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+ +The **modified Bessel function of the second kind of order zero** is defined as + +```math +K_0(x) = \int_0^\infty e^{-x \cosh t} \, dt, \quad x > 0. +``` + + + + + +
+ + + +
+ +## Usage + +```javascript +var k0 = require( '@stdlib/math/base/special/besselk0' ); +``` + +#### k0( x ) + +Computes the [modified Bessel function of the second kind][modified-bessel-second-kind] of order zero at `x`. + +```javascript +var v = k0( 1.0 ); +// returns ~0.421 + +v = k0( 10.0 ); +// returns ~0.000018 + +v = k0( Infinity ); +// returns 0.0 +``` + +If `x < 0` or `x` is `NaN`, the function returns `NaN`. + +```javascript +var v =k0( -1.0 ); +// returns NaN + +v = k0( -Infinity ); +// returns NaN + +v = k0( NaN ); +// returns NaN +``` + +
+ + + +
+ +## Examples + + + +```javascript +var uniform = require( '@stdlib/random/array/uniform' ); +var logEachMap = require( '@stdlib/console/log-each-map' ); +var besselk0 = require( '@stdlib/math/base/special/besselk0' ); + +var opts = { + 'dtype': 'float64' +}; +var x = uniform( 100, 0.0, 100.0, opts ); + +logEachMap( 'besselk0(%lf) = %lf', x, besselk0 ); +``` + +
+ + + + + +* * * + +
+ +## C APIs + + + +
+ +
+ + + + + +
+ +### Usage + +```c +#include "stdlib/math/base/special/besselk0.h" +``` + +#### stdlib_base_besselk0( x ) + +Computes the [modified Bessel function of the second kind][modified-bessel-second-kind] of order zero at `x`. + +```c +double out = stdlib_base_besselk0( 0.0 ); +// returns Infinity + +out = stdlib_base_besselk0( 1.0 ); +// returns ~0.421 +``` + +The function accepts the following arguments: + +- **x**: `[in] double` input value. + +```c +double stdlib_base_besselk0( const double x ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +### Examples + +```c +#include "stdlib/math/base/special/besselk0.h" +#include + +int main( void ) { + const double x[] = { 0.0, 1.0, 2.0, 3.0, 4.0 }; + + double y; + int i; + for ( i = 0; i < 5; i++ ) { + y = stdlib_base_besselk0( x[ i ] ); + printf( "besselk0(%lf) = %lf\n", x[ i ], y ); + } +} +``` + +
+ + + +
+ + + + + +
+ +* * * + +## See Also + +- [`@stdlib/math/base/special/besselj0`][@stdlib/math/base/special/besselj0]: compute the Bessel function of the first kind of order zero. +- [`@stdlib/math/base/special/besselj1`][@stdlib/math/base/special/besselj1]: compute the Bessel function of the first kind of order one. +- [`@stdlib/math/base/special/bessely1`][@stdlib/math/base/special/bessely1]: compute the Bessel function of the second kind of order one. + +
+ + + + + +
+ +[modified-bessel-second-kind]: https://en.wikipedia.org/wiki/Bessel_function#Modified_Bessel_functions:_I%CE%B1,_K%CE%B1 + + + +[@stdlib/math/base/special/besselj0]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/besselj0 + +[@stdlib/math/base/special/besselj1]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/besselj1 + +[@stdlib/math/base/special/bessely1]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/bessely1 + + + +
+ + diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/benchmark.js b/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/benchmark.js new file mode 100644 index 000000000000..5f17cb37cc82 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/benchmark.js @@ -0,0 +1,54 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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 uniform = require( '@stdlib/random/array/uniform' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var pkg = require( './../package.json' ).name; +var k0 = require( './../lib' ); + + +// MAIN // + +bench( pkg, function benchmark( b ) { + var x; + var y; + var i; + + // Avoid x = 0 where K0 diverges: + x = uniform( 100, 1.0e-6, 100000.0 ); + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + y = k0( x[ i % x.length ] ); + if ( isnan( y ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + + if ( isnan( y ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/benchmark.native.js b/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/benchmark.native.js new file mode 100644 index 000000000000..c7516e9ab1ae --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/benchmark.native.js @@ -0,0 +1,64 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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 uniform = require( '@stdlib/random/array/uniform' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var tryRequire = require( '@stdlib/utils/try-require' ); +var format = require( '@stdlib/string/format' ); +var pkg = require( './../package.json' ).name; + + +// VARIABLES // + +var k0 = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( k0 instanceof Error ) +}; + + +// MAIN // + +bench( format( '%s::native', pkg, opts ), function benchmark( b ) { + var x; + var y; + var i; + + // Avoid x = 0 where K0 diverges: + x = uniform( 100, 1.0e-6, 100000.0 ); + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + y = k0( x[ i % x.length ] ); + if ( isnan( y ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + + if ( isnan( y ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/c/Makefile b/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/c/Makefile new file mode 100644 index 000000000000..979768abbcec --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/c/Makefile @@ -0,0 +1,146 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2026 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/besselk0/benchmark/c/benchmark.c b/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/c/benchmark.c new file mode 100644 index 000000000000..b469e3ca9154 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/c/benchmark.c @@ -0,0 +1,149 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +/** +* Benchmark `besselk0`. +* +* ## Notes +* +* * We assume the [GNU C library][2], which provides additional exotic functions. +* +* [1]: http://en.cppreference.com/w/c/numeric/math +* [2]: https://www.gnu.org/software/libc/manual/html_node/Special-Functions.html +*/ + +#include "stdlib/math/base/special/besselk0.h" +#include +#include +#include +#include + +#define NAME "besselk0" +#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 ); + printf( "# total %d\n", total ); + printf( "# pass %d\n", passing ); + printf( "#\n" ); + printf( "# ok\n" ); +} + +/** +* Prints benchmark results. +* +* @param elapsed elapsed time in seconds +*/ +static void print_results( double elapsed ) { + double rate = (double)ITERATIONS / elapsed; + printf( " ---\n" ); + printf( " iterations: %d\n", ITERATIONS ); + printf( " elapsed: %0.9f\n", elapsed ); + printf( " rate: %0.9f\n", rate ); + printf( " ...\n" ); +} + +/** +* Returns a clock time. +* +* @return clock time +*/ +static double tic( void ) { + struct timeval now; + gettimeofday( &now, NULL ); + return (double)now.tv_sec + (double)now.tv_usec / 1.0e6; +} + +/** +* Generates a random number on the interval (0, 1]. +* +* @return random number +*/ +static double rand_double( void ) { + int r = rand(); + return ( (double)r + 1.0 ) / ( (double)RAND_MAX + 1.0 ); +} + +/** +* Runs a benchmark. +* +* @return elapsed time in seconds +*/ +static double benchmark( void ) { + double x[ 100 ]; + double elapsed; + double y; + double t; + int i; + + // Generate positive inputs; avoid zero where K0 diverges: + for ( i = 0; i < 100; i++ ) { + x[ i ] = rand_double() * 100.0; + } + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + y = stdlib_base_besselk0( x[ i % 100 ] ); + 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; + + // 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 ); + return 0; +} diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/c/native/Makefile b/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/c/native/Makefile new file mode 100644 index 000000000000..979768abbcec --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/c/native/Makefile @@ -0,0 +1,146 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2026 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/besselk0/benchmark/c/native/benchmark.c b/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/c/native/benchmark.c new file mode 100644 index 000000000000..1b4834f0b957 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/c/native/benchmark.c @@ -0,0 +1,142 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +/** +* Benchmark `besselk0`. +*/ + +#include "stdlib/math/base/special/besselk0.h" +#include +#include +#include +#include + +#define NAME "besselk0" +#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 benchmark results. +* +* @param elapsed elapsed time in seconds +*/ +static void print_results( double elapsed ) { + double rate = (double)ITERATIONS / elapsed; + printf( " ---\n" ); + printf( " iterations: %d\n", ITERATIONS ); + printf( " elapsed: %0.9f\n", elapsed ); + printf( " rate: %0.9f\n", rate ); + printf( " ...\n" ); +} + +/** +* Returns a clock time. +* +* @return clock time +*/ +static double tic( void ) { + struct timeval now; + gettimeofday( &now, NULL ); + return (double)now.tv_sec + (double)now.tv_usec / 1.0e6; +} + +/** +* Generates a random number on the interval (0,1]. +* +* @return random number +*/ +static double rand_double( void ) { + int r = rand(); + return ( (double)r + 1.0 ) / ( (double)RAND_MAX + 1.0 ); +} + +/** +* Runs a benchmark. +* +* @return elapsed time in seconds +*/ +static double benchmark( void ) { + double x[ 100 ]; + double elapsed; + double y; + double t; + int i; + + // Generate positive inputs; avoid zero where K0 diverges: + for ( i = 0; i < 100; i++ ) { + x[ i ] = rand_double() * 100000.0; + } + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + y = stdlib_base_besselk0( x[ i % 100 ] ); + 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 ); + return 0; +} diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/julia/REQUIRE b/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/julia/REQUIRE new file mode 100644 index 000000000000..98645e192e41 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/julia/REQUIRE @@ -0,0 +1,2 @@ +julia 1.5 +BenchmarkTools 0.5.0 diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/julia/benchmark.jl b/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/julia/benchmark.jl new file mode 100755 index 000000000000..d641c2eed942 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/julia/benchmark.jl @@ -0,0 +1,98 @@ +#!/usr/bin/env julia +# +# @license Apache-2.0 +# +# Copyright (c) 2026 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 BenchmarkTools +using Printf +using SpecialFunctions + +# Benchmark variables: +name = "besselk0"; +repeats = 3; + +""" + print_version() + +Prints the TAP version. +""" +function print_version() + @printf( "TAP version 13\n" ); +end + +""" + print_summary( total, passing ) + +Print the benchmark summary. +""" +function print_summary( total, 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" ); +end + +""" + print_results( iterations, elapsed ) + +Print benchmark results. +""" +function print_results( iterations, elapsed ) + rate = iterations / elapsed + + @printf( " ---\n" ); + @printf( " iterations: %d\n", iterations ); + @printf( " elapsed: %0.9f\n", elapsed ); + @printf( " rate: %0.9f\n", rate ); + @printf( " ...\n" ); +end + +""" + benchmark() + +Run a benchmark. +""" +function benchmark() + t = BenchmarkTools.@benchmark besselk( 0, rand() * 100000.0 + eps() ) samples=1e6 + + # Compute the total elapsed time (convert from ns to seconds): + s = sum( t.times ) / 1.0e9; + + # Determine the number of "iterations": + iter = length( t.times ); + + [ iter, s ]; +end + +""" + main() + +Run benchmarks. +""" +function main() + print_version(); + for i in 1:repeats + @printf( "# julia::%s\n", name ); + results = benchmark(); + print_results( results[ 1 ], results[ 2 ] ); + @printf( "ok %d benchmark finished\n", i ); + end + print_summary( repeats, repeats ); +end + +main(); diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/python/scipy/benchmark.py b/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/python/scipy/benchmark.py new file mode 100644 index 000000000000..15598a31c8d4 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/python/scipy/benchmark.py @@ -0,0 +1,84 @@ +#!/usr/bin/env python +# +# @license Apache-2.0 +# +# Copyright (c) 2026 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +# + +"""Benchmark scipy.special.k0.""" + +from __future__ import print_function +import timeit + +NAME = "besselk0" +REPEATS = 3 +ITERATIONS = 1000000 + + +def print_version(): + """Print the TAP version.""" + print("TAP version 13") + + +def print_summary(total, passing): + """Print the benchmark summary.""" + print("#") + print("1.." + str(total)) # TAP plan + print("# total " + str(total)) + print("# pass " + str(passing)) + print("#") + print("# ok") + + +def print_results(elapsed): + """Print benchmark results.""" + rate = ITERATIONS / elapsed + + print(" ---") + print(" iterations: " + str(ITERATIONS)) + print(" elapsed: " + str(elapsed)) + print(" rate: " + str(rate)) + print(" ...") + + +def benchmark(): + """Run the benchmark and print benchmark results.""" + setup = ( + "from scipy.special import k0; " + "from random import random;" + ) + # Avoid zero where K0 diverges: + stmt = "y = k0(random()*100000.0 + 1e-12)" + + t = timeit.Timer(stmt, setup=setup) + + print_version() + + for i in range(REPEATS): + print("# python::scipy::" + NAME) + elapsed = t.timeit(number=ITERATIONS) + print_results(elapsed) + print("ok " + str(i + 1) + " benchmark finished") + + print_summary(REPEATS, REPEATS) + + +def main(): + """Run the benchmark.""" + benchmark() + + +if __name__ == "__main__": + main() diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/r/DESCRIPTION b/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/r/DESCRIPTION new file mode 100644 index 000000000000..b63be35491b8 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/r/DESCRIPTION @@ -0,0 +1,9 @@ +Package: besselk0-benchmarks +Title: Benchmarks +Version: 0.0.0 +Authors@R: person("stdlib", "js", role = c("aut","cre")) +Description: Benchmarks. +Depends: R (>=4.5.0) +Imports: + microbenchmark +LazyData: true diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/r/benchmark.R b/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/r/benchmark.R new file mode 100755 index 000000000000..28271fc13c6b --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/benchmark/r/benchmark.R @@ -0,0 +1,84 @@ +#!/usr/bin/env Rscript +# +# @license Apache-2.0 +# +# Copyright (c) 2026 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. +# + +# Set the precision to 16 digits: +options( digits = 16L ) + +#' Run benchmarks. +#' +#' @examples +#' main() +main <- function() { + # Define benchmark parameters: + name <- 'besselk0' + iterations <- 1000000L + repeats <- 3L + + #' Print the TAP version. + print_version <- function() { + cat( 'TAP version 13\n' ) + } + + #' Print the TAP summary. + print_summary <- function( total, passing ) { + cat( '#\n' ) + cat( paste0( '1..', total, '\n' ) ) + cat( paste0( '# total ', total, '\n' ) ) + cat( paste0( '# pass ', passing, '\n' ) ) + cat( '#\n' ) + cat( '# ok\n' ) + } + + #' Print benchmark results. + print_results <- function( iterations, elapsed ) { + rate <- iterations / elapsed + cat( ' ---\n' ) + cat( paste0( ' iterations: ', iterations, '\n' ) ) + cat( paste0( ' elapsed: ', elapsed, '\n' ) ) + cat( paste0( ' rate: ', rate, '\n' ) ) + cat( ' ...\n' ) + } + + #' Run a benchmark. + benchmark <- function( iterations ) { + results <- microbenchmark::microbenchmark( + besselK( + runif( 1L ) * 100000.0 + .Machine[['double.eps']], + 0L + ), + times = iterations + ) + + elapsed <- sum( results[['time']] ) + elapsed <- elapsed / 1.0e9 + + elapsed + } + + print_version() + for ( i in seq_len( repeats ) ) { + cat( paste0( '# r::', name, '\n' ) ) + elapsed <- benchmark( iterations ) + print_results( iterations, elapsed ) + cat( paste0( 'ok ', i, ' benchmark finished\n' ) ) + } + print_summary( repeats, repeats ) +} + +main() diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/binding.gyp b/lib/node_modules/@stdlib/math/base/special/besselk0/binding.gyp new file mode 100644 index 000000000000..0d6508a12e99 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/binding.gyp @@ -0,0 +1,170 @@ +# @license Apache-2.0 +# +# Copyright (c) 2026 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/besselk0/docs/repl.txt b/lib/node_modules/@stdlib/math/base/special/besselk0/docs/repl.txt new file mode 100644 index 000000000000..1aa09bc89c47 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/docs/repl.txt @@ -0,0 +1,34 @@ + +{{alias}}( x ) + Computes the modified Bessel function of the second kind of order zero. + + Parameters + ---------- + x: number + Input value. + + Returns + ------- + y: number + Function value. + + Examples + -------- + > var y = {{alias}}( 0.0 ) + +Infinity + > y = {{alias}}( 1.0 ) + ~0.421 + > y = {{alias}}( 5.0 ) + ~0.00369 + > y = {{alias}}( -1.0 ) + NaN + > y = {{alias}}( {{alias:@stdlib/constants/float64/pinf}} ) + 0.0 + > y = {{alias}}( {{alias:@stdlib/constants/float64/ninf}} ) + NaN + > y = {{alias}}( NaN ) + NaN + + See Also + -------- + diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/docs/types/index.d.ts b/lib/node_modules/@stdlib/math/base/special/besselk0/docs/types/index.d.ts new file mode 100644 index 000000000000..0a8aa45abee2 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/docs/types/index.d.ts @@ -0,0 +1,61 @@ +/* +* @license Apache-2.0 +* +* Copyright (c) 2026 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 + +/** +* Computes the modified Bessel function of the second kind of order zero. +* +* ## Notes +* +* - Accuracy for subnormal `x` is very poor. Full accuracy is achieved at approximately +* `1.0e-308` but degrades rapidly as `x → 0`. +* +* @param x - input value +* @returns evaluated Bessel function +* +* @example +* var v = k0( 0.0 ); +* // returns Infinity +* +* @example +* var v = k0( 1.0 ); +* // returns ~0.421 +* +* @example +* var v = k0( 5.0 ); +* // returns ~0.00369 +* +* @example +* var v = k0( -1.0 ); +* // returns NaN +* +* @example +* var v = k0( Infinity ); +* // returns 0.0 +* +* @example +* var v = k0( NaN ); +* // returns NaN +*/ +declare function k0( x: number ): number; + + +// EXPORTS // + +export = k0; diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/docs/types/test.ts b/lib/node_modules/@stdlib/math/base/special/besselk0/docs/types/test.ts new file mode 100644 index 000000000000..275b811db805 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/docs/types/test.ts @@ -0,0 +1,45 @@ +/* +* @license Apache-2.0 +* +* Copyright (c) 2026 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 k0 = require( './index' ); + + +// TESTS // + +// The function returns a number... +{ + k0( 8 ); // $ExpectType number +} + +// The compiler throws an error if the function is provided a value other than a number... +{ + k0( true ); // $ExpectError + k0( false ); // $ExpectError + k0( null ); // $ExpectError + k0( undefined ); // $ExpectError + k0( '5' ); // $ExpectError + k0( [] ); // $ExpectError + k0( {} ); // $ExpectError + k0( ( x: number ): number => x ); // $ExpectError +} + +// The compiler throws an error if the function is provided insufficient arguments... +{ + k0(); // $ExpectError +} + diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/examples/c/Makefile b/lib/node_modules/@stdlib/math/base/special/besselk0/examples/c/Makefile new file mode 100644 index 000000000000..c8f8e9a1517b --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/examples/c/Makefile @@ -0,0 +1,146 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2026 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/besselk0/examples/c/example.c b/lib/node_modules/@stdlib/math/base/special/besselk0/examples/c/example.c new file mode 100644 index 000000000000..1f5983c700f4 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/examples/c/example.c @@ -0,0 +1,31 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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/besselk0.h" +#include + +int main( void ) { + const double x[] = { 0.5, 1.0, 2.0, 3.0, 4.0 }; + + double y; + int i; + for ( i = 0; i < 5; i++ ) { + y = stdlib_base_besselk0( x[ i ] ); + printf( "besselk0(%lf) = %lf\n", x[ i ], y ); + } +} diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/examples/index.js b/lib/node_modules/@stdlib/math/base/special/besselk0/examples/index.js new file mode 100644 index 000000000000..0ab716a380db --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/examples/index.js @@ -0,0 +1,32 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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 uniform = require( '@stdlib/random/array/uniform' ); +var logEachMap = require( '@stdlib/console/log-each-map' ); +var besselk0 = require( './../lib' ); + +var opts = { + 'dtype': 'float64' +}; + +// Generate random values on (0, 100]; avoid zero where K0 diverges: +var x = uniform( 100, 1.0e-6, 100.0, opts ); + +logEachMap( 'besselk0(%lf) = %lf', x, besselk0 ); diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/include.gypi b/lib/node_modules/@stdlib/math/base/special/besselk0/include.gypi new file mode 100644 index 000000000000..bee8d41a2caf --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/include.gypi @@ -0,0 +1,53 @@ +# @license Apache-2.0 +# +# Copyright (c) 2026 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': [ + ' 1 + if ( x < LOG_MAX ) { + return ( r3( 1.0 / x ) + 1.0 ) * + exp( -x ) / sqrt( x ); + } + + // overflow-safe + ex = exp( -x * 0.5 ); + return ( r3( 1.0 / x ) + 1.0 ) * + ex / sqrt( x ) * ex; +} + + +// EXPORTS // + +module.exports = k0; diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/lib/native.js b/lib/node_modules/@stdlib/math/base/special/besselk0/lib/native.js new file mode 100644 index 000000000000..ac46b15b95c9 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/lib/native.js @@ -0,0 +1,62 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var addon = require( './../src/addon.node' ); + + +// MAIN // + +/** +* Computes the modified Bessel function of the second kind of order zero. +* +* @private +* @param {number} x - input value +* @returns {number} evaluated Bessel function +* +* @example +* var v = k0( 0.0 ); +* // returns Infinity +* +* @example +* var v = k0( 1.0 ); +* // returns ~0.421 +* +* @example +* var v = k0( -1.0 ); +* // returns NaN +* +* @example +* var v = k0( Infinity ); +* // returns 0.0 +* +* @example +* var v = k0( NaN ); +* // returns NaN +*/ +function k0( x ) { + return addon( x ); +} + + +// EXPORTS // + +module.exports = k0; diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/lib/poly_p2.js b/lib/node_modules/@stdlib/math/base/special/besselk0/lib/poly_p2.js new file mode 100644 index 000000000000..8899cfc828e3 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/lib/poly_p2.js @@ -0,0 +1,47 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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'; + +// 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 0.11593151565841245; + } + return 0.11593151565841245 + (x * (0.27898287891460316 + (x * (0.02524892993216122 + (x * (0.0008460350907213638 + (x * (0.000014914719243096176 + (x * (1.6271068924220885e-7 + (x * (1.2082661023927562e-9 + (x * 6.611686391749704e-12))))))))))))); // eslint-disable-line max-len +} + + +// EXPORTS // + +module.exports = evalpoly; diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/lib/rational_p1q1.js b/lib/node_modules/@stdlib/math/base/special/besselk0/lib/rational_p1q1.js new file mode 100644 index 000000000000..055663c9374f --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/lib/rational_p1q1.js @@ -0,0 +1,64 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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'; + +// MAIN // + +/** +* Evaluates a rational function (i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\)). +* +* ## Notes +* +* - Coefficients should be sorted in ascending degree. +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @private +* @param {number} x - value at which to evaluate the rational function +* @returns {number} evaluated rational function +*/ +function evalrational( x ) { + var ax; + var s1; + var s2; + if ( x === 0.0 ) { + return -0.13725090026855463; + } + if ( x < 0.0 ) { + ax = -x; + } else { + ax = x; + } + if ( ax <= 1.0 ) { + s1 = -0.13725090026855463 + (x * (0.2574916117833313 + (x * (0.013954746021468694 + (x * (0.0005445476986653927 + (x * 0.000007125159422136622))))))); // eslint-disable-line max-len + s2 = 1.0 + (x * (-0.054583334380177886 + (x * (0.0012910528169752513 + (x * (-0.000013676539469785865 + (x * 0.0))))))); // eslint-disable-line max-len + } else { + x = 1.0 / x; + s1 = 0.000007125159422136622 + (x * (0.0005445476986653927 + (x * (0.013954746021468694 + (x * (0.2574916117833313 + (x * -0.13725090026855463))))))); // eslint-disable-line max-len + s2 = 0.0 + (x * (-0.000013676539469785865 + (x * (0.0012910528169752513 + (x * (-0.054583334380177886 + (x * 1.0))))))); // eslint-disable-line max-len + } + return s1 / s2; +} + + +// EXPORTS // + +module.exports = evalrational; diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/lib/rational_p3q3.js b/lib/node_modules/@stdlib/math/base/special/besselk0/lib/rational_p3q3.js new file mode 100644 index 000000000000..b828c4409beb --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/lib/rational_p3q3.js @@ -0,0 +1,64 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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'; + +// MAIN // + +/** +* Evaluates a rational function (i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\)). +* +* ## Notes +* +* - Coefficients should be sorted in ascending degree. +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @private +* @param {number} x - value at which to evaluate the rational function +* @returns {number} evaluated rational function +*/ +function evalrational( x ) { + var ax; + var s1; + var s2; + if ( x === 0.0 ) { + return 0.25331413731550023; + } + if ( x < 0.0 ) { + ax = -x; + } else { + ax = x; + } + if ( ax <= 1.0 ) { + s1 = 0.25331413731550023 + (x * (3.6283421339845954 + (x * (18.68441889406606 + (x * (43.062439810634125 + (x * (44.24116209627428 + (x * (15.620953393562205 + (x * (-1.8101389782294108 + (x * (-1.4142379942699959 + (x * -0.09369168119754924))))))))))))))); // eslint-disable-line max-len + s2 = 1.0 + (x * (14.941946948799083 + (x * (82.65296455388554 + (x * (216.2779506621867 + (x * (284.51451551842223 + (x * (185.1714491916335 + (x * (54.865407174397234 + (x * (6.118075837628957 + (x * 0.1586261269326235))))))))))))))); // eslint-disable-line max-len + } else { + x = 1.0 / x; + s1 = -0.09369168119754924 + (x * (-1.4142379942699959 + (x * (-1.8101389782294108 + (x * (15.620953393562205 + (x * (44.24116209627428 + (x * (43.062439810634125 + (x * (18.68441889406606 + (x * (3.6283421339845954 + (x * 0.25331413731550023))))))))))))))); // eslint-disable-line max-len + s2 = 0.1586261269326235 + (x * (6.118075837628957 + (x * (54.865407174397234 + (x * (185.1714491916335 + (x * (284.51451551842223 + (x * (216.2779506621867 + (x * (82.65296455388554 + (x * (14.941946948799083 + (x * 1.0))))))))))))))); // eslint-disable-line max-len + } + return s1 / s2; +} + + +// EXPORTS // + +module.exports = evalrational; diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/manifest.json b/lib/node_modules/@stdlib/math/base/special/besselk0/manifest.json new file mode 100644 index 000000000000..473e27626ea7 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/manifest.json @@ -0,0 +1,84 @@ +{ + "options": { + "task": "build" + }, + "fields": [ + { + "field": "src", + "resolve": true, + "relative": true + }, + { + "field": "include", + "resolve": true, + "relative": true + }, + { + "field": "libraries", + "resolve": false, + "relative": false + }, + { + "field": "libpath", + "resolve": true, + "relative": false + } + ], + "confs": [ + { + "task": "build", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/math/base/napi/unary", + "@stdlib/math/base/special/sqrt", + "@stdlib/math/base/special/exp", + "@stdlib/math/base/special/ln", + "@stdlib/constants/float64/pinf", + "@stdlib/constants/float64/ninf" + ] + }, + { + "task": "benchmark", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/math/base/special/sqrt", + "@stdlib/math/base/special/exp", + "@stdlib/math/base/special/ln", + "@stdlib/constants/float64/pinf", + "@stdlib/constants/float64/ninf" + ] + }, + { + "task": "examples", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/math/base/special/sqrt", + "@stdlib/math/base/special/exp", + "@stdlib/math/base/special/ln", + "@stdlib/constants/float64/pinf", + "@stdlib/constants/float64/ninf" + ] + } + ] +} diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/package.json b/lib/node_modules/@stdlib/math/base/special/besselk0/package.json new file mode 100644 index 000000000000..fc6f6de58a9a --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/package.json @@ -0,0 +1,137 @@ +{ + "name": "@stdlib/math/base/special/besselk0", + "version": "0.0.0", + "description": "Compute the modified Bessel function of the second kind of order zero.", + "license": "Apache-2.0 AND BSL-1.0", + "author": { + "name": "The Stdlib Authors", + "url": "https://github.com/stdlib-js/stdlib/graphs/contributors" + }, + "contributors": [ + { + "name": "The Stdlib Authors", + "url": "https://github.com/stdlib-js/stdlib/graphs/contributors" + } + ], + "main": "./lib", + "gypfile": true, + "directories": { + "benchmark": "./benchmark", + "doc": "./docs", + "example": "./examples", + "include": "./include", + "lib": "./lib", + "scripts": "./scripts", + "src": "./src", + "test": "./test" + }, + "types": "./docs/types", + "scripts": {}, + "homepage": "https://github.com/stdlib-js/stdlib", + "repository": { + "type": "git", + "url": "git://github.com/stdlib-js/stdlib.git" + }, + "bugs": { + "url": "https://github.com/stdlib-js/stdlib/issues" + }, + "dependencies": {}, + "devDependencies": {}, + "engines": { + "node": ">=0.10.0", + "npm": ">2.7.0" + }, + "os": [ + "aix", + "darwin", + "freebsd", + "linux", + "macos", + "openbsd", + "sunos", + "win32", + "windows" + ], + "keywords": [ + "stdlib", + "stdmath", + "mathematics", + "math", + "special", + "bessel", + "k0", + "number" + ], + "__stdlib__": { + "scaffold": { + "$schema": "math/base@v1.0", + "base_alias": "besselk0", + "alias": "besselk0", + "pkg_desc": "compute the modified Bessel function of the second kind of order zero for a double-precision floating-point number", + "desc": "computes the modified Bessel function of the second kind of order zero for a double-precision floating-point number", + "short_desc": "modified Bessel function of the second kind of order zero", + "parameters": [ + { + "name": "x", + "desc": "input value", + "type": { + "javascript": "number", + "jsdoc": "number", + "c": "double", + "dtype": "float64" + }, + "domain": [ + { + "min": 0, + "max": "infinity" + } + ], + "rand": { + "prng": "random/base/uniform", + "parameters": [ + 0.01, + 100 + ] + }, + "example_values": [ + 73.4, + 0.11, + 5.07, + 120.8, + 0.63, + 44.2, + 2.9, + 89.5, + 0.02, + 15.3, + 33.7, + 0.95, + 7.8, + 58.1, + 101.3, + 0.27, + 24.6, + 12.9, + 66.4, + 150.2 + ] + } + ], + "output_policy": "real_floating_point_and_generic", + "returns": { + "desc": "evaluated Bessel function", + "type": { + "javascript": "number", + "jsdoc": "number", + "c": "double", + "dtype": "float64" + } + }, + "keywords": [ + "bessel", + "k0" + ], + "extra_keywords": [] + } + } +} diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/scripts/evalrational.js b/lib/node_modules/@stdlib/math/base/special/besselk0/scripts/evalrational.js new file mode 100644 index 000000000000..3bd564d77240 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/scripts/evalrational.js @@ -0,0 +1,176 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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 and rational functions +* used by the modified Bessel function of the second kind of order zero (K0). +* +* If any coefficients change, this script should be rerun. +*/ +'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 licenseHeader = require( '@stdlib/_tools/licenses/header' ); +var compile = require( '@stdlib/math/base/tools/evalrational-compile' ); +var compilePoly = require( '@stdlib/math/base/tools/evalpoly-compile' ); +var compileC = require( '@stdlib/math/base/tools/evalrational-compile-c' ); +var compilePolyC = require( '@stdlib/math/base/tools/evalpoly-compile-c' ); +var substringBefore = require( '@stdlib/string/substring-before' ); +var substringAfter = require( '@stdlib/string/substring-after' ); +var format = require( '@stdlib/string/format' ); + + +// VARIABLES // + +// Small-x rational (Boost: P/Q): +var P1 = [ + -1.3725090026855463e-01, + 2.5749161178333129e-01, + 1.3954746021468693e-02, + 5.4454769866539268e-04, + 7.1251594221366221e-06 +]; + +var Q1 = [ + 1.000000000000000000e+00, + -5.4583334380177885e-02, + 1.2910528169752513e-03, + -1.3676539469785866e-05, + 0.0000000000000000e+00 +]; + +// Small-x polynomial (Boost: P2): +var P2 = [ + 1.1593151565841245e-01, + 2.7898287891460317e-01, + 2.5248929932161219e-02, + 8.4603509072136378e-04, + 1.4914719243096175e-05, + 1.6271068924220885e-07, + 1.2082661023927561e-09, + 6.6116863917497043e-12 +]; + +// Large-x rational (Boost: P/Q): +var P3 = [ + 2.5331413731550024e-01, + 3.6283421339845952e+00, + 1.8684418894066061e+01, + 4.3062439810634128e+01, + 4.4241162096274282e+01, + 1.5620953393562205e+01, + -1.8101389782294109e+00, + -1.4142379942699959e+00, + -9.3691681197549246e-02 +]; + +var Q3 = [ + 1.0, + 1.4941946948799083e+01, + 8.2652964553885542e+01, + 2.1627795066218670e+02, + 2.8451451551842222e+02, + 1.8517144919163350e+02, + 5.4865407174397235e+01, + 6.1180758376289570e+00, + 1.5862612693262351e-01 +]; + +// 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 string between two markers in a text. +* +* @private +* @param {string} text - input text +* @param {string} id - marker id +* @param {string} str - string to insert +* @returns {string} modified text +*/ +function insert( text, id, str ) { + var before; + var after; + + before = substringBefore( text, '// BEGIN: '+id ); + after = substringAfter( text, '// END: '+id ); + + return format( '%s// BEGIN: %s\n\n%s\n// END: %s%s', before, id, str, id, after ); +} + + +// MAIN // + +/** +* Main execution sequence. +* +* @private +*/ +function main() { + var fpath; + var copts; + var opts; + var file; + + opts = { + 'encoding': 'utf8' + }; + + // JS evaluators: + fpath = resolve( __dirname, '..', 'lib', 'rational_p1q1.js' ); + writeFileSync( fpath, header + compile( P1, Q1 ), opts ); + + fpath = resolve( __dirname, '..', 'lib', 'poly_p2.js' ); + writeFileSync( fpath, header + compilePoly( P2 ), opts ); + + fpath = resolve( __dirname, '..', 'lib', 'rational_p3q3.js' ); + writeFileSync( fpath, header + compile( P3, Q3 ), opts ); + + // C evaluators: + copts = { + 'dtype': 'double', + 'name': '' + }; + fpath = resolve( __dirname, '..', 'src', 'main.c' ); + file = readFileSync( fpath, opts ); + + copts.name = 'rational_p1q1'; + file = insert( file, copts.name, compileC( P1, Q1, copts ) ); + + copts.name = 'poly_p2'; + file = insert( file, copts.name, compilePolyC( P2, copts ) ); + + copts.name = 'rational_p3q3'; + file = insert( file, copts.name, compileC( P3, Q3, copts ) ); + + writeFileSync( fpath, file, opts ); +} + +main(); diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/src/Makefile b/lib/node_modules/@stdlib/math/base/special/besselk0/src/Makefile new file mode 100644 index 000000000000..2caf905cedbe --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/src/Makefile @@ -0,0 +1,70 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2026 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/besselk0/src/addon.c b/lib/node_modules/@stdlib/math/base/special/besselk0/src/addon.c new file mode 100644 index 000000000000..66a90172def8 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/src/addon.c @@ -0,0 +1,22 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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/besselk0.h" +#include "stdlib/math/base/napi/unary.h" + +STDLIB_MATH_BASE_NAPI_MODULE_D_D( stdlib_base_besselk0 ) diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/src/main.c b/lib/node_modules/@stdlib/math/base/special/besselk0/src/main.c new file mode 100644 index 000000000000..4588f6b8fd28 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/src/main.c @@ -0,0 +1,188 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +* +* +* ## Notice +* +* The original C++ code and copyright notice are from the +* [Boost library]{@link https://www.boost.org/doc/libs/1_85_0/boost/math/special_functions/detail/bessel_k0.hpp}. +* The implementation has been modified for use in stdlib. +* +* ```text +* Copyright Xiaogang Zhang, 2006. +* +* Use, modification and distribution are subject to the +* Boost Software License, Version 1.0. (See accompanying file +* LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt) +* ``` +*/ + +#include "stdlib/math/base/special/besselk0.h" +#include "stdlib/math/base/special/ln.h" +#include "stdlib/math/base/special/exp.h" +#include "stdlib/math/base/special/sqrt.h" +#include "stdlib/constants/float64/pinf.h" + +/* Begin auto-generated functions. The following functions are auto-generated. Do not edit directly. */ + +// BEGIN: rational_p1q1 + +/** +* Evaluates a rational function (i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\)). +* +* ## Notes +* +* - Coefficients should be sorted in ascending degree. +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the rational function +* @return evaluated rational function +*/ +static double rational_p1q1( const double x ) { + double ax; + double ix; + double s1; + double s2; + if ( x == 0.0 ) { + return -0.13725090026855463; + } + if ( x < 0.0 ) { + ax = -x; + } else { + ax = x; + } + if ( ax <= 1.0 ) { + s1 = -0.13725090026855463 + (x * (0.2574916117833313 + (x * (0.013954746021468694 + (x * (0.0005445476986653927 + (x * 0.000007125159422136622))))))); + s2 = 1.0 + (x * (-0.054583334380177886 + (x * (0.0012910528169752513 + (x * (-0.000013676539469785865 + (x * 0.0))))))); + } else { + ix = 1.0 / x; + s1 = 0.000007125159422136622 + (ix * (0.0005445476986653927 + (ix * (0.013954746021468694 + (ix * (0.2574916117833313 + (ix * -0.13725090026855463))))))); + s2 = 0.0 + (ix * (-0.000013676539469785865 + (ix * (0.0012910528169752513 + (ix * (-0.054583334380177886 + (ix * 1.0))))))); + } + return s1 / s2; +} + +// END: rational_p1q1// BEGIN: poly_p2 + +/** +* 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 double poly_p2( const double x ) { + return 0.11593151565841245 + (x * (0.27898287891460316 + (x * (0.02524892993216122 + (x * (0.0008460350907213638 + (x * (0.000014914719243096176 + (x * (1.6271068924220885e-7 + (x * (1.2082661023927562e-9 + (x * 6.611686391749704e-12))))))))))))); +} + +// END: poly_p2// BEGIN: rational_p3q3 + +/** +* Evaluates a rational function (i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\)). +* +* ## Notes +* +* - Coefficients should be sorted in ascending degree. +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the rational function +* @return evaluated rational function +*/ +static double rational_p3q3( const double x ) { + double ax; + double ix; + double s1; + double s2; + if ( x == 0.0 ) { + return 0.25331413731550023; + } + if ( x < 0.0 ) { + ax = -x; + } else { + ax = x; + } + if ( ax <= 1.0 ) { + s1 = 0.25331413731550023 + (x * (3.6283421339845954 + (x * (18.68441889406606 + (x * (43.062439810634125 + (x * (44.24116209627428 + (x * (15.620953393562205 + (x * (-1.8101389782294108 + (x * (-1.4142379942699959 + (x * -0.09369168119754924))))))))))))))); + s2 = 1.0 + (x * (14.941946948799083 + (x * (82.65296455388554 + (x * (216.2779506621867 + (x * (284.51451551842223 + (x * (185.1714491916335 + (x * (54.865407174397234 + (x * (6.118075837628957 + (x * 0.1586261269326235))))))))))))))); + } else { + ix = 1.0 / x; + s1 = -0.09369168119754924 + (ix * (-1.4142379942699959 + (ix * (-1.8101389782294108 + (ix * (15.620953393562205 + (ix * (44.24116209627428 + (ix * (43.062439810634125 + (ix * (18.68441889406606 + (ix * (3.6283421339845954 + (ix * 0.25331413731550023))))))))))))))); + s2 = 0.1586261269326235 + (ix * (6.118075837628957 + (ix * (54.865407174397234 + (ix * (185.1714491916335 + (ix * (284.51451551842223 + (ix * (216.2779506621867 + (ix * (82.65296455388554 + (ix * (14.941946948799083 + (ix * 1.0))))))))))))))); + } + return s1 / s2; +} + +// END: rational_p3q3 + +/* End auto-generated functions. */ + +/** +* Computes the modified Bessel function of the second kind of order zero. +* +* ## Notes +* +* - The function has a logarithmic singularity at `x = 0`. +* - Accuracy for subnormal `x` is poor due to underflow. +* +* @param x input value +* @return evaluated modified Bessel function +* +* @example +* double y = stdlib_base_besselk0( 1.0 ); +* // returns ~0.421024 +*/ +double stdlib_base_besselk0( const double x ) { + double a; + double ex; + + if ( x < 0.0 ) { + return 0.0 / 0.0; // NaN + } + if ( x == 0.0 ) { + return STDLIB_CONSTANT_FLOAT64_PINF; + } + if ( x == STDLIB_CONSTANT_FLOAT64_PINF ) { + return 0.0; + } + + /* Small-x: x <= 1 */ + if ( x <= 1.0 ) { + a = ( x * x ) * 0.25; + a = ( rational_p1q1( a ) + 1.1372509002685547 ) * a + 1.0; + return poly_p2( x * x ) - stdlib_base_ln( x ) * a; + } + + /* Large-x */ + if ( x < 709.782712893384 ) { + return ( rational_p3q3( 1.0 / x ) + 1.0 ) * + stdlib_base_exp( -x ) / stdlib_base_sqrt( x ); + } + + /* Overflow-safe exponential split */ + ex = stdlib_base_exp( -0.5 * x ); + return ( rational_p3q3( 1.0 / x ) + 1.0 ) * + ex / stdlib_base_sqrt( x ) * ex; +} diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/test/fixtures/julia/REQUIRE b/lib/node_modules/@stdlib/math/base/special/besselk0/test/fixtures/julia/REQUIRE new file mode 100644 index 000000000000..06bfe7391215 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/test/fixtures/julia/REQUIRE @@ -0,0 +1,3 @@ +julia 1.5 +JSON 0.21 +SpecialFunctions 0.10.3 diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/test/fixtures/julia/large_positive.json b/lib/node_modules/@stdlib/math/base/special/besselk0/test/fixtures/julia/large_positive.json new file mode 100644 index 000000000000..86457a075ea6 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/test/fixtures/julia/large_positive.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/test/fixtures/julia/medium_positive.json b/lib/node_modules/@stdlib/math/base/special/besselk0/test/fixtures/julia/medium_positive.json new file mode 100644 index 000000000000..042413dadac8 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/test/fixtures/julia/medium_positive.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/math/base/special/besselk0/test/fixtures/julia/runner.jl new file mode 100644 index 000000000000..4d8f4364eccb --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/test/fixtures/julia/runner.jl @@ -0,0 +1,82 @@ +#!/usr/bin/env julia +# +# @license Apache-2.0 +# +# Copyright (c) 2026 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 +using SpecialFunctions + +""" + gen( x, name ) + +Generate fixture data for the modified Bessel function of the +second kind of order zero (K₀) and write to file. + +# Arguments + +* `x`: domain (positive values only) +* `name::AbstractString`: output filename + +# Examples + +```julia +julia> x = range( 1.0e-6, stop = 10.0, length = 2001 ); +julia> gen( x, "data.json" ); +``` +""" +function gen( x, name ) + y = Array{Float64}( undef, length(x) ); + for i in eachindex(x) + y[i] = besselk( 0, x[i] ); + end + + # Store data to be written to file as a collection: + data = Dict([ + ("x", x), + ("expected", y) + ]); + + # 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 ); + +# Very small values: +x = range( 1.0e-5, stop = 0.8, length = 5003 ); +gen( x, "very_small.json" ); + +# Positive small values: +x = range( 0.8, stop = 3.0, length = 5003 ); +gen( x, "small_positive.json" ); + +# Positive medium values: +x = range( 3.0, stop = 20.0, length = 5003 ); +gen( x, "medium_positive.json" ); + +# Positive Large values: +x = range( 20.0, stop = 50.0, length = 5003 ); +gen( x, "large_positive.json" ); diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/test/fixtures/julia/small_positive.json b/lib/node_modules/@stdlib/math/base/special/besselk0/test/fixtures/julia/small_positive.json new file mode 100644 index 000000000000..48964f72bb70 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/test/fixtures/julia/small_positive.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/test/fixtures/julia/very_small.json b/lib/node_modules/@stdlib/math/base/special/besselk0/test/fixtures/julia/very_small.json new file mode 100644 index 000000000000..f51ca090ef68 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/test/fixtures/julia/very_small.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/test/test.js b/lib/node_modules/@stdlib/math/base/special/besselk0/test/test.js new file mode 100644 index 000000000000..8110e7435fd0 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/test/test.js @@ -0,0 +1,168 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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 isnan = require( '@stdlib/math/base/assert/is-nan' ); +var randu = require( '@stdlib/random/base/randu' ); +var PINF = require( '@stdlib/constants/float64/pinf' ); +var NINF = require( '@stdlib/constants/float64/ninf' ); +var EPS = require( '@stdlib/constants/float64/eps' ); +var abs = require( '@stdlib/math/base/special/abs' ); +var k0 = require( './../lib' ); + + +// FIXTURES // + +var largePositive = require( './fixtures/julia/large_positive.json' ); +var mediumPositive = require( './fixtures/julia/medium_positive.json' ); +var smallPositive = require( './fixtures/julia/small_positive.json' ); +var smaller = require( './fixtures/julia/very_small.json' ); + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof k0, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function evaluates the modified Bessel function of the second kind of order zero (K₀) (large positive values)', function test( t ) { + var expected = largePositive.expected; + var delta; + var tol; + var y; + var x = largePositive.x; + var i; + + for ( i = 0; i < x.length; i++ ) { + y = k0( x[i] ); + if ( y === expected[i] ) { + t.strictEqual( y, expected[i] ); + } else { + delta = abs( y - expected[i] ); + tol = 1000.0 * EPS * abs( expected[i] ); + t.ok( delta <= tol, 'within tolerance' ); + } + } + t.end(); +}); + +tape( 'the function evaluates the modified Bessel function of the second kind of order zero (K₀) (medium positive values)', function test( t ) { + var expected = mediumPositive.expected; + var delta; + var tol; + var y; + var x = mediumPositive.x; + var i; + + for ( i = 0; i < x.length; i++ ) { + y = k0( x[i] ); + if ( y === expected[i] ) { + t.strictEqual( y, expected[i] ); + } else { + delta = abs( y - expected[i] ); + tol = 800.0 * EPS * abs( expected[i] ); + t.ok( delta <= tol, 'within tolerance' ); + } + } + t.end(); +}); + +tape( 'the function evaluates the modified Bessel function of the second kind of order zero (K₀) (small positive values)', function test( t ) { + var expected = smallPositive.expected; + var delta; + var tol; + var y; + var x = smallPositive.x; + var i; + + for ( i = 0; i < x.length; i++ ) { + y = k0( x[i] ); + if ( y === expected[i] ) { + t.strictEqual( y, expected[i] ); + } else { + delta = abs( y - expected[i] ); + tol = 1200.0 * EPS * abs( expected[i] ); + t.ok( delta <= tol, 'within tolerance' ); + } + } + t.end(); +}); + +tape( 'the function evaluates the modified Bessel function of the second kind of order zero (K₀) (smaller positive values)', function test( t ) { + var expected = smaller.expected; + var delta; + var tol; + var y; + var x = smaller.x; + var i; + + for ( i = 0; i < x.length; i++ ) { + y = k0( x[i] ); + if ( y === expected[i] ) { + t.strictEqual( y, expected[i] ); + } else { + delta = abs( y - expected[i] ); + tol = 10.0 * EPS * abs( expected[i] ); + t.ok( delta <= tol, 'within tolerance' ); + } + } + t.end(); +}); + +tape( 'the function returns NaN for negative numbers', function test( t ) { + var v; + var x; + var i; + + for ( i = 0; i < 1000; i++ ) { + x = -( randu() * 100.0 ) - EPS; + v = k0( x ); + t.ok( isnan( v ), 'returns NaN' ); + } + t.end(); +}); + +tape( 'the function returns +Infinity if provided 0.0', function test( t ) { + var v = k0( 0.0 ); + t.strictEqual( v, PINF, 'returns +Infinity' ); + t.end(); +}); + +tape( 'the function returns NaN if provided NaN', function test( t ) { + var v = k0( NaN ); + t.ok( isnan( v ), 'returns NaN' ); + t.end(); +}); + +tape( 'the function returns 0.0 if provided +Infinity', function test( t ) { + var v = k0( PINF ); + t.strictEqual( v, 0.0, 'returns 0.0' ); + t.end(); +}); + +tape( 'the function returns NaN if provided -Infinity', function test( t ) { + var v = k0( NINF ); + t.ok( isnan( v ), 'returns NaN' ); + t.end(); +}); diff --git a/lib/node_modules/@stdlib/math/base/special/besselk0/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/besselk0/test/test.native.js new file mode 100644 index 000000000000..768d033b78cb --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/besselk0/test/test.native.js @@ -0,0 +1,177 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var resolve = require( 'path' ).resolve; +var tape = require( 'tape' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var randu = require( '@stdlib/random/base/randu' ); +var PINF = require( '@stdlib/constants/float64/pinf' ); +var NINF = require( '@stdlib/constants/float64/ninf' ); +var EPS = require( '@stdlib/constants/float64/eps' ); +var abs = require( '@stdlib/math/base/special/abs' ); +var tryRequire = require( '@stdlib/utils/try-require' ); + + +// VARIABLES // + +var k0 = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( k0 instanceof Error ) +}; + + +// FIXTURES // + +var largePositive = require( './fixtures/julia/large_positive.json' ); +var mediumPositive = require( './fixtures/julia/medium_positive.json' ); +var smallPositive = require( './fixtures/julia/small_positive.json' ); +var smaller = require( './fixtures/julia/very_small.json' ); + + +// TESTS // + +tape( 'main export is a function', opts, function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof k0, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function evaluates the modified Bessel function of the second kind of order zero (K₀) (large positive values)', opts, function test( t ) { + var expected = largePositive.expected; + var delta; + var tol; + var x = largePositive.x; + var y; + var i; + + for ( i = 0; i < x.length; i++ ) { + y = k0( x[i] ); + if ( y === expected[i] ) { + t.strictEqual( y, expected[i] ); + } else { + delta = abs( y - expected[i] ); + tol = 1000.0 * EPS * abs( expected[i] ); + t.ok( delta <= tol, 'within tolerance' ); + } + } + t.end(); +}); + +tape( 'the function evaluates the modified Bessel function of the second kind of order zero (K₀) (medium positive values)', opts, function test( t ) { + var expected = mediumPositive.expected; + var delta; + var tol; + var x = mediumPositive.x; + var y; + var i; + + for ( i = 0; i < x.length; i++ ) { + y = k0( x[i] ); + if ( y === expected[i] ) { + t.strictEqual( y, expected[i] ); + } else { + delta = abs( y - expected[i] ); + tol = 900.0 * EPS * abs( expected[i] ); + t.ok( delta <= tol, 'within tolerance' ); + } + } + t.end(); +}); + +tape( 'the function evaluates the modified Bessel function of the second kind of order zero (K₀) (small positive values)', opts, function test( t ) { + var expected = smallPositive.expected; + var delta; + var tol; + var x = smallPositive.x; + var y; + var i; + + for ( i = 0; i < x.length; i++ ) { + y = k0( x[i] ); + if ( y === expected[i] ) { + t.strictEqual( y, expected[i] ); + } else { + delta = abs( y - expected[i] ); + tol = 1200.0 * EPS * abs( expected[i] ); + t.ok( delta <= tol, 'within tolerance' ); + } + } + t.end(); +}); + +tape( 'the function evaluates the modified Bessel function of the second kind of order zero (K₀) (smaller positive values)', opts, function test( t ) { + var expected = smaller.expected; + var delta; + var tol; + var x = smaller.x; + var y; + var i; + + for ( i = 0; i < x.length; i++ ) { + y = k0( x[i] ); + if ( y === expected[i] ) { + t.strictEqual( y, expected[i] ); + } else { + delta = abs( y - expected[i] ); + tol = 10.0 * EPS * abs( expected[i] ); + t.ok( delta <= tol, 'within tolerance' ); + } + } + t.end(); +}); + +tape( 'the function returns NaN for negative numbers', opts, function test( t ) { + var v; + var x; + var i; + + for ( i = 0; i < 1000; i++ ) { + x = -( randu() * 100.0 ) - EPS; + v = k0( x ); + t.ok( isnan( v ), 'returns NaN' ); + } + t.end(); +}); + +tape( 'the function returns +Infinity if provided 0.0', opts, function test( t ) { + var v = k0( 0.0 ); + t.strictEqual( v, PINF, 'returns +Infinity' ); + t.end(); +}); + +tape( 'the function returns NaN if provided NaN', opts, function test( t ) { + var v = k0( NaN ); + t.ok( isnan( v ), 'returns NaN' ); + t.end(); +}); + +tape( 'the function returns 0.0 if provided +Infinity', opts, function test( t ) { + var v = k0( PINF ); + t.strictEqual( v, 0.0, 'returns 0.0' ); + t.end(); +}); + +tape( 'the function returns NaN if provided -Infinity', opts, function test( t ) { + var v = k0( NINF ); + t.ok( isnan( v ), 'returns NaN' ); + t.end(); +});