time-to-botec

Benchmark sampling in different programming languages
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main.js (3277B)

      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 factory = require( './factory.js' );
     24 var randint32 = require( './rand_int32.js' );
     25 
     26 
     27 // MAIN //
     28 
     29 /**
     30 * Generates a pseudorandom integer on the interval \\( [1,2^{31}-1) \\).
     31 *
     32 * ## Method
     33 *
     34 * Linear congruential generators (LCGs) use the recurrence relation
     35 *
     36 * ```tex
     37 * X_{n+1} = ( a \cdot X_n + c ) \operatorname{mod}(m)
     38 * ```
     39 *
     40 * where the modulus \\( m \\) is a prime number or power of a prime number and \\( a \\) is a primitive root modulo \\( m \\).
     41 *
     42 * <!-- <note> -->
     43 *
     44 * For an LCG to be a Lehmer RNG, the seed \\( X_0 \\) must be coprime to \\( m \\).
     45 *
     46 * <!-- </note> -->
     47 *
     48 * In this implementation, the constants \\( a \\), \\( c \\), and \\( m \\) have the values
     49 *
     50 * ```tex
     51 * \begin{align*}
     52 * a &= 7^5 = 16807 \\
     53 * c &= 0 \\
     54 * m &= 2^{31} - 1 = 2147483647
     55 * \end{align*}
     56 * ```
     57 *
     58 * <!-- <note> -->
     59 *
     60 * The constant \\( m \\) is a Mersenne prime (modulo \\(31\\)).
     61 *
     62 * <!-- </note> -->
     63 *
     64 * <!-- <note> -->
     65 *
     66 * The constant \\( a \\) is a primitive root (modulo \\(31\\)).
     67 *
     68 * <!-- </note> -->
     69 *
     70 * Accordingly, the maximum possible product is
     71 *
     72 * ```tex
     73 * 16807 \cdot (m - 1) \approx 2^{46}
     74 * ```
     75 *
     76 * The values for \\( a \\), \\( c \\), and \\( m \\) are taken from Park and Miller, "Random Number Generators: Good Ones Are Hard To Find". Park's and Miller's article is also the basis for a recipe in the second edition of _Numerical Recipes in C_.
     77 *
     78 * This implementation subsequently shuffles the output of a linear congruential pseudorandom number generator (LCG) using a shuffle table in accordance with the Bays-Durham algorithm.
     79 *
     80 *
     81 * ## Notes
     82 *
     83 * -   The generator has a period of approximately \\(2.1\mbox{e}9\\) (see [Numerical Recipes in C, 2nd Edition](#references), p. 279).
     84 *
     85 *
     86 * ## References
     87 *
     88 * -   Bays, Carter, and S. D. Durham. 1976. "Improving a Poor Random Number Generator." _ACM Transactions on Mathematical Software_ 2 (1). New York, NY, USA: ACM: 59–64. doi:[10.1145/355666.355670](http://dx.doi.org/10.1145/355666.355670).
     89 * -   Herzog, T.N., and G. Lord. 2002. _Applications of Monte Carlo Methods to Finance and Insurance_. ACTEX Publications. [https://books.google.com/books?id=vC7I\\\_gdX-A0C](https://books.google.com/books?id=vC7I\_gdX-A0C).
     90 * -   Press, William H., Brian P. Flannery, Saul A. Teukolsky, and William T. Vetterling. 1992. _Numerical Recipes in C: The Art of Scientific Computing, Second Edition_. Cambridge University Press.
     91 *
     92 *
     93 * @function minstd
     94 * @type {PRNG}
     95 * @returns {PositiveInteger} pseudorandom integer
     96 *
     97 * @example
     98 * var v = minstd();
     99 * // returns <number>
    100 */
    101 var minstd = factory({
    102 	'seed': randint32()
    103 });
    104 
    105 
    106 // EXPORTS //
    107 
    108 module.exports = minstd;