MersenneTwister.java
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You 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.
*/
package org.apache.commons.rng.core.source32;
import java.util.Arrays;
import org.apache.commons.rng.core.util.NumberFactory;
/**
* This class implements a powerful pseudo-random number generator
* developed by Makoto Matsumoto and Takuji Nishimura during
* 1996-1997.
*
* <p>
* This generator features an extremely long period
* (2<sup>19937</sup>-1) and 623-dimensional equidistribution up to
* 32 bits accuracy. The home page for this generator is located at
* <a href="http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html">
* http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html</a>.
* </p>
*
* <p>
* This generator is described in a paper by Makoto Matsumoto and
* Takuji Nishimura in 1998:
* <a href="http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/ARTICLES/mt.pdf">
* Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudo-Random
* Number Generator</a>,
* ACM Transactions on Modeling and Computer Simulation, Vol. 8, No. 1,
* January 1998, pp 3--30
* </p>
*
* <p>
* This class is mainly a Java port of the
* <a href="http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/emt19937ar.html">
* 2002-01-26 version of the generator</a> written in C by Makoto Matsumoto
* and Takuji Nishimura. Here is their original copyright:
* </p>
*
* <table style="background-color: #E0E0E0; width: 80%">
* <caption>Mersenne Twister licence</caption>
* <tr><td style="padding: 10px">Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
* All rights reserved.</td></tr>
*
* <tr><td style="padding: 10px">Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* <ol>
* <li>Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.</li>
* <li>Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.</li>
* <li>The names of its contributors may not be used to endorse or promote
* products derived from this software without specific prior written
* permission.</li>
* </ol></td></tr>
*
* <tr><td style="padding: 10px"><strong>THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
* CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES,
* INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS
* BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
* OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
* OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
* USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
* DAMAGE.</strong></td></tr>
* </table>
*
* @see <a href="https://en.wikipedia.org/wiki/Mersenne_Twister">Mersenne Twister (Wikipedia)</a>
* @since 1.0
*/
public class MersenneTwister extends IntProvider {
/** Mask 32 most significant bits. */
private static final long INT_MASK_LONG = 0xffffffffL;
/** Most significant w-r bits. */
private static final long UPPER_MASK_LONG = 0x80000000L;
/** Least significant r bits. */
private static final long LOWER_MASK_LONG = 0x7fffffffL;
/** Most significant w-r bits. */
private static final int UPPER_MASK = 0x80000000;
/** Least significant r bits. */
private static final int LOWER_MASK = 0x7fffffff;
/** Size of the bytes pool. */
private static final int N = 624;
/** Period second parameter. */
private static final int M = 397;
/** X * MATRIX_A for X = {0, 1}. */
private static final int[] MAG01 = {0x0, 0x9908b0df};
/** Bytes pool. */
private final int[] mt = new int[N];
/** Current index in the bytes pool. */
private int mti;
/**
* Creates a new random number generator.
*
* @param seed Initial seed.
*/
public MersenneTwister(int[] seed) {
setSeedInternal(seed);
}
/** {@inheritDoc} */
@Override
protected byte[] getStateInternal() {
final int[] s = Arrays.copyOf(mt, N + 1);
s[N] = mti;
return composeStateInternal(NumberFactory.makeByteArray(s),
super.getStateInternal());
}
/** {@inheritDoc} */
@Override
protected void setStateInternal(byte[] s) {
final byte[][] c = splitStateInternal(s, (N + 1) * 4);
final int[] tmp = NumberFactory.makeIntArray(c[0]);
System.arraycopy(tmp, 0, mt, 0, N);
mti = tmp[N];
super.setStateInternal(c[1]);
}
/**
* Initializes the generator with the given seed.
*
* @param seed Initial seed.
*/
private void setSeedInternal(int[] seed) {
fillStateMersenneTwister(mt, seed);
// Initial index.
mti = N;
}
/**
* Utility for wholly filling a {@code state} array with non-zero
* bytes, even if the {@code seed} has a smaller size.
* The procedure is the one defined by the standard implementation
* of the algorithm.
*
* @param state State to be filled (must be allocated).
* @param inputSeed Seed (cannot be {@code null}).
*/
private static void fillStateMersenneTwister(int[] state,
int[] inputSeed) {
// Accept empty seed.
final int[] seed = (inputSeed.length == 0) ? new int[1] : inputSeed;
initializeState(state);
final int nextIndex = mixSeedAndState(state, seed);
mixState(state, nextIndex);
state[0] = (int) UPPER_MASK_LONG; // MSB is 1, ensuring non-zero initial array.
}
/**
* Fill the state using a defined pseudo-random sequence.
*
* @param state State to be filled (must be allocated).
*/
private static void initializeState(int[] state) {
long mt = 19650218 & INT_MASK_LONG;
state[0] = (int) mt;
for (int i = 1; i < state.length; i++) {
mt = (1812433253L * (mt ^ (mt >> 30)) + i) & INT_MASK_LONG;
state[i] = (int) mt;
}
}
/**
* Mix the seed into the state using a non-linear combination. The procedure
* uses {@code k} steps where {@code k = max(state.length, seed.length)}. If
* the seed is smaller than the state it is wrapped to obtain enough values.
* If the seed is larger than the state then the procedure visits entries in
* the state multiple times.
*
* <p>Returns the index immediately after the most recently visited position
* in the state array.</p>
*
* @param state State to be filled (must be allocated).
* @param seed Seed (must be at least length 1).
* @return the next index
*/
private static int mixSeedAndState(int[] state, final int[] seed) {
final int stateSize = state.length;
int i = 1;
int j = 0;
for (int k = Math.max(stateSize, seed.length); k > 0; k--) {
final long a = (state[i] & LOWER_MASK_LONG) | ((state[i] < 0) ? UPPER_MASK_LONG : 0);
final long b = (state[i - 1] & LOWER_MASK_LONG) | ((state[i - 1] < 0) ? UPPER_MASK_LONG : 0);
final long c = (a ^ ((b ^ (b >> 30)) * 1664525L)) + seed[j] + j; // Non linear.
state[i] = (int) (c & INT_MASK_LONG);
i++;
j++;
if (i >= stateSize) {
state[0] = state[stateSize - 1];
i = 1;
}
if (j >= seed.length) {
j = 0;
}
}
return i;
}
/**
* Mix each position of the state using a non-linear combination. The
* procedure starts from the specified index in the state array and wraps
* iteration through the array if required.
*
* @param state State to be filled (must be allocated).
* @param startIndex The index to begin within the state array.
*/
private static void mixState(int[] state, int startIndex) {
final int stateSize = state.length;
int i = startIndex;
for (int k = stateSize - 1; k > 0; k--) {
final long a = (state[i] & LOWER_MASK_LONG) | ((state[i] < 0) ? UPPER_MASK_LONG : 0);
final long b = (state[i - 1] & LOWER_MASK_LONG) | ((state[i - 1] < 0) ? UPPER_MASK_LONG : 0);
final long c = (a ^ ((b ^ (b >> 30)) * 1566083941L)) - i; // Non linear.
state[i] = (int) (c & INT_MASK_LONG);
i++;
if (i >= stateSize) {
state[0] = state[stateSize - 1];
i = 1;
}
}
}
/** {@inheritDoc} */
@Override
public int next() {
int y;
if (mti >= N) { // Generate N words at one time.
int mtNext = mt[0];
for (int k = 0; k < N - M; ++k) {
final int mtCurr = mtNext;
mtNext = mt[k + 1];
y = (mtCurr & UPPER_MASK) | (mtNext & LOWER_MASK);
mt[k] = mt[k + M] ^ (y >>> 1) ^ MAG01[y & 1];
}
for (int k = N - M; k < N - 1; ++k) {
final int mtCurr = mtNext;
mtNext = mt[k + 1];
y = (mtCurr & UPPER_MASK) | (mtNext & LOWER_MASK);
mt[k] = mt[k + (M - N)] ^ (y >>> 1) ^ MAG01[y & 1];
}
y = (mtNext & UPPER_MASK) | (mt[0] & LOWER_MASK);
mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ MAG01[y & 1];
mti = 0;
}
y = mt[mti++];
// Tempering.
y ^= y >>> 11;
y ^= (y << 7) & 0x9d2c5680;
y ^= (y << 15) & 0xefc60000;
y ^= y >>> 18;
return y;
}
}