/** * * Grabbed by Kevin from http://www.math.keio.ac.jp/~matumoto/cokus.c * 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 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 unsigned int state[ N + 1 ]; // state vector + 1 extra to not violate ANSI C static unsigned int *next; // next random value is computed from here static int left = -1; // can *next++ this many times before reloading void seedMT( unsigned int seed ) // Defined in cokus_c.c { // // 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. // unsigned int x = ( seed | 1U ) & 0xFFFFFFFFU, *s = state; int j; for ( left = 0, *s++ = x, j = N; --j; *s++ = ( x *= 69069U ) & 0xFFFFFFFFU ) ; } unsigned int reloadMT( void ) { unsigned int * p0 = state, *p2 = state + 2, *pM = state + M, s0, s1; 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 ) { unsigned int y; if ( --left < 0 ) return ( reloadMT() ); y = *next++; y ^= ( y >> 11 ); y ^= ( y << 7 ) & 0x9D2C5680U; y ^= ( y << 15 ) & 0xEFC60000U; return ( y ^ ( y >> 18 ) ); // This change made so the value returned is in the same range as what rand() returns // return(y ^ (y >> 18)) % 32767; } float frandomMT( void ) { return ( float ) ( ( double ) randomMT() / 4294967296.0 ); } /* 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 int) randomMT(), (j%7)==6 ? "\n" : ""); return(EXIT_SUCCESS); } */