time-to-botec

Benchmark sampling in different programming languages
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acos.js (3088B)

      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 asin = require( './../../../../base/special/asin' );
     39 var sqrt = require( './../../../../base/special/sqrt' );
     40 var PIO4 = require( '@stdlib/constants/float64/fourth-pi' );
     41 
     42 
     43 // VARIABLES //
     44 
     45 var MOREBITS = 6.123233995736765886130e-17; // pi/2 = PIO2 + MOREBITS.
     46 
     47 
     48 // MAIN //
     49 
     50 /**
     51 * Computes the arccosine of a number.
     52 *
     53 * ## Method
     54 *
     55 * -   Analytically,
     56 *
     57 *     ```tex
     58 *     \operatorname{acos}(x) = \frac{\pi}{2} - \operatorname{asin}(x)
     59 *     ```
     60 *
     61 *     However, if \\(\|x\|\\) is near \\(1\\), there is cancellation error in subtracting \\(\opertorname{asin}(x)\\) from \\(\pi/2\\). Hence, if \\(x < -0.5\\),
     62 *
     63 *     ```tex
     64 *     \operatorname{acos}(x) = \pi - 2.0 \cdot \operatorname{asin}(\sqrt{(1+x)/2})
     65 *     ```
     66 *
     67 *     or, if \\(x > +0.5\\),
     68 *
     69 *     ```tex
     70 *     \operatorname{acos}(x) = 2.0 \cdot \operatorname{asin}( \sqrt{(1-x)/2} )}
     71 *     ```
     72 *
     73 * ## Notes
     74 *
     75 * -   Relative error:
     76 *
     77 *     | arithmetic | domain | # trials | peak    | rms     |
     78 *     |:-----------|:------:|:---------|:--------|:--------|
     79 *     | DEC        | -1, 1  | 50000    | 3.3e-17 | 8.2e-18 |
     80 *     | IEEE       | -1, 1  | 10^6     | 2.2e-16 | 6.5e-17 |
     81 *
     82 *
     83 * @param {number} x - input value
     84 * @returns {number} arccosine (in radians)
     85 *
     86 * @example
     87 * var v = acos( 1.0 );
     88 * // returns 0.0
     89 *
     90 * @example
     91 * var v = acos( 0.707 ); // ~pi/4
     92 * // returns ~0.7855
     93 *
     94 * @example
     95 * var v = acos( NaN );
     96 * // returns NaN
     97 */
     98 function acos( x ) {
     99 	var z;
    100 	if ( isnan( x ) ) {
    101 		return NaN;
    102 	}
    103 	if ( x < -1.0 || x > 1.0 ) {
    104 		return NaN;
    105 	}
    106 	if ( x > 0.5 ) {
    107 		return 2.0 * asin( sqrt( 0.5 - (0.5*x) ) );
    108 	}
    109 	z = PIO4 - asin( x );
    110 	z += MOREBITS;
    111 	z += PIO4;
    112 	return z;
    113 }
    114 
    115 
    116 // EXPORTS //
    117 
    118 module.exports = acos;