// 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. // #include #include // // 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 long 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(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); } uint32 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)); } inline uint32 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)); } #if 0 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