sinpi.js (2342B)
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 * => sin(-x) = -sin(x) 24 * => sin(+n) = +0, where `n` is a positive integer 25 * => sin(-n) = -sin(+n) = -0, where `n` is a positive integer 26 * => cos(-x) = cos(x) 27 */ 28 29 30 // MODULES // 31 32 var isnan = require( './../../../../base/assert/is-nan' ); 33 var isInfinite = require( './../../../../base/assert/is-infinite' ); 34 var cos = require( './../../../../base/special/cos' ); 35 var sin = require( './../../../../base/special/sin' ); 36 var abs = require( './../../../../base/special/abs' ); 37 var copysign = require( './../../../../base/special/copysign' ); 38 var PI = require( '@stdlib/constants/float64/pi' ); 39 40 41 // MAIN // 42 43 /** 44 * Computes the value of `sin(πx)`. 45 * 46 * @param {number} x - input value 47 * @returns {number} function value 48 * 49 * @example 50 * var y = sinpi( 0.0 ); 51 * // returns 0.0 52 * 53 * @example 54 * var y = sinpi( 0.5 ); 55 * // returns 1.0 56 * 57 * @example 58 * var y = sinpi( 0.9 ); 59 * // returns ~0.309 60 * 61 * @example 62 * var y = sinpi( NaN ); 63 * // returns NaN 64 */ 65 function sinpi( x ) { 66 var ar; 67 var r; 68 if ( isnan( x ) ) { 69 return NaN; 70 } 71 if ( isInfinite( x ) ) { 72 return NaN; 73 } 74 // Argument reduction (reduce to [0,2))... 75 r = x % 2.0; // sign preserving 76 ar = abs( r ); 77 78 // If `x` is an integer, the mod is an integer... 79 if ( ar === 0.0 || ar === 1.0 ) { 80 return copysign( 0.0, r ); 81 } 82 if ( ar < 0.25 ) { 83 return sin( PI*r ); 84 } 85 // In each of the following, we further reduce to [-π/4,π/4)... 86 if ( ar < 0.75 ) { 87 ar = 0.5 - ar; 88 return copysign( cos( PI*ar ), r ); 89 } 90 if ( ar < 1.25 ) { 91 r = copysign( 1.0, r ) - r; 92 return sin( PI*r ); 93 } 94 if ( ar < 1.75 ) { 95 ar -= 1.5; 96 return -copysign( cos( PI*ar ), r ); 97 } 98 r -= copysign( 2.0, r ); 99 return sin( PI*r ); 100 } 101 102 103 // EXPORTS // 104 105 module.exports = sinpi;