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RNG-168: LXM family of random number generators
Add support for generators included in JDK 17:

L32X64Mix
L64X128StarStar
L64X128Mix
L64X256Mix
L64X1024Mix
L128X128Mix
L128X256Mix
L128X1024Mix

Added benchmark for support routines for computing the unsigned long
multiplications in the 128-bit LCG (linear congruential generator).

Added a benchmark for the jump function to allow comparison with the
equivalent base XBG (xor-based generator).

Added a faster carry computation than the method provided in the
reference LXM paper.
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aherbert committed Apr 17, 2022
1 parent 6a279c5 commit d5e653c43ec68d55e23ad8ad5a3cc755567ffdb9
Showing 40 changed files with 8,422 additions and 6 deletions.
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/*
* 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 org.apache.commons.rng.JumpableUniformRandomProvider;
import org.apache.commons.rng.LongJumpableUniformRandomProvider;
import org.apache.commons.rng.UniformRandomProvider;
import org.apache.commons.rng.core.util.NumberFactory;

/**
* A 32-bit all purpose generator.
*
* <p>This is a member of the LXM family of generators: L=Linear congruential generator;
* X=Xor based generator; and M=Mix. This member uses a 32-bit LCG and 64-bit Xor-based
* generator. It is named as {@code "L32X64MixRandom"} in the {@code java.util.random}
* package introduced in JDK 17; the LXM family is described in further detail in:
*
* <blockquote>Steele and Vigna (2021) LXM: better splittable pseudorandom number generators
* (and almost as fast). Proceedings of the ACM on Programming Languages, Volume 5,
* Article 148, pp 1–31.</blockquote>
*
* <p>Memory footprint is 128 bits and the period is 2<sup>32</sup> (2<sup>64</sup> - 1).
*
* <p>This generator implements {@link LongJumpableUniformRandomProvider}.
* In addition instances created with a different additive parameter for the LCG are robust
* against accidental correlation in a multi-threaded setting. The additive parameters must be
* different in the most significant 31-bits.
*
* @see <a href="https://doi.org/10.1145/3485525">Steele &amp; Vigna (2021) Proc. ACM Programming
* Languages 5, 1-31</a>
* @see <a href="https://docs.oracle.com/en/java/javase/17/docs/api/java.base/java/util/random/package-summary.html">
* JDK 17 java.util.random javadoc</a>
* @since 1.5
*/
public final class L32X64Mix extends IntProvider implements LongJumpableUniformRandomProvider {
// Implementation note:
// This does not extend AbstractXoRoShiRo64 as the XBG function is re-implemented
// inline to allow parallel pipelining. Inheritance would provide only the XBG state.

/** LCG multiplier. */
private static final int M = LXMSupport.M32;
/** Size of the state vector. */
private static final int SEED_SIZE = 4;

/** Per-instance LCG additive parameter (must be odd).
* Cannot be final to support RestorableUniformRandomProvider. */
private int la;
/** State of the LCG generator. */
private int ls;
/** State 0 of the XBG generator. */
private int x0;
/** State 1 of the XBG generator. */
private int x1;

/**
* Creates a new instance.
*
* @param seed Initial seed.
* If the length is larger than 4, only the first 4 elements will
* be used; if smaller, the remaining elements will be automatically
* set. A seed containing all zeros in the last two elements
* will create a non-functional XBG sub-generator and a low
* quality output with a period of 2<sup>32</sup>.
*
* <p>The 1st element is used to set the LCG increment; the least significant bit
* is set to odd to ensure a full period LCG. The 2nd element is used
* to set the LCG state.</p>
*/
public L32X64Mix(int[] seed) {
setState(extendSeed(seed, SEED_SIZE));
}

/**
* Creates a new instance using a 4 element seed.
* A seed containing all zeros in the last two elements
* will create a non-functional XBG sub-generator and a low
* quality output with a period of 2<sup>32</sup>.
*
* <p>The 1st element is used to set the LCG increment; the least significant bit
* is set to odd to ensure a full period LCG. The 2nd element is used
* to set the LCG state.</p>
*
* @param seed0 Initial seed element 0.
* @param seed1 Initial seed element 1.
* @param seed2 Initial seed element 2.
* @param seed3 Initial seed element 3.
*/
public L32X64Mix(int seed0, int seed1, int seed2, int seed3) {
// Additive parameter must be odd
la = seed0 | 1;
ls = seed1;
x0 = seed2;
x1 = seed3;
}

/**
* Creates a copy instance.
*
* @param source Source to copy.
*/
private L32X64Mix(L32X64Mix source) {
super(source);
la = source.la;
ls = source.ls;
x0 = source.x0;
x1 = source.x1;
}

/**
* Copies the state into the generator state.
*
* @param state the new state
*/
private void setState(int[] state) {
// Additive parameter must be odd
la = state[0] | 1;
ls = state[1];
x0 = state[2];
x1 = state[3];
}

/** {@inheritDoc} */
@Override
protected byte[] getStateInternal() {
return composeStateInternal(NumberFactory.makeByteArray(new int[] {la, ls, x0, x1}),
super.getStateInternal());
}

/** {@inheritDoc} */
@Override
protected void setStateInternal(byte[] s) {
final byte[][] c = splitStateInternal(s, SEED_SIZE * Integer.BYTES);
setState(NumberFactory.makeIntArray(c[0]));
super.setStateInternal(c[1]);
}

/** {@inheritDoc} */
@Override
public int next() {
// LXM generate.
// Old state is used for the output allowing parallel pipelining
// on processors that support multiple concurrent instructions.

final int s0 = x0;
final int s = ls;

// Mix
final int z = LXMSupport.lea32(s + s0);

// LCG update
ls = M * s + la;

// XBG update
int s1 = x1;

s1 ^= s0;
x0 = Integer.rotateLeft(s0, 26) ^ s1 ^ (s1 << 9); // a, b
x1 = Integer.rotateLeft(s1, 13); // c

return z;
}

/**
* Creates a copy of the UniformRandomProvider and then <em>retreats</em> the state of the
* current instance. The copy is returned.
*
* <p>The jump is performed by advancing the state of the LCG sub-generator by 1 cycle.
* The XBG state is unchanged. The jump size is the equivalent of moving the state
* <em>backwards</em> by (2<sup>64</sup> - 1) positions. It can provide up to 2<sup>32</sup>
* non-overlapping subsequences.</p>
*/
@Override
public UniformRandomProvider jump() {
final UniformRandomProvider copy = new L32X64Mix(this);
// Advance the LCG 1 step
ls = M * ls + la;
resetCachedState();
return copy;
}

/**
* Creates a copy of the UniformRandomProvider and then <em>retreats</em> the state of the
* current instance. The copy is returned.
*
* <p>The jump is performed by advancing the state of the LCG sub-generator by
* 2<sup>16</sup> cycles. The XBG state is unchanged. The jump size is the equivalent
* of moving the state <em>backwards</em> by 2<sup>16</sup> (2<sup>64</sup> - 1)
* positions. It can provide up to 2<sup>16</sup> non-overlapping subsequences of
* length 2<sup>16</sup> (2<sup>64</sup> - 1); each subsequence can provide up to
* 2<sup>16</sup> non-overlapping subsequences of length (2<sup>64</sup> - 1) using
* the {@link #jump()} method.</p>
*/
@Override
public JumpableUniformRandomProvider longJump() {
final JumpableUniformRandomProvider copy = new L32X64Mix(this);
// Advance the LCG 2^16 steps
ls = LXMSupport.M32P * ls + LXMSupport.C32P * la;
resetCachedState();
return copy;
}
}
@@ -0,0 +1,82 @@
/*
* 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;

/**
* Utility support for the LXM family of generators. The LXM family is described
* in further detail in:
*
* <blockquote>Steele and Vigna (2021) LXM: better splittable pseudorandom number generators
* (and almost as fast). Proceedings of the ACM on Programming Languages, Volume 5,
* Article 148, pp 1–31.</blockquote>
*
* <p>Constants are provided to advance the state of an LCG by a power of 2 in a single
* multiply operation to support jump operations.
*
* @see <a href="https://doi.org/10.1145/3485525">Steele &amp; Vigna (2021) Proc. ACM Programming
* Languages 5, 1-31</a>
* @since 1.5
*/
final class LXMSupport {
/** 32-bit LCG multiplier. Note: (M % 8) = 5. */
static final int M32 = 0xadb4a92d;
/** Jump constant {@code m'} for an advance of the 32-bit LCG by 2^16.
* Computed as: {@code m' = m^(2^16) (mod 2^32)}. */
static final int M32P = 0x65640001;
/** Jump constant precursor for {@code c'} for an advance of the 32-bit LCG by 2^16.
* Computed as:
* <pre>
* product_{i=0}^{15} { M^(2^i) + 1 } (mod 2^32)
* </pre>
* <p>The jump is computed for the LCG with an update step of {@code s = m * s + c} as:
* <pre>
* s = m' * s + c' * c
* </pre>
*/
static final int C32P = 0x046b0000;

/** No instances. */
private LXMSupport() {}

/**
* Perform a 32-bit mixing function using Doug Lea's 32-bit mix constants and shifts.
*
* <p>This is based on the original 32-bit mix function of Austin Appleby's
* MurmurHash3 modified to use a single mix constant and 16-bit shifts, which may have
* a performance advantage on some processors.
*
* <p>The code was kindly provided by Guy Steele as a printing constraint led to
* its omission from Steele and Vigna's paper.
*
* <p>Note from Guy Steele:
* <blockquote>
* The constant 0xd36d884b was chosen by Doug Lea by taking the (two’s-complement)
* negation of the decimal constant 747796405, which appears in Table 5 of L’Ecuyer’s
* classic paper “Tables of Linear Congruential Generators of Different Sizes and Good
* Lattice Structure” (January 1999); the constant in lea64 was chosen in a similar manner.
* These choices were based on his engineering intuition and then validated by testing.
* </blockquote>
*
* @param x the input value
* @return the output value
*/
static int lea32(int x) {
x = (x ^ (x >>> 16)) * 0xd36d884b;
x = (x ^ (x >>> 16)) * 0xd36d884b;
return x ^ (x >>> 16);
}
}

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