diff --git a/lib/node_modules/@stdlib/math/base/special/erfinv/README.md b/lib/node_modules/@stdlib/math/base/special/erfinv/README.md index 2b3c8d74824a..9bb8c83c75a9 100644 --- a/lib/node_modules/@stdlib/math/base/special/erfinv/README.md +++ b/lib/node_modules/@stdlib/math/base/special/erfinv/README.md @@ -123,6 +123,94 @@ for ( i = 0; i < x.length; i++ ) { + + +* * * + +
+ +## C APIs + + + +
+ +
+ + + + + +
+ +### Usage + +```c +#include "stdlib/math/base/special/erfinv.h" +``` + +#### stdlib_base_erfinv( x ) + +Evaluates the [inverse error function][inverse-error-function]. + +```c +double out = stdlib_base_erfinv( 0.5 ); +// returns ~0.4769 + +out = stdlib_base_erfinv( 0.8 ); +// returns ~0.9062 +``` + +The function accepts the following arguments: + +- **x**: `[in] double` input value. + +```c +double stdlib_base_erfinv( const double x ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +### Examples + +```c +#include "stdlib/math/base/special/erfinv.h" +#include +#include + +int main() { + const double x[] = { -1.0, -0.78, -0.56, -0.33, -0.11, 0.11, 0.33, 0.56, 0.78, 1.0 }; + double v; + int i; + for ( i = 0; i < 10; i++ ) { + v = stdlib_base_erfinv( x[ i ] ); + printf( "x: %lf, erfinv(x): %lf\n", x[ i ], v ); + } +} +``` + +
+ + + +
+ + +
diff --git a/lib/node_modules/@stdlib/math/base/special/erfinv/benchmark/benchmark.native.js b/lib/node_modules/@stdlib/math/base/special/erfinv/benchmark/benchmark.native.js new file mode 100644 index 000000000000..3ae4319a3278 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/erfinv/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 erfinv = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( erfinv 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()*2.0 ) - 1.0; + y = erfinv( 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/erfinv/benchmark/c/native/Makefile b/lib/node_modules/@stdlib/math/base/special/erfinv/benchmark/c/native/Makefile new file mode 100644 index 000000000000..f69e9da2b4d3 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/erfinv/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/erfinv/benchmark/c/native/benchmark.c b/lib/node_modules/@stdlib/math/base/special/erfinv/benchmark/c/native/benchmark.c new file mode 100644 index 000000000000..2b6e8921b679 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/erfinv/benchmark/c/native/benchmark.c @@ -0,0 +1,136 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +/** +* Benchmark `erfinv`. +*/ +#include "stdlib/math/base/special/erfinv.h" +#include +#include +#include +#include +#include + +#define NAME "erfinv" +#define ITERATIONS 1000000 +#define REPEATS 3 + +/** +* Prints the TAP version. +*/ +void print_version() { + printf( "TAP version 13\n" ); +} + +/** +* Prints the TAP summary. +* +* @param total total number of tests +* @param passing total number of passing tests +*/ +void print_summary( int total, int passing ) { + printf( "#\n" ); + printf( "1..%d\n", total ); // TAP plan + printf( "# total %d\n", total ); + printf( "# pass %d\n", passing ); + printf( "#\n" ); + printf( "# ok\n" ); +} + +/** +* Prints benchmarks results. +* +* @param elapsed elapsed time in seconds +*/ +void print_results( double elapsed ) { + double rate = (double)ITERATIONS / elapsed; + printf( " ---\n" ); + printf( " iterations: %d\n", ITERATIONS ); + printf( " elapsed: %0.9f\n", elapsed ); + printf( " rate: %0.9f\n", rate ); + printf( " ...\n" ); +} + +/** +* Returns a clock time. +* +* @return clock time +*/ +double tic() { + struct timeval now; + gettimeofday( &now, NULL ); + return (double)now.tv_sec + (double)now.tv_usec/1.0e6; +} + +/** +* Generates a random number on the interval [0,1]. +* +* @return random number +*/ +double rand_double() { + int r = rand(); + return (double)r / ( (double)RAND_MAX + 1.0 ); +} + +/** +* Runs a benchmark. +* +* @return elapsed time in seconds +*/ +double benchmark() { + double elapsed; + double x; + double y; + double t; + int i; + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + x = ( 2.0 * rand_double() ) - 1.0; + y = stdlib_base_erfinv( 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/erfinv/binding.gyp b/lib/node_modules/@stdlib/math/base/special/erfinv/binding.gyp new file mode 100644 index 000000000000..ec3992233442 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/erfinv/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/erfinv/examples/c/Makefile b/lib/node_modules/@stdlib/math/base/special/erfinv/examples/c/Makefile new file mode 100644 index 000000000000..6aed70daf167 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/erfinv/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/erfinv/examples/c/example.c b/lib/node_modules/@stdlib/math/base/special/erfinv/examples/c/example.c new file mode 100644 index 000000000000..8d12f525de9a --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/erfinv/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/erfinv.h" +#include +#include + +int main() { + const double x[] = { -1.0, -0.78, -0.56, -0.33, -0.11, 0.11, 0.33, 0.56, 0.78, 1.0 }; + double v; + int i; + for ( i = 0; i < 10; i++ ) { + v = stdlib_base_erfinv( x[ i ] ); + printf( "x: %lf, erfinv(x): %lf\n", x[ i ], v ); + } +} diff --git a/lib/node_modules/@stdlib/math/base/special/erfinv/include.gypi b/lib/node_modules/@stdlib/math/base/special/erfinv/include.gypi new file mode 100644 index 000000000000..575cb043c0bf --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/erfinv/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 Y1 = 8.91314744949340820313e-2; +static const double Y2 = 2.249481201171875; +static const double Y3 = 8.07220458984375e-1; +static const double Y4 = 9.3995571136474609375e-1; +static const double Y5 = 9.8362827301025390625e-1; + +/* Begin auto-generated functions. The following functions are auto-generated. Do not edit directly. */ + +// BEGIN: rational_p1q1 + +/** +* Evaluates a rational function (i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\)). +* +* ## Notes +* +* - Coefficients should be sorted in ascending degree. +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the rational function +* @return evaluated rational function +*/ +static double rational_p1q1( const double x ) { + double ax; + double ix; + double s1; + double s2; + if ( x == 0.0 ) { + return -0.0005087819496582806; + } + if ( x < 0.0 ) { + ax = -x; + } else { + ax = x; + } + if ( ax <= 1.0 ) { + s1 = -0.0005087819496582806 + (x * (-0.008368748197417368 + (x * (0.03348066254097446 + (x * (-0.012692614766297404 + (x * (-0.03656379714117627 + (x * (0.02198786811111689 + (x * (0.008226878746769157 + (x * (-0.005387729650712429 + (x * (0.0 + (x * 0.0))))))))))))))))); + s2 = 1.0 + (x * (-0.9700050433032906 + (x * (-1.5657455823417585 + (x * (1.5622155839842302 + (x * (0.662328840472003 + (x * (-0.7122890234154284 + (x * (-0.05273963823400997 + (x * (0.07952836873415717 + (x * (-0.0023339375937419 + (x * 0.0008862163904564247))))))))))))))))); + } else { + ix = 1.0 / x; + s1 = 0.0 + (ix * (0.0 + (ix * (-0.005387729650712429 + (ix * (0.008226878746769157 + (ix * (0.02198786811111689 + (ix * (-0.03656379714117627 + (ix * (-0.012692614766297404 + (ix * (0.03348066254097446 + (ix * (-0.008368748197417368 + (ix * -0.0005087819496582806))))))))))))))))); + s2 = 0.0008862163904564247 + (ix * (-0.0023339375937419 + (ix * (0.07952836873415717 + (ix * (-0.05273963823400997 + (ix * (-0.7122890234154284 + (ix * (0.662328840472003 + (ix * (1.5622155839842302 + (ix * (-1.5657455823417585 + (ix * (-0.9700050433032906 + (ix * 1.0))))))))))))))))); + } + return s1 / s2; +} + +// END: rational_p1q1 + +// BEGIN: rational_p2q2 + +/** +* Evaluates a rational function (i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\)). +* +* ## Notes +* +* - Coefficients should be sorted in ascending degree. +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the rational function +* @return evaluated rational function +*/ +static double rational_p2q2( const double x ) { + double ax; + double ix; + double s1; + double s2; + if ( x == 0.0 ) { + return -0.20243350835593876; + } + if ( x < 0.0 ) { + ax = -x; + } else { + ax = x; + } + if ( ax <= 1.0 ) { + s1 = -0.20243350835593876 + (x * (0.10526468069939171 + (x * (8.3705032834312 + (x * (17.644729840837403 + (x * (-18.851064805871424 + (x * (-44.6382324441787 + (x * (17.445385985570866 + (x * (21.12946554483405 + (x * -3.6719225470772936))))))))))))))); + s2 = 1.0 + (x * (6.242641248542475 + (x * (3.971343795334387 + (x * (-28.66081804998 + (x * (-20.14326346804852 + (x * (48.560921310873994 + (x * (10.826866735546016 + (x * (-22.643693341313973 + (x * 1.7211476576120028))))))))))))))); + } else { + ix = 1.0 / x; + s1 = -3.6719225470772936 + (ix * (21.12946554483405 + (ix * (17.445385985570866 + (ix * (-44.6382324441787 + (ix * (-18.851064805871424 + (ix * (17.644729840837403 + (ix * (8.3705032834312 + (ix * (0.10526468069939171 + (ix * -0.20243350835593876))))))))))))))); + s2 = 1.7211476576120028 + (ix * (-22.643693341313973 + (ix * (10.826866735546016 + (ix * (48.560921310873994 + (ix * (-20.14326346804852 + (ix * (-28.66081804998 + (ix * (3.971343795334387 + (ix * (6.242641248542475 + (ix * 1.0))))))))))))))); + } + return s1 / s2; +} + +// END: rational_p2q2 + +// BEGIN: rational_p3q3 + +/** +* Evaluates a rational function (i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\)). +* +* ## Notes +* +* - Coefficients should be sorted in ascending degree. +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the rational function +* @return evaluated rational function +*/ +static double rational_p3q3( const double x ) { + double ax; + double ix; + double s1; + double s2; + if ( x == 0.0 ) { + return -0.1311027816799519; + } + if ( x < 0.0 ) { + ax = -x; + } else { + ax = x; + } + if ( ax <= 1.0 ) { + s1 = -0.1311027816799519 + (x * (-0.16379404719331705 + (x * (0.11703015634199525 + (x * (0.38707973897260434 + (x * (0.3377855389120359 + (x * (0.14286953440815717 + (x * (0.029015791000532906 + (x * (0.0021455899538880526 + (x * (-6.794655751811263e-7 + (x * (2.8522533178221704e-8 + (x * -6.81149956853777e-10))))))))))))))))))); + s2 = 1.0 + (x * (3.4662540724256723 + (x * (5.381683457070069 + (x * (4.778465929458438 + (x * (2.5930192162362027 + (x * (0.848854343457902 + (x * (0.15226433829533179 + (x * (0.011059242293464892 + (x * (0.0 + (x * (0.0 + (x * 0.0))))))))))))))))))); + } else { + ix = 1.0 / x; + s1 = -6.81149956853777e-10 + (ix * (2.8522533178221704e-8 + (ix * (-6.794655751811263e-7 + (ix * (0.0021455899538880526 + (ix * (0.029015791000532906 + (ix * (0.14286953440815717 + (ix * (0.3377855389120359 + (ix * (0.38707973897260434 + (ix * (0.11703015634199525 + (ix * (-0.16379404719331705 + (ix * -0.1311027816799519))))))))))))))))))); + s2 = 0.0 + (ix * (0.0 + (ix * (0.0 + (ix * (0.011059242293464892 + (ix * (0.15226433829533179 + (ix * (0.848854343457902 + (ix * (2.5930192162362027 + (ix * (4.778465929458438 + (ix * (5.381683457070069 + (ix * (3.4662540724256723 + (ix * 1.0))))))))))))))))))); + } + return s1 / s2; +} + +// END: rational_p3q3 + +// BEGIN: rational_p4q4 + +/** +* Evaluates a rational function (i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\)). +* +* ## Notes +* +* - Coefficients should be sorted in ascending degree. +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the rational function +* @return evaluated rational function +*/ +static double rational_p4q4( const double x ) { + double ax; + double ix; + double s1; + double s2; + if ( x == 0.0 ) { + return -0.0350353787183178; + } + if ( x < 0.0 ) { + ax = -x; + } else { + ax = x; + } + if ( ax <= 1.0 ) { + s1 = -0.0350353787183178 + (x * (-0.0022242652921344794 + (x * (0.018557330651423107 + (x * (0.009508047013259196 + (x * (0.0018712349281955923 + (x * (0.00015754461742496055 + (x * (0.00000460469890584318 + (x * (-2.304047769118826e-10 + (x * 2.6633922742578204e-12))))))))))))))); + s2 = 1.0 + (x * (1.3653349817554064 + (x * (0.7620591645536234 + (x * (0.22009110576413124 + (x * (0.03415891436709477 + (x * (0.00263861676657016 + (x * (0.00007646752923027944 + (x * (0.0 + (x * 0.0))))))))))))))); + } else { + ix = 1.0 / x; + s1 = 2.6633922742578204e-12 + (ix * (-2.304047769118826e-10 + (ix * (0.00000460469890584318 + (ix * (0.00015754461742496055 + (ix * (0.0018712349281955923 + (ix * (0.009508047013259196 + (ix * (0.018557330651423107 + (ix * (-0.0022242652921344794 + (ix * -0.0350353787183178))))))))))))))); + s2 = 0.0 + (ix * (0.0 + (ix * (0.00007646752923027944 + (ix * (0.00263861676657016 + (ix * (0.03415891436709477 + (ix * (0.22009110576413124 + (ix * (0.7620591645536234 + (ix * (1.3653349817554064 + (ix * 1.0))))))))))))))); + } + return s1 / s2; +} + +// END: rational_p4q4 + +// BEGIN: rational_p5q5 + +/** +* Evaluates a rational function (i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\)). +* +* ## Notes +* +* - Coefficients should be sorted in ascending degree. +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the rational function +* @return evaluated rational function +*/ +static double rational_p5q5( const double x ) { + double ax; + double ix; + double s1; + double s2; + if ( x == 0.0 ) { + return -0.016743100507663373; + } + if ( x < 0.0 ) { + ax = -x; + } else { + ax = x; + } + if ( ax <= 1.0 ) { + s1 = -0.016743100507663373 + (x * (-0.0011295143874558028 + (x * (0.001056288621524929 + (x * (0.00020938631748758808 + (x * (0.000014962478375834237 + (x * (4.4969678992770644e-7 + (x * (4.625961635228786e-9 + (x * (-2.811287356288318e-14 + (x * 9.905570997331033e-17))))))))))))))); + s2 = 1.0 + (x * (0.5914293448864175 + (x * (0.1381518657490833 + (x * (0.016074608709367652 + (x * (0.0009640118070051656 + (x * (0.000027533547476472603 + (x * (2.82243172016108e-7 + (x * (0.0 + (x * 0.0))))))))))))))); + } else { + ix = 1.0 / x; + s1 = 9.905570997331033e-17 + (ix * (-2.811287356288318e-14 + (ix * (4.625961635228786e-9 + (ix * (4.4969678992770644e-7 + (ix * (0.000014962478375834237 + (ix * (0.00020938631748758808 + (ix * (0.001056288621524929 + (ix * (-0.0011295143874558028 + (ix * -0.016743100507663373))))))))))))))); + s2 = 0.0 + (ix * (0.0 + (ix * (2.82243172016108e-7 + (ix * (0.000027533547476472603 + (ix * (0.0009640118070051656 + (ix * (0.016074608709367652 + (ix * (0.1381518657490833 + (ix * (0.5914293448864175 + (ix * 1.0))))))))))))))); + } + return s1 / s2; +} + +// END: rational_p5q5 + +/* End auto-generated functions. */ + +/** +* Evaluates the inverse error function. +* +* @param x input value +* @return output value +* +* @example +* double out = stdlib_base_erfinv( 0.5 ); +* // returns ~0.4769 +*/ +double stdlib_base_erfinv( const double x ) { + double sign; + double ax; + double qs; + double q; + double g; + double r; + + // Special case: NaN + if ( stdlib_base_is_nan( x ) ) { + return 0.0 / 0.0; // NaN + } + // Special case: 1 + if ( x == 1.0 ) { + return STDLIB_CONSTANT_FLOAT64_PINF; + } + // Special case: -1 + if ( x == -1.0 ) { + return STDLIB_CONSTANT_FLOAT64_NINF; + } + // Special case: +-0 + if ( x == 0.0 ) { + return x; + } + // Special case: |x| > 1 (range error) + if ( x > 1.0 || x < -1.0 ) { + return 0.0 / 0.0; // NaN + } + // Argument reduction (reduce to interval [0,1]). If `x` is negative, we can safely negate the value, taking advantage of the error function being an odd function; i.e., `erf(-x) = -erf(x)`. + if ( x < 0.0 ) { + sign = -1.0; + ax = -x; + } else { + sign = 1.0; + ax = x; + } + q = 1.0 - ax; + + // |x| <= 0.5 + if ( ax <= 0.5 ) { + g = ax * ( ax + 10.0 ); + r = rational_p1q1( ax ); + return sign * ( ( g * Y1 ) + ( g * r ) ); + } + // 1-|x| >= 0.25 + if ( q >= 0.25 ) { + g = stdlib_base_sqrt( -2.0 * stdlib_base_ln( q ) ); + q -= 0.25; + r = rational_p2q2( q ); + return sign * ( g / ( Y2 + r ) ); + } + q = stdlib_base_sqrt( -stdlib_base_ln( q ) ); + + // q < 3 + if ( q < 3.0 ) { + qs = q - 1.125; + r = rational_p3q3( qs ); + return sign * ( ( Y3 * q ) + ( r * q ) ); + } + // q < 6 + if ( q < 6.0 ) { + qs = q - 3.0; + r = rational_p4q4( qs ); + return sign * ( ( Y4 * q ) + ( r * q ) ); + } + // q < 18 + qs = q - 6.0; + r = rational_p5q5( qs ); + return sign * ( ( Y5 * q ) + ( r * q ) ); +} diff --git a/lib/node_modules/@stdlib/math/base/special/erfinv/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/erfinv/test/test.native.js new file mode 100644 index 000000000000..d83981fb3410 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/erfinv/test/test.native.js @@ -0,0 +1,251 @@ +/** +* @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 isNegativeZero = require( '@stdlib/math/base/assert/is-negative-zero' ); +var isPositiveZero = require( '@stdlib/math/base/assert/is-positive-zero' ); +var PINF = require( '@stdlib/constants/float64/pinf' ); +var NINF = require( '@stdlib/constants/float64/ninf' ); +var tryRequire = require( '@stdlib/utils/try-require' ); +var EPS = require( '@stdlib/constants/float64/eps' ); +var abs = require( '@stdlib/math/base/special/abs' ); + + +// FIXTURES // + +var x1 = require( './fixtures/julia/x_-0.5_0.5.json' ); +var x2 = require( './fixtures/julia/x_-0.5_-0.75.json' ); +var x3 = require( './fixtures/julia/x_0.5_0.75.json' ); +var x4 = require( './fixtures/julia/x_0.75_0.9998.json' ); +var x5 = require( './fixtures/julia/x_0.9998_0.9999..8.json' ); +var x6 = require( './fixtures/julia/x_0.9999..8_1.json' ); + + +// VARIABLES // + +var erfinv = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( erfinv instanceof Error ) +}; + + +// TESTS // + +tape( 'main export is a function', opts, function test( t ) { + t.ok( true, __filename ); + t.equal( typeof erfinv, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'if provided `NaN`, the function returns `NaN`', opts, function test( t ) { + var y = erfinv( NaN ); + t.equal( isnan( y ), true, 'returns NaN' ); + t.end(); +}); + +tape( 'if provided `1`, the function returns `+infinity`', opts, function test( t ) { + var y = erfinv( 1.0 ); + t.equal( y, PINF, 'returns +infinity' ); + t.end(); +}); + +tape( 'if provided `-1`, the function returns `-infinity`', opts, function test( t ) { + var y = erfinv( -1.0 ); + t.equal( y, NINF, 'returns `-infinity`' ); + t.end(); +}); + +tape( 'if provided `-0`, the function returns `-0`', opts, function test( t ) { + var y = erfinv( -0.0 ); + t.equal( isNegativeZero( y ), true, 'returns `-0`' ); + t.end(); +}); + +tape( 'if provided `0`, the function returns `0`', opts, function test( t ) { + var y = erfinv( 0.0 ); + t.equal( isPositiveZero( y ), true, 'returns `+0`' ); + t.end(); +}); + +tape( 'if provided a value which is either less than `-1` or greater than `1`, the function returns `NaN`', opts, function test( t ) { + var values; + var i; + var v; + + values = [ + 3.14, + -3.14, + -1.00000001, + 1.00000001, + PINF, + NINF + ]; + + for ( i = 0; i < values.length; i++ ) { + v = erfinv( values[i] ); + t.equal( isnan( v ), true, 'returns NaN when provided '+values[i] ); + } + t.end(); +}); + +tape( 'the function evaluates the inverse error function for `x` on the interval `[-0.5,0.5]', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + expected = x1.expected; + x = x1.x; + for ( i = 0; i < x.length; i++ ) { + y = erfinv( x[i] ); + if ( y === expected[i] ) { + t.equal( y, expected[i], 'x: '+x[i]+', y: '+y+', expected: '+expected[i] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 3.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. y: '+y+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol ); + } + } + t.end(); +}); + +tape( 'the function evaluates the inverse error function for `x` on the interval `[-0.5,-0.75]', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + expected = x2.expected; + x = x2.x; + for ( i = 0; i < x.length; i++ ) { + y = erfinv( x[i] ); + if ( y === expected[i] ) { + t.equal( y, expected[i], 'x: '+x[i]+', y: '+y+', expected: '+expected[i] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 2.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. y: '+y+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol ); + } + } + t.end(); +}); + +tape( 'the function evaluates the inverse error function for `x` on the interval `[0.5,0.75]', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + expected = x3.expected; + x = x3.x; + for ( i = 0; i < x.length; i++ ) { + y = erfinv( x[i] ); + if ( y === expected[i] ) { + t.equal( y, expected[i], 'x: '+x[i]+', y: '+y+', expected: '+expected[i] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 2.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. y: '+y+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol ); + } + } + t.end(); +}); + +tape( 'the function evaluates the inverse error function for `x` on the interval `[0.75,0.9998]', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + expected = x4.expected; + x = x4.x; + for ( i = 0; i < x.length; i++ ) { + y = erfinv( x[i] ); + if ( y === expected[i] ) { + t.equal( y, expected[i], 'x: '+x[i]+', y: '+y+', expected: '+expected[i] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 14.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. y: '+y+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol ); + } + } + t.end(); +}); + +tape( 'the function evaluates the inverse error function for `x` on the interval `[0.9998,0.9999..8]', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + expected = x5.expected; + x = x5.x; + for ( i = 0; i < x.length; i++ ) { + y = erfinv( x[i] ); + if ( y === expected[i] ) { + t.equal( y, expected[i], 'x: '+x[i]+', y: '+y+', expected: '+expected[i] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 9.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. y: '+y+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol ); + } + } + t.end(); +}); + +tape( 'the function evaluates the inverse error function for `x` on the interval `[0.9999..8,1]', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + expected = x6.expected; + x = x6.x; + for ( i = 0; i < x.length; i++ ) { + y = erfinv( x[i] ); + if ( expected[ i ] === null ) { + expected[ i ] = PINF; + } + if ( y === expected[i] ) { + t.equal( y, expected[i], 'x: '+x[i]+', y: '+y+', expected: '+expected[i] ); + } else { + delta = abs( y - expected[ i ] ); + tol = EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. y: '+y+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol ); + } + } + t.end(); +});