SMALLEST_NORMAL; + } + C = f; + D = 0; + do { + upperIncompleteGammaFract( &zz, aa, &k, v ); + D = v[ 1 ] + ( v[ 0 ] * D ); + if ( D == 0.0 ) { + D = STDLIB_CONSTANT_FLOAT32_SMALLEST_NORMAL; + } + C = v[ 1 ] + ( v[ 0 ] / C ); + if ( C == 0.0 ) { + C = STDLIB_CONSTANT_FLOAT32_SMALLEST_NORMAL; + } + D = 1.0 / D; + delta = C * D; + f *= delta; + } while ( ( stdlib_base_abs( delta - 1.0 ) > factor ) && --maxIter ); // eslint-disable-line no-plusplus + + return a0 / f; +} + +/** +* Evaluate the lower incomplete gamma integral via a series expansion and divide by `gamma(z)` to normalize. +* +* @private +* @param a - function parameter +* @param z - function parameter +* @returns function value +*/ +static double upperGammaFraction( const double a, const double z ){ + return 1.0 / ( z - a + 1.0 + continuedFraction( a, z )); +} + +/** +* Calculates normalized Q when a is an integer. +* +* @private +* @param a - function parameter +* @param x - function parameter +* @returns upper gamma fraction +*/ +static double finiteGammaQ( double a, double x ) { + double term; + double sum; + double e; + double n; + + 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 a - function parameter +* @param x - function parameter +* @returns upper gamma fraction +*/ +static double finiteHalfGammaQ( double a, double x ) { + double half; + double term; + double sum; + double e; + double n; + + e = stdlib_base_erfc( stdlib_base_sqrt(x) ); + if ( e != 0 && a > 1.0 ) { + term = stdlib_base_exp( -x ) / stdlib_base_sqrt( STDLIB_CONSTANT_FLOAT64_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; +} + +/** +* Calculates the power term prefix `(z^a)(e^-z)` used in the non-normalized incomplete gammas. +* +* @private +* @param a - function parameter +* @param z - function parameter +* @returns power term prefix +*/ + +static double fullIGammaPrefix( double a, 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 ) ) { + 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 { + prefix = stdlib_base_exp( alz - z ); + } + } + else { + /* eslint-disable no-lonely-if */ + 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 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, double x ){ + double p; + int i; + + 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 gamma functions when `a` is large and `x ~ a` (IEEE double precision or 10^-17). +* +* @private +* @param a - function parameter +* @param x - function parameter +* @returns value of asymptotic expansion +*/ +static double igammaTemmeLarge( double a, double x ){ + double workspace[10]; + double result; + double sigma; + double phi; + double 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 ] = 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 ); + if ( x < a ) { + result = -result; + } + result += stdlib_base_erfc( stdlib_base_sqrt(y) ) / 2.0; + return result; +} +/** +* Creates a function to evaluate a series expansion of the incomplete gamma function. +* +* @private +* @param a1 - function parameter +* @param z1 - function parameter +* @returns series function +*/ +static double lowerIncompleteGammaSeries( double *result, double *a, const double z ){ + double r = *result; + *a += 1.0; + *result *= (z)/(*a); + return r; +} + +/** +* Sum the elements of the series given by the supplied function. +* +* @private +* @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 sumseries2( double a, double z, double initialValue ){ + double result = initialValue; + double aa = a; + double zz = z; + double prevterm = 1.0; + double nextTerm; + int i; + + for( i = 0; i < MAX_TERMS; i++ ){ + nextTerm = lowerIncompleteGammaSeries( &prevterm, &aa, zz ); + result += nextTerm; + if( + stdlib_base_abs(STDLIB_CONSTANT_FLOAT64_EPS * result) >= stdlib_base_abs(nextTerm) + ){ + break; + } + } + return result; +} + +/** +* Sums elements of the series expansion of the lower incomplete gamma function. +* +* ## Method +* +* - Multiply result by `((z^a) * (e^-z) / a)` to get the full lower incomplete integral. +* - Divide by `tgamma(a)` to get the normalized value. +* +* @private +* @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( double a, double z, double initialValue ){ + double result; + initialValue = (initialValue != 0) ? initialValue : 0.0; + result = sumseries2( a, z, initialValue ); + return result; +} + +// MAIN // + +/** +* 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 >= MAX_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 - 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 +* @returns function value +*/ +double API_SUFFIX(stdlib_base_gammainc)( double x, double a, bool regularized, bool upper ) { + double initValue; + double result; + double res[2]; + double sigma; + double gam; + double fa; + double g; + bool optimisedInvert; + bool normalized; + bool isHalfInt; + bool useTemme; + bool isSmallA; + bool invert; + bool isInt; + int evalMethod; + + initValue = 0.0; + optimisedInvert = false; + + if ( x < 0.0 || a <= 0.0 ) { + return 0.0/0.0; + } + normalized = regularized; + invert = upper; + result = 0.0; + if ( a >= MAX_FACTORIAL && !normalized ) { + if ( invert && ( a * 4.0 < x ) ) { + // This is method 4 below, 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: + result = ( a * stdlib_base_ln(x) ) - x; + initValue = 0; + result += stdlib_base_ln( lowerGammaSeries( a, x, initValue ) / a ); + } + else { + result = stdlib_base_gammainc( 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 = 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 * stdlib_base_ln( x ) ) - x; + initValue = 0.0; + result += stdlib_base_ln( lowerGammaSeries( a, x, initValue ) / a ); + } + } + else { + result = stdlib_base_ln( result ) + stdlib_base_gammaln( a ); + } + } + if ( result > STDLIB_CONSTANT_FLOAT64_MAX_LN ) { + return STDLIB_CONSTANT_FLOAT64_PINF; + } + return stdlib_base_exp( result ); + } + 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 < 0.5 ) { + // Changeover criterion chosen to give a changeover at Q ~ 0.33: + if ( -0.4 / stdlib_base_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 ( normalized && a > 20 ) { + 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 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 (normalized == false ) { + result *= stdlib_base_gamma( a ); + } + break; + case 1: + result = finiteHalfGammaQ( a, x ); + if ( normalized == false ) { + result *= stdlib_base_gamma( a ); + } + break; + case 2: + // Compute P: + result = ( normalized ) ? + regularisedGammaPrefix( a, x ) : + fullIGammaPrefix( a, x ); + if ( result != 0.0 ) { + initValue = 0.0; + optimisedInvert = false; + if ( invert ) { + initValue = ( normalized ) ? 1.0 : stdlib_base_gamma( a ); + if ( + normalized || + result >= 1.0 || + STDLIB_CONSTANT_FLOAT64_MAX * result > initValue + ) { + initValue /= result; + if ( + normalized || + a < 1.0 || + ( STDLIB_CONSTANT_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; + tgammaSmallUpperPart( a, x, invert, res ); + result = res[ 0 ]; + g = res[ 1 ]; + invert = false; + if ( normalized ) { + result /= g; + } + break; + case 4: + // Compute Q: + result = ( normalized ) ? + 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 = ( normalized ) ? + 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; + } + if ( normalized && result > 1.0 ) { + result = 1.0; + } + if ( invert ) { + gam = ( normalized ) ? 1.0 : stdlib_base_gamma( a ); + result = gam - result; + } + return 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..707ac15e434e --- /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 NaN' ); + + val = gammainc( 4, NaN, true, false ); + t.strictEqual( isnan( val ), true, 'returns NaN' ); + + 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 NaN' ); + + // Case: s = 0 + val = gammainc( 0.1, 0, true, false ); + t.strictEqual( isnan( val ), true, 'returns NaN' ); + + // Case: s < 0 + val = gammainc( 0.1, -2, true, false ); + t.strictEqual( isnan( val ), true, 'returns NaN' ); + + 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.ok( val === 0, 'returns 0' ); + } + t.end(); +}); + +tape( '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.equal( b1, b2, 'returned result is ' + ( (b2) ? 'finite' : 'not finite' ) ); + + b1 = isnan( actual ); + b2 = isnan( expected1[ i ] ); + t.equal( b1, b2, 'returned result is ' + ( (b1) ? '' : 'not' ) + ' NaN' ); + 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 ] + '.' ); + } + } + 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.equal( b1, b2, 'returned result is ' + ( (b2) ? 'finite' : 'not finite' ) ); + + b1 = isnan( actual ); + b2 = isnan( expected2[ i ] ); + t.equal( b1, b2, 'returned result is ' + ( (b1) ? '' : 'not' ) + ' NaN' ); + 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.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.equal( b1, b2, 'returned result is ' + ( (b2) ? 'finite' : 'not finite' ) ); + + b1 = isnan( actual ); + b2 = isnan( expected3[ i ] ); + t.equal( b1, b2, 'returned result is ' + ( (b1) ? '' : 'not' ) + ' NaN' ); + 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.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.equal( b1, b2, 'returned result is ' + ( (b2) ? 'finite' : 'not finite' ) ); + + b1 = isnan( actual ); + b2 = isnan( expected4[ i ] ); + t.equal( b1, b2, 'returned result is ' + ( (b1) ? '' : 'not' ) + ' NaN' ); + 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.end(); +});