107 lines
4.0 KiB
JavaScript
107 lines
4.0 KiB
JavaScript
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/**
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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 randuint32 = require( './rand_uint32.js' );
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// MAIN //
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/**
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* Generates a pseudorandom integer on the interval \\( [1,2^{32}-1) \\).
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*
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* ## Method
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*
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* - When generating normalized double-precision floating-point numbers, we first generate two pseudorandom integers \\( x \\) and \\( y \\) on the interval \\( [1,2^{32}-1) \\) for a combined \\( 64 \\) random bits.
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*
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* - We would like \\( 53 \\) random bits to generate a 53-bit precision integer and, thus, want to discard \\( 11 \\) of the generated bits.
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*
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* - We do so by discarding \\( 5 \\) bits from \\( x \\) and \\( 6 \\) bits from \\( y \\).
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*
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* - Accordingly, \\( x \\) contains \\( 27 \\) random bits, which are subsequently shifted left \\( 26 \\) bits (multiplied by \\( 2^{26} \\), and \\( y \\) contains \\( 26 \\) random bits to fill in the lower \\( 26 \\) bits. When summed, they combine to comprise \\( 53 \\) random bits of a double-precision floating-point integer.
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*
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* - As an example, suppose, for the sake of argument, the 32-bit PRNG generates the maximum unsigned 32-bit integer \\( 2^{32}-1 \\) twice in a row. Then,
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*
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* ```javascript
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* x = 4294967295 >>> 5; // 00000111111111111111111111111111
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* y = 4294967295 >>> 6; // 00000011111111111111111111111111
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* ```
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*
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* Multiplying \\( x \\) by \\( 2^{26} \\) returns \\( 9007199187632128 \\), which, in binary, is
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*
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* ```binarystring
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* 0 10000110011 11111111111111111111 11111100000000000000000000000000
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* ```
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*
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* Adding \\( y \\) yields \\( 9007199254740991 \\) (the maximum "safe" double-precision floating-point integer value), which, in binary, is
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*
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* ```binarystring
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* 0 10000110011 11111111111111111111 11111111111111111111111111111111
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* ```
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*
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* - Similarly, suppose the 32-bit PRNG generates the following values
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*
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* ```javascript
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* x = 1 >>> 5; // 0 => 00000000000000000000000000000000
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* y = 64 >>> 6; // 1 => 00000000000000000000000000000001
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* ```
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*
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* Multiplying \\( x \\) by \\( 2^{26} \\) returns \\( 0 \\), which, in binary, is
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*
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* ```binarystring
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* 0 00000000000 00000000000000000000 00000000000000000000000000000000
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* ```
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*
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* Adding \\( y \\) yields \\( 1 \\), which, in binary, is
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*
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* ```binarystring
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* 0 01111111111 00000000000000000000 00000000000000000000000000000000
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* ```
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*
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* - As different combinations of \\( x \\) and \\( y \\) are generated, different combinations of double-precision floating-point exponent and significand bits will be toggled, thus generating pseudorandom double-precision floating-point numbers.
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*
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*
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* ## References
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*
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* - Matsumoto, Makoto, and Takuji Nishimura. 1998. "Mersenne Twister: A 623-dimensionally Equidistributed Uniform Pseudo-random Number Generator." _ACM Transactions on Modeling and Computer Simulation_ 8 (1). New York, NY, USA: ACM: 3–30. doi:[10.1145/272991.272995][@matsumoto:1998a].
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* - Harase, Shin. 2017. "Conversion of Mersenne Twister to double-precision floating-point numbers." _ArXiv_ abs/1708.06018 (September). <https://arxiv.org/abs/1708.06018>.
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*
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* [@matsumoto:1998a]: https://doi.org/10.1145/272991.272995
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*
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*
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* @function mt19937
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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 = mt19937();
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* // returns <number>
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*/
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var mt19937 = factory({
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'seed': randuint32()
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});
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// EXPORTS //
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module.exports = mt19937;
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