20 * |
20 * |
21 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
21 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
22 * or visit www.oracle.com if you need additional information or have any |
22 * or visit www.oracle.com if you need additional information or have any |
23 * questions. |
23 * questions. |
24 */ |
24 */ |
25 package java.util; |
25 |
|
26 package java.util.random; |
26 |
27 |
27 import java.math.BigInteger; |
28 import java.math.BigInteger; |
28 import java.util.concurrent.atomic.AtomicLong; |
29 import java.util.concurrent.atomic.AtomicLong; |
29 |
30 |
30 /** |
31 /** |
31 * A generator of uniform pseudorandom values applicable for use in |
32 * A generator of uniform pseudorandom values applicable for use in |
32 * (among other contexts) isolated parallel computations that may |
33 * (among other contexts) isolated parallel computations that may |
33 * generate subtasks. Class {@code Xoshiro256StarStar} implements |
34 * generate subtasks. Class {@link Xoshiro256StarStar} implements |
34 * interfaces {@link java.util.Rng} and {@link java.util.LeapableRng}, |
35 * interfaces {@link RandomNumberGenerator} and {@link LeapableRNG}, |
35 * and therefore supports methods for producing pseudorandomly chosen |
36 * and therefore supports methods for producing pseudorandomly chosen |
36 * numbers of type {@code int}, {@code long}, {@code float}, and {@code double} |
37 * numbers of type {@code int}, {@code long}, {@code float}, and {@code double} |
37 * as well as creating new {@code Xoshiro256StarStar} objects |
38 * as well as creating new {@link Xoshiro256StarStar} objects |
38 * by "jumping" or "leaping". |
39 * by "jumping" or "leaping". |
39 * |
40 * <p> |
40 * <p>Series of generated values pass the TestU01 BigCrush and PractRand test suites |
41 * Series of generated values pass the TestU01 BigCrush and PractRand test suites |
41 * that measure independence and uniformity properties of random number generators. |
42 * that measure independence and uniformity properties of random number generators. |
42 * (Most recently validated with |
43 * (Most recently validated with |
43 * <a href="http://simul.iro.umontreal.ca/testu01/tu01.html">version 1.2.3 of TestU01</a> |
44 * <a href="http://simul.iro.umontreal.ca/testu01/tu01.html">version 1.2.3 of TestU01</a> |
44 * and <a href="http://pracrand.sourceforge.net">version 0.90 of PractRand</a>. |
45 * and <a href="http://pracrand.sourceforge.net">version 0.90 of PractRand</a>. |
45 * Note that TestU01 BigCrush was used to test not only values produced by the {@code nextLong()} |
46 * Note that TestU01 BigCrush was used to test not only values produced by the {@code nextLong()} |
46 * method but also the result of bit-reversing each value produced by {@code nextLong()}.) |
47 * method but also the result of bit-reversing each value produced by {@code nextLong()}.) |
47 * These tests validate only the methods for certain |
48 * These tests validate only the methods for certain |
48 * types and ranges, but similar properties are expected to hold, at |
49 * types and ranges, but similar properties are expected to hold, at |
49 * least approximately, for others as well. |
50 * least approximately, for others as well. |
50 * |
51 * <p> |
51 * <p>The class {@code Xoshiro256StarStar} uses the {@code xoshiro256} algorithm, |
52 * The class {@link Xoshiro256StarStar} uses the {@code xoshiro256} algorithm, |
52 * version 1.0 (parameters 17, 45), with the "**" scrambler (a mixing function). |
53 * version 1.0 (parameters 17, 45), with the "**" scrambler (a mixing function). |
53 * Its state consists of four {@code long} fields {@code x0}, {@code x1}, {@code x2}, |
54 * Its state consists of four {@code long} fields {@code x0}, {@code x1}, {@code x2}, |
54 * and {@code x3}, which can take on any values provided that they are not all zero. |
55 * and {@code x3}, which can take on any values provided that they are not all zero. |
55 * The period of this generator is 2<sup>256</sup>-1. |
56 * The period of this generator is 2<sup>256</sup>-1. |
56 * |
57 * <p> |
57 * <p>The 64-bit values produced by the {@code nextLong()} method are equidistributed. |
58 * The 64-bit values produced by the {@code nextLong()} method are equidistributed. |
58 * To be precise, over the course of the cycle of length 2<sup>256</sup>-1, |
59 * To be precise, over the course of the cycle of length 2<sup>256</sup>-1, |
59 * each nonzero {@code long} value is generated 2<sup>192</sup> times, |
60 * each nonzero {@code long} value is generated 2<sup>192</sup> times, |
60 * but the value 0 is generated only 2<sup>192</sup>-1 times. |
61 * but the value 0 is generated only 2<sup>192</sup>-1 times. |
61 * The values produced by the {@code nextInt()}, {@code nextFloat()}, and {@code nextDouble()} |
62 * The values produced by the {@code nextInt()}, {@code nextFloat()}, and {@code nextDouble()} |
62 * methods are likewise equidistributed. |
63 * methods are likewise equidistributed. |
63 * |
64 * <p> |
64 * <p>In fact, the 64-bit values produced by the {@code nextLong()} method are 4-equidistributed. |
65 * In fact, the 64-bit values produced by the {@code nextLong()} method are 4-equidistributed. |
65 * To be precise: consider the (overlapping) length-4 subsequences of the cycle of 64-bit |
66 * To be precise: consider the (overlapping) length-4 subsequences of the cycle of 64-bit |
66 * values produced by {@code nextLong()} (assuming no other methods are called that would |
67 * values produced by {@code nextLong()} (assuming no other methods are called that would |
67 * affect the state). There are 2<sup>256</sup>-1 such subsequences, and each subsequence, |
68 * affect the state). There are 2<sup>256</sup>-1 such subsequences, and each subsequence, |
68 * which consists of 4 64-bit values, can have one of 2<sup>256</sup> values. Of those |
69 * which consists of 4 64-bit values, can have one of 2<sup>256</sup> values. Of those |
69 * 2<sup>256</sup> subsequence values, each one is generated exactly once over the course |
70 * 2<sup>256</sup> subsequence values, each one is generated exactly once over the course |
70 * of the entire cycle, except that the subsequence (0, 0, 0, 0) never appears. |
71 * of the entire cycle, except that the subsequence (0, 0, 0, 0) never appears. |
71 * The values produced by the {@code nextInt()}, {@code nextFloat()}, and {@code nextDouble()} |
72 * The values produced by the {@code nextInt()}, {@code nextFloat()}, and {@code nextDouble()} |
72 * methods are likewise 4-equidistributed, but note that that the subsequence (0, 0, 0, 0) |
73 * methods are likewise 4-equidistributed, but note that that the subsequence (0, 0, 0, 0) |
73 * can also appear (but occurring somewhat less frequently than all other subsequences), |
74 * can also appear (but occurring somewhat less frequently than all other subsequences), |
74 * because the values produced by those methods have fewer than 64 randomly chosen bits. |
75 * because the values produced by those methods have fewer than 64 randomly chosen bits. |
75 * |
76 * <p> |
76 * <p>Instances {@code Xoshiro256StarStar} are <em>not</em> thread-safe. |
77 * Instances {@link Xoshiro256StarStar} are <em>not</em> thread-safe. |
77 * They are designed to be used so that each thread as its own instance. |
78 * They are designed to be used so that each thread as its own instance. |
78 * The methods {@link #jump} and {@link #leap} and {@link #jumps} and {@link #leaps} |
79 * The methods {@link #jump} and {@link #leap} and {@link #jumps} and {@link #leaps} |
79 * can be used to construct new instances of {@code Xoshiro256StarStar} that traverse |
80 * can be used to construct new instances of {@link Xoshiro256StarStar} that traverse |
80 * other parts of the state cycle. |
81 * other parts of the state cycle. |
81 * |
82 * <p> |
82 * <p>Instances of {@code Xoshiro256StarStar} are not cryptographically |
83 * Instances of {@link Xoshiro256StarStar} are not cryptographically |
83 * secure. Consider instead using {@link java.security.SecureRandom} |
84 * secure. Consider instead using {@link java.security.SecureRandom} |
84 * in security-sensitive applications. Additionally, |
85 * in security-sensitive applications. Additionally, |
85 * default-constructed instances do not use a cryptographically random |
86 * default-constructed instances do not use a cryptographically random |
86 * seed unless the {@linkplain System#getProperty system property} |
87 * seed unless the {@linkplain System#getProperty system property} |
87 * {@code java.util.secureRandomSeed} is set to {@code true}. |
88 * {@code java.util.secureRandomSeed} is set to {@code true}. |
88 * |
89 * |
89 * @author Guy Steele |
90 * @since 14 |
90 * @since 1.9 |
|
91 */ |
91 */ |
92 public final class Xoshiro256StarStar implements LeapableRng { |
92 public final class Xoshiro256StarStar implements LeapableRNG { |
93 |
93 |
94 /* |
94 /* |
95 * Implementation Overview. |
95 * Implementation Overview. |
96 * |
96 * |
97 * This is an implementation of the xoroshiro128** algorithm written |
97 * This is an implementation of the xoroshiro128** algorithm written |
155 * @param x1 second word of the initial state |
155 * @param x1 second word of the initial state |
156 * @param x2 third word of the initial state |
156 * @param x2 third word of the initial state |
157 * @param x3 fourth word of the initial state |
157 * @param x3 fourth word of the initial state |
158 */ |
158 */ |
159 public Xoshiro256StarStar(long x0, long x1, long x2, long x3) { |
159 public Xoshiro256StarStar(long x0, long x1, long x2, long x3) { |
160 this.x0 = x0; |
|
161 this.x1 = x1; |
|
162 this.x2 = x2; |
|
163 this.x3 = x3; |
|
164 // If x0, x1, x2, and x3 are all zero, we must choose nonzero values. |
|
165 if ((x0 | x1 | x2 | x3) == 0) { |
|
166 // At least three of the four values generated here will be nonzero. |
|
167 this.x0 = RngSupport.mixStafford13(x0 += RngSupport.GOLDEN_RATIO_64); |
|
168 this.x1 = (x0 += RngSupport.GOLDEN_RATIO_64); |
|
169 this.x2 = (x0 += RngSupport.GOLDEN_RATIO_64); |
|
170 this.x3 = (x0 += RngSupport.GOLDEN_RATIO_64); |
|
171 } |
|
172 } |
|
173 |
|
174 /** |
|
175 * Creates a new instance of {@code Xoshiro256StarStar} using the |
|
176 * specified {@code long} value as the initial seed. Instances of |
|
177 * {@code Xoshiro256StarStar} created with the same seed in the same |
|
178 * program generate identical sequences of values. |
|
179 * |
|
180 * @param seed the initial seed |
|
181 */ |
|
182 public Xoshiro256StarStar(long seed) { |
|
183 // Using a value with irregularly spaced 1-bits to xor the seed |
|
184 // argument tends to improve "pedestrian" seeds such as 0 or |
|
185 // other small integers. We may as well use SILVER_RATIO_64. |
|
186 // |
|
187 // The x values are then filled in as if by a SplitMix PRNG with |
|
188 // GOLDEN_RATIO_64 as the gamma value and Stafford13 as the mixer. |
|
189 this(RngSupport.mixStafford13(seed ^= RngSupport.SILVER_RATIO_64), |
|
190 RngSupport.mixStafford13(seed += RngSupport.GOLDEN_RATIO_64), |
|
191 RngSupport.mixStafford13(seed += RngSupport.GOLDEN_RATIO_64), |
|
192 RngSupport.mixStafford13(seed + RngSupport.GOLDEN_RATIO_64)); |
|
193 } |
|
194 |
|
195 /** |
|
196 * Creates a new instance of {@code Xoshiro256StarStar} that is likely to |
|
197 * generate sequences of values that are statistically independent |
|
198 * of those of any other instances in the current program execution, |
|
199 * but may, and typically does, vary across program invocations. |
|
200 */ |
|
201 public Xoshiro256StarStar() { |
|
202 // Using GOLDEN_RATIO_64 here gives us a good Weyl sequence of values. |
|
203 this(defaultGen.getAndAdd(RngSupport.GOLDEN_RATIO_64)); |
|
204 } |
|
205 |
|
206 /** |
|
207 * Creates a new instance of {@code Xoshiro256StarStar} using the specified array of |
|
208 * initial seed bytes. Instances of {@code Xoshiro256StarStar} created with the same |
|
209 * seed array in the same program execution generate identical sequences of values. |
|
210 * |
|
211 * @param seed the initial seed |
|
212 */ |
|
213 public Xoshiro256StarStar(byte[] seed) { |
|
214 // Convert the seed to 4 long values, which are not all zero. |
|
215 long[] data = RngSupport.convertSeedBytesToLongs(seed, 4, 4); |
|
216 long x0 = data[0], x1 = data[1], x2 = data[2], x3 = data[3]; |
|
217 this.x0 = x0; |
160 this.x0 = x0; |
218 this.x1 = x1; |
161 this.x1 = x1; |
219 this.x2 = x2; |
162 this.x2 = x2; |
220 this.x3 = x3; |
163 this.x3 = x3; |
|
164 // If x0, x1, x2, and x3 are all zero, we must choose nonzero values. |
|
165 if ((x0 | x1 | x2 | x3) == 0) { |
|
166 // At least three of the four values generated here will be nonzero. |
|
167 this.x0 = RNGSupport.mixStafford13(x0 += RNGSupport.GOLDEN_RATIO_64); |
|
168 this.x1 = (x0 += RNGSupport.GOLDEN_RATIO_64); |
|
169 this.x2 = (x0 += RNGSupport.GOLDEN_RATIO_64); |
|
170 this.x3 = (x0 += RNGSupport.GOLDEN_RATIO_64); |
|
171 } |
|
172 } |
|
173 |
|
174 /** |
|
175 * Creates a new instance of {@link Xoshiro256StarStar} using the |
|
176 * specified {@code long} value as the initial seed. Instances of |
|
177 * {@link Xoshiro256StarStar} created with the same seed in the same |
|
178 * program generate identical sequences of values. |
|
179 * |
|
180 * @param seed the initial seed |
|
181 */ |
|
182 public Xoshiro256StarStar(long seed) { |
|
183 // Using a value with irregularly spaced 1-bits to xor the seed |
|
184 // argument tends to improve "pedestrian" seeds such as 0 or |
|
185 // other small integers. We may as well use SILVER_RATIO_64. |
|
186 // |
|
187 // The x values are then filled in as if by a SplitMix PRNG with |
|
188 // GOLDEN_RATIO_64 as the gamma value and Stafford13 as the mixer. |
|
189 this(RNGSupport.mixStafford13(seed ^= RNGSupport.SILVER_RATIO_64), |
|
190 RNGSupport.mixStafford13(seed += RNGSupport.GOLDEN_RATIO_64), |
|
191 RNGSupport.mixStafford13(seed += RNGSupport.GOLDEN_RATIO_64), |
|
192 RNGSupport.mixStafford13(seed + RNGSupport.GOLDEN_RATIO_64)); |
|
193 } |
|
194 |
|
195 /** |
|
196 * Creates a new instance of {@link Xoshiro256StarStar} that is likely to |
|
197 * generate sequences of values that are statistically independent |
|
198 * of those of any other instances in the current program execution, |
|
199 * but may, and typically does, vary across program invocations. |
|
200 */ |
|
201 public Xoshiro256StarStar() { |
|
202 // Using GOLDEN_RATIO_64 here gives us a good Weyl sequence of values. |
|
203 this(DEFAULT_GEN.getAndAdd(RNGSupport.GOLDEN_RATIO_64)); |
|
204 } |
|
205 |
|
206 /** |
|
207 * Creates a new instance of {@link Xoshiro256StarStar} using the specified array of |
|
208 * initial seed bytes. Instances of {@link Xoshiro256StarStar} created with the same |
|
209 * seed array in the same program execution generate identical sequences of values. |
|
210 * |
|
211 * @param seed the initial seed |
|
212 */ |
|
213 public Xoshiro256StarStar(byte[] seed) { |
|
214 // Convert the seed to 4 long values, which are not all zero. |
|
215 long[] data = RNGSupport.convertSeedBytesToLongs(seed, 4, 4); |
|
216 long x0 = data[0], x1 = data[1], x2 = data[2], x3 = data[3]; |
|
217 this.x0 = x0; |
|
218 this.x1 = x1; |
|
219 this.x2 = x2; |
|
220 this.x3 = x3; |
221 } |
221 } |
222 |
222 |
223 /* ---------------- public methods ---------------- */ |
223 /* ---------------- public methods ---------------- */ |
224 |
224 |
225 public Xoshiro256StarStar copy() { return new Xoshiro256StarStar(x0, x1, x2, x3); } |
225 public Xoshiro256StarStar copy() { |
|
226 return new Xoshiro256StarStar(x0, x1, x2, x3); |
|
227 } |
226 |
228 |
227 /** |
229 /** |
228 * Returns a pseudorandom {@code long} value. |
230 * Returns a pseudorandom {@code long} value. |
229 * |
231 * |
230 * @return a pseudorandom {@code long} value |
232 * @return a pseudorandom {@code long} value |
231 */ |
233 */ |
232 |
234 public long nextLong() { |
233 public long nextLong() { |
235 final long z = x0; |
234 final long z = x0; |
236 long q0 = x0, q1 = x1, q2 = x2, q3 = x3; |
235 long q0 = x0, q1 = x1, q2 = x2, q3 = x3; |
237 { long t = q1 << 17; q2 ^= q0; q3 ^= q1; q1 ^= q2; q0 ^= q3; q2 ^= t; q3 = Long.rotateLeft(q3, 45); } // xoshiro256 1.0 |
236 { long t = q1 << 17; q2 ^= q0; q3 ^= q1; q1 ^= q2; q0 ^= q3; q2 ^= t; q3 = Long.rotateLeft(q3, 45); } // xoshiro256 1.0 |
238 x0 = q0; x1 = q1; x2 = q2; x3 = q3; |
237 x0 = q0; x1 = q1; x2 = q2; x3 = q3; |
239 return Long.rotateLeft(z * 5, 7) * 9; // "starstar" mixing function |
238 return Long.rotateLeft(z * 5, 7) * 9; // "starstar" mixing function |
240 } |
239 } |
241 |
240 |
242 public BigInteger period() { |
241 public BigInteger period() { return thePeriod; } |
243 return PERIOD; |
242 |
244 } |
243 |
245 |
244 public double defaultJumpDistance() { return 0x1.0p64; } |
246 public double defaultJumpDistance() { |
245 public double defaultLeapDistance() { return 0x1.0p96; } |
247 return 0x1.0p64; |
|
248 } |
|
249 |
|
250 public double defaultLeapDistance() { |
|
251 return 0x1.0p96; |
|
252 } |
246 |
253 |
247 private static final long[] JUMP_TABLE = { |
254 private static final long[] JUMP_TABLE = { |
248 0x180ec6d33cfd0abaL, 0xd5a61266f0c9392cL, 0xa9582618e03fc9aaL, 0x39abdc4529b1661cL }; |
255 0x180ec6d33cfd0abaL, 0xd5a61266f0c9392cL, 0xa9582618e03fc9aaL, 0x39abdc4529b1661cL }; |
249 |
256 |
250 private static final long[] LEAP_TABLE = { |
257 private static final long[] LEAP_TABLE = { |
251 0x76e15d3efefdcbbfL, 0xc5004e441c522fb3L, 0x77710069854ee241L, 0x39109bb02acbe635L }; |
258 0x76e15d3efefdcbbfL, 0xc5004e441c522fb3L, 0x77710069854ee241L, 0x39109bb02acbe635L }; |
252 |
259 |
253 /* This is the jump function for the generator. It is equivalent |
260 /** |
254 to 2**128 calls to next(); it can be used to generate 2**128 |
261 * This is the jump function for the generator. It is equivalent to 2**128 calls to next(); it |
255 non-overlapping subsequences for parallel computations. */ |
262 * can be used to generate 2**128 non-overlapping subsequences for parallel computations. |
256 |
263 */ |
257 public void jump() { jumpAlgorithm(JUMP_TABLE); } |
264 public void jump() { |
258 |
265 jumpAlgorithm(JUMP_TABLE); |
259 /* This is the long-jump function for the generator. It is equivalent to |
266 } |
260 2**192 calls to next(); it can be used to generate 2**64 starting points, |
267 |
261 from each of which jump() will generate 2**64 non-overlapping |
268 /** |
262 subsequences for parallel distributed computations. */ |
269 * This is the long-jump function for the generator. It is equivalent to 2**192 calls to next(); |
263 |
270 * it can be used to generate 2**64 starting points, from each of which jump() will generate |
264 public void leap() { jumpAlgorithm(LEAP_TABLE); } |
271 * 2**64 non-overlapping subsequences for parallel distributed computations. |
|
272 */ |
|
273 public void leap() { |
|
274 jumpAlgorithm(LEAP_TABLE); |
|
275 } |
265 |
276 |
266 private void jumpAlgorithm(long[] table) { |
277 private void jumpAlgorithm(long[] table) { |
267 long s0 = 0, s1 = 0, s2 = 0, s3 = 0; |
278 long s0 = 0, s1 = 0, s2 = 0, s3 = 0; |
268 for (int i = 0; i < table.length; i++) { |
279 for (int i = 0; i < table.length; i++) { |
269 for (int b = 0; b < 64; b++) { |
280 for (int b = 0; b < 64; b++) { |
270 if ((table[i] & (1L << b)) != 0) { |
281 if ((table[i] & (1L << b)) != 0) { |
271 s0 ^= x0; |
282 s0 ^= x0; |
272 s1 ^= x1; |
283 s1 ^= x1; |
273 s2 ^= x2; |
284 s2 ^= x2; |
274 s3 ^= x3; |
285 s3 ^= x3; |
275 } |
286 } |
276 nextLong(); |
287 nextLong(); |
277 } |
288 } |
278 x0 = s0; |
289 x0 = s0; |
279 x1 = s1; |
290 x1 = s1; |
280 x2 = s2; |
291 x2 = s2; |
281 x3 = s3; |
292 x3 = s3; |
282 } |
293 } |
283 } |
294 } |
284 |
295 |
285 } |
296 } |