time-to-botec

Benchmark sampling in different programming languages
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spence.js (3100B)

      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 1985, 1987, 1989, 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 ln = require( './../../../../base/special/ln' );
     39 var PI_SQUARED = require( '@stdlib/constants/float64/pi-squared' );
     40 var polyvalA = require( './polyval_a.js' );
     41 var polyvalB = require( './polyval_b.js' );
     42 
     43 
     44 // MAIN //
     45 
     46 /**
     47 * Evaluates Spence’s function, which is also known as the dilogarithm.
     48 *
     49 * ## Method
     50 *
     51 * -   A rational approximation gives the integral in the interval (0.5, 1.5).
     52 * -   Transformation formulas for \\( \tfrac{1}{x} \\) and \\( 1 - x \\) are employed outside the basic expansion range.
     53 *
     54 * ## Notes
     55 *
     56 * -   Relative error:
     57 *
     58 *     | arithmetic | domain      | # trials | peak    | rms     |
     59 *     |:----------:|:-----------:|:--------:|:-------:|:-------:|
     60 *     | IEEE       | 0,4         | 30000    | 3.9e-15 | 5.4e-16 |
     61 *
     62 *
     63 * @param {NonNegativeNumber} x - input value
     64 * @returns {number} function value
     65 *
     66 * @example
     67 * var v = spence( 3.0 );
     68 * // returns ~-1.437
     69 *
     70 * @example
     71 * var v = spence( 0.0 );
     72 * // returns ~1.645
     73 *
     74 * @example
     75 * var v = spence( -9.0 );
     76 * // returns NaN
     77 *
     78 * @example
     79 * var v = spence( NaN );
     80 * // returns NaN
     81 */
     82 function spence( x ) {
     83 	var flg;
     84 	var w;
     85 	var y;
     86 	var z;
     87 
     88 	if ( isnan( x ) || x < 0.0 ) {
     89 		return NaN;
     90 	}
     91 	if ( x === 1.0 ) {
     92 		return 0.0;
     93 	}
     94 	if ( x === 0.0 ) {
     95 		return ( PI_SQUARED / 6.0 );
     96 	}
     97 	flg = 0;
     98 	if ( x > 2.0 ) {
     99 		x = 1.0 / x;
    100 		flg |= 2;
    101 	}
    102 	if ( x > 1.5 ) {
    103 		w = (1.0 / x) - 1.0;
    104 		flg |= 2;
    105 	}
    106 	else if ( x < 0.5 ) {
    107 		w = -x;
    108 		flg |= 1;
    109 	}
    110 	else {
    111 		w = x - 1.0;
    112 	}
    113 	y = -w * polyvalA( w ) / polyvalB( w );
    114 	if ( flg & 1 ) {
    115 		y = ( PI_SQUARED/6.0 ) - ( ln( x ) * ln( 1.0-x ) ) - y;
    116 	}
    117 	if ( flg & 2 ) {
    118 		z = ln( x );
    119 		y = -( 0.5 * z * z ) - y;
    120 	}
    121 	return y;
    122 }
    123 
    124 
    125 // EXPORTS //
    126 
    127 module.exports = spence;