diff --git a/LICENSE b/LICENSE index 5965a0b2c..d1534e6cb 100644 --- a/LICENSE +++ b/LICENSE @@ -207,6 +207,28 @@ FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. +* Cephes + +Copyright (c) 1984-2000 Stephen L. Moshier + +Some software in this archive may be from the book _Methods and Programs for +Mathematical Functions_ (Prentice-Hall or Simon & Schuster International, 1989) +or from the Cephes Mathematical Library, a commercial product. In either event, +it is copyrighted by the author. What you see here may be used freely but it +comes with no support or guarantee. + +Stephen L. Moshier +moshier@na-net.ornl.gov + +* FreeBSD + +Copyright (C) 1993-2004 by Sun Microsystems, Inc. All rights reserved. + +Developed at SunPro, a Sun Microsystems, Inc. business. +Permission to use, copy, modify, and distribute this +software is freely granted, provided that this notice +is preserved. + * Go Copyright (c) 2009 The Go Authors. All rights reserved. @@ -237,28 +259,6 @@ THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. -* Cephes - -Copyright (c) 1984-2000 Stephen L. Moshier - -Some software in this archive may be from the book _Methods and Programs for -Mathematical Functions_ (Prentice-Hall or Simon & Schuster International, 1989) -or from the Cephes Mathematical Library, a commercial product. In either event, -it is copyrighted by the author. What you see here may be used freely but it -comes with no support or guarantee. - -Stephen L. Moshier -moshier@na-net.ornl.gov - -* FreeBSD - -Copyright (C) 1993-2004 by Sun Microsystems, Inc. All rights reserved. - -Developed at SunPro, a Sun Microsystems, Inc. business. -Permission to use, copy, modify, and distribute this -software is freely granted, provided that this notice -is preserved. - * Faddeeva Copyright (c) 2012 Massachusetts Institute of Technology @@ -282,18 +282,13 @@ LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. -* SLATEC Common Mathematical Library - -Public domain. - -* FDLIBM - -Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. - -Developed at SunPro, a Sun Microsystems, Inc. business. -Permission to use, copy, modify, and distribute this -software is freely granted, provided that this notice -is preserved. +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT +SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE +FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE, +ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +DEALINGS IN THE SOFTWARE. Apache License Version 2.0, January 2004 http://www.apache.org/licenses/ @@ -325,3 +320,11 @@ LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. +* SLATEC Common Mathematical Library + +Public domain. + +* FDLIBM + +Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. + diff --git a/base/special/asecd/README.md b/base/special/asecd/README.md new file mode 100644 index 000000000..cf41b31b9 --- /dev/null +++ b/base/special/asecd/README.md @@ -0,0 +1,104 @@ + + +# asecd + +> Compute the [arcsecant][arcsecant] (in degrees) of a double-precision floating-point number. + +
+ +## Usage + +```javascript +var asecd = require( '@stdlib/math/base/special/asecd' ); +``` + +#### asecd( x ) + +Computes the [arcsecant][arcsecant] (in degrees) of a double-precision floating-point number. + +```javascript +var sqrt = require( '@stdlib/math/base/special/sqrt' ); +var v = asecd( 1 ); +// returns 0.0 + +v = asecd( 2 * sqrt( 3 ) / 3 ); +// returns ~30.0 + +v = asecd( sqrt( 2 ) ); +// returns ~45.0 + +v = asecd( 2 ); +// returns ~60.0 + +v = asecd( Infinity ); +// returns 90.0 + +v = asecd( NaN ); +// returns NaN +``` + +
+ + + +
+ +## Examples + + + +```javascript +var linspace = require( '@stdlib/array/base/linspace' ); +var asecd = require( '@stdlib/math/base/special/asecd' ); + +var x = linspace( -1.0, 1.0, 100 ); + +var i; +for ( i = 0; i < x.length; i++ ) { + console.log( asecd( x[ i ] ) ); +} +``` + +
+ + + + + +
+ +
+ + + + + +
+ +[arcsecant]: https://en.wikipedia.org/wiki/Inverse_trigonometric_functions + + + + + +
+ + diff --git a/base/special/asecd/benchmark/benchmark.js b/base/special/asecd/benchmark/benchmark.js new file mode 100644 index 000000000..14382e238 --- /dev/null +++ b/base/special/asecd/benchmark/benchmark.js @@ -0,0 +1,51 @@ +/** +* @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 pkg = require( './../package.json' ).name; +var asecd = 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()*2.0 ) + 1.0; + y = asecd( 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/asecd/docs/repl.txt b/base/special/asecd/docs/repl.txt new file mode 100644 index 000000000..8efa3174a --- /dev/null +++ b/base/special/asecd/docs/repl.txt @@ -0,0 +1,29 @@ + +{{alias}}( x ) + Computes the arcsecant (in degrees) of a double-precision floating-point + number. + + If `x` does not satisy `x >= 1` or `x <= -1`, the function returns NaN. + + Parameters + ---------- + x: number + Input value. + + Returns + ------- + y: number + Arcsecant (in degrees). + + Examples + -------- + > var y = {{alias}}( 0.0 ) + NaN + > y = {{alias}}( 2 ) + ~60.0 + > y = {{alias}}( NaN ) + NaN + + See Also + -------- + diff --git a/base/special/asecd/docs/types/index.d.ts b/base/special/asecd/docs/types/index.d.ts new file mode 100644 index 000000000..acd0c7efc --- /dev/null +++ b/base/special/asecd/docs/types/index.d.ts @@ -0,0 +1,56 @@ +/* +* @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 arcsecant (in degrees) of a double-precision floating-point number. +* +* @param x - input value +* @returns arcsecant (in degrees) +* +* @example +* var v = asecd( 1 ); +* // returns 0.0 +* +* @example +* var v = asecd( 2 * Math.sqrt( 3 ) / 3 ); +* // returns ~30.0 +* +* @example +* var v = asecd( Math.sqrt( 2 ) ); +* // returns ~45.0 +* +* @example +* var v = asecd( 2 ); +* // returns ~60.0 +* +* @example +* var v = asecd( Infinity ); +* // returns 90.0 +* +* @example +* var v = asecd( NaN ); +* // returns NaN +*/ +declare function asecd( x: number ): number; + + +// EXPORTS // + +export = asecd; diff --git a/base/special/asecd/docs/types/test.ts b/base/special/asecd/docs/types/test.ts new file mode 100644 index 000000000..b3ff1efc5 --- /dev/null +++ b/base/special/asecd/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 asecd = require( './index' ); + + +// TESTS // + +// The function returns a number... +{ + asecd( 1.2 ); // $ExpectType number +} + +// The compiler throws an error if the function is provided a value other than a number... +{ + asecd( true ); // $ExpectError + asecd( false ); // $ExpectError + asecd( null ); // $ExpectError + asecd( undefined ); // $ExpectError + asecd( '5' ); // $ExpectError + asecd( [] ); // $ExpectError + asecd( {} ); // $ExpectError + asecd( ( x: number ): number => x ); // $ExpectError +} + +// The compiler throws an error if the function is provided insufficient arguments... +{ + asecd(); // $ExpectError +} diff --git a/base/special/asecd/examples/index.js b/base/special/asecd/examples/index.js new file mode 100644 index 000000000..ee2a14839 --- /dev/null +++ b/base/special/asecd/examples/index.js @@ -0,0 +1,29 @@ +/** +* @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 asecd = require( './../lib' ); + +var x = linspace( -10.0, 10.0, 100 ); + +var i; +for ( i = 0; i < x.length; i++ ) { + console.log( 'asecd(%d) = %d', x[ i ], asecd( x[ i ] ) ); +} diff --git a/base/special/asecd/lib/index.js b/base/special/asecd/lib/index.js new file mode 100644 index 000000000..9d4ac4f04 --- /dev/null +++ b/base/special/asecd/lib/index.js @@ -0,0 +1,55 @@ +/** +* @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'; + +/** +* Compute the arcsecant (in degrees) of a double-precision floating-point number. +* +* @module @stdlib/math/base/special/asecd +* +* @example +* var asecd = require( '@stdlib/math/base/special/asecd' ); +* +* var v = asecd( 1 ); +* // returns 0.0 +* +* v = asecd( 2 * Math.sqrt( 3 ) / 3 ); +* // returns ~30.0 +* +* v = asecd( Math.sqrt( 2 ) ); +* // returns ~45.0 +* +* v = asecd( 2 ); +* // returns ~60.0 +* +* v = asecd( Infinity ); +* // returns 90.0 +* +* v = asecd( NaN ); +* // returns NaN +*/ + +// MODULES // + +var main = require( './main.js' ); + + +// EXPORTS // + +module.exports = main; diff --git a/base/special/asecd/lib/main.js b/base/special/asecd/lib/main.js new file mode 100644 index 000000000..8ded6bc8e --- /dev/null +++ b/base/special/asecd/lib/main.js @@ -0,0 +1,67 @@ +/** +* @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 rad2deg = require( './../../../../base/special/rad2deg' ); +var asec = require( './../../../../base/special/asec' ); + + +// MAIN // + +/** +* Computes the arcsecant (in degrees) of a double-precision floating-point number. +* +* @param {number} x - input value +* @returns {number} arcsecant (in degrees) +* +* @example +* var v = asecd( 1 ); +* // returns 0.0 +* +* @example +* var v = asecd( 2 * Math.sqrt( 3 ) / 3 ); +* // returns ~30.0 +* +* @example +* var v = asecd( Math.sqrt( 2 ) ); +* // returns ~45.0 +* +* @example +* var v = asecd( 2 ); +* // returns ~60.0 +* +* @example +* var v = asecd( Infinity ); +* // returns 90.0 +* +* @example +* var v = asecd( NaN ); +* // returns NaN +*/ +function asecd( x ) { + var rad = asec( x ); + return rad2deg( rad ); +} + + +// EXPORTS // + +module.exports = asecd; diff --git a/base/special/asecd/package.json b/base/special/asecd/package.json new file mode 100644 index 000000000..cc8c3298e --- /dev/null +++ b/base/special/asecd/package.json @@ -0,0 +1,68 @@ +{ + "name": "@stdlib/math/base/special/asecd", + "version": "0.0.0", + "description": "Compute the arcsecant (in degrees) of a double-precision floating-point number.", + "license": "Apache-2.0", + "author": { + "name": "The Stdlib Authors", + "url": "https://github.com/stdlib-js/stdlib/graphs/contributors" + }, + "contributors": [ + { + "name": "The Stdlib Authors", + "url": "https://github.com/stdlib-js/stdlib/graphs/contributors" + } + ], + "main": "./lib", + "gypfile": true, + "directories": { + "benchmark": "./benchmark", + "doc": "./docs", + "example": "./examples", + "lib": "./lib", + "test": "./test" + }, + "types": "./docs/types", + "scripts": {}, + "homepage": "https://github.com/stdlib-js/stdlib", + "repository": { + "type": "git", + "url": "git://github.com/stdlib-js/stdlib.git" + }, + "bugs": { + "url": "https://github.com/stdlib-js/stdlib/issues" + }, + "dependencies": {}, + "devDependencies": {}, + "engines": { + "node": ">=0.10.0", + "npm": ">2.7.0" + }, + "os": [ + "aix", + "darwin", + "freebsd", + "linux", + "macos", + "openbsd", + "sunos", + "win32", + "windows" + ], + "keywords": [ + "stdlib", + "stdmath", + "mathematics", + "math", + "math.asin", + "asin", + "degree", + "arcsecant", + "sine", + "inverse", + "trig", + "trigonometry", + "radians", + "angle" + ] +} diff --git a/base/special/asecd/test/fixtures/julia/REQUIRE b/base/special/asecd/test/fixtures/julia/REQUIRE new file mode 100644 index 000000000..ae40bf736 --- /dev/null +++ b/base/special/asecd/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/asecd/test/fixtures/julia/negative.json b/base/special/asecd/test/fixtures/julia/negative.json new file mode 100644 index 000000000..175286887 --- /dev/null +++ b/base/special/asecd/test/fixtures/julia/negative.json @@ -0,0 +1 @@ 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\ No newline at end of file diff --git a/base/special/asecd/test/fixtures/julia/runner.jl b/base/special/asecd/test/fixtures/julia/runner.jl new file mode 100644 index 000000000..a9923274a --- /dev/null +++ b/base/special/asecd/test/fixtures/julia/runner.jl @@ -0,0 +1,69 @@ +#!/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( -1, stop = 1, length = 2001 ); +julia> gen( x, \"data.json\" ); +``` +""" +function gen( domain, name ) + x = collect( domain ); + y = asecd.( 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 ); + +# Generate fixture data for negative values: +x = range( -1.0, stop = -1000.0, length = 2003 ); +gen( x, "negative.json" ); + +# Generate fixture data for positive values: +x = range( 1.0, stop = 1000.0, length = 2003 ); +gen( x, "positive.json" ); \ No newline at end of file diff --git a/base/special/asecd/test/test.js b/base/special/asecd/test/test.js new file mode 100644 index 000000000..1235bba1e --- /dev/null +++ b/base/special/asecd/test/test.js @@ -0,0 +1,119 @@ +/** +* @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 EPS = require( '@stdlib/constants/float64/eps' ); +var randu = require('@stdlib/random/base/randu'); +var asecd = require( './../lib' ); + + +// FIXTURES // + +var negative = require( './fixtures/julia/negative.json' ); +var positive = require( './fixtures/julia/positive.json' ); + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof asecd, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function returns `NaN` if provided `NaN`', function test( t ) { + var v = asecd( NaN ); + t.equal( isnan( v ), true, 'returns NaN' ); + t.end(); +}); + +tape( 'the function returns `NaN` if provided a value greater than `-1`', function test( t ) { + var v; + var i; + + for ( i = 0; i < 1e3; i++ ) { + v = -randu() - EPS; + t.equal( isnan( asecd( v ) ), true, 'returns NaN when provided '+v ); + } + t.end(); +}); + +tape( 'the function returns `NaN` if provided a value less than `+1`', function test( t ) { + var v; + var i; + + for ( i = 0; i < 1e3; i++ ) { + v = (randu()) + EPS; + t.equal( isnan( asecd( v ) ), true, 'returns NaN when provided '+v ); + } + t.end(); +}); + +tape( 'the function computes the arcsecant in degrees (negative values)', function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = negative.x; + expected = negative.expected; + + for ( i = 0; i < x.length; i++ ) { + y = asecd( x[i] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: '+x[i]+'. E: '+expected[i] ); + } else { + delta = abs( y - expected[i] ); + tol = 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 arcsecant in degrees (positive values)', function test( t ) { + var expected; + var delta; + var tol; + var x; + var y; + var i; + + x = positive.x; + expected = positive.expected; + + for ( i = 0; i < x.length; i++ ) { + y = asecd( x[i] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'x: '+x[i]+'. E: '+expected[i] ); + } else { + delta = abs( y - expected[i] ); + tol = EPS * abs( expected[i] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. y: '+y+'. E: '+expected[i]+'. tol: '+tol+'. Δ: '+delta+'.' ); + } + } + t.end(); +});