time-to-botec

Benchmark sampling in different programming languages
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exp2.js (3483B)

      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 // TODO: replace with TOMS (Openlibm) algo (updating license header and long comment)
     36 
     37 // MODULES //
     38 
     39 var FLOAT64_MAX_BASE2_EXPONENT = require( '@stdlib/constants/float64/max-base2-exponent' ); // eslint-disable-line id-length
     40 var FLOAT64_MIN_BASE2_EXPONENT = require( '@stdlib/constants/float64/min-base2-exponent' ); // eslint-disable-line id-length
     41 var round = require( './../../../../base/special/round' );
     42 var ldexp = require( './../../../../base/special/ldexp' );
     43 var isnan = require( './../../../../base/assert/is-nan' );
     44 var PINF = require( '@stdlib/constants/float64/pinf' );
     45 var polyvalP = require( './polyval_p.js' );
     46 var polyvalQ = require( './polyval_q.js' );
     47 
     48 
     49 // MAIN //
     50 
     51 /**
     52 * Evaluates the base `2` exponential function.
     53 *
     54 * ## Method
     55 *
     56 * -   Range reduction is accomplished by separating the argument into an integer \\( k \\) and fraction \\( f \\) such that
     57 *
     58 *     ```tex
     59 *     2^x = 2^k 2^f
     60 *     ```
     61 *
     62 * -   A Pade' approximate
     63 *
     64 *     ```tex
     65 *     1 + 2x \frac{\mathrm{P}\left(x^2\right)}{\mathrm{Q}\left(x^2\right) - x \mathrm{P}\left(x^2\right)}
     66 *     ```
     67 *
     68 *     approximates \\( 2^x \\) in the basic range \\( \[-0.5, 0.5] \\).
     69 *
     70 *
     71 * ## Notes
     72 *
     73 * -   Relative error:
     74 *
     75 *     | arithmetic | domain      | # trials | peak    | rms     |
     76 *     |:----------:|:-----------:|:--------:|:-------:|:-------:|
     77 *     | IEEE       | -1022,+1024 | 30000    | 1.8e-16 | 5.4e-17 |
     78 *
     79 *
     80 * @param {number} x - input value
     81 * @returns {number} function value
     82 *
     83 * @example
     84 * var v = exp2( 3.0 );
     85 * // returns 8.0
     86 *
     87 * @example
     88 * var v = exp2( -9.0 );
     89 * // returns ~0.002
     90 *
     91 * @example
     92 * var v = exp2( 0.0 );
     93 * // returns 1.0
     94 *
     95 * @example
     96 * var v = exp2( NaN );
     97 * // returns NaN
     98 */
     99 function exp2( x ) {
    100 	var px;
    101 	var xx;
    102 	var n;
    103 	if ( isnan( x ) ) {
    104 		return x;
    105 	}
    106 	if ( x > FLOAT64_MAX_BASE2_EXPONENT ) {
    107 		return PINF;
    108 	}
    109 	if ( x < FLOAT64_MIN_BASE2_EXPONENT ) {
    110 		return 0.0;
    111 	}
    112 	// Separate into integer and fractional parts...
    113 	n = round( x );
    114 	x -= n;
    115 
    116 	xx = x * x;
    117 	px = x * polyvalP( xx );
    118 	x = px / ( polyvalQ( xx ) - px );
    119 	x = 1.0 + ldexp( x, 1 );
    120 
    121 	// Scale by power of 2:
    122 	return ldexp( x, n );
    123 }
    124 
    125 
    126 // EXPORTS //
    127 
    128 module.exports = exp2;