26 package java.util.random; |
26 package java.util.random; |
27 |
27 |
28 import java.math.BigInteger; |
28 import java.math.BigInteger; |
29 import java.util.concurrent.atomic.AtomicLong; |
29 import java.util.concurrent.atomic.AtomicLong; |
30 import java.util.random.RandomGenerator.SplittableGenerator; |
30 import java.util.random.RandomGenerator.SplittableGenerator; |
31 import java.util.random.RandomSupport.AbstractSplittableGenerator; |
31 import java.util.random.RandomSupport.AbstractSplittableWithBrineGenerator; |
32 |
32 |
33 /** |
33 /** |
34 * A generator of uniform pseudorandom values applicable for use in |
34 * A generator of uniform pseudorandom values applicable for use in |
35 * (among other contexts) isolated parallel computations that may |
35 * (among other contexts) isolated parallel computations that may |
36 * generate subtasks. Class {@link L64X256MixRandom} implements |
36 * generate subtasks. Class {@link L64X256MixRandom} implements |
52 * least approximately, for others as well. |
52 * least approximately, for others as well. |
53 * <p> |
53 * <p> |
54 * {@link L64X256MixRandom} is a specific member of the LXM family of algorithms |
54 * {@link L64X256MixRandom} is a specific member of the LXM family of algorithms |
55 * for pseudorandom number generators. Every LXM generator consists of two |
55 * for pseudorandom number generators. Every LXM generator consists of two |
56 * subgenerators; one is an LCG (Linear Congruential Generator) and the other is |
56 * subgenerators; one is an LCG (Linear Congruential Generator) and the other is |
57 * an Xorshift generator. Each output of an LXM generator is the sum of one |
57 * an Xorshift generator. Each output of an LXM generator is the result of |
58 * output from each subgenerator, possibly processed by a final mixing function |
58 * combining state from the LCG with state from the Xorshift generator by |
59 * (and {@link L64X256MixRandom} does use a mixing function). |
59 * using a Mixing function (and then the state of the LCG and the state of the |
|
60 * Xorshift generator are advanced). |
60 * <p> |
61 * <p> |
61 * The LCG subgenerator for {@link L64X256MixRandom} has an update step of the |
62 * The LCG subgenerator for {@link L64X256MixRandom} has an update step of the |
62 * form {@code s = m * s + a}, where {@code s}, {@code m}, and {@code a} are all |
63 * form {@code s = m * s + a}, where {@code s}, {@code m}, and {@code a} are all |
63 * of type {@code long}; {@code s} is the mutable state, the multiplier {@code m} |
64 * of type {@code long}; {@code s} is the mutable state, the multiplier {@code m} |
64 * is fixed (the same for all instances of {@link L64X256MixRandom}) and the addend |
65 * is fixed (the same for all instances of {@link L64X256MixRandom}) and the addend |
71 * version 1.0 (parameters 17, 45), without any final scrambler such as "+" or "**". |
72 * version 1.0 (parameters 17, 45), without any final scrambler such as "+" or "**". |
72 * Its state consists of four {@code long} fields {@code x0}, {@code x1}, {@code x2}, |
73 * Its state consists of four {@code long} fields {@code x0}, {@code x1}, {@code x2}, |
73 * and {@code x3}, which can take on any values provided that they are not all zero. |
74 * and {@code x3}, which can take on any values provided that they are not all zero. |
74 * The period of this subgenerator is 2<sup>256</sup>-1. |
75 * The period of this subgenerator is 2<sup>256</sup>-1. |
75 * <p> |
76 * <p> |
76 * The mixing function for {@link L64X256MixRandom} is the 64-bit MurmurHash3 finalizer. |
77 * The mixing function for {@link L64X256MixRandom} is {@link RandomSupport.mixLea64} |
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78 * applied to the argument {@code (s + x0)}. |
77 * <p> |
79 * <p> |
78 * Because the periods 2<sup>64</sup> and 2<sup>256</sup>-1 of the two subgenerators |
80 * Because the periods 2<sup>64</sup> and 2<sup>256</sup>-1 of the two subgenerators |
79 * are relatively prime, the <em>period</em> of any single {@link L64X256MixRandom} object |
81 * are relatively prime, the <em>period</em> of any single {@link L64X256MixRandom} object |
80 * (the length of the series of generated 64-bit values before it repeats) is the product |
82 * (the length of the series of generated 64-bit values before it repeats) is the product |
81 * of the periods of the subgenerators, that is, 2<sup>64</sup>(2<sup>256</sup>-1), |
83 * of the periods of the subgenerators, that is, 2<sup>64</sup>(2<sup>256</sup>-1), |
96 * There are 2<sup>64</sup>(2<sup>256</sup>-1) such subsequences, and each subsequence, |
98 * There are 2<sup>64</sup>(2<sup>256</sup>-1) such subsequences, and each subsequence, |
97 * which consists of 4 64-bit values, can have one of 2<sup>256</sup> values. Of those |
99 * which consists of 4 64-bit values, can have one of 2<sup>256</sup> values. Of those |
98 * 2<sup>256</sup> subsequence values, nearly all of them (2<sup>256</sup>-2<sup>64</sup>) |
100 * 2<sup>256</sup> subsequence values, nearly all of them (2<sup>256</sup>-2<sup>64</sup>) |
99 * occur 2<sup>64</sup> times over the course of the entire cycle, and the other |
101 * occur 2<sup>64</sup> times over the course of the entire cycle, and the other |
100 * 2<sup>64</sup> subsequence values occur only 2<sup>64</sup>-1 times. So the ratio |
102 * 2<sup>64</sup> subsequence values occur only 2<sup>64</sup>-1 times. So the ratio |
101 * of the probability of getting one of the less common subsequence values and the |
103 * of the probability of getting any specific one of the less common subsequence values and the |
102 * probability of getting one of the more common subsequence values is 1-2<sup>-64</sup>. |
104 * probability of getting any specific one of the more common subsequence values is 1-2<sup>-64</sup>. |
103 * (Note that the set of 2<sup>64</sup> less-common subsequence values will differ from |
105 * (Note that the set of 2<sup>64</sup> less-common subsequence values will differ from |
104 * one instance of {@link L64X256MixRandom} to another, as a function of the additive |
106 * one instance of {@link L64X256MixRandom} to another, as a function of the additive |
105 * parameter of the LCG.) The values produced by the {@code nextInt()}, {@code nextFloat()}, |
107 * parameter of the LCG.) The values produced by the {@code nextInt()}, {@code nextFloat()}, |
106 * and {@code nextDouble()} methods are likewise 4-equidistributed. |
108 * and {@code nextDouble()} methods are likewise 4-equidistributed. |
107 * <p> |
109 * <p> |
178 */ |
180 */ |
179 private static final BigInteger PERIOD = |
181 private static final BigInteger PERIOD = |
180 BigInteger.ONE.shiftLeft(256).subtract(BigInteger.ONE).shiftLeft(64); |
182 BigInteger.ONE.shiftLeft(256).subtract(BigInteger.ONE).shiftLeft(64); |
181 |
183 |
182 /* |
184 /* |
183 * Multiplier used in the LCG portion of the algorithm, taken from |
185 * Multiplier used in the LCG portion of the algorithm. |
184 * Pierre L'Ecuyer, Tables of linear congruential generators of |
186 * Chosen based on research by Sebastiano Vigna and Guy Steele (2019). |
185 * different sizes and good lattice structure, <em>Mathematics of |
187 * The spectral scores for dimensions 2 through 8 for the multiplier 0xd1342543de82ef95 |
186 * Computation</em> 68, 225 (January 1999), pages 249-260, |
188 * are [0.958602, 0.937479, 0.870757, 0.822326, 0.820405, 0.813065, 0.760215]. |
187 * Table 4 (first multiplier for size 2<sup>64</sup>). |
189 */ |
188 */ |
190 |
189 |
191 private static final long M = 0xd1342543de82ef95L; |
190 private static final long M = 2862933555777941757L; |
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191 |
192 |
192 /* ---------------- instance fields ---------------- */ |
193 /* ---------------- instance fields ---------------- */ |
193 |
194 |
194 /** |
195 /** |
195 * The parameter that is used as an additive constant for the LCG. |
196 * The parameter that is used as an additive constant for the LCG. |
225 this.x1 = x1; |
226 this.x1 = x1; |
226 this.x2 = x2; |
227 this.x2 = x2; |
227 this.x3 = x3; |
228 this.x3 = x3; |
228 // If x0, x1, x2, and x3 are all zero, we must choose nonzero values. |
229 // If x0, x1, x2, and x3 are all zero, we must choose nonzero values. |
229 if ((x0 | x1 | x2 | x3) == 0) { |
230 if ((x0 | x1 | x2 | x3) == 0) { |
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231 long v = s; |
230 // At least three of the four values generated here will be nonzero. |
232 // At least three of the four values generated here will be nonzero. |
231 this.x0 = RandomSupport.mixStafford13(s += RandomSupport.GOLDEN_RATIO_64); |
233 this.x0 = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64); |
232 this.x1 = RandomSupport.mixStafford13(s += RandomSupport.GOLDEN_RATIO_64); |
234 this.x1 = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64); |
233 this.x2 = RandomSupport.mixStafford13(s += RandomSupport.GOLDEN_RATIO_64); |
235 this.x2 = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64); |
234 this.x3 = RandomSupport.mixStafford13(s + RandomSupport.GOLDEN_RATIO_64); |
236 this.x3 = RandomSupport.mixStafford13(v + RandomSupport.GOLDEN_RATIO_64); |
235 } |
237 } |
236 } |
238 } |
237 |
239 |
238 /** |
240 /** |
239 * Creates a new instance of {@link L64X256MixRandom} using the |
241 * Creates a new instance of {@link L64X256MixRandom} using the |
250 // |
252 // |
251 // The seed is hashed by mixMurmur64 to produce the `a` parameter. |
253 // The seed is hashed by mixMurmur64 to produce the `a` parameter. |
252 // The seed is hashed by mixStafford13 to produce the initial `x0`, |
254 // The seed is hashed by mixStafford13 to produce the initial `x0`, |
253 // which will then be used to produce the first generated value. |
255 // which will then be used to produce the first generated value. |
254 // The other x values are filled in as if by a SplitMix PRNG with |
256 // The other x values are filled in as if by a SplitMix PRNG with |
255 // GOLDEN_RATIO_64 as the gamma value and Stafford13 as the mixer. |
257 // GOLDEN_RATIO_64 as the gamma value and mixStafford13 as the mixer. |
256 this(RandomSupport.mixMurmur64(seed ^= RandomSupport.SILVER_RATIO_64), |
258 this(RandomSupport.mixMurmur64(seed ^= RandomSupport.SILVER_RATIO_64), |
257 1, |
259 1, |
258 RandomSupport.mixStafford13(seed), |
260 RandomSupport.mixStafford13(seed), |
259 RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
261 RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
260 RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
262 RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
293 } |
295 } |
294 |
296 |
295 /* ---------------- public methods ---------------- */ |
297 /* ---------------- public methods ---------------- */ |
296 |
298 |
297 /** |
299 /** |
298 * Constructs and returns a new instance of {@link L64X256MixRandom} |
300 * Given 63 bits of "brine", constructs and returns a new instance of |
299 * that shares no mutable state with this instance. |
301 * {@code L64X256MixRandom} that shares no mutable state with this instance. |
300 * However, with very high probability, the set of values collectively |
302 * However, with very high probability, the set of values collectively |
301 * generated by the two objects has the same statistical properties as if |
303 * generated by the two objects has the same statistical properties as if |
302 * same the quantity of values were generated by a single thread using |
304 * same the quantity of values were generated by a single thread using |
303 * a single {@link L64X256MixRandom} object. Either or both of the two |
305 * a single {@code L64X256MixRandom} object. Either or both of the two |
304 * objects may be further split using the {@code split} method, |
306 * objects may be further split using the {@code split} method, |
305 * and the same expected statistical properties apply to the |
307 * and the same expected statistical properties apply to the |
306 * entire set of generators constructed by such recursive splitting. |
308 * entire set of generators constructed by such recursive splitting. |
307 * |
309 * |
308 * @param source a {@link SplittableGenerator} instance to be used instead |
310 * @param source a {@code SplittableGenerator} instance to be used instead |
309 * of this one as a source of pseudorandom bits used to |
311 * of this one as a source of pseudorandom bits used to |
310 * initialize the state of the new ones. |
312 * initialize the state of the new ones. |
311 * |
313 * @param brine a long value, of which the low 63 bits are used to choose |
312 * @return a new instance of {@link L64X256MixRandom} |
314 * the {@code a} parameter for the new instance. |
313 */ |
315 * @return a new instance of {@code L64X256MixRandom} |
314 public L64X256MixRandom split(SplittableGenerator source) { |
316 */ |
315 // Literally pick a new instance "at random". |
317 public SplittableGenerator split(SplittableGenerator source, long brine) { |
316 return new L64X256MixRandom(source.nextLong(), source.nextLong(), |
318 // Pick a new instance "at random", but use the brine for `a`. |
317 source.nextLong(), source.nextLong(), |
319 return new L64X256MixRandom(brine << 1, source.nextLong(), |
318 source.nextLong(), source.nextLong()); |
320 source.nextLong(), source.nextLong(), |
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321 source.nextLong(), source.nextLong()); |
319 } |
322 } |
320 |
323 |
321 /** |
324 /** |
322 * Returns a pseudorandom {@code long} value. |
325 * Returns a pseudorandom {@code long} value. |
323 * |
326 * |
324 * @return a pseudorandom {@code long} value |
327 * @return a pseudorandom {@code long} value |
325 */ |
328 */ |
326 public long nextLong() { |
329 public long nextLong() { |
327 final long z = s + x0; |
330 // Compute the result based on current state information |
328 s = M * s + a; // LCG |
331 // (this allows the computation to be overlapped with state update). |
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332 final long result = RandomSupport.mixLea64(s + x0); |
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333 // Update the LCG subgenerator |
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334 s = M * s + a; |
|
335 // Update the Xorshift subgenerator |
329 long q0 = x0, q1 = x1, q2 = x2, q3 = x3; |
336 long q0 = x0, q1 = x1, q2 = x2, q3 = x3; |
330 { // xoshiro256 1.0 |
337 { // xoshiro256 1.0 |
331 long t = q1 << 17; |
338 long t = q1 << 17; |
332 q2 ^= q0; |
339 q2 ^= q0; |
333 q3 ^= q1; |
340 q3 ^= q1; |