mt.c

该文件为c++的数学函数库!是一个非常有用的编程工具.它含有各种数学函数,为科学计算、工程应用等程序编写提供方便！

/* This program is free software; you can redistribute it and/or
   modify it under the terms of the GNU General Public License as
   published by the Free Software Foundation; either version 2 of the
   License, or (at your option) any later version.

   This program 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
   General Public License for more details.  You should have received
   a copy of the GNU General Public License along with this program;
   if not, write to the Free Foundation, Inc., 59 Temple Place, Suite
   330, Boston, MA 02111-1307 USA

   Original implementation was copyright (C) 1997 Makoto Matsumoto and
   Takuji Nishimura. Coded by Takuji Nishimura, considering the
   suggestions by Topher Cooper and Marc Rieffel in July-Aug. 1997, "A
   C-program for MT19937: Integer version (1998/4/6)"

   This implementation copyright (C) 1998 Brian Gough. I reorganized
   the code to use the module framework of GSL.  The license on this
   implementation was changed from LGPL to GPL, following paragraph 3
   of the LGPL, version 2.

   Update:

   The seeding procedure has been updated to match the 10/99 release
   of MT19937.

   Update:

   The seeding procedure has been updated again to match the 2002
   release of MT19937

   The original code included the comment: "When you use this, send an
   email to: [e-mail] with an appropriate reference to
   your work".

   Makoto Matsumoto has a web page with more information about the
   generator, http://www.math.keio.ac.jp/~matumoto/emt.html. 

   The paper below has details of the algorithm.

   From: Makoto Matsumoto and Takuji Nishimura, "Mersenne Twister: A
   623-dimensionally equidistributerd uniform pseudorandom number
   generator". ACM Transactions on Modeling and Computer Simulation,
   Vol. 8, No. 1 (Jan. 1998), Pages 3-30

   You can obtain the paper directly from Makoto Matsumoto's web page.

   The period of this generator is 2^{19937} - 1.

*/

#include <config.h>
#include <stdlib.h>
#include <gsl/gsl_rng.h>

static inline unsigned long int mt_get (void *vstate);
static double mt_get_double (void *vstate);
static void mt_set (void *state, unsigned long int s);

#define N 624   /* Period parameters */
#define M 397

/* most significant w-r bits */
static const unsigned long UPPER_MASK = 0x80000000UL;   

/* least significant r bits */
static const unsigned long LOWER_MASK = 0x7fffffffUL;   

typedef struct
  {
    unsigned long mt[N];
    int mti;
  }
mt_state_t;

static inline unsigned long
mt_get (void *vstate)
{
  mt_state_t *state = (mt_state_t *) vstate;

  unsigned long k ;
  unsigned long int *const mt = state->mt;

#define MAGIC(y) (((y)&0x1) ? 0x9908b0dfUL : 0)

  if (state->mti >= N)
    {   /* generate N words at one time */
      int kk;

      for (kk = 0; kk < N - M; kk++)
        {
          unsigned long y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
          mt[kk] = mt[kk + M] ^ (y >> 1) ^ MAGIC(y);
        }
      for (; kk < N - 1; kk++)
        {
          unsigned long y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
          mt[kk] = mt[kk + (M - N)] ^ (y >> 1) ^ MAGIC(y);
        }

      {
        unsigned long y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
        mt[N - 1] = mt[M - 1] ^ (y >> 1) ^ MAGIC(y);
      }

      state->mti = 0;
    }

  /* Tempering */
  
  k = mt[state->mti];
  k ^= (k >> 11);
  k ^= (k << 7) & 0x9d2c5680UL;
  k ^= (k << 15) & 0xefc60000UL;
  k ^= (k >> 18);

  state->mti++;

  return k;
}

static double
mt_get_double (void * vstate)
{
  return mt_get (vstate) / 4294967296.0 ;
}

static void
mt_set (void *vstate, unsigned long int s)
{
  mt_state_t *state = (mt_state_t *) vstate;
  int i;

  if (s == 0)
    s = 4357;   /* the default seed is 4357 */

  state->mt[0]= s & 0xffffffffUL;

  for (i = 1; i < N; i++)
    {
      /* See Knuth's "Art of Computer Programming" Vol. 2, 3rd
         Ed. p.106 for multiplier. */

      state->mt[i] =
        (1812433253UL * (state->mt[i-1] ^ (state->mt[i-1] >> 30)) + i);
      
      state->mt[i] &= 0xffffffffUL;
    }

  state->mti = i;
}

static void
mt_1999_set (void *vstate, unsigned long int s)
{
  mt_state_t *state = (mt_state_t *) vstate;
  int i;

  if (s == 0)
    s = 4357;   /* the default seed is 4357 */

  /* This is the October 1999 version of the seeding procedure. It
     was updated by the original developers to avoid the periodicity
     in the simple congruence originally used.

     Note that an ANSI-C unsigned long integer arithmetic is
     automatically modulo 2^32 (or a higher power of two), so we can
     safely ignore overflow. */

#define LCG(x) ((69069 * x) + 1) &0xffffffffUL

  for (i = 0; i < N; i++)
    {
      state->mt[i] = s & 0xffff0000UL;
      s = LCG(s);
      state->mt[i] |= (s &0xffff0000UL) >> 16;
      s = LCG(s);
    }

  state->mti = i;
}

/* This is the original version of the seeding procedure, no longer
   used but available for compatibility with the original MT19937. */

static void
mt_1998_set (void *vstate, unsigned long int s)
{
  mt_state_t *state = (mt_state_t *) vstate;
  int i;

  if (s == 0)
    s = 4357;   /* the default seed is 4357 */

  state->mt[0] = s & 0xffffffffUL;

#define LCG1998(n) ((69069 * n) & 0xffffffffUL)

  for (i = 1; i < N; i++)
    state->mt[i] = LCG1998 (state->mt[i - 1]);

  state->mti = i;
}

static const gsl_rng_type mt_type =
{"mt19937",                     /* name */
 0xffffffffUL,                  /* RAND_MAX  */
 0,                             /* RAND_MIN  */
 sizeof (mt_state_t),
 &mt_set,
 &mt_get,
 &mt_get_double};

static const gsl_rng_type mt_1999_type =
{"mt19937_1999",                /* name */
 0xffffffffUL,                  /* RAND_MAX  */
 0,                             /* RAND_MIN  */
 sizeof (mt_state_t),
 &mt_1999_set,
 &mt_get,
 &mt_get_double};

static const gsl_rng_type mt_1998_type =
{"mt19937_1998",                /* name */
 0xffffffffUL,                  /* RAND_MAX  */
 0,                             /* RAND_MIN  */
 sizeof (mt_state_t),
 &mt_1998_set,
 &mt_get,
 &mt_get_double};

const gsl_rng_type *gsl_rng_mt19937 = &mt_type;
const gsl_rng_type *gsl_rng_mt19937_1999 = &mt_1999_type;
const gsl_rng_type *gsl_rng_mt19937_1998 = &mt_1998_type;

/* MT19937 is the default generator, so define that here too */

const gsl_rng_type *gsl_rng_default = &mt_type;
unsigned long int gsl_rng_default_seed = 0;