diff --git a/lib/node_modules/@stdlib/math/base/special/gamma/README.md b/lib/node_modules/@stdlib/math/base/special/gamma/README.md index 9497ef59428..44494ffeacd 100644 --- a/lib/node_modules/@stdlib/math/base/special/gamma/README.md +++ b/lib/node_modules/@stdlib/math/base/special/gamma/README.md @@ -121,6 +121,95 @@ for ( i = 0; i < x.length; i++ ) { + + +* * * + +
+ +## C APIs + + + +
+ +
+ + + + + +
+ +### Usage + +```c +#include "stdlib/math/base/special/gamma.h" +``` + +#### stdlib_base_gamma( x ) + +Evaluates the [gamma function][gamma-function]. + +```c +double out = stdlib_base_gamma( 4.0 ); +// returns 6.0 + +out = stdlib_base_gamma( -1.5 ); +// returns ~2.363 +``` + +The function accepts the following arguments: + +- **x**: `[in] double` input value. + +```c +double stdlib_base_gamma( const double x ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +### Examples + +```c +#include "stdlib/math/base/special/gamma.h" +#include +#include + +int main( void ) { + const double x[] = { 4.0, -1.5, -0.5, 0.5 }; + + double y; + int i; + for ( i = 0; i < 4; i++ ) { + y = stdlib_base_gamma( x[ i ] ); + printf( "gamma(%lf) = %lf\n", x[ i ], y ); + } +} +``` + +
+ + + +
+ + +
diff --git a/lib/node_modules/@stdlib/math/base/special/gamma/benchmark/benchmark.native.js b/lib/node_modules/@stdlib/math/base/special/gamma/benchmark/benchmark.native.js new file mode 100644 index 00000000000..a2377c28a7e --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma/benchmark/benchmark.native.js @@ -0,0 +1,60 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* 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 randu = require( '@stdlib/random/base/randu' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var tryRequire = require( '@stdlib/utils/try-require' ); +var pkg = require( './../package.json' ).name; + + +// VARIABLES // + +var gamma = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( gamma instanceof Error ) +}; + + +// MAIN // + +bench( pkg+'::native', opts, function benchmark( b ) { + var x; + var y; + var i; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + x = ( randu() * 171.0 ) - 0.0; + y = gamma( x ); + if ( isnan( y ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( y ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); diff --git a/lib/node_modules/@stdlib/math/base/special/gamma/benchmark/c/native/Makefile b/lib/node_modules/@stdlib/math/base/special/gamma/benchmark/c/native/Makefile new file mode 100644 index 00000000000..f69e9da2b4d --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma/benchmark/c/native/Makefile @@ -0,0 +1,146 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2024 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# 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/gamma/benchmark/c/native/benchmark.c b/lib/node_modules/@stdlib/math/base/special/gamma/benchmark/c/native/benchmark.c new file mode 100644 index 00000000000..6e9752ad99d --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma/benchmark/c/native/benchmark.c @@ -0,0 +1,136 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* 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. +*/ + +/** +* Benchmark `gamma`. +*/ +#include "stdlib/math/base/special/gamma.h" +#include +#include +#include +#include +#include + +#define NAME "gamma" +#define ITERATIONS 1000000 +#define REPEATS 3 + +/** +* Prints the TAP version. +*/ +void print_version() { + printf( "TAP version 13\n" ); +} + +/** +* Prints the TAP summary. +* +* @param total total number of tests +* @param passing total number of passing tests +*/ +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 +*/ +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 +*/ +double tic() { + struct timeval now; + gettimeofday( &now, NULL ); + return (double)now.tv_sec + (double)now.tv_usec / 1.0e6; +} + +/** +* Generates a random number on the interval [0,1]. +* +* @return random number +*/ +double rand_double() { + int r = rand(); + return (double)r / ( (double)RAND_MAX + 1.0 ); +} + +/** +* Runs a benchmark. +* +* @return elapsed time in seconds +*/ +double benchmark() { + double elapsed; + double x; + double y; + double t; + int i; + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + x = ( 171.0 * rand_double() ) - 0.0; + y = stdlib_base_gamma( x ); + 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/gamma/binding.gyp b/lib/node_modules/@stdlib/math/base/special/gamma/binding.gyp new file mode 100644 index 00000000000..ec399223344 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma/binding.gyp @@ -0,0 +1,170 @@ +# @license Apache-2.0 +# +# Copyright (c) 2024 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# 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/gamma/examples/c/Makefile b/lib/node_modules/@stdlib/math/base/special/gamma/examples/c/Makefile new file mode 100644 index 00000000000..6aed70daf16 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma/examples/c/Makefile @@ -0,0 +1,146 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2024 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# 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/gamma/examples/c/example.c b/lib/node_modules/@stdlib/math/base/special/gamma/examples/c/example.c new file mode 100644 index 00000000000..34ecb2281ad --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma/examples/c/example.c @@ -0,0 +1,31 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* 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/gamma.h" +#include + +int main( void ) { + const double x[] = { 4.0, -1.5, -0.5, 0.5 }; + + double y; + int i; + for ( i = 0; i < 4; i++ ) { + y = stdlib_base_gamma( x[ i ] ); + printf( "gamma(%lf) = %lf\n", x[ i ], y ); + } +} diff --git a/lib/node_modules/@stdlib/math/base/special/gamma/include.gypi b/lib/node_modules/@stdlib/math/base/special/gamma/include.gypi new file mode 100644 index 00000000000..575cb043c0b --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma/include.gypi @@ -0,0 +1,53 @@ +# @license Apache-2.0 +# +# Copyright (c) 2024 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# 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': [ + ' + +static const double MAX_STIRLING = 143.01608; + +/* Begin auto-generated functions. The following functions are auto-generated. Do not edit directly. */ + +// BEGIN: poly_p + +/** +* 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 poly_p( const double x ) { + return 0.08333333333334822 + (x * (0.0034722222160545866 + (x * (-0.0026813261780578124 + (x * (-0.00022954996161337813 + (x * 0.0007873113957930937))))))); +} + +// END: poly_p + +// BEGIN: rational_pq + +/** +* Evaluates a rational function (i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\)). +* +* ## Notes +* +* - Coefficients should be sorted in ascending degree. +* - 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 rational function +* @return evaluated rational function +*/ +static double rational_pq( const double x ) { + double ax; + double ix; + double s1; + double s2; + if ( x == 0.0 ) { + return 1.0; + } + if ( x < 0.0 ) { + ax = -x; + } else { + ax = x; + } + if ( ax <= 1.0 ) { + s1 = 1.0 + (x * (0.4942148268014971 + (x * (0.20744822764843598 + (x * (0.04763678004571372 + (x * (0.010421379756176158 + (x * (0.0011913514700658638 + (x * (0.00016011952247675185 + (x * 0.0))))))))))))); + s2 = 1.0 + (x * (0.0714304917030273 + (x * (-0.23459179571824335 + (x * (0.035823639860549865 + (x * (0.011813978522206043 + (x * (-0.004456419138517973 + (x * (0.0005396055804933034 + (x * -0.000023158187332412014))))))))))))); + } else { + ix = 1.0 / x; + s1 = 0.0 + (ix * (0.00016011952247675185 + (ix * (0.0011913514700658638 + (ix * (0.010421379756176158 + (ix * (0.04763678004571372 + (ix * (0.20744822764843598 + (ix * (0.4942148268014971 + (ix * 1.0))))))))))))); + s2 = -0.000023158187332412014 + (ix * (0.0005396055804933034 + (ix * (-0.004456419138517973 + (ix * (0.011813978522206043 + (ix * (0.035823639860549865 + (ix * (-0.23459179571824335 + (ix * (0.0714304917030273 + (ix * 1.0))))))))))))); + } + return s1 / s2; +} + +// END: rational_pq + +/* End auto-generated functions. */ + +/** +* Evaluates the gamma function using Stirling's formula. The polynomial is valid for \\(33 \leq x \leq 172\\). +* +* @param x input value +* @return function value +*/ +static double stirlingApprox( const double x ) { + double w; + double y; + double v; + + w = 1.0 / x; + w = 1.0 + ( w * poly_p( w ) ); + y = stdlib_base_exp( x ); + + // Check `x` to avoid `pow()` overflow... + if ( x > MAX_STIRLING ) { + v = stdlib_base_pow( x, ( 0.5 * x ) - 0.25 ); + y = v * ( v / y ); + } else { + y = stdlib_base_pow( x, x - 0.5 ) / y; + } + return STDLIB_CONSTANT_FLOAT64_SQRT_TWO_PI * y * w; +} + +/** +* Evaluates the gamma function using a small-value approximation. +* +* @param x input value +* @param z scale factor +* @return function value +*/ +static double smallApprox( const double x, const double z ) { + return z / ( ( 1.0 + ( STDLIB_CONSTANT_FLOAT64_EULERGAMMA * x ) ) * x ); +} + +/** +* Evaluates the gamma function. +* +* ## Method +* +* 1. Arguments \\(|x| \leq 34\\) are reduced by recurrence and the function approximated by a rational function of degree \\(6/7\\) in the interval \\((2,3)\\). +* 2. Large negative arguments are made positive using a reflection formula. +* 3. Large arguments are handled by Stirling's formula. +* +* ## Notes +* +* - Relative error: +* +* | arithmetic | domain | # trials | peak | rms | +* |:----------:|:---------:|:--------:|:-------:|:-------:| +* | DEC | -34,34 | 10000 | 1.3e-16 | 2.5e-17 | +* | IEEE | -170,-33 | 20000 | 2.3e-15 | 3.3e-16 | +* | IEEE | -33, 33 | 20000 | 9.4e-16 | 2.2e-16 | +* | IEEE | 33, 171.6 | 20000 | 2.3e-15 | 3.2e-16 | +* +* - Error for arguments outside the test range will be larger owing to error amplification by the exponential function. +* +* @param x input value +* @return function value +* +* @example +* double v = stdlib_base_gamma( 4.0 ); +* // returns 6.0 +*/ +double stdlib_base_gamma( const double x ) { + double sign; + double xc; + int32_t i; + double p; + double q; + double z; + + if ( ( stdlib_base_is_integer( x ) && x < 0 ) || x == STDLIB_CONSTANT_FLOAT64_NINF || stdlib_base_is_nan( x ) ) { + return 0.0 / 0.0; // NaN + } + if ( x == 0.0 ) { + if ( stdlib_base_is_negative_zero( x ) ) { + return STDLIB_CONSTANT_FLOAT64_NINF; + } + return STDLIB_CONSTANT_FLOAT64_PINF; + } + if ( x > 171.61447887182298 ) { + return STDLIB_CONSTANT_FLOAT64_PINF; + } + if ( x < -170.5674972726612 ) { + return 0.0; + } + q = stdlib_base_abs( x ); + if ( q > 33.0 ) { + if ( x >= 0.0 ) { + return stirlingApprox( x ); + } + p = stdlib_base_floor( q ); + + // Check whether `x` is even... + i = (int32_t)p; + if ( ( i & 1 ) == 0 ) { + sign = -1.0; + } else { + sign = 1.0; + } + z = q - p; + if ( z > 0.5 ) { + p += 1.0; + z = q - p; + } + z = q * stdlib_base_sin( STDLIB_CONSTANT_FLOAT64_PI * z ); + return sign * STDLIB_CONSTANT_FLOAT64_PI / ( stdlib_base_abs( z ) * stirlingApprox( q ) ); + } + + // Reduce `x`... + z = 1.0; + xc = x; + while ( xc >= 3.0 ) { + xc -= 1.0; + z *= xc; + } + while ( xc < 0.0 ) { + if ( xc > -1.0e-9 ) { + return smallApprox( xc, z ); + } + z /= xc; + xc += 1.0; + } + while ( xc < 2.0 ) { + if ( xc < 1.0e-9 ) { + return smallApprox( xc, z ); + } + z /= xc; + xc += 1.0; + } + if ( xc == 2.0 ) { + return z; + } + xc -= 2.0; + return z * rational_pq( xc ); +} diff --git a/lib/node_modules/@stdlib/math/base/special/gamma/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/gamma/test/test.native.js new file mode 100644 index 00000000000..e6689d923ac --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma/test/test.native.js @@ -0,0 +1,193 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* 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 isnan = require( '@stdlib/math/base/assert/is-nan' ); +var incrspace = require( '@stdlib/array/base/incrspace' ); +var abs = require( '@stdlib/math/base/special/abs' ); +var max = require( '@stdlib/math/base/special/maxn' ); +var PINF = require( '@stdlib/constants/float64/pinf' ); +var NINF = require( '@stdlib/constants/float64/ninf' ); +var tryRequire = require( '@stdlib/utils/try-require' ); + + +// VARIABLES // + +var gamma = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( gamma instanceof Error ) +}; + + +// FIXTURES // + +var data1 = require( './fixtures/r/data1.json' ); +var expected1 = require( './fixtures/r/expected1.json' ); +var data2 = require( './fixtures/r/data2.json' ); +var expected2 = require( './fixtures/r/expected2.json' ); + + +// TESTS // + +tape( 'main export is a function', opts, function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof gamma, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'if provided a negative integer, the function returns `NaN`', opts, function test( t ) { + var values = incrspace( -1.0, -1000.0, -1.0 ); + var v; + var i; + + for ( i = 0; i < values.length; i++ ) { + v = gamma( values[ i ] ); + t.equal( isnan( v ), true, 'returns NaN when provided ' + values[ i ] ); + } + t.end(); +}); + +tape( 'if provided negative infinity, the function returns `NaN`', opts, function test( t ) { + var v = gamma( NINF ); + t.equal( isnan( v ), true, 'returns expected value when provided negative infinity' ); + t.end(); +}); + +tape( 'if provided `NaN`, the function returns `NaN`', opts, function test( t ) { + var v = gamma( NaN ); + t.equal( isnan( v ), true, 'returns expected value when provided a NaN' ); + t.end(); +}); + +tape( 'if provided `-0`, the function returns negative infinity', opts, function test( t ) { + var v = gamma( -0.0 ); + t.equal( v, NINF, 'returns -infinity' ); + t.end(); +}); + +tape( 'if provided `+0`, the function returns positive infinity', opts, function test( t ) { + var v = gamma( 0.0 ); + t.equal( v, PINF, 'returns +infinity' ); + t.end(); +}); + +tape( 'if `x > 171.6144...`, the function returns positive infinity', opts, function test( t ) { + var values = incrspace( 172.0, 1000.0, 10.1234 ); + var v; + var i; + + for ( i = 0; i < values.length; i++ ) { + v = gamma( values[ i ] ); + t.equal( v, PINF, 'returns +infinity when provided ' + values[ i ] ); + } + t.end(); +}); + +tape( 'if `x < -170.56749...`, the function returns zero', opts, function test( t ) { + var values = incrspace( -170.57, -1000.0, -10.1234 ); + var v; + var i; + + for ( i = 0; i < values.length; i++ ) { + v = gamma( values[ i ] ); + t.equal( v, 0.0, 'returns 0 when provided ' + values[ i ] ); + } + t.end(); +}); + +tape( 'the function evaluates the gamma function (positive integers)', opts, function test( t ) { + var delta; + var tol; + var v; + var i; + + for ( i = 0; i < data1.length; i++ ) { + v = gamma( data1[ i ] ); + delta = abs( v - expected1[ i ] ); + tol = 2.75e-12 * max( 1.0, abs( v ), abs( expected1[ i ] ) ); + t.ok( delta <= tol, 'within tolerance. x: ' + data1[ i ] + '. Value: ' + v + '. Expected: ' + expected1[ i ] + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function evaluates the gamma function (decimal values)', opts, function test( t ) { + var delta; + var tol; + var v; + var i; + + for ( i = 0; i < data2.length; i++ ) { + v = gamma( data2[ i ] ); + delta = abs( v - expected2[ i ] ); + tol = 2.75e-12 * max( 1.0, abs( v ), abs( expected2[ i ] ) ); + t.ok( delta <= tol, 'within tolerance. x: ' + data2[ i ] + '. Value: ' + v + '. Expected: ' + expected2[ i ] + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'if provided a positive integer, the function returns the factorial of (n-1)', opts, function test( t ) { + t.equal( gamma( 4.0 ), 6.0, 'returns 6' ); + t.equal( gamma( 5.0 ), 24.0, 'returns 24' ); + t.equal( gamma( 6.0 ), 120.0, 'returns 120' ); + t.end(); +}); + +tape( 'the function uses a small value approximation near left boundaries (abs(x)<33)', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var v; + + x = -20.99999999999999; + v = gamma( x ); + + expected = -1.8364310433257593e-6; + + delta = abs( v - expected ); + tol = 1.0e-14; + + t.ok( delta < tol, 'within tolerance. x: ' + x + '. Value: ' + v + '. Expected: ' + expected + '. Tolerance: ' + tol + '.' ); + + t.end(); +}); + +tape( 'the function uses a small value approximation near right boundaries (abs(x)<33)', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var v; + + x = -20.00000000000001; + v = gamma( x ); + + expected = -3.856505190983844e-5; + + delta = abs( v - expected ); + tol = 1.0e-14; + + t.ok( delta < tol, 'within tolerance. x: ' + x + '. Value: ' + v + '. Expected: ' + expected + '. Tolerance: ' + tol + '.' ); + + t.end(); +});