109 lines
3.2 KiB
JavaScript
109 lines
3.2 KiB
JavaScript
/**
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* @license Apache-2.0
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*
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* Copyright (c) 2018 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var factory = require( './factory.js' );
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var randint32 = require( './rand_int32.js' );
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// MAIN //
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/**
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* Generates a pseudorandom integer on the interval \\( [1,2^{31}-1) \\).
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*
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* ## Method
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*
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* Linear congruential generators (LCGs) use the recurrence relation
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*
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* ```tex
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* X_{n+1} = ( a \cdot X_n + c ) \operatorname{mod}(m)
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* ```
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*
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* where the modulus \\( m \\) is a prime number or power of a prime number and \\( a \\) is a primitive root modulo \\( m \\).
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*
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* <!-- <note> -->
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*
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* For an LCG to be a Lehmer RNG, the seed \\( X_0 \\) must be coprime to \\( m \\).
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*
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* <!-- </note> -->
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*
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* In this implementation, the constants \\( a \\), \\( c \\), and \\( m \\) have the values
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*
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* ```tex
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* \begin{align*}
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* a &= 7^5 = 16807 \\
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* c &= 0 \\
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* m &= 2^{31} - 1 = 2147483647
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* \end{align*}
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* ```
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*
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* <!-- <note> -->
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*
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* The constant \\( m \\) is a Mersenne prime (modulo \\(31\\)).
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*
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* <!-- </note> -->
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*
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* <!-- <note> -->
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*
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* The constant \\( a \\) is a primitive root (modulo \\(31\\)).
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*
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* <!-- </note> -->
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*
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* Accordingly, the maximum possible product is
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*
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* ```tex
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* 16807 \cdot (m - 1) \approx 2^{46}
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* ```
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*
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* 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_.
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*
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* 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.
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*
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*
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* ## Notes
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*
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* - The generator has a period of approximately \\(2.1\mbox{e}9\\) (see [Numerical Recipes in C, 2nd Edition](#references), p. 279).
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*
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*
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* ## References
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*
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* - 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).
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* - 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).
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* - 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.
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*
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*
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* @function minstd
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* @type {PRNG}
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* @returns {PositiveInteger} pseudorandom integer
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*
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* @example
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* var v = minstd();
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* // returns <number>
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*/
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var minstd = factory({
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'seed': randint32()
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});
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// EXPORTS //
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module.exports = minstd;
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