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"
21 /*---------------------------------------------------------------------*/
23 /*---------------------------------------------------------------------*/
26 #define norm 2.328306549295727688e-10
27 #define m1 4294967087.0
28 #define m2 4294944443.0
32 #define a23n 1370589.0
34 #define two17 131072.0
35 #define two53 9007199254740992.0
36 #define fact 5.9604644775390625e-8 /* 1 / 2^24 */
41 /* Default initial seed of the package. Will be updated to become
42 the seed of the next created stream. */
43 static double nextSeed[6] = { 12345, 12345, 12345, 12345, 12345, 12345 };
46 /* The following are the transition matrices of the two MRG components */
47 /* (in matrix form), raised to the powers -1, 1, 2^76, and 2^127, resp.*/
48 static double InvA1[3][3] = { /* Inverse of A1p0 */
49 { 184888585.0, 0.0, 1945170933.0 },
54 static double InvA2[3][3] = { /* Inverse of A2p0 */
55 { 0.0, 360363334.0, 4225571728.0 },
60 static double A1p0[3][3] = {
63 { -810728.0, 1403580.0, 0.0 }
66 static double A2p0[3][3] = {
69 { -1370589.0, 0.0, 527612.0 }
72 static double A1p76[3][3] = {
73 { 82758667.0, 1871391091.0, 4127413238.0 },
74 { 3672831523.0, 69195019.0, 1871391091.0 },
75 { 3672091415.0, 3528743235.0, 69195019.0 }
78 static double A2p76[3][3] = {
79 { 1511326704.0, 3759209742.0, 1610795712.0 },
80 { 4292754251.0, 1511326704.0, 3889917532.0 },
81 { 3859662829.0, 4292754251.0, 3708466080.0 }
84 static double A1p127[3][3] = {
85 { 2427906178.0, 3580155704.0, 949770784.0 },
86 { 226153695.0, 1230515664.0, 3580155704.0 },
87 { 1988835001.0, 986791581.0, 1230515664.0 }
90 static double A2p127[3][3] = {
91 { 1464411153.0, 277697599.0, 1610723613.0 },
92 { 32183930.0, 1464411153.0, 1022607788.0 },
93 { 2824425944.0, 32183930.0, 2093834863.0 }
100 /*-------------------------------------------------------------------------*/
102 static double MultModM (double a, double s, double c, double m)
103 /* Compute (a*s + c) % m. m must be < 2^35. Works also for s, c < 0 */
108 if ((v >= two53) || (v <= -two53)) {
109 a1 = (long) (a / two17);
114 v = v * two17 + a * s + c;
117 if ((v -= a1 * m) < 0.0)
124 /*-------------------------------------------------------------------------*/
126 static void MatVecModM (double A[3][3], double s[3], double v[3], double m)
127 /* Returns v = A*s % m. Assumes that -m < s[i] < m. */
128 /* Works even if v = s. */
132 for (i = 0; i < 3; ++i) {
133 x[i] = MultModM (A[i][0], s[0], 0.0, m);
134 x[i] = MultModM (A[i][1], s[1], x[i], m);
135 x[i] = MultModM (A[i][2], s[2], x[i], m);
137 for (i = 0; i < 3; ++i)
142 /*-------------------------------------------------------------------------*/
144 static void MatMatModM (double A[3][3], double B[3][3], double C[3][3],
146 /* Returns C = A*B % m. Work even if A = C or B = C or A = B = C. */
149 double V[3], W[3][3];
150 for (i = 0; i < 3; ++i) {
151 for (j = 0; j < 3; ++j)
153 MatVecModM (A, V, V, m);
154 for (j = 0; j < 3; ++j)
157 for (i = 0; i < 3; ++i) {
158 for (j = 0; j < 3; ++j)
164 /*-------------------------------------------------------------------------*/
166 static void MatTwoPowModM (double A[3][3], double B[3][3], double m, long e)
167 /* Compute matrix B = (A^(2^e) % m); works even if A = B */
171 /* initialize: B = A */
173 for (i = 0; i < 3; i++) {
174 for (j = 0; j < 3; ++j)
178 /* Compute B = A^{2^e} */
179 for (i = 0; i < e; i++)
180 MatMatModM (B, B, B, m);
184 /*-------------------------------------------------------------------------*/
186 static void MatPowModM (double A[3][3], double B[3][3], double m, long n)
187 /* Compute matrix B = A^n % m ; works even if A = B */
192 /* initialize: W = A; B = I */
193 for (i = 0; i < 3; i++) {
194 for (j = 0; j < 3; ++j) {
199 for (j = 0; j < 3; ++j)
202 /* Compute B = A^n % m using the binary decomposition of n */
205 MatMatModM (W, B, B, m);
206 MatMatModM (W, W, W, m);
212 /*-------------------------------------------------------------------------*/
214 static double U01 (RngStream g)
220 p1 = a12 * g->Cg[1] - a13n * g->Cg[0];
230 p2 = a21 * g->Cg[5] - a23n * g->Cg[3];
240 u = ((p1 > p2) ? (p1 - p2) * norm : (p1 - p2 + m1) * norm);
241 return (g->Anti) ? (1 - u) : u;
245 /*-------------------------------------------------------------------------*/
247 static double U01d (RngStream g)
253 return (u < 1.0) ? u : (u - 1.0);
255 /* Don't forget that U01() returns 1 - u in the antithetic case */
256 u += (U01(g) - 1.0) * fact;
257 return (u < 0.0) ? u + 1.0 : u;
262 /*-------------------------------------------------------------------------*/
264 static int CheckSeed (unsigned long seed[6])
266 /* Check that the seeds are legitimate values. Returns 0 if legal seeds,
270 for (i = 0; i < 3; ++i) {
272 fprintf (stderr, "****************************************\n"
273 "ERROR: Seed[%1d] >= m1, Seed is not set.\n"
274 "****************************************\n\n", i);
278 for (i = 3; i < 6; ++i) {
280 fprintf (stderr, "****************************************\n"
281 "ERROR: Seed[%1d] >= m1, Seed is not set.\n"
282 "****************************************\n\n", i);
286 if (seed[0] == 0 && seed[1] == 0 && seed[2] == 0) {
287 fprintf (stderr, "****************************\n"
288 "ERROR: First 3 seeds = 0.\n"
289 "****************************\n\n");
292 if (seed[3] == 0 && seed[4] == 0 && seed[5] == 0) {
293 fprintf (stderr, "****************************\n"
294 "ERROR: Last 3 seeds = 0.\n"
295 "****************************\n\n");
303 /*---------------------------------------------------------------------*/
305 /*---------------------------------------------------------------------*/
308 RngStream RngStream_CreateStream (const char name[])
314 g = (RngStream) malloc (sizeof (struct RngStream_InfoState));
316 printf ("RngStream_CreateStream: No more memory\n\n");
321 g->name = (char *) malloc ((len + 1) * sizeof (char));
322 strncpy (g->name, name, len + 1);
328 for (i = 0; i < 6; ++i) {
329 g->Bg[i] = g->Cg[i] = g->Ig[i] = nextSeed[i];
331 MatVecModM (A1p127, nextSeed, nextSeed, m1);
332 MatVecModM (A2p127, &nextSeed[3], &nextSeed[3], m2);
336 /*-------------------------------------------------------------------------*/
338 void RngStream_DeleteStream (RngStream * p)
347 /*-------------------------------------------------------------------------*/
349 void RngStream_ResetStartStream (RngStream g)
352 for (i = 0; i < 6; ++i)
353 g->Cg[i] = g->Bg[i] = g->Ig[i];
356 /*-------------------------------------------------------------------------*/
358 void RngStream_ResetNextSubstream (RngStream g)
361 MatVecModM (A1p76, g->Bg, g->Bg, m1);
362 MatVecModM (A2p76, &g->Bg[3], &g->Bg[3], m2);
363 for (i = 0; i < 6; ++i)
367 /*-------------------------------------------------------------------------*/
369 void RngStream_ResetStartSubstream (RngStream g)
372 for (i = 0; i < 6; ++i)
376 /*-------------------------------------------------------------------------*/
378 int RngStream_SetPackageSeed (unsigned long seed[6])
381 if (CheckSeed (seed))
382 return -1; /* FAILURE */
383 for (i = 0; i < 6; ++i)
384 nextSeed[i] = seed[i];
385 return 0; /* SUCCESS */
388 /*-------------------------------------------------------------------------*/
390 int RngStream_SetSeed (RngStream g, unsigned long seed[6])
393 if (CheckSeed (seed))
394 return -1; /* FAILURE */
395 for (i = 0; i < 6; ++i)
396 g->Cg[i] = g->Bg[i] = g->Ig[i] = seed[i];
397 return 0; /* SUCCESS */
400 /*-------------------------------------------------------------------------*/
402 void RngStream_AdvanceState (RngStream g, long e, long c)
404 double B1[3][3], C1[3][3], B2[3][3], C2[3][3];
407 MatTwoPowModM (A1p0, B1, m1, e);
408 MatTwoPowModM (A2p0, B2, m2, e);
410 MatTwoPowModM (InvA1, B1, m1, -e);
411 MatTwoPowModM (InvA2, B2, m2, -e);
415 MatPowModM (A1p0, C1, m1, c);
416 MatPowModM (A2p0, C2, m2, c);
418 MatPowModM (InvA1, C1, m1, -c);
419 MatPowModM (InvA2, C2, m2, -c);
423 MatMatModM (B1, C1, C1, m1);
424 MatMatModM (B2, C2, C2, m2);
427 MatVecModM (C1, g->Cg, g->Cg, m1);
428 MatVecModM (C2, &g->Cg[3], &g->Cg[3], m2);
431 /*-------------------------------------------------------------------------*/
433 void RngStream_GetState (RngStream g, unsigned long seed[6])
436 for (i = 0; i < 6; ++i)
440 /*-------------------------------------------------------------------------*/
442 void RngStream_WriteState (RngStream g)
447 printf ("The current state of the Rngstream");
448 if (g->name && (strlen (g->name) > 0))
449 printf (" %s", g->name);
450 printf (":\n Cg = { ");
452 for (i = 0; i < 5; i++) {
453 printf ("%lu, ", (unsigned long) g->Cg[i]);
455 printf ("%lu }\n\n", (unsigned long) g->Cg[5]);
458 /*-------------------------------------------------------------------------*/
460 void RngStream_WriteStateFull (RngStream g)
465 printf ("The RngStream");
466 if (g->name && (strlen (g->name) > 0))
467 printf (" %s", g->name);
468 printf (":\n Anti = %s\n", (g->Anti ? "true" : "false"));
469 printf (" IncPrec = %s\n", (g->IncPrec ? "true" : "false"));
472 for (i = 0; i < 5; i++) {
473 printf ("%lu, ", (unsigned long) (g->Ig[i]));
475 printf ("%lu }\n", (unsigned long) g->Ig[5]);
478 for (i = 0; i < 5; i++) {
479 printf ("%lu, ", (unsigned long) (g->Bg[i]));
481 printf ("%lu }\n", (unsigned long) g->Bg[5]);
484 for (i = 0; i < 5; i++) {
485 printf ("%lu, ", (unsigned long) (g->Cg[i]));
487 printf ("%lu }\n\n", (unsigned long) g->Cg[5]);
490 /*-------------------------------------------------------------------------*/
492 void RngStream_IncreasedPrecis (RngStream g, int incp)
497 /*-------------------------------------------------------------------------*/
499 void RngStream_SetAntithetic (RngStream g, int a)
504 /*-------------------------------------------------------------------------*/
506 double RngStream_RandU01 (RngStream g)
514 /*-------------------------------------------------------------------------*/
516 int RngStream_RandInt (RngStream g, int i, int j)
518 return i + (int) ((j - i + 1.0) * RngStream_RandU01 (g));
521 /* Undefine this terms, or supernovae build will fail. */