/* This is the ``Mersenne Twister'' random number generator MT19937, which * generates pseudorandom integers uniformly distributed in 0..(2^32 - 1) * starting from any odd seed in 0..(2^32 - 1). This version is a recode * by Shawn Cokus (Cokus@math.washington.edu) on March 8, 1998 of a version by * Takuji Nishimura (who had suggestions from Topher Cooper and Marc Rieffel in * July-August 1997). * * Effectiveness of the recoding (on Goedel2.math.washington.edu, a DEC Alpha * running OSF/1) using GCC -O3 as a compiler: before recoding: 51.6 sec. to * generate 300 million random numbers; after recoding: 24.0 sec. for the same * (i.e., 46.5% of original time), so speed is now about 12.5 million random * number generations per second on this machine. * * According to the URL <http: *www.math.keio.ac.jp/~matumoto/emt.html> * (and paraphrasing a bit in places), the Mersenne Twister is ``designed * with consideration of the flaws of various existing generators,'' has * a period of 2^19937 - 1, gives a sequence that is 623-dimensionally * equidistributed, and ``has passed many stringent tests, including the * die-hard test of G. Marsaglia and the load test of P. Hellekalek and * S. Wegenkittl.'' It is efficient in memory usage (typically using 2506 * to 5012 bytes of static data, depending on data type sizes, and the code * is quite short as well). It generates random numbers in batches of 624 * at a time, so the caching and pipelining of modern systems is exploited. * It is also divide- and mod-free. * * This library is free software; you can redistribute it and/or modify it * under the terms of the GNU Library General Public License as published by * the Free Software Foundation (either version 2 of the License or, at your * option, any later version). This library 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 Library General Public License for more details. You should have * received a copy of the GNU Library General Public License along with this * library; if not, write to the Free Software Foundation, Inc., 59 Temple * Place, Suite 330, Boston, MA 02111-1307, USA. * * The code as Shawn received it included the following notice: * * Copyright (C) 1997 Makoto Matsumoto and Takuji Nishimura. When * you use this, send an e-mail to <matumoto@math.keio.ac.jp> with * an appropriate reference to your work. * * It would be nice to CC: <Cokus@math.washington.edu> when you write. */ #include <sys/types.h> #include <unistd.h> #include "systime.h" #include "misc.h" #define N (624) /* length of state vector */ #define M (397) /* a period parameter */ #define K (0x9908B0DFU) /* a magic constant */ #define hiBit(u) ((u) & 0x80000000U) /* mask all but highest bit of u */ #define loBit(u) ((u) & 0x00000001U) /* mask all but lowest bit of u */ #define loBits(u) ((u) & 0x7FFFFFFFU) /* mask the highest bit of u */ #define mixBits(u, v) (hiBit(u)|loBits(v)) /* move hi bit of u to hi bit of v */ static uint32 state[N+1]; /* state vector + 1 extra to not violate ANSI C */ static uint32 *next; /* next random value is computed from here */ static int left = -1; /* can *next++ this many times before reloading */ static void seedMT(uint32 seed) { /* * We initialize state[0..(N-1)] via the generator * * x_new = (69069 * x_old) mod 2^32 * * from Line 15 of Table 1, p. 106, Sec. 3.3.4 of Knuth's * _The Art of Computer Programming_, Volume 2, 3rd ed. * * Notes (SJC): I do not know what the initial state requirements * of the Mersenne Twister are, but it seems this seeding generator * could be better. It achieves the maximum period for its modulus * (2^30) iff x_initial is odd (p. 20-21, Sec. 3.2.1.2, Knuth); if * x_initial can be even, you have sequences like 0, 0, 0, ...; * 2^31, 2^31, 2^31, ...; 2^30, 2^30, 2^30, ...; 2^29, 2^29 + 2^31, * 2^29, 2^29 + 2^31, ..., etc. so I force seed to be odd below. * * Even if x_initial is odd, if x_initial is 1 mod 4 then * * the lowest bit of x is always 1, * the next-to-lowest bit of x is always 0, * the 2nd-from-lowest bit of x alternates ... 0 1 0 1 0 1 0 1 ... , * the 3rd-from-lowest bit of x 4-cycles ... 0 1 1 0 0 1 1 0 ... , * the 4th-from-lowest bit of x has the 8-cycle ... 0 0 0 1 1 1 1 0 ... , * ... * * and if x_initial is 3 mod 4 then * * the lowest bit of x is always 1, * the next-to-lowest bit of x is always 1, * the 2nd-from-lowest bit of x alternates ... 0 1 0 1 0 1 0 1 ... , * the 3rd-from-lowest bit of x 4-cycles ... 0 0 1 1 0 0 1 1 ... , * the 4th-from-lowest bit of x has the 8-cycle ... 0 0 1 1 1 1 0 0 ... , * ... * * The generator's potency (min. s>=0 with (69069-1)^s = 0 mod 2^32) is * 16, which seems to be alright by p. 25, Sec. 3.2.1.3 of Knuth. It * also does well in the dimension 2..5 spectral tests, but it could be * better in dimension 6 (Line 15, Table 1, p. 106, Sec. 3.3.4, Knuth). * * Note that the random number user does not see the values generated * here directly since reloadMT() will always munge them first, so maybe * none of all of this matters. In fact, the seed values made here could * even be extra-special desirable if the Mersenne Twister theory says * so-- that's why the only change I made is to restrict to odd seeds. */ register uint32 x = (seed | 1U) & 0xFFFFFFFFU, *s = state; register int j; for(left=0, *s++=x, j=N; --j; *s++ = (x*=69069U) & 0xFFFFFFFFU); } void random_init(uint32 seed) { if (seed == 0) { struct timeval t; pid_t pid = getpid(); pid_t ppid = getppid(); gettimeofday(&t, 0); seed = t.tv_sec ^ t.tv_usec ^ (t.tv_usec << 12) ^ pid ^ (pid << 16) ^ ppid ^ (ppid << 16); } seedMT(seed); } static uint32 reloadMT(void) { register uint32 *p0=state, *p2=state+2, *pM=state+M, s0, s1; register int j; if (left < -1) random_init(4357U); left=N-1, next=state+1; for(s0=state[0], s1=state[1], j=N-M+1; --j; s0=s1, s1=*p2++) *p0++ = *pM++ ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0U); for(pM=state, j=M; --j; s0=s1, s1=*p2++) *p0++ = *pM++ ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0U); s1 = state[0], *p0 = *pM ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0U); s1 ^= (s1 >> 11); s1 ^= (s1 << 7) & 0x9D2C5680U; s1 ^= (s1 << 15) & 0xEFC60000U; return s1 ^ (s1 >> 18); } uint32 random_int(void) { uint32 y; if(--left < 0) return reloadMT(); y = *next++; y ^= (y >> 11); y ^= (y << 7) & 0x9D2C5680U; y ^= (y << 15) & 0xEFC60000U; return y ^ (y >> 18); }

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