diff --git a/lib/node_modules/@stdlib/math/base/special/expf/README.md b/lib/node_modules/@stdlib/math/base/special/expf/README.md new file mode 100755 index 000000000000..1d4a061fea39 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/README.md @@ -0,0 +1,230 @@ + + +# expf + +> Natural [exponential function][exponential-function] of single-precision floating-point number. + +
+ +The natural [exponential function][exponential-function] is defined as + + + +```math +y = e^x +``` + + + + + +where `e` is [Euler's][@stdlib/constants/float64/e] number. + +
+ + + +
+ +## Usage + +```javascript +var expf = require( '@stdlib/math/base/special/expf' ); +``` + +#### expf( x ) + +Evaluates the natural [exponential function][exponential-function] of single-precision floating-point number. + +```javascript +var v = expf( 4.0 ); +// returns ~54.5982 + +v = expf( -9.0 ); +// returns ~1.234e-4 + +v = expf( 0.0 ); +// returns 1.0 + +v = expf( NaN ); +// returns NaN +``` + +
+ + + +
+ +## Examples + + + +```javascript +var randu = require( '@stdlib/random/base/randu' ); +var expf = require( '@stdlib/math/base/special/expf' ); + +var x; +var i; + +for ( i = 0; i < 100; i++ ) { + x = (randu()*100.0) - 50.0; + console.log( 'e^%d = %d', x, expf( x ) ); +} +``` + +
+ + + + + +* * * + +
+ +## C APIs + + + +
+ +
+ + + + + +
+ +### Usage + +```c +#include "stdlib/math/base/special/expf.h" +``` + +#### stdlib_base_expf( x ) + +Evaluates the natural [exponential function][exponential-function] of single-precision floating-point number. + +```c +float out = stdlib_base_expf( 4.0 ); +// returns ~54.5982 + +out = stdlib_base_expf( -9.0 ); +// returns ~1.234e-4 +``` + +The function accepts the following arguments: + +- **x**: `[in] float` input value. + +```c +float stdlib_base_exp( const float x ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +### Examples + +```c +#include "stdlib/math/base/special/expf.h" +#include +#include + +int main( void ) { + float x; + float v; + int i; + + for ( i = 0; i < 100; i++ ) { + x = ( (float)rand() / (float)RAND_MAX ) * 10.0; + v = stdlib_base_expf( x ); + printf( "e^%f = %f\n", x, v ); + } +} +``` + +
+ + + +
+ + + + + +
+ +* * * + +## See Also + +- [`@stdlib/math/base/special/exp10`][@stdlib/math/base/special/exp10]: base 10 exponential function. +- [`@stdlib/math/base/special/exp2`][@stdlib/math/base/special/exp2]: base 2 exponential function. +- [`@stdlib/math/base/special/expm1`][@stdlib/math/base/special/expm1]: compute exp(x) - 1. +- [`@stdlib/math/base/special/ln`][@stdlib/math/base/special/ln]: evaluate the natural logarithm of a double-precision floating-point number. + +
+ + + + + +
+ +[exponential-function]: https://en.wikipedia.org/wiki/Exponential_function + +[@stdlib/constants/float64/e]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/constants/float64/e + + + +[@stdlib/math/base/special/exp10]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/exp10 + +[@stdlib/math/base/special/exp2]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/exp2 + +[@stdlib/math/base/special/expm1]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/expm1 + +[@stdlib/math/base/special/ln]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/ln + + + +
+ + diff --git a/lib/node_modules/@stdlib/math/base/special/expf/benchmark/benchmark.js b/lib/node_modules/@stdlib/math/base/special/expf/benchmark/benchmark.js new file mode 100755 index 000000000000..1a6c2a5f6097 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/benchmark/benchmark.js @@ -0,0 +1,72 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2018 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 bench = require( '@stdlib/bench' ); +var randu = require( '@stdlib/random/base/randu' ); +var isnanf = require( '@stdlib/math/base/assert/is-nanf' ); +var pkg = require( './../package.json' ).name; +var expf = require( './../lib' ); + + +// MAIN // + +bench( pkg, function benchmark( b ) { + var x; + var y; + var i; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + x = ( randu()*100.0 ) - 50.0; + y = expf( x ); + if ( isnanf( y ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnanf( y ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); + +bench( pkg+'::built-in', function benchmark( b ) { + var x; + var y; + var i; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + x = ( randu()*100.0 ) - 50.0; + y = Math.exp( x ); // eslint-disable-line stdlib/no-builtin-math + if ( isnanf( y ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnanf( y ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); diff --git a/lib/node_modules/@stdlib/math/base/special/expf/benchmark/benchmark.native.js b/lib/node_modules/@stdlib/math/base/special/expf/benchmark/benchmark.native.js new file mode 100755 index 000000000000..8f943bcfe55a --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/benchmark/benchmark.native.js @@ -0,0 +1,60 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2022 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 isnanf = require( '@stdlib/math/base/assert/is-nanf' ); +var tryRequire = require( '@stdlib/utils/try-require' ); +var pkg = require( './../package.json' ).name; + + +// VARIABLES // + +var expf = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( expf 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()*100.0 ) - 50.0; + y = expf( x ); + if ( isnanf( y ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnanf( y ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); diff --git a/lib/node_modules/@stdlib/math/base/special/expf/benchmark/c/Makefile b/lib/node_modules/@stdlib/math/base/special/expf/benchmark/c/Makefile new file mode 100755 index 000000000000..7f6bbc4c205c --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/benchmark/c/Makefile @@ -0,0 +1,146 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2021 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/expf/benchmark/c/benchmark.c b/lib/node_modules/@stdlib/math/base/special/expf/benchmark/c/benchmark.c new file mode 100755 index 000000000000..b2aa393702ce --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/benchmark/c/benchmark.c @@ -0,0 +1,133 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2022 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/expf.h" +#include +#include +#include +#include +#include + +#define NAME "expf" +#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 float rand_float( void ) { + int r = rand(); + return (float)r / ( (float)RAND_MAX + 1.0f ); +} + +/** +* Runs a benchmark. +* +* @return elapsed time in seconds +*/ +static double benchmark( void ) { + double elapsed; + float x; + float y; + double t; + int i; + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + x = ( 100.0*rand_float() ) - 50.0; + y = stdlib_base_expf( 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/expf/binding.gyp b/lib/node_modules/@stdlib/math/base/special/expf/binding.gyp new file mode 100755 index 000000000000..f2b466aef5c4 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/binding.gyp @@ -0,0 +1,170 @@ +# @license Apache-2.0 +# +# Copyright (c) 2023 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/expf/docs/repl.txt b/lib/node_modules/@stdlib/math/base/special/expf/docs/repl.txt new file mode 100755 index 000000000000..b90a090e8e0c --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/docs/repl.txt @@ -0,0 +1,28 @@ + +{{alias}}( x ) + Evaluates the natural exponential function of single-precision floating-point number. + + Parameters + ---------- + x: number + Input value. + + Returns + ------- + y: number + Function value. + + Examples + -------- + > var y = {{alias}}( 4.0 ) + ~54.5982 + > y = {{alias}}( -9.0 ) + ~1.234e-4 + > y = {{alias}}( 0.0 ) + 1.0 + > y = {{alias}}( NaN ) + NaN + + See Also + -------- + diff --git a/lib/node_modules/@stdlib/math/base/special/expf/docs/types/index.d.ts b/lib/node_modules/@stdlib/math/base/special/expf/docs/types/index.d.ts new file mode 100755 index 000000000000..e045baa7ec3d --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/docs/types/index.d.ts @@ -0,0 +1,48 @@ +/* +* @license Apache-2.0 +* +* Copyright (c) 2019 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. +*/ + +// TypeScript Version: 4.1 + +/** +* Evaluates the natural exponential function of single-precision floating-point number. +* +* @param x - input value +* @returns function value +* +* @example +* var v = expf( 4.0 ); +* // returns ~54.5982 +* +* @example +* var v = expf( -9.0 ); +* // returns ~1.234e-4 +* +* @example +* var v = expf( 0.0 ); +* // returns 1.0 +* +* @example +* var v = expf( NaN ); +* // returns NaN +*/ +declare function expf( x: number ): number; + + +// EXPORTS // + +export = expf; diff --git a/lib/node_modules/@stdlib/math/base/special/expf/docs/types/test.ts b/lib/node_modules/@stdlib/math/base/special/expf/docs/types/test.ts new file mode 100755 index 000000000000..e2ff29750af1 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/docs/types/test.ts @@ -0,0 +1,44 @@ +/* +* @license Apache-2.0 +* +* Copyright (c) 2019 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. +*/ + +import expf = require( './index' ); + + +// TESTS // + +// The function returns a number... +{ + expf( 0.5 ); // $ExpectType number +} + +// The compiler throws an error if the function is provided a value other than a number... +{ + expf( true ); // $ExpectError + expf( false ); // $ExpectError + expf( null ); // $ExpectError + expf( undefined ); // $ExpectError + expf( '5' ); // $ExpectError + expf( [] ); // $ExpectError + expf( {} ); // $ExpectError + expf( ( x: number ): number => x ); // $ExpectError +} + +// The compiler throws an error if the function is provided insufficient arguments... +{ + expf(); // $ExpectError +} diff --git a/lib/node_modules/@stdlib/math/base/special/expf/examples/c/Makefile b/lib/node_modules/@stdlib/math/base/special/expf/examples/c/Makefile new file mode 100755 index 000000000000..f0ae66fecf01 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/examples/c/Makefile @@ -0,0 +1,146 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2023 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/expf/examples/c/example.c b/lib/node_modules/@stdlib/math/base/special/expf/examples/c/example.c new file mode 100755 index 000000000000..34c144d92e09 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/examples/c/example.c @@ -0,0 +1,33 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2022 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/expf.h" +#include +#include + +int main( void ) { + float x; + float v; + int i; + + for ( i = 0; i < 100; i++ ) { + x = ( (float)rand() / (float)RAND_MAX ) * 10.0; + v = stdlib_base_expf( x ); + printf( "e^%f = %f\n", x, v ); + } +} diff --git a/lib/node_modules/@stdlib/math/base/special/expf/examples/index.js b/lib/node_modules/@stdlib/math/base/special/expf/examples/index.js new file mode 100755 index 000000000000..b17c5ce770d5 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/examples/index.js @@ -0,0 +1,30 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2018 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'; + +var randu = require( '@stdlib/random/base/randu' ); +var expf = require( './../lib' ); + +var x; +var i; + +for ( i = 0; i < 100; i++ ) { + x = (randu()*10.0) - 5.0; + console.log( 'e^%d = %d', x, expf( x ) ); +} diff --git a/lib/node_modules/@stdlib/math/base/special/expf/include.gypi b/lib/node_modules/@stdlib/math/base/special/expf/include.gypi new file mode 100755 index 000000000000..78db9faf8c74 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/include.gypi @@ -0,0 +1,53 @@ +# @license Apache-2.0 +# +# Copyright (c) 2023 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': [ + ' --> +* +* \\( r \\) can be represented as \\( r = \mathrm{hi} - \mathrm{lo} \\) for better accuracy. +* +* +* +* 2. We approximate of \\( e^{r} \\) by a special rational function on the interval \\(\[0,0.34658]\\): +* +* ```tex +* \begin{align*} +* R\left(r^2\right) &= r \cdot \frac{ e^{r}+1 }{ e^{r}-1 } \\ +* &= 2 + \frac{r^2}{6} - \frac{r^4}{360} + \ldots +* \end{align*} +* ``` +* +* We use a special Remes algorithm on \\(\[0,0.34658]\\) to generate a polynomial of degree \\(5\\) to approximate \\(R\\). The maximum error of this polynomial approximation is bounded by \\(2^{-59}\\). In other words, +* +* ```tex +* R(z) \sim 2 + P_1 z + P_2 z^2 + P_3 z^3 + P_4 z^4 + P_5 z^5 +* ``` +* +* where \\( z = r^2 \\) and +* +* ```tex +* \left| 2 + P_1 z + \ldots + P_5 z^5 - R(z) \right| \leq 2^{-59} +* ``` +* +* +* +* The values of \\( P_1 \\) to \\( P_5 \\) are listed in the source code. +* +* +* +* The computation of \\( e^{r} \\) thus becomes +* +* ```tex +* \begin{align*} +* e^{r} &= 1 + \frac{2r}{R-r} \\ +* &= 1 + r + \frac{r \cdot R_1(r)}{2 - R_1(r)}\ \text{for better accuracy} +* \end{align*} +* ``` +* +* where +* +* ```tex +* R_1(r) = r - P_1\ r^2 + P_2\ r^4 + \ldots + P_5\ r^{10} +* ``` +* +* 3. We scale back to obtain \\( e^{x} \\). From step 1, we have +* +* ```tex +* e^{x} = 2^k e^{r} +* ``` +* +* ## Special Cases +* +* ```tex +* \begin{align*} +* e^\infty &= \infty \\ +* e^{-\infty} &= 0 \\ +* e^{\mathrm{NaN}} &= \mathrm{NaN} \\ +* e^0 &= 1\ \mathrm{is\ exact\ for\ finite\ argument\ only} +* \end{align*} +* ``` +* +* ## Notes +* +* - According to an error analysis, the error is always less than \\(1\\) ulp (unit in the last place). +* +* - For an IEEE double, +* +* - if \\(x > 7.09782712893383973096\mbox{e+}02\\), then \\(e^{x}\\) overflows +* - if \\(x < -7.45133219101941108420\mbox{e+}02\\), then \\(e^{x}\\) underflows +* +* - The hexadecimal values included in the source code are the intended ones for the used constants. Decimal values may be used, provided that the compiler will convert from decimal to binary accurately enough to produce the intended hexadecimal values. +* +* @param {number} x - input value +* @returns {number} function value +* +* @example +* var v = expf( 4.0 ); +* // returns ~54.5982 +* +* @example +* var v = expf( -9.0 ); +* // returns ~1.234e-4 +* +* @example +* var v = expf( 0.0 ); +* // returns 1.0 +* +* @example +* var v = expf( NaN ); +* // returns NaN +*/ +function expf( x ) { + var hi; + var lo; + var k; + + if ( isnanf( x ) || x === PINF ) { + return x; + } + if ( x === NINF ) { + return 0.0; + } + if ( x > OVERFLOW ) { + return PINF; + } + if ( x < UNDERFLOW ) { + return 0.0; + } + if ( + x > NEG_NEARZERO && + x < NEARZERO + ) { + return float64ToFloat32( 1.0 + x ); + } + // Reduce and compute `r = hi - lo` for extra precision... + if ( x < 0.0 ) { + k = truncf( (LOG2_E*x) - 0.5 ); + } else { + k = truncf( (LOG2_E*x) + 0.5 ); + } + hi = float64ToFloat32( x - float64ToFloat32(k*LN2_HI) ); + lo = float64ToFloat32( k * LN2_LO ); + + return expmulti( hi, lo, k ); +} + + +// EXPORTS // + +module.exports = expf; diff --git a/lib/node_modules/@stdlib/math/base/special/expf/lib/native.js b/lib/node_modules/@stdlib/math/base/special/expf/lib/native.js new file mode 100755 index 000000000000..a3255c36f9bd --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/lib/native.js @@ -0,0 +1,58 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2022 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 // + +/** +* Evaluates the natural exponential function of single-precision floating-point number. +* +* @private +* @param {number} x - input value +* @returns {number} function value +* +* @example +* var v = expf( 4.0 ); +* // returns ~54.5982 +* +* @example +* var v = expf( -9.0 ); +* // returns ~1.234e-4 +* +* @example +* var v = expf( 0.0 ); +* // returns 1.0 +* +* @example +* var v = expf( NaN ); +* // returns NaN +*/ +function expf( x ) { + return addon( x ); +} + + +// EXPORTS // + +module.exports = expf; diff --git a/lib/node_modules/@stdlib/math/base/special/expf/lib/polyval_p.js b/lib/node_modules/@stdlib/math/base/special/expf/lib/polyval_p.js new file mode 100644 index 000000000000..695734694450 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/lib/polyval_p.js @@ -0,0 +1,52 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2022 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. +*/ + +/* This is a generated file. Do not edit directly. */ +'use strict'; + +// MODULES // + +var float64ToFloat32 = require( '@stdlib/number/float64/base/to-float32' ); + + +// MAIN // + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @private +* @param {number} x - value at which to evaluate the polynomial +* @returns {number} evaluated polynomial +*/ +function evalpoly( x ) { + if ( x === 0.0 ) { + return 0.16666602; + } + return float64ToFloat32(0.16666666666666602 + float64ToFloat32(x * float64ToFloat32(-0.0027777777777015593 + float64ToFloat32(x * (0.00006613756321437934 + float64ToFloat32(x * float64ToFloat32(-0.0000016533902205465252 + float64ToFloat32(x * 4.1381367970572385e-8)))))))); // eslint-disable-line max-len +} + + +// EXPORTS // + +module.exports = evalpoly; diff --git a/lib/node_modules/@stdlib/math/base/special/expf/manifest.json b/lib/node_modules/@stdlib/math/base/special/expf/manifest.json new file mode 100755 index 000000000000..89b346b9cee3 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/manifest.json @@ -0,0 +1,107 @@ +{ + "options": { + "task": "build", + "wasm": false + }, + "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", + "wasm": false, + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/math/base/napi/unary", + "@stdlib/math/base/assert/is-nanf", + "@stdlib/constants/float32/ninf", + "@stdlib/constants/float32/pinf", + "@stdlib/math/base/special/truncf", + "@stdlib/math/base/special/ldexpf" + ] + }, + { + "task": "benchmark", + "wasm": false, + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/math/base/assert/is-nanf", + "@stdlib/constants/float32/ninf", + "@stdlib/constants/float32/pinf", + "@stdlib/math/base/special/truncf", + "@stdlib/math/base/special/ldexpf" + ] + }, + { + "task": "examples", + "wasm": false, + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/math/base/assert/is-nanf", + "@stdlib/constants/float32/ninf", + "@stdlib/constants/float32/pinf", + "@stdlib/math/base/special/truncf", + "@stdlib/math/base/special/ldexpf" + ] + }, + { + "task": "build", + "wasm": true, + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/math/base/assert/is-nanf", + "@stdlib/constants/float32/ninf", + "@stdlib/constants/float32/pinf", + "@stdlib/math/base/special/truncf", + "@stdlib/math/base/special/ldexpf" + ] + } + ] + } diff --git a/lib/node_modules/@stdlib/math/base/special/expf/package.json b/lib/node_modules/@stdlib/math/base/special/expf/package.json new file mode 100755 index 000000000000..f56cbaffae7b --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/package.json @@ -0,0 +1,145 @@ +{ + "name": "@stdlib/math/base/special/expf", + "version": "0.0.0", + "description": "Natural exponential function of single-precision floating-point number.", + "license": "Apache-2.0", + "author": { + "name": "The Stdlib Authors", + "url": "https://github.com/stdlib-js/stdlib/graphs/contributors" + }, + "contributors": [ + { + "name": "The Stdlib Authors", + "url": "https://github.com/stdlib-js/stdlib/graphs/contributors" + } + ], + "main": "./lib", + "gypfile": true, + "directories": { + "benchmark": "./benchmark", + "doc": "./docs", + "example": "./examples", + "include": "./include", + "lib": "./lib", + "scripts": "./scripts", + "src": "./src", + "test": "./test" + }, + "types": "./docs/types", + "scripts": {}, + "homepage": "https://github.com/stdlib-js/stdlib", + "repository": { + "type": "git", + "url": "git://github.com/stdlib-js/stdlib.git" + }, + "bugs": { + "url": "https://github.com/stdlib-js/stdlib/issues" + }, + "dependencies": {}, + "devDependencies": {}, + "engines": { + "node": ">=0.10.0", + "npm": ">2.7.0" + }, + "os": [ + "aix", + "darwin", + "freebsd", + "linux", + "macos", + "openbsd", + "sunos", + "win32", + "windows" + ], + "keywords": [ + "stdlib", + "stdmath", + "mathematics", + "math", + "special", + "function", + "math.exp", + "expf", + "natural", + "exponential", + "euler", + "power", + "number" + ], + "__stdlib__": { + "scaffold": { + "$schema": "math/base@v1.0", + "base_alias": "exp", + "alias": "exp", + "pkg_desc": "evaluate the natural exponential function of single-precision floating-point number", + "desc": "evaluates the natural exponential function of single-precision floating-point number", + "short_desc": "natural exponential function", + "parameters": [ + { + "name": "x", + "desc": "input value", + "type": { + "javascript": "number", + "jsdoc": "number", + "c": "double", + "dtype": "float64" + }, + "domain": [ + { + "min": "-infinity", + "max": "infinity" + } + ], + "rand": { + "prng": "random/base/uniform", + "parameters": [ + -10, + 10 + ] + }, + "example_values": [ + -1.2, + 2, + -3.1, + -4.7, + 5.5, + 6.7, + 8.9, + -10.2, + 11.3, + -12.4, + 13.5, + 14.6, + -15.7, + 16.8, + -17.9, + 18.1, + -19.11, + 20.12, + -21.15, + 23.78 + ] + } + ], + "returns": { + "desc": "function value", + "type": { + "javascript": "number", + "jsdoc": "number", + "c": "float", + "dtype": "float32" + } + }, + "keywords": [ + "natural", + "exponential", + "exp", + "power" + ], + "extra_keywords": [ + "math.exp" + ] + } + } + } diff --git a/lib/node_modules/@stdlib/math/base/special/expf/src/Makefile b/lib/node_modules/@stdlib/math/base/special/expf/src/Makefile new file mode 100755 index 000000000000..904c7dc4bd7a --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/src/Makefile @@ -0,0 +1,70 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2023 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/expf/src/addon.c b/lib/node_modules/@stdlib/math/base/special/expf/src/addon.c new file mode 100755 index 000000000000..17ca5fe4dcc2 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/src/addon.c @@ -0,0 +1,24 @@ + +/** +* @license Apache-2.0 +* +* Copyright (c) 2022 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/expf.h" +#include "stdlib/math/base/napi/unary.h" + +// cppcheck-suppress shadowFunction +STDLIB_MATH_BASE_NAPI_MODULE_F_F( stdlib_base_expf ) diff --git a/lib/node_modules/@stdlib/math/base/special/expf/src/main.c b/lib/node_modules/@stdlib/math/base/special/expf/src/main.c new file mode 100755 index 000000000000..03727de78548 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/src/main.c @@ -0,0 +1,254 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2022 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 following copyrights, licenses, and long comment were part of the original implementation available as part of [Go]{@link https://github.com/golang/go/blob/cb07765045aed5104a3df31507564ac99e6ddce8/src/math/exp.go}, which in turn was based on an implementation available as part of [FreeBSD]{@link https://svnweb.freebsd.org/base/release/9.3.0/lib/msun/src/e_exp.c}. The implementation follows the original, but has been modified according to project conventions. +* +* ```text +* Copyright (c) 2009 The Go Authors. All rights reserved. +* +* Redistribution and use in source and binary forms, with or without +* modification, are permitted provided that the following conditions are +* met: +* +* * Redistributions of source code must retain the above copyright +* notice, this list of conditions and the following disclaimer. +* * Redistributions in binary form must reproduce the above +* copyright notice, this list of conditions and the following disclaimer +* in the documentation and/or other materials provided with the +* distribution. +* * Neither the name of Google Inc. nor the names of its +* contributors may be used to endorse or promote products derived from +* this software without specific prior written permission. +* +* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT +* OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT +* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, +* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY +* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +* ``` +* +* ```text +* Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. +* +* Developed at SunPro, a Sun Microsystems, Inc. business. +* Permission to use, copy, modify, and distribute this +* software is freely granted, provided that this notice +* is preserved. +* ``` +*/ + +#include "stdlib/math/base/special/expf.h" +#include "stdlib/math/base/assert/is_nanf.h" +#include "stdlib/math/base/special/truncf.h" +#include "stdlib/constants/float32/ninf.h" +#include "stdlib/constants/float32/pinf.h" +#include "stdlib/math/base/special/ldexpf.h" +#include + +static const float LN2_HI = 6.93147180369123816490e-01f; +static const float LN2_LO = 1.90821492927058770002e-10f; +static const float LOG2_E = 1.44269504088896338700e+00f; +static const float EXP_OVERFLOW = 88.7f; +static const float EXP_UNDERFLOW = -87.63f; +static const float NEARZERO = 1.0f / (1 << 28); // 2^-28 +static const float NEG_NEARZERO = -NEARZERO; + + +/* Begin auto-generated functions. The following functions are auto-generated. Do not edit directly. */ + +// BEGIN: polyval_p + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static float polyval_p( const float x ) { + return 0.16666666666666602f + (x * (-0.0027777777777015593f + (x * (0.00006613756321437934f + (x * (-0.0000016533902205465252f + (x * 4.1381367970572385e-8f))))))); +} + +// END: polyval_p + +/* End auto-generated functions. */ + +/** +* Computes \\(e^{r} 2^k\\) where \\(r = \mathrm{hi} - \mathrm{lo}\\) and \\(|r| \leq \ln(2)/2\\). +* +* @param hi upper bound +* @param lo lower bound +* @param k power of 2 +* @return function value +*/ +static float expmulti( const float hi, const float lo, const int32_t k ) { + float r; + float t; + float c; + float y; + + r = hi - lo; + t = r * r; + c = r - (t * polyval_p( t )); + y = 1.0f - ( lo - ( ( r * c ) / ( 2.0f - c ) ) - hi); + + return stdlib_base_ldexpf( y, k ); +} + +/** +* Evaluates the natural exponential function of single-precision floating-point number. +* +* ## Method +* +* 1. We reduce \\( x \\) to an \\( r \\) so that \\( |r| \leq 0.5 \cdot \ln(2) \approx 0.34658 \\). Given \\( x \\), we find an \\( r \\) and integer \\( k \\) such that +* +* ```tex +* \begin{align*} +* x &= k \cdot \ln(2) + r \\ +* |r| &\leq 0.5 \cdot \ln(2) +* \end{align*} +* ``` +* +* +* +* \\( r \\) can be represented as \\( r = \mathrm{hi} - \mathrm{lo} \\) for better accuracy. +* +* +* +* 2. We approximate of \\( e^{r} \\) by a special rational function on the interval \\(\[0,0.34658]\\): +* +* ```tex +* \begin{align*} +* R\left(r^2\right) &= r \cdot \frac{ e^{r}+1 }{ e^{r}-1 } \\ +* &= 2 + \frac{r^2}{6} - \frac{r^4}{360} + \ldots +* \end{align*} +* ``` +* +* We use a special Remes algorithm on \\(\[0,0.34658]\\) to generate a polynomial of degree \\(5\\) to approximate \\(R\\). The maximum error of this polynomial approximation is bounded by \\(2^{-59}\\). In other words, +* +* ```tex +* R(z) \sim 2 + P_1 z + P_2 z^2 + P_3 z^3 + P_4 z^4 + P_5 z^5 +* ``` +* +* where \\( z = r^2 \\) and +* +* ```tex +* \left| 2 + P_1 z + \ldots + P_5 z^5 - R(z) \right| \leq 2^{-59} +* ``` +* +* +* +* The values of \\( P_1 \\) to \\( P_5 \\) are listed in the source code. +* +* +* +* The computation of \\( e^{r} \\) thus becomes +* +* ```tex +* \begin{align*} +* e^{r} &= 1 + \frac{2r}{R-r} \\ +* &= 1 + r + \frac{r \cdot R_1(r)}{2 - R_1(r)}\ \text{for better accuracy} +* \end{align*} +* ``` +* +* where +* +* ```tex +* R_1(r) = r - P_1\ r^2 + P_2\ r^4 + \ldots + P_5\ r^{10} +* ``` +* +* 3. We scale back to obtain \\( e^{x} \\). From step 1, we have +* +* ```tex +* e^{x} = 2^k e^{r} +* ``` +* +* +* ## Special Cases +* +* ```tex +* \begin{align*} +* e^\infty &= \infty \\ +* e^{-\infty} &= 0 \\ +* e^{\mathrm{NaN}} &= \mathrm{NaN} \\ +* e^0 &= 1\ \mathrm{is\ exact\ for\ finite\ argument\ only} +* \end{align*} +* ``` +* +* ## Notes +* +* - According to an error analysis, the error is always less than \\(1\\) ulp (unit in the last place). +* +* - For an IEEE double, +* +* - if \\(x > 7.09782712893383973096\mbox{e+}02\\), then \\(e^{x}\\) overflows +* - if \\(x < -7.45133219101941108420\mbox{e+}02\\), then \\(e^{x}\\) underflows +* +* - The hexadecimal values included in the source code are the intended ones for the used constants. Decimal values may be used, provided that the compiler will convert from decimal to binary accurately enough to produce the intended hexadecimal values. +* +* @param x input value +* @return output value +* +* @example +* double out = stdlib_base_exp( 0.0f ); +* // returns 1.0 +*/ +float stdlib_base_expf( const float x ) { + float hi; + float lo; + int32_t k; + + if ( stdlib_base_is_nanf( x ) || x == STDLIB_CONSTANT_FLOAT32_PINF ) { + return x; + } + if ( x == STDLIB_CONSTANT_FLOAT32_NINF ) { + return 0.0f; + } + if ( x > EXP_OVERFLOW ) { + return STDLIB_CONSTANT_FLOAT32_PINF; + } + if ( x < EXP_UNDERFLOW ) { + return 0.0f; + } + if ( x > NEG_NEARZERO && x < NEARZERO ) { + return 1.0f + x; + } + // Reduce and compute `r = hi - lo` for extra precision... + if ( x < 0.0 ) { + k = stdlib_base_truncf( ( LOG2_E * x ) - 0.5f ); + } else { + k = stdlib_base_truncf( ( LOG2_E * x ) + 0.5f ); + } + hi = x - ( k * LN2_HI ); + lo = k * LN2_LO; + + return expmulti( hi, lo, k ); +} diff --git a/lib/node_modules/@stdlib/math/base/special/expf/test/fixtures/julia/REQUIRE b/lib/node_modules/@stdlib/math/base/special/expf/test/fixtures/julia/REQUIRE new file mode 100644 index 000000000000..308c3be89c85 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/test/fixtures/julia/REQUIRE @@ -0,0 +1,2 @@ +julia 1.5 +JSON 0.21 diff --git a/lib/node_modules/@stdlib/math/base/special/expf/test/fixtures/julia/medium_negative.json b/lib/node_modules/@stdlib/math/base/special/expf/test/fixtures/julia/medium_negative.json new file mode 100644 index 000000000000..68f6ca5a7b8c --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/test/fixtures/julia/medium_negative.json @@ -0,0 +1 @@ +{"expected":[5.293782e-18,5.5033182e-18,5.721149e-18,5.947601e-18,6.183017e-18,6.427751e-18,6.6821718e-18,6.946689e-18,7.221651e-18,7.507495e-18,7.804654e-18,8.1135756e-18,8.434724e-18,8.768584e-18,9.115659e-18,9.476472e-18,9.851604e-18,1.02415465e-17,1.0646924e-17,1.1068347e-17,1.150645e-17,1.19618936e-17,1.2435365e-17,1.2927577e-17,1.3439323e-17,1.3971274e-17,1.4524279e-17,1.5099175e-17,1.5696824e-17,1.631813e-17,1.6964028e-17,1.7635492e-17,1.8333605e-17,1.9059277e-17,1.9813676e-17,2.0597932e-17,2.1413233e-17,2.2260803e-17,2.3141923e-17,2.4057918e-17,2.501017e-17,2.6000212e-17,2.7029342e-17,2.809921e-17,2.921142e-17,3.0367656e-17,3.156966e-17,3.2819238e-17,3.4118275e-17,3.546887e-17,3.6872783e-17,3.833227e-17,3.9849525e-17,4.1426833e-17,4.3066576e-17,4.477122e-17,4.654334e-17,4.8385784e-17,5.0300975e-17,5.229197e-17,5.436177e-17,5.6513496e-17,5.87504e-17,6.1075833e-17,6.349331e-17,6.6006736e-17,6.861939e-17,7.133546e-17,7.415903e-17,7.7094365e-17,8.014589e-17,8.331819e-17,8.661606e-17,9.0044466e-17,9.360893e-17,9.7314126e-17,1.0116598e-16,1.051703e-16,1.0933311e-16,1.1366069e-16,1.1815956e-16,1.2283652e-16,1.2769907e-16,1.3275361e-16,1.3800822e-16,1.4347081e-16,1.4914962e-16,1.550532e-16,1.6119046e-16,1.6757065e-16,1.7420403e-16,1.8109931e-16,1.8826751e-16,1.9571946e-16,2.0346635e-16,2.1151988e-16,2.1989219e-16,2.2859588e-16,2.3764407e-16,2.4705135e-16,2.5683005e-16,2.6699582e-16,2.7756394e-16,2.8855038e-16,2.9997166e-16,3.1184505e-16,3.241884e-16,3.3702157e-16,3.5036144e-16,3.642293e-16,3.786461e-16,3.9363355e-16,4.092142e-16,4.2541158e-16,4.4225006e-16,4.597568e-16,4.779547e-16,4.9687297e-16,5.1653996e-16,5.369855e-16,5.5824024e-16,5.803363e-16,6.0330695e-16,6.2718687e-16,6.520144e-16,6.7782223e-16,7.046515e-16,7.325428e-16,7.6153805e-16,7.9168093e-16,8.2301697e-16,8.5559333e-16,8.894625e-16,9.246689e-16,9.612688e-16,9.993174e-16,1.038872e-15,1.0799923e-15,1.1227402e-15,1.1671801e-15,1.2133836e-15,1.2614112e-15,1.31134e-15,1.363245e-15,1.4172044e-15,1.4732997e-15,1.5316154e-15,1.5922392e-15,1.6552689e-15,1.7207871e-15,1.7888986e-15,1.8597062e-15,1.9333165e-15,2.0098402e-15,2.0893931e-15,2.1720947e-15,2.2580698e-15,2.3474567e-15,2.4403729e-15,2.536967e-15,2.6373843e-15,2.7417762e-15,2.8503002e-15,2.9631197e-15,3.080405e-15,3.2023444e-15,3.3290987e-15,3.4608697e-15,3.5978567e-15,3.740266e-15,3.8883115e-15,4.0422174e-15,4.2022147e-15,4.368562e-15,4.541477e-15,4.721236e-15,4.9081104e-15,5.102381e-15,5.304342e-15,5.5142963e-15,5.732561e-15,5.9594655e-15,6.1953743e-15,6.4405976e-15,6.695527e-15,6.9605466e-15,7.236057e-15,7.522472e-15,7.820223e-15,8.12976e-15,8.451582e-15,8.786109e-15,9.133878e-15,9.495411e-15,9.871256e-15,1.0261976e-14,1.0668162e-14,1.1090425e-14,1.15294466e-14,1.1985801e-14,1.2460218e-14,1.2953414e-14,1.34661315e-14,1.3999143e-14,1.4553253e-14,1.5129323e-14,1.5728165e-14,1.6350712e-14,1.69979e-14,1.7670739e-14,1.8370176e-14,1.9097296e-14,1.9853199e-14,2.063906e-14,2.1455988e-14,2.2305252e-14,2.318813e-14,2.4106e-14,2.5060156e-14,2.6052077e-14,2.708326e-14,2.8155314e-14,2.926975e-14,3.0428293e-14,3.1632693e-14,3.288483e-14,3.4186467e-14,3.5539622e-14,3.6946337e-14,3.8408807e-14,3.9929092e-14,4.150955e-14,4.3152564e-14,4.4860617e-14,4.663636e-14,4.8482306e-14,5.0401313e-14,5.239628e-14,5.4470314e-14,5.6626338e-14,5.88677e-14,6.1197785e-14,6.362021e-14,6.6138406e-14,6.8756266e-14,7.1477756e-14,7.4307104e-14,7.72483e-14,8.030591e-14,8.348455e-14,8.678917e-14,9.022443e-14,9.3795665e-14,9.750825e-14,1.0136798e-13,1.0538029e-13,1.0955141e-13,1.1388763e-13,1.1839572e-13,1.2308202e-13,1.2795381e-13,1.3301843e-13,1.3828351e-13,1.4375728e-13,1.4944743e-13,1.553628e-13,1.6151231e-13,1.6790555e-13,1.7455152e-13,1.8146056e-13,1.8864307e-13,1.9611025e-13,2.0387262e-13,2.1194223e-13,2.2033124e-13,2.2905275e-13,2.3811904e-13,2.4754417e-13,2.5734238e-13,2.6752892e-13,2.7811816e-13,2.8912652e-13,3.0057063e-13,3.1246829e-13,3.248363e-13,3.3769385e-13,3.5106033e-13,3.6495587e-13,3.7940216e-13,3.944195e-13,4.1003128e-13,4.26261e-13,4.4313395e-13,4.606739e-13,4.7890815e-13,4.978641e-13,5.1757134e-13,5.3805766e-13,5.5935486e-13,5.814951e-13,6.0451275e-13,6.2844033e-13,6.53315e-13,6.7917433e-13,7.060585e-13,7.3400547e-13,7.630586e-13,7.932617e-13,8.246619e-13,8.573033e-13,8.912368e-13,9.265134e-13,9.631882e-13,1.0013127e-12,1.0409463e-12,1.0821487e-12,1.1249819e-12,1.1695127e-12,1.2158039e-12,1.2639274e-12,1.3139558e-12,1.365967e-12,1.4200341e-12,1.4762414e-12,1.5346734e-12,1.5954214e-12,1.6585707e-12,1.7242197e-12,1.7924672e-12,1.8634196e-12,1.9371768e-12,2.0138533e-12,2.093565e-12,2.176436e-12,2.2625827e-12,2.3521395e-12,2.445241e-12,2.5420326e-12,2.6426502e-12,2.7472508e-12,2.8559913e-12,2.969042e-12,3.0865614e-12,3.2087325e-12,3.3357395e-12,3.4677734e-12,3.6050405e-12,3.747734e-12,3.8960753e-12,4.0502883e-12,4.210613e-12,4.3772763e-12,4.550536e-12,4.730654e-12,4.9179103e-12,5.1125692e-12,5.314933e-12,5.5253068e-12,5.744018e-12,5.971376e-12,6.2077327e-12,6.453445e-12,6.7088956e-12,6.974445e-12,7.250505e-12,7.537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diff --git a/lib/node_modules/@stdlib/math/base/special/expf/test/fixtures/julia/medium_positive.json b/lib/node_modules/@stdlib/math/base/special/expf/test/fixtures/julia/medium_positive.json new file mode 100644 index 000000000000..48555a0d6613 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/test/fixtures/julia/medium_positive.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/expf/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/math/base/special/expf/test/fixtures/julia/runner.jl new file mode 100755 index 000000000000..6392c869f0bc --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/test/fixtures/julia/runner.jl @@ -0,0 +1,80 @@ +#!/usr/bin/env julia +# +# @license Apache-2.0 +# +# Copyright (c) 2018 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. + +import JSON + +""" + gen( domain, filepath ) + +Generate fixture data and write to file. + +# Arguments + +* `domain`: domain +* `filepath::AbstractString`: filepath of the output file + +# Examples + +``` julia +julia> x = range( -100, stop = 100, length = 2001 ); +julia> gen( x, \"./data.json\" ); +``` +""" +function gen( domain, filepath ) + x = Float32.( collect( domain ) ); + y = Float32.( exp.( Float32.( x ) ) ); + data = Dict([ + ("x", x), + ("expected", y) + ]); + outfile = open( filepath, "w" ); + write( outfile, JSON.json(data) ); + write( outfile, "\n" ); + close( outfile ); +end + +# Get the filename: +file = @__FILE__; + +# Extract the directory in which this file resides: +dir = dirname( file ); + +# Medium negative values: +x = range( -39.78, stop = -1.0, length = 1000 ); +out = joinpath( dir, "./medium_negative.json" ); +gen( x, out ); + +# Medium positive values: +x = range( 1.0, stop = 39.78, length = 1000 ); +out = joinpath( dir, "./medium_positive.json" ); +gen( x, out ); + +# Small negative values: +x = range( -1.0, stop = -87.63, length = 1000 ); +out = joinpath( dir, "./small_negative.json" ); +gen( x, out ); + +# Small positive values: +x = range( 88.7, stop = 1.0, length = 1000 ); +out = joinpath( dir, "./small_positive.json" ); +gen( x, out ); + +# Tiny values: +x = range( -38.7, stop = -87.63, length = 1000 ); +out = joinpath( dir, "./tiny.json" ); +gen( x, out ); diff --git a/lib/node_modules/@stdlib/math/base/special/expf/test/fixtures/julia/small_negative.json b/lib/node_modules/@stdlib/math/base/special/expf/test/fixtures/julia/small_negative.json new file mode 100644 index 000000000000..df8217ff01a7 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/test/fixtures/julia/small_negative.json @@ -0,0 +1 @@ +{"expected":[0.36787945,0.33732218,0.30930313,0.28361142,0.26005378,0.23845287,0.21864623,0.20048477,0.18383187,0.1685622,0.1545609,0.14172256,0.12995064,0.11915651,0.109259,0.100183606,0.091862045,0.084231675,0.077235125,0.070819736,0.06493723,0.059543323,0.054597467,0.05006243,0.045904078,0.042091142,0.03859492,0.035389107,0.032449566,0.029754205,0.027282728,0.025016539,0.022938581,0.021033231,0.019286145,0.017684173,0.01621527,0.01486838,0.013633365,0.012500935,0.011462568,0.010510447,0.009637416,0.008836902,0.008102882,0.0074298307,0.0068126856,0.006246803,0.005727921,0.005252142,0.0048158825,0.0044158604,0.004049065,0.0037127372,0.0034043456,0.00312157,0.0028622812,0.0026245313,0.0024065294,0.0022066357,0.0020233456,0.0018552801,0.0017011748,0.0015598692,0.0014303015,0.0013114961,0.0012025592,0.0011026709,0.0010110796,0.0009270962,0.00085008825,0.00077947724,0.0007147314,0.0006553636,0.00060092704,0.00055101217,0.00050524337,0.0004632763,0.0004247949,0.0003895101,0.00035715618,0.0003274895,0.0003002872,0.0002753444,0.00025247346,0.00023150221,0.0002122729,0.00019464086,0.00017847338,0.00016364883,0.00015005564,0.00013759155,0.00012616276,0.00011568329,0.00010607427,9.7263415e-5,8.918432e-5,8.1776394e-5,7.498379e-5,6.8755406e-5,6.304437e-5,5.78077e-5,5.3006013e-5,4.8603168e-5,4.4566037e-5,4.086424e-5,3.746993e-5,3.4357563e-5,3.1503714e-5,2.8886918e-5,2.648748e-5,2.4287323e-5,2.2269942e-5,2.0420131e-5,1.8723971e-5,1.71687e-5,1.5742615e-5,1.4434983e-5,1.3235968e-5,1.2136547e-5,1.1128448e-5,1.0204084e-5,9.356501e-6,8.579321e-6,7.866695e-6,7.213263e-6,6.6141006e-6,6.0647126e-6,5.560959e-6,5.0990484e-6,4.6755054e-6,4.287143e-6,3.93104e-6,3.604515e-6,3.3051128e-6,3.0305798e-6,2.7788503e-6,2.5480304e-6,2.336383e-6,2.1423157e-6,1.9643664e-6,1.8012e-6,1.6515867e-6,1.5144008e-6,1.3886098e-6,1.2732676e-6,1.167506e-6,1.0705293e-6,9.816077e-7,9.0007234e-7,8.2530954e-7,7.567567e-7,6.938982e-7,6.3626084e-7,5.83411e-7,5.349506e-7,4.905159e-7,4.497721e-7,4.1241262e-7,3.7815633e-7,3.4674548e-7,3.1794372e-7,2.9153432e-7,2.6731857e-7,2.4511425e-7,2.2475429e-7,2.060855e-7,1.8896739e-7,1.7327118e-7,1.5887872e-7,1.4568162e-7,1.3358085e-7,1.224852e-7,1.1231131e-7,1.02982284e-7,9.4428344e-8,8.658475e-8,7.939267e-8,7.279814e-8,6.6751234e-8,6.120673e-8,5.6122648e-8,5.1460976e-8,4.718642e-8,4.3267008e-8,3.967308e-8,3.6377745e-8,3.3356063e-8,3.0585433e-8,2.8044884e-8,2.5715412e-8,2.3579387e-8,2.1620789e-8,1.9824917e-8,1.817818e-8,1.666826e-8,1.5283728e-8,1.4014227e-8,1.2850149e-8,1.1782787e-8,1.0804061e-8,9.9066515e-9,9.083766e-9,8.3292475e-9,7.637387e-9,7.0030084e-9,6.42131e-9,5.8879306e-9,5.398866e-9,4.9504143e-9,4.539222e-9,4.162176e-9,3.816456e-9,3.499446e-9,3.2087741e-9,2.9422405e-9,2.6978515e-9,2.473757e-9,2.2682811e-9,2.0798687e-9,1.90711e-9,1.748698e-9,1.603444e-9,1.4702584e-9,1.3481328e-9,1.2361538e-9,1.133474e-9,1.0393251e-9,9.529946e-10,8.738367e-10,8.0125234e-10,7.346985e-10,6.736715e-10,6.177148e-10,5.66405e-10,5.193581e-10,4.762181e-10,4.3666154e-10,4.0039144e-10,3.6713332e-10,3.366384e-10,3.086759e-10,2.8303657e-10,2.5952643e-10,2.3796956e-10,2.1820286e-10,2.0007844e-10,1.8345912e-10,1.6822059e-10,1.5424752e-10,1.4143538e-10,1.2968718e-10,1.1891485e-10,1.09037515e-10,9.998042e-11,9.167582e-11,8.406086e-11,7.707857e-11,7.067612e-11,6.4805605e-11,5.942259e-11,5.4486814e-11,4.996092e-11,4.5811056e-11,4.2005805e-11,3.8516634e-11,3.5317357e-11,3.2383755e-11,2.969389e-11,2.7227396e-11,2.4965826e-11,2.2892065e-11,2.0990598e-11,1.9247035e-11,1.7648332e-11,1.6182392e-11,1.4838245e-11,1.3605722e-11,1.24755995e-11,1.1439326e-11,1.048913e-11,9.617879e-12,8.81898e-12,8.086456e-12,7.414762e-12,6.7988753e-12,6.2341334e-12,5.7163124e-12,5.2414926e-12,4.8061225e-12,4.4069067e-12,4.040859e-12,3.705209e-12,3.397446e-12,3.1152405e-12,2.8564761e-12,2.6192108e-12,2.4016488e-12,2.2021623e-12,2.019242e-12,1.8515192e-12,1.6977245e-12,1.5567078e-12,1.4274014e-12,1.3088382e-12,1.2001208e-12,1.1004361e-12,1.0090294e-12,9.252173e-13,8.4836494e-13,7.7789636e-13,7.1328257e-13,6.5403444e-13,5.9970887e-13,5.4989466e-13,5.0421917e-13,4.623367e-13,4.2393397e-13,3.887203e-13,3.5643233e-13,3.2682562e-13,2.9967877e-13,2.7478624e-13,2.519619e-13,2.310329e-13,2.118424e-13,1.9424628e-13,1.7811142e-13,1.6331707e-13,1.497513e-13,1.3731263e-13,1.259069e-13,1.1544877e-13,1.0585914e-13,9.706624e-14,8.900353e-14,8.1610696e-14,7.483179e-14,6.861609e-14,6.2916564e-14,5.769046e-14,5.2898563e-14,4.8504596e-14,4.4475694e-14,4.0781367e-14,3.7393974e-14,3.428788e-14,3.143985e-14,2.8828333e-14,2.6433786e-14,2.423809e-14,2.222482e-14,2.0378737e-14,1.8686033e-14,1.7133896e-14,1.5710686e-14,1.4405721e-14,1.3209124e-14,1.21119215e-14,1.11058776e-14,1.01833986e-14,9.337543e-15,8.561912e-15,7.850741e-15,7.198641e-15,6.6007054e-15,6.052413e-15,5.5496858e-15,5.0887164e-15,4.666018e-15,4.278448e-15,3.9230708e-15,3.5972117e-15,3.2984064e-15,3.0244334e-15,2.7732172e-15,2.5428674e-15,2.3316422e-15,2.1379709e-15,1.9603862e-15,1.7975521e-15,1.6482371e-15,1.5113308e-15,1.3857962e-15,1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diff --git a/lib/node_modules/@stdlib/math/base/special/expf/test/fixtures/julia/small_positive.json b/lib/node_modules/@stdlib/math/base/special/expf/test/fixtures/julia/small_positive.json new file mode 100644 index 000000000000..7ffdf2e41e1a --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/test/fixtures/julia/small_positive.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/expf/test/fixtures/julia/tiny.json b/lib/node_modules/@stdlib/math/base/special/expf/test/fixtures/julia/tiny.json new file mode 100644 index 000000000000..f139152a3ca5 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/test/fixtures/julia/tiny.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/expf/test/test.js b/lib/node_modules/@stdlib/math/base/special/expf/test/test.js new file mode 100755 index 000000000000..5174771755e1 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/test/test.js @@ -0,0 +1,165 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2018 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 tape = require( 'tape' ); +var isnanf = require( '@stdlib/math/base/assert/is-nanf' ); +var abs = require( '@stdlib/math/base/special/abs' ); +var PINF = require( '@stdlib/constants/float32/pinf' ); +var NINF = require( '@stdlib/constants/float32/ninf' ); +var EPS = require( '@stdlib/constants/float64/eps' ); +var expf = require( './../lib' ); + + +// FIXTURES // + +var mediumNegative = require( './fixtures/julia/medium_negative.json' ); +var mediumPositive = require( './fixtures/julia/medium_positive.json' ); +var smallNegative = require( './fixtures/julia/small_negative.json' ); +var smallPositive = require( './fixtures/julia/small_positive.json' ); +var tiny = require( './fixtures/julia/tiny.json' ); + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof expf, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function accurately computes the natural exponential function for negative medium numbers', function test( t ) { + var expected; + var delta; + var tol; + var x; + var v; + var i; + + x = mediumNegative.x; + expected = mediumNegative.expected; + + for ( i = 0; i < x.length; i++ ) { + v = expf( x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function accurately computes the natural exponential function for positive medium numbers', function test( t ) { + var expected; + var delta; + var tol; + var x; + var v; + var i; + + x = mediumPositive.x; + expected = mediumPositive.expected; + + for ( i = 0; i < x.length; i++ ) { + v = expf( x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function accurately computes the natural exponential function for negative small numbers', function test( t ) { + var expected; + var delta; + var tol; + var x; + var v; + var i; + + x = smallNegative.x; + expected = smallNegative.expected; + + for ( i = 0; i < x.length; i++ ) { + v = expf( x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function accurately computes the natural exponential function for positive small numbers', function test( t ) { + var expected; + var delta; + var tol; + var x; + var v; + var i; + + x = smallPositive.x; + expected = smallPositive.expected; + + for ( i = 0; i < x.length; i++ ) { + v = expf( x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function accurately computes the natural exponential function for very small `x`', function test( t ) { + var expected; + var delta; + var tol; + var x; + var v; + var i; + + x = tiny.x; + expected = tiny.expected; + + for ( i = 0; i < x.length; i++ ) { + v = expf( x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function returns `0` if provided a `-infinity`', function test( t ) { + var val = expf( NINF ); + t.equal( val, 0.0, 'returns 0' ); + t.end(); +}); + +tape( 'the function returns `+infinity` if provided a `+infinity`', function test( t ) { + var val = expf( PINF ); + t.equal( val, PINF, 'returns +infinity' ); + t.end(); +}); + +tape( 'the function returns `NaN` if provided a `NaN`', function test( t ) { + var val = expf( NaN ); + t.equal( isnanf( val ), true, 'returns NaN' ); + t.end(); +}); diff --git a/lib/node_modules/@stdlib/math/base/special/expf/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/expf/test/test.native.js new file mode 100755 index 000000000000..c03a416bd325 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expf/test/test.native.js @@ -0,0 +1,174 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2022 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 isnanf = require( '@stdlib/math/base/assert/is-nanf' ); +var abs = require( '@stdlib/math/base/special/abs' ); +var PINF = require( '@stdlib/constants/float32/pinf' ); +var NINF = require( '@stdlib/constants/float32/ninf' ); +var tryRequire = require( '@stdlib/utils/try-require' ); +var EPS = require( '@stdlib/constants/float64/eps' ); + + +// FIXTURES // + +var mediumNegative = require( './fixtures/julia/medium_negative.json' ); +var mediumPositive = require( './fixtures/julia/medium_positive.json' ); +var smallNegative = require( './fixtures/julia/small_negative.json' ); +var smallPositive = require( './fixtures/julia/small_positive.json' ); +var tiny = require( './fixtures/julia/tiny.json' ); + + +// VARIABLES // + +var expf = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( expf instanceof Error ) +}; + + +// TESTS // + +tape( 'main export is a function', opts, function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof expf, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function accurately computes the natural exponential function for negative medium numbers', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var v; + var i; + + x = mediumNegative.x; + expected = mediumNegative.expected; + + for ( i = 0; i < x.length; i++ ) { + v = expf( x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function accurately computes the natural exponential function for positive medium numbers', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var v; + var i; + + x = mediumPositive.x; + expected = mediumPositive.expected; + + for ( i = 0; i < x.length; i++ ) { + v = expf( x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function accurately computes the natural exponential function for negative small numbers', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var v; + var i; + + x = smallNegative.x; + expected = smallNegative.expected; + + for ( i = 0; i < x.length; i++ ) { + v = expf( x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function accurately computes the natural exponential function for positive small numbers', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var v; + var i; + + x = smallPositive.x; + expected = smallPositive.expected; + + for ( i = 0; i < x.length; i++ ) { + v = expf( x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function accurately computes the natural exponential function for very small `x`', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var v; + var i; + + x = tiny.x; + expected = tiny.expected; + + for ( i = 0; i < x.length; i++ ) { + v = expf( x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function returns `0` if provided a `-infinity`', opts, function test( t ) { + var val = expf( NINF ); + t.equal( val, 0.0, 'returns 0' ); + t.end(); +}); + +tape( 'the function returns `+infinity` if provided a `+infinity`', opts, function test( t ) { + var val = expf( PINF ); + t.equal( val, PINF, 'returns +infinity' ); + t.end(); +}); + +tape( 'the function returns `NaN` if provided a `NaN`', opts, function test( t ) { + var val = expf( NaN ); + t.equal( isnanf( val ), true, 'returns NaN' ); + t.end(); +});