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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. diff --git a/lib/node_modules/@stdlib/math/base/special/powf/README.md b/lib/node_modules/@stdlib/math/base/special/powf/README.md new file mode 100644 index 000000000000..d1da22325c2a --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/README.md @@ -0,0 +1,240 @@ + + +# Exponential Function + +> [Exponential function][exponential-function] for a single-precision floating-point number. + +
+ +The [exponential function][exponential-function] is defined as + + + +```math +y = b^x +``` + + + + + +where `b` is the **base** and `x` is the **exponent**. + +
+ + + +
+ +## Usage + +```javascript +var powf = require( '@stdlib/math/base/special/powf' ); +``` + +#### powf( base, exponent ) + +Evaluates the [exponential function][exponential-function] for a single-precision floating-point number. + +```javascript +var v = powf( 2.0, 3.0 ); +// returns 8.0 + +v = powf( 4.0, 0.5 ); +// returns 2.0 + +v = powf( 100.0, 0.0 ); +// returns 1.0 + +v = powf( 3.1415927410125732, 5.0 ); +// returns ~306.0197 + +v = powf( 3.1415927410125732, -0.2 ); +// returns ~0.7954 + +v = powf( NaN, 3.0 ); +// returns NaN + +v = powf( 5.0, NaN ); +// returns NaN + +v = powf( NaN, NaN ); +// returns NaN +``` + +
+ + + +
+ +## Examples + + + +```javascript +var randu = require( '@stdlib/random/base/randu' ); +var roundf = require( '@stdlib/math/base/special/roundf' ); +var powf = require( '@stdlib/math/base/special/powf' ); + +var b; +var x; +var i; + +for ( i = 0; i < 100; i++ ) { + b = roundf( randu()*10.0 ); + x = roundf( randu()*10.0 ) - 5.0; + console.log( '%d^%d = %d', b, x, powf( b, x ) ); +} +``` + +
+ + + + + +* * * + +
+ +## C APIs + + + +
+ +
+ + + + + +
+ +### Usage + +```c +#include "stdlib/math/base/special/powf.h" +``` + +#### stdlib_base_powf( base, exponent ) + +Evaluates the exponential function for a single-precision floating-point number. + +```c +float out = stdlib_base_powf( 3.1415927410125732f, 5.0f ); +// returns ~306.0197f + +out = stdlib_base_powf( 4.0f, 0.5f ); +// returns 2.0f +``` + +The function accepts the following arguments: + +- **base**: `[in] float` base. +- **exponent**: `[in] float` exponent. + +```c +float stdlib_base_powf( const float base, const float exponent ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +### Examples + +```c +#include "stdlib/math/base/special/powf.h" +#include +#include + +int main( void ) { + float out; + float b; + float x; + int i; + + for ( i = 0; i < 100; i++ ) { + b = ( ( (float)rand() / (float)RAND_MAX ) * 10.0f ); + x = ( ( (float)rand() / (float)RAND_MAX ) * 10.0f ) - 5.0f; + out = stdlib_base_powf( b, x ); + printf( "powf(%f, %f) = %f\n", b, x, out ); + } +} +``` + +
+ + + +
+ + + + + +
+ +* * * + +## See Also + +- [`@stdlib/math/base/special/expf`][@stdlib/math/base/special/expf]: natural exponential function. +- [`@stdlib/math/base/special/powm1`][@stdlib/math/base/special/powm1]: evaluate bˣ - 1. + +
+ + + + + +
+ +[exponential-function]: https://en.wikipedia.org/wiki/Exponential_function + + + +[@stdlib/math/base/special/expf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/expf + +[@stdlib/math/base/special/powm1]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/powm1 + + + +
+ + diff --git a/lib/node_modules/@stdlib/math/base/special/powf/benchmark/benchmark.js b/lib/node_modules/@stdlib/math/base/special/powf/benchmark/benchmark.js new file mode 100644 index 000000000000..1ea8ca5cdd32 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/benchmark/benchmark.js @@ -0,0 +1,76 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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-nan' ); +var pkg = require( './../package.json' ).name; +var powf = require( './../lib' ); + + +// MAIN // + +bench( pkg, function benchmark( b ) { + var x; + var y; + var z; + var i; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + x = ( randu()*100.0 ) - 0.0; + y = ( randu()*100.0 ) - 50.0; + z = powf( x, y ); + if ( isnanf( z ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnanf( z ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); + +bench( pkg+'::built-in', function benchmark( b ) { + var x; + var y; + var z; + var i; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + x = ( randu()*100.0 ) - 0.0; + y = ( randu()*100.0 ) - 50.0; + z = Math.powf( x, y ); // eslint-disable-line stdlib/no-builtin-math + if ( isnanf( z ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnanf( z ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); diff --git a/lib/node_modules/@stdlib/math/base/special/powf/benchmark/benchmark.native.js b/lib/node_modules/@stdlib/math/base/special/powf/benchmark/benchmark.native.js new file mode 100644 index 000000000000..a6061673bc92 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/benchmark/benchmark.native.js @@ -0,0 +1,62 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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-nan' ); +var tryRequire = require( '@stdlib/utils/try-require' ); +var pkg = require( './../package.json' ).name; + + +// VARIABLES // + +var powf = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( powf instanceof Error ) +}; + + +// MAIN // + +bench( pkg+'::native', opts, function benchmark( b ) { + var v; + var x; + var y; + var i; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + v = ( randu()*100.0 ) - 0.0; + x = ( randu()*100.0 ) - 50.0; + y = powf( v, 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/powf/benchmark/c/Makefile b/lib/node_modules/@stdlib/math/base/special/powf/benchmark/c/Makefile new file mode 100644 index 000000000000..d564e8b2d6f9 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/benchmark/c/Makefile @@ -0,0 +1,127 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2025 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 C targets: +c_targets := benchmark.out + + +# RULES # + +#/ +# Compiles C source files. +# +# @param {string} [C_COMPILER] - C compiler +# @param {string} [CFLAGS] - C compiler flags +# @param {(string|void)} [fPIC] - compiler flag indicating whether to generate position independent code +# +# @example +# make +# +# @example +# make all +#/ +all: $(c_targets) + +.PHONY: all + +#/ +# Compiles C source files. +# +# @private +# @param {string} CC - C compiler +# @param {string} CFLAGS - C compiler flags +# @param {(string|void)} fPIC - compiler flag indicating whether to generate position independent code +#/ +$(c_targets): %.out: %.c + $(QUIET) $(CC) $(CFLAGS) $(fPIC) -o $@ $< -lm + +#/ +# 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/powf/benchmark/c/benchmark.c b/lib/node_modules/@stdlib/math/base/special/powf/benchmark/c/benchmark.c new file mode 100644 index 000000000000..c25def4fd0c3 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/benchmark/c/benchmark.c @@ -0,0 +1,134 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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 +#include +#include +#include +#include + +#define NAME "powf" +#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; + float z; + double t; + int i; + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + x = ( 100.0f*rand_float() ) - 0.0f; + y = ( 100.0f*rand_float() ) - 50.0f; + z = powf( x, y ); + if ( z != z ) { + printf( "should not return NaN\n" ); + break; + } + } + elapsed = tic() - t; + if ( z != z ) { + printf( "should not return NaN\n" ); + } + return elapsed; +} + +/** +* Main execution sequence. +*/ +int main( void ) { + double elapsed; + int i; + + // Use the current time to seed the random number generator: + srand( time( NULL ) ); + + print_version(); + for ( i = 0; i < REPEATS; i++ ) { + printf( "# c::%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/powf/benchmark/c/native/Makefile b/lib/node_modules/@stdlib/math/base/special/powf/benchmark/c/native/Makefile new file mode 100644 index 000000000000..a4bd7b38fd74 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/benchmark/c/native/Makefile @@ -0,0 +1,146 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2025 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/powf/benchmark/c/native/benchmark.c b/lib/node_modules/@stdlib/math/base/special/powf/benchmark/c/native/benchmark.c new file mode 100644 index 000000000000..f9f2870f73aa --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/benchmark/c/native/benchmark.c @@ -0,0 +1,135 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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/powf.h" +#include +#include +#include +#include +#include + +#define NAME "powf" +#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 b; + float x; + float y; + double t; + int i; + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + b = rand_float() * 10.0f; + x = rand_float() * 5.0f; + y = stdlib_base_powf( b, 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/powf/binding.gyp b/lib/node_modules/@stdlib/math/base/special/powf/binding.gyp new file mode 100644 index 000000000000..68a1ca11d160 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/binding.gyp @@ -0,0 +1,170 @@ +# @license Apache-2.0 +# +# Copyright (c) 2025 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/powf/docs/repl.txt b/lib/node_modules/@stdlib/math/base/special/powf/docs/repl.txt new file mode 100644 index 000000000000..04afe597090f --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/docs/repl.txt @@ -0,0 +1,40 @@ + +{{alias}}( b, x ) + Evaluates the exponential function `bˣ` for a single-precision + floating-point number. + + Parameters + ---------- + b: number + Base. + + x: number + Exponent. + + Returns + ------- + y: number + Function value. + + Examples + -------- + > var y = {{alias}}( 2.0, 3.0 ) + 8.0 + > y = {{alias}}( 4.0, 0.5 ) + 2.0 + > y = {{alias}}( 100.0, 0.0 ) + 1.0 + > y = {{alias}}( {{alias:@stdlib/constants/float32/pi}}, 5.0 ) + ~306.0197 + > y = {{alias}}( {{alias:@stdlib/constants/float32/pi}}, -0.2 ) + ~0.7954 + > y = {{alias}}( NaN, 3.0 ) + NaN + > y = {{alias}}( 5.0, NaN ) + NaN + > y = {{alias}}( NaN, NaN ) + NaN + + See Also + -------- + diff --git a/lib/node_modules/@stdlib/math/base/special/powf/docs/types/index.d.ts b/lib/node_modules/@stdlib/math/base/special/powf/docs/types/index.d.ts new file mode 100644 index 000000000000..eb15235cc688 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/docs/types/index.d.ts @@ -0,0 +1,65 @@ +/* +* @license Apache-2.0 +* +* Copyright (c) 2025 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 exponential function for a single-precision floating-point number. +* +* @param b - base +* @param x - exponent +* @returns function value +* +* @example +* var v = powf( 2.0, 3.0 ); +* // returns 8.0 +* +* @example +* var v = powf( 4.0, 0.5 ); +* // returns 2.0 +* +* @example +* var v = powf( 100.0, 0.0 ); +* // returns 1.0 +* +* @example +* var v = powf( 3.1415927410125732, 5.0 ); +* // returns ~306.0197 +* +* @example +* var v = powf( 3.1415927410125732, -0.2 ); +* // returns ~0.7954 +* +* @example +* var v = powf( NaN, 3.0 ); +* // returns NaN +* +* @example +* var v = powf( 5.0, NaN ); +* // returns NaN +* +* @example +* var v = powf( NaN, NaN ); +* // returns NaN +*/ +declare function powf( b: number, x: number ): number; + + +// EXPORTS // + +export = powf; diff --git a/lib/node_modules/@stdlib/math/base/special/powf/docs/types/test.ts b/lib/node_modules/@stdlib/math/base/special/powf/docs/types/test.ts new file mode 100644 index 000000000000..65810932a669 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/docs/types/test.ts @@ -0,0 +1,56 @@ +/* +* @license Apache-2.0 +* +* Copyright (c) 2025 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 powf = require( './index' ); + + +// TESTS // + +// The function returns a number... +{ + powf( 8, 2 ); // $ExpectType number +} + +// The compiler throws an error if the function is provided values other than two numbers... +{ + powf( true, 3 ); // $ExpectError + powf( false, 2 ); // $ExpectError + powf( '5', 1 ); // $ExpectError + powf( [], 1 ); // $ExpectError + powf( {}, 2 ); // $ExpectError + powf( ( x: number ): number => x, 2 ); // $ExpectError + + powf( 9, true ); // $ExpectError + powf( 9, false ); // $ExpectError + powf( 5, '5' ); // $ExpectError + powf( 8, [] ); // $ExpectError + powf( 9, {} ); // $ExpectError + powf( 8, ( x: number ): number => x ); // $ExpectError + + powf( [], true ); // $ExpectError + powf( {}, false ); // $ExpectError + powf( false, '5' ); // $ExpectError + powf( {}, [] ); // $ExpectError + powf( '5', ( x: number ): number => x ); // $ExpectError +} + +// The compiler throws an error if the function is provided insufficient arguments... +{ + powf(); // $ExpectError + powf( 3 ); // $ExpectError +} diff --git a/lib/node_modules/@stdlib/math/base/special/powf/examples/c/Makefile b/lib/node_modules/@stdlib/math/base/special/powf/examples/c/Makefile new file mode 100644 index 000000000000..25ced822f96a --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/examples/c/Makefile @@ -0,0 +1,146 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2025 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/powf/examples/c/example.c b/lib/node_modules/@stdlib/math/base/special/powf/examples/c/example.c new file mode 100644 index 000000000000..83d68964bb42 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/examples/c/example.c @@ -0,0 +1,35 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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/powf.h" +#include +#include + +int main( void ) { + float out; + float b; + float x; + int i; + + for ( i = 0; i < 100; i++ ) { + b = ( ( (float)rand() / (float)RAND_MAX ) * 10.0f ); + x = ( ( (float)rand() / (float)RAND_MAX ) * 10.0f ) - 5.0f; + out = stdlib_base_powf( b, x ); + printf( "powf(%f, %f) = %f\n", b, x, out ); + } +} diff --git a/lib/node_modules/@stdlib/math/base/special/powf/examples/index.js b/lib/node_modules/@stdlib/math/base/special/powf/examples/index.js new file mode 100644 index 000000000000..e389258c36a6 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/examples/index.js @@ -0,0 +1,33 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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 roundf = require( '@stdlib/math/base/special/roundf' ); +var powf = require('./../lib'); + +var b; +var x; +var i; + +for ( i = 0; i < 100; i++ ) { + b = roundf( randu()*10.0 ); + x = roundf( randu()*10.0 ) - 5.0; + console.log( '%d^%d = %d', b, x, powf( b, x ) ); +} diff --git a/lib/node_modules/@stdlib/math/base/special/powf/include.gypi b/lib/node_modules/@stdlib/math/base/special/powf/include.gypi new file mode 100644 index 000000000000..ecfaf82a3279 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/include.gypi @@ -0,0 +1,53 @@ +# @license Apache-2.0 +# +# Copyright (c) 2025 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': [ + ' 0 00000001 00000000000000000000000 => 0x00800000 = 8388608 +var MIN_NORM_WORD = 0x00800000|0; // asm type annotation + +// 1.0 => 0 01111111 00000000000000000000000 => 0x3f800000 = 1065353216 +var ONE_WORD = 0x3f800000|0; // asm type annotation + +// Mask to clear lower 12 mantissa bits: +var TRUNC_MASK = 0xfffff000|0; // asm type annotation + +// 0x20000000 = 536870912 => 0 01000000 00000000000000000000000 +var SIGNIFICAND_HALF_WORD = 0x20000000|0; // asm type annotation + +// 0x00400000 = 4194304 => 0 00000000000 10000000000000000000 +var EXP_CORRECTION_WORD = 0x00400000|0; // asm type annotation + +var TWO24 = f32( 16777216.0 ); // 0x4b800000 + +// 2/(3*LN2) +var CP = f32( 9.6179670095e-01 ); // 0x3f76384f + +// (float)CP +var CP_HI = f32( 9.6191406250e-01 ); // 0x3f764000 =12b cp + +// Low: CP_HI +var CP_LO = f32( -1.1736857402e-04 ); // 0xb8f623c6 + +var BP = [ + f32( 1.0 ), + f32( 1.5 ) +]; +var DP_HI = [ + f32( 0.0 ), + f32( 5.84960938e-01 ) // 0x3f15c000 +]; +var DP_LO = [ + f32( 0.0 ), + f32( 1.56322085e-06 ) // 0x35d1cfdc +]; + +var ONE = f32( 1.0 ); +var THREE = f32( 3.0 ); + + +// MAIN // + +/** +* Computes \\(\operatorname{log2}(ax)\\). +* +* @private +* @param {Array} out - output array +* @param {number} ax - absolute value of `x` +* @param {number} ahx - high word of `ax` +* @returns {Array} output array containing a tuple comprised of high and low parts +* +* @example +* var t = log2axf( [ 0.0, 0.0 ], 9.0, 1075970048 ); // => [ t1, t2 ] +* // returns [ 3.169923782348633, 0.0000012190936795504075 ] +*/ +function log2axf( out, ax, ahx ) { + var tmp; + var ss; // `hs + ls` + var s2; // `ss` squared + var hs; + var ls; + var ht; + var lt; + var bp; // `BP` constant + var dp; // `DP` constant + var hp; + var lp; + var hz; + var lz; + var t1; + var t2; + var t; + var r; + var u; + var v; + var n; + var j; + var k; + + n = 0|0; // asm type annotation + + // Check if `x` is subnormal... + if ( ahx < MIN_NORM_WORD ) { + ax = f32( ax * TWO24 ); + n -= 24|0; // asm type annotation + ahx = toWordf( ax ) | 0; // asm type annotation + } + // Extract the unbiased exponent of `x`: + n += ((ahx >> NUM_SIGNIFICAND_BITS) - BIAS)|0; // asm type annotation + + // Isolate the significand bits of `x`: + j = (ahx & SIGNIFICAND_MASK)|0; // asm type annotation + + // Normalize `ahx` by setting the (biased) exponent to `127`: + ahx = (j | ONE_WORD)|0; // asm type annotation + + // Determine the interval of `|x|` by comparing significand bits... + + // |x| < sqrt(3/2) + if ( j <= 0x1CC471 ) { // 0 00000000001 11001100100010001110 + k = 0; + } + // |x| < sqrt(3) + else if ( j < 0x5DB3D7 ) { // 0 00000000010 11101101100111110111 + k = 1; + } + // |x| >= sqrt(3) + else { + k = 0; + n += 1|0; // asm type annotation + ahx -= MIN_NORM_WORD; + } + // Load the normalized word into `|x|`: + ax = fromWordf( ahx ); + + // Compute `ss = hs + ls = (x-1)/(x+1)` or `(x-1.5)/(x+1.5)`: + bp = BP[ k ]; // BP[0] = 1.0, BP[1] = 1.5 + u = f32( ax - bp ); // (x-1) || (x-1.5) + v = f32( ONE / f32( ax + bp ) ); // 1/(x+1) || 1/(x+1.5) + ss = f32( u * v ); + tmp = toWordf( ss ) | 0; // asm type annotation + hs = fromWordf( tmp & TRUNC_MASK ); + + // Compute `ht = ax + bp` (via manipulation, i.e., bit flipping): + tmp = ((ahx>>1) & TRUNC_MASK) | SIGNIFICAND_HALF_WORD; + tmp += EXP_CORRECTION_WORD; + tmp += (k << 21); // `(k<<21)` can be considered the word equivalent of `1.0` or `1.5` + ht = fromWordf( tmp ); + lt = f32( ax - f32( ht - bp ) ); + ls = f32( v * f32( f32( u - f32(hs*ht) ) - f32( hs*lt ) ) ); + + // Compute `log(ax)`... + + s2 = f32( ss * ss ); + r = f32( f32( s2 * s2 ) * polyvalL( s2 ) ); + r = f32( r + f32( ls * f32(hs + ss) ) ); + s2 = f32( hs * hs ); + ht = f32( f32( THREE + s2 ) + r ); + tmp = toWordf( ht ) | 0; // asm type annotation + ht = fromWordf( tmp & TRUNC_MASK ); + lt = f32( r - f32( f32(ht-THREE) - s2 ) ); + + // u+v = ss*(1+...): + u = f32( hs * ht ); + v = f32( f32( ls*ht ) + f32( lt*ss ) ); + + // 2/(3LN2) * (ss+...): + hp = f32( u + v ); + tmp = toWordf( hp ) | 0; // asm type annotation + hp = fromWordf( tmp & TRUNC_MASK ); + lp = f32( v - f32( hp - u ) ); + hz = f32( CP_HI * hp ); // CP_HI+CP_LO = 2/(3*LN2) + lz = f32( f32( f32( CP_LO*hp ) + f32( lp*CP ) ) + DP_LO[ k ] ); + + // log2(ax) = (ss+...)*2/(3*LN2) = n + dp + hz + lz + dp = DP_HI[ k ]; + t = f32( n ); + t1 = f32( f32( f32(hz+lz) + dp ) + t ); // log2(ax) + tmp = toWordf( t1 ) | 0; // asm type annotation + t1 = fromWordf( tmp & TRUNC_MASK ); + t2 = f32( lz - f32( f32( f32(t1-t) - dp ) - hz ) ); + + out[ 0 ] = t1; + out[ 1 ] = t2; + return out; +} + + +// EXPORTS // + +module.exports = log2axf; diff --git a/lib/node_modules/@stdlib/math/base/special/powf/lib/logxf.js b/lib/node_modules/@stdlib/math/base/special/powf/lib/logxf.js new file mode 100644 index 000000000000..de7a88d3b295 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/lib/logxf.js @@ -0,0 +1,98 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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 copyright and license were part of the original implementation available as part of [FreeBSD]{@link https://svnweb.freebsd.org/base/release/12.2.0/lib/msun/src/e_powf.c}. The implementation follows the original, but has been modified for JavaScript. +* +* ```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. +* ``` +*/ + +'use strict'; + +// MODULES // + +var fromWordf = require( '@stdlib/number/float32/base/from-word' ); +var toWordf = require( '@stdlib/number/float32/base/to-word' ); +var f32 = require( '@stdlib/number/float64/base/to-float32' ); +var polyvalW = require( './polyval_w.js' ); + + +// VARIABLES // + +// Mask to clear lower 12 mantissa bits: +var TRUNC_MASK = 0xfffff000|0; // asm type annotation + +// 1/LN2 +var INV_LN2 = f32( 1.4426950216e+00 ); // 0x3fb8aa3b + +// High (16 bits): 1/LN2 +var INV_LN2_HI = f32( 1.4426879883e+00 ); // 0x3fb8aa00 + +// Low: 1/LN2 +var INV_LN2_LO = f32( 7.0526075433e-06 ); // 0x36eca570 + + +// MAIN // + +/** +* Computes \\(\operatorname{log}(x)\\) assuming \\(|1-x|\\) is small and using the approximation \\(x - x^2/2 + x^3/3 - x^4/4\\). +* +* @private +* @param {Array} out - output array +* @param {number} ax - absolute value of `x` +* @returns {Array} output array containing a tuple comprised of high and low parts +* +* @example +* var t = logxf( [ 0.0, 0.0 ], 9.0 ); +* // Expected output: [ -1265.7236328125, -0.0008163940840404393 ] +*/ +function logxf( out, ax ) { + var tmp; + var t2; + var t1; + var t; + var w; + var u; + var v; + + t = f32( ax - 1.0 ); // `t` has `20` trailing zeros + w = f32( f32( t * t ) * polyvalW( t ) ); + u = f32( INV_LN2_HI * t ); // `INV_LN2_HI` has `16` significant bits + v = f32( f32( t*INV_LN2_LO ) - f32( w*INV_LN2 ) ); + t1 = f32( u + v ); + tmp = toWordf( t1 ) | 0; // asm type annotation + t1 = fromWordf( tmp & TRUNC_MASK ); + t2 = f32( f32( v ) - f32( t1 - u ) ); + + out[ 0 ] = t1; + out[ 1 ] = t2; + return out; +} + + +// EXPORTS // + +module.exports = logxf; diff --git a/lib/node_modules/@stdlib/math/base/special/powf/lib/main.js b/lib/node_modules/@stdlib/math/base/special/powf/lib/main.js new file mode 100644 index 000000000000..dc4f3fb5c16e --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/lib/main.js @@ -0,0 +1,305 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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 copyright and license were part of the original implementation available as part of [FreeBSD]{@link https://svnweb.freebsd.org/base/release/12.2.0/lib/msun/src/e_powf.c}. The implementation follows the original, but has been modified for JavaScript. +* +* ```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. +* ``` +*/ + +'use strict'; + +// MODULES // + +var isnanf = require( '@stdlib/math/base/assert/is-nanf' ); +var isOddf = require( '@stdlib/math/base/assert/is-oddf' ); +var isInfinitef = require( '@stdlib/math/base/assert/is-infinitef' ); +var isIntegerf = require( '@stdlib/math/base/assert/is-integerf' ); +var sqrtf = require( '@stdlib/math/base/special/sqrtf' ); +var absf = require( '@stdlib/math/base/special/absf' ); +var fromWordf = require( '@stdlib/number/float32/base/from-word' ); +var toWordf = require( '@stdlib/number/float32/base/to-word' ); +var f32 = require( '@stdlib/number/float64/base/to-float32' ); +var NINF = require( '@stdlib/constants/float32/ninf' ); +var PINF = require( '@stdlib/constants/float32/pinf' ); +var ABS_MASK = require( '@stdlib/constants/float32/abs-mask' ); +var xIsZerof = require( './x_is_zerof.js' ); +var yIsInfinitef = require( './y_is_infinitef.js' ); +var log2axf = require( './log2axf.js' ); +var logxf = require( './logxf.js' ); +var pow2f = require( './pow2f.js' ); + + +// VARIABLES // + +var ZERO = f32( 0.0 ); +var HALF = f32( 0.5 ); +var ONE = f32( 1.0 ); +var TWO = f32( 2.0 ); +var THREE = f32( 3.0 ); +var FOUR = f32( 4.0 ); +var NEG_ZERO = f32( -0.0 ); +var NEG_HALF = f32( -0.5 ); +var NEG_ONE = f32( -1.0 ); +var HUGE = f32( 1.0e30 ); +var TINY = f32( 1.0e-30 ); + +// -(128-log2(ovfl+.5ulp)) +var OVT = f32( 4.2995665694e-08 ); + +// 2^27 = 134217728.0 => 1 0011010 00000000000000000000000 => 0x4d000000 = 1291845632 +var Y_LARGE_WORD = 0x4d000000|0; // asm type annotation + +// 0.9999994039535522 => 0 01111110 11111111111111111110110 => 0x3f7ffff6 = 1065353206 +var X_BELOW_ONE_WORD = 0x3f7ffff6|0; // asm type annotation + +// 1.0000008344650269 => 0 01111111 00000000000000000000111 => 0x3f800007 = 1065353223 +var X_ABOVE_ONE_WORD = 0x3f800007|0; // asm type annotation + +// Mask to clear lower 12 significand bits: +var TRUNC_MASK_12 = 0xfffff000|0; // asm type annotation + +// 128 => 0 10000110 00000000000000000000000 => 0x43000000 = 1124073472 +var Z_OVF_WORD = 0x43000000|0; // asm type annotation + +// 150 => 0 10000110 00101100000000000000000 => 0x43160000 = 1125515264 +var Z_UNF_WORD = 0x43160000|0; // asm type annotation + +// -150 => 1 10000110 00101100000000000000000 => 0xc3160000 = 3272998912 +var Z_NEG_UNF_WORD = 0xc3160000|0; // asm type annotation + +// Log workspace: +var LOG_WORKSPACE = [ 0.0, 0.0 ]; + + +// MAIN // + +/** +* Evaluates the exponential function for a single-precision floating-point number. +* +* @param {number} x - base +* @param {number} y - exponent +* @returns {number} function value +* +* @example +* var v = powf( 2.0, 3.0 ); +* // returns 8.0 +* +* @example +* var v = powf( 4.0, 0.5 ); +* // returns 2.0 +* +* @example +* var v = powf( 100.0, 0.0 ); +* // returns 1.0 +* +* @example +* var v = powf( 3.1415927410125732, 5.0 ); +* // returns ~306.0197 +* +* @example +* var v = powf( 3.1415927410125732, -0.2 ); +* // returns ~0.7954 +* +* @example +* var v = powf( NaN, 3.0 ); +* // returns NaN +* +* @example +* var v = powf( 5.0, NaN ); +* // returns NaN +* +* @example +* var v = powf( NaN, NaN ); +* // returns NaN +*/ +function powf( x, y ) { + var tmp; + var ahx; // absolute value word `x` + var ahy; // absolute value word `y` + var ax; // absolute value `x` + var hx; // word representation of `x ` + var hy; // word representation of `y` + var sn; + var y1; + var hp; + var lp; + var t; + var z; // y prime + var j; + + x = f32( x ); + y = f32( y ); + + if ( y === ZERO ) { + return ONE; + } + if ( x === ONE ) { + return ONE; + } + if ( isnanf( x ) || isnanf( y ) ) { + return NaN; + } + + // Other special cases `y`... + if ( y === ONE ) { + return x; + } + if ( y === NEG_ONE ) { + return f32( ONE / x ); + } + if ( y === HALF ) { + return sqrtf( x ); + } + if ( y === NEG_HALF ) { + return f32( ONE / sqrtf( x ) ); + } + if ( y === TWO ) { + return f32( x * x ); + } + if ( y === THREE ) { + return f32( f32( x * x ) * x ); + } + if ( y === FOUR ) { + x = f32( x * x ); + return f32( x * x ); + } + if ( isInfinitef( y ) ) { // y is +-inf + return yIsInfinitef( x, y ); + } + + // Other special cases `x`... + if ( x === ZERO ) { + return xIsZerof( x, y ); + } + if ( x === NEG_ONE ) { + if ( isIntegerf( y ) ) { + return ( isOddf( y ) ) ? NEG_ONE : ONE; + } + } + if ( isInfinitef( x ) ) { + if ( x === NINF ) { + // `pow( 1/x, -y )` + return powf( NEG_ZERO, f32( -y ) ); + } + if ( y < ZERO ) { + return ZERO; + } + return PINF; + } + if ( + x < ZERO && + isIntegerf( y ) === false + ) { + // Signal NaN... + return NaN; // (-1)**non-int is NaN + } + ax = absf( x ); + hx = toWordf( x ) | 0; // asm type annotation + hy = toWordf( y ) | 0; // asm type annotation + + // Remove the sign bits (i.e., get absolute values): + ahx = (hx & ABS_MASK) | 0; // asm type annotation + ahy = (hy & ABS_MASK) | 0; // asm type annotation + + // Determine the sign of the result... + if ( x < ZERO && isOddf( y ) ) { + sn = NEG_ONE; + } else { + sn = ONE; + } + + // Case 1: `|y|` is huge + // If |y| > 2^27 + if ( ahy > Y_LARGE_WORD ) { + // Over- or underflow if `x` is not close to unity... + if ( ahx < X_BELOW_ONE_WORD ) { + // y < 0 + if ( y < ZERO ) { + // Signal overflow... + return f32( f32( sn * HUGE ) * HUGE ); + } + // Signal underflow... + return f32( f32( sn * TINY ) * TINY ); + } + if ( ahx > X_ABOVE_ONE_WORD ) { + // y > 0 + if ( y > ZERO ) { + // Signal overflow... + return f32( f32( sn * HUGE ) * HUGE ); + } + // Signal underflow... + return f32( f32( sn * TINY ) * TINY ); + } + // At this point, `|1-x|` is tiny (`<= 2^-20`). Suffice to compute `log(x)` by `x - x^2/2 + x^3/3 - x^4/4`. + t = logxf( LOG_WORKSPACE, ax ); + } + // Case 2: `|y|` is not huge... + else { + t = log2axf( LOG_WORKSPACE, ax, ahx ); + } + // Split `y` into `y1 + y2` and compute `(y1+y2) * (t1+t2)`... + tmp = toWordf( y ) | 0; // asm type annotation + y1 = fromWordf( tmp & TRUNC_MASK_12 ); + lp = f32( f32( f32( y-y1 ) * t[0] ) + f32( y * t[1] ) ); + hp = f32( y1 * t[0] ); + z = f32( lp + hp ); + j = toWordf( z ) | 0; // asm type annotation + + // z > 128 + if ( j > Z_OVF_WORD ) { + // Signal overflow... + return f32( f32( sn * HUGE ) * HUGE ); + } + // z == 128 + if ( j === Z_OVF_WORD ) { + if ( f32( lp+OVT ) > f32( z-hp ) ) { + // Signal overflow... + return f32( f32( sn * HUGE ) * HUGE ); + } + } + // z <= -150 + if ( (j&ABS_MASK) > Z_UNF_WORD ) { + // Signal underflow... + return f32( f32( sn * TINY ) * TINY ); + } + // z == -150 + if ( j === Z_NEG_UNF_WORD ) { + if ( lp <= f32( z-hp ) ) { + // Signal underflow... + return f32( f32( sn * TINY ) * TINY ); + } + } + // Compute `2^(hp+lp)`... + z = pow2f( j, hp, lp ); + + return f32( sn * z ); +} + + +// EXPORTS // + +module.exports = powf; diff --git a/lib/node_modules/@stdlib/math/base/special/powf/lib/native.js b/lib/node_modules/@stdlib/math/base/special/powf/lib/native.js new file mode 100644 index 000000000000..3fcf39fadf05 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/lib/native.js @@ -0,0 +1,74 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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 exponential function for a single-precision floating-point number. +* +* @private +* @param {number} x - base +* @param {number} y - exponent +* @returns {number} function value +* +* @example +* var v = powf( 2.0, 3.0 ); +* // returns 8.0 +* +* @example +* var v = powf( 4.0, 0.5 ); +* // returns 2.0 +* +* @example +* var v = powf( 100.0, 0.0 ); +* // returns 1.0 +* +* @example +* var v = powf( 3.1415927410125732, 5.0 ); +* // returns ~306.0197 +* +* @example +* var v = powf( 3.1415927410125732, -0.2 ); +* // returns ~0.7954 +* +* @example +* var v = powf( NaN, 3.0 ); +* // returns NaN +* +* @example +* var v = powf( 5.0, NaN ); +* // returns NaN +* +* @example +* var v = powf( NaN, NaN ); +*/ +function powf( x, y ) { + return addon( x, y ); +} + + +// EXPORTS // + +module.exports = powf; diff --git a/lib/node_modules/@stdlib/math/base/special/powf/lib/polyval_l.js b/lib/node_modules/@stdlib/math/base/special/powf/lib/polyval_l.js new file mode 100644 index 000000000000..32fee4e9dbb8 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/lib/polyval_l.js @@ -0,0 +1,52 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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 0.6000000238418579; + } + return float64ToFloat32(0.6000000238418579 + float64ToFloat32(x * float64ToFloat32(0.4285714328289032 + float64ToFloat32(x * float64ToFloat32(0.3333333432674408 + float64ToFloat32(x * float64ToFloat32(0.2727281153202057 + float64ToFloat32(x * float64ToFloat32(0.23066075146198273 + float64ToFloat32(x * 0.20697501301765442)))))))))); // eslint-disable-line max-len +} + + +// EXPORTS // + +module.exports = evalpoly; diff --git a/lib/node_modules/@stdlib/math/base/special/powf/lib/polyval_p.js b/lib/node_modules/@stdlib/math/base/special/powf/lib/polyval_p.js new file mode 100644 index 000000000000..7d909f3999df --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/lib/polyval_p.js @@ -0,0 +1,52 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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 0.1666666716337204; + } + return float64ToFloat32(0.1666666716337204 + float64ToFloat32(x * float64ToFloat32(-0.0027777778450399637 + float64ToFloat32(x * float64ToFloat32(0.0000661375597701408 + float64ToFloat32(x * float64ToFloat32(-0.0000016533901998627698 + float64ToFloat32(x * 4.138136944220605e-8)))))))); // eslint-disable-line max-len +} + + +// EXPORTS // + +module.exports = evalpoly; diff --git a/lib/node_modules/@stdlib/math/base/special/powf/lib/polyval_w.js b/lib/node_modules/@stdlib/math/base/special/powf/lib/polyval_w.js new file mode 100644 index 000000000000..00db478d695f --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/lib/polyval_w.js @@ -0,0 +1,52 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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 0.5; + } + return float64ToFloat32(0.5 + float64ToFloat32(x * float64ToFloat32(-0.3333333432674408 + float64ToFloat32(x * 0.25)))); // eslint-disable-line max-len +} + + +// EXPORTS // + +module.exports = evalpoly; diff --git a/lib/node_modules/@stdlib/math/base/special/powf/lib/pow2f.js b/lib/node_modules/@stdlib/math/base/special/powf/lib/pow2f.js new file mode 100644 index 000000000000..7cad10eb4a57 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/lib/pow2f.js @@ -0,0 +1,141 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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 copyright and license were part of the original implementation available as part of [FreeBSD]{@link https://svnweb.freebsd.org/base/release/12.2.0/lib/msun/src/e_powf.c}. The implementation follows the original, but has been modified for JavaScript. +* +* ```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. +* ``` +*/ + +'use strict'; + +// MODULES // + +var fromWordf = require( '@stdlib/number/float32/base/from-word' ); +var toWordf = require( '@stdlib/number/float32/base/to-word' ); +var f32 = require( '@stdlib/number/float64/base/to-float32' ); +var ldexpf = require( '@stdlib/math/base/special/ldexpf' ); +var LN2 = require( '@stdlib/constants/float32/ln-two' ); +var BIAS = require( '@stdlib/constants/float32/exponent-bias' ); +var ABS_MASK = require( '@stdlib/constants/float32/abs-mask' ); +var SIGNIFICAND_MASK = require( '@stdlib/constants/float32/significand-mask' ); +var NUM_SIGNIFICAND_BITS = require( '@stdlib/constants/float32/num-significand-bits' ); +var polyvalP = require( './polyval_p.js' ); + + +// VARIABLES // + +// 1.1754943508222875e-38 => 0 00000001 00000000000000000000000 => 0x00800000 = 8388608 +var MIN_NORM_WORD = 0x00800000|0; // asm type annotation + +// 0.5 => 0 01111110 00000000000000000000000 => 0x3f000000 = 1056964608 +var HALF_WORD = 0x3f000000|0; // asm type annotation + +// Mask to clear lower 15 significand bits: +var TRUNC_MASK_15 = 0xffff8000|0; // asm type annotation + +// High: LN2 +var LN2_HI = f32( 6.93145752e-01 ); // 0x3f317200 + +// Low: LN2 +var LN2_LO = f32( 1.42860654e-06 ); // 0x35bfbe8c + +var ONE = f32( 1.0 ); +var TWO = f32( 2.0 ); + + +// MAIN // + +/** +* Computes \\(2^{\mathrm{hp} + \mathrm{lp}\\). +* +* @private +* @param {number} j - word of `hp + lp` +* @param {number} hp - first power summand +* @param {number} lp - second power summand +* @returns {number} function value +* +* @example +* var z = pow2f( 1065961648, -0.3398475646972656, -0.000002438187359100815 ); +* // returns ~0.79 +*/ +function pow2f( j, hp, lp ) { + var ahs; + var tmp; + var t1; + var t; + var r; + var u; + var v; + var w; + var z; + var n; + var i; + var k; + + i = ( j & ABS_MASK ) |0; // asm type annotation + k = ((i>>NUM_SIGNIFICAND_BITS) - BIAS)|0; // asm type annotation + n = 0; + + // `|z| > 0.5`, set `n = [z+0.5]` + if ( i > HALF_WORD ) { + n = (j + (MIN_NORM_WORD>>(k+1)))|0; // asm type annotation + k = (((n & ABS_MASK)>>NUM_SIGNIFICAND_BITS) - BIAS)|0; // new k for n + tmp = ((n & ~(SIGNIFICAND_MASK >> k)))|0; // asm type annotation + t = fromWordf( tmp ); + n = (((n & SIGNIFICAND_MASK)|MIN_NORM_WORD) >> (NUM_SIGNIFICAND_BITS-k))>>>0; // eslint-disable-line max-len + if ( j < 0 ) { + n = -n; + } + hp = f32( hp - t ); + } + t = f32( lp + hp ); + ahs = toWordf( t ); + t = fromWordf( ahs & TRUNC_MASK_15 ); + u = f32( t * LN2_HI ); + v = f32( f32( f32( lp - f32(t-hp) )*LN2 ) + f32( t*LN2_LO ) ); + z = f32( u + v ); + w = f32( v - f32( z - u ) ); + t = f32( z * z ); + t1 = f32( z - f32( t*polyvalP( t ) ) ); + r = f32( f32( f32(z*t1) / f32(t1-TWO) ) - f32( w + f32(z*w) ) ); + z = f32( ONE - f32(r - z) ); + j = toWordf( z ) |0; // asm type annotation + j += ( (n>>>0) << NUM_SIGNIFICAND_BITS) |0; // asm type annotation + + // Check for subnormal output... + if ( (j>>NUM_SIGNIFICAND_BITS) <= 0 ) { + z = ldexpf( z, n ); + } else { + z = fromWordf( j ); + } + return z; +} + + +// EXPORTS // + +module.exports = pow2f; diff --git a/lib/node_modules/@stdlib/math/base/special/powf/lib/x_is_zerof.js b/lib/node_modules/@stdlib/math/base/special/powf/lib/x_is_zerof.js new file mode 100644 index 000000000000..788a5634c4be --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/lib/x_is_zerof.js @@ -0,0 +1,106 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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 copyright and license were part of the original implementation available as part of [FreeBSD]{@link https://svnweb.freebsd.org/base/release/9.3.0/lib/msun/src/s_pow.c}. The implementation follows the original, but has been modified for JavaScript. +* +* ```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. +* ``` +*/ + +'use strict'; + +// MODULES // + +var isOddf = require( '@stdlib/math/base/assert/is-oddf' ); +var copysignf = require( '@stdlib/math/base/special/copysignf' ); +var f32 = require( '@stdlib/number/float64/base/to-float32' ); +var NINF = require( '@stdlib/constants/float32/ninf' ); +var PINF = require( '@stdlib/constants/float32/pinf' ); + + +// VARIABLES // + +var ZERO = f32( 0.0 ); + + +// MAIN // + +/** +* Evaluates the exponential function when \\(|x| = 0\\). +* +* @private +* @param {number} x - base +* @param {number} y - exponent +* @returns {number} function value +* +* @example +* var v = powf( 0.0, 2 ); +* // returns 0.0 +* +* @example +* var v = powf( -0.0, -9 ); +* // returns -Infinity +* +* @example +* var v = powf( 0.0, -9 ); +* // returns Infinity +* +* @example +* var v = powf( -0.0, 9 ); +* // returns 0.0 +* +* @example +* var v = powf( 0.0, -Infinity ); +* // returns Infinity +* +* @example +* var v = powf( 0.0, Infinity ); +* // returns 0.0 +*/ +function powf( x, y ) { + if ( y === NINF ) { + return PINF; + } + if ( y === PINF ) { + return ZERO; + } + if ( y > ZERO ) { + if ( isOddf( y ) ) { + return x; // handles +-0 + } + return ZERO; + } + // y < 0.0 + if ( isOddf( y ) ) { + return copysignf( PINF, x ); // handles +-0 + } + return PINF; +} + + +// EXPORTS // + +module.exports = powf; diff --git a/lib/node_modules/@stdlib/math/base/special/powf/lib/y_is_infinitef.js b/lib/node_modules/@stdlib/math/base/special/powf/lib/y_is_infinitef.js new file mode 100644 index 000000000000..0ebc33e7461a --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/lib/y_is_infinitef.js @@ -0,0 +1,95 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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 absf = require( '@stdlib/math/base/special/absf' ); +var PINF = require( '@stdlib/constants/float32/pinf' ); +var f32 = require( '@stdlib/number/float64/base/to-float32' ); + + +// VARIABLES // + +var NEG_ONE = f32( -1.0 ); +var ZERO = f32( 0.0 ); +var ONE = f32( 1.0 ); + + +// MAIN // + +/** +* Evaluates the exponential function when \\( y = \pm \infty\\). +* +* @private +* @param {number} x - base +* @param {number} y - exponent +* @returns {number} function value +* +* @example +* var v = powf( -1.0, Infinity ); +* // returns 1.0 +* +* @example +* var v = powf( -1.0, -Infinity ); +* // returns 1.0 +* +* @example +* var v = powf( 1.0, Infinity ); +* // returns 1.0 +* +* @example +* var v = powf( 1.0, -Infinity ); +* // returns 1.0 +* +* @example +* var v = powf( 0.5, Infinity ); +* // returns 0.0 +* +* @example +* var v = powf( 0.5, -Infinity ); +* // returns Infinity +* +* @example +* var v = powf( 1.5, -Infinity ); +* // returns 0.0 +* +* @example +* var v = powf( 1.5, Infinity ); +* // returns Infinity +*/ +function powf( x, y ) { + if ( x === NEG_ONE ) { + return ONE; + } + if ( x === ONE ) { + return ONE; + } + // (|x| > 1 && y === NINF) || (|x| < 1 && y === PINF) + if ( (absf(x) < ONE) === (y === PINF) ) { + return ZERO; + } + // (|x| > 1 && y === PINF) || (|x| < 1 && y === NINF) + return PINF; +} + + +// EXPORTS // + +module.exports = powf; diff --git a/lib/node_modules/@stdlib/math/base/special/powf/package.json b/lib/node_modules/@stdlib/math/base/special/powf/package.json new file mode 100644 index 000000000000..1ac64db64844 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/package.json @@ -0,0 +1,188 @@ +{ + "name": "@stdlib/math/base/special/powf", + "version": "0.0.0", + "description": "Exponential function.", + "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", + "math.powf", + "powf", + "power", + "natural", + "exponential", + "function", + "number" + ], + "__stdlib__": { + "scaffold": { + "$schema": "math/base@v1.0", + "base_alias": "powf", + "alias": "powf", + "pkg_desc": "exponential function", + "desc": "exponential function", + "short_desc": "exponential function", + "parameters": [ + { + "name": "x", + "desc": "base", + "type": { + "javascript": "number", + "jsdoc": "number", + "c": "float", + "dtype": "float32" + }, + "domain": [ + { + "min": "-infinity", + "max": "infinity" + } + ], + "rand": { + "prng": "random/base/uniform", + "parameters": [ + -10, + 10 + ] + }, + "example_values": [ + -1.2, + 2, + -3.1, + 4, + 5.5, + 100, + 8.9, + 3.1415927410125732, + 11.3, + -3.1415927410125732, + 13.5, + 14.6, + -15.7, + 16.8, + -17.9, + 10, + -19.11, + 20.12, + -21.15, + 1 + ] + }, + { + "name": "y", + "desc": "exponent", + "type": { + "javascript": "number", + "jsdoc": "number", + "c": "float", + "dtype": "float32" + }, + "domain": [ + { + "min": "-infinity", + "max": "infinity" + } + ], + "rand": { + "prng": "random/base/uniform", + "parameters": [ + -10, + 10 + ] + }, + "example_values": [ + 1.2, + -2, + 3, + -0.5, + 0, + -5.6, + 8.9, + -10, + 1.5, + -12, + 13.5, + 14.6, + -15.7, + 6, + -17, + 18, + -9, + 2.12, + -1.15, + -2 + ] + } + ], + "returns": { + "desc": "function value", + "type": { + "javascript": "number", + "jsdoc": "number", + "c": "float", + "dtype": "float32" + } + }, + "keywords": [ + "natural", + "exponential", + "powf", + "power" + ], + "extra_keywords": [ + "math.powf" + ] + } + } +} diff --git a/lib/node_modules/@stdlib/math/base/special/powf/scripts/evalpoly.js b/lib/node_modules/@stdlib/math/base/special/powf/scripts/evalpoly.js new file mode 100644 index 000000000000..8b74e12d3628 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/scripts/evalpoly.js @@ -0,0 +1,154 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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 script compiles modules for evaluating polynomial functions. If any polynomial coefficients change, this script should be rerun to update the compiled files. +*/ +'use strict'; + +// MODULES // + +var resolve = require( 'path' ).resolve; +var readFileSync = require( '@stdlib/fs/read-file' ).sync; +var writeFileSync = require( '@stdlib/fs/write-file' ).sync; +var currentYear = require( '@stdlib/time/current-year' ); +var substringBefore = require( '@stdlib/string/substring-before' ); +var substringAfter = require( '@stdlib/string/substring-after' ); +var format = require( '@stdlib/string/format' ); +var licenseHeader = require( '@stdlib/_tools/licenses/header' ); +var compile = require( '@stdlib/math/base/tools/evalpoly-compile' ); +var compileC = require( '@stdlib/math/base/tools/evalpoly-compile-c' ); + + +// VARIABLES // + +// Polynomial coefficients ordered in ascending degree... +var L = [ + 6.0000002384e-01, // 0x3F19999A + 4.2857143283e-01, // 0x3EDB6DB7 + 3.3333334327e-01, // 0x3EAAAAAB + 2.7272811532e-01, // 0x3E8BA305 + 2.3066075146e-01, // 0x3E6C3255 + 2.0697501302e-01 // 0x3E53F142 +]; + +// `x - x^2/2 + x^3/3 - x^4/4`... +var W = [ + 0.5, + -3.33333343e-01, + 0.25 +]; + +var P = [ + 1.6666667163e-01, // 0x3E2AAAAB + -2.7777778450e-03, // 0xBB360B61 + 6.6137559770e-05, // 0x388AB355 + -1.6533901999e-06, // 0xB5DDEA0E + 4.1381369442e-08 // 0x3331BB4C +]; + +// Header to add to output files: +var header = licenseHeader( 'Apache-2.0', 'js', { + 'year': currentYear(), + 'copyright': 'The Stdlib Authors' +}); +header += '\n/* This is a generated file. Do not edit directly. */\n'; + + +// FUNCTIONS // + +/** +* Inserts a compiled function into file content. +* +* @private +* @param {string} text - source content +* @param {string} id - function identifier +* @param {string} str - function string +* @returns {string} updated content +*/ +function insert( text, id, str ) { + var before; + var after; + var begin; + var end; + + begin = '// BEGIN: '+id; + end = '// END: '+id; + + before = substringBefore( text, begin ); + after = substringAfter( text, end ); + + return format( '%s// BEGIN: %s\n\n%s\n%s%s', before, id, str, end, after ); +} + + +// MAIN // + +/** +* Main execution sequence. +* +* @private +*/ +function main() { + var fpath; + var copts; + var opts; + var file; + var str; + + opts = { + 'encoding': 'utf8', + 'dtype': 'float32' + }; + + fpath = resolve( __dirname, '..', 'lib', 'polyval_l.js' ); + str = header + compile( L, opts ); + writeFileSync( fpath, str, opts ); + + fpath = resolve( __dirname, '..', 'lib', 'polyval_w.js' ); + str = header + compile( W, opts ); + writeFileSync( fpath, str, opts ); + + fpath = resolve( __dirname, '..', 'lib', 'polyval_p.js' ); + str = header + compile( P, opts ); + writeFileSync( fpath, str, opts ); + + copts = { + 'dtype': 'float', + 'name': '' + }; + + fpath = resolve( __dirname, '..', 'src', 'main.c' ); + file = readFileSync( fpath, opts ); + + copts.name = 'polyval_l'; + str = compileC( L, copts ); + file = insert( file, copts.name, str ); + + copts.name = 'polyval_w'; + str = compileC( W, copts ); + file = insert( file, copts.name, str ); + + copts.name = 'polyval_p'; + str = compileC( P, copts ); + file = insert( file, copts.name, str ); + + writeFileSync( fpath, file, opts ); +} + +main(); diff --git a/lib/node_modules/@stdlib/math/base/special/powf/src/Makefile b/lib/node_modules/@stdlib/math/base/special/powf/src/Makefile new file mode 100644 index 000000000000..bcf18aa46655 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/src/Makefile @@ -0,0 +1,70 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2024 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +#/ + +# VARIABLES # + +ifndef VERBOSE + QUIET := @ +else + QUIET := +endif + +# Determine the OS ([1][1], [2][2]). +# +# [1]: https://en.wikipedia.org/wiki/Uname#Examples +# [2]: http://stackoverflow.com/a/27776822/2225624 +OS ?= $(shell uname) +ifneq (, $(findstring MINGW,$(OS))) + OS := WINNT +else +ifneq (, $(findstring MSYS,$(OS))) + OS := WINNT +else +ifneq (, $(findstring CYGWIN,$(OS))) + OS := WINNT +else +ifneq (, $(findstring Windows_NT,$(OS))) + OS := WINNT +endif +endif +endif +endif + + +# RULES # + +#/ +# Removes generated files for building an add-on. +# +# @example +# make clean-addon +#/ +clean-addon: + $(QUIET) -rm -f *.o *.node + +.PHONY: clean-addon + +#/ +# Removes generated files. +# +# @example +# make clean +#/ +clean: clean-addon + +.PHONY: clean diff --git a/lib/node_modules/@stdlib/math/base/special/powf/src/addon.c b/lib/node_modules/@stdlib/math/base/special/powf/src/addon.c new file mode 100644 index 000000000000..ff8767b9e48c --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/src/addon.c @@ -0,0 +1,22 @@ +/** +* @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/pow.h" +#include "stdlib/math/base/napi/binary.h" + +STDLIB_MATH_BASE_NAPI_MODULE_DD_D( stdlib_base_pow ) diff --git a/lib/node_modules/@stdlib/math/base/special/powf/src/main.c b/lib/node_modules/@stdlib/math/base/special/powf/src/main.c new file mode 100644 index 000000000000..0db309f1e749 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/src/main.c @@ -0,0 +1,730 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +* +* +* ## Notice +* +* The following copyright and license were part of the original implementation available as part of [FreeBSD]{@link https://svnweb.freebsd.org/base/release/9.3.0/lib/msun/src/s_pow.c}. The implementation follows the original, but has been modified for JavaScript. +* +* ```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/pow.h" +#include "stdlib/math/base/special/abs.h" +#include "stdlib/constants/float64/pinf.h" +#include "stdlib/constants/float64/high_word_abs_mask.h" +#include "stdlib/number/float64/base/get_high_word.h" +#include "stdlib/math/base/assert/is_odd.h" +#include "stdlib/math/base/special/copysign.h" +#include "stdlib/constants/float64/ninf.h" +#include "stdlib/number/float64/base/set_high_word.h" +#include "stdlib/number/float64/base/set_low_word.h" +#include "stdlib/math/base/special/ldexp.h" +#include "stdlib/constants/float64/ln_two.h" +#include "stdlib/constants/float64/exponent_bias.h" +#include "stdlib/constants/float64/high_word_significand_mask.h" +#include "stdlib/math/base/assert/is_nan.h" +#include "stdlib/math/base/assert/is_infinite.h" +#include "stdlib/math/base/assert/is_integer.h" +#include "stdlib/math/base/special/sqrt.h" +#include "stdlib/number/float64/base/to_words.h" +#include "stdlib/constants/float64/num_high_word_significand_bits.h" + +// 0x3fefffff = 1072693247 => 0 01111111110 11111111111111111111 => biased exponent: 1022 = -1+1023 => 2^-1 +static const int32_t HIGH_MAX_NEAR_UNITY = 0x3fefffff; + +static const double HUGE_VALUE = 1.0e300; + +static const double TINY_VALUE = 1.0e-300; + +// 0x00100000 = 1048576 => 0 00000000001 00000000000000000000 => biased exponent: 1 = -1022+1023 => 2^-1022 +static const int32_t HIGH_MIN_NORMAL_EXP = 0x00100000; + +// 0x3fe00000 = 1071644672 => 0 01111111110 00000000000000000000 => biased exponent: 1022 = -1+1023 => 2^-1 +static const int32_t HIGH_BIASED_EXP_NEG_1 = 0x3fe00000; + +// High: LN2 +static const double LN2_HI = 6.93147182464599609375e-01; // 0x3FE62E43, 0x00000000 + +// Low: LN2 +static const double LN2_LO = -1.90465429995776804525e-09; // 0xBE205C61, 0x0CA86C39 + +// 1/LN2 +static const double INV_LN2 = 1.44269504088896338700e+00; // 0x3FF71547, 0x652B82FE + +// High (24 bits): 1/LN2 +static const double INV_LN2_HI = 1.44269502162933349609e+00; // 0x3FF71547, 0x60000000 + +// Low: 1/LN2 +static const double INV_LN2_LO = 1.92596299112661746887e-08; // 0x3E54AE0B, 0xF85DDF44 + +// 0x000fffff = 1048575 => 0 00000000000 11111111111111111111 +static const int32_t HIGH_SIGNIFICAND_MASK = 0x000fffff; + +// 0x3ff00000 = 1072693248 => 0 01111111111 00000000000000000000 => biased exponent: 1023 = 0+1023 => 2^0 = 1 +static const int32_t HIGH_BIASED_EXP_0 = 0x3ff00000; + +// 0x20000000 = 536870912 => 0 01000000000 00000000000000000000 => biased exponent: 512 = -511+1023 +static const int32_t HIGH_BIASED_EXP_NEG_512 = 0x20000000; + +// 0x00080000 = 524288 => 0 00000000000 10000000000000000000 +static const int32_t HIGH_SIGNIFICAND_HALF = 0x00080000; + +static const double TWO53 = 9007199254740992.0; // 0x43400000, 0x00000000 + +// 2/(3*LN2) +static const double CP = 9.61796693925975554329e-01; // 0x3FEEC709, 0xDC3A03FD + +// (float)CP +static const double CP_HI = 9.61796700954437255859e-01; // 0x3FEEC709, 0xE0000000 + +// Low: CP_HI +static const double CP_LO = -7.02846165095275826516e-09; // 0xBE3E2FE0, 0x145B01F5 + +static const double BP [2] = { 1.0, 1.5 }; + +static const double DP_HI [2] = { 0.0, 5.84962487220764160156e-01 }; // 0x3FE2B803, 0x40000000 + +static const double DP_LO [2] = { 0.0, 1.35003920212974897128e-08 }; // 0x3E4CFDEB, 0x43CFD006 + +// 0x41e00000 = 1105199104 => 0 10000011110 00000000000000000000 => biased exponent: 1054 = 31+1023 => 2^31 +static const int32_t HIGH_BIASED_EXP_31 = 0x41e00000; + +// 0x43f00000 = 1139802112 => 0 10000111111 00000000000000000000 => biased exponent: 1087 = 64+1023 => 2^64 +static const int32_t HIGH_BIASED_EXP_64 = 0x43f00000; + +// 0x40900000 = 1083179008 => 0 10000001001 00000000000000000000 => biased exponent: 1033 = 10+1023 => 2^10 = 1024 +static const int32_t HIGH_BIASED_EXP_10 = 0x40900000; + +// 0x4090cc00 = 1083231232 => 0 10000001001 00001100110000000000 +static const int32_t HIGH_1075 = 0x4090cc00; + +// 0xc090cc00 = 3230714880 => 1 10000001001 00001100110000000000 +static const uint32_t HIGH_NEG_1075 = 0xc090cc00; + +static const int32_t HIGH_NUM_NONSIGN_BITS = 31; + +// -(1024-log2(ovfl+.5ulp)) +static const double OVT = 8.0085662595372944372e-17; + +/* Begin auto-generated functions. The following functions are auto-generated. Do not edit directly. */ + +// BEGIN: polyval_l + +/** +* 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_l( const float x ) { + return 0.60000002384f + (x * (0.42857143283f + (x * (0.33333334327f + (x * (0.27272811532f + (x * (0.23066075146f + (x * 0.20697501302f))))))))); +} + +// END: polyval_l + +// BEGIN: polyval_w + +/** +* 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_w( const float x ) { + return 0.5f + (x * (-0.333333343f + (x * 0.25f))); +} + +// END: polyval_w + +// 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 0.16666667163f + (x * (-0.002777777845f + (x * (0.00006613755977f + (x * (-0.0000016533901999f + (x * 4.1381369442e-8f))))))); +} + +// END: polyval_p + +/* End auto-generated functions. */ + +/** +* Evaluates the exponential function when \\( y = \pm \infty\\). +* +* @param x base +* @param y exponent +* @return output value +* +* @example +* double out = y_is_infinite( -1.0, 1.0/0.0 ); +* // returns NaN +* +* @example +* double out = y_is_infinite( 1.5, -1.0/0.0 ); +* // returns 0.0 +*/ +static double y_is_infinite( const double x, const double y ) { + if ( x == -1.0 ) { + return 0.0 / 0.0; // NaN + } + if ( x == 1.0 ) { + return 1.0; + } + // (|x| > 1 && y == NINF) || (|x| < 1 && y == PINF) + if ( ( stdlib_base_abs( x ) < 1.0 ) == ( y == STDLIB_CONSTANT_FLOAT64_PINF ) ) { + return 0.0; + } + // (|x| > 1 && y == PINF) || (|x| < 1 && y == NINF) + return STDLIB_CONSTANT_FLOAT64_PINF; +} + +/** +* Evaluates the exponential function when \\(|y| > 2^64\\). +* +* @param x base +* @param y exponent +* @return output value +* +* @example +* double out = y_is_huge( 9.0, 3.6893488147419103e19 ); +* // returns Infinity +* +* @example +* double out = y_is_huge( -3.14, -3.6893488147419103e19 ); +* // returns 0.0 +*/ +static double y_is_huge( const double x, const double y ) { + uint32_t ahx; + uint32_t hx; + + stdlib_base_float64_get_high_word( x, &hx ); + ahx = ( hx & STDLIB_CONSTANT_FLOAT64_HIGH_WORD_ABS_MASK ); + + if ( ahx <= HIGH_MAX_NEAR_UNITY ) { + if ( y < 0 ) { + // Signal overflow... + return HUGE_VALUE * HUGE_VALUE; + } + // Signal underflow... + return TINY_VALUE * TINY_VALUE; + } + // `x` has a biased exponent greater than or equal to `0`... + + if ( y > 0 ) { + // Signal overflow... + return HUGE_VALUE * HUGE_VALUE; + } + // Signal underflow... + return TINY_VALUE * TINY_VALUE; +} + +/** +* Evaluates the exponential function when \\(|x| = 0\\). +* +* @param x base +* @param y exponent +* @return output value +* +* @example +* double out = x_is_zero( 0.0, 2 ); +* // returns 0.0 +* +* @example +* double out = x_is_zero( 0.0, -9 ); +* // returns Infinity +*/ +static double x_is_zero( const double x, const double y ) { + if ( y == STDLIB_CONSTANT_FLOAT64_NINF ) { + return STDLIB_CONSTANT_FLOAT64_PINF; + } + if ( y == STDLIB_CONSTANT_FLOAT64_PINF ) { + return 0.0; + } + if ( y > 0.0 ) { + if ( stdlib_base_is_odd( y ) ) { + return x; // handles +-0 + } + return 0.0; + } + // y < 0.0 + if ( stdlib_base_is_odd( y ) ) { + return stdlib_base_copysign( STDLIB_CONSTANT_FLOAT64_PINF, x ); // handles +-0 + } + return STDLIB_CONSTANT_FLOAT64_PINF; +} + +/** +* Computes \\(2^{\mathrm{hp} + \mathrm{lp}\\). +* +* @param j high word of `hp + lp` +* @param hp first power summand +* @param lp second power summand +* @return function value +* +* @example +* double out = pow2( 1065961648, -0.3398475646972656, -0.000002438187359100815 ); +* // returns ~0.79 +*/ +static double pow2( uint32_t j, const double hp, const double lp ) { + uint32_t tmp; + double hpc; + int32_t jc; + int32_t nc; + int32_t i; + int32_t k; + int32_t n; + double t1; + double t; + double r; + double u; + double v; + double w; + double z; + + hpc = hp; + jc = (int32_t)j; + i = ( j & STDLIB_CONSTANT_FLOAT64_HIGH_WORD_ABS_MASK ); + k = ( ( i >> STDLIB_CONSTANT_FLOAT64_NUM_HIGH_WORD_SIGNIFICAND_BITS ) - STDLIB_CONSTANT_FLOAT64_EXPONENT_BIAS ); + n = 0; + nc = (int32_t)n; + + // `|z| > 0.5`, set `n = z+0.5` + if ( i > HIGH_BIASED_EXP_NEG_1 ) { + n = ( j + ( HIGH_MIN_NORMAL_EXP >> ( k + 1 ) ) ); + k = ( ( ( n & STDLIB_CONSTANT_FLOAT64_HIGH_WORD_ABS_MASK ) >> STDLIB_CONSTANT_FLOAT64_NUM_HIGH_WORD_SIGNIFICAND_BITS ) - STDLIB_CONSTANT_FLOAT64_EXPONENT_BIAS ); // new k for n + tmp = ( ( n & ~( HIGH_SIGNIFICAND_MASK >> k ) ) ); + t = 0.0; + stdlib_base_float64_set_high_word( tmp, &t ); + n = ( ( ( n & HIGH_SIGNIFICAND_MASK ) | HIGH_MIN_NORMAL_EXP ) >> ( STDLIB_CONSTANT_FLOAT64_NUM_HIGH_WORD_SIGNIFICAND_BITS - k ) ); + nc = (int32_t)n; + if ( jc < 0 ) { + nc = -nc; + } + hpc -= t; + } + t = lp + hpc; + stdlib_base_float64_set_low_word( 0, &t ); + u = t * LN2_HI; + v = ( ( lp - ( t - hpc ) ) * STDLIB_CONSTANT_FLOAT64_LN2 ) + ( t * LN2_LO ); + z = u + v; + w = v - ( z - u ); + t = z * z; + t1 = z - ( t * polyval_p( t ) ); + r = ( ( z * t1 ) / ( t1 - 2.0 ) ) - ( w + ( z * w ) ); + z = 1.0 - ( r - z ); + stdlib_base_float64_get_high_word( z, &j ); + j = j + ( nc << STDLIB_CONSTANT_FLOAT64_NUM_HIGH_WORD_SIGNIFICAND_BITS ); + jc = (int32_t)j; + + // Check for subnormal output... + if ( ( jc >> STDLIB_CONSTANT_FLOAT64_NUM_HIGH_WORD_SIGNIFICAND_BITS ) <= 0 ) { + z = stdlib_base_ldexp( z, nc ); + } else { + stdlib_base_float64_set_high_word( j, &z ); + } + return z; +} + +/** +* Computes \\(\operatorname{log}(x)\\) assuming \\(|1-x|\\) is small and using the approximation \\(x - x^2/2 + x^3/3 - x^4/4\\). +* +* @param ax absolute value of x +* @param o1 destination for output1 +* @param o2 destination for output2 +* +* @example +* logx( 9.0, &o1, &o2 ); +*/ +void logx( const double ax, double *o1, double *o2 ) { + double t2; + double t1; + double t; + double w; + double u; + double v; + + t = ax - 1.0; // `t` has `20` trailing zeros + w = t * t * polyval_w( t ); + u = INV_LN2_HI * t; // `INV_LN2_HI` has `21` significant bits + v = ( t * INV_LN2_LO ) - ( w * INV_LN2 ); + t1 = u + v; + stdlib_base_float64_set_low_word( 0, &t1 ); + t2 = v - (t1 - u); + + *o1 = t1; + *o2 = t2; +} + +/** +* Computes \\(\operatorname{log2}(ax)\\). +* +* @param ax absolute value of x +* @param ahx high word of ax +* @param o1 destination for output1 +* @param o2 destination for output2 +* +* @example +* log2ax( 9.0, 1075970048, &o1, &o2 ); +*/ +void log2ax( const double ax, const int32_t ahx, double *o1, double *o2 ) { + uint32_t ahxcc; + uint32_t tmp; + int32_t ahxc; + double axc; + int32_t n; + int32_t j; + int32_t k; + double ss; // hs + ls + double s2; // ss squared + double hs; + double ls; + double ht; + double lt; + double bp; // BP constant + double dp; // DP constant + double hp; + double lp; + double hz; + double lz; + double t1; + double t2; + double t; + double r; + double u; + double v; + + n = 0; + axc = ax; + ahxc = ahx; + ahxcc = (uint32_t)ahx; + // Check if `x` is subnormal... + if ( ahxc < HIGH_MIN_NORMAL_EXP ) { + axc *= TWO53; + n -= 53; + stdlib_base_float64_get_high_word( axc, &ahxcc ); + ahxc = (int32_t)ahxcc; + } + // Extract the unbiased exponent of `x`: + n += ( ( ahxc >> STDLIB_CONSTANT_FLOAT64_NUM_HIGH_WORD_SIGNIFICAND_BITS ) - STDLIB_CONSTANT_FLOAT64_EXPONENT_BIAS ); + + // Isolate the significand bits of `x`: + j = ( ahxc & HIGH_SIGNIFICAND_MASK ); + + // Normalize `ahx` by setting the (biased) exponent to `1023`: + ahxc = ( j|HIGH_BIASED_EXP_0 ); + + // Determine the interval of `|x|` by comparing significand bits... + + // |x| < sqrt(3/2) + if ( j <= 0x3988E ) { // 0 00000000000 00111001100010001110 + k = 0; + } + // |x| < sqrt(3) + else if ( j < 0xBB67A ) { // 0 00000000000 10111011011001111010 + k = 1; + } + // |x| >= sqrt(3) + else { + k = 0; + n += 1; + ahxc -= HIGH_MIN_NORMAL_EXP; + } + ahxcc = (uint32_t)ahxc; + + // Load the normalized high word into `|x|`: + stdlib_base_float64_set_high_word( ahxcc, &axc ); + + // Compute `ss = hs + ls = (x-1)/(x+1)` or `(x-1.5)/(x+1.5)`: + bp = BP[ k ]; // BP[0] = 1.0, BP[1] = 1.5 + u = axc - bp; // (x-1) || (x-1.5) + v = 1.0 / (axc + bp); // 1/(x+1) || 1/(x+1.5) + ss = u * v; + hs = ss; + stdlib_base_float64_set_low_word( 0, &hs ); // set all low word (less significant significand) bits to 0s + + // Compute `ht = ax + bp` (via manipulation, i.e., bit flipping, of the high word): + tmp = ( ( ahxc >> 1 ) | HIGH_BIASED_EXP_NEG_512) + HIGH_SIGNIFICAND_HALF; + tmp += ( k << 18 ); // `(k<<18)` can be considered the word equivalent of `1.0` or `1.5` + ht = 0.0; + stdlib_base_float64_set_high_word( tmp, &ht ); + lt = axc - ( ht - bp ); + ls = v * ( ( u - ( hs * ht ) ) - ( hs * lt ) ); + + // Compute `log(ax)`... + + s2 = ss * ss; + r = s2 * s2 * polyval_l( s2 ); + r += ls * (hs + ss); + s2 = hs * hs; + ht = 3.0 + s2 + r; + stdlib_base_float64_set_low_word( 0, &ht ); + lt = r - ( ( ht - 3.0 ) - s2 ); + + // u+v = ss*(1+...): + u = hs * ht; + v = ( ls * ht ) + ( lt * ss ); + + // 2/(3LN2) * (ss+...): + hp = u + v; + stdlib_base_float64_set_low_word( 0, &hp ); + lp = v - ( hp - u ); + hz = CP_HI * hp; // CP_HI+CP_LO = 2/(3*LN2) + lz = ( CP_LO * hp ) + ( lp*CP ) + DP_LO[ k ]; + + // log2(ax) = (ss+...)*2/(3*LN2) = n + dp + hz + lz + dp = DP_HI[ k ]; + t = n; + t1 = ( ( hz + lz ) + dp ) + t; // log2(ax) + stdlib_base_float64_set_low_word( 0, &t1 ); + t2 = lz - ( ( ( t1 - t ) - dp ) - hz ); + + *o1 = t1; + *o2 = t2; +} + +/** +* Evaluates the exponential function. +* +* @param x base +* @param y exponent +* @return function value +* +* @example +* double out = stdlib_base_pow( 2.0, 3.0 ); +* // returns 8.0 +* +* @example +* double out = stdlib_base_pow( 4.0, 0.5 ); +* // returns 2.0 +*/ +double stdlib_base_pow( const double x, const double y ) { + uint32_t hx; // high word `x` + uint32_t lx; // low word `x` + uint32_t hy; // high word `y` + uint32_t ly; // low word `y` + int32_t ahx; // absolute value high word `x` + int32_t ahy; // absolute value high word `y` + uint32_t i; + uint32_t j; + int32_t ic; + int32_t jc; + int32_t sx; // sign `x` + int32_t sy; // sign `y` + double ax; // absolute value `x` + double y1; + double hp; + double lp; + double t1; + double t2; + double xc; + double z; // y prime + + xc = x; + if ( stdlib_base_is_nan( xc ) || stdlib_base_is_nan( y ) ) { + return 0.0/0.0; // NaN + } + + // Split `y` into high and low words: + stdlib_base_float64_to_words( y, &hy, &ly ); + + // Special cases `y`... + if ( ly == 0 ) { + if ( y == 0.0 ) { + return 1.0; + } + if ( y == 1.0 ) { + return xc; + } + if ( y == -1.0 ) { + return 1.0 / xc; + } + if ( y == 0.5 ) { + return stdlib_base_sqrt( xc ); + } + if ( y == -0.5 ) { + return 1.0 / stdlib_base_sqrt( xc ); + } + if ( y == 2.0 ) { + return xc * xc; + } + if ( y == 3.0 ) { + return xc * xc * xc; + } + if ( y == 4.0 ) { + xc *= xc; + return xc * xc; + } + if ( stdlib_base_is_infinite( y ) ) { + return y_is_infinite( xc, y ); + } + } + // Split `x` into high and low words: + stdlib_base_float64_to_words( xc, &hx, &lx ); + + // Special cases `x`... + if ( lx == 0 ) { + if ( hx == 0 ) { + return x_is_zero( xc, y ); + } + if ( xc == 1.0 ) { + return 1.0; + } + if ( + xc == -1.0 && + stdlib_base_is_odd( y ) + ) { + return -1.0; + } + if ( stdlib_base_is_infinite( xc ) ) { + if ( xc == STDLIB_CONSTANT_FLOAT64_NINF ) { + // `stdlib_base_pow( 1/x, -y )` + return stdlib_base_pow( -0.0, -y ); + } + if ( y < 0.0 ) { + return 0.0; + } + return STDLIB_CONSTANT_FLOAT64_PINF; + } + } + if ( + xc < 0.0 && + stdlib_base_is_integer( y ) == false + ) { + // Signal NaN... + return 0.0/0.0; + } + ax = stdlib_base_abs( x ); + + // Remove the sign bits (i.e., get absolute values): + ahx = ( hx & STDLIB_CONSTANT_FLOAT64_HIGH_WORD_ABS_MASK ); + ahy = ( hy & STDLIB_CONSTANT_FLOAT64_HIGH_WORD_ABS_MASK ); + + // Extract the sign bits: + sx = ( hx >> HIGH_NUM_NONSIGN_BITS ); + sy = ( hy >> HIGH_NUM_NONSIGN_BITS ); + + // Determine the sign of the result... + if ( sx && stdlib_base_is_odd( y ) ) { + sx = -1; + } else { + sx = 1; + } + // Case 1: `|y|` is huge... + + // |y| > 2^31 + if ( ahy > HIGH_BIASED_EXP_31 ) { + // `|y| > 2^64`, then must over- or underflow... + if ( ahy > HIGH_BIASED_EXP_64 ) { + return y_is_huge( xc, y ); + } + // Over- or underflow if `x` is not close to unity... + if ( ahx < HIGH_MAX_NEAR_UNITY ) { + // y < 0 + if ( sy == 1 ) { + // Signal overflow... + return sx * HUGE_VALUE * HUGE_VALUE; + } + // Signal underflow... + return sx * TINY_VALUE * TINY_VALUE; + } + if ( ahx > HIGH_BIASED_EXP_0 ) { + // y > 0 + if ( sy == 0 ) { + // Signal overflow... + return sx * HUGE_VALUE * HUGE_VALUE; + } + // Signal underflow... + return sx * TINY_VALUE * TINY_VALUE; + } + // At this point, `|1-x|` is tiny (`<= 2^-20`). Suffice to compute `log(x)` by `x - x^2/2 + x^3/3 - x^4/4`. + logx( ax, &t1, &t2 ); + } + // Case 2: `|y|` is not huge... + else { + log2ax( ax, ahx, &t1, &t2 ); + } + + // Split `y` into `y1 + y2` and compute `(y1+y2) * (t1+t2)`... + y1 = y; + stdlib_base_float64_set_low_word( 0, &y1 ); + lp = ( ( y - y1 ) * t1 ) + ( y * t2 ); + hp = y1 * t1; + z = lp + hp; + + // Note: *can* be more performant to use `getHighWord` and `getLowWord` directly, but using `toWords` looks cleaner. + stdlib_base_float64_to_words( z, &j, &i ); + jc = (int32_t)j; + ic = (int32_t)i; + + // z >= 1024 + if ( jc >= HIGH_BIASED_EXP_10 ) { + // z > 1024 + if ( ( ( jc - HIGH_BIASED_EXP_10 )|ic ) != 0 ) { + // Signal overflow... + return sx * HUGE_VALUE * HUGE_VALUE; + } + if ( ( lp + OVT ) > ( z - hp ) ) { + // Signal overflow... + return sx * HUGE_VALUE * HUGE_VALUE; + } + } + // z <= -1075 + else if ( ( j & STDLIB_CONSTANT_FLOAT64_HIGH_WORD_ABS_MASK ) >= HIGH_1075 ) { + // z < -1075 + if ( ( ( j - HIGH_NEG_1075 )|i ) != 0 ) { + // Signal underflow... + return sx * TINY_VALUE * TINY_VALUE; + } + if ( lp <= ( z - hp ) ) { + // Signal underflow... + return sx * TINY_VALUE * TINY_VALUE; + } + } + // Compute `2^(hp+lp)`... + z = pow2( j, hp, lp ); + return sx * z; +} diff --git a/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/REQUIRE b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/REQUIRE new file mode 100644 index 000000000000..308c3be89c85 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/REQUIRE @@ -0,0 +1,2 @@ +julia 1.5 +JSON 0.21 diff --git a/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/base_near_unity_huge.json b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/base_near_unity_huge.json new file mode 100644 index 000000000000..0d808a31defd --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/base_near_unity_huge.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/base_near_unity_large.json b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/base_near_unity_large.json new file mode 100644 index 000000000000..57b2746c79b8 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/base_near_unity_large.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/base_near_unity_small.json b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/base_near_unity_small.json new file mode 100644 index 000000000000..a959e341987e --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/base_near_unity_small.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/cubed_large.json b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/cubed_large.json new file mode 100644 index 000000000000..33deb029aace --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/cubed_large.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/cubed_small.json b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/cubed_small.json new file mode 100644 index 000000000000..9a0c93ef971a --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/cubed_small.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/decimal_decimal.json b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/decimal_decimal.json new file mode 100644 index 000000000000..76495c0d9b1a --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/decimal_decimal.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/decimal_integer.json b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/decimal_integer.json new file mode 100644 index 000000000000..f1d728e1f4e0 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/decimal_integer.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/integer_decimal.json b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/integer_decimal.json new file mode 100644 index 000000000000..68de5abe738d --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/integer_decimal.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/integer_integer.json b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/integer_integer.json new file mode 100644 index 000000000000..0d8592205f7a --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/integer_integer.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/large_small.json b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/large_small.json new file mode 100644 index 000000000000..e0aee5c70f34 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/large_small.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/negative_exp_large_large.json b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/negative_exp_large_large.json new file mode 100644 index 000000000000..6d901cf5d07a --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/negative_exp_large_large.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/negative_exp_large_small.json b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/negative_exp_large_small.json new file mode 100644 index 000000000000..f1af6471c61b --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/negative_exp_large_small.json @@ -0,0 +1 @@ +{"expected":[1.0821583e-14,1.73713e-40,8.917742e-13,4.4575786e-19,3.042949e-17,5.434071e-22,1.0047125e-28,1.2087884e-7,0.0,2.9922873e-38,1.3870946e-37,7.254115e-18,2.9318e-18,1.369e-42,0.0,9.788262e-26,2.008574e-31,0.0,0.01593566,8.9690595e-32,2.7708e-41,3.5269444e-12,0.0,1.595278e-23,0.5358438,7.019023e-27,0.0,0.001629152,0.1902885,0.0010604587,0.0,2.918551e-13,0.21860369,3.5896992e-35,4.1977332e-6,4.5565e-41,0.0,7.809374e-19,0.0,0.28925827,4.8131227e-7,2.1253575e-33,0.0,2.9498192e-13,0.0026798127,4.8576606e-29,1.8134591e-19,2.705121e-11,1.3223018e-33,4.4065655e-7,1.8204124e-13,2.975e-42,9.0533935e-12,0.8946212,0.0,6.2354497e-34,1.3006649e-36,2.4218903e-22,0.0,0.0,0.0,6.11e-43,1.5853758e-6,4.581121e-27,0.013883959,3.0e-45,0.054812446,0.003541324,0.12080938,0.0,0.0,0.0,4.661754e-36,0.0,4.1057e-41,7.940681e-38,7.10457e-40,6.5741016e-13,0.62660044,1.1263181e-15,2.1172394e-20,3.1960443e-8,0.35946068,1.336523e-36,3.6044937e-30,2.2e-44,5.3332066e-17,2.7561483e-17,0.0,0.0,0.0,0.0,1.5479629e-25,0.0,1.9086633e-31,0.0,1.240344e-39,7.742585e-28,0.0,1.18e-43,3.3795846e-31,5.705386e-14,0.0,1.4477987e-6,0.0,0.0,1.0382201e-13,1.0e-45,4.8607215e-32,6.4405706e-25,1.5983682e-20,0.047195856,0.0,5.2313622e-14,2.1703074e-19,0.0,1.0e-45,0.0,2.4e-44,3.2756405e-23,0.0006921538,1.04292496e-32,3.9e-44,0.0,3.093089e-35,1.8625403e-30,7.7783444e-20,4.8415847e-17,7.474501e-10,3.0258976e-11,7.2246134e-28,1.5034209e-33,0.0,0.0,0.0,0.0,1.1272544e-25,0.6207725,1.7717296e-10,6.616437e-20,1.5025885e-23,2.390296e-39,0.024761528,8.3e-44,0.0,3.9029717e-21,1.3233746e-5,1.8373739e-25,1.5903957e-27,0.0,0.0,4.038019e-34,0.0,1.7224779e-18,0.0,4.8540376e-27,2.1977807e-36,3.136811e-39,0.0,1.1033508e-19,6.7088094e-37,0.0,0.0,0.0,2.1268728e-14,0.0,0.0,7.0694413e-37,0.0,0.0,4.8189265e-20,0.0,0.0,0.0,2.2508443e-6,1.1033365e-28,0.0,2.834629e-31,0.0016348743,0.0,8.22697e-40,0.0,2.3103776e-13,5.719178e-38,0.0,9.648615e-27,1.3446496e-17,0.0,3.3163455e-5,0.0,0.0,8.3364776e-23,8.16924e-28,4.351334e-6,2.8310854e-9,8.5e-44,0.0,6.2563566e-26,8.362838e-28,3.9614378e-11,0.0,1.0e-45,7.622404e-27,6.840267e-5,0.0,0.0,0.0,6.4281884e-29,4.988404e-35,1.7760815e-22,0.0,3.6e-44,0.0,2.3358255e-12,1.0740396e-38,0.0,1.488021e-20,0.0,1.201572e-5,0.0,0.0011042124,4.6542328e-7,7.0e-45,6.443308e-7,0.0,0.004113246,5.2904956e-9,3.2125466e-35,0.0,7.6312226e-38,0.00021976892,0.014284486,2.0911843e-24,7.0265585e-37,3.6879795e-9,2.953916e-21,4.2894712e-32,5.379949e-35,0.047356877,0.0,4.2198498e-13,0.0,3.9942964e-16,6.363825e-10,6.167318e-39,0.0,0.0,2.5380669e-9,0.0,6.8224397e-22,0.0,5.4346618e-8,3.0403255e-35,9.737642e-34,2.68241e-39,6.453654e-8,1.3078771e-24,3.279263e-26,1.0341098e-12,5.379185e-39,0.0,5.246517e-21,0.0,2.9552e-41,0.0,0.0,4.552434e-29,1.3664017e-20,0.0,1.967098e-28,2.023463e-15,0.0,0.4455727,3.402127e-24,1.2684674e-11,0.0,2.2401345e-16,0.0,8.905885e-19,0.0,1.495464e-29,5.726235e-12,0.0,0.0,7.8755726e-38,0.0,4.0769173e-8,0.056948893,1.7347986e-33,0.0,3.7337586e-38,0.00078957604,2.9237e-41,0.1919296,4.0774146e-5,2.6698145e-31,1.5e-44,8.041617e-18,3.0736916e-34,1.3174567e-10,2.9131658e-10,0.0,0.0,4.05e-43,2.9076227e-28,8.467029e-7,9.50628e-40,3.1113793e-33,0.008605436,0.0,0.0,1.6999018e-5,5.617217e-34,1.8023211e-8,1.6619301e-37,1.242397e-13,0.0,0.0,5.9380546e-27,0.0,0.0021836082,1.0e-45,3.9749732e-16,0.0,0.018944954,1.5587535e-18,0.0,1.0821168e-13,1.9037771e-26,2.3674597e-16,0.0,6.177517e-26,0.0,0.0053776237,6.8956484e-5,9.032671e-14,0.0,0.0,0.0,0.0,0.0,1.0667102e-18,9.208397e-8,0.0,0.0,1.7001242e-10,1.0608765e-28,2.3662166e-34,1.5581444e-28,2.3276526e-16,1.5200687e-13,2.1812523e-17,6.4196755e-9,9.75251e-38,1.9362279e-13,0.0,0.0,0.0,7.406947e-33,1.4432048e-37,1.25816e-40,1.4366287e-21,1.2414552e-32,0.0,6.4232167e-37,8.664441e-5,1.0e-45,3.4581016e-15,0.0,0.0,1.9179447e-21,0.0,0.0001861669,0.0,3.1326252e-28,1.9670912e-38,0.0,8.0e-45,2.1827887e-14,6.445054e-37,4.5866384e-16,3.815829e-9,3.793e-42,0.3661855,2.196713e-9,1.9064535e-10,1.1182534e-16,0.0,0.0,1.5588986e-28,7.0411354e-35,2.784513e-16,0.0,2.1171e-41,0.0,5.1027345e-14,3.065e-42,0.0,9.112684e-5,5.287423e-20,5.188739e-36,0.3372772,1.3838878e-25,6.470169e-16,0.0,0.0,1.5838376e-9,4.0e-45,3.720698e-5,3.9415103e-17,2.7278205e-32,0.0,0.0069300616,0.0,0.0,0.0,1.1042687e-29,0.0,7.35912e-16,3.56268e-39,0.0,3.2843547e-18,5.4409916e-13,0.0,0.0,0.0,0.0,0.0,2.7958108e-6,0.0,0.0032399783,3.081818e-39,2.6130544e-36,4.9470516e-17,0.0,4.649241e-27,0.0,2.4678606e-20,2.9018387e-12,1.1526679e-6,9.6788524e-14,1.7391318e-22,4.538193e-33,1.0863497e-28,5.4997952e-5,0.0,4.86e-43,0.0,3.22604e-40,0.0,0.0,7.99762e-26,0.0,0.0,1.591819e-14,2.1e-44,0.00038166705,0.5001146,0.038623184,8.848149e-11,7.997021e-33,1.9987308e-10,2.0701878e-5,1.0074189e-14,4.4400714e-9,1.6328908e-14,0.0,1.1686666e-37,1.8e-44,1.83644e-40,0.0,1.0e-45,7.685991e-37,0.0,0.009919068,5.046e-32,3.860557e-23,1.9318288e-31,0.0,7.0478854e-15,0.0,5.293e-42,0.0,0.0,1.2621746e-37,1.0e-45,0.0,2.404485e-39,4.197049e-23,1.503917e-18,1.0217857e-36,4.6051496e-12,1.9752681e-14,1.3077915e-9,9.4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diff --git a/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/negative_exp_small_large.json b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/negative_exp_small_large.json new file mode 100644 index 000000000000..ca49301aa0ba --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/negative_exp_small_large.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/negative_exp_small_small.json b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/negative_exp_small_small.json new file mode 100644 index 000000000000..84b9bdb47f1b --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/negative_exp_small_small.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/runner.jl new file mode 100755 index 000000000000..df0730c9074d --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/runner.jl @@ -0,0 +1,179 @@ +#!/usr/bin/env julia +# +# @license Apache-2.0 +# +# Copyright (c) 2025 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( x, y, name ) + +Generate fixture data and write to file. + +# Arguments + +* `x`: base domain +* `y`: exponent domain +* `name::AbstractString`: output filename + +# Examples + +``` julia +julia> x = range( -1000, stop = 1000, length = 2001 ); +julia> y = range( 0, stop = 1000, length = 1001 ); +julia> gen( x, y, \"data.json\" ); +``` +""" +function gen( x, y, name ) + z = Array{Float32}( undef, length(x) ); + for i in eachindex(x) + z[ i ] = x[i]^y[i]; + end + + # Store data to be written to file as a collection: + data = Dict([ + ("x", x), + ("y", y), + ("expected", z) + ]); + + # Based on the script directory, create an output filepath: + filepath = joinpath( dir, name ); + + # Write the data to the output filepath as JSON: + 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 ); + +# Squares (x small): +x = Float32.( range( -1000, stop = 1000, length = 2001 ) ); +y = zeros( 2001 ); +y[:] .= 2.0f0; +gen( x, y, "squared_small.json" ); + +# Squares (x large): +x = Float32.( range( 3.14e8, stop = 3.14e18, length = 2001 ) ); +y = zeros( 2001 ); +y[:] .= 2.0f0; +gen( x, y, "squared_large.json" ); + +# Cubes (x small): +x = Float32.( range( -1000, stop = 1000, length = 2001 ) ); +y = zeros( 2001 ); +y[:] .= 3.0f0; +gen( x, y, "cubed_small.json" ); + +# Cubes (x large): +x = Float32.( range( -9.99e6, stop = -4.641588833612779e12, length = 2001 ) ); +y = zeros( 2001 ); +y[:] .= 3.0f0; +gen( x, y, "cubed_large.json" ); + +# To the 4th power (x small): +x = Float32.( range( -1000, stop = 1000, length = 2001 ) ); +y = zeros( 2001 ); +y[:] .= 4.0f0; +gen( x, y, "to_the_fourth_small.json" ); + +# To the 4th power (x large): +x = Float32.( range( 1.234e4, stop = 3.14e9, length = 2001 ) ); +y = zeros( 2001 ); +y[:] .= 4.0f0; +gen( x, y, "to_the_fourth_large.json" ); + +# Base near unity (y small): +x = Float32.( range( 0.9999990463256836, stop = 1.0000009536743164, length = 500 ) ); +y = Float32.( range( -10, stop = 10, length = 500 ) ); +gen( x, y, "base_near_unity_small.json" ); + +# Base near unity (y large): +x = Float32.( range( 0.9999990463256836, stop = 1.0000009536743164, length = 500 ) ); +y = Float32.( range( 100, stop = 709, length = 500 ) ); +gen( x, y, "base_near_unity_large.json" ); + +# Base near unity (y huge): +x = Float32.( range( 0.9999999999990463256836, stop = 1.0000000000009536743164, length = 500 ) ); +y = Float32.( range( 1.8446744073709552e13, stop = 4.294967296e13, length = 500 ) ); +gen( x, y, "base_near_unity_huge.json" ); + +# Subnormal results: +z = Float32.( range( 3.14e-39, stop = 3.14e-44, length = 2001 ) ); +x = Float32.( range( 3.14e-41, stop = 3.14e-45, length = 2001 ) ); +y = log.(z) ./ log.(x); +gen( x, y, "subnormal_results.json" ); + +# Negative exponents (x small, y small): +x = Float32.( range( 0, stop = 10, length = 5001 ) ); +y = Float32.( rand( 5001 ) .* -100 ); +gen( x, y, "negative_exp_small_small.json" ); + +# Negative exponents (x large, y small): +x = Float32.( range( 1e5, stop = 1e8, length = 5001 ) ); +y = Float32.( rand( 5001 ) .* -10 ); +gen( x, y, "negative_exp_large_small.json" ); + +# Negative exponents (x small, y large): +x = Float32.( range( 0, stop = 10, length = 5001 ) ); +y = Float32.( rand( 5001 ) .* -(2.0^20) ); +gen( x, y, "negative_exp_small_large.json" ); + +# Negative exponents (x large, y large): +x = Float32.( range( 1e20, stop = 1e30, length = 5001 ) ); +y = Float32.( rand( 5001 ) .* -(2.0^20) ); +gen( x, y, "negative_exp_large_large.json" ); + +# x small, y small: +x = Float32.( rand( 5001 ) .* 100 ); +y = Float32.( rand( 5001 ) .* 100 ); +gen( x, y, "small_small.json" ); + +# x small, y large: +x = Float32.( rand( 5001 ) .* 1.9988548118735103 ); +y = Float32.( rand( 5001 ) .* 2.0^10 ); +gen( x, y, "small_large.json" ); + +# x large, y small: +x = Float32.( rand( 5001 ) .* 5e10 ); +y = Float32.( rand( 5001 ) .* 10 ); +gen( x, y, "large_small.json" ); + +# Random (x decimal, y decimal): +x = Float32.( rand( 5001 ) .* 500 ); +y = Float32.( rand( 5001 ) .* 100 ); +gen( x, y, "decimal_decimal.json" ); + +# Random (x decimal, y integer): +x = Float32.( rand( 5001 ) .* 500 ); +y = round.( rand(5001) .* 100 ); +gen( x, y, "decimal_integer.json" ); + +# Random (x integer, y decimal): +x = round.( rand(5001) .* 500 ); +y = Float32.( rand( 5001 ) .* 100 ); +gen( x, y, "integer_decimal.json" ); + +# Random (x integer, y integer): +x = round.( rand(5001) .* 500 ); +y = round.( rand(5001) .* 100 ); +gen( x, y, "integer_integer.json" ); diff --git a/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/small_large.json b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/small_large.json new file mode 100644 index 000000000000..246d328a21e0 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/small_large.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/small_small.json b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/small_small.json new file mode 100644 index 000000000000..fc50613cdffc --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/small_small.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/squared_large.json b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/squared_large.json new file mode 100644 index 000000000000..98562b0ff485 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/squared_large.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/squared_small.json b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/squared_small.json new file mode 100644 index 000000000000..2ccec40b4c93 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/squared_small.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/subnormal_results.json b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/subnormal_results.json new file mode 100644 index 000000000000..126a73b0b19c --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/subnormal_results.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/to_the_fourth_large.json b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/to_the_fourth_large.json new file mode 100644 index 000000000000..1a811fb18139 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/to_the_fourth_large.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/to_the_fourth_small.json b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/to_the_fourth_small.json new file mode 100644 index 000000000000..2186e3040fd9 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/test/fixtures/julia/to_the_fourth_small.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/powf/test/test.js b/lib/node_modules/@stdlib/math/base/special/powf/test/test.js new file mode 100644 index 000000000000..111e5e5f6112 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/test/test.js @@ -0,0 +1,1064 @@ +/** +* @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 sqrtf = require( '@stdlib/math/base/special/sqrtf' ); +var absf = require( '@stdlib/math/base/special/absf' ); +var randu = require( '@stdlib/random/base/randu' ); +var f32 = require( '@stdlib/number/float64/base/to-float32' ); +var ulpdiff = require( '@stdlib/number/float32/base/ulp-difference' ); +var roundf = require( '@stdlib/math/base/special/roundf' ); +var PINF = require( '@stdlib/constants/float32/pinf' ); +var NINF = require( '@stdlib/constants/float32/ninf' ); +var EPS = require( '@stdlib/constants/float32/eps' ); +var MAX_SAFE_INTEGER = require( '@stdlib/constants/float32/max-safe-integer' ); +var isnanf = require( '@stdlib/math/base/assert/is-nanf' ); +var isPositiveZerof = require( '@stdlib/math/base/assert/is-positive-zerof' ); +var isNegativeZerof = require( '@stdlib/math/base/assert/is-negative-zerof' ); +var powf = require( './../lib' ); + + +// FIXTURES // + +var squaredSmall = require( './fixtures/julia/squared_small.json' ); +var squaredLarge = require( './fixtures/julia/squared_large.json' ); +var cubedSmall = require( './fixtures/julia/cubed_small.json' ); +var cubedLarge = require( './fixtures/julia/cubed_large.json' ); +var toTheFourthSmall = require( './fixtures/julia/to_the_fourth_small.json' ); +var toTheFourthLarge = require( './fixtures/julia/to_the_fourth_large.json' ); +var baseNearUnitySmall = require( './fixtures/julia/base_near_unity_small.json' ); +var baseNearUnityLarge = require( './fixtures/julia/base_near_unity_large.json' ); +var baseNearUnityHuge = require( './fixtures/julia/base_near_unity_huge.json' ); +var subnormalResults = require( './fixtures/julia/subnormal_results.json' ); +var negativeExpSmallSmall = require( './fixtures/julia/negative_exp_small_small.json' ); +var negativeExpSmallLarge = require( './fixtures/julia/negative_exp_small_large.json' ); +var negativeExpLargeSmall = require( './fixtures/julia/negative_exp_large_small.json' ); +var negativeExpLargeLarge = require( './fixtures/julia/negative_exp_large_large.json' ); +var smallSmall = require( './fixtures/julia/small_small.json' ); +var smallLarge = require( './fixtures/julia/small_large.json' ); +var largeSmall = require( './fixtures/julia/large_small.json' ); +var decimalDecimal = require( './fixtures/julia/decimal_decimal.json' ); +var decimalInteger = require( './fixtures/julia/decimal_integer.json' ); +var integerDecimal = require( './fixtures/julia/integer_decimal.json' ); +var integerInteger = require( './fixtures/julia/integer_integer.json' ); + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof powf, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function accepts two parameters: a base and an exponent', function test( t ) { + t.strictEqual( powf.length, 2.0, 'arity is 2' ); + t.end(); +}); + +tape( 'the function evaluates the exponential function (`y = 2` and `x` small)', function test( t ) { + var expected; + var actual; + var x; + var y; + var i; + + x = squaredSmall.x; + y = squaredSmall.y; + expected = squaredSmall.expected; + for ( i = 0; i < x.length; i++ ) { + x[ i ] = f32( x[ i ] ); + y[ i ] = f32( y[ i ] ); + expected[ i ] = f32( expected[ i ] ); + actual = powf( x[ i ], y[ i ] ); + t.strictEqual( actual, expected[ i ], 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function evaluates the exponential function (`y = 2` and `x` large)', function test( t ) { + var expected; + var actual; + var x; + var y; + var i; + + x = squaredLarge.x; + y = squaredLarge.y; + expected = squaredLarge.expected; + for ( i = 0; i < x.length; i++ ) { + x[ i ] = f32( x[ i ] ); + y[ i ] = f32( y[ i ] ); + expected[ i ] = f32( expected[ i ] ); + actual = powf( x[ i ], y[ i ] ); + t.strictEqual( actual, expected[ i ], 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function evaluates the exponential function (`y = 3` and `x` small)', function test( t ) { + var expected; + var actual; + var x; + var y; + var i; + + x = cubedSmall.x; + y = cubedSmall.y; + expected = cubedSmall.expected; + for ( i = 0; i < x.length; i++ ) { + x[ i ] = f32( x[ i ] ); + y[ i ] = f32( y[ i ] ); + expected[ i ] = f32( expected[ i ] ); + actual = powf( x[ i ], y[ i ] ); + t.strictEqual( actual, expected[ i ], 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function evaluates the exponential function (`y = 3` and `x` large)', function test( t ) { + var expected; + var actual; + var x; + var y; + var i; + + x = cubedLarge.x; + y = cubedLarge.y; + expected = cubedLarge.expected; + for ( i = 0; i < x.length; i++ ) { + x[ i ] = f32( x[ i ] ); + y[ i ] = f32( y[ i ] ); + expected[ i ] = f32( expected[ i ] ); + actual = powf( x[ i ], y[ i ] ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 1, true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function evaluates the exponential function (`y = 4` and `x` small)', function test( t ) { + var expected; + var actual; + var x; + var y; + var i; + + x = toTheFourthSmall.x; + y = toTheFourthSmall.y; + expected = toTheFourthSmall.expected; + for ( i = 0; i < x.length; i++ ) { + x[ i ] = f32( x[ i ] ); + y[ i ] = f32( y[ i ] ); + expected[ i ] = f32( expected[ i ] ); + actual = powf( x[ i ], y[ i ] ); + t.strictEqual( actual, expected[ i ], 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function evaluates the exponential function (`y = 4` and `x` large)', function test( t ) { + var expected; + var actual; + var x; + var y; + var i; + + x = toTheFourthLarge.x; + y = toTheFourthLarge.y; + expected = toTheFourthLarge.expected; + for ( i = 0; i < x.length; i++ ) { + x[ i ] = f32( x[ i ] ); + y[ i ] = f32( y[ i ] ); + expected[ i ] = f32( expected[ i ] ); + actual = powf( x[ i ], y[ i ] ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 2, true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function evaluates the exponential function (`x ~ 1`, `y` small)', function test( t ) { + var expected; + var actual; + var x; + var y; + var i; + + x = baseNearUnitySmall.x; + y = baseNearUnitySmall.y; + expected = baseNearUnitySmall.expected; + for ( i = 0; i < x.length; i++ ) { + x[ i ] = f32( x[ i ] ); + y[ i ] = f32( y[ i ] ); + expected[ i ] = f32( expected[ i ] ); + actual = powf( x[ i ], y[ i ] ); + t.strictEqual( actual, expected[ i ], 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function evaluates the exponential function (`x ~ 1`, `y` large)', function test( t ) { + var expected; + var actual; + var x; + var y; + var i; + + x = baseNearUnityLarge.x; + y = baseNearUnityLarge.y; + expected = baseNearUnityLarge.expected; + for ( i = 0; i < x.length; i++ ) { + x[ i ] = f32( x[ i ] ); + y[ i ] = f32( y[ i ] ); + expected[ i ] = f32( expected[ i ] ); + actual = powf( x[ i ], y[ i ] ); + t.strictEqual( actual, expected[ i ], 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function evaluates the exponential function (`x ~ 1`, `y` huge)', function test( t ) { + var expected; + var actual; + var x; + var y; + var i; + + x = baseNearUnityHuge.x; + y = baseNearUnityHuge.y; + expected = baseNearUnityHuge.expected; + for ( i = 0; i < x.length; i++ ) { + x[ i ] = f32( x[ i ] ); + y[ i ] = f32( y[ i ] ); + expected[ i ] = f32( expected[ i ] ); + actual = powf( x[ i ], y[ i ] ); + t.strictEqual( actual, expected[ i ], 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function evaluates the exponential function (subnormal results)', function test( t ) { + var expected; + var actual; + var x; + var y; + var i; + + x = subnormalResults.x; + y = subnormalResults.y; + expected = subnormalResults.expected; + for ( i = 0; i < x.length; i++ ) { + x[ i ] = f32( x[ i ] ); + y[ i ] = f32( y[ i ] ); + expected[ i ] = f32( expected[ i ] ); + actual = powf( x[ i ], y[ i ] ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 1, true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function evaluates the exponential function (negative exponents; `x` small, `y` small)', function test( t ) { + var expected; + var actual; + var x; + var y; + var i; + + x = negativeExpSmallSmall.x; + y = negativeExpSmallSmall.y; + expected = negativeExpSmallSmall.expected; + for ( i = 0; i < x.length; i++ ) { + x[ i ] = f32( x[ i ] ); + y[ i ] = f32( y[ i ] ); + actual = powf( x[ i ], y[ i ] ); + if ( expected[ i ] === null ) { + t.strictEqual( actual, PINF, 'returns expected value' ); + } else { + expected[ i ] = f32( expected[ i ] ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 1, true, 'returns expected value' ); + } + } + t.end(); +}); + +tape( 'the function evaluates the exponential function (negative exponents; `x` small, `y` large)', function test( t ) { + var expected; + var actual; + var x; + var y; + var i; + + x = negativeExpSmallLarge.x; + y = negativeExpSmallLarge.y; + expected = negativeExpSmallLarge.expected; + for ( i = 0; i < x.length; i++ ) { + x[ i ] = f32( x[ i ] ); + y[ i ] = f32( y[ i ] ); + actual = powf( x[ i ], y[ i ] ); + if ( expected[ i ] === null ) { + t.strictEqual( actual, PINF, 'returns expected value' ); + } else { + expected[ i ] = f32( expected[ i ] ); + t.strictEqual( actual, expected[ i ], 'returns expected value' ); + } + } + t.end(); +}); + +tape( 'the function evaluates the exponential function (negative exponents; `x` large, `y` small)', function test( t ) { + var expected; + var actual; + var x; + var y; + var i; + + x = negativeExpLargeSmall.x; + y = negativeExpLargeSmall.y; + expected = negativeExpLargeSmall.expected; + for ( i = 0; i < x.length; i++ ) { + x[ i ] = f32( x[ i ] ); + y[ i ] = f32( y[ i ] ); + actual = powf( x[ i ], y[ i ] ); + if ( expected[ i ] === null ) { + t.strictEqual( actual, PINF, 'returns expected value' ); + } else { + expected[ i ] = f32( expected[ i ] ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 1, true, 'returns expected value' ); + } + } + t.end(); +}); + +tape( 'the function evaluates the exponential function (negative exponents; `x` large, `y` large)', function test( t ) { + var expected; + var actual; + var x; + var y; + var i; + + x = negativeExpLargeLarge.x; + y = negativeExpLargeLarge.y; + expected = negativeExpLargeLarge.expected; + for ( i = 0; i < x.length; i++ ) { + x[ i ] = f32( x[ i ] ); + y[ i ] = f32( y[ i ] ); + actual = powf( x[ i ], y[ i ] ); + if ( expected[ i ] === null ) { + t.strictEqual( actual, PINF, 'returns expected value' ); + } else { + expected[ i ] = f32( expected[ i ] ); + t.strictEqual( actual, expected[ i ], 'returns expected value' ); + } + } + t.end(); +}); + +tape( 'the function evaluates the exponential function (near overflow)', function test( t ) { + var x; + var y; + var v; + + x = f32( 2.0 ); + y = 128; + v = powf( x, y ); + t.strictEqual( v, PINF, 'returns expected value' ); + + x = f32( 2.0 ); + y = 127; + v = powf( x, y ); + t.strictEqual( v, f32( 1.7014118e38 ), 'returns expected value' ); // Referenced against Julia + + x = f32( 2.011355585648339 ); + y = 127; + v = powf( x, y ); + t.strictEqual( v, PINF, 'returns expected value' ); + + x = f32( 2.0 ); + y = 129; + v = powf( x, y ); + t.strictEqual( v, PINF, 'returns expected value' ); + + x = f32( 1.998647974895499 ); + y = 129; + v = powf( x, y ); + t.strictEqual( v, PINF, 'returns expected value' ); + + x = f32( f32( 2.0 ) + f32( EPS*f32(2.0) ) ); + y = 128; + v = powf( x, y ); + t.strictEqual( v, PINF, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function evaluates the exponential function (near underflow)', function test( t ) { + var x; + var y; + var v; + + x = f32( 2.0 ); + y = -150; + v = powf( x, y ); + t.strictEqual( v, f32( 0.0 ), 'returns expected value' ); + + x = f32( 1.9999998807907104 ); + y = -149; + v = powf( x, y ); + t.strictEqual( v, f32( 1.4013109094411322e-45 ), 'returns expected value' ); // Referenced against Julia + + x = f32( 1.9999998807907104 ); + y = -150; + v = powf( x, y ); + t.strictEqual( v, f32( 7.00655496482888e-46 ), 'returns expected value' ); // Referenced against Julia + + x = f32( 1.9999999999999999 ); + y = -150; + v = powf( x, y ); + t.strictEqual( v, f32( 0.0 ), 'returns expected value' ); + + t.end(); +}); + +tape( 'the function evaluates the exponential function (small `x`, large `y`)', function test( t ) { + var expected; + var actual; + var x; + var y; + var i; + + x = smallLarge.x; + y = smallLarge.y; + expected = smallLarge.expected; + for ( i = 0; i < x.length; i++ ) { + x[ i ] = f32( x[ i ] ); + y[ i ] = f32( y[ i ] ); + actual = powf( x[ i ], y[ i ] ); + if ( expected[ i ] === null ) { + t.strictEqual( actual, PINF, 'returns expected value' ); + } else { + expected[ i ] = f32( expected[ i ] ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 1, true, 'returns expected value' ); + } + } + t.end(); +}); + +tape( 'the function evaluates the exponential function (large `x`, small `y`)', function test( t ) { + var expected; + var actual; + var x; + var y; + var i; + + x = largeSmall.x; + y = largeSmall.y; + expected = largeSmall.expected; + for ( i = 0; i < x.length; i++ ) { + x[ i ] = f32( x[ i ] ); + y[ i ] = f32( y[ i ] ); + actual = powf( x[ i ], y[ i ] ); + if ( expected[ i ] === null ) { + t.strictEqual( actual, PINF, 'returns expected value' ); + } else { + expected[ i ] = f32( expected[ i ] ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 1, true, 'returns expected value' ); + } + } + t.end(); +}); + +tape( 'the function evaluates the exponential function (small `x`, small `y`)', function test( t ) { + var expected; + var actual; + var x; + var y; + var i; + + x = smallSmall.x; + y = smallSmall.y; + expected = smallSmall.expected; + for ( i = 0; i < x.length; i++ ) { + x[ i ] = f32( x[ i ] ); + y[ i ] = f32( y[ i ] ); + actual = powf( x[ i ], y[ i ] ); + if ( expected[ i ] === null ) { + t.strictEqual( actual, PINF, 'returns expected value' ); + } else { + expected[ i ] = f32( expected[ i ] ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 1, true, 'returns expected value' ); + } + } + t.end(); +}); + +tape( 'the function evaluates the exponential function (decimal `x`, decimal `y`)', function test( t ) { + var expected; + var actual; + var x; + var y; + var i; + + x = decimalDecimal.x; + y = decimalDecimal.y; + expected = decimalDecimal.expected; + for ( i = 0; i < x.length; i++ ) { + x[ i ] = f32( x[ i ] ); + y[ i ] = f32( y[ i ] ); + actual = powf( x[ i ], y[ i ] ); + if ( expected[ i ] === null ) { + t.strictEqual( actual, PINF, 'returns expected value' ); + } else { + expected[ i ] = f32( expected[ i ] ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 1, true, 'returns expected value' ); + } + } + t.end(); +}); + +tape( 'the function evaluates the exponential function (decimal `x`, integer `y`)', function test( t ) { + var expected; + var actual; + var x; + var y; + var i; + + x = decimalInteger.x; + y = decimalInteger.y; + expected = decimalInteger.expected; + for ( i = 0; i < x.length; i++ ) { + x[ i ] = f32( x[ i ] ); + y[ i ] = f32( y[ i ] ); + actual = powf( x[ i ], y[ i ] ); + if ( expected[ i ] === null ) { + t.strictEqual( actual, PINF, 'returns expected value' ); + } else { + expected[ i ] = f32( expected[ i ] ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 1, true, 'returns expected value' ); + } + } + t.end(); +}); + +tape( 'the function evaluates the exponential function (integer `x`, decimal `y`)', function test( t ) { + var expected; + var actual; + var x; + var y; + var i; + + x = integerDecimal.x; + y = integerDecimal.y; + expected = integerDecimal.expected; + for ( i = 0; i < x.length; i++ ) { + x[ i ] = f32( x[ i ] ); + y[ i ] = f32( y[ i ] ); + actual = powf( x[ i ], y[ i ] ); + if ( expected[ i ] === null ) { + t.strictEqual( actual, PINF, 'returns expected value' ); + } else { + expected[ i ] = f32( expected[ i ] ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 1, true, 'returns expected value' ); + } + } + t.end(); +}); + +tape( 'the function evaluates the exponential function (integer `x`, integer `y`)', function test( t ) { + var expected; + var actual; + var x; + var y; + var i; + + x = integerInteger.x; + y = integerInteger.y; + expected = integerInteger.expected; + for ( i = 0; i < x.length; i++ ) { + x[ i ] = f32( x[ i ] ); + y[ i ] = f32( y[ i ] ); + actual = powf( x[ i ], y[ i ] ); + if ( expected[ i ] === null ) { + t.strictEqual( actual, PINF, 'returns expected value' ); + } else { + expected[ i ] = f32( expected[ i ] ); + t.strictEqual( ulpdiff( actual, expected[ i ] ) <= 1, true, 'returns expected value' ); + } + } + t.end(); +}); + +tape( 'the function returns `NaN` if provided `NaN` for the exponent', function test( t ) { + var v; + + v = powf( f32( -3.0 ), NaN ); + t.strictEqual( isnanf( v ), true, 'returns expected value' ); + + v = powf( f32( 0.0 ), NaN ); + t.strictEqual( isnanf( v ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns `NaN` if provided `NaN` for the base and `y != 0`', function test( t ) { + var v; + + v = powf( NaN, f32( 5.0 ) ); + t.strictEqual( isnanf( v ), true, 'returns expected value' ); + + v = powf( NaN, f32( 1.0 ) ); + t.strictEqual( isnanf( v ), true, 'returns expected value' ); + + v = powf( NaN, f32( 0.0 ) ); + t.strictEqual( isnanf( v ), false, 'returns expected value' ); + + t.end(); +}); + +tape( 'any number raised to the zero power is `1`', function test( t ) { + var x; + var v; + var i; + + for ( i = 0; i < 100; i++ ) { + x = f32( f32( randu()*1.0e6 ) - 5.0e5 ); + v = powf( x, f32( 0.0 ) ); + t.strictEqual( v, f32( 1.0 ), 'returns expected value' ); + } + t.strictEqual( powf( PINF, f32( 0.0 ) ), f32( 1.0 ), 'returns expected value' ); + t.strictEqual( powf( NINF, f32( 0.0 ) ), f32( 1.0 ), 'returns expected value' ); + t.strictEqual( powf( f32( 0.0 ), f32( 0.0 ) ), f32( 1.0 ), 'returns expected value' ); + t.end(); +}); + +tape( 'any number raised to the `-1` power is the reciprocal of that number', function test( t ) { + var x; + var v; + var i; + for ( i = 0; i < 100; i++ ) { + x = f32( f32( randu()*1.0e6 ) - 5.0e5 ); + v = powf( x, f32( -1.0 ) ); + t.strictEqual( v, f32( f32(1.0)/x ), 'returns expected value' ); + } + t.strictEqual( isPositiveZerof( powf( PINF, f32( -1.0 ) ) ), true, 'returns expected value' ); + t.strictEqual( isNegativeZerof( powf( NINF, f32( -1.0 ) ) ), true, 'returns expected value' ); + t.strictEqual( powf( f32( 0.0 ), f32( -1.0 ) ), PINF, 'returns expected value' ); + t.strictEqual( powf( f32( -0.0 ), f32( -1.0 ) ), NINF, 'returns expected value' ); + t.end(); +}); + +tape( 'unity raised to any power is `1`', function test( t ) { + var y; + var v; + var i; + for ( i = 0; i < 100; i++ ) { + y = f32( f32( randu()*1.0e6 ) - 5.0e5 ); + v = powf( f32( 1.0 ), y ); + t.strictEqual( v, f32( 1.0 ), 'returns expected value' ); + } + t.strictEqual( powf( f32( 1.0 ), PINF ), f32( 1.0 ), 'returns expected value' ); + t.strictEqual( powf( f32( 1.0 ), NINF ), f32( 1.0 ), 'returns expected value' ); + t.strictEqual( powf( f32( 1.0 ), f32( 0.0 ) ), f32( 1.0 ), 'returns expected value' ); + t.end(); +}); + +tape( '`-1` raised to any odd integer is `-1`', function test( t ) { + var v; + var i; + for ( i = -51; i < 53; i += 2 ) { + v = powf( f32( -1.0 ), i ); + t.strictEqual( v, f32( -1.0 ), 'returns expected value' ); + } + t.end(); +}); + +tape( '`+-0` raised to `-infinity` is `+infinity`', function test( t ) { + var v; + + v = powf( f32( +0.0 ), NINF ); + t.strictEqual( v, PINF, 'returns expected value' ); + + v = powf( f32( -0.0 ), NINF ); + t.strictEqual( v, PINF, 'returns expected value' ); + + t.end(); +}); + +tape( '`+-0` raised to `+infinity` is `0`', function test( t ) { + var v; + + v = powf( f32( +0.0 ), PINF ); + t.strictEqual( isPositiveZerof( v ), true, 'returns expected value' ); + + v = powf( f32( -0.0 ), PINF ); + t.strictEqual( isPositiveZerof( v ), true, 'returns expected value' ); + + t.end(); +}); + +tape( '`+-0` raised to any positive finite number which is not an odd integer is `0`', function test( t ) { + var y; + var i; + var v; + + y = [ + 2, + f32( 3.14 ), + f32( 1.0e5 ), + f32( 5.1 ), + f32( 9.999999 ) + ]; + + for ( i = 0; i < y.length; i++ ) { + v = powf( f32( +0.0 ), y[ i ] ); + t.strictEqual( isPositiveZerof( v ), true, 'returns expected value' ); + + v = powf( f32( -0.0 ), y[ i ] ); + t.strictEqual( isPositiveZerof( v ), true, 'returns expected value' ); + } + t.end(); +}); + +tape( '`+-0` raised to any positive odd integer is `+-0`', function test( t ) { + var i; + var v; + + for ( i = 1; i < 101; i += 2 ) { + v = powf( f32( +0.0 ), i ); + t.strictEqual( isPositiveZerof( v ), true, 'returns expected value' ); + + v = powf( f32( -0.0 ), i ); + t.strictEqual( isNegativeZerof( v ), true, 'returns expected value' ); + } + t.end(); +}); + +tape( '`+-0` raised to any negative finite number which is not an odd integer is `+infinity`', function test( t ) { + var y; + var i; + var v; + + y = [ + -2, + f32( -3.14 ), + f32( -1.0e5 ), + f32( -5.1 ), + f32( -9.999999 ) + ]; + + for ( i = 0; i < y.length; i++ ) { + v = powf( f32( +0.0 ), y[ i ] ); + t.strictEqual( v, PINF, 'returns expected value' ); + + v = powf( f32( -0.0 ), y[ i ] ); + t.strictEqual( v, PINF, 'returns expected value' ); + } + t.end(); +}); + +tape( '`+-0` raised to any negative odd integer is `+-infinity`', function test( t ) { + var i; + var v; + + for ( i = -101; i < 0; i += 2 ) { + v = powf( f32( +0.0 ), i ); + t.strictEqual( v, PINF, 'returns expected value' ); + + v = powf( f32( -0.0 ), i ); + t.strictEqual( v, NINF, 'returns expected value' ); + } + t.end(); +}); + +tape( '`+-1` raised to `+-infinity` is `1`', function test( t ) { + var v; + + v = powf( f32( -1.0 ), PINF ); + t.strictEqual( v, f32( 1.0 ), 'returns expected value' ); + + v = powf( f32( -1.0 ), NINF ); + t.strictEqual( v, f32( 1.0 ), 'returns expected value' ); + + v = powf( f32( 1.0 ), PINF ); + t.strictEqual( v, f32( 1.0 ), 'returns expected value' ); + + v = powf( f32( 1.0 ), NINF ); + t.strictEqual( v, f32( 1.0 ), 'returns expected value' ); + + t.end(); +}); + +tape( 'raising any number to the `1/2` power returns the same results as evaluating the principal square root', function test( t ) { + var x; + var v; + var i; + for ( i = 0; i < 500; i++ ) { + x = f32( randu()*1.0e5 ); + v = powf( x, f32( 0.5 ) ); + t.strictEqual( v, sqrtf( x ), 'returns expected value' ); + } + t.end(); +}); + +tape( 'raising any number to the `-1/2` power returns the same results as evaluating the inverse of the principal square root', function test( t ) { + var x; + var v; + var i; + for ( i = 0; i < 500; i++ ) { + x = f32( randu()*1.0e5 ); + v = powf( x, f32( -0.5 ) ); + t.strictEqual( v, f32( f32(1.0)/sqrtf( x ) ), 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function returns `+infinity` if a positive number greater than `1` is raised to `+infinity`', function test( t ) { + var x; + var v; + var i; + for ( i = 0; i < 100; i++ ) { + x = f32( f32( f32(1.0) + f32( randu()*1.0e5 ) ) ); + v = powf( x, PINF ); + t.strictEqual( v, PINF, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function returns `+infinity` if a negative number less than `-1` is raised to `+infinity`', function test( t ) { + var x; + var v; + var i; + for ( i = 0; i < 100; i++ ) { + x = f32( f32( -randu()*1.0e5 ) - f32( 1.0 ) ); + v = powf( x, PINF ); + t.strictEqual( v, PINF, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function returns `+infinity` if `-infinity` is raised to `+infinity`', function test( t ) { + var v = powf( NINF, PINF ); + t.strictEqual( v, PINF, 'returns expected value' ); + t.end(); +}); + +tape( 'the function returns `(-0)^y` if `-infinity` is raised to a numeric `y` power', function test( t ) { + var y; + var v; + var i; + + for ( i = 0; i < 100; i++ ) { + y = f32( f32( randu()*100.0 ) - f32( 50.0 ) ); + v = powf( NINF, y ); + t.strictEqual( v, powf( f32( -0.0 ), -y ), 'returns expected value' ); + } + + v = powf( NINF, NINF ); + t.strictEqual( v, powf( f32( -0.0 ), PINF ), 'returns expected value' ); + + v = powf( NINF, PINF ); + t.strictEqual( v, powf( f32( -0.0 ), NINF ), 'returns expected value' ); + + v = powf( NINF, f32( 5.0 ) ); + t.strictEqual( v, powf( f32( -0.0 ), f32( -5.0 ) ), 'returns expected value' ); + + v = powf( NINF, f32( 2.0 ) ); + t.strictEqual( v, powf( f32( -0.0 ), f32( -2.0 ) ), 'returns expected value' ); + + v = powf( NINF, f32( -5.0 ) ); + t.strictEqual( v, powf( f32( -0.0 ), f32( 5.0 ) ), 'returns expected value' ); + + v = powf( NINF, f32( -2.0 ) ); + t.strictEqual( v, powf( f32( -0.0 ), f32( 2.0 ) ), 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns `0` if a positive number greater than `1` is raised to `-infinity`', function test( t ) { + var x; + var v; + var i; + for ( i = 0; i < 100; i++ ) { + x = f32( f32( f32(1.0) + f32( randu()*1.0e5 ) ) ); + v = powf( x, NINF ); + t.strictEqual( v, f32( 0.0 ), 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function returns `0` if `+infinity` is raised to `-infinity`', function test( t ) { + var v = powf( PINF, NINF ); + t.strictEqual( v, f32( 0.0 ), 'returns expected value' ); + t.end(); +}); + +tape( 'the function returns `0` if `+infinity` is raised to any negative finite number', function test( t ) { + var y; + var v; + var i; + for ( i = 0; i < 100; i++ ) { + y = f32( -f32(randu() * 1.0e5) - EPS ); + v = powf( PINF, y ); + t.strictEqual( isPositiveZerof( v ), true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function returns `+infinity` if `+infinity` is raised to any positive finite number', function test( t ) { + var y; + var v; + var i; + for ( i = 0; i < 100; i++ ) { + y = f32( f32( randu()*1.0e5 ) + EPS ); + v = powf( PINF, y ); + t.strictEqual( v, PINF, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function returns `0` if a negative number less than `-1` is raised to `-infinity`', function test( t ) { + var x; + var v; + var i; + for ( i = 0; i < 100; i++ ) { + x = f32( f32( -randu()*1.0e5 ) - f32( 1.0 ) ); + v = powf( x, NINF ); + t.strictEqual( v, f32( 0.0 ), 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function returns `NaN` if asked to raise a negative number to an exponent whose absolute value is greater than 0 but less than 1', function test( t ) { + var x; + var y; + var v; + var i; + + for ( i = 0; i < 100; i++ ) { + x = f32( f32( -randu()*1.0e5 ) - EPS ); + y = f32( randu() ); + if ( y === 0.0 || y === 1.0 ) { + continue; + } + v = powf( x, y ); + t.strictEqual( isnanf( v ), true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'if `y > 2^27` and `|x|` significantly less than unity, the function underflows', function test( t ) { + var exp; + var x; + var y; + var v; + var i; + + for ( i = 0; i < 100; i++ ) { + x = f32( f32( 0.5 ) * randu() ); + + exp = roundf( randu()*27.0 ) + 27; + y = powf( f32( 2.0 ), exp ); + + v = powf( x, y ); + t.strictEqual( isPositiveZerof( v ), true, 'returns expected value' ); + + if ( y < MAX_SAFE_INTEGER ) { + y += 1; + v = powf( -x, y ); + t.strictEqual( isNegativeZerof( v ), true, 'returns expected value' ); + } + } + t.end(); +}); + +tape( 'if `y < -(2^27)` and `|x|` significantly less than unity, the function overflows', function test( t ) { + var exp; + var x; + var y; + var v; + var i; + + for ( i = 0; i < 100; i++ ) { + x = f32( f32( 0.5 ) * randu() ); + + exp = roundf( randu()*27.0 ) + 27; + y = -powf( f32( 2.0 ), exp ); + + v = powf( x, y ); + t.strictEqual( v, PINF, 'returns expected value' ); + + if ( absf( y ) < MAX_SAFE_INTEGER ) { + y -= 1; + v = powf( -x, y ); + t.strictEqual( v, NINF, 'returns expected value' ); + } + } + t.end(); +}); + +tape( 'if `y < -(2^27)` and `|x|` significantly greater than unity, the function underflows', function test( t ) { + var exp; + var x; + var y; + var v; + var i; + + for ( i = 0; i < 100; i++ ) { + x = f32( f32( 2.0 ) + f32( randu()*1.0e5 ) ); + + exp = roundf( randu()*32.0 ) + 32; + y = -powf( f32( 2.0 ), exp ); + + v = powf( x, y ); + t.strictEqual( isPositiveZerof( v ), true, 'returns expected value' ); + + if ( absf( y ) < MAX_SAFE_INTEGER ) { + y -= 1; + v = powf( -x, y ); + t.strictEqual( isNegativeZerof( v ), true, 'returns expected value' ); + } + } + t.end(); +}); + +tape( 'if `y > 2^27` and `|x|` significantly greater than unity, the function overflows', function test( t ) { + var exp; + var x; + var y; + var v; + var i; + + for ( i = 0; i < 100; i++ ) { + x = f32( f32( 2.0 ) + f32( randu()*1.0e5 ) ); + + exp = roundf( randu()*32.0 ) + 32; + y = powf( f32( 2.0 ), exp ); + + v = powf( x, y ); + t.strictEqual( v, PINF, 'returns expected value' ); + + if ( y < MAX_SAFE_INTEGER ) { + y += 1; + v = powf( -x, y ); + t.strictEqual( v, NINF, 'returns expected value' ); + } + } + t.end(); +}); diff --git a/lib/node_modules/@stdlib/math/base/special/powf/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/powf/test/test.native.js new file mode 100644 index 000000000000..e69de29bb2d1 diff --git a/lib/node_modules/@stdlib/math/base/special/powf/test/test.x_is_zero.js b/lib/node_modules/@stdlib/math/base/special/powf/test/test.x_is_zero.js new file mode 100644 index 000000000000..15afa5815b2e --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/powf/test/test.x_is_zero.js @@ -0,0 +1,110 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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 PINF = require( '@stdlib/constants/float32/pinf' ); +var NINF = require( '@stdlib/constants/float32/ninf' ); +var f32 = require( '@stdlib/number/float64/base/to-float32' ); +var isPositiveZerof = require( '@stdlib/math/base/assert/is-positive-zerof' ); +var isNegativeZerof = require( '@stdlib/math/base/assert/is-negative-zerof' ); +var powf = require( './../lib/x_is_zerof.js' ); + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof powf, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function returns `+infinity` if `y = -infinity`', function test( t ) { + var v; + + v = powf( f32( 0.0 ), NINF ); + t.strictEqual( v, PINF, 'returns expected value' ); + + v = powf( f32( -0.0 ), NINF ); + t.strictEqual( v, PINF, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns `+0` if `y = +infinity`', function test( t ) { + var v; + + v = powf( f32( 0.0 ), PINF ); + t.strictEqual( isPositiveZerof( v ), true, 'returns expected value' ); + + v = powf( f32( -0.0 ), PINF ); + t.strictEqual( isPositiveZerof( v ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns `x` if `y` is an odd positive integer', function test( t ) { + var v; + + v = powf( f32( 0.0 ), 5 ); + t.strictEqual( isPositiveZerof( v ), true, 'returns expected value' ); + + v = powf( f32( -0.0 ), 5 ); + t.strictEqual( isNegativeZerof( v ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns `+0` if `y` is positive but not an odd integer', function test( t ) { + var v; + + v = powf( f32( 0.0 ), 4 ); + t.strictEqual( isPositiveZerof( v ), true, 'returns expected value' ); + + v = powf( f32( -0.0 ), f32( 3.14 ) ); + t.strictEqual( isPositiveZerof( v ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns `+-infinity` if `y` is a negative odd integer', function test( t ) { + var v; + + v = powf( f32( 0.0 ), -5 ); + t.strictEqual( v, PINF, 'returns expected value' ); + + v = powf( f32( -0.0 ), -5 ); + t.strictEqual( v, NINF, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns `+infinity` if `y` is negative but not an odd integer', function test( t ) { + var v; + + v = powf( f32( 0.0 ), -4 ); + t.strictEqual( v, PINF, 'returns expected value' ); + + v = powf( f32( -0.0 ), f32( -3.14 ) ); + t.strictEqual( v, PINF, 'returns expected value' ); + + t.end(); +});