time-to-botec

Benchmark sampling in different programming languages
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sinh.js (3331B)

      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 PINF = require( '@stdlib/constants/float64/pinf' );
     38 var NINF = require( '@stdlib/constants/float64/ninf' );
     39 var abs = require( './../../../../base/special/abs' );
     40 var exp = require( './../../../../base/special/exp' );
     41 var LN2 = require( '@stdlib/constants/float64/ln-two' );
     42 var rateval = require( './rational_pq.js' );
     43 
     44 
     45 // VARIABLES //
     46 
     47 // ln(2^1024)
     48 var MAXLOG = 7.09782712893383996843e2;
     49 
     50 // ln(2^-1022)
     51 var MINLOG = -7.08396418532264106224e2;
     52 
     53 var POS_OVERFLOW = MAXLOG + LN2;
     54 var NEG_OVERFLOW = MINLOG - LN2;
     55 
     56 var LARGE = MAXLOG - LN2;
     57 
     58 
     59 // MAIN //
     60 
     61 /**
     62 * Computes the hyperbolic sine of a number.
     63 *
     64 * ## Method
     65 *
     66 * The range is partitioned into two segments. If \\( |x| \le 1 \\), we use a rational function of the form
     67 *
     68 * ```tex
     69 * x + x^3 \frac{\mathrm{P}(x)}{\mathrm{Q}(x)}
     70 * ```
     71 *
     72 * Otherwise, the calculation is
     73 *
     74 * ```tex
     75 * \operatorname{sinh}(x) = \frac{ e^x - e^{-x} }{2}.
     76 * ```
     77 *
     78 * ## Notes
     79 *
     80 * -   Relative error:
     81 *
     82 *     | arithmetic | domain   | # trials | peak    | rms     |
     83 *     |:----------:|:--------:|:--------:|:-------:|:-------:|
     84 *     | DEC        | +- 88    | 50000    | 4.0e-17 | 7.7e-18 |
     85 *     | IEEE       | +-MAXLOG | 30000    | 2.6e-16 | 5.7e-17 |
     86 *
     87 *
     88 * @param {number} x - input value (in radians)
     89 * @returns {number} hyperbolic sine
     90 *
     91 * @example
     92 * var v = sinh( 0.0 );
     93 * // returns 0.0
     94 *
     95 * @example
     96 * var v = sinh( 2.0 );
     97 * // returns ~3.627
     98 *
     99 * @example
    100 * var v = sinh( -2.0 );
    101 * // returns ~-3.627
    102 *
    103 * @example
    104 * var v = sinh( NaN );
    105 * // returns NaN
    106 */
    107 function sinh( x ) {
    108 	var a;
    109 	if ( x === 0.0 ) {
    110 		return x; // handles `+-0`
    111 	}
    112 	a = abs( x );
    113 	if ( x > POS_OVERFLOW || x < NEG_OVERFLOW ) {
    114 		return ( x > 0.0 ) ? PINF : NINF;
    115 	}
    116 	if ( a > 1.0 ) {
    117 		if ( a >= LARGE ) {
    118 			a = exp( 0.5*a );
    119 			a *= 0.5 * a;
    120 			if ( x < 0.0 ) {
    121 				a = -a;
    122 			}
    123 			return a;
    124 		}
    125 		a = exp( a );
    126 		a = (0.5*a) - (0.5/a);
    127 		if ( x < 0.0 ) {
    128 			a = -a;
    129 		}
    130 		return a;
    131 	}
    132 	a *= a;
    133 	return x + ( x*a*rateval( a ) );
    134 }
    135 
    136 
    137 // EXPORTS //
    138 
    139 module.exports = sinh;