optimization-algorithms/lab3/twister.c

// http://www.math.keio.ac.jp/~matumoto/ver980409.html

// 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 <stdio.h>
#include <stdlib.h>

//
// 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));
}


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));
}

#ifdef NOCOMPILE
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