diff --git a/lib/node_modules/@stdlib/math/base/special/gamma1pm1/README.md b/lib/node_modules/@stdlib/math/base/special/gamma1pm1/README.md index ccf18b2874a..108770906da 100644 --- a/lib/node_modules/@stdlib/math/base/special/gamma1pm1/README.md +++ b/lib/node_modules/@stdlib/math/base/special/gamma1pm1/README.md @@ -75,6 +75,91 @@ for ( i = 0; i < 100; i++ ) { + + +* * * + +
+ +## C APIs + + + +
+ +
+ + + + + +
+ +### Usage + +```c +#include "stdlib/math/base/special/gamma1pm1.h" +``` + +#### stdlib_base_gamma1pm1( x ) + +Computes `gamma(x+1) - 1` without cancellation errors for small `x` and where `gamma(x)` is the [gamma function][@stdlib/math/base/special/gamma]. + +```c +double out = stdlib_base_gamma1pm1( 0.2 ); +// returns ~-0.082 +``` + +The function accepts the following arguments: + +- **x**: `[in] double` input value. + +```c +double stdlib_base_gamma1pm1( const double x ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +### Examples + +```c +#include "stdlib/math/base/special/gamma1pm1.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_gamma1pm1( x[ i ] ); + printf( "gamma1pm1(%lf) = %lf\n", x[ i ], y ); + } +} +``` + +
+ + + +
+ + +
diff --git a/lib/node_modules/@stdlib/math/base/special/gamma1pm1/benchmark/benchmark.native.js b/lib/node_modules/@stdlib/math/base/special/gamma1pm1/benchmark/benchmark.native.js new file mode 100644 index 00000000000..84d4ee07f18 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma1pm1/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 gamma1pm1 = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( gamma1pm1 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() * 10.0 ) - 5.0; + y = gamma1pm1( 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/gamma1pm1/benchmark/c/native/Makefile b/lib/node_modules/@stdlib/math/base/special/gamma1pm1/benchmark/c/native/Makefile new file mode 100644 index 00000000000..f69e9da2b4d --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma1pm1/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/gamma1pm1/benchmark/c/native/benchmark.c b/lib/node_modules/@stdlib/math/base/special/gamma1pm1/benchmark/c/native/benchmark.c new file mode 100644 index 00000000000..e7a64893177 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma1pm1/benchmark/c/native/benchmark.c @@ -0,0 +1,133 @@ +/** +* @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/gamma1pm1.h" +#include +#include +#include +#include +#include + +#define NAME "gamma1pm1" +#define ITERATIONS 1000000 +#define REPEATS 3 + +/** +* Prints the TAP version. +*/ +static void print_version( void ) { + printf( "TAP version 13\n" ); +} + +/** +* Prints the TAP summary. +* +* @param total total number of tests +* @param passing total number of passing tests +*/ +static void print_summary( int total, int passing ) { + printf( "#\n" ); + printf( "1..%d\n", total ); // TAP plan + printf( "# total %d\n", total ); + printf( "# pass %d\n", passing ); + printf( "#\n" ); + printf( "# ok\n" ); +} + +/** +* Prints benchmarks results. +* +* @param elapsed elapsed time in seconds +*/ +static void print_results( double elapsed ) { + double rate = (double)ITERATIONS / elapsed; + printf( " ---\n" ); + printf( " iterations: %d\n", ITERATIONS ); + printf( " elapsed: %0.9f\n", elapsed ); + printf( " rate: %0.9f\n", rate ); + printf( " ...\n" ); +} + +/** +* Returns a clock time. +* +* @return clock time +*/ +static double tic( void ) { + struct timeval now; + gettimeofday( &now, NULL ); + return (double)now.tv_sec + (double)now.tv_usec / 1.0e6; +} + +/** +* Generates a random number on the interval [0,1). +* +* @return random number +*/ +static double rand_double( void ) { + int r = rand(); + return (double)r / ( (double)RAND_MAX + 1.0 ); +} + +/** +* Runs a benchmark. +* +* @return elapsed time in seconds +*/ +static double benchmark( void ) { + double elapsed; + double x; + double y; + double t; + int i; + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + x = ( 10.0 * rand_double() ) - 5.0; + y = stdlib_base_gamma1pm1( 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/gamma1pm1/binding.gyp b/lib/node_modules/@stdlib/math/base/special/gamma1pm1/binding.gyp new file mode 100644 index 00000000000..ec399223344 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma1pm1/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/gamma1pm1/docs/types/index.d.ts b/lib/node_modules/@stdlib/math/base/special/gamma1pm1/docs/types/index.d.ts index e86dc0066a6..5de9dfab87b 100644 --- a/lib/node_modules/@stdlib/math/base/special/gamma1pm1/docs/types/index.d.ts +++ b/lib/node_modules/@stdlib/math/base/special/gamma1pm1/docs/types/index.d.ts @@ -25,28 +25,28 @@ * @returns function value * * @example -* var v = gammap1m1( 0.2 ); +* var v = gamma1pm1( 0.2 ); * // returns ~-0.082 * * @example -* var v = gammap1m1( -9.2 ); +* var v = gamma1pm1( -9.2 ); * // returns ~-1.0 * * @example -* var v = gammap1m1( 0.0 ); +* var v = gamma1pm1( 0.0 ); * // returns 0.0 * * @example -* var v = gammap1m1( -3.0 ); +* var v = gamma1pm1( -3.0 ); * // returns NaN * * @example -* var v = gammap1m1( NaN ); +* var v = gamma1pm1( NaN ); * // returns NaN */ -declare function gammap1m1( x: number ): number; +declare function gamma1pm1( x: number ): number; // EXPORTS // -export = gammap1m1; +export = gamma1pm1; diff --git a/lib/node_modules/@stdlib/math/base/special/gamma1pm1/docs/types/test.ts b/lib/node_modules/@stdlib/math/base/special/gamma1pm1/docs/types/test.ts index b94543eb801..bcd00388112 100644 --- a/lib/node_modules/@stdlib/math/base/special/gamma1pm1/docs/types/test.ts +++ b/lib/node_modules/@stdlib/math/base/special/gamma1pm1/docs/types/test.ts @@ -16,29 +16,29 @@ * limitations under the License. */ -import gammap1m1 = require( './index' ); +import gamma1pm1 = require( './index' ); // TESTS // // The function returns a number... { - gammap1m1( 8 ); // $ExpectType number + gamma1pm1( 8 ); // $ExpectType number } // The compiler throws an error if the function is provided a value other than a number... { - gammap1m1( true ); // $ExpectError - gammap1m1( false ); // $ExpectError - gammap1m1( null ); // $ExpectError - gammap1m1( undefined ); // $ExpectError - gammap1m1( '5' ); // $ExpectError - gammap1m1( [] ); // $ExpectError - gammap1m1( {} ); // $ExpectError - gammap1m1( ( x: number ): number => x ); // $ExpectError + gamma1pm1( true ); // $ExpectError + gamma1pm1( false ); // $ExpectError + gamma1pm1( null ); // $ExpectError + gamma1pm1( undefined ); // $ExpectError + gamma1pm1( '5' ); // $ExpectError + gamma1pm1( [] ); // $ExpectError + gamma1pm1( {} ); // $ExpectError + gamma1pm1( ( x: number ): number => x ); // $ExpectError } // The compiler throws an error if the function is provided insufficient arguments... { - gammap1m1(); // $ExpectError + gamma1pm1(); // $ExpectError } diff --git a/lib/node_modules/@stdlib/math/base/special/gamma1pm1/examples/c/Makefile b/lib/node_modules/@stdlib/math/base/special/gamma1pm1/examples/c/Makefile new file mode 100644 index 00000000000..6aed70daf16 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma1pm1/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/gamma1pm1/examples/c/example.c b/lib/node_modules/@stdlib/math/base/special/gamma1pm1/examples/c/example.c new file mode 100644 index 00000000000..68279aebf6a --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma1pm1/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/gamma1pm1.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_gamma1pm1( x[ i ] ); + printf( "gamma1pm1(%lf) = %lf\n", x[ i ], y ); + } +} diff --git a/lib/node_modules/@stdlib/math/base/special/gamma1pm1/examples/index.js b/lib/node_modules/@stdlib/math/base/special/gamma1pm1/examples/index.js index 58e63dfeee2..2f056eb414e 100644 --- a/lib/node_modules/@stdlib/math/base/special/gamma1pm1/examples/index.js +++ b/lib/node_modules/@stdlib/math/base/special/gamma1pm1/examples/index.js @@ -19,12 +19,12 @@ 'use strict'; var randu = require( '@stdlib/random/base/randu' ); -var gammap1m1 = require( './../lib' ); +var gamma1pm1 = require( './../lib' ); var x; var i; for ( i = 0; i < 100; i++ ) { x = (randu()*10.0) - 5.0; - console.log( 'gamma(%d+1) - 1 = %d', x, gammap1m1( x ) ); + console.log( 'gamma(%d+1) - 1 = %d', x, gamma1pm1( x ) ); } diff --git a/lib/node_modules/@stdlib/math/base/special/gamma1pm1/include.gypi b/lib/node_modules/@stdlib/math/base/special/gamma1pm1/include.gypi new file mode 100644 index 00000000000..575cb043c0b --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma1pm1/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': [ + ' 2 \\), begin by performing argument reduction until \\( z \\) is in \\(\[2,3)\\). Use the following form: +* +* ```tex +* \operatorname{gammaln}(z) = (z-2)(z+1)(Y + R(z-2)) +* ``` +* +* where \\( R(z-2) \\) is a rational approximation optimized for low absolute error. As long as the absolute error is small compared to the constant \\( Y \\), then any rounding error in the computation will get wiped out. +* +* 2. If \\( z < 1 \\), use recurrence to shift to \\( z \\) in the interval \\(\[1,2\]\\). Then, use one of two approximations: one for \\( z \\) in \\(\[1,1.5\]\\) and one for \\( z \\) in \\(\[1.5,2\]\\): +* +* - For \(( z \\) in \\(\[1,1.5\]\\), use +* +* ```tex +* \operatorname{gammaln}(z) = (z-1)(z-2)(Y + R(z-1)) +* ``` +* +* where \\( R(z-1) \\) is a rational approximation optimized for low absolute error. As long as the absolute error is small compared to the constant \\( Y \\), then any rounding error in the computation will get wiped out. +* +* - For \\( z \\) in \\(\[1.5,2\]\\), use +* +* ```tex +* \operatorname{gammaln}(z) = (2-z)(1-z)(Y + R(2-z)) +* ``` +* +* where \\( R(2-z) \\) is a rational approximation optimized for low absolute error. As long as the absolute error is small compared to the constant \\( Y \\), then any rounding error in the computation will get wiped out. +* +* ## Notes +* +* - Relative error: +* +* | function | peak | maximum deviation | +* |:--------:|:------------:|:-----------------:| +* | R(Z-2) | 4.231e-18 | 5.900e-24 | +* | R(Z-1) | 1.230011e-17 | 3.139e-021 | +* | R(2-Z) | 1.797565e-17 | 2.151e-021 | +* +* @param z input value +* @param zm1 `z` minus one +* @param zm2 `z` minus two +* @return function value +*/ +static double lgammaSmallImp( const double z, const double zm1, const double zm2 ) { + double prefix; + double result; + double zm1c; + double zm2c; + double zc; + double r; + double R; + + if ( z < STDLIB_CONSTANT_FLOAT64_EPS ) { + return -stdlib_base_ln( z ); + } + if ( zm1 == 0.0 || zm2 == 0.0 ) { + return 0.0; + } + result = 0.0; + zc = z; + zm1c = zm1; + zm2c = zm2; + if ( zc > 2.0 ) { + if ( zc >= 3.0 ) { + do { + zc -= 1.0; + zm2c -= 1.0; + result += stdlib_base_ln( zc ); + } while ( zc >= 3.0 ); + zm2c = zc - 2.0; + } + r = zm2c * ( zc + 1.0 ); + R = rational_p1q1( zm2c ); + result += ( r * Y1 ) + ( r * R ); + return result; + } + if ( zc < 1.0 ) { + result += -stdlib_base_ln( zc ); + zm2c = zm1c; + zm1c = zc; + zc += 1.0; + } + if ( zc <= 1.5 ) { + r = rational_p2q2( zm1c ); + prefix = zm1c * zm2c; + result += ( prefix * Y2 ) + ( prefix * r ); + return result; + } + + // Case: 1.5 < zc <= 2 + r = zm2c * zm1c; + R = rational_p3q3( -zm2c ); + result += ( r * Y3 ) + ( r * R ); + return result; +} + +/** +* Computes `gamma(x+1) - 1`. +* +* @param x input value +* @return function value +* +* @example +* double out = stdlib_base_gamma1pm1( 0.2 ); +* // returns ~-0.082 +*/ +double stdlib_base_gamma1pm1( const double x ) { + if ( stdlib_base_is_nan( x ) ) { + return 0.0 / 0.0; // NaN + } + if ( x < 0.0 ) { + if ( x < -0.5 ) { + // Best method is simply to subtract 1 from gamma: + return stdlib_base_gamma( 1.0 + x ) - 1.0; + } + + // Use expm1 on the logarithm of gamma: + return stdlib_base_expm1( -stdlib_base_log1p( x ) + lgammaSmallImp( x + 2.0, x + 1.0, x ) ); + } + if ( x < 2.0 ) { + // Use expm1 on the logarithm of gamma: + return stdlib_base_expm1( lgammaSmallImp( x + 1.0, x, x - 1.0 ) ); + } + + // Best method is simply to subtract 1 from gamma: + return stdlib_base_gamma( 1.0 + x ) - 1.0; +} diff --git a/lib/node_modules/@stdlib/math/base/special/gamma1pm1/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/gamma1pm1/test/test.native.js new file mode 100644 index 00000000000..39a9e04a850 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma1pm1/test/test.native.js @@ -0,0 +1,132 @@ +/** +* @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 gamma = require( '@stdlib/math/base/special/gamma' ); +var abs = require( '@stdlib/math/base/special/abs' ); +var incrspace = require( '@stdlib/array/base/incrspace' ); +var EPS = require( '@stdlib/constants/float64/eps' ); +var tryRequire = require( '@stdlib/utils/try-require' ); + + +// VARIABLES // + +var gamma1pm1 = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( gamma1pm1 instanceof Error ) +}; + + +// FIXTURES // + +var smallPositive = require( './fixtures/cpp/small_positive.json' ); +var smallNegative = require( './fixtures/cpp/small_negative.json' ); + + +// TESTS // + +tape( 'main export is a function', opts, function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof gamma1pm1, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function computes `gamma(x+1) - 1` for most `x` (negative)', opts, function test( t ) { + var expected; + var val; + var x; + var y; + var i; + x = incrspace( -170.5, -0.5, 0.5 ); + for ( i = 0; i < x.length; i++ ) { + // Add 0.1, as the gamma function is not defined for negative integers: + val = x[ i ] + 0.1; + y = gamma1pm1( val ); + expected = gamma( val+1.0 ) - 1.0; + t.equal( y, expected, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function computes `gamma(x+1) - 1` for most `x` (positive)', opts, function test( t ) { + var expected; + var val; + var x; + var y; + var i; + x = incrspace( 2.0, 170.5, 0.5 ); + for ( i = 0; i < x.length; i++ ) { + val = x[ i ]; + y = gamma1pm1( val ); + expected = gamma( val+1.0 ) - 1.0; + t.equal( y, expected, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function accurately computes `gamma(x+1) - 1` for small negative numbers', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var v; + var i; + + x = smallNegative.x; + expected = smallNegative.expected; + + for ( i = 0; i < x.length; i++ ) { + v = gamma1pm1( x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = 5.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. E: ' + expected[ i ] + '. Δ: ' + delta + '. tol: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function accurately computes `gamma(x+1) - 1` for small positive numbers', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var v; + var i; + + x = smallPositive.x; + expected = smallPositive.expected; + + for ( i = 0; i < x.length; i++ ) { + v = gamma1pm1( x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = 2.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. E: ' + expected[ i ] + '. Δ: ' + delta + '. tol: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function returns `NaN` if provided `NaN`', opts, function test( t ) { + var val = gamma1pm1( NaN ); + t.equal( isnan( val ), true, 'equals expected value' ); + t.end(); +});