cospi.js (2337B)
1 /** 2 * @license Apache-2.0 3 * 4 * Copyright (c) 2018 The Stdlib Authors. 5 * 6 * Licensed under the Apache License, Version 2.0 (the "License"); 7 * you may not use this file except in compliance with the License. 8 * You may obtain a copy of the License at 9 * 10 * http://www.apache.org/licenses/LICENSE-2.0 11 * 12 * Unless required by applicable law or agreed to in writing, software 13 * distributed under the License is distributed on an "AS IS" BASIS, 14 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 15 * See the License for the specific language governing permissions and 16 * limitations under the License. 17 */ 18 19 'use strict'; 20 21 /* 22 * Notes: 23 * => cos(-x) = cos(x) 24 * => sin(-x) = -sin(x) 25 * => cos(π/2) = 0 26 * => cos(0) = 1 27 * => cos(π) = -1 28 */ 29 30 31 // MODULES // 32 33 var isnan = require( './../../../../base/assert/is-nan' ); 34 var isInfinite = require( './../../../../base/assert/is-infinite' ); 35 var abs = require( './../../../../base/special/abs' ); 36 var cos = require( './../../../../base/special/cos' ); 37 var sin = require( './../../../../base/special/sin' ); 38 var floor = require( './../../../../base/special/floor' ); 39 var PI = require( '@stdlib/constants/float64/pi' ); 40 var MAX_INTEGER = require( '@stdlib/constants/float64/max-safe-integer' ); 41 42 43 // VARIABLES // 44 45 MAX_INTEGER += 1; 46 47 48 // MAIN // 49 50 /** 51 * Computes the value of `cos(πx)`. 52 * 53 * @param {number} x - input value 54 * @returns {number} function value 55 * 56 * @example 57 * var y = cospi( 0.0 ); 58 * // returns 1.0 59 * 60 * @example 61 * var y = cospi( 0.5 ); 62 * // returns 0.0 63 * 64 * @example 65 * var y = cospi( 0.1 ); 66 * // returns ~0.951 67 * 68 * @example 69 * var y = cospi( NaN ); 70 * // returns NaN 71 */ 72 function cospi( x ) { 73 var ax; 74 var ix; 75 var rx; 76 var y; 77 if ( isnan( x ) ) { 78 return NaN; 79 } 80 if ( isInfinite( x ) ) { 81 return NaN; 82 } 83 ax = abs( x ); 84 if ( ax > MAX_INTEGER ) { 85 // Always even integer... 86 return 1.0; 87 } 88 // Argument reduction (reduce to [0,1))... 89 ix = floor( ax ); 90 rx = ax - ix; 91 if ( rx === 0.5 ) { 92 return 0.0; 93 } 94 if ( rx < 0.25 ) { 95 y = cos( PI*rx ); 96 } 97 else if ( rx < 0.75 ) { 98 rx = 0.5 - rx; 99 y = sin( PI*rx ); // recall sin(-x) = -sin(x), thus returned result will be properly signed 100 } 101 else { 102 rx = 1.0 - rx; 103 y = -cos( PI*rx ); 104 } 105 // If the integer of `x` is odd, we need to flip the sign... 106 return ( ix%2 === 1 ) ? -y : y; 107 } 108 109 110 // EXPORTS // 111 112 module.exports = cospi;