XorSAR++/+* PRNG, 16-bit State Example and Working Code, 4 to 28-Bit State Constants, 64-Bit State Example ASM Dump
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Cerian Knight
Dec 29, 2018, 7:30:37 PM12/29/18
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Normal approaches to creating pseudo-randomness often fall victim to artifacts from the structure of traditional math operations, excessive complexity, trivial or accidental invertibility, unusable portions of state, escape-from-zero issues, and/or run slowly due to the use of conventional non-linear functions.
The XorSAR (for Signed Arithmetic Rotation) class of PRNGs attempts to escape those pitfalls by using two simple rotation operations, but one is a custom signed rotation on a single state variable, and the other is a standard rotation on the state sum added or multiplied by a constant (A) and then xor masked with another constant (B). In that way randomness in the bits is propagated simultaneously from both ends, as well as toward the middle by twisting (C) the stream to normalize the endpoint randomness throughout. The result is that nearly all remnants of order are disseminated across all bits fairly evenly (when the best constants are used) to ensure that common failings in statistical tests do not occur prematurely.
As a consequence of the design focus on the extremes of statistical randomness, speed, and code simplicity, while retaining
desirable equidistribution properties, some other desirable properties of a general purpose PRNG must have necessarily been lost in the process? The short answer may be 'yes', as the equations describing the generator as a whole, or its individual bits, are difficult to express comprehensibly in any form (linear, modular, etc., by me anyway). This makes it difficult to expandthe state/period to a more useful size, create independent steams, or implement seek-ability. On the plus-side, invertibilityis more of a challenge, but likely a meaningless consideration for this generator class in its current non-cryptographic form.
The simplest possible useful example that demonstrates the power of this method (and signed arithmetic rotation, in particular) is the following 16-bit state / 8-bit output XorSAR8+* 1D and 2D code with a period of 65535 (full ++ and +* code farther down):
// Introductory example C++ XorSAR+* code (c) Chris Rutz
#include <stdint.h>
// Seed state not everywhere 0
uint8_t s[2] = {0,1};
inline uint8_t rar8(int8_t x) {
return (uint8_t)
inline uint8_t xorSAR16ps1D() {
uint8_t result1D = (s[0] - s[1]); // this 1D code line has been revised to use subtraction, as xor is sub-optimal
uint8_t tmp = (s[0] + s[1]) * A;
s[0] = rar8(s[1]);
s[1] = tmp; // Normal bit xor and rotation here is not possible in this example, due to the chosen A constant
return result1D; } // Optional bit xor to map the single missing output to zero is not needed, due to the chosen A constant
inline uint8_t xorSAR16ps2D() {
uint8_t result2D = (s[0] + s[1]) * A;
s[0] = rar8(s[1]);
s[1] = result2D;
return result2D; }
In the above case the rest of the normal XorSAR constants associated with A = 115 cancel to zero (B/C/D/X/Y all = 0), which makes this code the fastest, though not the most statistically random (as it is running with 'one hand tied behind its back'), of the plus star class. However, do not be fooled by the simplicity... even this example case exceeds the statistical randomness of many comparable PRNGs of the same state size (for both 1D and 2D).
XorSAR is very fast in a 128-bit state form... ready for full testing if/when full-period 64-bit constants become available (which will determine the efficacy of this algorithmic methodology). If the A/B constants are changed to dynamic variables and the D constant = 0, the speed of the 128-bit ++ 2D variant is comparable to xoroshiro128**and Lehmer128 (when it is similarly optimized with dynamic variables for constants, as the default implementation formany PRNGs does not take into account the pipeline burden of in-lining normal constants with code under modern CPU architectures).Full period 4-bit to 28-bit state constants, with arbitrary bit width rotation code, added as the first reply to this post: Constants
Example 128-bit state assembly language code added as second reply (using fictitious ABC constants), thus demonstrating the underlying simplicity of the C++ code, which (hopefully at 32-bit state and above) belies its power: xorSAR128pp ASM
Let me know if you find this useful, have comments... or if you have some magical way to find constants required to extend this logic to a 32-bit state, or beyond. I believe that mathematical study of the properties of and solutions to systems of equations involving signed arithmetic right rotations could be very useful, with possible applications beyond PRNGs (e.g., fast-hash, cryptographic, holographic data storage/compression, astrophysics, etc.) becoming somewhat more plausible as one studies the obfuscated order resulting from the algorithmic implementation. For example, as a speculative thought-experiment, try extending the logic of the rar function (modified to invert the lsb before shifting zero bits left on to itself) down to a single set bit of input and you will reach a logical impasse reminiscent of either cooper-pairs in superconductors or quantum-entangled qubits, where the math might be better expressed as a wave-function, which collapseswhen additional bits are added.
16-bit state / 8-bit output / 1 and 2-Dimensional Equidistribution - Working Code:
// Original work (c) Chris Rutz, free for all uses in this 16-bit state form.
// Example C++ code of my XorSAR++ class generator with a period of 65535.
// Fast 8-bit output, 16-bit state.
// 1 or 2-dimensional equidistribution (short by a single 0 output, when D is used).
// PRNG combines output scrambler with calculation, while maintaining 2-dimensional equidistribution,
// reducible to 1D by returning xor of state.
// Inspired by G. Marsaglia, S. Vigna/D. Blackman, M. O'Neill, and my work with pre-selection masks
// for use with Echelle gratings used in some AES/OES (atomic/optical emission spectrometer) variants.
#include <stdint.h>
// Best known constants for 16-bit state 1D/2D ++ variant (for all ++/+*
const uint8_t A = 0xeb; // Constant A ADD
const uint8_t B = 0x73; // Constant B XOR
const int C = 3; // Constant C ROL (0 is fastest, but much less random)
const uint8_t D2 = 0x04; // Remap short 2D output to zero (only if required, 0 is fastest)
const uint8_t D1 = 0xe5; // Remap short 1D output to zero (only if required, 0 is fastest)
const uint8_t X = 0x5e; // Seed state 0 XOR mask const uint8_t Y = 0xbb; // Seed state 1 XOR maskconst uint8_t W = 8; // Output word size
// 16-bit state must not be directly seeded with above X and Y values simultaneously
uint8_t s[2];
// Call this function to seed properly with 16 random bits, not everywhere zero
void xorSAR16_seed(uint16_t seed) {
s[0] = seed ^ X;
s[1] = (seed >> W) ^ Y; }
// 8-bit signed arithmetic right rotation
inline uint8_t rar8(int8_t x) {
return (uint8_t)(x / 2 ^ ((W -
// Old rar8, may be faster with some compilers
// inline uint8_t rar8o(int8_t x) {
// uint8_t tmp = (x / 2) ^ (x << (W - 1));
// if (x!=-1) { return tmp; } else { return 1 << (W - 2); } }
// 8-bit unsigned left rotation
inline uint8_t rol8(uint8_t x, int k) {
return (x << k) | (x >> (W
// 2-Dimensional output ++ variant (fastest overall)
inline uint8_t xorSAR16pp2D() {
uint8_t result = s[0] + s[1] + A;
s[0] = rar8(s[1]);
s[1] = rol8(result ^ B, C);
return result ^ D2; } // Use D2 constant, only if required
// 2-Dimensional output +* variant (most random 2D)
inline uint8_t xorSAR16ps2D() {
uint8_t result = (s[0] + s[1]) * A;
s[0] = rar8(s[1]);
s[1] = rol8(result ^ B, C);
return result ^ D2; } // Use D2 constant, only if required
// 1-Dimensional output ++ variant (fastest 1D)
inline uint8_t xorSAR16pp1D() {
uint8_t result = s[0] ^ s[1]; // this 1D code line currently under review, as xor is sub-optimal
s[0] = rar8(s[1]);
s[1] = rol8(tmp ^ B, C);
return result ^ D1; } // Use D1 constant, only if required
// 1-Dimensional output +* variant (most statistically random overall)
inline uint8_t xorSAR16ps1D() {
uint8_t result = s[0] ^ s[1]; // this 1D code line currently under review, as xor is sub-optimal
s[0] = rar8(s[1]);
s[1] = rol8(tmp ^ B, C);
return result ^ D1; } // Use D1 constant, only if required
// Constants (hex) for 8-bit output / 16-bit state / 65535 period XorSAR16plusplus:
// A B C D2 D1 X Y
// D9 6 0 54 7B 29 52
// 41 2C 0 EA 25 E3 C6
// D2 2D 0 B 35 13 26
// B5 5B 0 72 BD 94 29
// 59 86 0 D4 7B 29 52
// C1 AC 0 6A 25 E3 C6
// 52 AD 0 8B 35 13 26
// 35 DB 0 F2 BD 94 29
// 5C 23 2 79 DD B4 69
// DC A3 2 F9 DD B4 69
// 81 1F 3 9 68 D8 B0
// EB 73 3 4 E5 5E BB //recommended for fast 2D
// 1 9F 3 89 68 D8 B0
// 6B F3 3 84 E5 5E BB
// 8C 3 4 2F 23 E1 C2
// C1 50 4 3A 75 D3 A6
// E7 68 4 C6 1F F5 EA
// C 83 4 AF 23 E1 C2
// 41 D0 4 BA 75 D3 A6
// 67 E8 4 46 1F F5 EA
// EC 6B 5 44 96 73 E5
// 6C EB 5 C4 96 73 E5
// 1 2F 6 50 AF 70 DF
// 81 AF 6 D0 AF 70 DF
// 7F 52 7 90 D1 B0 61
// 52 76 7 FB 25 E3 C6
// FF D2 7 10 D1 B0 61
// D2 F6 7 7B 25 E3 C6
// Constants (hex) for 8-bit output / 16-bit state / 65535 period XorSAR16plusstar:
// A B C D2 D1 X Y
// 73 0 0 0 0 0 0 // Constants for Preliminary Example
// D1 69 0 6 D8 B7 6F
// D9 40 1 60 60 20 40
// D1 58 2 70 70 D0 A0
// 27 20 4 78 C6 43 85
// D7 91 4 A4 FA A9 53 // Excellent statistics, both 1D and 2D
// 93 F8 4 6F C5 BC 79
// BD 64 5 8F C3 BE 7D
// FF 2D 7 EF D1 B0 61
// 9B C7 7 2B 4D 3B 76
// 27 DF 7 83 39 17 2ECerian Knight
Dec 29, 2018, 8:40:44 PM12/29/18
to xorsar...@googlegroups.com
Below is a list of the full period constants for 2-bit to 14-bit output / 4-bit to 28-bit state xorSARpp and XorSARps, for reference.
However, code modification is required to support output word bit sizes other than 8/16/32/64. Example arbitrary bit rotation code at bottom of this post.
XorSARpp:
Word(b) State(b) Period A B C D2 D1 X Y
2 4 15 0 2 0 3 3 2 1
2 4 15 1 0 0 2 1 3 2
2 4 15 2 0 0 1 3 2 1
2 4 15 3 2 0 0 1 3 2
2 4 15 0 1 1 3 3 2 1
2 4 15 0 3 1 0 2 1 3
2 4 15 1 1 1 1 0 0 0
2 4 15 1 3 1 2 1 3 2
2 4 15 2 1 1 2 2 1 3
2 4 15 2 3 1 1 3 2 1
2 4 15 3 1 1 0 1 3 2
2 4 15 3 3 1 3 0 0 0
3 6 63 1 4 0 1 6 3 5
3 6 63 5 0 0 5 6 3 5
3 6 63 2 2 1 2 0 0 0
3 6 63 6 6 1 6 0 0 0
4 8 255 4 4 0 4 0 0 0
4 8 255 12 12 0 12 0 0 0
4 8 255 4 12 1 8 4 12 8
4 8 255 12 4 1 0 4 12 8
4 8 255 1 0 3 4 3 1 2
4 8 255 1 10 3 0 15 10 5
4 8 255 4 4 3 4 0 0 0
4 8 255 9 2 3 8 15 10 5
4 8 255 9 8 3 12 3 1 2
4 8 255 12 12 3 12 0 0 0
5 10 1023 0 27 0 21 9 7 14
5 10 1023 1 5 0 13 12 4 8
5 10 1023 10 6 0 30 4 28 24
5 10 1023 16 11 0 5 9 7 14
5 10 1023 17 21 0 29 12 4 8
5 10 1023 26 22 0 14 4 28 24
5 10 1023 3 8 2 9 6 2 4
5 10 1023 19 24 2 25 6 2 4
5 10 1023 1 11 3 9 8 24 16
5 10 1023 5 15 3 13 8 24 16
5 10 1023 17 27 3 25 8 24 16
5 10 1023 21 31 3 29 8 24 16
5 10 1023 6 7 4 27 9 7 14
5 10 1023 11 13 4 18 23 8 31
5 10 1023 13 14 4 4 23 18 5
5 10 1023 22 23 4 11 9 7 14
5 10 1023 27 29 4 2 23 8 31
5 10 1023 29 30 4 20 23 18 5
6 12 4095 3 55 0 31 28 52 40
6 12 4095 11 60 0 30 19 49 34
6 12 4095 17 47 0 35 10 6 12
6 12 4095 35 23 0 63 28 52 40
6 12 4095 43 28 0 62 19 49 34
6 12 4095 49 15 0 3 10 6 12
6 12 4095 25 21 2 62 25 55 46
6 12 4095 28 35 2 34 6 2 4
6 12 4095 57 53 2 30 25 55 46
6 12 4095 60 3 2 2 6 2 4
6 12 4095 14 23 4 9 51 20 39
6 12 4095 46 55 4 41 51 20 39
6 12 4095 4 42 5 29 37 30 59
6 12 4095 36 10 5 61 37 30 59
7 14 16383 11 81 0 88 77 68 9
7 14 16383 18 116 0 0 14 122 116
7 14 16383 75 17 0 24 77 68 9
7 14 16383 82 52 0 64 14 122 116
7 14 16383 25 43 2 114 21 115 102
7 14 16383 89 107 2 50 21 115 102
7 14 16383 46 20 4 52 6 2 4
7 14 16383 110 84 4 116 6 2 4
7 14 16383 6 93 6 54 78 59 117
7 14 16383 28 51 6 1 85 76 25
7 14 16383 43 61 6 34 103 40 79
7 14 16383 55 82 6 70 15 5 10
7 14 16383 70 29 6 118 78 59 117
7 14 16383 92 115 6 65 85 76 25
7 14 16383 107 125 6 98 103 40 79
7 14 16383 119 18 6 6 15 5 10
8 16 65535 53 219 0 242 189 148 41
8 16 65535 65 44 0 234 37 227 198
8 16 65535 82 173 0 139 53 19 38
8 16 65535 89 134 0 212 123 41 82
8 16 65535 181 91 0 114 189 148 41
8 16 65535 193 172 0 106 37 227 198
8 16 65535 210 45 0 11 53 19 38
8 16 65535 217 6 0 84 123 41 82
8 16 65535 92 35 2 121 221 180 105
8 16 65535 220 163 2 249 221 180 105
8 16 65535 1 159 3 137 104 216 176
8 16 65535 107 243 3 132 229 94 187
8 16 65535 129 31 3 9 104 216 176
8 16 65535 235 115 3 4 229 94 187
8 16 65535 12 131 4 175 35 225 194
8 16 65535 65 208 4 186 117 211 166
8 16 65535 103 232 4 70 31 245 234
8 16 65535 140 3 4 47 35 225 194
8 16 65535 193 80 4 58 117 211 166
8 16 65535 231 104 4 198 31 245 234
8 16 65535 108 235 5 196 150 115 229
8 16 65535 236 107 5 68 150 115 229
8 16 65535 1 47 6 80 175 112 223
8 16 65535 129 175 6 208 175 112 223
8 16 65535 82 118 7 251 37 227 198
8 16 65535 127 82 7 144 209 176 97
8 16 65535 210 246 7 123 37 227 198
8 16 65535 255 210 7 16 209 176 97
9 18 262143 0 85 0 255 255 85 170
9 18 262143 9 501 0 102 345 202 403
9 18 262143 12 36 0 404 104 472 432
9 18 262143 135 297 0 54 399 144 287
9 18 262143 256 341 0 511 255 85 170
9 18 262143 265 245 0 358 345 202 403
9 18 262143 268 292 0 148 104 472 432
9 18 262143 391 41 0 310 399 144 287
9 18 262143 42 197 2 216 78 58 116
9 18 262143 59 172 2 185 126 42 84
9 18 262143 298 453 2 472 78 58 116
9 18 262143 315 428 2 441 126 42 84
9 18 262143 7 380 3 312 305 272 33
9 18 262143 104 322 3 197 33 31 62
9 18 262143 263 124 3 56 305 272 33
9 18 262143 360 66 3 453 33 31 62
9 18 262143 103 305 4 244 113 47 94
9 18 262143 240 132 4 219 11 505 498
9 18 262143 359 49 4 500 113 47 94
9 18 262143 496 388 4 475 11 505 498
9 18 262143 21 63 5 371 94 458 404
9 18 262143 122 416 5 89 415 160 319
9 18 262143 166 33 5 79 37 483 454
9 18 262143 198 337 5 443 233 423 334
9 18 262143 277 319 5 115 94 458 404
9 18 262143 378 160 5 345 415 160 319
9 18 262143 422 289 5 335 37 483 454
9 18 262143 454 81 5 187 233 423 334
9 18 262143 66 437 6 120 452 189 377
9 18 262143 322 181 6 376 452 189 377
9 18 262143 71 314 7 242 75 57 114
9 18 262143 226 277 7 322 350 203 405
9 18 262143 327 58 7 498 75 57 114
9 18 262143 482 21 7 66 350 203 405
9 18 262143 5 139 8 166 157 395 278
9 18 262143 261 395 8 422 157 395 278
10 20 1048575 104 791 0 593 485 163 326
10 20 1048575 355 232 0 387 990 693 363
10 20 1048575 405 705 0 921 500 172 344
10 20 1048575 419 799 0 468 941 358 715
10 20 1048575 492 979 0 789 165 99 198
10 20 1048575 616 279 0 81 485 163 326
10 20 1048575 867 744 0 899 990 693 363
10 20 1048575 917 193 0 409 500 172 344
10 20 1048575 931 287 0 980 941 358 715
10 20 1048575 1004 467 0 277 165 99 198
10 20 1048575 49 86 2 1014 961 322 643
10 20 1048575 379 809 2 895 500 172 344
10 20 1048575 561 598 2 502 961 322 643
10 20 1048575 891 297 2 383 500 172 344
10 20 1048575 159 741 3 529 624 465 929
10 20 1048575 295 1005 3 718 407 141 282
10 20 1048575 351 474 3 277 836 317 633
10 20 1048575 473 238 3 404 59 1001 978
10 20 1048575 671 229 3 17 624 465 929
10 20 1048575 807 493 3 206 407 141 282
10 20 1048575 863 986 3 789 836 317 633
10 20 1048575 985 750 3 916 59 1001 978
10 20 1048575 142 272 4 778 380 212 424
10 20 1048575 654 784 4 266 380 212 424
10 20 1048575 346 923 5 713 367 805 586
10 20 1048575 858 411 5 201 367 805 586
10 20 1048575 376 71 7 949 449 191 382
10 20 1048575 888 583 7 437 449 191 382
10 20 1048575 186 44 8 718 484 860 696
10 20 1048575 698 556 8 206 484 860 696
10 20 1048575 8 80 9 176 72 56 112
10 20 1048575 295 542 9 575 280 776 528
10 20 1048575 393 1012 9 805 348 820 616
10 20 1048575 520 592 9 688 72 56 112
10 20 1048575 807 30 9 63 280 776 528
10 20 1048575 905 500 9 293 348 820 616
11 22 4194303 242 1502 0 1447 1093 1084 121
11 22 4194303 502 101 0 958 1590 1517 987
11 22 4194303 597 1352 0 429 1686 627 1253
11 22 4194303 787 448 0 1434 631 1581 1114
11 22 4194303 860 583 0 2041 865 1759 1470
11 22 4194303 865 1328 0 622 241 1967 1886
11 22 4194303 910 349 0 1636 1188 925 1849
11 22 4194303 1004 806 0 707 1303 1266 485
11 22 4194303 1266 478 0 423 1093 1084 121
11 22 4194303 1526 1125 0 1982 1590 1517 987
11 22 4194303 1621 328 0 1453 1686 627 1253
11 22 4194303 1811 1472 0 410 631 1581 1114
11 22 4194303 1884 1607 0 1017 865 1759 1470
11 22 4194303 1889 304 0 1646 241 1967 1886
11 22 4194303 1934 1373 0 612 1188 925 1849
11 22 4194303 2028 1830 0 1731 1303 1266 485
11 22 4194303 194 185 3 1060 666 1654 1260
11 22 4194303 1218 1209 3 36 666 1654 1260
11 22 4194303 608 684 5 206 1644 549 1097
11 22 4194303 707 447 5 1435 728 1608 1168
11 22 4194303 922 866 5 76 810 1766 1484
11 22 4194303 1632 1708 5 1230 1644 549 1097
11 22 4194303 1731 1471 5 411 728 1608 1168
11 22 4194303 1946 1890 5 1100 810 1766 1484
11 22 4194303 472 491 7 1237 1273 938 1875
11 22 4194303 651 1757 7 1278 371 209 418
11 22 4194303 1496 1515 7 213 1273 938 1875
11 22 4194303 1675 733 7 254 371 209 418
11 22 4194303 280 1354 8 1096 816 272 544
11 22 4194303 1304 330 8 72 816 272 544
11 22 4194303 110 1187 9 731 337 207 414
11 22 4194303 393 829 9 360 2015 1354 661
11 22 4194303 1134 163 9 1755 337 207 414
11 22 4194303 1417 1853 9 1384 2015 1354 661
11 22 4194303 43 1668 10 1053 1002 1702 1356
11 22 4194303 524 217 10 1493 965 323 646
11 22 4194303 525 1255 10 1370 689 1647 1246
11 22 4194303 1067 644 10 29 1002 1702 1356
11 22 4194303 1548 1241 10 469 965 323 646
11 22 4194303 1549 231 10 346 689 1647 1246
12 24 16777215 36 1659 0 2653 565 3603 3110
12 24 16777215 718 1879 0 4074 3298 1119 2237
12 24 16777215 1006 1272 0 2603 2489 1898 3795
12 24 16777215 1077 644 0 11 3016 2375 655
12 24 16777215 1348 1283 0 3701 1741 3515 2934
12 24 16777215 1504 1330 0 2921 2421 1838 3675
12 24 16777215 1644 291 0 1472 3730 2673 1251
12 24 16777215 1996 2982 0 130 1718 3474 2852
12 24 16777215 2084 3707 0 605 565 3603 3110
12 24 16777215 2766 3927 0 2026 3298 1119 2237
12 24 16777215 3054 3320 0 555 2489 1898 3795
12 24 16777215 3125 2692 0 2059 3016 2375 655
12 24 16777215 3396 3331 0 1653 1741 3515 2934
12 24 16777215 3552 3378 0 873 2421 1838 3675
12 24 16777215 3692 2339 0 3520 3730 2673 1251
12 24 16777215 4044 934 0 2178 1718 3474 2852
12 24 16777215 88 3974 2 1469 1177 3191 2286
12 24 16777215 219 2582 2 558 147 113 226
12 24 16777215 894 606 2 2167 1269 3155 2214
12 24 16777215 923 1351 2 3672 577 3647 3198
12 24 16777215 976 3020 2 3931 2931 2350 605
12 24 16777215 1643 2804 2 1909 3332 2819 1543
12 24 16777215 2136 1926 2 3517 1177 3191 2286
12 24 16777215 2267 534 2 2606 147 113 226
12 24 16777215 2942 2654 2 119 1269 3155 2214
12 24 16777215 2971 3399 2 1624 577 3647 3198
12 24 16777215 3024 972 2 1883 2931 2350 605
12 24 16777215 3691 756 2 3957 3332 2819 1543
12 24 16777215 524 2595 3 1661 909 379 758
12 24 16777215 741 3117 3 2029 2310 1795 3589
12 24 16777215 2572 547 3 3709 909 379 758
12 24 16777215 2789 1069 3 4077 2310 1795 3589
12 24 16777215 186 3363 4 2604 2188 2171 247
12 24 16777215 2234 1315 4 556 2188 2171 247
12 24 16777215 98 1417 5 1078 3090 3057 2019
12 24 16777215 2146 3465 5 3126 3090 3057 2019
12 24 16777215 1185 3313 6 2559 606 458 916
12 24 16777215 3233 1265 6 511 606 458 916
12 24 16777215 415 1571 8 1249 826 278 556
12 24 16777215 621 1388 8 1732 1063 3101 2106
12 24 16777215 961 1803 8 3610 2393 2248 401
12 24 16777215 2463 3619 8 3297 826 278 556
12 24 16777215 2669 3436 8 3780 1063 3101 2106
12 24 16777215 3009 3851 8 1562 2393 2248 401
12 24 16777215 1683 3784 10 908 2809 2472 849
12 24 16777215 3731 1736 10 2956 2809 2472 849
12 24 16777215 236 1515 11 2543 1283 769 1538
12 24 16777215 1761 1368 11 890 2713 2440 785
12 24 16777215 2010 3663 11 1589 3619 2590 1085
12 24 16777215 2284 3563 11 495 1283 769 1538
12 24 16777215 3809 3416 11 2938 2713 2440 785
12 24 16777215 4058 1615 11 3637 3619 2590 1085Incomplete 13 and 14:
13 26 67108863 6803 5330 0 4325 5676 4635 1079
13 26 67108863 7110 241 0 2791 3869 1291 2582
13 26 67108863 1138 1263 8 433 319 7957 7722
13 26 67108863 6564 6480 8 6330 7944 5383 2575
13 26 67108863 523 1117 10 1651 5222 3107 6213
13 26 67108863 1949 6961 11 413 5630 4949 1707
13 26 67108863 702 7737 12 7394 6618 2231 4461
14 28 2^28-1 12651 13193 2 5516 5149 3083 6166
14 28 2^28-1 13143 7060 2 12041 15180 10555 4727
XorSARps:
Word State Period A B C D2 D1 X Y
2 4 15 1 2 0 3 3 2 1
2 4 15 3 1 0 3 1 3 2
2 4 15 1 1 1 3 3 2 1
2 4 15 1 3 1 0 2 1 3
2 4 15 3 0 1 0 0 0 0
2 4 15 3 2 1 3 1 3 2
3 6 63 3 2 0 6 2 6 4
3 6 63 5 3 0 0 6 5 3
3 6 63 3 6 1 0 6 3 5
3 6 63 3 0 2 0 0 0 0
3 6 63 3 6 2 0 6 5 3
4 8 255 3 3 0 10 12 5 9
4 8 255 13 3 0 5 5 3 6
4 8 255 9 12 1 10 2 14 12
4 8 255 5 10 2 1 1 15 14
4 8 255 7 8 2 4 10 9 3
4 8 255 7 13 2 5 3 1 2
4 8 255 13 2 2 9 1 15 14
5 10 1023 1 27 0 21 9 7 14
5 10 1023 7 29 3 21 3 1 2
5 10 1023 19 11 4 0 30 11 21
6 12 4095 21 38 0 10 26 54 44
6 12 4095 43 17 0 15 17 15 30
6 12 4095 49 37 0 16 46 27 53
6 12 4095 49 48 0 16 16 48 32
6 12 4095 59 49 0 15 1 63 62
6 12 4095 13 56 2 12 58 41 19
6 12 4095 19 51 2 50 6 2 4
6 12 4095 31 40 4 7 37 30 59
6 12 4095 7 60 5 27 41 26 51
6 12 4095 25 18 5 7 31 53 42
6 12 4095 37 3 5 39 27 9 18
6 12 4095 43 39 5 11 29 11 22
7 14 16383 101 66 2 84 52 108 88
7 14 16383 123 41 4 68 114 47 93
7 14 16383 43 71 5 16 78 59 117
7 14 16383 85 52 5 75 95 32 127
7 14 16383 121 62 5 40 102 35 69
7 14 16383 15 121 6 24 8 120 112
7 14 16383 65 37 6 79 111 90 53
7 14 16383 75 126 6 8 102 93 59
8 16 65535 115 0 0 0 0 0 0
8 16 65535 209 105 0 6 216 183 111
8 16 65535 217 64 1 96 96 32 64
8 16 65535 209 88 2 112 112 208 160
8 16 65535 39 32 4 120 198 67 133
8 16 65535 147 248 4 111 197 188 121
8 16 65535 215 145 4 164 250 169 83
8 16 65535 189 100 5 143 195 190 125
8 16 65535 39 223 7 131 57 23 46
8 16 65535 155 199 7 43 77 59 118
8 16 65535 255 45 7 239 209 176 97
9 18 262143 1 85 0 255 255 85 170
9 18 262143 77 223 0 12 442 361 211
9 18 262143 133 261 0 290 308 275 39
9 18 262143 271 286 0 410 198 66 132
9 18 262143 425 272 0 48 176 400 288
9 18 262143 451 461 0 450 264 263 15
9 18 262143 15 9 3 208 430 357 203
9 18 262143 455 69 3 15 377 296 81
9 18 262143 421 399 4 102 464 335 159
9 18 262143 473 246 6 496 112 464 416
9 18 262143 453 162 7 215 467 334 157
9 18 262143 95 9 8 461 147 113 226
10 20 1048575 643 41 0 334 980 691 359
10 20 1048575 691 1013 4 127 249 87 174
10 20 1048575 65 492 5 526 624 559 95
10 20 1048575 365 928 5 609 57 23 46
10 20 1048575 399 747 5 719 705 576 129
10 20 1048575 5 361 7 850 804 739 455
10 20 1048575 117 862 7 291 935 360 719
10 20 1048575 513 169 7 451 955 662 301
10 20 1048575 581 586 7 366 342 818 612
10 20 1048575 671 596 8 605 387 129 258
11 22 4194303 15 1618 0 702 666 1654 1260
11 22 4194303 1035 1516 0 932 364 1828 1608
11 22 4194303 675 122 3 1011 1645 550 1099
11 22 4194303 439 749 5 1064 1254 1117 187
11 22 4194303 947 880 5 1028 1490 847 1693
11 22 4194303 617 128 6 853 1009 1711 1374
11 22 4194303 655 1659 7 403 577 1599 1150
11 22 4194303 1001 299 9 1087 1511 1186 325
11 22 4194303 333 1493 10 1798 2012 693 1385
11 22 4194303 1327 1765 10 1524 844 1732 1416
11 22 4194303 1507 1504 10 96 928 352 704
12 24 16777215 3629 2690 0 2230 814 282 564
12 24 16777215 3925 913 2 1176 2614 1555 3109
12 24 16777215 1287 2693 3 3925 451 3905 3714
12 24 16777215 1409 1566 3 1426 2640 1585 3169
12 24 16777215 1453 2925 3 2222 2324 1805 3609
12 24 16777215 339 1062 4 595 1277 939 1878
12 24 16777215 3895 769 4 3958 1218 958 1916
12 24 16777215 3925 253 4 972 2714 2441 787
12 24 16777215 3583 867 5 1131 393 135 270
12 24 16777215 2213 3566 8 1690 3820 2651 1207
12 24 16777215 3427 2225 8 1879 1409 895 1790
12 24 16777215 105 1363 10 3792 400 3952 3808
12 24 16777215 3301 1540 10 3485 1429 883 1766
// Rotation functions for non-intrinsic bit widths (2-bit to 31-bit, unoptimized code, since these functions may be looped to fill a fast look-up array)
static inline uint32_t rarx(int32_t x, int w) {
return ((uint32_t)((-(x & (1 << (w - 1))) | x) / 2 ^ (x << (w - 1))) & ((1 << w) - 1)) >> (int)(x == ((1 << w) - 1)); }
static inline uint32_t rolx(uint32_t x, int k, int w) {
return ((x << k) | (x >> (w - k))) & ((1 << w) - 1); }Cerian Knight
Dec 30, 2018, 12:32:35 AM12/30/18
to xorsar...@googlegroups.com
Original 8-bit output / 16-bit state C++ code post: Click Here
Tiny GCC -O3 assembly language dump of 128-bit state, 64-bit word/output C++ code with fictitious ABC constants and D=0.
Using updated rar64 function to remove use of cmove asm instruction, for better support of MSVC, etc., and now using dynamic constants for speed/smaller code.
To reach its greatest potential, the rar8/16/32/64 functions would need to be implemented in hardware and/or as an ASM primitive.
xorSAR128pp2D():
mov rcx, QWORD PTR s[rip+8]
mov rax, QWORD PTR s[rip]
mov rdx, rcx
mov rsi, rcx
add rax, rcx
add rax, QWORD PTR A[rip] //A constant (dynamic for speed)
shr rdx, 63
sal rsi, 63
add rdx, rcx
sar rdx
xor rdx, rsi
cmp rcx, -1
sete cl
shr rdx, cl
mov QWORD PTR s[rip], rdx
mov rdx, QWORD PTR B[rip] //B constant (dynamic for speed)
xor rdx, rax
rol rdx, 13 //C constant
mov QWORD PTR s[rip+8], rdx
ret
s:
.zero 16
B:
.quad 5949946252051827096
A:
.quad 4067921595744811285Reply all
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