/* sre_random.c * * Portable random number generator, and sampling routines. * * SRE, Tue Oct 1 15:24:11 2002 [St. Louis] * CVS $Id: sre_random.c,v 1.1 2002/10/09 14:26:09 eddy Exp) */ #include #include #include #include "sre_random.h" static int sre_randseed = 42; /* default seed for sre_random() */ /* Function: sre_random() * * Purpose: Return a uniform deviate x, 0.0 <= x < 1.0. * * sre_randseed is a static variable, set * by sre_srandom(). When it is non-zero, * we re-seed. * * Implements L'Ecuyer's algorithm for combining output * of two linear congruential generators, plus a Bays-Durham * shuffle. This is essentially ran2() from Numerical Recipes, * sans their nonhelpful Rand/McNally-esque code obfuscation. * * Overflow errors are avoided by Schrage's algorithm: * az % m = a(z%q) - r(z/q) (+m if <0) * where q=m/a, r=m%a * * Requires that long int's have at least 32 bits. * This function uses statics and is NOT THREADSAFE. * * Reference: Press et al. Numerical Recipes in C, 1992. * * Reliable and portable, but slow. Benchmarks on wrasse, * using Linux gcc and Linux glibc rand() (see randspeed, in Testsuite): * sre_random(): 0.5 usec/call * rand(): 0.2 usec/call */ double sre_random(void) { static long rnd1; /* random number from LCG1 */ static long rnd2; /* random number from LCG2 */ static long rnd; /* random number we return */ static long tbl[64]; /* table for Bays/Durham shuffle */ long x,y; int i; /* Magic numbers a1,m1, a2,m2 from L'Ecuyer, for 2 LCGs. * q,r derive from them (q=m/a, r=m%a) and are needed for Schrage's algorithm. */ long a1 = 40014; long m1 = 2147483563; long q1 = 53668; long r1 = 12211; long a2 = 40692; long m2 = 2147483399; long q2 = 52774; long r2 = 3791; if (sre_randseed > 0) { rnd1 = sre_randseed; rnd2 = sre_randseed; /* Fill the table for Bays/Durham */ for (i = 0; i < 64; i++) { x = a1*(rnd1%q1); /* LCG1 in action... */ y = r1*(rnd1/q1); rnd1 = x-y; if (rnd1 < 0) rnd1 += m1; x = a2*(rnd2%q2); /* LCG2 in action... */ y = r2*(rnd2/q2); rnd2 = x-y; if (rnd2 < 0) rnd2 += m2; tbl[i] = rnd1-rnd2; if (tbl[i] < 0) tbl[i] += m1; } sre_randseed = 0; /* drop the flag. */ }/* end of initialization*/ x = a1*(rnd1%q1); /* LCG1 in action... */ y = r1*(rnd1/q1); rnd1 = x-y; if (rnd1 < 0) rnd1 += m1; x = a2*(rnd2%q2); /* LCG2 in action... */ y = r2*(rnd2/q2); rnd2 = x-y; if (rnd2 < 0) rnd2 += m2; /* Choose our random number from the table... */ i = (int) (((double) rnd / (double) m1) * 64.); rnd = tbl[i]; /* and replace with a new number by L'Ecuyer. */ tbl[i] = rnd1-rnd2; if (tbl[i] < 0) tbl[i] += m1; return ((double) rnd / (double) m1); } /* Function: sre_srandom() * * Purpose: Initialize with a random seed. Seed must be * >= 0 to work; we silently enforce this. */ void sre_srandom(int seed) { if (seed < 0) seed = -1 * seed; if (seed == 0) seed = 42; sre_randseed = seed; } /* Function: sre_random_positive() * Date: SRE, Wed Apr 17 13:34:32 2002 [St. Louis] * * Purpose: Assure 0 < x < 1 (positive uniform deviate) */ double sre_random_positive(void) { double x; do { x = sre_random(); } while (x == 0.0); return x; } /* Function: ExponentialRandom() * Date: SRE, Mon Sep 6 21:24:29 1999 [St. Louis] * * Purpose: Pick an exponentially distributed random variable * 0 > x >= infinity * * Args: (void) * * Returns: x */ double ExponentialRandom(void) { double x; do x = sre_random(); while (x == 0.0); return -log(x); } /* Function: Gaussrandom() * * Pick a Gaussian-distributed random variable * with some mean and standard deviation, and * return it. * * Based on RANLIB.c public domain implementation. * Thanks to the authors, Barry W. Brown and James Lovato, * University of Texas, M.D. Anderson Cancer Center, Houston TX. * Their implementation is from Ahrens and Dieter, "Extensions * of Forsythe's method for random sampling from the normal * distribution", Math. Comput. 27:927-937 (1973). * * Impenetrability of the code is to be blamed on its FORTRAN/f2c lineage. * */ double Gaussrandom(double mean, double stddev) { static double a[32] = { 0.0,3.917609E-2,7.841241E-2,0.11777,0.1573107,0.1970991,0.2372021,0.2776904, 0.3186394,0.36013,0.4022501,0.4450965,0.4887764,0.5334097,0.5791322, 0.626099,0.6744898,0.7245144,0.7764218,0.8305109,0.8871466,0.9467818, 1.00999,1.077516,1.150349,1.229859,1.318011,1.417797,1.534121,1.67594, 1.862732,2.153875 }; static double d[31] = { 0.0,0.0,0.0,0.0,0.0,0.2636843,0.2425085,0.2255674,0.2116342,0.1999243, 0.1899108,0.1812252,0.1736014,0.1668419,0.1607967,0.1553497,0.1504094, 0.1459026,0.14177,0.1379632,0.1344418,0.1311722,0.128126,0.1252791, 0.1226109,0.1201036,0.1177417,0.1155119,0.1134023,0.1114027,0.1095039 }; static double t[31] = { 7.673828E-4,2.30687E-3,3.860618E-3,5.438454E-3,7.0507E-3,8.708396E-3, 1.042357E-2,1.220953E-2,1.408125E-2,1.605579E-2,1.81529E-2,2.039573E-2, 2.281177E-2,2.543407E-2,2.830296E-2,3.146822E-2,3.499233E-2,3.895483E-2, 4.345878E-2,4.864035E-2,5.468334E-2,6.184222E-2,7.047983E-2,8.113195E-2, 9.462444E-2,0.1123001,0.136498,0.1716886,0.2276241,0.330498,0.5847031 }; static double h[31] = { 3.920617E-2,3.932705E-2,3.951E-2,3.975703E-2,4.007093E-2,4.045533E-2, 4.091481E-2,4.145507E-2,4.208311E-2,4.280748E-2,4.363863E-2,4.458932E-2, 4.567523E-2,4.691571E-2,4.833487E-2,4.996298E-2,5.183859E-2,5.401138E-2, 5.654656E-2,5.95313E-2,6.308489E-2,6.737503E-2,7.264544E-2,7.926471E-2, 8.781922E-2,9.930398E-2,0.11556,0.1404344,0.1836142,0.2790016,0.7010474 }; static long i; static double snorm,u,s,ustar,aa,w,y,tt; u = sre_random(); s = 0.0; if(u > 0.5) s = 1.0; u += (u-s); u = 32.0*u; i = (long) (u); if(i == 32) i = 31; if(i == 0) goto S100; /* * START CENTER */ ustar = u-(double)i; aa = *(a+i-1); S40: if(ustar <= *(t+i-1)) goto S60; w = (ustar-*(t+i-1))**(h+i-1); S50: /* * EXIT (BOTH CASES) */ y = aa+w; snorm = y; if(s == 1.0) snorm = -y; return (stddev*snorm + mean); S60: /* * CENTER CONTINUED */ u = sre_random(); w = u*(*(a+i)-aa); tt = (0.5*w+aa)*w; goto S80; S70: tt = u; ustar = sre_random(); S80: if(ustar > tt) goto S50; u = sre_random(); if(ustar >= u) goto S70; ustar = sre_random(); goto S40; S100: /* * START TAIL */ i = 6; aa = *(a+31); goto S120; S110: aa += *(d+i-1); i += 1; S120: u += u; if(u < 1.0) goto S110; u -= 1.0; S140: w = u**(d+i-1); tt = (0.5*w+aa)*w; goto S160; S150: tt = u; S160: ustar = sre_random(); if(ustar > tt) goto S50; u = sre_random(); if(ustar >= u) goto S150; u = sre_random(); goto S140; } /* Functions: DChoose(), FChoose() * * Purpose: Make a random choice from a normalized distribution. * DChoose() is for double-precision vectors; * FChoose() is for single-precision float vectors. * Returns the number of the choice. */ int DChoose(double *p, int N) { double roll; /* random fraction */ double sum; /* integrated prob */ int i; /* counter over the probs */ roll = sre_random(); sum = 0.0; for (i = 0; i < N; i++) { sum += p[i]; if (roll < sum) return i; } return (int) (sre_random() * N); /* bulletproof */ } int FChoose(float *p, int N) { float roll; /* random fraction */ float sum; /* integrated prob */ int i; /* counter over the probs */ roll = sre_random(); sum = 0.0; for (i = 0; i < N; i++) { sum += p[i]; if (roll < sum) return i; } return (int) (sre_random() * N); /* bulletproof */ }