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..f0d87333d6ea --- /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, 100.0 ); + y = uniform( 100, 1.0, 100.0 ); + + 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, 100.0 ); + y = uniform( 100, 1.0, 100.0 ); + + 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, 100.0 ); + y = uniform( 100, 1.0, 100.0 ); + + 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, 100.0 ); + y = uniform( 100, 1.0, 100.0 ); + + 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..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/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/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..082ef4c69653 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/src/addon.c @@ -0,0 +1,44 @@ +/** +* @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 + +/** +* 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..543a6d1e1461 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/src/main.c @@ -0,0 +1,1048 @@ +/** +* @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 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/assert/is_nan.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/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 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. */ + +// BEGIN: polyval_c0 + +/** +* 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_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 double polyval_c8( const double x ) { + return -0.0006526239185953094 + (x * (0.0008394987206720873 + (x * -0.000438297098541721))); +} + +// END: polyval_c8 + +/* End auto-generated functions. */ + +/** +* Evaluates a series expansion of the upper incomplete gamma fraction and stores the numerator and denominator in an output array. +* +* @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; + *k += 1.0; + out[ 0 ] = ( *k ) * ( a - (*k) ); + out[ 1 ] = *z; + return; +} + +/** +* Evaluates a continued fraction expansion of the lower incomplete gamma integral. +* +* ```text +* a1 +* --------------- +* b1 + a2 +* ---------- +* b2 + a3 +* ----- +* b3 + ... +* ``` +* +* @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; + 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 = 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 = SMALLEST_NORMAL; + } + C = out[ 1 ] + ( out[ 0 ] / C ); + if ( C == 0.0 ) { + C = SMALLEST_NORMAL; + } + D = 1.0 / D; + delta = C * D; + f *= delta; + } while ( ( stdlib_base_abs( delta - 1.0 ) > factor ) && --maxIterC ); + + return a0 / f; +} + +/** +* Evaluates the upper incomplete gamma integral via a series expansion and divide by `gamma(z)` to normalize. +* +* ## 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, EPS, MAX_ITERATIONS ) ); +} + +/** +* Computes the next term in the series expansion of the lower incomplete gamma 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; + + r = *result; + *a += 1.0; + *result *= z / ( *a ); + return r; +} + +/** +* Helper function to sum the elements of the series expansion of the lower incomplete gamma function. +* +* @param a function parameter +* @param z function parameter +* @param initialValue initial value for the series +* @return sum of series +*/ +static double sumSeries1( 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(EPS * sum) < stdlib_base_abs(nextTerm) ) && --counter ); + + return sum; +} + +/** +* 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 `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 sumSeries1( a, z, initValue ); +} + +/** +* Calculates normalized Q when a is an integer. +* +* @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; + int32_t 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. +* +* @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; + int32_t n; + + 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) / gamma(a)`. +* +* @param a input value +* @param z input value +* @returns function value +*/ +static double regularisedGammaPrefix( const double a, const double z ) { + double prefix; + double amza; + double agh; + double alz; + double amz; + double sq; + double d; + + agh = a + GAMMA_LANCZOS_G - 0.5; + d = ( (z - a) - GAMMA_LANCZOS_G + 0.5 ) / agh; + if ( a < 1.0 ) { + // 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 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_log1pmx( 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 ); + amz = a - z; + if ( + stdlib_base_min(alz, amz) <= MIN_LN || + stdlib_base_max(alz, amz) >= MAX_LN + ) { + amza = amz / a; + if ( + 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 ( + 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: + sq = stdlib_base_pow( z / agh, a / 4.0 ) * stdlib_base_exp( amz / 4.0 ); + prefix = sq * sq; + prefix *= prefix; + } + else if ( + amza > MIN_LN && + amza < 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 ) / 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. +* +* @param a function parameter +* @param z function parameter +* @returns power term prefix +*/ +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 < 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 ); + } + else { + prefix = stdlib_base_exp( alz - z ); + } + } + else { + if ( alz > MIN_LN ) { + prefix = stdlib_base_pow( z, a ) * stdlib_base_exp( -z ); + } else if ( z/a < MAX_LN ) { + prefix = stdlib_base_pow( z / stdlib_base_exp(z/a), a ); + } else { + prefix = stdlib_base_exp( alz - z ); + } + } + return prefix; +} + +/** +* Computes the next term in the series for the full upper fraction (Q) when `a` is very small. +* +* @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, const double x, int32_t* n, double* result ) { + double r; + + r = ( *result ) / ( *a ); + *result *= x; + *n += 1; + *result /= ( *n ); + *a += 1.0; + return r; +} + +/** +* Sums the elements of the series given by the full upper fraction (Q) when `a` is very small. +* +* @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; + 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; + + // Repeatedly call function... + do { + nextTerm = smallGamma2Series( &ac, xc, &n, &result ); + sum += nextTerm; + } + while ( ( stdlib_base_abs(EPS * sum) < stdlib_base_abs(nextTerm) ) && --counter ); + + return sum; +} + +/** +* Compute the full upper fraction (Q) when `a` is very small. +* +* @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; + 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 * sumSeries2( a, x, ( initialValue-result ) / p ); + if ( invert ) { + result = -result; + } + out[ 0 ] = result; + out[ 1 ] = pgam; +} + +/** +* Computes the next term in the series for the full upper fraction (Q) when `x` is large. +* +* @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 x, double* result ) { + double r; + + r = *result; + *result *= ( *a ) / x; + *a -= 1.0; + return r; +} + +/** +* Sums the elements of the series given by the full upper fraction (Q) when `x` is large. +* +* @param a function parameter +* @param x function parameter +* @return sum of series +*/ +static double sumSeries3( const double a, const double x ) { + 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 { + nextTerm = tgammaILargeXSeries( &ac, x, &result ); + sum += nextTerm; + } + while ( ( stdlib_base_abs(EPS * sum) < stdlib_base_abs(nextTerm) ) && --counter ); + + return sum; +} + +/** +* Computes the asymptotic expansion of the full upper fraction (Q) when `x` is large. +* +* @param a function parameter +* @param x function parameter +* @return function value +*/ +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 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; + double p; + + 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). +* +* @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 ]; + 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( TWO_PI * a ); + if ( x < a ) { + result = -result; + } + result += stdlib_base_erfc( stdlib_base_sqrt(y) ) / 2.0; + return result; +} + +/** +* Main entry point for evaluating all the four incomplete gamma functions (lower, upper, regularized lower, and regularized upper). +* +* @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 +*/ +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; + + result = 0.0; + invert = upper; + isSmallA = ( a < 30 ) && ( a <= x + 1.0 ) && ( x < 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 < 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 { + 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; + } + } 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; + } + } + + 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 ) { + // 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 ) { + initValue = ( regularized ) ? 1.0 : stdlib_base_gamma( a ); + if ( + regularized || + result >= 1.0 || + MAX * result > initValue + ) { + initValue /= result; + if ( + regularized || + a < 1.0 || + ( 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, 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; + } + if ( invert ) { + gam = ( regularized ) ? 1.0 : stdlib_base_gamma( a ); + result = gam - result; + } + return result; +} + +/** +* 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-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 +* @return function value +* +* @example +* 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; + double result; + bool invert; + + if ( x < 0.0 || a <= 0.0 ) { + return 0.0 / 0.0; // NaN + } + invert = upper; + if ( a >= MAX_NTH_FACTORIAL && !regularized ) { + if ( invert && ( a * 4.0 < x ) ) { + // 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 in `igammaFinal`, done in logs: + 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 = stdlib_base_ln( result ) - a + ( ( a-0.5 ) * stdlib_base_ln(a) ); + result += stdlib_base_ln( SQRT_TWO_PI ); + } else { + // 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 ); + } + } else { + result = stdlib_base_ln( result ) + stdlib_base_gammaln( a ); + } + } + if ( result > MAX_LN ) { + return PINF; + } + return stdlib_base_exp( result ); + } + // If no special handling is required then we proceed as normal: + return igammaFinal( a, x, regularized, invert ); +} 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..2cf85093302e --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/huge.json @@ -0,0 +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 new file mode 100644 index 000000000000..1de0eadb306e --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/large.json @@ -0,0 +1 @@ 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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/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 new file mode 100644 index 000000000000..93d20a45efe7 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/medium.json @@ -0,0 +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 48ba6d3685a9..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 @@ -341,10 +341,32 @@ 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_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, "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 ); 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..9645e723e164 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/fixtures/cpp/small.json @@ -0,0 +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 a9ac362f35b1..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 @@ -21,22 +21,17 @@ // MODULES // 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 largeXSmallS = require( './fixtures/cpp/large_x_small_s.json' ); +var largeXMediumS = require( './fixtures/cpp/large_x_medium_s.json' ); // TESTS // @@ -50,11 +45,11 @@ 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 +58,16 @@ 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(); }); @@ -81,112 +76,296 @@ 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; - for ( i = 0; i < x.length; i++ ) { - actual = gammainc( x[ i ], s[ i ] ); - b1 = isfinite( actual ); - b2 = isfinite( expected1[ i ] ); - t.strictEqual( b1, b2, 'returned result is ' + ( (b2) ? 'finite' : 'not finite' ) ); + expected = small.lower_regularized; + x = small.x; + s = small.s; - b1 = isnan( actual ); - b2 = isnan( expected1[ i ] ); - t.strictEqual( 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 ] + '.' ); - } + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], true, false ); + 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 ); + 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 for small `x` and small `s`', function test( t ) { + var expected; + var actual; + 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 ); + 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 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 ); + 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 x; + var s; + var i; - b1 = isfinite( actual ); - b2 = isfinite( expected2[ i ] ); - t.strictEqual( b1, b2, 'returned result is ' + ( (b2) ? 'finite' : 'not finite' ) ); + expected = medium.lower_regularized; + x = medium.x; + s = medium.s; - b1 = isnan( actual ); - b2 = isnan( expected2[ i ] ); - t.strictEqual( 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 ] + '.' ); - } + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], true, false ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 98, true, 'returns expected value within 98 ulp' ); } t.end(); }); -tape( 'the function correctly evaluates the unregularized lower 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 ); + 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 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 ); + 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 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 ); + 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 x; + var s; + var i; - b1 = isfinite( actual ); - b2 = isfinite( expected3[ i ] ); - t.strictEqual( b1, b2, 'returned result is ' + ( (b2) ? 'finite' : 'not finite' ) ); + expected = largeXSmallS.lower_regularized; + x = largeXSmallS.x; + s = largeXSmallS.s; - b1 = isnan( actual ); - b2 = isnan( expected3[ i ] ); - t.strictEqual( 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 ] + '.' ); - } + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], true, false ); + 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 x; + var s; + var i; + + 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 ); + 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 x; + var s; + var i; + + 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 ); + 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', function test( t ) { +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 delta; - var tol; - var b1; - var b2; + var x; + var s; var i; + + 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 ); + 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 x; + var s; + var i; + + expected = largeXMediumS.lower_regularized; + x = largeXMediumS.x; + s = largeXMediumS.s; - b1 = isfinite( actual ); - b2 = isfinite( expected4[ i ] ); - t.strictEqual( b1, b2, 'returned result is ' + ( (b2) ? 'finite' : 'not finite' ) ); - - b1 = isnan( actual ); - b2 = isnan( expected4[ i ] ); - t.strictEqual( 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 ] + '.' ); - } + for ( i = 0; i < x.length; i++ ) { + actual = gammainc( x[ i ], s[ i ], true, false ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 1, true, 'returns expected value within 1 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 x; + var s; + var i; + + 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 ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 134, true, 'returns expected value within 134 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 x; + var s; + var i; + + 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 ); + 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 x; + var s; + var i; + + 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 ); + 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 new file mode 100644 index 000000000000..b4ad79448f0c --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js @@ -0,0 +1,477 @@ +/** +* @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 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' ); + + +// VARIABLES // + +var gammainc = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( gammainc instanceof Error ) +}; + + +// FIXTURES // + +var small = require( './fixtures/cpp/small.json' ); +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 // + +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( isSameValue( val, NaN ), true, 'returns expected value' ); + + val = gammainc( 4, NaN, true, false ); + t.strictEqual( isSameValue( val, NaN ), 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( isSameValue( val, NaN ), true, 'returns expected value' ); + + // Case: s = 0 + val = gammainc( 0.1, 0, true, false ); + t.strictEqual( isSameValue( val, NaN ), true, 'returns expected value' ); + + // Case: s < 0 + val = gammainc( 0.1, -2, true, false ); + t.strictEqual( isSameValue( val, NaN ), 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( isSameValue( val, 0.0 ), true, 'returns expected value' ); + } + t.end(); +}); + +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 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 ); + 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 for small `x` and small `s`', opts, function test( t ) { + var expected; + var actual; + 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 ); + 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 for small `x` and small `s`', opts, function test( t ) { + var expected; + var actual; + 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 ); + 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`', opts, function test( t ) { + var expected; + var actual; + 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 ); + 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`', opts, function test( t ) { + var expected; + var actual; + 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 ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 98, true, 'returns expected value within 98 ulp' ); + } + 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 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 ); + 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`', opts, function test( t ) { + var expected; + var actual; + 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 ); + 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`', opts, function test( t ) { + var expected; + var actual; + 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 ); + 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`', opts, function test( t ) { + var expected; + var actual; + var x; + var s; + var i; + + 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 ); + 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`', opts, function test( t ) { + var expected; + var actual; + var x; + var s; + var i; + + 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 ); + 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`', opts, function test( t ) { + var expected; + var actual; + var x; + var s; + var i; + + 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 ); + 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`', opts, function test( t ) { + var expected; + var actual; + var x; + var s; + var i; + + 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 ); + 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`', opts, function test( t ) { + var expected; + var actual; + var x; + var s; + var i; + + 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 ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 1, true, 'returns expected value within 1 ulp' ); + } + 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 x; + var s; + var i; + + 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 ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 134, true, 'returns expected value within 134 ulp' ); + } + t.end(); +}); + +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 x; + var s; + var i; + + 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 ); + 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`', opts, function test( t ) { + var expected; + var actual; + var x; + var s; + var i; + + 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 ); + 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; + } + // 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(); +}); + +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; + } + // 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(); +}); + +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; + + 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; + } + // 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(); +}); + +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; + } + // 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(); +});