diff --git a/CHANGELOG.md b/CHANGELOG.md index fabc22aec..65a128a50 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -3588,6 +3588,28 @@ This release closes the following issue: +
+ +#### [@stdlib/math/base/special/fresnel](https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/fresnel) + +
+ +
+ +##### Features + +- [`f2f6164`](https://github.com/stdlib-js/stdlib/commit/f2f6164bcb23e3f0babda8fc651d2b3bc91be599) - add C implementation for `math/base/special/fresnel` + +
+ + + +
+ +
+ + +
#### [@stdlib/math/base/special/fresnelc](https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/fresnelc) @@ -5707,6 +5729,7 @@ A total of 30 people contributed to this release. Thank you to the following con
+- [`f2f6164`](https://github.com/stdlib-js/stdlib/commit/f2f6164bcb23e3f0babda8fc651d2b3bc91be599) - **feat:** add C implementation for `math/base/special/fresnel` _(by Gunj Joshi, Philipp Burckhardt)_ - [`62e247d`](https://github.com/stdlib-js/stdlib/commit/62e247daf7eb45f201cad1784619a344cbdcaff6) - **feat:** add C implementation for `math/base/special/powm1` [(#2660)](https://github.com/stdlib-js/stdlib/pull/2660) _(by Gunj Joshi)_ - [`f5d15f7`](https://github.com/stdlib-js/stdlib/commit/f5d15f7e0d12169f3016f1d499674b0ce9b2e0ea) - **feat:** add C implementation for `math/base/special/sincospi` [(#2687)](https://github.com/stdlib-js/stdlib/pull/2687 ) _(by Gunj Joshi)_ - [`3fa6956`](https://github.com/stdlib-js/stdlib/commit/3fa69566a55e9cbb28650eea285d90a73b06db36) - **bench:** fix makefile to allow for dependency resolution _(by Athan Reines)_ diff --git a/base/special/fresnel/README.md b/base/special/fresnel/README.md index eb95d1300..cebc9b0b6 100644 --- a/base/special/fresnel/README.md +++ b/base/special/fresnel/README.md @@ -116,6 +116,96 @@ for ( i = 0; i < x.length; i++ ) { + + +* * * + +
+ +## C APIs + + + +
+ +
+ + + + + +
+ +### Usage + +```c +#include "stdlib/math/base/special/fresnel.h" +``` + +#### stdlib_base_fresnel( x, &S, &C ) + +Simultaneously computes the [Fresnel integrals][fresnel-integral] S(x) and C(x). + +```c +double S; +double C; + +stdlib_base_fresnel( 4.0, &S, &C ); +``` + +The function accepts the following arguments: + +- **x**: `[in] double` input value. +- **S**: `[out] double*` destination for S(x). +- **C**: `[out] double*` destination for C(x). + +```c +void stdlib_base_fresnel( const double x, double *S, double *C ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +### Examples + +```c +#include "stdlib/math/base/special/fresnel.h" +#include + +int main( void ) { + const double x[] = { 0.0, 1.57, 3.14, 6.28 }; + + double S; + double C; + int i; + for ( i = 0; i < 4; i++ ) { + stdlib_base_fresnel( x[ i ], &S, &C ); + printf( "x: %lf => S(x): %lf, C(x): %lf\n", x[ i ], S, C ); + } +} +``` + +
+ + + +
+ + +
diff --git a/base/special/fresnel/benchmark/benchmark.native.js b/base/special/fresnel/benchmark/benchmark.native.js new file mode 100644 index 000000000..e145c813f --- /dev/null +++ b/base/special/fresnel/benchmark/benchmark.native.js @@ -0,0 +1,60 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var resolve = require( 'path' ).resolve; +var bench = require( '@stdlib/bench' ); +var randu = require( '@stdlib/random/base/randu' ); +var isnan = require( './../../../../base/assert/is-nan' ); +var tryRequire = require( '@stdlib/utils/try-require' ); +var pkg = require( './../package.json' ).name; + + +// VARIABLES // + +var fresnel = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( fresnel instanceof Error ) +}; + + +// MAIN // + +bench( pkg+'::native', opts, function benchmark( b ) { + var x; + var y; + var i; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + x = ( randu() * 20.0 ) - 10.0; + y = fresnel( x ); + if ( isnan( y[0] ) || isnan( y[1] ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( y[0] ) || isnan( y[1] ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); diff --git a/base/special/fresnel/benchmark/c/native/Makefile b/base/special/fresnel/benchmark/c/native/Makefile new file mode 100644 index 000000000..f69e9da2b --- /dev/null +++ b/base/special/fresnel/benchmark/c/native/Makefile @@ -0,0 +1,146 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2024 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +#/ + +# VARIABLES # + +ifndef VERBOSE + QUIET := @ +else + QUIET := +endif + +# Determine the OS ([1][1], [2][2]). +# +# [1]: https://en.wikipedia.org/wiki/Uname#Examples +# [2]: http://stackoverflow.com/a/27776822/2225624 +OS ?= $(shell uname) +ifneq (, $(findstring MINGW,$(OS))) + OS := WINNT +else +ifneq (, $(findstring MSYS,$(OS))) + OS := WINNT +else +ifneq (, $(findstring CYGWIN,$(OS))) + OS := WINNT +else +ifneq (, $(findstring Windows_NT,$(OS))) + OS := WINNT +endif +endif +endif +endif + +# Define the program used for compiling C source files: +ifdef C_COMPILER + CC := $(C_COMPILER) +else + CC := gcc +endif + +# Define the command-line options when compiling C files: +CFLAGS ?= \ + -std=c99 \ + -O3 \ + -Wall \ + -pedantic + +# Determine whether to generate position independent code ([1][1], [2][2]). +# +# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options +# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option +ifeq ($(OS), WINNT) + fPIC ?= +else + fPIC ?= -fPIC +endif + +# List of includes (e.g., `-I /foo/bar -I /beep/boop/include`): +INCLUDE ?= + +# List of source files: +SOURCE_FILES ?= + +# List of libraries (e.g., `-lopenblas -lpthread`): +LIBRARIES ?= + +# List of library paths (e.g., `-L /foo/bar -L /beep/boop`): +LIBPATH ?= + +# List of C targets: +c_targets := benchmark.out + + +# RULES # + +#/ +# Compiles source files. +# +# @param {string} [C_COMPILER] - C compiler (e.g., `gcc`) +# @param {string} [CFLAGS] - C compiler options +# @param {(string|void)} [fPIC] - compiler flag determining whether to generate position independent code (e.g., `-fPIC`) +# @param {string} [INCLUDE] - list of includes (e.g., `-I /foo/bar -I /beep/boop/include`) +# @param {string} [SOURCE_FILES] - list of source files +# @param {string} [LIBPATH] - list of library paths (e.g., `-L /foo/bar -L /beep/boop`) +# @param {string} [LIBRARIES] - list of libraries (e.g., `-lopenblas -lpthread`) +# +# @example +# make +# +# @example +# make all +#/ +all: $(c_targets) + +.PHONY: all + +#/ +# Compiles C source files. +# +# @private +# @param {string} CC - C compiler (e.g., `gcc`) +# @param {string} CFLAGS - C compiler options +# @param {(string|void)} fPIC - compiler flag determining whether to generate position independent code (e.g., `-fPIC`) +# @param {string} INCLUDE - list of includes (e.g., `-I /foo/bar`) +# @param {string} SOURCE_FILES - list of source files +# @param {string} LIBPATH - list of library paths (e.g., `-L /foo/bar`) +# @param {string} LIBRARIES - list of libraries (e.g., `-lopenblas`) +#/ +$(c_targets): %.out: %.c + $(QUIET) $(CC) $(CFLAGS) $(fPIC) $(INCLUDE) -o $@ $(SOURCE_FILES) $< $(LIBPATH) -lm $(LIBRARIES) + +#/ +# Runs compiled benchmarks. +# +# @example +# make run +#/ +run: $(c_targets) + $(QUIET) ./$< + +.PHONY: run + +#/ +# Removes generated files. +# +# @example +# make clean +#/ +clean: + $(QUIET) -rm -f *.o *.out + +.PHONY: clean diff --git a/base/special/fresnel/benchmark/c/native/benchmark.c b/base/special/fresnel/benchmark/c/native/benchmark.c new file mode 100644 index 000000000..2da231964 --- /dev/null +++ b/base/special/fresnel/benchmark/c/native/benchmark.c @@ -0,0 +1,134 @@ +/** +* @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/fresnel.h" +#include +#include +#include +#include +#include + +#define NAME "fresnel" +#define ITERATIONS 1000000 +#define REPEATS 3 + +/** +* Prints the TAP version. +*/ +static void print_version( void ) { + printf( "TAP version 13\n" ); +} + +/** +* Prints the TAP summary. +* +* @param total total number of tests +* @param passing total number of passing tests +*/ +static void print_summary( int total, int passing ) { + printf( "#\n" ); + printf( "1..%d\n", total ); // TAP plan + printf( "# total %d\n", total ); + printf( "# pass %d\n", passing ); + printf( "#\n" ); + printf( "# ok\n" ); +} + +/** +* Prints benchmarks results. +* +* @param elapsed elapsed time in seconds +*/ +static void print_results( double elapsed ) { + double rate = (double)ITERATIONS / elapsed; + printf( " ---\n" ); + printf( " iterations: %d\n", ITERATIONS ); + printf( " elapsed: %0.9f\n", elapsed ); + printf( " rate: %0.9f\n", rate ); + printf( " ...\n" ); +} + +/** +* Returns a clock time. +* +* @return clock time +*/ +static double tic( void ) { + struct timeval now; + gettimeofday( &now, NULL ); + return (double)now.tv_sec + (double)now.tv_usec / 1.0e6; +} + +/** +* Generates a random number on the interval [0,1). +* +* @return random number +*/ +static double rand_double( void ) { + int r = rand(); + return (double)r / ( (double)RAND_MAX + 1.0 ); +} + +/** +* Runs a benchmark. +* +* @return elapsed time in seconds +*/ +static double benchmark( void ) { + double elapsed; + double C; + double S; + double x; + double t; + int i; + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + x = ( 20.0 * rand_double() ) - 10.0; + stdlib_base_fresnel( x, &S, &C ); + if ( C != C || S != S) { + printf( "unexpected results\n" ); + break; + } + } + elapsed = tic() - t; + if ( C != C || S != S) { + printf( "unexpected results\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/base/special/fresnel/binding.gyp b/base/special/fresnel/binding.gyp new file mode 100644 index 000000000..ec3992233 --- /dev/null +++ b/base/special/fresnel/binding.gyp @@ -0,0 +1,170 @@ +# @license Apache-2.0 +# +# Copyright (c) 2024 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +# A `.gyp` file for building a Node.js native add-on. +# +# [1]: https://gyp.gsrc.io/docs/InputFormatReference.md +# [2]: https://gyp.gsrc.io/docs/UserDocumentation.md +{ + # List of files to include in this file: + 'includes': [ + './include.gypi', + ], + + # Define variables to be used throughout the configuration for all targets: + 'variables': { + # Target name should match the add-on export name: + 'addon_target_name%': 'addon', + + # Set variables based on the host OS: + 'conditions': [ + [ + 'OS=="win"', + { + # Define the object file suffix: + 'obj': 'obj', + }, + { + # Define the object file suffix: + 'obj': 'o', + } + ], # end condition (OS=="win") + ], # end conditions + }, # end variables + + # Define compile targets: + 'targets': [ + + # Target to generate an add-on: + { + # The target name should match the add-on export name: + 'target_name': '<(addon_target_name)', + + # Define dependencies: + 'dependencies': [], + + # Define directories which contain relevant include headers: + 'include_dirs': [ + # Local include directory: + '<@(include_dirs)', + ], + + # List of source files: + 'sources': [ + '<@(src_files)', + ], + + # Settings which should be applied when a target's object files are used as linker input: + 'link_settings': { + # Define libraries: + 'libraries': [ + '<@(libraries)', + ], + + # Define library directories: + 'library_dirs': [ + '<@(library_dirs)', + ], + }, + + # C/C++ compiler flags: + 'cflags': [ + # Enable commonly used warning options: + '-Wall', + + # Aggressive optimization: + '-O3', + ], + + # C specific compiler flags: + 'cflags_c': [ + # Specify the C standard to which a program is expected to conform: + '-std=c99', + ], + + # C++ specific compiler flags: + 'cflags_cpp': [ + # Specify the C++ standard to which a program is expected to conform: + '-std=c++11', + ], + + # Linker flags: + 'ldflags': [], + + # Apply conditions based on the host OS: + 'conditions': [ + [ + 'OS=="mac"', + { + # Linker flags: + 'ldflags': [ + '-undefined dynamic_lookup', + '-Wl,-no-pie', + '-Wl,-search_paths_first', + ], + }, + ], # end condition (OS=="mac") + [ + 'OS!="win"', + { + # C/C++ flags: + 'cflags': [ + # Generate platform-independent code: + '-fPIC', + ], + }, + ], # end condition (OS!="win") + ], # end conditions + }, # end target <(addon_target_name) + + # Target to copy a generated add-on to a standard location: + { + 'target_name': 'copy_addon', + + # Declare that the output of this target is not linked: + 'type': 'none', + + # Define dependencies: + 'dependencies': [ + # Require that the add-on be generated before building this target: + '<(addon_target_name)', + ], + + # Define a list of actions: + 'actions': [ + { + 'action_name': 'copy_addon', + 'message': 'Copying addon...', + + # Explicitly list the inputs in the command-line invocation below: + 'inputs': [], + + # Declare the expected outputs: + 'outputs': [ + '<(addon_output_dir)/<(addon_target_name).node', + ], + + # Define the command-line invocation: + 'action': [ + 'cp', + '<(PRODUCT_DIR)/<(addon_target_name).node', + '<(addon_output_dir)/<(addon_target_name).node', + ], + }, + ], # end actions + }, # end target copy_addon + ], # end targets +} diff --git a/base/special/fresnel/examples/c/Makefile b/base/special/fresnel/examples/c/Makefile new file mode 100644 index 000000000..6aed70daf --- /dev/null +++ b/base/special/fresnel/examples/c/Makefile @@ -0,0 +1,146 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2024 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +#/ + +# VARIABLES # + +ifndef VERBOSE + QUIET := @ +else + QUIET := +endif + +# Determine the OS ([1][1], [2][2]). +# +# [1]: https://en.wikipedia.org/wiki/Uname#Examples +# [2]: http://stackoverflow.com/a/27776822/2225624 +OS ?= $(shell uname) +ifneq (, $(findstring MINGW,$(OS))) + OS := WINNT +else +ifneq (, $(findstring MSYS,$(OS))) + OS := WINNT +else +ifneq (, $(findstring CYGWIN,$(OS))) + OS := WINNT +else +ifneq (, $(findstring Windows_NT,$(OS))) + OS := WINNT +endif +endif +endif +endif + +# Define the program used for compiling C source files: +ifdef C_COMPILER + CC := $(C_COMPILER) +else + CC := gcc +endif + +# Define the command-line options when compiling C files: +CFLAGS ?= \ + -std=c99 \ + -O3 \ + -Wall \ + -pedantic + +# Determine whether to generate position independent code ([1][1], [2][2]). +# +# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options +# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option +ifeq ($(OS), WINNT) + fPIC ?= +else + fPIC ?= -fPIC +endif + +# List of includes (e.g., `-I /foo/bar -I /beep/boop/include`): +INCLUDE ?= + +# List of source files: +SOURCE_FILES ?= + +# List of libraries (e.g., `-lopenblas -lpthread`): +LIBRARIES ?= + +# List of library paths (e.g., `-L /foo/bar -L /beep/boop`): +LIBPATH ?= + +# List of C targets: +c_targets := example.out + + +# RULES # + +#/ +# Compiles source files. +# +# @param {string} [C_COMPILER] - C compiler (e.g., `gcc`) +# @param {string} [CFLAGS] - C compiler options +# @param {(string|void)} [fPIC] - compiler flag determining whether to generate position independent code (e.g., `-fPIC`) +# @param {string} [INCLUDE] - list of includes (e.g., `-I /foo/bar -I /beep/boop/include`) +# @param {string} [SOURCE_FILES] - list of source files +# @param {string} [LIBPATH] - list of library paths (e.g., `-L /foo/bar -L /beep/boop`) +# @param {string} [LIBRARIES] - list of libraries (e.g., `-lopenblas -lpthread`) +# +# @example +# make +# +# @example +# make all +#/ +all: $(c_targets) + +.PHONY: all + +#/ +# Compiles C source files. +# +# @private +# @param {string} CC - C compiler (e.g., `gcc`) +# @param {string} CFLAGS - C compiler options +# @param {(string|void)} fPIC - compiler flag determining whether to generate position independent code (e.g., `-fPIC`) +# @param {string} INCLUDE - list of includes (e.g., `-I /foo/bar`) +# @param {string} SOURCE_FILES - list of source files +# @param {string} LIBPATH - list of library paths (e.g., `-L /foo/bar`) +# @param {string} LIBRARIES - list of libraries (e.g., `-lopenblas`) +#/ +$(c_targets): %.out: %.c + $(QUIET) $(CC) $(CFLAGS) $(fPIC) $(INCLUDE) -o $@ $(SOURCE_FILES) $< $(LIBPATH) -lm $(LIBRARIES) + +#/ +# Runs compiled examples. +# +# @example +# make run +#/ +run: $(c_targets) + $(QUIET) ./$< + +.PHONY: run + +#/ +# Removes generated files. +# +# @example +# make clean +#/ +clean: + $(QUIET) -rm -f *.o *.out + +.PHONY: clean diff --git a/base/special/fresnel/examples/c/example.c b/base/special/fresnel/examples/c/example.c new file mode 100644 index 000000000..ba00e3bed --- /dev/null +++ b/base/special/fresnel/examples/c/example.c @@ -0,0 +1,32 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +#include "stdlib/math/base/special/fresnel.h" +#include + +int main( void ) { + const double x[] = { 0.0, 1.57, 3.14, 6.28 }; + + double C; + double S; + int i; + for ( i = 0; i < 4; i++ ) { + stdlib_base_fresnel( x[ i ], &S, &C ); + printf( "x: %lf => S(x): %lf, C(x): %lf\n", x[ i ], S, C ); + } +} diff --git a/base/special/fresnel/include.gypi b/base/special/fresnel/include.gypi new file mode 100644 index 000000000..575cb043c --- /dev/null +++ b/base/special/fresnel/include.gypi @@ -0,0 +1,53 @@ +# @license Apache-2.0 +# +# Copyright (c) 2024 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +# A GYP include file for building a Node.js native add-on. +# +# Main documentation: +# +# [1]: https://gyp.gsrc.io/docs/InputFormatReference.md +# [2]: https://gyp.gsrc.io/docs/UserDocumentation.md +{ + # Define variables to be used throughout the configuration for all targets: + 'variables': { + # Source directory: + 'src_dir': './src', + + # Include directories: + 'include_dirs': [ + '} S(x) and C(x) +* +* @example +* var v = fresnel( 0.0 ); +* // returns [ 0.0, 0.0 ] +* +* @example +* var v = fresnel( 1.0 ); +* // returns [ ~0.438, ~0.780 ] +* +* @example +* var v = fresnel( Infinity ); +* // returns [ ~0.5, ~0.5 ] +* +* @example +* var v = fresnel( -Infinity ); +* // returns [ ~-0.5, ~-0.5 ] +* +* @example +* var v = fresnel( NaN ); +* // returns [ NaN, NaN ] +*/ +function fresnel( x ) { + var out = new Float64Array( 2 ); + addon( x, out ); + return out; +} + + +// EXPORTS // + +module.exports = fresnel; diff --git a/base/special/fresnel/lib/rational_pcqc.js b/base/special/fresnel/lib/rational_pcqc.js index 2db23f3c5..214173bcc 100644 --- a/base/special/fresnel/lib/rational_pcqc.js +++ b/base/special/fresnel/lib/rational_pcqc.js @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2022 The Stdlib Authors. +* 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. @@ -22,7 +22,7 @@ // MAIN // /** -* Evaluates a rational function, i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\). +* Evaluates a rational function (i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\)). * * ## Notes * diff --git a/base/special/fresnel/lib/rational_pfqf.js b/base/special/fresnel/lib/rational_pfqf.js index d27b41e21..5049776dc 100644 --- a/base/special/fresnel/lib/rational_pfqf.js +++ b/base/special/fresnel/lib/rational_pfqf.js @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2022 The Stdlib Authors. +* 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. @@ -22,7 +22,7 @@ // MAIN // /** -* Evaluates a rational function, i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\). +* Evaluates a rational function (i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\)). * * ## Notes * diff --git a/base/special/fresnel/lib/rational_pgqg.js b/base/special/fresnel/lib/rational_pgqg.js index 74c14eb8c..aa1a708b6 100644 --- a/base/special/fresnel/lib/rational_pgqg.js +++ b/base/special/fresnel/lib/rational_pgqg.js @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2022 The Stdlib Authors. +* 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. @@ -22,7 +22,7 @@ // MAIN // /** -* Evaluates a rational function, i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\). +* Evaluates a rational function (i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\)). * * ## Notes * diff --git a/base/special/fresnel/lib/rational_psqs.js b/base/special/fresnel/lib/rational_psqs.js index f2a456b09..a67669d8a 100644 --- a/base/special/fresnel/lib/rational_psqs.js +++ b/base/special/fresnel/lib/rational_psqs.js @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2022 The Stdlib Authors. +* 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. @@ -22,7 +22,7 @@ // MAIN // /** -* Evaluates a rational function, i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\). +* Evaluates a rational function (i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\)). * * ## Notes * diff --git a/base/special/fresnel/manifest.json b/base/special/fresnel/manifest.json new file mode 100644 index 000000000..72d03e6f6 --- /dev/null +++ b/base/special/fresnel/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/napi/argv", + "@stdlib/napi/argv-double", + "@stdlib/napi/argv-float64array", + "@stdlib/napi/export", + "@stdlib/math/base/special/abs", + "@stdlib/math/base/special/sincos", + "@stdlib/constants/float64/pi", + "@stdlib/constants/float64/half-pi" + ] + }, + { + "task": "benchmark", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/math/base/special/abs", + "@stdlib/math/base/special/sincos", + "@stdlib/constants/float64/pi", + "@stdlib/constants/float64/half-pi" + ] + }, + { + "task": "examples", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/math/base/special/abs", + "@stdlib/math/base/special/sincos", + "@stdlib/constants/float64/pi", + "@stdlib/constants/float64/half-pi" + ] + } + ] +} diff --git a/base/special/fresnel/scripts/evalrational.js b/base/special/fresnel/scripts/evalrational.js index afed48e59..ce48e1fe6 100644 --- a/base/special/fresnel/scripts/evalrational.js +++ b/base/special/fresnel/scripts/evalrational.js @@ -24,10 +24,15 @@ // 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( './../../../../base/tools/evalrational-compile' ); +var compileC = require( './../../../../base/tools/evalrational-compile-c' ); +var substringBefore = require( '@stdlib/string/substring-before' ); +var substringAfter = require( '@stdlib/string/substring-after' ); +var format = require( '@stdlib/string/format' ); // VARIABLES // @@ -144,6 +149,33 @@ var header = licenseHeader( 'Apache-2.0', 'js', { 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 // /** @@ -153,7 +185,9 @@ header += '\n/* This is a generated file. Do not edit directly. */\n'; */ function main() { var fpath; + var copts; var opts; + var file; var str; opts = { @@ -175,6 +209,32 @@ function main() { fpath = resolve( __dirname, '..', 'lib', 'rational_pgqg.js' ); str = header + compile( PG, QG ); writeFileSync( fpath, str, opts ); + + copts = { + 'dtype': 'double', + 'name': '' + }; + + fpath = resolve( __dirname, '..', 'src', 'main.c' ); + file = readFileSync( fpath, opts ); + + copts.name = 'rational_psqs'; + str = compileC( PS, QS, copts ); + file = insert( file, copts.name, str ); + + copts.name = 'rational_pcqc'; + str = compileC( PC, QC, copts ); + file = insert( file, copts.name, str ); + + copts.name = 'rational_pfqf'; + str = compileC( PF, QF, copts ); + file = insert( file, copts.name, str ); + + copts.name = 'rational_pgqg'; + str = compileC( PG, QG, copts ); + file = insert( file, copts.name, str ); + + writeFileSync( fpath, file, opts ); } main(); diff --git a/base/special/fresnel/src/Makefile b/base/special/fresnel/src/Makefile new file mode 100644 index 000000000..bcf18aa46 --- /dev/null +++ b/base/special/fresnel/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/base/special/fresnel/src/addon.c b/base/special/fresnel/src/addon.c new file mode 100644 index 000000000..bec1e2f68 --- /dev/null +++ b/base/special/fresnel/src/addon.c @@ -0,0 +1,41 @@ +/** +* @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/fresnel.h" +#include "stdlib/napi/argv.h" +#include "stdlib/napi/argv_double.h" +#include "stdlib/napi/argv_float64array.h" +#include "stdlib/napi/export.h" +#include + +/** +* Receives JavaScript callback invocation data. +* +* @param env environment under which the function is invoked +* @param info callback data +* @return Node-API value +*/ +static napi_value addon( napi_env env, napi_callback_info info ) { + STDLIB_NAPI_ARGV( env, info, argv, argc, 2 ); + STDLIB_NAPI_ARGV_DOUBLE( env, x, argv, 0 ); + STDLIB_NAPI_ARGV_FLOAT64ARRAY( env, y, ylen, argv, 1 ); + stdlib_base_fresnel( x, &y[ 0 ], &y[ 1 ] ); + return NULL; +} + +STDLIB_NAPI_MODULE_EXPORT_FCN( addon ) diff --git a/base/special/fresnel/src/main.c b/base/special/fresnel/src/main.c new file mode 100644 index 000000000..19cd0dd56 --- /dev/null +++ b/base/special/fresnel/src/main.c @@ -0,0 +1,288 @@ +/** +* @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 original C code, long comment, copyright, license, and constants are from [Cephes]{@link http://www.netlib.org/cephes}. The implementation follows the original, but has been modified for JavaScript. +* +* ```text +* Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier +* +* Some software in this archive may be from the book _Methods and Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster International, 1989) or from the Cephes Mathematical Library, a commercial product. In either event, it is copyrighted by the author. What you see here may be used freely but it comes with no support or guarantee. +* +* Stephen L. Moshier +* moshier@na-net.ornl.gov +* ``` +*/ + +#include "stdlib/math/base/special/fresnel.h" +#include "stdlib/math/base/special/sincos.h" +#include "stdlib/math/base/special/abs.h" +#include "stdlib/constants/float64/half_pi.h" +#include "stdlib/constants/float64/pi.h" + +/* Begin auto-generated functions. The following functions are auto-generated. Do not edit directly. */ + +// BEGIN: rational_psqs + +/** +* 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_psqs( const double x ) { + double ax; + double ix; + double s1; + double s2; + if ( x == 0.0 ) { + return 0.5235987755982989; + } + if ( x < 0.0 ) { + ax = -x; + } else { + ax = x; + } + if ( ax <= 1.0 ) { + s1 = 318016297876.5678 + (x * (-44297951805.96978 + (x * (2548908805.7337637 + (x * (-62974148.62058625 + (x * (708840.0452577386 + (x * (-2991.8191940101983 + (x * 0.0))))))))))); + s2 = 607366389490.0846 + (x * (22441179564.534092 + (x * (419320245.8981112 + (x * (5173438.887700964 + (x * (45584.78108065326 + (x * (281.3762688899943 + (x * 1.0))))))))))); + } else { + ix = 1.0 / x; + s1 = 0.0 + (ix * (-2991.8191940101983 + (ix * (708840.0452577386 + (ix * (-62974148.62058625 + (ix * (2548908805.7337637 + (ix * (-44297951805.96978 + (ix * 318016297876.5678))))))))))); + s2 = 1.0 + (ix * (281.3762688899943 + (ix * (45584.78108065326 + (ix * (5173438.887700964 + (ix * (419320245.8981112 + (ix * (22441179564.534092 + (ix * 607366389490.0846))))))))))); + } + return s1 / s2; +} + +// END: rational_psqs + +// BEGIN: rational_pcqc + +/** +* 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_pcqc( const double x ) { + double ax; + double ix; + double s1; + double s2; + if ( x == 0.0 ) { + return 1.0; + } + if ( x < 0.0 ) { + ax = -x; + } else { + ax = x; + } + if ( ax <= 1.0 ) { + s1 = 1.0 + (x * (-0.20552590095501388 + (x * (0.018884331939670384 + (x * (-0.0006451914356839651 + (x * (0.000009504280628298596 + (x * (-4.9884311457357354e-8 + (x * 0.0))))))))))); + s2 = 1.0 + (x * (0.04121420907221998 + (x * (0.0008680295429417843 + (x * (0.000012226278902417902 + (x * (1.2500186247959882e-7 + (x * (9.154392157746574e-10 + (x * 3.99982968972496e-12))))))))))); + } else { + ix = 1.0 / x; + s1 = 0.0 + (ix * (-4.9884311457357354e-8 + (ix * (0.000009504280628298596 + (ix * (-0.0006451914356839651 + (ix * (0.018884331939670384 + (ix * (-0.20552590095501388 + (ix * 1.0))))))))))); + s2 = 3.99982968972496e-12 + (ix * (9.154392157746574e-10 + (ix * (1.2500186247959882e-7 + (ix * (0.000012226278902417902 + (ix * (0.0008680295429417843 + (ix * (0.04121420907221998 + (ix * 1.0))))))))))); + } + return s1 / s2; +} + +// END: rational_pcqc + +// BEGIN: rational_pfqf + +/** +* 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_pfqf( const double x ) { + double ax; + double ix; + double s1; + double s2; + if ( x == 0.0 ) { + return 2.999999999999634; + } + if ( x < 0.0 ) { + ax = -x; + } else { + ax = x; + } + if ( ax <= 1.0 ) { + s1 = 3.763297112699879e-20 + (x * (1.3428327623306275e-16 + (x * (1.7201074326816183e-13 + (x * (1.0230451416490724e-10 + (x * (3.055689837902576e-8 + (x * (0.0000046361374928786735 + (x * (0.000345017939782574 + (x * (0.011522095507358577 + (x * (0.1434079197807589 + (x * (0.4215435550436775 + (x * 0.0))))))))))))))))))); + s2 = 1.2544323709001127e-20 + (x * (4.5200143407412973e-17 + (x * (5.887545336215784e-14 + (x * (3.6014002958937136e-11 + (x * (1.1269922476399903e-8 + (x * (0.0000018462756734893055 + (x * (0.00015593440916415301 + (x * (0.0064405152650885865 + (x * (0.11688892585919138 + (x * (0.7515863983533789 + (x * 1.0))))))))))))))))))); + } else { + ix = 1.0 / x; + s1 = 0.0 + (ix * (0.4215435550436775 + (ix * (0.1434079197807589 + (ix * (0.011522095507358577 + (ix * (0.000345017939782574 + (ix * (0.0000046361374928786735 + (ix * (3.055689837902576e-8 + (ix * (1.0230451416490724e-10 + (ix * (1.7201074326816183e-13 + (ix * (1.3428327623306275e-16 + (ix * 3.763297112699879e-20))))))))))))))))))); + s2 = 1.0 + (ix * (0.7515863983533789 + (ix * (0.11688892585919138 + (ix * (0.0064405152650885865 + (ix * (0.00015593440916415301 + (ix * (0.0000018462756734893055 + (ix * (1.1269922476399903e-8 + (ix * (3.6014002958937136e-11 + (ix * (5.887545336215784e-14 + (ix * (4.5200143407412973e-17 + (ix * 1.2544323709001127e-20))))))))))))))))))); + } + return s1 / s2; +} + +// END: rational_pfqf + +// BEGIN: rational_pgqg + +/** +* 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_pgqg( const double x ) { + double ax; + double ix; + double s1; + double s2; + if ( x == 0.0 ) { + return 1.0; + } + if ( x < 0.0 ) { + ax = -x; + } else { + ax = x; + } + if ( ax <= 1.0 ) { + s1 = 1.8695871016278324e-22 + (x * (8.363544356306774e-19 + (x * (1.375554606332618e-15 + (x * (1.0826804113902088e-12 + (x * (4.4534441586175015e-10 + (x * (9.828524436884223e-8 + (x * (0.000011513882611188428 + (x * (0.0006840793809153931 + (x * (0.018764858409257526 + (x * (0.1971028335255234 + (x * (0.5044420736433832 + (x * 0.0))))))))))))))))))))); + s2 = 1.8695871016278324e-22 + (x * (8.391588162831187e-19 + (x * (1.3879653125957886e-15 + (x * (1.1027321506624028e-12 + (x * (4.6068072814652043e-10 + (x * (1.0431458965757199e-7 + (x * (0.000012754507566772912 + (x * (0.0008146791071843061 + (x * (0.02536037414203388 + (x * (0.33774898912002 + (x * (1.4749575992512833 + (x * 1.0))))))))))))))))))))); + } else { + ix = 1.0 / x; + s1 = 0.0 + (ix * (0.5044420736433832 + (ix * (0.1971028335255234 + (ix * (0.018764858409257526 + (ix * (0.0006840793809153931 + (ix * (0.000011513882611188428 + (ix * (9.828524436884223e-8 + (ix * (4.4534441586175015e-10 + (ix * (1.0826804113902088e-12 + (ix * (1.375554606332618e-15 + (ix * (8.363544356306774e-19 + (ix * 1.8695871016278324e-22))))))))))))))))))))); + s2 = 1.0 + (ix * (1.4749575992512833 + (ix * (0.33774898912002 + (ix * (0.02536037414203388 + (ix * (0.0008146791071843061 + (ix * (0.000012754507566772912 + (ix * (1.0431458965757199e-7 + (ix * (4.6068072814652043e-10 + (ix * (1.1027321506624028e-12 + (ix * (1.3879653125957886e-15 + (ix * (8.391588162831187e-19 + (ix * 1.8695871016278324e-22))))))))))))))))))))); + } + return s1 / s2; +} + +// END: rational_pgqg + +/* End auto-generated functions. */ + +/** +* Computes the Fresnel integrals S(x) and C(x) and assigns results to a provided output array. +* +* ## Method +* +* Evaluates the Fresnel integrals +* +* ```tex +* \begin{align*} +* \operatorname{S}(x) &= \int_0^x \sin\left(\frac{\pi}{2} t^2\right)\,\mathrm{d}t, \\ +* \operatorname{C}(x) &= \int_0^x \cos\left(\frac{\pi}{2} t^2\right)\,\mathrm{d}t. +* \end{align*} +* ``` +* +* The integrals are evaluated by a power series for \\( x < 1 \\). For \\( x >= 1 \\) auxiliary functions \\( f(x) \\) and \\( g(x) \\) are employed such that +* +* ```tex +* \begin{align*} +* \operatorname{C}(x) &= \frac{1}{2} + f(x) \sin\left( \frac{\pi}{2} x^2 \right) - g(x) \cos\left( \frac{\pi}{2} x^2 \right), \\ +* \operatorname{S}(x) &= \frac{1}{2} - f(x) \cos\left( \frac{\pi}{2} x^2 \right) - g(x) \sin\left( \frac{\pi}{2} x^2 \right). +* \end{align*} +* ``` +* +* ## Notes +* +* - Relative error on test interval \\( \[0,10\] \\): +* +* | arithmetic | function | # trials | peak | rms | +* |:----------:|:--------:|:--------:|:-------:|:-------:| +* | IEEE | S(x) | 10000 | 2.0e-15 | 3.2e-16 | +* | IEEE | C(x) | 10000 | 1.8e-15 | 3.3e-16 | +* +* @param x input value +* @param S destination to store S(x) +* @param C destination to store C(x) +* +* @example +* double x = 0.0; +* +* double S; +* double C; +* stdlib_base_fresnel( x, &S, &C ); +*/ +void stdlib_base_fresnel( const double x, double* S, double* C ) { + double x2; + double xa; + double f; + double g; + double t; + double u; + double s; + double c; + + xa = stdlib_base_abs( x ); + x2 = xa * xa; + if ( x2 < 2.5625 ) { + t = x2 * x2; + *S = xa * x2 * rational_psqs( t ); + *C = xa * rational_pcqc( t ); + } else if ( xa > 36974.0 ) { + *C = 0.5; + *S = 0.5; + } else { + // Asymptotic power series auxiliary functions for large arguments... + x2 = xa * xa; + t = STDLIB_CONSTANT_FLOAT64_PI * x2; + u = 1.0 / ( t * t ); + t = 1.0 / t; + f = 1.0 - ( u * rational_pfqf( u ) ); + g = t * rational_pgqg( u ); + t = STDLIB_CONSTANT_FLOAT64_HALF_PI * x2; + stdlib_base_sincos( t, &s, &c ); + t = STDLIB_CONSTANT_FLOAT64_PI * xa; + *C = 0.5 + ( ( ( f * s ) - ( g * c ) ) / t ); + *S = 0.5 - ( ( ( f * c ) + ( g * s ) ) / t ); + } + if ( x < 0.0 ) { + *C = -*C; + *S = -*S; + } + return; +} diff --git a/base/special/fresnel/test/test.native.js b/base/special/fresnel/test/test.native.js new file mode 100644 index 000000000..9a6238d71 --- /dev/null +++ b/base/special/fresnel/test/test.native.js @@ -0,0 +1,226 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var resolve = require( 'path' ).resolve; +var tape = require( 'tape' ); +var isnan = require( './../../../../base/assert/is-nan' ); +var PINF = require( '@stdlib/constants/float64/pinf' ); +var NINF = require( '@stdlib/constants/float64/ninf' ); +var EPS = require( '@stdlib/constants/float64/eps' ); +var abs = require( './../../../../base/special/abs' ); +var randu = require( '@stdlib/random/base/randu' ); +var tryRequire = require( '@stdlib/utils/try-require' ); + + +// VARIABLES // + +var fresnel = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( fresnel instanceof Error ) +}; + + +// FIXTURES // + +var smallPositive = require( './fixtures/c/cephes/small.json' ); +var mediumPositive = require( './fixtures/c/cephes/medium.json' ); +var largePositive = require( './fixtures/c/cephes/large.json' ); +var hugePositive = require( './fixtures/c/cephes/huge.json' ); + + +// TESTS // + +tape( 'main export is a function', opts, function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof fresnel, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function computes Fresnel integrals (small positive values)', opts, function test( t ) { + var delta; + var tol; + var C; + var S; + var x; + var y; + var i; + + x = smallPositive.x; + S = smallPositive.S; + C = smallPositive.C; + + for ( i = 0; i < x.length; i++ ) { + y = fresnel( x[i] ); + if ( y[0] === S[i] ) { + t.equal( y[0], S[i], 'x: '+x[i]+'. Expected: '+S[i] ); + } else { + delta = abs( y[0] - S[i] ); + tol = 4.0 * EPS * abs( S[i] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. S: '+y[0]+'. Expected: '+S[i]+'. tol: '+tol+'. delta: '+delta+'.' ); + } + if ( y[1] === C[i] ) { + t.equal( y[1], C[i], 'x: '+x[i]+'. Expected: '+C[i] ); + } else { + delta = abs( y[1] - C[i] ); + tol = 4.0 * EPS * abs( C[i] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. C: '+y[1]+'. Expected: '+C[i]+'. tol: '+tol+'. delta: '+delta+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes Fresnel integrals (medium positive values)', opts, function test( t ) { + var delta; + var tol; + var C; + var S; + var x; + var y; + var i; + + x = mediumPositive.x; + S = mediumPositive.S; + C = mediumPositive.C; + + for ( i = 0; i < x.length; i++ ) { + y = fresnel( x[i] ); + if ( y[0] === S[i] ) { + t.equal( y[0], S[i], 'x: '+x[i]+'. Expected: '+S[i] ); + } else { + delta = abs( y[0] - S[i] ); + tol = 1.5 * EPS * abs( S[i] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. S: '+y[0]+'. Expected: '+S[i]+'. tol: '+tol+'. delta: '+delta+'.' ); + } + if ( y[1] === C[i] ) { + t.equal( y[1], C[i], 'x: '+x[i]+'. Expected: '+C[i] ); + } else { + delta = abs( y[1] - C[i] ); + tol = 1.5 * EPS * abs( C[i] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. C: '+y[1]+'. Expected: '+C[i]+'. tol: '+tol+'. delta: '+delta+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes Fresnel integrals (large positive values)', opts, function test( t ) { + var delta; + var tol; + var C; + var S; + var x; + var y; + var i; + + x = largePositive.x; + S = largePositive.S; + C = largePositive.C; + + for ( i = 0; i < x.length; i++ ) { + y = fresnel( x[i] ); + if ( y[0] === S[i] ) { + t.equal( y[0], S[i], 'x: '+x[i]+'. Expected: '+S[i] ); + } else { + delta = abs( y[0] - S[i] ); + tol = 1.5 * EPS * abs( S[i] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. S: '+y[0]+'. Expected: '+S[i]+'. tol: '+tol+'. delta: '+delta+'.' ); + } + if ( y[1] === C[i] ) { + t.equal( y[1], C[i], 'x: '+x[i]+'. Expected: '+C[i] ); + } else { + delta = abs( y[1] - C[i] ); + tol = 1.5 * EPS * abs( C[i] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. C: '+y[1]+'. Expected: '+C[i]+'. tol: '+tol+'. delta: '+delta+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes Fresnel integrals (very large positive values)', opts, function test( t ) { + var delta; + var tol; + var C; + var S; + var x; + var y; + var i; + + x = hugePositive.x; + S = hugePositive.S; + C = hugePositive.C; + + for ( i = 0; i < x.length; i++ ) { + y = fresnel( x[i] ); + if ( y[0] === S[i] ) { + t.equal( y[0], S[i], 'x: '+x[i]+'. Expected: '+S[i] ); + } else { + delta = abs( y[0] - S[i] ); + tol = 1.5 * EPS * abs( S[i] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. S: '+y[0]+'. Expected: '+S[i]+'. tol: '+tol+'. delta: '+delta+'.' ); + } + if ( y[1] === C[i] ) { + t.equal( y[1], C[i], 'x: '+x[i]+'. Expected: '+C[i] ); + } else { + delta = abs( y[1] - C[i] ); + tol = 1.5 * EPS * abs( C[i] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. C: '+y[1]+'. Expected: '+C[i]+'. tol: '+tol+'. delta: '+delta+'.' ); + } + } + t.end(); +}); + +tape( 'the function is an odd function of x', opts, function test( t ) { + var yn; + var yp; + var x; + var i; + + for ( i = 0; i < 500; i++ ) { + x = randu() * 10000.0; + yn = fresnel( -x ); + yp = fresnel( x ); + + t.equal( yp[0], -yn[0], 'S(x) = -S(-x)' ); + t.equal( yp[1], -yn[1], 'C(x) = -C(-x)' ); + } + t.end(); +}); + +tape( 'the function returns `[0.5, 0.5]` if provided `+infinity`', opts, function test( t ) { + var v = fresnel( PINF ); + t.equal( v[0], 0.5, 'returns 0.5' ); + t.equal( v[1], 0.5, 'returns 0.5' ); + t.end(); +}); + +tape( 'the function returns `[-0.5, -0.5]` if provided `-infinity`', opts, function test( t ) { + var v = fresnel( NINF ); + t.equal( v[0], -0.5, 'returns -0.5' ); + t.equal( v[1], -0.5, 'returns -0.5' ); + t.end(); +}); + +tape( 'the function returns `[NaN, NaN]` if provided a `NaN`', opts, function test( t ) { + var v = fresnel( NaN ); + t.equal( isnan( v[0] ), true, 'returns expected value' ); + t.equal( isnan( v[1] ), true, 'returns expected value' ); + t.end(); +});