time-to-botec

Benchmark sampling in different programming languages
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asin.js (3311B)

      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 * ## Notice
     20 *
     21 * The original C code, long comment, copyright, license, and constants are from [Cephes]{@link http://www.netlib.org/cephes}. The implementation follows the original, but has been modified for JavaScript.
     22 *
     23 * ```text
     24 * Copyright 1984, 1995, 2000 by Stephen L. Moshier
     25 *
     26 * 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.
     27 *
     28 * Stephen L. Moshier
     29 * moshier@na-net.ornl.gov
     30 * ```
     31 */
     32 
     33 'use strict';
     34 
     35 // MODULES //
     36 
     37 var isnan = require( './../../../../base/assert/is-nan' );
     38 var sqrt = require( './../../../../base/special/sqrt' );
     39 var PIO4 = require( '@stdlib/constants/float64/fourth-pi' );
     40 var ratevalPQ = require( './rational_pq.js' );
     41 var ratevalRS = require( './rational_rs.js' );
     42 
     43 
     44 // VARIABLES //
     45 
     46 var MOREBITS = 6.123233995736765886130e-17; // pi/2 = PIO2 + MOREBITS
     47 
     48 
     49 // MAIN //
     50 
     51 /**
     52 * Computes the arcsine of a number.
     53 *
     54 * ## Method
     55 *
     56 * -   A rational function of the form
     57 *
     58 *     ```tex
     59 *     x + x^3 \frac{P(x^2)}{Q(x^2)}
     60 *     ```
     61 *
     62 *     is used for \\(\|x\|\\) in the interval \\(\[0, 0.5\]\\). If \\(\|x\| > 0.5\\), it is transformed by the identity
     63 *
     64 *     ```tex
     65 *     \operatorname{asin}(x) = \frac{\pi}{2} - 2 \operatorname{asin}( \sqrt{ (1-x)/2 } )
     66 *     ```
     67 *
     68 * ## Notes
     69 *
     70 * -   Relative error:
     71 *
     72 *     | arithmetic | domain | # trials | peak    | rms     |
     73 *     |:-----------|:-------|:---------|:--------|:--------|
     74 *     | DEC        | -1, 1  | 40000    | 2.6e-17 | 7.1e-18 |
     75 *     | IEEE       | -1, 1  | 10^6     | 1.9e-16 | 5.4e-17 |
     76 *
     77 * @param {number} x - input value
     78 * @returns {number} arcsine (in radians)
     79 *
     80 * @example
     81 * var v = asin( 0.0 );
     82 * // returns ~0.0
     83 *
     84 * @example
     85 * var v = asin( 3.141592653589793/4.0 );
     86 * // returns ~0.903
     87 *
     88 * @example
     89 * var v = asin( -3.141592653589793/6.0 );
     90 * // returns ~-0.551
     91 *
     92 * @example
     93 * var v = asin( NaN );
     94 * // returns NaN
     95 */
     96 function asin( x ) {
     97 	var sgn;
     98 	var zz;
     99 	var a;
    100 	var p;
    101 	var z;
    102 
    103 	if ( isnan( x ) ) {
    104 		return NaN;
    105 	}
    106 	if ( x > 0.0 ) {
    107 		a = x;
    108 	} else {
    109 		sgn = true;
    110 		a = -x;
    111 	}
    112 	if ( a > 1.0 ) {
    113 		return NaN;
    114 	}
    115 	if ( a > 0.625 ) {
    116 		// arcsin(1-x) = pi/2 - sqrt(2x)(1+R(x))
    117 		zz = 1.0 - a;
    118 		p = zz * ratevalRS( zz );
    119 		zz = sqrt( zz + zz );
    120 		z = PIO4 - zz;
    121 		zz = ( zz*p ) - MOREBITS;
    122 		z -= zz;
    123 		z += PIO4;
    124 	} else {
    125 		if ( a < 1.0e-8 ) {
    126 			return x;
    127 		}
    128 		zz = a * a;
    129 		z = zz * ratevalPQ( zz );
    130 		z = ( a*z ) + a;
    131 	}
    132 	return ( sgn ) ? -z : z;
    133 }
    134 
    135 
    136 // EXPORTS //
    137 
    138 module.exports = asin;