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1   /*
2    * Licensed to the Apache Software Foundation (ASF) under one or more
3    * contributor license agreements.  See the NOTICE file distributed with
4    * this work for additional information regarding copyright ownership.
5    * The ASF licenses this file to You under the Apache License, Version 2.0
6    * (the "License"); you may not use this file except in compliance with
7    * the License.  You may obtain a copy of the License at
8    *
9    *      http://www.apache.org/licenses/LICENSE-2.0
10   *
11   * Unless required by applicable law or agreed to in writing, software
12   * distributed under the License is distributed on an "AS IS" BASIS,
13   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14   * See the License for the specific language governing permissions and
15   * limitations under the License.
16   */
17  package org.apache.commons.rng.core.source32;
18  
19  import org.apache.commons.rng.core.util.NumberFactory;
20  
21  /**
22   * This abstract class is a base for algorithms from the Permuted Congruential Generator (PCG)
23   * family that use an internal 64-bit Linear Congruential Generator (LCG) and output 32-bits
24   * per cycle.
25   *
26   * <h2>Note: PCG generators may exhibit massive stream correlation</h2>
27   *
28   * <p>Although the seed size is 128 bits, only the first 64 are effective: in effect,
29   * two seeds that only differ by the last 64 bits may produce highly correlated sequences.
30   *
31   * <p>Due to the use of an underlying linear congruential generator (LCG) alterations
32   * to the 128 bit seed have the following effect: the first 64-bits alter the
33   * generator state; the second 64 bits, with the exception of the most significant bit,
34   * which is discarded, choose between one of two alternative LCGs
35   * where the output of the chosen LCG is the same sequence except for an additive
36   * constant determined by the seed bits. The result is that seeds that differ
37   * only in the last 64-bits will have a 50% chance of producing highly correlated
38   * output sequences.
39  
40   * <p>Consider using the fixed increment variant where the 64-bit seed sets the
41   * generator state.
42   *
43   * <p>For further information see:
44   * <ul>
45   *  <li>
46   *   <blockquote>
47   *    Durst, M.J. (1989) <i>Using Linear Congruential Generators For Parallel Random Number Generation.
48   *    Section 3.1: Different additive constants in a maximum potency congruential generator</i>.
49   *    1989 Winter Simulation Conference Proceedings, Washington, DC, USA, 1989, pp. 462-466.
50   *   </blockquote>
51   *  </li>
52   * </ul>
53   *
54   * @see <a href="http://www.pcg-random.org/">
55   *  PCG, A Family of Better Random Number Generators</a>
56   * @see <a href="https://ieeexplore.ieee.org/document/718715">Durst, M.J. (1989)
57   *  Using Linear Congruential Generators For Parallel Random Number Generation</a>
58   * @see <a href="https://issues.apache.org/jira/browse/RNG-123">
59   *  PCG generators may exhibit massive stream correlation</a>
60   * @since 1.3
61   */
62  abstract class AbstractPcg6432 extends IntProvider {
63      /** Size of the seed array. */
64      private static final int SEED_SIZE = 2;
65      /** The default increment. */
66      private static final long DEFAULT_INCREMENT = 1442695040888963407L;
67  
68      /** The state of the LCG. */
69      private long state;
70  
71      /** The increment of the LCG. */
72      private long increment;
73  
74      /**
75       * Creates a new instance using a default increment.
76       *
77       * @param seed Initial state.
78       * @since 1.4
79       */
80      AbstractPcg6432(Long seed) {
81          increment = DEFAULT_INCREMENT;
82          state = bump(seed + this.increment);
83      }
84  
85      /**
86       * Creates a new instance.
87       *
88       * @param seed Initial seed.
89       * If the length is larger than 2, only the first 2 elements will
90       * be used; if smaller, the remaining elements will be automatically set.
91       *
92       * <p>The 1st element is used to set the LCG state. The 2nd element is used
93       * to set the LCG increment; the most significant bit
94       * is discarded by left shift and the increment is set to odd.</p>
95       */
96      AbstractPcg6432(long[] seed) {
97          if (seed.length < SEED_SIZE) {
98              final long[] tmp = new long[SEED_SIZE];
99              fillState(tmp, seed);
100             setSeedInternal(tmp);
101         } else {
102             setSeedInternal(seed);
103         }
104     }
105 
106     /**
107      * Seeds the RNG.
108      *
109      * @param seed Seed.
110      */
111     private void setSeedInternal(long[] seed) {
112         // Ensure the increment is odd to provide a maximal period LCG.
113         this.increment = (seed[1] << 1) | 1;
114         this.state = bump(seed[0] + this.increment);
115     }
116 
117     /**
118      * Provides the next state of the LCG.
119      *
120      * @param input Current state.
121      * @return next state
122      */
123     private long bump(long input) {
124         return input * 6364136223846793005L + increment;
125     }
126 
127     /** {@inheritDoc} */
128     @Override
129     public int next() {
130         final long x = state;
131         state = bump(state);
132         return transform(x);
133     }
134 
135     /**
136      * Transform the 64-bit state of the generator to a 32-bit output.
137      * The transformation function shall vary with respect to different generators.
138      *
139      * @param x State.
140      * @return the output
141      */
142     protected abstract int transform(long x);
143 
144     /** {@inheritDoc} */
145     @Override
146     protected byte[] getStateInternal() {
147         // The increment is divided by 2 before saving.
148         // This transform is used in the reference PCG code; it prevents restoring from
149         // a byte state a non-odd increment that results in a sub-maximal period generator.
150         return composeStateInternal(NumberFactory.makeByteArray(
151                 new long[] {state, increment >>> 1}),
152                 super.getStateInternal());
153     }
154 
155     /** {@inheritDoc} */
156     @Override
157     protected void setStateInternal(byte[] s) {
158         final byte[][] c = splitStateInternal(s, SEED_SIZE * 8);
159         final long[] tempseed = NumberFactory.makeLongArray(c[0]);
160         state = tempseed[0];
161         // Reverse the transform performed during getState to make the increment odd again.
162         increment = tempseed[1] << 1 | 1;
163         super.setStateInternal(c[1]);
164     }
165 }