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add SMID-oriented fast mersenne twister
author Robert McIntyre <rlm@mit.edu>
date Sun, 04 Mar 2012 17:38:32 -0600
parents f9f4f1b99eed
children
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22:8870086b716c 23:bf9169ad4222
1 /**
2 * @file SFMT.c
3 * @brief SIMD oriented Fast Mersenne Twister(SFMT)
4 *
5 * @author Mutsuo Saito (Hiroshima University)
6 * @author Makoto Matsumoto (Hiroshima University)
7 *
8 * Copyright (C) 2006,2007 Mutsuo Saito, Makoto Matsumoto and Hiroshima
9 * University. All rights reserved.
10 *
11 * The new BSD License is applied to this software, see LICENSE.txt
12 */
13 #include <string.h>
14 #include <assert.h>
15 #include "SFMT.h"
16 #include "SFMT-params.h"
17
18 #if defined(__BIG_ENDIAN__) && !defined(__amd64) && !defined(BIG_ENDIAN64)
19 #define BIG_ENDIAN64 1
20 #endif
21 #if defined(HAVE_ALTIVEC) && !defined(BIG_ENDIAN64)
22 #define BIG_ENDIAN64 1
23 #endif
24 #if defined(ONLY64) && !defined(BIG_ENDIAN64)
25 #if defined(__GNUC__)
26 #error "-DONLY64 must be specified with -DBIG_ENDIAN64"
27 #endif
28 #undef ONLY64
29 #endif
30 /*------------------------------------------------------
31 128-bit SIMD data type for Altivec, SSE2 or standard C
32 ------------------------------------------------------*/
33 #if defined(HAVE_ALTIVEC)
34 #if !defined(__APPLE__)
35 #include <altivec.h>
36 #endif
37 /** 128-bit data structure */
38 union W128_T {
39 vector unsigned int s;
40 uint32_t u[4];
41 };
42 /** 128-bit data type */
43 typedef union W128_T w128_t;
44
45 #elif defined(HAVE_SSE2)
46 #include <emmintrin.h>
47
48 /** 128-bit data structure */
49 union W128_T {
50 __m128i si;
51 uint32_t u[4];
52 };
53 /** 128-bit data type */
54 typedef union W128_T w128_t;
55
56 #else
57
58 /** 128-bit data structure */
59 struct W128_T {
60 uint32_t u[4];
61 };
62 /** 128-bit data type */
63 typedef struct W128_T w128_t;
64
65 #endif
66
67 /*--------------------------------------
68 FILE GLOBAL VARIABLES
69 internal state, index counter and flag
70 --------------------------------------*/
71 /** the 128-bit internal state array */
72 static w128_t sfmt[N];
73 /** the 32bit integer pointer to the 128-bit internal state array */
74 static uint32_t *psfmt32 = &sfmt[0].u[0];
75 #if !defined(BIG_ENDIAN64) || defined(ONLY64)
76 /** the 64bit integer pointer to the 128-bit internal state array */
77 static uint64_t *psfmt64 = (uint64_t *)&sfmt[0].u[0];
78 #endif
79 /** index counter to the 32-bit internal state array */
80 static int idx;
81 /** a flag: it is 0 if and only if the internal state is not yet
82 * initialized. */
83 static int initialized = 0;
84 /** a parity check vector which certificate the period of 2^{MEXP} */
85 static uint32_t parity[4] = {PARITY1, PARITY2, PARITY3, PARITY4};
86
87 /*----------------
88 STATIC FUNCTIONS
89 ----------------*/
90 inline static int idxof(int i);
91 inline static void rshift128(w128_t *out, w128_t const *in, int shift);
92 inline static void lshift128(w128_t *out, w128_t const *in, int shift);
93 inline static void gen_rand_all(void);
94 inline static void gen_rand_array(w128_t *array, int size);
95 inline static uint32_t func1(uint32_t x);
96 inline static uint32_t func2(uint32_t x);
97 static void period_certification(void);
98 #if defined(BIG_ENDIAN64) && !defined(ONLY64)
99 inline static void swap(w128_t *array, int size);
100 #endif
101
102 #if defined(HAVE_ALTIVEC)
103 #include "SFMT-alti.h"
104 #elif defined(HAVE_SSE2)
105 #include "SFMT-sse2.h"
106 #endif
107
108 /**
109 * This function simulate a 64-bit index of LITTLE ENDIAN
110 * in BIG ENDIAN machine.
111 */
112 #ifdef ONLY64
113 inline static int idxof(int i) {
114 return i ^ 1;
115 }
116 #else
117 inline static int idxof(int i) {
118 return i;
119 }
120 #endif
121 /**
122 * This function simulates SIMD 128-bit right shift by the standard C.
123 * The 128-bit integer given in in is shifted by (shift * 8) bits.
124 * This function simulates the LITTLE ENDIAN SIMD.
125 * @param out the output of this function
126 * @param in the 128-bit data to be shifted
127 * @param shift the shift value
128 */
129 #ifdef ONLY64
130 inline static void rshift128(w128_t *out, w128_t const *in, int shift) {
131 uint64_t th, tl, oh, ol;
132
133 th = ((uint64_t)in->u[2] << 32) | ((uint64_t)in->u[3]);
134 tl = ((uint64_t)in->u[0] << 32) | ((uint64_t)in->u[1]);
135
136 oh = th >> (shift * 8);
137 ol = tl >> (shift * 8);
138 ol |= th << (64 - shift * 8);
139 out->u[0] = (uint32_t)(ol >> 32);
140 out->u[1] = (uint32_t)(ol & 0xffffffff);
141 out->u[2] = (uint32_t)(oh >> 32);
142 out->u[3] = (uint32_t)(oh & 0xffffffff);
143 }
144 #else
145 inline static void rshift128(w128_t *out, w128_t const *in, int shift) {
146 uint64_t th, tl, oh, ol;
147
148 th = ((uint64_t)in->u[3] << 32) | ((uint64_t)in->u[2]);
149 tl = ((uint64_t)in->u[1] << 32) | ((uint64_t)in->u[0]);
150
151 oh = th >> (shift * 8);
152 ol = tl >> (shift * 8);
153 ol |= th << (64 - shift * 8);
154 out->u[1] = (uint32_t)(ol >> 32);
155 out->u[0] = (uint32_t)(ol & 0xffffffff);
156 out->u[3] = (uint32_t)(oh >> 32);
157 out->u[2] = (uint32_t)(oh & 0xffffffff);
158 }
159 #endif
160 /**
161 * This function simulates SIMD 128-bit left shift by the standard C.
162 * The 128-bit integer given in in is shifted by (shift * 8) bits.
163 * This function simulates the LITTLE ENDIAN SIMD.
164 * @param out the output of this function
165 * @param in the 128-bit data to be shifted
166 * @param shift the shift value
167 */
168 #ifdef ONLY64
169 inline static void lshift128(w128_t *out, w128_t const *in, int shift) {
170 uint64_t th, tl, oh, ol;
171
172 th = ((uint64_t)in->u[2] << 32) | ((uint64_t)in->u[3]);
173 tl = ((uint64_t)in->u[0] << 32) | ((uint64_t)in->u[1]);
174
175 oh = th << (shift * 8);
176 ol = tl << (shift * 8);
177 oh |= tl >> (64 - shift * 8);
178 out->u[0] = (uint32_t)(ol >> 32);
179 out->u[1] = (uint32_t)(ol & 0xffffffff);
180 out->u[2] = (uint32_t)(oh >> 32);
181 out->u[3] = (uint32_t)(oh & 0xffffffff);
182 }
183 #else
184 inline static void lshift128(w128_t *out, w128_t const *in, int shift) {
185 uint64_t th, tl, oh, ol;
186
187 th = ((uint64_t)in->u[3] << 32) | ((uint64_t)in->u[2]);
188 tl = ((uint64_t)in->u[1] << 32) | ((uint64_t)in->u[0]);
189
190 oh = th << (shift * 8);
191 ol = tl << (shift * 8);
192 oh |= tl >> (64 - shift * 8);
193 out->u[1] = (uint32_t)(ol >> 32);
194 out->u[0] = (uint32_t)(ol & 0xffffffff);
195 out->u[3] = (uint32_t)(oh >> 32);
196 out->u[2] = (uint32_t)(oh & 0xffffffff);
197 }
198 #endif
199
200 /**
201 * This function represents the recursion formula.
202 * @param r output
203 * @param a a 128-bit part of the internal state array
204 * @param b a 128-bit part of the internal state array
205 * @param c a 128-bit part of the internal state array
206 * @param d a 128-bit part of the internal state array
207 */
208 #if (!defined(HAVE_ALTIVEC)) && (!defined(HAVE_SSE2))
209 #ifdef ONLY64
210 inline static void do_recursion(w128_t *r, w128_t *a, w128_t *b, w128_t *c,
211 w128_t *d) {
212 w128_t x;
213 w128_t y;
214
215 lshift128(&x, a, SL2);
216 rshift128(&y, c, SR2);
217 r->u[0] = a->u[0] ^ x.u[0] ^ ((b->u[0] >> SR1) & MSK2) ^ y.u[0]
218 ^ (d->u[0] << SL1);
219 r->u[1] = a->u[1] ^ x.u[1] ^ ((b->u[1] >> SR1) & MSK1) ^ y.u[1]
220 ^ (d->u[1] << SL1);
221 r->u[2] = a->u[2] ^ x.u[2] ^ ((b->u[2] >> SR1) & MSK4) ^ y.u[2]
222 ^ (d->u[2] << SL1);
223 r->u[3] = a->u[3] ^ x.u[3] ^ ((b->u[3] >> SR1) & MSK3) ^ y.u[3]
224 ^ (d->u[3] << SL1);
225 }
226 #else
227 inline static void do_recursion(w128_t *r, w128_t *a, w128_t *b, w128_t *c,
228 w128_t *d) {
229 w128_t x;
230 w128_t y;
231
232 lshift128(&x, a, SL2);
233 rshift128(&y, c, SR2);
234 r->u[0] = a->u[0] ^ x.u[0] ^ ((b->u[0] >> SR1) & MSK1) ^ y.u[0]
235 ^ (d->u[0] << SL1);
236 r->u[1] = a->u[1] ^ x.u[1] ^ ((b->u[1] >> SR1) & MSK2) ^ y.u[1]
237 ^ (d->u[1] << SL1);
238 r->u[2] = a->u[2] ^ x.u[2] ^ ((b->u[2] >> SR1) & MSK3) ^ y.u[2]
239 ^ (d->u[2] << SL1);
240 r->u[3] = a->u[3] ^ x.u[3] ^ ((b->u[3] >> SR1) & MSK4) ^ y.u[3]
241 ^ (d->u[3] << SL1);
242 }
243 #endif
244 #endif
245
246 #if (!defined(HAVE_ALTIVEC)) && (!defined(HAVE_SSE2))
247 /**
248 * This function fills the internal state array with pseudorandom
249 * integers.
250 */
251 inline static void gen_rand_all(void) {
252 int i;
253 w128_t *r1, *r2;
254
255 r1 = &sfmt[N - 2];
256 r2 = &sfmt[N - 1];
257 for (i = 0; i < N - POS1; i++) {
258 do_recursion(&sfmt[i], &sfmt[i], &sfmt[i + POS1], r1, r2);
259 r1 = r2;
260 r2 = &sfmt[i];
261 }
262 for (; i < N; i++) {
263 do_recursion(&sfmt[i], &sfmt[i], &sfmt[i + POS1 - N], r1, r2);
264 r1 = r2;
265 r2 = &sfmt[i];
266 }
267 }
268
269 /**
270 * This function fills the user-specified array with pseudorandom
271 * integers.
272 *
273 * @param array an 128-bit array to be filled by pseudorandom numbers.
274 * @param size number of 128-bit pseudorandom numbers to be generated.
275 */
276 inline static void gen_rand_array(w128_t *array, int size) {
277 int i, j;
278 w128_t *r1, *r2;
279
280 r1 = &sfmt[N - 2];
281 r2 = &sfmt[N - 1];
282 for (i = 0; i < N - POS1; i++) {
283 do_recursion(&array[i], &sfmt[i], &sfmt[i + POS1], r1, r2);
284 r1 = r2;
285 r2 = &array[i];
286 }
287 for (; i < N; i++) {
288 do_recursion(&array[i], &sfmt[i], &array[i + POS1 - N], r1, r2);
289 r1 = r2;
290 r2 = &array[i];
291 }
292 for (; i < size - N; i++) {
293 do_recursion(&array[i], &array[i - N], &array[i + POS1 - N], r1, r2);
294 r1 = r2;
295 r2 = &array[i];
296 }
297 for (j = 0; j < 2 * N - size; j++) {
298 sfmt[j] = array[j + size - N];
299 }
300 for (; i < size; i++, j++) {
301 do_recursion(&array[i], &array[i - N], &array[i + POS1 - N], r1, r2);
302 r1 = r2;
303 r2 = &array[i];
304 sfmt[j] = array[i];
305 }
306 }
307 #endif
308
309 #if defined(BIG_ENDIAN64) && !defined(ONLY64) && !defined(HAVE_ALTIVEC)
310 inline static void swap(w128_t *array, int size) {
311 int i;
312 uint32_t x, y;
313
314 for (i = 0; i < size; i++) {
315 x = array[i].u[0];
316 y = array[i].u[2];
317 array[i].u[0] = array[i].u[1];
318 array[i].u[2] = array[i].u[3];
319 array[i].u[1] = x;
320 array[i].u[3] = y;
321 }
322 }
323 #endif
324 /**
325 * This function represents a function used in the initialization
326 * by init_by_array
327 * @param x 32-bit integer
328 * @return 32-bit integer
329 */
330 static uint32_t func1(uint32_t x) {
331 return (x ^ (x >> 27)) * (uint32_t)1664525UL;
332 }
333
334 /**
335 * This function represents a function used in the initialization
336 * by init_by_array
337 * @param x 32-bit integer
338 * @return 32-bit integer
339 */
340 static uint32_t func2(uint32_t x) {
341 return (x ^ (x >> 27)) * (uint32_t)1566083941UL;
342 }
343
344 /**
345 * This function certificate the period of 2^{MEXP}
346 */
347 static void period_certification(void) {
348 int inner = 0;
349 int i, j;
350 uint32_t work;
351
352 for (i = 0; i < 4; i++)
353 inner ^= psfmt32[idxof(i)] & parity[i];
354 for (i = 16; i > 0; i >>= 1)
355 inner ^= inner >> i;
356 inner &= 1;
357 /* check OK */
358 if (inner == 1) {
359 return;
360 }
361 /* check NG, and modification */
362 for (i = 0; i < 4; i++) {
363 work = 1;
364 for (j = 0; j < 32; j++) {
365 if ((work & parity[i]) != 0) {
366 psfmt32[idxof(i)] ^= work;
367 return;
368 }
369 work = work << 1;
370 }
371 }
372 }
373
374 /*----------------
375 PUBLIC FUNCTIONS
376 ----------------*/
377 /**
378 * This function returns the identification string.
379 * The string shows the word size, the Mersenne exponent,
380 * and all parameters of this generator.
381 */
382 const char *get_idstring(void) {
383 return IDSTR;
384 }
385
386 /**
387 * This function returns the minimum size of array used for \b
388 * fill_array32() function.
389 * @return minimum size of array used for fill_array32() function.
390 */
391 int get_min_array_size32(void) {
392 return N32;
393 }
394
395 /**
396 * This function returns the minimum size of array used for \b
397 * fill_array64() function.
398 * @return minimum size of array used for fill_array64() function.
399 */
400 int get_min_array_size64(void) {
401 return N64;
402 }
403
404 #ifndef ONLY64
405 /**
406 * This function generates and returns 32-bit pseudorandom number.
407 * init_gen_rand or init_by_array must be called before this function.
408 * @return 32-bit pseudorandom number
409 */
410 uint32_t gen_rand32(void) {
411 uint32_t r;
412
413 assert(initialized);
414 if (idx >= N32) {
415 gen_rand_all();
416 idx = 0;
417 }
418 r = psfmt32[idx++];
419 return r;
420 }
421 #endif
422 /**
423 * This function generates and returns 64-bit pseudorandom number.
424 * init_gen_rand or init_by_array must be called before this function.
425 * The function gen_rand64 should not be called after gen_rand32,
426 * unless an initialization is again executed.
427 * @return 64-bit pseudorandom number
428 */
429 uint64_t gen_rand64(void) {
430 #if defined(BIG_ENDIAN64) && !defined(ONLY64)
431 uint32_t r1, r2;
432 #else
433 uint64_t r;
434 #endif
435
436 assert(initialized);
437 assert(idx % 2 == 0);
438
439 if (idx >= N32) {
440 gen_rand_all();
441 idx = 0;
442 }
443 #if defined(BIG_ENDIAN64) && !defined(ONLY64)
444 r1 = psfmt32[idx];
445 r2 = psfmt32[idx + 1];
446 idx += 2;
447 return ((uint64_t)r2 << 32) | r1;
448 #else
449 r = psfmt64[idx / 2];
450 idx += 2;
451 return r;
452 #endif
453 }
454
455 #ifndef ONLY64
456 /**
457 * This function generates pseudorandom 32-bit integers in the
458 * specified array[] by one call. The number of pseudorandom integers
459 * is specified by the argument size, which must be at least 624 and a
460 * multiple of four. The generation by this function is much faster
461 * than the following gen_rand function.
462 *
463 * For initialization, init_gen_rand or init_by_array must be called
464 * before the first call of this function. This function can not be
465 * used after calling gen_rand function, without initialization.
466 *
467 * @param array an array where pseudorandom 32-bit integers are filled
468 * by this function. The pointer to the array must be \b "aligned"
469 * (namely, must be a multiple of 16) in the SIMD version, since it
470 * refers to the address of a 128-bit integer. In the standard C
471 * version, the pointer is arbitrary.
472 *
473 * @param size the number of 32-bit pseudorandom integers to be
474 * generated. size must be a multiple of 4, and greater than or equal
475 * to (MEXP / 128 + 1) * 4.
476 *
477 * @note \b memalign or \b posix_memalign is available to get aligned
478 * memory. Mac OSX doesn't have these functions, but \b malloc of OSX
479 * returns the pointer to the aligned memory block.
480 */
481 void fill_array32(uint32_t *array, int size) {
482 assert(initialized);
483 assert(idx == N32);
484 assert(size % 4 == 0);
485 assert(size >= N32);
486
487 gen_rand_array((w128_t *)array, size / 4);
488 idx = N32;
489 }
490 #endif
491
492 /**
493 * This function generates pseudorandom 64-bit integers in the
494 * specified array[] by one call. The number of pseudorandom integers
495 * is specified by the argument size, which must be at least 312 and a
496 * multiple of two. The generation by this function is much faster
497 * than the following gen_rand function.
498 *
499 * For initialization, init_gen_rand or init_by_array must be called
500 * before the first call of this function. This function can not be
501 * used after calling gen_rand function, without initialization.
502 *
503 * @param array an array where pseudorandom 64-bit integers are filled
504 * by this function. The pointer to the array must be "aligned"
505 * (namely, must be a multiple of 16) in the SIMD version, since it
506 * refers to the address of a 128-bit integer. In the standard C
507 * version, the pointer is arbitrary.
508 *
509 * @param size the number of 64-bit pseudorandom integers to be
510 * generated. size must be a multiple of 2, and greater than or equal
511 * to (MEXP / 128 + 1) * 2
512 *
513 * @note \b memalign or \b posix_memalign is available to get aligned
514 * memory. Mac OSX doesn't have these functions, but \b malloc of OSX
515 * returns the pointer to the aligned memory block.
516 */
517 void fill_array64(uint64_t *array, int size) {
518 assert(initialized);
519 assert(idx == N32);
520 assert(size % 2 == 0);
521 assert(size >= N64);
522
523 gen_rand_array((w128_t *)array, size / 2);
524 idx = N32;
525
526 #if defined(BIG_ENDIAN64) && !defined(ONLY64)
527 swap((w128_t *)array, size /2);
528 #endif
529 }
530
531 /**
532 * This function initializes the internal state array with a 32-bit
533 * integer seed.
534 *
535 * @param seed a 32-bit integer used as the seed.
536 */
537 void init_gen_rand(uint32_t seed) {
538 int i;
539
540 psfmt32[idxof(0)] = seed;
541 for (i = 1; i < N32; i++) {
542 psfmt32[idxof(i)] = 1812433253UL * (psfmt32[idxof(i - 1)]
543 ^ (psfmt32[idxof(i - 1)] >> 30))
544 + i;
545 }
546 idx = N32;
547 period_certification();
548 initialized = 1;
549 }
550
551 /**
552 * This function initializes the internal state array,
553 * with an array of 32-bit integers used as the seeds
554 * @param init_key the array of 32-bit integers, used as a seed.
555 * @param key_length the length of init_key.
556 */
557 void init_by_array(uint32_t *init_key, int key_length) {
558 int i, j, count;
559 uint32_t r;
560 int lag;
561 int mid;
562 int size = N * 4;
563
564 if (size >= 623) {
565 lag = 11;
566 } else if (size >= 68) {
567 lag = 7;
568 } else if (size >= 39) {
569 lag = 5;
570 } else {
571 lag = 3;
572 }
573 mid = (size - lag) / 2;
574
575 memset(sfmt, 0x8b, sizeof(sfmt));
576 if (key_length + 1 > N32) {
577 count = key_length + 1;
578 } else {
579 count = N32;
580 }
581 r = func1(psfmt32[idxof(0)] ^ psfmt32[idxof(mid)]
582 ^ psfmt32[idxof(N32 - 1)]);
583 psfmt32[idxof(mid)] += r;
584 r += key_length;
585 psfmt32[idxof(mid + lag)] += r;
586 psfmt32[idxof(0)] = r;
587
588 count--;
589 for (i = 1, j = 0; (j < count) && (j < key_length); j++) {
590 r = func1(psfmt32[idxof(i)] ^ psfmt32[idxof((i + mid) % N32)]
591 ^ psfmt32[idxof((i + N32 - 1) % N32)]);
592 psfmt32[idxof((i + mid) % N32)] += r;
593 r += init_key[j] + i;
594 psfmt32[idxof((i + mid + lag) % N32)] += r;
595 psfmt32[idxof(i)] = r;
596 i = (i + 1) % N32;
597 }
598 for (; j < count; j++) {
599 r = func1(psfmt32[idxof(i)] ^ psfmt32[idxof((i + mid) % N32)]
600 ^ psfmt32[idxof((i + N32 - 1) % N32)]);
601 psfmt32[idxof((i + mid) % N32)] += r;
602 r += i;
603 psfmt32[idxof((i + mid + lag) % N32)] += r;
604 psfmt32[idxof(i)] = r;
605 i = (i + 1) % N32;
606 }
607 for (j = 0; j < N32; j++) {
608 r = func2(psfmt32[idxof(i)] + psfmt32[idxof((i + mid) % N32)]
609 + psfmt32[idxof((i + N32 - 1) % N32)]);
610 psfmt32[idxof((i + mid) % N32)] ^= r;
611 r -= i;
612 psfmt32[idxof((i + mid + lag) % N32)] ^= r;
613 psfmt32[idxof(i)] = r;
614 i = (i + 1) % N32;
615 }
616
617 idx = N32;
618 period_certification();
619 initialized = 1;
620 }