time-to-botec

Benchmark sampling in different programming languages
Log | Files | Refs | README

acosh.js (2846B)

      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 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/e_acosh.c?view=markup}. The implementation follows the original, but has been modified for JavaScript.
     22 *
     23 * ```text
     24 * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
     25 *
     26 * Developed at SunPro, a Sun Microsystems, Inc. business.
     27 * Permission to use, copy, modify, and distribute this
     28 * software is freely granted, provided that this notice
     29 * is preserved.
     30 * ```
     31 */
     32 
     33 'use strict';
     34 
     35 // MODULES //
     36 
     37 var isnan = require( './../../../../base/assert/is-nan' );
     38 var log1p = require( './../../../../base/special/log1p' );
     39 var sqrt = require( './../../../../base/special/sqrt' );
     40 var LN2 = require( '@stdlib/constants/float64/ln-two' );
     41 var ln = require( './../../../../base/special/ln' );
     42 
     43 
     44 // VARIABLES //
     45 
     46 var HUGE = 1 << 28; // 2**28
     47 
     48 
     49 // MAIN //
     50 
     51 /**
     52 * Computes the hyperbolic arccosine of a number.
     53 *
     54 * ## Method
     55 *
     56 * Based on
     57 *
     58 * ```tex
     59 * \operatorname{acosh}(x) = \log \left[ x + \sqrt{ x^2 - 1 } \right]
     60 * ```
     61 *
     62 * we have
     63 *
     64 * ```tex
     65 * \operatorname{acosh}(x) = \begin{cases}
     66 * \log(x) + \tfrac{\ln}{2} & \text{ if x is large } \\
     67 * \log \left( 2x-\tfrac{1}{\sqrt{x^2-1}+x} \right) & \text{ if } x > 2 \\
     68 * \operatorname{log1p}\left( x - 1 + \sqrt{ 2 \cdot (x-1) + (x-1)^2 } \right) & \text{ otherwise }
     69 * \end{cases}
     70 * ```
     71 *
     72 * ## Special Cases
     73 *
     74 * ```tex
     75 * \begin{align*}
     76 * \operatorname{acosh}(x) &= \mathrm{NaN}\ \text{ if } x < 1 \\
     77 * \end{align*}
     78 * ```
     79 *
     80 * @param {number} x - input value
     81 * @returns {number} hyperbolic arccosine (in radians)
     82 *
     83 * @example
     84 * var v = acosh( 1.0 );
     85 * // returns 0.0
     86 *
     87 * @example
     88 * var v = acosh( 2.0 );
     89 * // returns ~1.317
     90 *
     91 * @example
     92 * var v = acosh( NaN );
     93 * // returns NaN
     94 */
     95 function acosh( x ) {
     96 	var t;
     97 	if ( isnan( x ) ) {
     98 		return NaN;
     99 	}
    100 	if ( x < 1.0 ) {
    101 		return NaN;
    102 	}
    103 	if ( x === 1.0 ) {
    104 		return 0.0;
    105 	}
    106 	if ( x >= HUGE ) {
    107 		return ln( x ) + LN2;
    108 	}
    109 	if ( x > 2.0 ) {
    110 		return ln( (2.0*x) - ( 1.0 / ( x + sqrt( (x*x) - 1.0 ) ) ) );
    111 	}
    112 	// Case: 2 >= x > 1
    113 	t = x - 1.0;
    114 	return log1p( t + sqrt( (2.0*t) + (t*t) ) );
    115 }
    116 
    117 
    118 // EXPORTS //
    119 
    120 module.exports = acosh;