// 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