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/**
* @license Apache-2.0
*
* Copyright (c) 2018 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
'use strict';
// MODULES //
var factory = require( './factory.js' );
var randuint32 = require( './rand_uint32.js' );
// MAIN //
/**
* Generates a pseudorandom integer on the interval \\( [1,2^{32}-1) \\).
*
* ## Method
*
* - 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.
*
* - We would like \\( 53 \\) random bits to generate a 53-bit precision integer and, thus, want to discard \\( 11 \\) of the generated bits.
*
* - We do so by discarding \\( 5 \\) bits from \\( x \\) and \\( 6 \\) bits from \\( y \\).
*
* - 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.
*
* - 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,
*
* ```javascript
* x = 4294967295 >>> 5; // 00000111111111111111111111111111
* y = 4294967295 >>> 6; // 00000011111111111111111111111111
* ```
*
* Multiplying \\( x \\) by \\( 2^{26} \\) returns \\( 9007199187632128 \\), which, in binary, is
*
* ```binarystring
* 0 10000110011 11111111111111111111 11111100000000000000000000000000
* ```
*
* Adding \\( y \\) yields \\( 9007199254740991 \\) (the maximum "safe" double-precision floating-point integer value), which, in binary, is
*
* ```binarystring
* 0 10000110011 11111111111111111111 11111111111111111111111111111111
* ```
*
* - Similarly, suppose the 32-bit PRNG generates the following values
*
* ```javascript
* x = 1 >>> 5; // 0 => 00000000000000000000000000000000
* y = 64 >>> 6; // 1 => 00000000000000000000000000000001
* ```
*
* Multiplying \\( x \\) by \\( 2^{26} \\) returns \\( 0 \\), which, in binary, is
*
* ```binarystring
* 0 00000000000 00000000000000000000 00000000000000000000000000000000
* ```
*
* Adding \\( y \\) yields \\( 1 \\), which, in binary, is
*
* ```binarystring
* 0 01111111111 00000000000000000000 00000000000000000000000000000000
* ```
*
* - 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.
*
*
* ## References
*
* - 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].
* - Harase, Shin. 2017. "Conversion of Mersenne Twister to double-precision floating-point numbers." _ArXiv_ abs/1708.06018 (September). <https://arxiv.org/abs/1708.06018>.
*
* [@matsumoto:1998a]: https://doi.org/10.1145/272991.272995
*
*
* @function mt19937
* @type {PRNG}
* @returns {PositiveInteger} pseudorandom integer
*
* @example
* var v = mt19937();
* // returns <number>
*/
var mt19937 = factory({
'seed': randuint32()
});
// EXPORTS //
module.exports = mt19937;
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