diff --git a/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/README.md b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/README.md index c3008750cae0..09067c724e75 100644 --- a/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/README.md +++ b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/README.md @@ -74,6 +74,99 @@ for ( i = 0; i < 100; i++ ) { + + +* * * + +
+ +## C APIs + + + +
+ +
+ + + + + +
+ +### Usage + +```c +#include "stdlib/math/base/special/gamma_delta_ratio.h" +``` + +#### stdlib_base_gamma_delta_ratio( z, delta ) + +Computes the ratio of two [gamma functions][@stdlib/math/base/special/gamma]. Specifically, the function evaluates `Γ( z ) / Γ( z + delta )`. + +```c +double out = stdlib_base_gamma_delta_ratio( 2.0, 3.0 ); +// returns ~0.042 + +out = stdlib_base_gamma_delta_ratio( 4.0, 0.5 ); +// returns ~0.516 +``` + +The function accepts the following arguments: + +- **z**: `[in] double` first gamma parameter. +- **delta**: `[in] double` difference. + +```c +double stdlib_base_gamma_delta_ratio( const double z, const double delta ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +### Examples + +```c +#include "stdlib/math/base/special/gamma_delta_ratio.h" +#include +#include + +int main( void ) { + double delta; + double out; + double z; + int i; + + for ( i = 0; i < 100; i++ ) { + z = (double)rand() * 10.0; + delta = (double)rand() * 10.0; + out = stdlib_base_gamma_delta_ratio( z, delta ); + printf( "gamma_delta_ratio(%lf, %lf) = %lf\n", z, delta, out ); + } +} +``` + +
+ + + +
+ + +
diff --git a/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/benchmark/benchmark.native.js b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/benchmark/benchmark.native.js new file mode 100644 index 000000000000..6703f762560c --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/benchmark/benchmark.native.js @@ -0,0 +1,86 @@ +/** +* @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 gamma = require( '@stdlib/math/base/special/gamma' ); +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 gammaDeltaRatio = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( gammaDeltaRatio instanceof Error ) +}; + + +// MAIN // + +bench( pkg+'::native', opts, function benchmark( b ) { + var delta; + var z; + var y; + var i; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + z = randu() * 100.0; + delta = randu() * 100.0; + y = gammaDeltaRatio( z, delta ); + 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(); +}); + +bench( pkg+'::native,naive', function benchmark( b ) { + var delta; + var z; + var y; + var i; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + z = randu() * 100.0; + delta = randu() * 100.0; + y = gamma( z ) / gamma( z + delta ); + 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-delta-ratio/benchmark/c/native/Makefile b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/benchmark/c/native/Makefile new file mode 100644 index 000000000000..f69e9da2b4d3 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/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-delta-ratio/benchmark/c/native/benchmark.c b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/benchmark/c/native/benchmark.c new file mode 100644 index 000000000000..4c81cb403735 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/benchmark/c/native/benchmark.c @@ -0,0 +1,135 @@ +/** +* @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_delta_ratio.h" +#include +#include +#include +#include +#include + +#define NAME "gamma-delta-ratio" +#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 delta; + double z; + double y; + double t; + int i; + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + z = ( rand_double() * 100.0 ); + delta = ( rand_double() * 100.0 ); + y = stdlib_base_gamma_delta_ratio( z, delta ); + 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-delta-ratio/binding.gyp b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/binding.gyp new file mode 100644 index 000000000000..ec3992233442 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/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-delta-ratio/examples/c/Makefile b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/examples/c/Makefile new file mode 100644 index 000000000000..6aed70daf167 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/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-delta-ratio/examples/c/example.c b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/examples/c/example.c new file mode 100644 index 000000000000..22994cb75645 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/examples/c/example.c @@ -0,0 +1,35 @@ +/** +* @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_delta_ratio.h" +#include +#include + +int main( void ) { + double delta; + double out; + double z; + int i; + + for ( i = 0; i < 100; i++ ) { + z = (double)rand() * 10.0; + delta = (double)rand() * 10.0; + out = stdlib_base_gamma_delta_ratio( z, delta ); + printf( "gamma_delta_ratio(%lf, %lf) = %lf\n", z, delta, out ); + } +} diff --git a/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/include.gypi b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/include.gypi new file mode 100644 index 000000000000..575cb043c0bf --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/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': [ + ' MAX_FACTORIAL ) { + if ( delta >= MAX_FACTORIAL ) { ratio = gammaDeltaRatioLanczos( delta, MAX_FACTORIAL-delta ); ratio *= z; ratio *= FACTORIAL_169; @@ -90,8 +90,8 @@ function gammaDeltaRatioLanczos( z, delta ) { } zgh = z + G - 0.5; if ( z + delta === z ) { - if ( abs(delta) < 10.0 ) { - result = exp( ( 0.5-z ) * log1p( delta/zgh ) ); + if ( abs( delta / zgh ) < EPSILON ) { + result = exp( -delta ); } else { result = 1.0; } diff --git a/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/lib/main.js b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/lib/main.js index 723a282271b5..37231b911aa0 100644 --- a/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/lib/main.js +++ b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/lib/main.js @@ -18,7 +18,7 @@ * * ## Notice * -* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_64_0/boost/math/special_functions/gamma.hpp}. The implementation has been modified for JavaScript. +* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_85_0/boost/math/special_functions/gamma.hpp}. The implementation has been modified for JavaScript. * * ```text * Copyright John Maddock 2006-7, 2013-14. @@ -40,14 +40,10 @@ var abs = require( '@stdlib/math/base/special/abs' ); var floor = require( '@stdlib/math/base/special/floor' ); var gamma = require( '@stdlib/math/base/special/gamma' ); var factorial = require( '@stdlib/math/base/special/factorial' ); +var MAX_FACTORIAL = require( '@stdlib/constants/float64/max-safe-nth-factorial' ); var gammaDeltaRatioLanczos = require( './gamma_delta_ratio_lanczos.js' ); -// VARIABLES // - -var MAX_FACTORIAL = 170; // TODO: consider moving to pkg - - // MAIN // /** diff --git a/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/lib/native.js b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/lib/native.js new file mode 100644 index 000000000000..def362108cb6 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/lib/native.js @@ -0,0 +1,55 @@ +/** +* @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 addon = require( './../src/addon.node' ); + + +// MAIN // + +/** +* Computes the ratio of two gamma functions. +* +* @private +* @param {number} z - first gamma parameter +* @param {number} delta - difference +* @returns {number} gamma ratio +* +* @example +* var y = gammaDeltaRatio( 2.0, 3.0 ); +* // returns ~0.042 +* +* @example +* var y = gammaDeltaRatio( 4.0, 0.5 ); +* // returns ~0.516 +* +* @example +* var y = gammaDeltaRatio( 100.0, 0.0 ); +* // returns 1.0 +*/ +function gammaDeltaRatio( z, delta ) { + return addon( z, delta ); +} + + +// EXPORTS // + +module.exports = gammaDeltaRatio; diff --git a/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/manifest.json b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/manifest.json new file mode 100644 index 000000000000..43ce4c187cd7 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/manifest.json @@ -0,0 +1,105 @@ +{ + "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/math/base/napi/binary", + "@stdlib/math/base/special/abs", + "@stdlib/math/base/special/floor", + "@stdlib/math/base/special/gamma", + "@stdlib/math/base/special/factorial", + "@stdlib/math/base/special/gamma-lanczos-sum", + "@stdlib/math/base/special/log1p", + "@stdlib/math/base/special/exp", + "@stdlib/math/base/special/pow", + "@stdlib/constants/float64/max-safe-nth-factorial", + "@stdlib/constants/float64/eps", + "@stdlib/constants/float64/e", + "@stdlib/constants/float64/gamma-lanczos-g" + ] + }, + { + "task": "benchmark", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/math/base/special/abs", + "@stdlib/math/base/special/floor", + "@stdlib/math/base/special/gamma", + "@stdlib/math/base/special/factorial", + "@stdlib/math/base/special/gamma-lanczos-sum", + "@stdlib/math/base/special/log1p", + "@stdlib/math/base/special/exp", + "@stdlib/math/base/special/pow", + "@stdlib/constants/float64/max-safe-nth-factorial", + "@stdlib/constants/float64/eps", + "@stdlib/constants/float64/e", + "@stdlib/constants/float64/gamma-lanczos-g" + ] + }, + { + "task": "examples", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/math/base/special/abs", + "@stdlib/math/base/special/floor", + "@stdlib/math/base/special/gamma", + "@stdlib/math/base/special/factorial", + "@stdlib/math/base/special/gamma-lanczos-sum", + "@stdlib/math/base/special/log1p", + "@stdlib/math/base/special/exp", + "@stdlib/math/base/special/pow", + "@stdlib/constants/float64/max-safe-nth-factorial", + "@stdlib/constants/float64/eps", + "@stdlib/constants/float64/e", + "@stdlib/constants/float64/gamma-lanczos-g" + ] + } + ] +} diff --git a/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/src/Makefile b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/src/Makefile new file mode 100644 index 000000000000..bcf18aa46655 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/src/Makefile @@ -0,0 +1,70 @@ +#/ +# @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 + + +# 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/gamma-delta-ratio/src/addon.c b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/src/addon.c new file mode 100644 index 000000000000..5f0e258d20da --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/src/addon.c @@ -0,0 +1,23 @@ +/** +* @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_delta_ratio.h" +#include "stdlib/math/base/napi/binary.h" + +// cppcheck-suppress shadowFunction +STDLIB_MATH_BASE_NAPI_MODULE_DD_D( stdlib_base_gamma_delta_ratio ) diff --git a/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/src/main.c b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/src/main.c new file mode 100644 index 000000000000..6b3ecd5e6b43 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/src/main.c @@ -0,0 +1,171 @@ +/** +* @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. +* +* +* ## Notice +* +* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_85_0/boost/math/special_functions/gamma.hpp}. The implementation has been modified for use in stdlib. +* +* ```text +* Copyright John Maddock 2006-7, 2013-14. +* Copyright Paul A. Bristow 2007, 2013-14. +* Copyright Nikhar Agrawal 2013-14. +* Copyright Christopher Kormanyos 2013-14. +* +* Use, modification and distribution are subject to the +* Boost Software License, Version 1.0. (See accompanying file +* LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt) +* ``` +*/ + +#include "stdlib/math/base/special/gamma_delta_ratio.h" +#include "stdlib/math/base/special/abs.h" +#include "stdlib/math/base/special/floor.h" +#include "stdlib/math/base/special/gamma.h" +#include "stdlib/math/base/special/factorial.h" +#include "stdlib/constants/float64/max_safe_nth_factorial.h" +#include "stdlib/math/base/special/gamma_lanczos_sum.h" +#include "stdlib/math/base/special/log1p.h" +#include "stdlib/math/base/special/exp.h" +#include "stdlib/math/base/special/pow.h" +#include "stdlib/constants/float64/eps.h" +#include "stdlib/constants/float64/e.h" +#include "stdlib/constants/float64/gamma_lanczos_g.h" + +static const double FACTORIAL_169 = 4.269068009004705e+304; + +/** +* Calculates the ratio of two gamma functions via Lanczos approximation. +* +* ## Notes +* +* - When \\( z < \epsilon \\), we get spurious numeric overflow unless we're very careful. This can occur either inside `lanczosSum(z)` or in the final combination of terms. To avoid this, split the product up into 2 (or 3) parts: +* +* ```tex +* \begin{align*} +* G(z) / G(L) &= 1 / (z \cdot G(L)) ; z < \eps, L = z + \delta = \delta \\ +* z * G(L) &= z * G(lim) \cdot (G(L)/G(lim)) ; lim = \text{largest factorial} +* \end{align*} +* ``` +* +* @param z first gamma parameter +* @param delta difference +* @returns gamma ratio +*/ +static double gammaDeltaRatioLanczos( const double z, const double delta ) { + double result; + double ratio; + double zgh; + + if ( z < STDLIB_CONSTANT_FLOAT64_EPS ) { + if ( delta >= STDLIB_CONSTANT_FLOAT64_MAX_SAFE_NTH_FACTORIAL ) { + ratio = gammaDeltaRatioLanczos( delta, STDLIB_CONSTANT_FLOAT64_MAX_SAFE_NTH_FACTORIAL - delta ); + ratio *= z; + ratio *= FACTORIAL_169; + return 1.0 / ratio; + } + return 1.0 / ( z * stdlib_base_gamma( z + delta ) ); + } + zgh = z + STDLIB_CONSTANT_FLOAT64_GAMMA_LANCZOS_G - 0.5; + if ( z + delta == z ) { + if ( stdlib_base_abs( delta / zgh ) < STDLIB_CONSTANT_FLOAT64_EPS ) { + result = stdlib_base_exp( -delta ); + } else { + result = 1.0; + } + } else { + if ( stdlib_base_abs( delta ) < 10.0 ) { + result = stdlib_base_exp( ( 0.5 - z ) * stdlib_base_log1p( delta / zgh ) ); + } else { + result = stdlib_base_pow( zgh / ( zgh + delta ), z - 0.5 ); + } + // Split up the calculation to avoid spurious overflow: + result *= stdlib_base_gamma_lanczos_sum( z ) / stdlib_base_gamma_lanczos_sum( z + delta ); + } + result *= stdlib_base_pow( STDLIB_CONSTANT_FLOAT64_E / ( zgh + delta ), delta ); + return result; +} + +/** +* Computes the ratio of two gamma functions. +* +* ## Notes +* +* - Specifically, the function evaluates +* +* ```tex +* \frac{ \Gamma( z ) }{ \Gamma( z + \delta ) } +* ``` +* +* @param z first gamma parameter +* @param delta difference +* @return gamma ratio +* +* @example +* double out = stdlib_base_gamma_delta_ratio( 2.0, 3.0 ); +* // returns ~0.042 +*/ +double stdlib_base_gamma_delta_ratio( const double z, const double delta ) { + double deltac; + double result; + double idelta; + double zc; + double iz; + + if ( z <= 0.0 || z + delta <= 0.0 ) { + // This isn't very sophisticated, or accurate, but it does work: + return stdlib_base_gamma( z ) / stdlib_base_gamma( z + delta ); + } + idelta = stdlib_base_floor( delta ); + if ( idelta == delta ) { + iz = stdlib_base_floor( z ); + if ( iz == z ) { + // As both `z` and `delta` are integers, see if we can use a table lookup: + if ( z <= STDLIB_CONSTANT_FLOAT64_MAX_SAFE_NTH_FACTORIAL && ( z + delta <= STDLIB_CONSTANT_FLOAT64_MAX_SAFE_NTH_FACTORIAL ) ) { + return stdlib_base_factorial( iz - 1.0 ) / stdlib_base_factorial( idelta + iz - 1.0 ); + } + } + if ( stdlib_base_abs( delta ) < 20.0 ) { + // As `delta` is a small integer, we can use a finite product: + if ( delta == 0.0 ) { + return 1.0; + } + zc = z; + deltac = delta; + if ( deltac < 0.0 ) { + zc -= 1.0; + result = zc; + deltac += 1.0; + while ( deltac != 0.0 ) { + zc -= 1.0; + result *= zc; + deltac += 1.0; + } + return result; + } + result = 1.0 / zc; + deltac -= 1.0; + while ( deltac != 0.0 ) { + zc += 1.0; + result /= zc; + deltac -= 1.0; + } + return result; + } + } + return gammaDeltaRatioLanczos( z, delta ); +} diff --git a/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/test/test.js b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/test/test.js index b3b7be5c0b0d..3b054292646d 100644 --- a/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/test/test.js +++ b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/test/test.js @@ -87,7 +87,7 @@ tape( 'the function evaluates the ratio of two gamma functions (decimals)', func for ( i = 0; i < z.length; i++ ) { v = gammaDeltaRatio( z[ i ], diff[ i ] ); delta = abs( v - expected[ i ] ); - tol = 350.0 * EPS * abs( expected[ i ] ); + tol = 337.0 * EPS * abs( expected[ i ] ); t.ok( delta <= tol, 'within tolerance. z: '+z[i]+'. delta: '+diff[i]+'. v: '+v+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol ); } t.end(); @@ -108,7 +108,7 @@ tape( 'the function evaluates the ratio of two gamma functions (small integers)' for ( i = 0; i < z.length; i++ ) { v = gammaDeltaRatio( z[ i ], diff[ i ] ); delta = abs( v - expected[ i ] ); - tol = 10.0 * EPS * abs( expected[ i ] ); + tol = 1.1 * EPS * abs( expected[ i ] ); t.ok( delta <= tol, 'within tolerance. z: '+z[i]+'. delta: '+diff[i]+'. v: '+v+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol ); } t.end(); @@ -129,7 +129,7 @@ tape( 'the function evaluates the ratio of two gamma functions (large integers)' for ( i = 0; i < z.length; i++ ) { v = gammaDeltaRatio( z[ i ], diff[ i ] ); delta = abs( v - expected[ i ] ); - tol = 150.0 * EPS * abs( expected[ i ] ); + tol = 129.0 * EPS * abs( expected[ i ] ); t.ok( delta <= tol, 'within tolerance. z: '+z[i]+'. delta: '+diff[i]+'. v: '+v+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol ); } t.end(); @@ -150,7 +150,7 @@ tape( 'the function evaluates the ratio of two gamma functions (non-integer `z`, for ( i = 0; i < z.length; i++ ) { v = gammaDeltaRatio( z[ i ], diff[ i ] ); delta = abs( v - expected[ i ] ); - tol = 150.0 * EPS * abs( expected[ i ] ); + tol = 129.0 * EPS * abs( expected[ i ] ); t.ok( delta <= tol, 'within tolerance. z: '+z[i]+'. delta: '+diff[i]+'. v: '+v+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol ); } t.end(); @@ -171,7 +171,7 @@ tape( 'the function evaluates the ratio of two gamma functions (tiny `z`, large for ( i = 0; i < z.length; i++ ) { v = gammaDeltaRatio( z[ i ], diff[ i ] ); delta = abs( v - expected[ i ] ); - tol = 100.0 * EPS * abs( expected[ i ] ); + tol = 3.3 * EPS * abs( expected[ i ] ); // Handle cases where either the expected value is zero or `v` is zero and the expected value is very small... if ( tol < 1.0e-300 ) { diff --git a/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/test/test.native.js new file mode 100644 index 000000000000..ab2dceadfb87 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/test/test.native.js @@ -0,0 +1,213 @@ +/** +* @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 abs = require( '@stdlib/math/base/special/abs' ); +var EPS = require( '@stdlib/constants/float64/eps' ); +var tryRequire = require( '@stdlib/utils/try-require' ); + + +// VARIABLES // + +var gammaDeltaRatio = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( gammaDeltaRatio instanceof Error ) +}; + + +// FIXTURES // + +var decimalsIntegers = require( './fixtures/cpp/decimals_integers.json' ); +var largeIntegers = require( './fixtures/cpp/large_integers.json' ); +var smallIntegers = require( './fixtures/cpp/small_integers.json' ); +var largeTiny = require( './fixtures/cpp/large_tiny.json' ); +var tinyLarge = require( './fixtures/cpp/tiny_large.json' ); +var decimals = require( './fixtures/cpp/decimals.json' ); + + +// TESTS // + +tape( 'main export is a function', opts, function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof gammaDeltaRatio, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function returns `NaN` if provided `NaN` for either parameter', opts, function test( t ) { + var v; + + v = gammaDeltaRatio( NaN, 5.0 ); + t.equal( isnan( v ), true, 'returns expected value' ); + + v = gammaDeltaRatio( 1.0, NaN ); + t.equal( isnan( v ), true, 'returns expected value' ); + + v = gammaDeltaRatio( NaN, NaN ); + t.equal( isnan( v ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns `0` for very large `z` and negligible `delta`', opts, function test( t ) { + var v; + + v = gammaDeltaRatio( 1.0e100, 20.7 ); + t.equal( v, 0.0, 'returns 0' ); + + v = gammaDeltaRatio( 1.0e120, 100.1 ); + t.equal( v, 0.0, 'returns 0' ); + + t.end(); +}); + +tape( 'the function evaluates the ratio of two gamma functions (decimals)', opts, function test( t ) { + var expected; + var delta; + var diff; + var tol; + var v; + var i; + var z; + + z = decimals.z; + diff = decimals.delta; + expected = decimals.expected; + for ( i = 0; i < z.length; i++ ) { + v = gammaDeltaRatio( z[ i ], diff[ i ] ); + delta = abs( v - expected[ i ] ); + tol = 337.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. z: '+z[i]+'. delta: '+diff[i]+'. v: '+v+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol ); + } + t.end(); +}); + +tape( 'the function evaluates the ratio of two gamma functions (small integers)', opts, function test( t ) { + var expected; + var delta; + var diff; + var tol; + var v; + var i; + var z; + + z = smallIntegers.z; + diff = smallIntegers.delta; + expected = smallIntegers.expected; + for ( i = 0; i < z.length; i++ ) { + v = gammaDeltaRatio( z[ i ], diff[ i ] ); + delta = abs( v - expected[ i ] ); + tol = 1.1 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. z: '+z[i]+'. delta: '+diff[i]+'. v: '+v+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol ); + } + t.end(); +}); + +tape( 'the function evaluates the ratio of two gamma functions (large integers)', opts, function test( t ) { + var expected; + var delta; + var diff; + var tol; + var v; + var i; + var z; + + z = largeIntegers.z; + diff = largeIntegers.delta; + expected = largeIntegers.expected; + for ( i = 0; i < z.length; i++ ) { + v = gammaDeltaRatio( z[ i ], diff[ i ] ); + delta = abs( v - expected[ i ] ); + tol = 129.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. z: '+z[i]+'. delta: '+diff[i]+'. v: '+v+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol ); + } + t.end(); +}); + +tape( 'the function evaluates the ratio of two gamma functions (non-integer `z`, integer `delta`)', opts, function test( t ) { + var expected; + var delta; + var diff; + var tol; + var v; + var i; + var z; + + z = decimalsIntegers.z; + diff = decimalsIntegers.delta; + expected = decimalsIntegers.expected; + for ( i = 0; i < z.length; i++ ) { + v = gammaDeltaRatio( z[ i ], diff[ i ] ); + delta = abs( v - expected[ i ] ); + tol = 129.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. z: '+z[i]+'. delta: '+diff[i]+'. v: '+v+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol ); + } + t.end(); +}); + +tape( 'the function evaluates the ratio of two gamma functions (tiny `z`, large `delta`)', opts, function test( t ) { + var expected; + var delta; + var diff; + var tol; + var v; + var i; + var z; + + z = tinyLarge.z; + diff = tinyLarge.delta; + expected = tinyLarge.expected; + for ( i = 0; i < z.length; i++ ) { + v = gammaDeltaRatio( z[ i ], diff[ i ] ); + delta = abs( v - expected[ i ] ); + tol = 3.3 * EPS * abs( expected[ i ] ); + + // Handle cases where either the expected value is zero or `v` is zero and the expected value is very small... + if ( tol < 1.0e-300 ) { + tol = 1.0e-300; + } + t.ok( delta <= tol, 'within tolerance. z: '+z[i]+'. delta: '+diff[i]+'. v: '+v+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol ); + } + t.end(); +}); + +tape( 'the function evaluates the ratio of two gamma functions (large `z`, tiny `delta`)', opts, function test( t ) { + var expected; + var delta; + var diff; + var tol; + var v; + var i; + var z; + + z = largeTiny.z; + diff = largeTiny.delta; + expected = largeTiny.expected; + for ( i = 0; i < z.length; i++ ) { + v = gammaDeltaRatio( z[ i ], diff[ i ] ); + delta = abs( v - expected[ i ] ); + tol = 1.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. z: '+z[i]+'. delta: '+diff[i]+'. v: '+v+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol ); + } + t.end(); +});