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* @license Apache-2.0
*
* Copyright (c) 2026 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.
*/
/**
* Xorshift128+ pseudorandom number generator (PRNG).
*
* ## Algorithm
*
* The Xorshift128+ algorithm generates 32-bit pseudorandom numbers using
* 64-bit state values (stored as 32-bit pairs). Entropy from both halves
* of the 64-bit output is mixed via XOR to preserve quality.
*
* ## Notes
*
* - Uses Uint32Array for state storage (@stdlib compatible).
* - Returns 32-bit unsigned integers via entropy mixing.
* - Entropy mixing: XOR(upper_32bits, lower_32bits).
* - Period: approximately 2^128.
*
* @example
* var factory = require( '@stdlib/random/base/xorshift128plus' );
*
* var rng = factory({
* 'seed': 12345
* });
*
* var v = rng();
* // returns <number>
*/
'use strict';
// MODULES //
var setReadOnly = require( '@stdlib/utils/define-nonenumerable-read-only-property' );
var setReadOnlyAccessor = require( '@stdlib/utils/define-nonenumerable-read-only-accessor' );
var setReadWriteAccessor = require( '@stdlib/utils/define-nonenumerable-read-write-accessor' );
var hasOwnProp = require( '@stdlib/assert/has-own-property' );
var isObject = require( '@stdlib/assert/is-plain-object' );
var isBoolean = require( '@stdlib/assert/is-boolean' ).isPrimitive;
var isNonNegativeInteger = require( '@stdlib/assert/is-nonnegative-integer' );
var Uint32Array = require( '@stdlib/array/uint32' );
var floor = require( '@stdlib/math/base/special/floor' );
var format = require( '@stdlib/string/format' );
var randu = require( '@stdlib/random/base/randu' );
// VARIABLES //
/**
* State array length (4 × 32-bit values = 2 × 64-bit values).
*
* @private
* @type {number}
*/
var STATE_ARRAY_SIZE = 4;
/**
* State array indices for first 64-bit value (s0).
*
* @private
* @type {number}
*/
var S0_HI_INDEX = 0;
var S0_LO_INDEX = 1;
/**
* State array indices for second 64-bit value (s1).
*
* @private
* @type {number}
*/
var S1_HI_INDEX = 2;
var S1_LO_INDEX = 3;
/**
* Normalization constant for converting to [0,1).
*
* @private
* @type {number}
*/
var NORMALIZATION_CONSTANT = 1.0 / 0x100000000;
// FUNCTIONS //
/**
* Performs left shift on 64-bit value stored as two 32-bit parts.
*
* @private
* @param {number} hi - high 32 bits
* @param {number} lo - low 32 bits
* @param {number} shift - shift amount (0-63)
* @returns {Array} [hi_shifted, lo_shifted]
*/
function shift64Left( hi, lo, shift ) {
var newHi;
var newLo;
if ( shift === 0 ) {
return [ hi, lo ];
}
if ( shift >= 64 ) {
return [ 0, 0 ];
}
if ( shift >= 32 ) {
return [ (lo << (shift - 32)) >>> 0, 0 ];
}
newHi = ((hi << shift) | (lo >>> (32 - shift))) >>> 0;
newLo = (lo << shift) >>> 0;
return [ newHi, newLo ];
}
/**
* Performs right shift on 64-bit value stored as two 32-bit parts.
*
* @private
* @param {number} hi - high 32 bits
* @param {number} lo - low 32 bits
* @param {number} shift - shift amount (0-63)
* @returns {Array} [hi_shifted, lo_shifted]
*/
function shift64Right( hi, lo, shift ) {
var newHi;
var newLo;
if ( shift === 0 ) {
return [ hi, lo ];
}
if ( shift >= 64 ) {
return [ 0, 0 ];
}
if ( shift >= 32 ) {
return [ 0, (hi >>> (shift - 32)) >>> 0 ];
}
newHi = (hi >>> shift) >>> 0;
newLo = (((lo >>> shift) | (hi << (32 - shift))) >>> 0);
return [ newHi, newLo ];
}
/**
* Adds two 64-bit values with carry handling.
*
* @private
* @param {number} hi1 - first value high 32 bits
* @param {number} lo1 - first value low 32 bits
* @param {number} hi2 - second value high 32 bits
* @param {number} lo2 - second value low 32 bits
* @returns {Array} [hi_result, lo_result]
*/
function add64( hi1, lo1, hi2, lo2 ) {
var carry;
var lo;
var hi;
lo = (lo1 + lo2) >>> 0;
carry = (lo < lo1) ? 1 : 0;
hi = (hi1 + hi2 + carry) >>> 0;
return [ hi, lo ];
}
/**
* Initializes state from seed.
*
* @private
* @param {Uint32Array} state - state array to initialize
* @param {number} seed - seed value
* @returns {Uint32Array} initialized state
*/
function initState( state, seed ) {
// Use seed to initialize s0 and s1
// Based on SplitMix64 constants for good distribution
var s0 = seed >>> 0;
var s1 = ((seed + 0x9e3779b97f4a7c15) >>> 0) ^ s0;
// Create initial 64-bit values
// s0_initial = seed * 2^32 + s0
// s1_initial = seed * 2^32 + s1
state[ S0_HI_INDEX ] = (s0 * 1103515245) >>> 0;
state[ S0_LO_INDEX ] = (s1 * 1103515245) >>> 0;
state[ S1_HI_INDEX ] = (s0 + 12345) >>> 0;
state[ S1_LO_INDEX ] = (s1 + 12345) >>> 0;
return state;
}
// MAIN //
/**
* Returns an Xorshift128+ pseudorandom number generator.
*
* @param {Object} [options] - configuration object
* @param {number} [options.seed] - seed value
* @param {Uint32Array} [options.state] - generator state
* @param {boolean} [options.copy=true] - copy state
* @throws {TypeError} options must be an object
* @throws {TypeError} invalid option value
* @throws {RangeError} invalid state array
* @returns {Function} PRNG function
*
* @example
* var rng = factory({
* 'seed': 1234
* });
*
* var v = rng();
* // throws 96092074
*/
function factory( options ) {
var STATE;
var opts;
var seed;
var tmp;
var i;
opts = {};
if ( arguments.length ) {
if ( !isObject( options ) ) {
throw new TypeError(format('invalid argument. Options must be an object. Received: %s', typeof options));
}
if ( hasOwnProp( options, 'copy' ) ) {
opts.copy = options.copy;
if ( !isBoolean( options.copy ) ) {
throw new TypeError(format('invalid option. `copy` must be a boolean. Received: %s', typeof options.copy));
}
}
if ( hasOwnProp( options, 'state' ) ) {
STATE = options.state;
opts.state = true;
if ( !(STATE instanceof Uint32Array) ) {
throw new TypeError('invalid option. `state` must be a Uint32Array.');
}
if ( STATE.length !== STATE_ARRAY_SIZE ) {
throw new RangeError(format('invalid option. `state` must have length %u. Received: %u.', STATE_ARRAY_SIZE, STATE.length));
}
if ( opts.copy !== false ) {
tmp = new Uint32Array( STATE_ARRAY_SIZE );
for ( i = 0; i < STATE_ARRAY_SIZE; i++ ) {
tmp[ i ] = STATE[ i ];
}
STATE = tmp;
}
}
if ( !opts.state ) {
if ( hasOwnProp( options, 'seed' ) ) {
seed = options.seed;
opts.seed = true;
if ( !isNonNegativeInteger( seed ) ) {
throw new TypeError('invalid option. `seed` must be a non-negative integer.');
}
} else {
seed = floor( randu() * 0x100000000 );
}
}
} else {
seed = floor( randu() * 0x100000000 );
}
if ( STATE === void 0 ) {
STATE = new Uint32Array( STATE_ARRAY_SIZE );
STATE = initState( STATE, seed );
}
/**
* Generates next pseudorandom 32-bit unsigned integer.
*
* Entropy mixing approach:
* 1. Compute 64-bit output using 32-bit state pairs
* 2. Mix upper and lower 32 bits via XOR
* 3. Return 32-bit mixed result
*
* @private
* @returns {number} pseudorandom 32-bit unsigned integer
*/
function next() {
var result;
var sumHi;
var sumLo;
var s0Hi;
var s0Lo;
var s1Hi;
var s1Lo;
var t;
// Load state
s0Hi = STATE[ S0_HI_INDEX ];
s0Lo = STATE[ S0_LO_INDEX ];
s1Hi = STATE[ S1_HI_INDEX ];
s1Lo = STATE[ S1_LO_INDEX ];
// s1 ^= s1 << 23
t = shift64Left( s1Hi, s1Lo, 23 );
s1Hi ^= t[ 0 ];
s1Lo ^= t[ 1 ];
// s1 ^= s1 >> 17
t = shift64Right( s1Hi, s1Lo, 17 );
s1Hi ^= t[ 0 ];
s1Lo ^= t[ 1 ];
// s1 ^= s0
s1Hi ^= s0Hi;
s1Lo ^= s0Lo;
// s1 ^= s0 >> 26
t = shift64Right( s0Hi, s0Lo, 26 );
s1Hi ^= t[ 0 ];
s1Lo ^= t[ 1 ];
// Update state
STATE[ S0_HI_INDEX ] = s1Hi;
STATE[ S0_LO_INDEX ] = s1Lo;
STATE[ S1_HI_INDEX ] = s0Hi;
STATE[ S1_LO_INDEX ] = s0Lo;
// Result = s1 + s0
result = add64( s1Hi, s1Lo, s0Hi, s0Lo );
sumHi = result[ 0 ];
sumLo = result[ 1 ];
// Entropy mixing
return (sumHi ^ sumLo) >>> 0;
}
/**
* Generates pseudorandom number on [0, 1).
*
* @private
* @returns {number} pseudorandom number
*/
function norm() {
return next() * NORMALIZATION_CONSTANT;
}
/**
* Returns current state.
*
* @private
* @returns {Uint32Array} state
*/
function getState() {
var out = new Uint32Array( STATE_ARRAY_SIZE );
var i;
for ( i = 0; i < STATE_ARRAY_SIZE; i++ ) {
out[ i ] = STATE[ i ];
}
return out;
}
/**
* Sets state.
*
* @private
* @param {Uint32Array} s - new state
* @throws {TypeError} state must be Uint32Array
* @throws {RangeError} state must have correct length
*/
function setState( s ) {
var i;
if ( !(s instanceof Uint32Array) ) {
throw new TypeError('invalid argument. `state` must be a Uint32Array.');
}
if ( s.length !== STATE_ARRAY_SIZE ) {
throw new RangeError(format('invalid argument. `state` must have length %u. Received: %u.', STATE_ARRAY_SIZE, s.length));
}
if ( opts.copy === false ) {
if ( opts.state ) {
for ( i = 0; i < STATE_ARRAY_SIZE; i++ ) {
STATE[ i ] = s[ i ];
}
} else {
STATE = s;
opts.state = true;
}
} else {
for ( i = 0; i < STATE_ARRAY_SIZE; i++ ) {
STATE[ i ] = s[ i ];
}
}
}
/**
* Returns copy of PRNG.
*
* @private
* @returns {Function} copy
*/
function copy() {
return factory({
'state': getState(),
'copy': true
});
}
/**
* Serializes state as JSON.
*
* @private
* @returns {Object} JSON representation
*/
function toJSON() {
return {
'type': 'PRNG',
'name': 'xorshift128+',
'state': getState(),
'params': []
};
}
/**
* Returns seed.
*
* @private
* @returns {number} seed
*/
function getSeed() {
return STATE[ S0_HI_INDEX ];
}
setReadOnly( next, 'NAME', 'xorshift128+' );
setReadOnly( next, 'normalized', norm );
setReadOnly( next, 'copy', copy );
setReadOnly( next, 'toJSON', toJSON );
setReadOnlyAccessor( next, 'seed', getSeed );
setReadWriteAccessor( next, 'state', getState, setState );
return next;
}
// EXPORTS //
module.exports = factory;
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