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random.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 <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 <sys/types.h>
#include <unistd.h>

#include "systime.h"
#include "misc.h"

#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 */


static 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);
}


void random_init(uint32 seed)
{
  if (seed == 0) {
    struct timeval t;
    pid_t pid = getpid();
    pid_t ppid = getppid();
    gettimeofday(&t, 0);
    seed = t.tv_sec ^ t.tv_usec ^ (t.tv_usec << 12) ^
      pid ^ (pid << 16) ^ ppid ^ (ppid << 16);
  }
  seedMT(seed);
}


static uint32 reloadMT(void)
{
  register uint32 *p0=state, *p2=state+2, *pM=state+M, s0, s1;
  register int    j;

  if (left < -1)
    random_init(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 random_int(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);
}

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