1 /***********************************************************************\
3 * File: RngStream.c for multiple streams of Random Numbers
5 * Copyright: Pierre L'Ecuyer, University of Montreal
7 * License: GPL version 2 or later
9 * Notice: Please contact P. L'Ecuyer at <lecuyer@iro.UMontreal.ca>
10 * for commercial purposes.
12 \***********************************************************************/
15 #include "xbt/RngStream.h"
16 #include "xbt/sysdep.h"
22 /*---------------------------------------------------------------------*/
24 /*---------------------------------------------------------------------*/
27 #define norm 2.328306549295727688e-10
28 #define m1 4294967087.0
29 #define m2 4294944443.0
33 #define a23n 1370589.0
35 #define two17 131072.0
36 #define two53 9007199254740992.0
37 #define fact 5.9604644775390625e-8 /* 1 / 2^24 */
42 /* Default initial seed of the package. Will be updated to become
43 the seed of the next created stream. */
44 static double nextSeed[6] = { 12345, 12345, 12345, 12345, 12345, 12345 };
47 /* The following are the transition matrices of the two MRG components */
48 /* (in matrix form), raised to the powers -1, 1, 2^76, and 2^127, resp.*/
49 static double InvA1[3][3] = { /* Inverse of A1p0 */
50 { 184888585.0, 0.0, 1945170933.0 },
55 static double InvA2[3][3] = { /* Inverse of A2p0 */
56 { 0.0, 360363334.0, 4225571728.0 },
61 static double A1p0[3][3] = {
64 { -810728.0, 1403580.0, 0.0 }
67 static double A2p0[3][3] = {
70 { -1370589.0, 0.0, 527612.0 }
73 static double A1p76[3][3] = {
74 { 82758667.0, 1871391091.0, 4127413238.0 },
75 { 3672831523.0, 69195019.0, 1871391091.0 },
76 { 3672091415.0, 3528743235.0, 69195019.0 }
79 static double A2p76[3][3] = {
80 { 1511326704.0, 3759209742.0, 1610795712.0 },
81 { 4292754251.0, 1511326704.0, 3889917532.0 },
82 { 3859662829.0, 4292754251.0, 3708466080.0 }
85 static double A1p127[3][3] = {
86 { 2427906178.0, 3580155704.0, 949770784.0 },
87 { 226153695.0, 1230515664.0, 3580155704.0 },
88 { 1988835001.0, 986791581.0, 1230515664.0 }
91 static double A2p127[3][3] = {
92 { 1464411153.0, 277697599.0, 1610723613.0 },
93 { 32183930.0, 1464411153.0, 1022607788.0 },
94 { 2824425944.0, 32183930.0, 2093834863.0 }
101 /*-------------------------------------------------------------------------*/
103 static double MultModM (double a, double s, double c, double m)
104 /* Compute (a*s + c) % m. m must be < 2^35. Works also for s, c < 0 */
109 if ((v >= two53) || (v <= -two53)) {
110 a1 = (long) (a / two17);
115 v = v * two17 + a * s + c;
118 if ((v -= a1 * m) < 0.0)
125 /*-------------------------------------------------------------------------*/
127 static void MatVecModM (double A[3][3], double s[3], double v[3], double m)
128 /* Returns v = A*s % m. Assumes that -m < s[i] < m. */
129 /* Works even if v = s. */
133 for (i = 0; i < 3; ++i) {
134 x[i] = MultModM (A[i][0], s[0], 0.0, m);
135 x[i] = MultModM (A[i][1], s[1], x[i], m);
136 x[i] = MultModM (A[i][2], s[2], x[i], m);
138 for (i = 0; i < 3; ++i)
143 /*-------------------------------------------------------------------------*/
145 static void MatMatModM (double A[3][3], double B[3][3], double C[3][3],
147 /* Returns C = A*B % m. Work even if A = C or B = C or A = B = C. */
150 double V[3], W[3][3];
151 for (i = 0; i < 3; ++i) {
152 for (j = 0; j < 3; ++j)
154 MatVecModM (A, V, V, m);
155 for (j = 0; j < 3; ++j)
158 for (i = 0; i < 3; ++i) {
159 for (j = 0; j < 3; ++j)
165 /*-------------------------------------------------------------------------*/
167 static void MatTwoPowModM (double A[3][3], double B[3][3], double m, long e)
168 /* Compute matrix B = (A^(2^e) % m); works even if A = B */
172 /* initialize: B = A */
174 for (i = 0; i < 3; i++) {
175 for (j = 0; j < 3; ++j)
179 /* Compute B = A^{2^e} */
180 for (i = 0; i < e; i++)
181 MatMatModM (B, B, B, m);
185 /*-------------------------------------------------------------------------*/
187 static void MatPowModM (double A[3][3], double B[3][3], double m, long n)
188 /* Compute matrix B = A^n % m ; works even if A = B */
193 /* initialize: W = A; B = I */
194 for (i = 0; i < 3; i++) {
195 for (j = 0; j < 3; ++j) {
200 for (j = 0; j < 3; ++j)
203 /* Compute B = A^n % m using the binary decomposition of n */
206 MatMatModM (W, B, B, m);
207 MatMatModM (W, W, W, m);
213 /*-------------------------------------------------------------------------*/
215 static double U01 (RngStream g)
221 p1 = a12 * g->Cg[1] - a13n * g->Cg[0];
231 p2 = a21 * g->Cg[5] - a23n * g->Cg[3];
241 u = ((p1 > p2) ? (p1 - p2) * norm : (p1 - p2 + m1) * norm);
242 return (g->Anti) ? (1 - u) : u;
246 /*-------------------------------------------------------------------------*/
248 static double U01d (RngStream g)
254 return (u < 1.0) ? u : (u - 1.0);
256 /* Don't forget that U01() returns 1 - u in the antithetic case */
257 u += (U01(g) - 1.0) * fact;
258 return (u < 0.0) ? u + 1.0 : u;
263 /*-------------------------------------------------------------------------*/
265 static int CheckSeed (unsigned long seed[6])
267 /* Check that the seeds are legitimate values. Returns 0 if legal seeds,
271 for (i = 0; i < 3; ++i) {
273 fprintf (stderr, "****************************************\n"
274 "ERROR: Seed[%1d] >= m1, Seed is not set.\n"
275 "****************************************\n\n", i);
279 for (i = 3; i < 6; ++i) {
281 fprintf (stderr, "****************************************\n"
282 "ERROR: Seed[%1d] >= m1, Seed is not set.\n"
283 "****************************************\n\n", i);
287 if (seed[0] == 0 && seed[1] == 0 && seed[2] == 0) {
288 fprintf (stderr, "****************************\n"
289 "ERROR: First 3 seeds = 0.\n"
290 "****************************\n\n");
293 if (seed[3] == 0 && seed[4] == 0 && seed[5] == 0) {
294 fprintf (stderr, "****************************\n"
295 "ERROR: Last 3 seeds = 0.\n"
296 "****************************\n\n");
304 /*---------------------------------------------------------------------*/
306 /*---------------------------------------------------------------------*/
309 RngStream RngStream_CreateStream (const char name[])
315 g = (RngStream) xbt_malloc (sizeof (struct RngStream_InfoState));
317 printf ("RngStream_CreateStream: No more memory\n\n");
322 g->name = (char *) xbt_malloc ((len + 1) * sizeof (char));
323 strncpy (g->name, name, len + 1);
329 for (i = 0; i < 6; ++i) {
330 g->Bg[i] = g->Cg[i] = g->Ig[i] = nextSeed[i];
332 MatVecModM (A1p127, nextSeed, nextSeed, m1);
333 MatVecModM (A2p127, &nextSeed[3], &nextSeed[3], m2);
337 /*-------------------------------------------------------------------------*/
339 void RngStream_DeleteStream (RngStream * p)
348 /*-------------------------------------------------------------------------*/
350 RngStream RngStream_CopyStream (const RngStream src)
355 printf ("RngStream_CopyStream: 'src' not initialized\n\n");
359 g = (RngStream) xbt_malloc (sizeof (struct RngStream_InfoState));
361 printf ("RngStream_CopyStream: No more memory\n\n");
364 memcpy((void*) g, (void*) src, sizeof (struct RngStream_InfoState));
369 /*-------------------------------------------------------------------------*/
371 void RngStream_ResetStartStream (RngStream g)
374 for (i = 0; i < 6; ++i)
375 g->Cg[i] = g->Bg[i] = g->Ig[i];
378 /*-------------------------------------------------------------------------*/
380 void RngStream_ResetNextSubstream (RngStream g)
383 MatVecModM (A1p76, g->Bg, g->Bg, m1);
384 MatVecModM (A2p76, &g->Bg[3], &g->Bg[3], m2);
385 for (i = 0; i < 6; ++i)
389 /*-------------------------------------------------------------------------*/
391 void RngStream_ResetStartSubstream (RngStream g)
394 for (i = 0; i < 6; ++i)
398 /*-------------------------------------------------------------------------*/
400 int RngStream_SetPackageSeed (unsigned long seed[6])
403 if (CheckSeed (seed))
404 return -1; /* FAILURE */
405 for (i = 0; i < 6; ++i)
406 nextSeed[i] = seed[i];
407 return 0; /* SUCCESS */
410 /*-------------------------------------------------------------------------*/
412 int RngStream_SetSeed (RngStream g, unsigned long seed[6])
415 if (CheckSeed (seed))
416 return -1; /* FAILURE */
417 for (i = 0; i < 6; ++i)
418 g->Cg[i] = g->Bg[i] = g->Ig[i] = seed[i];
419 return 0; /* SUCCESS */
422 /*-------------------------------------------------------------------------*/
424 void RngStream_AdvanceState (RngStream g, long e, long c)
426 double B1[3][3], C1[3][3], B2[3][3], C2[3][3];
429 MatTwoPowModM (A1p0, B1, m1, e);
430 MatTwoPowModM (A2p0, B2, m2, e);
432 MatTwoPowModM (InvA1, B1, m1, -e);
433 MatTwoPowModM (InvA2, B2, m2, -e);
437 MatPowModM (A1p0, C1, m1, c);
438 MatPowModM (A2p0, C2, m2, c);
440 MatPowModM (InvA1, C1, m1, -c);
441 MatPowModM (InvA2, C2, m2, -c);
445 MatMatModM (B1, C1, C1, m1);
446 MatMatModM (B2, C2, C2, m2);
449 MatVecModM (C1, g->Cg, g->Cg, m1);
450 MatVecModM (C2, &g->Cg[3], &g->Cg[3], m2);
453 /*-------------------------------------------------------------------------*/
455 void RngStream_GetState (RngStream g, unsigned long seed[6])
458 for (i = 0; i < 6; ++i)
462 /*-------------------------------------------------------------------------*/
464 void RngStream_WriteState (RngStream g)
469 printf ("The current state of the Rngstream");
470 if (g->name && (strlen (g->name) > 0))
471 printf (" %s", g->name);
472 printf (":\n Cg = { ");
474 for (i = 0; i < 5; i++) {
475 printf ("%lu, ", (unsigned long) g->Cg[i]);
477 printf ("%lu }\n\n", (unsigned long) g->Cg[5]);
480 /*-------------------------------------------------------------------------*/
482 void RngStream_WriteStateFull (RngStream g)
487 printf ("The RngStream");
488 if (g->name && (strlen (g->name) > 0))
489 printf (" %s", g->name);
490 printf (":\n Anti = %s\n", (g->Anti ? "true" : "false"));
491 printf (" IncPrec = %s\n", (g->IncPrec ? "true" : "false"));
494 for (i = 0; i < 5; i++) {
495 printf ("%lu, ", (unsigned long) (g->Ig[i]));
497 printf ("%lu }\n", (unsigned long) g->Ig[5]);
500 for (i = 0; i < 5; i++) {
501 printf ("%lu, ", (unsigned long) (g->Bg[i]));
503 printf ("%lu }\n", (unsigned long) g->Bg[5]);
506 for (i = 0; i < 5; i++) {
507 printf ("%lu, ", (unsigned long) (g->Cg[i]));
509 printf ("%lu }\n\n", (unsigned long) g->Cg[5]);
512 /*-------------------------------------------------------------------------*/
514 void RngStream_IncreasedPrecis (RngStream g, int incp)
519 /*-------------------------------------------------------------------------*/
521 void RngStream_SetAntithetic (RngStream g, int a)
526 /*-------------------------------------------------------------------------*/
528 double RngStream_RandU01 (RngStream g)
536 /*-------------------------------------------------------------------------*/
538 int RngStream_RandInt (RngStream g, int i, int j)
540 return i + (int) ((j - i + 1.0) * RngStream_RandU01 (g));
543 /* Undefine this terms, or supernovae build will fail. */