From 1ebb1d3caa16f6a6bc6bc363181382c761c89606 Mon Sep 17 00:00:00 2001 From: stdlib-bot Date: Tue, 29 Oct 2024 13:44:01 +0000 Subject: [PATCH] Auto-generated commit --- CHANGELOG.md | 50 +- base/special/sec/README.md | 193 + base/special/sec/benchmark/benchmark.js | 73 + .../special/sec/benchmark/benchmark.native.js | 60 + base/special/sec/benchmark/c/native/Makefile | 146 + .../sec/benchmark/c/native/benchmark.c | 133 + base/special/sec/binding.gyp | 170 + base/special/sec/docs/repl.txt | 27 + base/special/sec/docs/types/index.d.ts | 48 + base/special/sec/docs/types/test.ts | 44 + base/special/sec/examples/c/Makefile | 146 + base/special/sec/examples/c/example.c | 31 + base/special/sec/examples/index.js | 30 + base/special/sec/include.gypi | 53 + .../include/stdlib/math/base/special/sec.h | 38 + base/special/sec/lib/index.js | 52 + base/special/sec/lib/main.js | 61 + base/special/sec/lib/native.js | 62 + base/special/sec/manifest.json | 72 + base/special/sec/package.json | 68 + base/special/sec/src/Makefile | 70 + base/special/sec/src/addon.c | 23 + base/special/sec/src/main.c | 34 + base/special/sec/test/fixtures/julia/REQUIRE | 2 + .../test/fixtures/julia/huge_negative.json | 2006 ++++++++ .../test/fixtures/julia/huge_positive.json | 2006 ++++++++ .../test/fixtures/julia/large_negative.json | 2004 ++++++++ .../test/fixtures/julia/large_positive.json | 2006 ++++++++ .../test/fixtures/julia/medium_negative.json | 2006 ++++++++ .../test/fixtures/julia/medium_positive.json | 2006 ++++++++ .../special/sec/test/fixtures/julia/runner.jl | 113 + .../test/fixtures/julia/small_negative.json | 2004 ++++++++ .../test/fixtures/julia/small_positive.json | 2004 ++++++++ .../sec/test/fixtures/julia/smaller.json | 4050 +++++++++++++++++ .../test/fixtures/julia/tiny_negative.json | 1006 ++++ .../test/fixtures/julia/tiny_positive.json | 1006 ++++ .../fixtures/julia/very_large_negative.json | 1004 ++++ .../fixtures/julia/very_large_positive.json | 1004 ++++ base/special/sec/test/test.js | 396 ++ base/special/sec/test/test.native.js | 405 ++ 40 files changed, 26711 insertions(+), 1 deletion(-) create mode 100644 base/special/sec/README.md create mode 100644 base/special/sec/benchmark/benchmark.js create mode 100644 base/special/sec/benchmark/benchmark.native.js create mode 100644 base/special/sec/benchmark/c/native/Makefile create mode 100644 base/special/sec/benchmark/c/native/benchmark.c create mode 100644 base/special/sec/binding.gyp create mode 100644 base/special/sec/docs/repl.txt create mode 100644 base/special/sec/docs/types/index.d.ts create mode 100644 base/special/sec/docs/types/test.ts create mode 100644 base/special/sec/examples/c/Makefile create mode 100644 base/special/sec/examples/c/example.c create mode 100644 base/special/sec/examples/index.js create mode 100644 base/special/sec/include.gypi create mode 100644 base/special/sec/include/stdlib/math/base/special/sec.h create mode 100644 base/special/sec/lib/index.js create mode 100644 base/special/sec/lib/main.js create mode 100644 base/special/sec/lib/native.js create mode 100644 base/special/sec/manifest.json create mode 100644 base/special/sec/package.json create mode 100644 base/special/sec/src/Makefile create mode 100644 base/special/sec/src/addon.c create mode 100644 base/special/sec/src/main.c create mode 100644 base/special/sec/test/fixtures/julia/REQUIRE create mode 100644 base/special/sec/test/fixtures/julia/huge_negative.json create mode 100644 base/special/sec/test/fixtures/julia/huge_positive.json create mode 100644 base/special/sec/test/fixtures/julia/large_negative.json create mode 100644 base/special/sec/test/fixtures/julia/large_positive.json create mode 100644 base/special/sec/test/fixtures/julia/medium_negative.json create mode 100644 base/special/sec/test/fixtures/julia/medium_positive.json create mode 100644 base/special/sec/test/fixtures/julia/runner.jl create mode 100644 base/special/sec/test/fixtures/julia/small_negative.json create mode 100644 base/special/sec/test/fixtures/julia/small_positive.json create mode 100644 base/special/sec/test/fixtures/julia/smaller.json create mode 100644 base/special/sec/test/fixtures/julia/tiny_negative.json create mode 100644 base/special/sec/test/fixtures/julia/tiny_positive.json create mode 100644 base/special/sec/test/fixtures/julia/very_large_negative.json create mode 100644 base/special/sec/test/fixtures/julia/very_large_positive.json create mode 100644 base/special/sec/test/test.js create mode 100644 base/special/sec/test/test.native.js diff --git a/CHANGELOG.md b/CHANGELOG.md index 475fa24a3..6c6ffb8e2 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -494,6 +494,40 @@ +
+ +#### [@stdlib/math/base/special/sec](https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/sec) + +
+ +
+ +##### Features + +- [`ed4c8d6`](https://github.com/stdlib-js/stdlib/commit/ed4c8d65a020d119c4baa1eb6716751c75cf8a07) - add support for secant functionality `math/base/special/sec` [(#3027)](https://github.com/stdlib-js/stdlib/pull/3027) + +
+ + + +
+ +##### Closed Issues + +This release closes the following issue: + +[#225](https://github.com/stdlib-js/stdlib/issues/225) + +
+ + + +
+ +
+ + +
#### [@stdlib/math/base/special/xlogyf](https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/xlogyf) @@ -520,13 +554,26 @@ +
+ +### Closed Issues + +This release closes the following issue: + +[#225](https://github.com/stdlib-js/stdlib/issues/225) + +
+ + +
### Contributors -A total of 6 people contributed to this release. Thank you to the following contributors: +A total of 7 people contributed to this release. Thank you to the following contributors: - Aayush Khanna +- AbhijitRaut04 - Aman Bhansali - Athan Reines - Ayaka @@ -543,6 +590,7 @@ A total of 6 people contributed to this release. Thank you to the following cont
+- [`ed4c8d6`](https://github.com/stdlib-js/stdlib/commit/ed4c8d65a020d119c4baa1eb6716751c75cf8a07) - **feat:** add support for secant functionality `math/base/special/sec` [(#3027)](https://github.com/stdlib-js/stdlib/pull/3027) _(by AbhijitRaut04, Athan Reines, Philipp Burckhardt)_ - [`b18921a`](https://github.com/stdlib-js/stdlib/commit/b18921a136da2755efccfd6ae23c8b3f5aaa8f4a) - **feat:** add `math/base/special/acosdf` [(#3015)](https://github.com/stdlib-js/stdlib/pull/3015) _(by Aayush Khanna, Athan Reines)_ - [`60522bf`](https://github.com/stdlib-js/stdlib/commit/60522bfc0b5574d348301e788400178156731024) - **docs:** fix operator [(#3039)](https://github.com/stdlib-js/stdlib/pull/3039) _(by Gunj Joshi)_ - [`84b8294`](https://github.com/stdlib-js/stdlib/commit/84b8294c2d5494ff5eaaa2652dda81671e728068) - **feat:** add `math/base/special/nanmaxf` [(#3035)](https://github.com/stdlib-js/stdlib/pull/3035) _(by Gunj Joshi, Athan Reines)_ diff --git a/base/special/sec/README.md b/base/special/sec/README.md new file mode 100644 index 000000000..4ba7829d8 --- /dev/null +++ b/base/special/sec/README.md @@ -0,0 +1,193 @@ + + +# Secant + +> Evaluate the [secant][trigonometric-functions] of a number. + +
+ +
+ +
+ +## Usage + +```javascript +var sec = require( '@stdlib/math/base/special/sec' ); +``` + +## sec( x ) + +Evaluates the [secant][trigonometric-functions] of `x` (in radians). + +```javascript +var v = sec( 0.0 ); +// returns 1.0 + +v = sec( 3.141592653589793/2.0 ); +// returns 16331239353195370.0 + +v = sec( -3.141592653589793/3.0 ); +// returns ~1.9999999999999996 + +v = sec( 3.141592653589793/3.0 ); +// returns ~1.9999999999999996 + +v = sec( NaN ); +// returns NaN +``` + +
+ + + +
+ +## Examples + + + +```javascript +var linspace = require( '@stdlib/array/base/linspace' ); +var PI = require( '@stdlib/constants/float64/pi' ); +var sec = require( '@stdlib/math/base/special/sec' ); + +var x = linspace( -PI/2.0, PI/2.0, 100 ); + +var i; +for ( i = 0; i < x.length; i++ ) { + console.log( sec( x[ i ] ) ); +} +``` + +
+ + + + + +* * * + +
+ +## C APIs + + + +
+ +
+ + + + + +
+ +### Usage + +```c +#include "stdlib/math/base/special/sec.h" +``` + +#### stdlib_base_sec( x ) + +Evaluates the [secant][trigonometric-functions] of `x` (in radians). + +```c +double out = stdlib_base_sec( 0.0 ); +// returns 1.0 + +out = stdlib_base_cos( 3.141592653589793 / 2.0 ); +// returns 6.123233995736766e-17 +``` + +The function accepts the following arguments: + +- **x**: `[in] double` input value. + +```c +double stdlib_base_sec( const double x ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +### Examples + +```c +#include "stdlib/math/base/special/sec.h" +#include + +int main( void ) { + const double x[] = { 0.523, 0.785, 1.047, 3.14 }; + + double y; + int i; + for ( i = 0; i < 4; i++ ) { + y = stdlib_base_sec( x[ i ] ); + printf( "sec(%lf) = %lf\n", x[ i ], y ); + } +} +``` + +
+ + + +
+ + + + + +
+ +
+ + + + + +
+ +[trigonometric-functions]: https://en.wikipedia.org/wiki/Trigonometric_functions + + + + + +
+ + diff --git a/base/special/sec/benchmark/benchmark.js b/base/special/sec/benchmark/benchmark.js new file mode 100644 index 000000000..69c863a04 --- /dev/null +++ b/base/special/sec/benchmark/benchmark.js @@ -0,0 +1,73 @@ +/** +* @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 bench = require( '@stdlib/bench' ); +var randu = require( '@stdlib/random/base/randu' ); +var isnan = require( './../../../../base/assert/is-nan' ); +var cos = require( './../../../../base/special/cos' ); +var pkg = require( './../package.json' ).name; +var sec = require( './../lib' ); + + +// MAIN // + +bench( pkg, function benchmark( b ) { + var x; + var y; + var i; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + x = (randu() * 20.0) - 10.0; + y = sec( 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(); +}); + +bench( pkg + '::built-in', 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 = 1.0 / cos( 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/sec/benchmark/benchmark.native.js b/base/special/sec/benchmark/benchmark.native.js new file mode 100644 index 000000000..455209831 --- /dev/null +++ b/base/special/sec/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 sec = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( sec 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 = sec( 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/sec/benchmark/c/native/Makefile b/base/special/sec/benchmark/c/native/Makefile new file mode 100644 index 000000000..f69e9da2b --- /dev/null +++ b/base/special/sec/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/sec/benchmark/c/native/benchmark.c b/base/special/sec/benchmark/c/native/benchmark.c new file mode 100644 index 000000000..b1842520f --- /dev/null +++ b/base/special/sec/benchmark/c/native/benchmark.c @@ -0,0 +1,133 @@ +/** +* @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/sec.h" +#include +#include +#include +#include +#include + +#define NAME "sec" +#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 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_sec( 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/sec/binding.gyp b/base/special/sec/binding.gyp new file mode 100644 index 000000000..ec3992233 --- /dev/null +++ b/base/special/sec/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/sec/docs/repl.txt b/base/special/sec/docs/repl.txt new file mode 100644 index 000000000..db2bae923 --- /dev/null +++ b/base/special/sec/docs/repl.txt @@ -0,0 +1,27 @@ + +{{alias}}( x ) + Computes the secant of a number. + + Parameters + ---------- + x: number + Input value (in radians). + + Returns + ------- + y: number + Secant. + + Examples + -------- + > var y = {{alias}}( 0.0 ) + 1.0 + > y = {{alias}}( {{alias:@stdlib/constants/float64/pi}}/2.0 ) + 16331239353195370.0 + > y = {{alias}}( -{{alias:@stdlib/constants/float64/pi}}/3.0 ) + ~1.9999999999999996 + > y = {{alias}}( NaN ) + NaN + + See Also + -------- diff --git a/base/special/sec/docs/types/index.d.ts b/base/special/sec/docs/types/index.d.ts new file mode 100644 index 000000000..96254288f --- /dev/null +++ b/base/special/sec/docs/types/index.d.ts @@ -0,0 +1,48 @@ +/* +* @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. +*/ + +// TypeScript Version: 4.1 + +/** +* Computes the secant of a number. +* +* @param x - input value (in radians) +* @returns secant +* +* @example +* var v = sec( 0.0 ); +* // returns 1.0 +* +* @example +* var v = sec( 3.141592653589793/2.0 ); +* // returns 16331239353195370.0 +* +* @example +* var v = sec( -3.141592653589793/3.0 ); +* // returns ~1.9999999999999996 +* +* @example +* var v = sec( NaN ); +* // returns NaN +*/ +declare function sec( x: number ): number; + + +// EXPORTS // + +export = sec; diff --git a/base/special/sec/docs/types/test.ts b/base/special/sec/docs/types/test.ts new file mode 100644 index 000000000..4019a606c --- /dev/null +++ b/base/special/sec/docs/types/test.ts @@ -0,0 +1,44 @@ +/* +* @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. +*/ + +import sec = require( './index' ); + + +// TESTS // + +// The function returns a number... +{ + sec( 2 ); // $ExpectType number +} + +// The compiler throws an error if the function is provided a value other than a number... +{ + sec( true ); // $ExpectError + sec( false ); // $ExpectError + sec( null ); // $ExpectError + sec( undefined ); // $ExpectError + sec( '5' ); // $ExpectError + sec( [] ); // $ExpectError + sec( {} ); // $ExpectError + sec( ( x: number ): number => x ); // $ExpectError +} + +// The compiler throws an error if the function is provided insufficient arguments... +{ + sec(); // $ExpectError +} diff --git a/base/special/sec/examples/c/Makefile b/base/special/sec/examples/c/Makefile new file mode 100644 index 000000000..6aed70daf --- /dev/null +++ b/base/special/sec/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/sec/examples/c/example.c b/base/special/sec/examples/c/example.c new file mode 100644 index 000000000..e341d8bdf --- /dev/null +++ b/base/special/sec/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/sec.h" +#include + +int main( void ) { + const double x[] = { 0.523, 0.785, 1.047, 3.14 }; + + double y; + int i; + for ( i = 0; i < 4; i++ ) { + y = stdlib_base_sec( x[ i ] ); + printf( "sec(%lf) = %lf\n", x[ i ], y ); + } +} diff --git a/base/special/sec/examples/index.js b/base/special/sec/examples/index.js new file mode 100644 index 000000000..ec7bc015f --- /dev/null +++ b/base/special/sec/examples/index.js @@ -0,0 +1,30 @@ +/** +* @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'; + +var linspace = require( '@stdlib/array/base/linspace' ); +var TWO_PI = require( '@stdlib/constants/float64/two-pi' ); +var sec = require( './../lib' ); + +var x = linspace( -TWO_PI, TWO_PI, 100 ); + +var i; +for ( i = 0; i < x.length; i++ ) { + console.log( 'sec(%d) = %d', x[ i ], sec( x[ i ] ) ); +} diff --git a/base/special/sec/include.gypi b/base/special/sec/include.gypi new file mode 100644 index 000000000..575cb043c --- /dev/null +++ b/base/special/sec/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': [ + '=0.10.0", + "npm": ">2.7.0" + }, + "os": [ + "aix", + "darwin", + "freebsd", + "linux", + "macos", + "openbsd", + "sunos", + "win32", + "windows" + ], + "keywords": [ + "stdlib", + "stdmath", + "mathematics", + "math", + "math.cos", + "cos", + "cosine", + "sec", + "trig", + "trigonometry", + "radians", + "angle" + ] +} diff --git a/base/special/sec/src/Makefile b/base/special/sec/src/Makefile new file mode 100644 index 000000000..bcf18aa46 --- /dev/null +++ b/base/special/sec/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/sec/src/addon.c b/base/special/sec/src/addon.c new file mode 100644 index 000000000..40bb3e327 --- /dev/null +++ b/base/special/sec/src/addon.c @@ -0,0 +1,23 @@ +/** +* @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/sec.h" +#include "stdlib/math/base/napi/unary.h" + +// cppcheck-suppress shadowFunction +STDLIB_MATH_BASE_NAPI_MODULE_D_D( stdlib_base_sec ) diff --git a/base/special/sec/src/main.c b/base/special/sec/src/main.c new file mode 100644 index 000000000..4d139884a --- /dev/null +++ b/base/special/sec/src/main.c @@ -0,0 +1,34 @@ +/** +* @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/sec.h" +#include "stdlib/math/base/special/cos.h" + +/** +* Evaluates the cosecant of a number. +* +* @param x input value (in radians) +* @return secant +* +* @example +* double y = stdlib_base_sec( 3.141592653589793 / 2.0 ); +* // returns 16331239353195370.0 +*/ +double stdlib_base_sec( const double x ) { + return 1.0 / stdlib_base_cos( x ); +} diff --git a/base/special/sec/test/fixtures/julia/REQUIRE b/base/special/sec/test/fixtures/julia/REQUIRE new file mode 100644 index 000000000..ae40bf736 --- /dev/null +++ b/base/special/sec/test/fixtures/julia/REQUIRE @@ -0,0 +1,2 @@ +julia 1.5 +JSON 0.21 \ No newline at end of file diff --git a/base/special/sec/test/fixtures/julia/huge_negative.json b/base/special/sec/test/fixtures/julia/huge_negative.json new file mode 100644 index 000000000..5a75ae723 --- /dev/null +++ b/base/special/sec/test/fixtures/julia/huge_negative.json @@ -0,0 +1,2006 @@ +{ + "expected": [ + 11.156638017887909, + 1.2704068118116802, + 4.180454226467146, + -2.4356748521961293, + -1.1292307102493453, + -1.0167043383157772, + -1.5085807766926251, + -16.668682554839517, + 1.759237224924984, + 1.0419856300916297, + 1.0697242743423312, + 1.9903772529758692, + -8.251212008916879, + -1.3901609015744856, + -1.0072504491967709, + -1.1812479596472234, + -2.8266247875432193, + 3.18135505274521, + 1.1875472965575062, + 1.0030655706531908, + 1.3372951115845477, + 7.721483596232872, + -2.019575020053436, + -1.0879711039687816, + -1.0302651989803502, + -1.7382140877380639, + 28.65042106115765, + 1.5848750567251442, + 1.0295367976358973, + 1.1243275731938096, + 2.307680847003251, + -5.04108048417328, + -1.333900536320725, + -1.0000351182745697, + -1.2462744836224302, + -3.576183231724687, + 2.391374340024271, + 1.1342568117106437, + 1.0123569564328885, + 1.4417039707939896, + 8.449929768934275, + -1.78090173540327, + -1.034709381602863, + -1.0538950064229076, + -1.9621475464413132, + 21.670536349739198, + 1.4500229708323564, + 1.0045259895709842, + 1.130938454523418, + 2.765449005209118, + -2.9581193232878142, + -1.2514218375125001, + -1.0024424598381412, + -1.413166356010486, + -4.907555478953208, + 2.04978828004182, + 1.127537394265044, + 1.0281654033035077, + 1.717806699846439, + 24.746726568004977, + -1.601433054091961, + -1.0167087443281366, + -1.085424480304672, + -2.2682266357623715, + 8.061690936984334, + 1.343889954642629, + 1.0001404854322504, + 1.183388925589299, + 3.476276625508969, + -2.43580257367371, + -1.1853725057007105, + -1.0110563162238937, + -1.5378265176135644, + -7.8950505097576515, + 1.803234711055636, + 1.0866386160630845, + 1.05100144743814, + 1.9348414018822968, + -26.474351724934383, + -1.462947987882786, + -1.0288178985478338, + -1.2213108831797752, + -2.7070512440445453, + 4.970596372230001, + 1.1519803969856925, + 1.0018904458745699, + 1.2489464138843316, + 12.562797388133538, + -2.0810676442834932, + -1.1325211122331236, + -1.004277048871493, + -1.6979908075505181, + -20.499522155833425, + 1.9709352210713396, + 1.0183110538186402, + 1.0816365089075841, + 1.7740089318781982, + -4.0438105335843275, + -1.3541259443705087, + -1.0127819488917504, + -1.296275669768132, + -3.382031503513602, + 3.6088961624755087, + 1.1059495672446507, + 1.0098298472278604, + 1.3308048809512305, + 674.48164812617, + -1.8262648177123793, + -1.0905628904710256, + -1.0147177937410943, + -1.9084170317118503, + 34.01758868100464, + 1.744766529684393, + 1.0062737733871185, + 1.121169915025429, + 2.0102736037923585, + -3.103359378455869, + -1.2675841156247938, + -1.0032765374195936, + -1.3900975167118756, + -4.542407231048973, + 2.846494785697001, + 1.0697434641376224, + 1.0242064529134087, + 1.4335231513214022, + 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a/base/special/sec/test/fixtures/julia/runner.jl b/base/special/sec/test/fixtures/julia/runner.jl new file mode 100644 index 000000000..54f5cec55 --- /dev/null +++ b/base/special/sec/test/fixtures/julia/runner.jl @@ -0,0 +1,113 @@ +#!/usr/bin/env julia +# +# @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. + +import JSON + +""" + gen( domain, name ) + +Generate fixture data and write to file. + +# Arguments + +* `domain`: domain +* `name::AbstractString`: output filename + +# Examples + +``` julia +julia> x = range( -1000.0, stop = 1000.0, length = 2022 ); +julia> gen( x, \"data.json\" ); +``` +""" +function gen( domain, name ) + x = collect( domain ); + y = sec.( x ); + + # 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) ); + close( outfile ); +end + +# Get the filename: +file = @__FILE__; + +# Extract the directory in which this file resides: +dir = dirname( file ); + +# Negative tiny values: +x = range( -1.0e-300, stop = -1.0e-308, length = 500 ); +gen( x, "tiny_negative.json" ); + +# Positive tiny values: +x = range( 1.0e-300, stop = 1.0e-308, length = 500 ); +gen( x, "tiny_positive.json" ); + +# Small(er) values: +x = range( -pi, stop = pi, length = 2022 ); +gen( x, "smaller.json" ); + +# Negative small values: +x = range( -4.0*pi, stop = -pi, length = 1000 ); +gen( x, "small_negative.json" ); + +# Positive small values: +x = range( pi, stop = 4.0*pi, length = 1000 ); +gen( x, "small_positive.json" ); + +# Negative medium values: +x = range( -4.0*pi, stop = -12.0*pi, length = 1000 ); +gen( x, "medium_negative.json" ); + +# Positive medium values: +x = range( 4.0*pi, stop = 12.0*pi, length = 1000 ); +gen( x, "medium_positive.json" ); + +# Large negative values: +x = range( -12.0*pi, stop = -256.0*pi, length = 1000 ); +gen( x, "large_negative.json" ); + +# Large positive values: +x = range( 12.0*pi, stop = 256.0*pi, length = 1000 ); +gen( x, "large_positive.json" ); + +# Very large negative values: +x = range( -2.0^20*(pi/2.0), stop = -2.0^60*(pi/2.0), length = 500 ); +gen( x, "very_large_negative.json" ); + +# Very large positive values: +x = range( 2.0^20*(pi/2.0), stop = 2.0^60*(pi/2.0), length = 500 ); +gen( x, "very_large_positive.json" ); + +# Huge negative values: +x = range( -2.0^60*(pi/2.0), stop = -2.0^1000*(pi/2.0), length = 1000 ) +gen( x, "huge_negative.json" ); + +# Huge positive values: +x = range( 2.0^20*(pi/2.0), stop = 2.0^60*(pi/2.0), length = 1000 ) +gen( x, "huge_positive.json" ); diff --git a/base/special/sec/test/fixtures/julia/small_negative.json b/base/special/sec/test/fixtures/julia/small_negative.json new file mode 100644 index 000000000..fd1b49c06 --- /dev/null +++ b/base/special/sec/test/fixtures/julia/small_negative.json @@ -0,0 +1,2004 @@ +{ + "expected": [1, + 1.0000445038300918, + 1.0001780351283918, + 1.0004006533404892, + 1.0007124576141289, + 1.0011135869070056, + 1.0016042201379842, + 1.0021845763820487, + 1.0028549151093769, + 1.0036155364690282, + 1.004466781617821, + 1.0054090330950751, + 1.0064427152439857, + 1.0075682946804958, + 1.0087862808106407, + 1.0100972263974366, + 1.0115017281784915, + 1.0130004275356452, + 1.0145940112180385, + 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-0,0 +1,396 @@ +/** +* @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 tape = require( 'tape' ); +var isnan = require( './../../../../base/assert/is-nan' ); +var abs = require( './../../../../base/special/abs' ); +var PI = require( '@stdlib/constants/float64/pi' ); +var EPS = require( '@stdlib/constants/float64/eps' ); +var PINF = require( '@stdlib/constants/float64/pinf' ); +var NINF = require( '@stdlib/constants/float64/ninf' ); +var sec = require( './../lib' ); + + +// FIXTURES // + +var hugeNegative = require( './fixtures/julia/huge_negative.json' ); +var hugePositive = require( './fixtures/julia/huge_positive.json' ); +var veryLargeNegative = require( './fixtures/julia/very_large_negative.json' ); +var veryLargePositive = require( './fixtures/julia/very_large_positive.json' ); +var largeNegative = require( './fixtures/julia/large_negative.json' ); +var largePositive = require( './fixtures/julia/large_positive.json' ); +var mediumNegative = require( './fixtures/julia/medium_negative.json' ); +var mediumPositive = require( './fixtures/julia/medium_positive.json' ); +var smallNegative = require( './fixtures/julia/small_negative.json' ); +var smallPositive = require( './fixtures/julia/small_positive.json' ); +var smaller = require( './fixtures/julia/smaller.json' ); +var tinyNegative = require( './fixtures/julia/tiny_negative.json' ); +var tinyPositive = require( './fixtures/julia/tiny_positive.json' ); + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.true( typeof sec, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function computes the secant (huge negative values)', function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = hugeNegative.x; + expected = hugeNegative.expected; + + for ( i = 0; i < x.length; i++ ) { + y = sec( x[ i ] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 1.4 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + } + t.end(); +}); + +tape( 'the function computes the secant (huge positive values)', function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = hugePositive.x; + expected = hugePositive.expected; + + for ( i = 0; i < x.length; i++ ) { + y = sec( x[ i ] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 1.4 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + } + t.end(); +}); + +tape( 'the function computes the secant (very large positive values)', function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = veryLargePositive.x; + expected = veryLargePositive.expected; + + for ( i = 0; i < x.length; i++ ) { + y = sec( x[ i ] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 1.4 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + } + t.end(); +}); + +tape( 'the function computes the secant (very large negative values)', function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = veryLargeNegative.x; + expected = veryLargeNegative.expected; + + for (i = 0; i < x.length; i++) { + y = sec( x[ i ] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 1.4 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + } + t.end(); +}); + +tape( 'the function computes the secant (large positive values)', function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = largePositive.x; + expected = largePositive.expected; + + for ( i = 0; i < x.length; i++ ) { + y = sec( x[ i ] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 1.4 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + } + t.end(); +}); + +tape( 'the function computes the secant (large negative values)', function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = largeNegative.x; + expected = largeNegative.expected; + + for ( i = 0; i < x.length; i++ ) { + y = sec( x[ i ] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 1.4 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + } + t.end(); +}); + +tape( 'the function computes the secant (medium positive values)', function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = mediumPositive.x; + expected = mediumPositive.expected; + + for ( i = 0; i < x.length; i++ ) { + y = sec( x[ i ] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 1.4 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + } + t.end(); +}); + +tape( 'the function computes the secant (medium negative values)', function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = mediumNegative.x; + expected = mediumNegative.expected; + + for ( i = 0; i < x.length; i++ ) { + y = sec( x[ i ] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 1.4 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + } + t.end(); +}); + +tape( 'the function computes the secant (small positive values)', function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = smallPositive.x; + expected = smallPositive.expected; + + for ( i = 0; i < x.length; i++ ) { + y = sec( x[ i ] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ]); + } else { + delta = abs( y - expected[ i ] ); + tol = 1.4 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + } + t.end(); +}); + +tape( 'the function computes the secant (small negative values)', function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = smallNegative.x; + expected = smallNegative.expected; + + for ( i = 0; i < x.length; i++ ) { + y = sec( x[ i ] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ]); + } else { + delta = abs( y - expected[ i ] ); + tol = 1.4 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + } + t.end(); +}); + +tape( 'the function computes the secant (smaller values)', function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = smaller.x; + expected = smaller.expected; + + for ( i = 0; i < x.length; i++ ) { + y = sec( x[ i ] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 1.4 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + } + t.end(); +}); + +tape( 'the function computes the secant (tiny positive values)', function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = tinyPositive.x; + expected = tinyPositive.expected; + + for ( i = 0; i < x.length; i++ ) { + y = sec(x[i]); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 1.4 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + } + t.end(); +}); + +tape( 'the function computes the secant (tiny negative values)', function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = tinyNegative.x; + expected = tinyNegative.expected; + + for ( i = 0; i < x.length; i++ ) { + y = sec( x[ i ] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 1.4 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + } + t.end(); +}); + +tape( 'if provided a multiple of `-pi/2`, the function does not return `~+infinity` due to floating-point rounding errors', function test( t ) { + t.notEqual( sec( -PI / 2 ), PINF, 'returns expected value'); + t.end(); +}); + +tape( 'if provided a multiple of `pi/2`, the function does not return `~+infinity`', function test( t ) { + t.notEqual( sec( PI / 2 ), NINF, 'returns expected value'); + t.end(); +}); + +tape( 'if provided a `NaN`, the function returns `NaN`', function test( t ) { + var v = sec( NaN ); + t.equal(isnan(v), true, 'returns NaN'); + t.end(); +}); + +tape( 'if provided `+infinity`, the function returns `NaN`', function test( t ) { + var v = sec( PINF ); + t.equal( isnan( v ), true, 'returns NaN' ); + t.end(); +}); + +tape( 'if provided `-infinity`, the function returns `NaN`', function test( t ) { + var v = sec( NINF ); + t.equal( isnan( v ), true, 'returns NaN' ); + t.end(); +}); diff --git a/base/special/sec/test/test.native.js b/base/special/sec/test/test.native.js new file mode 100644 index 000000000..613114661 --- /dev/null +++ b/base/special/sec/test/test.native.js @@ -0,0 +1,405 @@ +/** +* @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 abs = require( './../../../../base/special/abs' ); +var PI = require( '@stdlib/constants/float64/pi' ); +var EPS = require( '@stdlib/constants/float64/eps' ); +var PINF = require( '@stdlib/constants/float64/pinf' ); +var NINF = require( '@stdlib/constants/float64/ninf' ); +var tryRequire = require( '@stdlib/utils/try-require' ); + + +// VARIABLES // + +var sec = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( sec instanceof Error ) +}; + + +// FIXTURES // + +var hugeNegative = require( './fixtures/julia/huge_negative.json' ); +var hugePositive = require( './fixtures/julia//huge_positive.json' ); +var veryLargeNegative = require( './fixtures/julia//very_large_negative.json' ); +var veryLargePositive = require( './fixtures/julia//very_large_positive.json' ); +var largeNegative = require( './fixtures/julia//large_negative.json' ); +var largePositive = require( './fixtures/julia//large_positive.json' ); +var mediumNegative = require( './fixtures/julia//medium_negative.json' ); +var mediumPositive = require( './fixtures/julia//medium_positive.json' ); +var smallNegative = require( './fixtures/julia//small_negative.json' ); +var smallPositive = require( './fixtures/julia//small_positive.json' ); +var smaller = require( './fixtures/julia//smaller.json' ); +var tinyNegative = require( './fixtures/julia//tiny_negative.json' ); +var tinyPositive = require( './fixtures/julia//tiny_positive.json' ); + + +// TESTS // + +tape( 'main export is a function', opts, function test( t ) { + t.ok(true, __filename); + t.true(typeof sec, 'function', 'main export is a function'); + t.end(); +}); + +tape( 'the function computes the secant (huge negative values)', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = hugeNegative.x; + expected = hugeNegative.expected; + + for ( i = 0; i < x.length; i++ ) { + y = sec( x[ i ] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 1.4 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + } + t.end(); +}); + +tape( 'the function computes the secant (huge positive values)', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = hugePositive.x; + expected = hugePositive.expected; + + for ( i = 0; i < x.length; i++ ) { + y = sec( x[ i ] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 1.4 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + } + t.end(); +}); + +tape( 'the function computes the secant (very large positive values)', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = veryLargePositive.x; + expected = veryLargePositive.expected; + + for ( i = 0; i < x.length; i++ ) { + y = sec( x[ i ] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 1.4 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + } + t.end(); +}); + +tape( 'the function computes the secant (very large negative values)', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = veryLargeNegative.x; + expected = veryLargeNegative.expected; + + for ( i = 0; i < x.length; i++ ) { + y = sec( x[ i ] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] ); + } else { + delta = abs(y - expected[ i ]); + tol = 1.4 * EPS * abs(expected[ i ]); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + } + t.end(); +}); + +tape( 'the function computes the secant (large positive values)', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = largePositive.x; + expected = largePositive.expected; + + for ( i = 0; i < x.length; i++ ) { + y = sec( x[ i ] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 1.4 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + } + t.end(); +}); + +tape( 'the function computes the secant (large negative values)', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = largeNegative.x; + expected = largeNegative.expected; + + for ( i = 0; i < x.length; i++ ) { + y = sec( x[ i ] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 1.4 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + } + t.end(); +}); + +tape( 'the function computes the secant (medium positive values)', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = mediumPositive.x; + expected = mediumPositive.expected; + + for ( i = 0; i < x.length; i++ ) { + y = sec( x[ i ] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 1.4 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + } + t.end(); +}); + +tape( 'the function computes the secant (medium negative values)', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = mediumNegative.x; + expected = mediumNegative.expected; + + for ( i = 0; i < x.length; i++ ) { + y = sec( x[ i ] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 1.4 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + } + t.end(); +}); + +tape( 'the function computes the secant (small positive values)', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = smallPositive.x; + expected = smallPositive.expected; + + for ( i = 0; i < x.length; i++ ) { + y = sec( x[ i ] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 1.4 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + } + t.end(); +}); + +tape( 'the function computes the secant (small negative values)', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = smallNegative.x; + expected = smallNegative.expected; + + for ( i = 0; i < x.length; i++ ) { + y = sec( x[ i ] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 1.4 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + } + t.end(); +}); + +tape( 'the function computes the secant (smaller values)', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = smaller.x; + expected = smaller.expected; + + for ( i = 0; i < x.length; i++ ) { + y = sec( x[ i ] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 1.4 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + } + t.end(); +}); + +tape( 'the function computes the secant (tiny positive values)', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = tinyPositive.x; + expected = tinyPositive.expected; + + for ( i = 0; i < x.length; i++ ) { + y = sec( x[ i ] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 1.4 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + } + t.end(); +}); + +tape( 'the function computes the secant (tiny negative values)', opts, function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = tinyNegative.x; + expected = tinyNegative.expected; + + for ( i = 0; i < x.length; i++ ) { + y = sec( x[ i ] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 1.4 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' ); + } + } + t.end(); +}); + +tape( 'if provided a multiple of `-pi/2`, the function does not return `~+infinity` due to floating-point rounding errors', opts, function test( t ) { + t.notEqual( sec( -PI / 2 ), PINF, 'returns expected value' ); + t.end(); +}); + +tape( 'if provided a multiple of `pi/2`, the function does not return `~+infinity`', opts, function test( t ) { + t.notEqual( sec( PI / 2 ), NINF, 'returns expected value' ); + t.end(); +}); + +tape( 'if provided a `NaN`, the function returns `expected value`', opts, function test( t ) { + var v = sec( NaN ); + t.equal( isnan( v ), true, 'returns NaN' ); + t.end(); +}); + +tape( 'if provided `+infinity`, the function returns `expected value`', opts, function test( t ) { + var v = sec( PINF ); + t.equal( isnan( v ), true, 'returns NaN' ); + t.end(); +}); + +tape( 'if provided `-infinity`, the function returns `expected value`', opts, function test( t ) { + var v = sec( NINF ); + t.equal( isnan( v ), true, 'returns NaN' ); + t.end(); +});