| /* |
| * 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 & 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; |
| /** |
| * The fractional part of the golden ratio, phi, scaled to 32-bits and rounded to odd. |
| * <pre> |
| * phi = (sqrt(5) - 1) / 2) * 2^32 |
| * </pre> |
| * @see <a href="https://en.wikipedia.org/wiki/Golden_ratio">Golden ratio</a> |
| */ |
| static final int GOLDEN_RATIO_32 = 0x9e3779b9; |
| |
| /** 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); |
| } |
| } |