3 * Portable random number generator, and sampling routines.
5 * SRE, Tue Oct 1 15:24:11 2002 [St. Louis]
6 * CVS $Id: sre_random.c,v 1.1 2002/10/09 14:26:09 eddy Exp)
12 #include "sre_random.h"
14 static int sre_randseed = 42; /* default seed for sre_random() */
16 /* Function: sre_random()
18 * Purpose: Return a uniform deviate x, 0.0 <= x < 1.0.
20 * sre_randseed is a static variable, set
21 * by sre_srandom(). When it is non-zero,
24 * Implements L'Ecuyer's algorithm for combining output
25 * of two linear congruential generators, plus a Bays-Durham
26 * shuffle. This is essentially ran2() from Numerical Recipes,
27 * sans their nonhelpful Rand/McNally-esque code obfuscation.
29 * Overflow errors are avoided by Schrage's algorithm:
30 * az % m = a(z%q) - r(z/q) (+m if <0)
33 * Requires that long int's have at least 32 bits.
34 * This function uses statics and is NOT THREADSAFE.
36 * Reference: Press et al. Numerical Recipes in C, 1992.
38 * Reliable and portable, but slow. Benchmarks on wrasse,
39 * using Linux gcc and Linux glibc rand() (see randspeed, in Testsuite):
40 * sre_random(): 0.5 usec/call
41 * rand(): 0.2 usec/call
46 static long rnd1; /* random number from LCG1 */
47 static long rnd2; /* random number from LCG2 */
48 static long rnd; /* random number we return */
49 static long tbl[64]; /* table for Bays/Durham shuffle */
53 /* Magic numbers a1,m1, a2,m2 from L'Ecuyer, for 2 LCGs.
54 * q,r derive from them (q=m/a, r=m%a) and are needed for Schrage's algorithm.
70 /* Fill the table for Bays/Durham */
71 for (i = 0; i < 64; i++) {
72 x = a1*(rnd1%q1); /* LCG1 in action... */
75 if (rnd1 < 0) rnd1 += m1;
77 x = a2*(rnd2%q2); /* LCG2 in action... */
80 if (rnd2 < 0) rnd2 += m2;
83 if (tbl[i] < 0) tbl[i] += m1;
85 sre_randseed = 0; /* drop the flag. */
86 }/* end of initialization*/
89 x = a1*(rnd1%q1); /* LCG1 in action... */
92 if (rnd1 < 0) rnd1 += m1;
94 x = a2*(rnd2%q2); /* LCG2 in action... */
97 if (rnd2 < 0) rnd2 += m2;
99 /* Choose our random number from the table... */
100 i = (int) (((double) rnd / (double) m1) * 64.);
102 /* and replace with a new number by L'Ecuyer. */
104 if (tbl[i] < 0) tbl[i] += m1;
106 return ((double) rnd / (double) m1);
109 /* Function: sre_srandom()
111 * Purpose: Initialize with a random seed. Seed must be
112 * >= 0 to work; we silently enforce this.
115 sre_srandom(int seed)
117 if (seed < 0) seed = -1 * seed;
118 if (seed == 0) seed = 42;
122 /* Function: sre_random_positive()
123 * Date: SRE, Wed Apr 17 13:34:32 2002 [St. Louis]
125 * Purpose: Assure 0 < x < 1 (positive uniform deviate)
128 sre_random_positive(void)
131 do { x = sre_random(); } while (x == 0.0);
135 /* Function: ExponentialRandom()
136 * Date: SRE, Mon Sep 6 21:24:29 1999 [St. Louis]
138 * Purpose: Pick an exponentially distributed random variable
146 ExponentialRandom(void)
150 do x = sre_random(); while (x == 0.0);
154 /* Function: Gaussrandom()
156 * Pick a Gaussian-distributed random variable
157 * with some mean and standard deviation, and
160 * Based on RANLIB.c public domain implementation.
161 * Thanks to the authors, Barry W. Brown and James Lovato,
162 * University of Texas, M.D. Anderson Cancer Center, Houston TX.
163 * Their implementation is from Ahrens and Dieter, "Extensions
164 * of Forsythe's method for random sampling from the normal
165 * distribution", Math. Comput. 27:927-937 (1973).
167 * Impenetrability of the code is to be blamed on its FORTRAN/f2c lineage.
171 Gaussrandom(double mean, double stddev)
173 static double a[32] = {
174 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,
175 0.626099,0.6744898,0.7245144,0.7764218,0.8305109,0.8871466,0.9467818,
176 1.00999,1.077516,1.150349,1.229859,1.318011,1.417797,1.534121,1.67594,
179 static double d[31] = {
180 0.0,0.0,0.0,0.0,0.0,0.2636843,0.2425085,0.2255674,0.2116342,0.1999243,
181 0.1899108,0.1812252,0.1736014,0.1668419,0.1607967,0.1553497,0.1504094,
182 0.1459026,0.14177,0.1379632,0.1344418,0.1311722,0.128126,0.1252791,
183 0.1226109,0.1201036,0.1177417,0.1155119,0.1134023,0.1114027,0.1095039
185 static double t[31] = {
186 7.673828E-4,2.30687E-3,3.860618E-3,5.438454E-3,7.0507E-3,8.708396E-3,
187 1.042357E-2,1.220953E-2,1.408125E-2,1.605579E-2,1.81529E-2,2.039573E-2,
188 2.281177E-2,2.543407E-2,2.830296E-2,3.146822E-2,3.499233E-2,3.895483E-2,
189 4.345878E-2,4.864035E-2,5.468334E-2,6.184222E-2,7.047983E-2,8.113195E-2,
190 9.462444E-2,0.1123001,0.136498,0.1716886,0.2276241,0.330498,0.5847031
192 static double h[31] = {
193 3.920617E-2,3.932705E-2,3.951E-2,3.975703E-2,4.007093E-2,4.045533E-2,
194 4.091481E-2,4.145507E-2,4.208311E-2,4.280748E-2,4.363863E-2,4.458932E-2,
195 4.567523E-2,4.691571E-2,4.833487E-2,4.996298E-2,5.183859E-2,5.401138E-2,
196 5.654656E-2,5.95313E-2,6.308489E-2,6.737503E-2,7.264544E-2,7.926471E-2,
197 8.781922E-2,9.930398E-2,0.11556,0.1404344,0.1836142,0.2790016,0.7010474
200 static double snorm,u,s,ustar,aa,w,y,tt;
209 if(i == 0) goto S100;
216 if(ustar <= *(t+i-1)) goto S60;
217 w = (ustar-*(t+i-1))**(h+i-1);
224 if(s == 1.0) snorm = -y;
225 return (stddev*snorm + mean);
236 ustar = sre_random();
238 if(ustar > tt) goto S50;
240 if(ustar >= u) goto S70;
241 ustar = sre_random();
255 if(u < 1.0) goto S110;
264 ustar = sre_random();
265 if(ustar > tt) goto S50;
267 if(ustar >= u) goto S150;
273 /* Functions: DChoose(), FChoose()
275 * Purpose: Make a random choice from a normalized distribution.
276 * DChoose() is for double-precision vectors;
277 * FChoose() is for single-precision float vectors.
278 * Returns the number of the choice.
281 DChoose(double *p, int N)
283 double roll; /* random fraction */
284 double sum; /* integrated prob */
285 int i; /* counter over the probs */
289 for (i = 0; i < N; i++)
292 if (roll < sum) return i;
294 return (int) (sre_random() * N); /* bulletproof */
297 FChoose(float *p, int N)
299 float roll; /* random fraction */
300 float sum; /* integrated prob */
301 int i; /* counter over the probs */
305 for (i = 0; i < N; i++)
308 if (roll < sum) return i;
310 return (int) (sre_random() * N); /* bulletproof */