/* ** 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 ** (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 with ** an appropriate reference to your work. ** ** It would be nice to CC: when you write. ** ** ** Adapted for XPilot by Bert Gijsbers: ** Changes for ANSI C. ** Indentation. ** No typedefs in external interface. ** ** $Id: randommt.c,v 5.1 2001/06/02 21:02:19 bertg Exp $ */ /* Our exported interface: */ void seedMT(unsigned int seed); unsigned int reloadMT(void); unsigned int randomMT(void); /* ** uint32 must be an unsigned integer type capable of holding at least 32 ** bits; exactly 32 should be fastest, but 64 is better on an Alpha with ** GCC at -O3 optimization so try your options and see what's best for you. */ typedef unsigned int uint32; #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 */ void seedMT(unsigned int 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) ; } unsigned int reloadMT(void) { register uint32 *p0 = state, *p2 = state + 2, *pM = state + M, s0, s1; register int j; if (left < -1) seedMT(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)); } unsigned int randomMT(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)); } #ifdef MT_MAIN #include #include #ifndef EXIT_SUCCESS #define EXIT_SUCCESS 0 #endif int main(void) { int j; /* you can seed with any uint32, but the best are odds in 0..(2^32 - 1) */ seedMT(4357U); /* print the first 2,002 random numbers seven to a line as an example */ for (j = 0; j < 2002; j++) printf(" %10lu%s", (unsigned long)randomMT(), (j % 7) == 6 ? "\n" : ""); return (EXIT_SUCCESS); } #endif