time-to-botec

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

improved_ziggurat.js (2609B)

      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 'use strict';
     20 
     21 // MODULES //
     22 
     23 var abs = require( '@stdlib/math/base/special/abs' );
     24 var exp = require( '@stdlib/math/base/special/exp' );
     25 var coordsArray = require( './coords_array.js' );
     26 var ratioArray = require( './ratio_array.js' );
     27 var sampleTail = require( './sample_tail.js' );
     28 
     29 
     30 // VARIABLES //
     31 
     32 // Number of blocks:
     33 var NUM_BLOCKS = 128;
     34 
     35 // Start of right tail (R):
     36 var START_RIGHT_TAIL = 3.442619855899;
     37 
     38 // `X` holds coordinates, such that each rectangle has same area:
     39 var X = coordsArray( NUM_BLOCKS, START_RIGHT_TAIL );
     40 
     41 // `R` holds `X[ i+1 ] / X[ i ]`:
     42 var R = ratioArray( X );
     43 
     44 // 127 => 0x7F => 00000000000000000000000001111111
     45 var LAST_7_BITS_MASK = 127|0; // asm type annotation
     46 
     47 
     48 // MAIN //
     49 
     50 /**
     51 * Returns a pseudorandom number generator which implements the improved Ziggurat algorithm for generating normally distributed pseudorandom numbers.
     52 *
     53 * @private
     54 * @param {PRNG} randu - PRNG for generating uniformly distributed numbers
     55 * @param {PRNG} randi - PRNG for generating uniformly distributed integers
     56 * @returns {number} pseudorandom number
     57 */
     58 function wrap( randu, randi ) {
     59 	return randn;
     60 
     61 	/**
     62 	* Generates a normally distributed pseudorandom number.
     63 	*
     64 	* @private
     65 	* @returns {number} pseudorandom number
     66 	*
     67 	* @example
     68 	* var r = randn();
     69 	* // returns <number>
     70 	*/
     71 	function randn() {
     72 		var f0;
     73 		var f1;
     74 		var x2;
     75 		var x;
     76 		var u;
     77 		var i;
     78 		var j;
     79 		while ( true ) {
     80 			u = ( 2.0*randu() ) - 1.0;
     81 			i = randi() & LAST_7_BITS_MASK;
     82 
     83 			// First try the rectangular boxes...
     84 			if ( abs( u ) < R[ i ] ) {
     85 				return u * X[ i ];
     86 			}
     87 			// If bottom box, sample from the tail...
     88 			if ( i === 0 ) {
     89 				return sampleTail( randu, START_RIGHT_TAIL, u < 0.0 );
     90 			}
     91 			// Is this a sample from the wedges?
     92 			x = u * X[ i ];
     93 			x2 = x * x;
     94 			j = i + 1;
     95 			f0 = exp( -0.5 * ( (X[ i ]*X[ i ]) - x2 ) );
     96 			f1 = exp( -0.5 * ( (X[ j ]*X[ j ]) - x2 ) );
     97 			if ( f1 + (randu()*(f0-f1)) < 1.0 ) {
     98 				return x;
     99 			}
    100 		}
    101 	}
    102 }
    103 
    104 
    105 // EXPORTS //
    106 
    107 module.exports = wrap;