diff --git a/lib/node_modules/@stdlib/math/base/special/sec/README.md b/lib/node_modules/@stdlib/math/base/special/sec/README.md new file mode 100644 index 00000000000..f5b5d068181 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/sec/README.md @@ -0,0 +1,76 @@ + + +# Secant + +> Compute the [secant][secant] of a number. + +
+ +## Usage + +```javascript +var sec = require( '@stdlib/math/base/special/sec' ); +``` + +#### sec( x ) + +Computes the [secant][secant] of a `number` (in radians). + +```javascript +var v = sec( 0.0 ); +// returns 1.0 + +v = sec( 3.141592653589793/4.0 ); +// returns ~1.4144 + +v = sec( -3.141592653589793/6.0 ); +// returns ~1.1547 + +v = sec( NaN ); +// returns NaN +``` + +
+ + + +
+ +## Examples + + + +```javascript +var linspace = require( '@stdlib/array/base/linspace' ); +var TWO_PI = require( '@stdlib/constants/float64/two-pi' ); +var sec = require( '@stdlib/math/base/special/sec' ); + +var x = linspace( 0.0, TWO_PI, 100 ); + +var i; +for ( i = 0; i < x.length; i++ ) { + console.log( sec( x[ i ] ) ); +} +``` + +
+ + diff --git a/lib/node_modules/@stdlib/math/base/special/sec/benchmark/benchmark.js b/lib/node_modules/@stdlib/math/base/special/sec/benchmark/benchmark.js new file mode 100644 index 00000000000..abc368e63d9 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/sec/benchmark/benchmark.js @@ -0,0 +1,72 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2018 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( '@stdlib/math/base/assert/is-nan' ); +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 / Math.cos( x ); // eslint-disable-line stdlib/no-builtin-math + if ( isnan( y ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( y ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); diff --git a/lib/node_modules/@stdlib/math/base/special/sec/examples/index.js b/lib/node_modules/@stdlib/math/base/special/sec/examples/index.js new file mode 100644 index 00000000000..2f07f6cc98c --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/sec/examples/index.js @@ -0,0 +1,30 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2018 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( 0.0, 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/lib/node_modules/@stdlib/math/base/special/sec/lib/index.js b/lib/node_modules/@stdlib/math/base/special/sec/lib/index.js new file mode 100644 index 00000000000..a276951d4bb --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/sec/lib/index.js @@ -0,0 +1,46 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2018 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 secant of a number. +* +* @module @stdlib/math/base/special/sec +* +* @example +* var sec = require( '@stdlib/math/base/special/sec' ); +* +* var v = sec( 0.0 ); +* // returns 1.0 +* +* v = sec( 3.141592653589793/4.0 ); +* // returns ~1.4144 +* +* v = sec( -3.141592653589793/6.0 ); +* // returns ~1.1547 +*/ + +// MODULES // + +var sec = require( './sec.js' ); + + +// EXPORTS // + +module.exports = sec; diff --git a/lib/node_modules/@stdlib/math/base/special/sec/lib/sec.js b/lib/node_modules/@stdlib/math/base/special/sec/lib/sec.js new file mode 100644 index 00000000000..e2e9dd08960 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/sec/lib/sec.js @@ -0,0 +1,69 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2018 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +* +* +* ## Notice +* +* The following copyright, license, and long comment were part of the original implementation available as part of [FreeBSD]{@link https://svnweb.freebsd.org/base/release/9.3.0/lib/msun/src/s_cos.c}. The implementation follows the original, but has been modified for JavaScript. +* +* ```text +* Copyright (C) 1993 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. +* ``` +*/ + +'use strict'; + +// MODULES // +var cos = require('@stdlib/math/base/special/cos/lib'); + +// MAIN // + +/** +* Computes the secant of a number. +* +* @param {number} x - input value (in radians) +* @returns {number} secant +* +* @example +* var v = sec( 0.0 ); +* // returns 1.0 +* +* @example +* var v = sec( 3.141592653589793/4.0 ); +* // returns ~1.4144 +* +* @example +* var v = sec( -3.141592653589793/6.0 ); +* // returns ~1.1547 +* +* @example +* var v = sec( NaN ); +* // returns NaN +*/ +function sec( x ) { + return 1 / cos(x); +} + + +// EXPORTS // + +module.exports = sec; diff --git a/lib/node_modules/@stdlib/math/base/special/sec/package.json b/lib/node_modules/@stdlib/math/base/special/sec/package.json new file mode 100644 index 00000000000..03604980272 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/sec/package.json @@ -0,0 +1,64 @@ +{ + "name": "@stdlib/math/base/special/cos", + "version": "0.0.0", + "description": "Compute the cosine of a 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", + "directories": { + "benchmark": "./benchmark", + "doc": "./docs", + "example": "./examples", + "lib": "./lib", + "scripts": "./scripts", + "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.cos", + "cos", + "cosine", + "trig", + "trigonometry", + "radians" + ] +} diff --git a/lib/node_modules/@stdlib/math/base/special/sec/test/fixtures/julia/REQUIRE b/lib/node_modules/@stdlib/math/base/special/sec/test/fixtures/julia/REQUIRE new file mode 100644 index 00000000000..308c3be89c8 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/sec/test/fixtures/julia/REQUIRE @@ -0,0 +1,2 @@ +julia 1.5 +JSON 0.21 diff --git a/lib/node_modules/@stdlib/math/base/special/sec/test/fixtures/julia/huge_negative.json b/lib/node_modules/@stdlib/math/base/special/sec/test/fixtures/julia/huge_negative.json new file mode 100644 index 00000000000..a16bb1fe134 --- /dev/null +++ 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\ No newline at end of file diff --git a/lib/node_modules/@stdlib/math/base/special/sec/test/fixtures/julia/huge_positive.json b/lib/node_modules/@stdlib/math/base/special/sec/test/fixtures/julia/huge_positive.json new file mode 100644 index 00000000000..240b326036a --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/sec/test/fixtures/julia/huge_positive.json @@ -0,0 +1 @@ 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\ No newline at end of file diff --git a/lib/node_modules/@stdlib/math/base/special/sec/test/fixtures/julia/large_negative.json b/lib/node_modules/@stdlib/math/base/special/sec/test/fixtures/julia/large_negative.json new file mode 100644 index 00000000000..0ee10472c21 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/sec/test/fixtures/julia/large_negative.json @@ -0,0 +1 @@ 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\ No newline at end of file diff --git a/lib/node_modules/@stdlib/math/base/special/sec/test/fixtures/julia/large_positive.json b/lib/node_modules/@stdlib/math/base/special/sec/test/fixtures/julia/large_positive.json new file mode 100644 index 00000000000..be74e3c6594 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/sec/test/fixtures/julia/large_positive.json @@ -0,0 +1 @@ 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\ No newline at end of file diff --git a/lib/node_modules/@stdlib/math/base/special/sec/test/fixtures/julia/medium_negative.json b/lib/node_modules/@stdlib/math/base/special/sec/test/fixtures/julia/medium_negative.json new file mode 100644 index 00000000000..98cd1a255cc --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/sec/test/fixtures/julia/medium_negative.json @@ -0,0 +1 @@ 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\ No newline at end of file diff --git a/lib/node_modules/@stdlib/math/base/special/sec/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/math/base/special/sec/test/fixtures/julia/runner.jl new file mode 100644 index 00000000000..bf2bdd3a619 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/sec/test/fixtures/julia/runner.jl @@ -0,0 +1,85 @@ +#!/usr/bin/env julia +# +# @license Apache-2.0 +# +# Copyright (c) 2018 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 = 2001 ); +julia> gen( x, \"data.json\" ); +``` +""" +function gen( domain, name ) + x = collect( domain ); + y = 1 / cos.( 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 medium sized values: +x = range( -256.0*pi, stop = 0.0, length = 4000 ) +gen( x, "medium_negative.json" ); + +# Positive medium sized values: +x = range( 0.0, stop = 256.0*pi, length = 4000 ) +gen( x, "medium_positive.json" ); + +# Negative large values: +x = range( -2.0^20*(pi/2.0), stop = -2.0^60*(pi/2.0), length = 4000 ) +gen( x, "large_negative.json" ); + +# Positive large values: +x = range( 2.0^20*(pi/2.0), stop = 2.0^60*(pi/2.0), length = 4000 ) +gen( x, "large_positive.json" ); + +# Negative huge values: +x = range( -2.0^60*(pi/2.0), stop = -2.0^1000*(pi/2.0), length = 4000 ) +gen( x, "huge_negative.json" ); + +# Positive huge values: +x = range( 2.0^60*(pi/2.0), stop = 2.0^1000*(pi/2.0), length = 4000 ) +gen( x, "huge_positive.json" ); diff --git a/lib/node_modules/@stdlib/math/base/special/sec/test/test.js b/lib/node_modules/@stdlib/math/base/special/sec/test/test.js new file mode 100644 index 00000000000..5b97b87303a --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/sec/test/test.js @@ -0,0 +1,216 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2018 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var tape = require( 'tape' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var abs = require( '@stdlib/math/base/special/abs' ); +var PINF = require( '@stdlib/constants/float64/pinf' ); +var NINF = require( '@stdlib/constants/float64/ninf' ); +var EPS = require( '@stdlib/constants/float64/eps' ); +var sec = require( './../lib' ); + + +// FIXTURES // + +var mediumNegative = require( './fixtures/julia/medium_negative.json' ); +var mediumPositive = require( './fixtures/julia/medium_positive.json' ); +var largeNegative = require( './fixtures/julia/large_negative.json' ); +var largePositive = require( './fixtures/julia/large_positive.json' ); +var hugeNegative = require( './fixtures/julia/huge_negative.json' ); +var hugePositive = require( './fixtures/julia/huge_positive.json' ); + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.equal( typeof sec, 'function', 'main export is a function' ); + 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]+'. Expected: '+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 secant (positive medium 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]+'. Expected: '+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 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]+'. Expected: '+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 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]+'. Expected: '+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 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]+'. Expected: '+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 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]+'. Expected: '+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 returns `NaN` if provided a `NaN`', function test( t ) { + var v = sec( NaN ); + t.equal( isnan( v ), true, 'returns NaN' ); + t.end(); +}); + +tape( 'the function returns `NaN` if provided a `+infinity`', function test( t ) { + var v = sec( PINF ); + t.equal( isnan( v ), true, 'returns NaN' ); + t.end(); +}); + +tape( 'the function returns `NaN` if provided a `-infinity`', function test( t ) { + var v = sec( NINF ); + t.equal( isnan( v ), true, 'returns NaN' ); + t.end(); +});