See
- The definition genrand2.cpp
- The description Random distributions
<project-file type=“source”/> <content> /* this file is a Tausworthe random number generator. I shamelessly copied
from the gls (Gnu Science Library) code, and adapted to myslef usage. the original copyright message is below */
/* rng/taus.c * * Copyright (C) 1996, 1997, 1998, 1999, 2000 James Theiler, Brian Gough * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 2 of the License, or (at * your option) any later version. * * This program is distributed in the hope that it will be useful, but * WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU * General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software * Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. */
/* This is a maximally equidistributed combined Tausworthe
generator. The sequence is,
x_n = (s1_n ^ s2_n ^ s3_n)
s1_{n+1} = (((s1_n & 4294967294) <<12) ^ (((s1_n <<13) ^ s1_n) >>19)) s2_{n+1} = (((s2_n & 4294967288) << 4) ^ (((s2_n << 2) ^ s2_n) >>25)) s3_{n+1} = (((s3_n & 4294967280) <<17) ^ (((s3_n << 3) ^ s3_n) >>11))
computed modulo 2^32. In the three formulas above '^' means exclusive-or (C-notation), not exponentiation. Note that the algorithm relies on the properties of 32-bit unsigned integers (it is formally defined on bit-vectors of length 32). I have added a bitmask to make it work on 64 bit machines.
We initialize the generator with s1_1 .. s3_1 = s_n MOD m, where s_n = (69069 * s_{n-1}) mod 2^32, and s_0 = s is the user-supplied seed.
The theoretical value of x_{10007} is 2733957125. The subscript 10007 means (1) seed the generator with s=1 (2) do six warm-up iterations, (3) then do 10000 actual iterations.
The period of this generator is about 2^88.
From: P. L'Ecuyer, "Maximally Equidistributed Combined Tausworthe Generators", Mathematics of Computation, 65, 213 (1996), 203--213.
This is available on the net from L'Ecuyer's home page,
http://www.iro.umontreal.ca/~lecuyer/myftp/papers/tausme.ps ftp://ftp.iro.umontreal.ca/pub/simulation/lecuyer/papers/tausme.ps
Update: April 2002
There is an erratum in the paper "Tables of Maximally Equidistributed Combined LFSR Generators", Mathematics of Computation, 68, 225 (1999), 261--269: http://www.iro.umontreal.ca/~lecuyer/myftp/papers/tausme2.ps
... the k_j most significant bits of z_j must be non- zero, for each j. (Note: this restriction also applies to the computer code given in [4], but was mistakenly not mentioned in that paper.) This affects the seeding procedure by imposing the requirement s1 > 1, s2 > 7, s3 > 15.
The generator taus2 has been added to satisfy this requirement. The original taus generator is unchanged.
Update: November 2002
There was a bug in the correction to the seeding procedure for s2. It affected the following seeds 254679140 1264751179 1519430319 2274823218 2529502358 3284895257 3539574397 (s2 < 8).
*/
#include “genrand2.h”
struct taus_state_t
{ unsigned long int s1, s2, s3; }
taus_state;
unsigned long genrand2i() {
#define MASK 0xffffffffUL #define TAUSWORTHE(s,a,b,c,d) (((s &c) «d) &MASK) ^ ((((s «a) &MASK)^s) »b)
taus_state.s1 = TAUSWORTHE (taus_state.s1, 13, 19, 4294967294UL, 12); taus_state.s2 = TAUSWORTHE (taus_state.s2, 2, 25, 4294967288UL, 4); taus_state.s3 = TAUSWORTHE (taus_state.s3, 3, 11, 4294967280UL, 17);
return (taus_state.s1 ^ taus_state.s2 ^ taus_state.s3);
}
float genrand2d() {
return genrand2i() / 4294967296.0 ;
}
void sgenrand2 (unsigned long int s) {
if (s == 0) s = 1; /* default seed is 1 */
#define LCG(n) ((69069 * n) & 0xffffffffUL)
taus_state.s1 = LCG (s); if (taus_state.s1 < 2) taus_state.s1 += 2UL; taus_state.s2 = LCG (taus_state.s1); if (taus_state.s2 < 8) taus_state.s2 += 8UL; taus_state.s3 = LCG (taus_state.s2); if (taus_state.s3 < 16) taus_state.s3 += 16UL;
/* "warm it up" */ genrand2i (); genrand2i (); genrand2i (); genrand2i (); genrand2i (); genrand2i (); return;
}
</content>