diff --git a/CHANGELOG.md b/CHANGELOG.md index 30d0680da..a5809c4d4 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -3587,6 +3587,28 @@ This release closes the following issue: +
+ +#### [@stdlib/math/base/special/fresnelc](https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/fresnelc) + +
+ +
+ +##### Features + +- [`4a2534a`](https://github.com/stdlib-js/stdlib/commit/4a2534a22c2ead42a6318bed2fce221286f9f7a8) - add C implementation for `math/base/special/fresnelc` [(#2680)](https://github.com/stdlib-js/stdlib/pull/2680) + +
+ + + +
+ +
+ + +
#### [@stdlib/math/base/special/fresnels](https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/fresnels) @@ -5604,6 +5626,7 @@ A total of 29 people contributed to this release. Thank you to the following con
+- [`4a2534a`](https://github.com/stdlib-js/stdlib/commit/4a2534a22c2ead42a6318bed2fce221286f9f7a8) - **feat:** add C implementation for `math/base/special/fresnelc` [(#2680)](https://github.com/stdlib-js/stdlib/pull/2680) _(by Gunj Joshi)_ - [`c476e32`](https://github.com/stdlib-js/stdlib/commit/c476e32e617de04644d9fbf399a34f80661778ea) - **feat:** add C implementation for `math/base/special/fresnels` [(#2675)](https://github.com/stdlib-js/stdlib/pull/2675) _(by Gunj Joshi)_ - [`7e04d9e`](https://github.com/stdlib-js/stdlib/commit/7e04d9e27fb5008c1cbc6e45e08ea6ad4b8993d2) - **refactor:** use max-safe-nth-factorial package [(#2676)](https://github.com/stdlib-js/stdlib/pull/2676 ) _(by Gunj Joshi)_ - [`26e46d5`](https://github.com/stdlib-js/stdlib/commit/26e46d57474904e02d69b98d8e06052333522257) - **docs:** fix missing `@private` tag [(#2672)](https://github.com/stdlib-js/stdlib/pull/2672) _(by Gunj Joshi)_ diff --git a/base/special/fresnelc/README.md b/base/special/fresnelc/README.md index 6953bfe4b..83b59b22c 100644 --- a/base/special/fresnelc/README.md +++ b/base/special/fresnelc/README.md @@ -100,6 +100,94 @@ for ( i = 0; i < x.length; i++ ) { + + +* * * + +
+ +## C APIs + + + +
+ +
+ + + + + +
+ +### Usage + +```c +#include "stdlib/math/base/special/fresnelc.h" +``` + +#### stdlib_base_fresnelc( x ) + +Computes the [Fresnel integral][fresnel-integral] C(x). + +```c +double out = stdlib_base_fresnelc( 0.0 ); +// returns ~0.0 + +out = stdlib_base_fresnelc( 1.0 ); +// returns ~0.780 +``` + +The function accepts the following arguments: + +- **x**: `[in] double` input value. + +```c +double stdlib_base_fresnelc( const double x ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +### Examples + +```c +#include "stdlib/math/base/special/fresnelc.h" +#include + +int main( void ) { + const double x[] = { 0.0, 3.14, 5.55, 10.0 }; + + double y; + int i; + for ( i = 0; i < 4; i++ ) { + y = stdlib_base_fresnelc( x[ i ] ); + printf( "fresnelc(%lf) = %lf\n", x[ i ], y ); + } +} +``` + +
+ + + +
+ + +
diff --git a/base/special/fresnelc/benchmark/benchmark.native.js b/base/special/fresnelc/benchmark/benchmark.native.js new file mode 100644 index 000000000..b0ae27e26 --- /dev/null +++ b/base/special/fresnelc/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 fresnelc = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( fresnelc 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 = fresnelc( x ); + if ( isnan( y ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( y ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); diff --git a/base/special/fresnelc/benchmark/c/native/Makefile b/base/special/fresnelc/benchmark/c/native/Makefile new file mode 100644 index 000000000..f69e9da2b --- /dev/null +++ b/base/special/fresnelc/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/fresnelc/benchmark/c/native/benchmark.c b/base/special/fresnelc/benchmark/c/native/benchmark.c new file mode 100644 index 000000000..5c2b01d64 --- /dev/null +++ b/base/special/fresnelc/benchmark/c/native/benchmark.c @@ -0,0 +1,136 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +/** +* Benchmark `fresnelc`. +*/ +#include "stdlib/math/base/special/fresnelc.h" +#include +#include +#include +#include +#include + +#define NAME "fresnelc" +#define ITERATIONS 1000000 +#define REPEATS 3 + +/** +* Prints the TAP version. +*/ +void print_version() { + printf( "TAP version 13\n" ); +} + +/** +* Prints the TAP summary. +* +* @param total total number of tests +* @param passing total number of passing tests +*/ +void print_summary( int total, int passing ) { + printf( "#\n" ); + printf( "1..%d\n", total ); // TAP plan + printf( "# total %d\n", total ); + printf( "# pass %d\n", passing ); + printf( "#\n" ); + printf( "# ok\n" ); +} + +/** +* Prints benchmarks results. +* +* @param elapsed elapsed time in seconds +*/ +void print_results( double elapsed ) { + double rate = (double)ITERATIONS / elapsed; + printf( " ---\n" ); + printf( " iterations: %d\n", ITERATIONS ); + printf( " elapsed: %0.9f\n", elapsed ); + printf( " rate: %0.9f\n", rate ); + printf( " ...\n" ); +} + +/** +* Returns a clock time. +* +* @return clock time +*/ +double tic() { + struct timeval now; + gettimeofday( &now, NULL ); + return (double)now.tv_sec + (double)now.tv_usec / 1.0e6; +} + +/** +* Generates a random number on the interval [0,1]. +* +* @return random number +*/ +double rand_double() { + int r = rand(); + return (double)r / ( (double)RAND_MAX + 1.0 ); +} + +/** +* Runs a benchmark. +* +* @return elapsed time in seconds +*/ +double benchmark() { + double elapsed; + double x; + double y; + double t; + int i; + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + x = ( 20.0 * rand_double() ) - 10.0; + y = stdlib_base_fresnelc( x ); + if ( y != y ) { + printf( "should not return NaN\n" ); + break; + } + } + elapsed = tic() - t; + if ( y != y ) { + printf( "should not return NaN\n" ); + } + return elapsed; +} + +/** +* Main execution sequence. +*/ +int main( void ) { + double elapsed; + int i; + + // Use the current time to seed the random number generator: + srand( time( NULL ) ); + + print_version(); + for ( i = 0; i < REPEATS; i++ ) { + printf( "# c::native::%s\n", NAME ); + elapsed = benchmark(); + print_results( elapsed ); + printf( "ok %d benchmark finished\n", i+1 ); + } + print_summary( REPEATS, REPEATS ); +} diff --git a/base/special/fresnelc/binding.gyp b/base/special/fresnelc/binding.gyp new file mode 100644 index 000000000..ec3992233 --- /dev/null +++ b/base/special/fresnelc/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/fresnelc/examples/c/Makefile b/base/special/fresnelc/examples/c/Makefile new file mode 100644 index 000000000..6aed70daf --- /dev/null +++ b/base/special/fresnelc/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/fresnelc/examples/c/example.c b/base/special/fresnelc/examples/c/example.c new file mode 100644 index 000000000..150cbd573 --- /dev/null +++ b/base/special/fresnelc/examples/c/example.c @@ -0,0 +1,31 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2024 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +#include "stdlib/math/base/special/fresnelc.h" +#include + +int main( void ) { + const double x[] = { 0.0, 3.14, 5.55, 10.0 }; + + double y; + int i; + for ( i = 0; i < 4; i++ ) { + y = stdlib_base_fresnelc( x[ i ] ); + printf( "fresnelc(%lf) = %lf\n", x[ i ], y ); + } +} diff --git a/base/special/fresnelc/include.gypi b/base/special/fresnelc/include.gypi new file mode 100644 index 000000000..575cb043c --- /dev/null +++ b/base/special/fresnelc/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': [ + '= 1 \\) auxiliary functions \\( f(x) \\) and \\( g(x) \\) are employed such that +* +* ```tex +* \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). +* ``` +* +* ## Notes +* +* - Relative error on test interval \\( \[0,10\] \\): +* +* | arithmetic | function | # trials | peak | rms | +* |:----------:|:--------:|:--------:|:-------:|:-------:| +* | IEEE | C(x) | 10000 | 1.8e-15 | 3.3e-16 | +* +* @example +* double v = stdlib_base_fresnelc( 1.0 ); +* // returns ~0.780 +*/ +double stdlib_base_fresnelc( const double x ) { + double x2; + double xa; + double C; + 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; + C = xa * rational_pcqc( t ); + } else if ( xa > 36974.0 ) { + C = 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 ); + } + if ( x < 0.0 ) { + C = -C; + } + return C; +} + diff --git a/base/special/fresnelc/test/test.native.js b/base/special/fresnelc/test/test.native.js new file mode 100644 index 000000000..05c77f4da --- /dev/null +++ b/base/special/fresnelc/test/test.native.js @@ -0,0 +1,186 @@ +/** +* @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 fresnelc = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( fresnelc 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 fresnelc, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function computes the Fresnel integral C(x) (small positive values)', opts, function test( t ) { + var delta; + var tol; + var C; + var x; + var y; + var i; + + x = smallPositive.x; + C = smallPositive.C; + + for ( i = 0; i < x.length; i++ ) { + y = fresnelc( x[i] ); + if ( y === C[ i ] ) { + t.equal( y, C[ i ], 'x: '+x[i]+'. Expected: '+C[i] ); + } else { + delta = abs( y - C[i] ); + tol = 4.0 * EPS * abs( C[i] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. Value: '+y+'. Expected: '+C[i]+'. tol: '+tol+'. delta: '+delta+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes the Fresnel integral C(x) (medium positive values)', opts, function test( t ) { + var delta; + var tol; + var C; + var x; + var y; + var i; + + x = mediumPositive.x; + C = mediumPositive.C; + + for ( i = 0; i < x.length; i++ ) { + y = fresnelc( x[i] ); + if ( y === C[ i ] ) { + t.equal( y, C[ i ], 'x: '+x[i]+'. Expected: '+C[i] ); + } else { + delta = abs( y - C[i] ); + tol = 1.5 * EPS * abs( C[i] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. Value: '+y+'. Expected: '+C[i]+'. tol: '+tol+'. delta: '+delta+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes the Fresnel integral C(x) (large positive values)', opts, function test( t ) { + var delta; + var tol; + var C; + var x; + var y; + var i; + + x = largePositive.x; + C = largePositive.C; + + for ( i = 0; i < x.length; i++ ) { + y = fresnelc( x[i] ); + if ( y === C[ i ] ) { + t.equal( y, C[ i ], 'x: '+x[i]+'. Expected: '+C[i] ); + } else { + delta = abs( y - C[i] ); + tol = 1.5 * EPS * abs( C[i] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. Value: '+y+'. Expected: '+C[i]+'. tol: '+tol+'. delta: '+delta+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes the Fresnel integral C(x) (very large positive values)', opts, function test( t ) { + var delta; + var tol; + var C; + var x; + var y; + var i; + + x = hugePositive.x; + C = hugePositive.C; + + for ( i = 0; i < x.length; i++ ) { + y = fresnelc( x[i] ); + if ( y === C[ i ] ) { + t.equal( y, C[ i ], 'x: '+x[i]+'. Expected: '+C[i] ); + } else { + delta = abs( y - C[i] ); + tol = 1.5 * EPS * abs( C[i] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. Value: '+y+'. 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 = fresnelc( -x ); + yp = fresnelc( x ); + + t.equal( yp, -yn, 'C(x) = -C(-x)' ); + } + t.end(); +}); + +tape( 'the function returns `0.5` if provided `+infinity`', opts, function test( t ) { + var v = fresnelc( PINF ); + t.equal( v, 0.5, 'returns 0.5' ); + t.end(); +}); + +tape( 'the function returns `-0.5` if provided `-infinity`', opts, function test( t ) { + var v = fresnelc( NINF ); + t.equal( v, -0.5, 'returns -0.5' ); + t.end(); +}); + +tape( 'the function returns `NaN` if provided a `NaN`', opts, function test( t ) { + var v = fresnelc( NaN ); + t.equal( isnan( v ), true, 'returns expected value' ); + t.end(); +});