diff --git a/lib/node_modules/@stdlib/math/base/special/betaln/README.md b/lib/node_modules/@stdlib/math/base/special/betaln/README.md index 031693313a9..6ea15f960c5 100644 --- a/lib/node_modules/@stdlib/math/base/special/betaln/README.md +++ b/lib/node_modules/@stdlib/math/base/special/betaln/README.md @@ -113,6 +113,93 @@ for ( x = 0; x < 10; x++ ) { + + +* * * + +
+ +## C APIs + + + +
+ +
+ + + + + +
+ +### Usage + +```c +#include "stdlib/math/base/special/betaln.h" +``` + +#### stdlib_base_betaln( x, y ) + +Evaluates the the [natural logarithm][natural-logarithm] of the [beta function][beta-function]. + +```c +double v = stdlib_base_betaln( 5.0, 0.2 ); +// returns ~1.218 +``` + +The function accepts the following arguments: + +- **x**: `[in] double` input value. +- **y**: `[in] double` input value. + +```c +double stdlib_base_betaln( const double x, const double y ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +### Examples + +```c +#include "stdlib/math/base/special/betaln.h" +#include + +int main( void ) { + const double x[] = { 24.0, 32.0, 48.0, 116.0, 33.0 }; + const double y[] = { 12.0, 6.0, 15.0, 52.0, 22.0 }; + + double out; + int i; + for ( i = 0; i < 5; i++ ) { + out = stdlib_base_betaln( x[ i ], y[ i ] ); + printf( "betaln(%lf, %lf) = %lf\n", x[ i ], y[ i ], out ); + } +} +``` + +
+ + + +
+ + +
diff --git a/lib/node_modules/@stdlib/math/base/special/betaln/benchmark/benchmark.native.js b/lib/node_modules/@stdlib/math/base/special/betaln/benchmark/benchmark.native.js new file mode 100644 index 00000000000..6f7e5ff5af4 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/betaln/benchmark/benchmark.native.js @@ -0,0 +1,62 @@ +/** +* @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 betaln = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( betaln instanceof Error ) +}; + + +// MAIN // + +bench( pkg+'::native', opts, function benchmark( b ) { + var x; + var y; + var z; + var i; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + x = ( randu() * 1000.0 ) - 0.0; + y = ( randu() * 1000.0 ) - 0.0; + z = betaln( x, y ); + if ( isnan( z ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( z ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); diff --git a/lib/node_modules/@stdlib/math/base/special/betaln/benchmark/c/native/Makefile b/lib/node_modules/@stdlib/math/base/special/betaln/benchmark/c/native/Makefile new file mode 100644 index 00000000000..f69e9da2b4d --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/betaln/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/betaln/benchmark/c/native/benchmark.c b/lib/node_modules/@stdlib/math/base/special/betaln/benchmark/c/native/benchmark.c new file mode 100644 index 00000000000..a35f36466b0 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/betaln/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/betaln.h" +#include +#include +#include +#include +#include + +#define NAME "betaln" +#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 z; + double t; + int i; + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + x = 1000.0 * rand_double() - 0.0; + y = 1000.0 * rand_double() - 0.0; + z = stdlib_base_betaln( x, y ); + if ( z != z ) { + printf( "should not return NaN\n" ); + break; + } + } + elapsed = tic() - t; + if ( z != z ) { + 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/betaln/binding.gyp b/lib/node_modules/@stdlib/math/base/special/betaln/binding.gyp new file mode 100644 index 00000000000..ec399223344 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/betaln/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/betaln/examples/c/Makefile b/lib/node_modules/@stdlib/math/base/special/betaln/examples/c/Makefile new file mode 100644 index 00000000000..6aed70daf16 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/betaln/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/betaln/examples/c/example.c b/lib/node_modules/@stdlib/math/base/special/betaln/examples/c/example.c new file mode 100644 index 00000000000..4f5e87282a1 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/betaln/examples/c/example.c @@ -0,0 +1,32 @@ +/** +* @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/betaln.h" +#include + +int main( void ) { + const double x[] = { 24.0, 32.0, 48.0, 116.0, 33.0 }; + const double y[] = { 12.0, 6.0, 15.0, 52.0, 22.0 }; + + double out; + int i; + for ( i = 0; i < 5; i++ ) { + out = stdlib_base_betaln( x[ i ], y[ i ] ); + printf( "betaln(%lf, %lf) = %lf\n", x[ i ], y[ i ], out ); + } +} diff --git a/lib/node_modules/@stdlib/math/base/special/betaln/include.gypi b/lib/node_modules/@stdlib/math/base/special/betaln/include.gypi new file mode 100644 index 00000000000..575cb043c0b --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/betaln/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 ALGMCS[ 15 ] = { + +0.1276642195630062933333333333333e-30, + -0.3401102254316748799999999999999e-29, + +0.1025680058010470912000000000000e-27, + -0.3547598158101070547199999999999e-26, + +0.1429227355942498147573333333333e-24, + -0.6831888753985766870111999999999e-23, + +0.3962837061046434803679306666666e-21, + -0.2868042435334643284144622399999e-19, + +0.2683181998482698748957538846666e-17, + -0.3399615005417721944303330599666e-15, + +0.6221098041892605227126015543416e-13, + -0.1809129475572494194263306266719e-10, + +0.9810825646924729426157171547487e-8, + -0.1384948176067563840732986059135e-4, + +0.1666389480451863247205729650822e+0 +}; +static const int32_t LEN = 15; +static const double XBIG = 94906265.62425156; +static const double XMAX = 3.745194030963158e306; + +/** +* Evaluate the n-term Chebyshev series at `x`. +* +* ## References +* +* - Broucke, Roger. 1973. "Algorithm: Ten Subroutines for the Manipulation of Chebyshev Series." _Communications of the ACM_ 16 (4). New York, NY, USA: ACM: 254–56. doi:[10.1145/362003.362037](https://doi.org/10.1145/362003.362037). +* - Fox, Leslie, and Ian Bax Parker. 1968. _Chebyshev polynomials in numerical analysis_. Oxford Mathematical Handbooks. London, United Kingdom: Oxford University Press. . +* +* @param x value at which the series is to be evaluated +* @returns series value +*/ +static double dceval( const double x ) { + double twox; + double b2; + double b1; + double b0; + int32_t i; + + if ( x < -1.1 || x > 1.1 ) { + return 0.0 / 0.0; // NaN + } + b1 = 0.0; + b0 = 0.0; + twox = 2.0 * x; + for ( i = 0; i < LEN; i++ ) { + b2 = b1; + b1 = b0; + b0 = ( twox * b1 ) - b2 + ALGMCS[ i ]; + } + return ( b0 - b2 ) * 0.5; +} + +/** +* Compute the log gamma correction factor for `x >= 10`. +* +* ```tex +* \log(\gamma(x)) = \log(\sqrt{2*\Pi}) + (x-0.5) \cdot \log(x) - x \operatorname{R9LGMC}(x). +* ``` +* +* @param x input value +* @return correction value +*/ +static double gammaCorrection( const double x ) { + if ( x < 10.0 ) { + return 0.0 / 0.0; // NaN + } + + // Check for underflow... + if ( x >= XMAX ) { + return 0.0; + } + if ( x < XBIG ) { + return dceval( ( 2.0 * stdlib_base_pow( 10.0 / x, 2.0 ) ) - 1.0 ) / x; + } + return 1.0 / ( x * 12.0 ); +} + +/** +* Evaluate the natural logarithm of the beta function. +* +* @param a first input value +* @param b second input value +* @returns natural logarithm of beta function +* +* @example +* double out = stdlib_base_betaln( 5.0, 0.2 ); +* // returns ~1.218 +*/ +double stdlib_base_betaln( const double a, const double b ) { + double corr; + double p; + double q; + + p = stdlib_base_min( a, b ); + q = stdlib_base_max( a, b ); + + if ( p < 0.0 ) { + return 0.0 / 0.0; // NaN + } + if ( p == 0.0 ) { + return STDLIB_CONSTANT_FLOAT64_PINF; + } + if ( q == STDLIB_CONSTANT_FLOAT64_PINF ) { + return STDLIB_CONSTANT_FLOAT64_NINF; + } + + // Case: p and q are big + if ( p >= 10.0 ) { + corr = gammaCorrection( p ) + gammaCorrection( q ) - gammaCorrection( p + q ); + return ( -0.5 * stdlib_base_ln( q ) ) + STDLIB_CONSTANT_FLOAT64_LN_SQRT_TWO_PI + corr + ( ( p - 0.5 ) * stdlib_base_ln( p / ( p + q ) ) ) + ( q * stdlib_base_log1p( -p / ( p + q ) ) ); + } + + // Case: p is small, but q is big + if ( q >= 10.0 ) { + corr = gammaCorrection( q ) - gammaCorrection( p + q ); + return stdlib_base_gammaln( p ) + corr + p - ( p * stdlib_base_ln( p + q ) ) + ( ( q - 0.5 ) * stdlib_base_log1p( -p / ( p + q ) ) ); + } + + // Case: p and q are small + return stdlib_base_ln( stdlib_base_gamma( p ) * ( stdlib_base_gamma( q ) / stdlib_base_gamma( p + q ) ) ); +} diff --git a/lib/node_modules/@stdlib/math/base/special/betaln/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/betaln/test/test.native.js new file mode 100644 index 00000000000..f7816081456 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/betaln/test/test.native.js @@ -0,0 +1,114 @@ +/** +* @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 isInfinite = require( '@stdlib/math/base/assert/is-infinite' ); +var isnan = require( '@stdlib/assert/is-nan' ); +var PINF = require( '@stdlib/constants/float64/pinf' ); +var EPS = require( '@stdlib/constants/float64/eps' ); +var tryRequire = require( '@stdlib/utils/try-require' ); +var abs = require( '@stdlib/math/base/special/abs' ); + + +// VARIABLES // + +var betaln = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( betaln instanceof Error ) +}; + + +// FIXTURES // + +var arg1 = require( './fixtures/r/arg1.json' ); +var arg2 = require( './fixtures/r/arg2.json' ); +var expected = require( './fixtures/r/expected.json' ); +var i; +var v; +for ( i = 0; i < expected.length; i++ ) { + v = expected[ i ]; + if ( v === 'Inf' ) { + expected[ i ] = PINF; + } + else if ( v === 'NaN' ) { + expected[ i ] = NaN; + } +} + + +// TESTS // + +tape( 'main export is a function', opts, function test( t ) { + t.ok( true, __filename ); + t.ok( typeof betaln === 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function returns `NaN` if provided a `NaN`', opts, function test( t ) { + var val = betaln( NaN, 2.0 ); + t.ok( isnan( val ), 'returns expected value' ); + val = betaln( 2.0, NaN ); + t.ok( isnan( val ), 'returns expected value' ); + t.end(); +}); + +tape( 'the function returns `NaN` if provided negative values', opts, function test( t ) { + var val = betaln( -2.0, 5.0 ); + t.ok( isnan( val ), 'returns expected value' ); + val = betaln( 4.0, -3.0 ); + t.ok( isnan( val ), 'returns expected value' ); + t.end(); +}); + +tape( 'the function returns +Infinity if at least one argument is zero', opts, function test( t ) { + var val = betaln( 0.0, 2.0 ); + t.equal( val, PINF, 'returns +Infinity' ); + val = betaln( 1.0, 0.0 ); + t.equal( val, PINF, 'returns +Infinity' ); + t.end(); +}); + +tape( 'the function evaluates the natural logarithm of the beta function', opts, function test( t ) { + var actual; + var delta; + var tol; + var b1; + var b2; + var i; + for ( i = 0; i < arg1.length; i++ ) { + actual = betaln( arg1[ i ], arg2[ i ] ); + b1 = isInfinite( actual ); + b2 = isInfinite( expected[ i ] ); + t.equal( b1, b2, 'returned result is ' + ( (b2) ? 'not finite' : 'finite' ) ); + + b1 = isnan( actual ); + b2 = isnan( expected[ i ] ); + t.equal( b1, b2, 'returned result is ' + ( (b1) ? '' : 'not' ) + ' NaN' ); + if ( !b1 ) { + delta = abs( actual - expected[ i ] ); + tol = 2.0 * EPS * abs( expected[ i ] ); + t.equal( delta <= tol, true, 'returned result is within tolerance. actual: ' + actual + '; expected: ' + expected[ i ] + '.' ); + } + } + t.end(); +});