knuthran.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！

/* rng/knuthran.c
 * 
 * Copyright (C) 2001 Brian Gough, Carlo Perassi
 * 
 * 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 Software
 * Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
 */

/*
 * This generator is taken from
 *
 * Donald E. Knuth
 * The Art of Computer Programming
 * Volume 2
 * Third Edition
 * Addison-Wesley
 * Section 3.6
 *
 * The comments are taken from the book
 * Our comments are signed
 */

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

#define BUFLEN 2009             /* [Brian]: length of the buffer aa[] */
#define KK 100                  /* the long lag */
#define LL 37                   /* the short lag */
#define MM (1L << 30)           /* the modulus */
#define TT 70                   /* guaranteed separation between streams */

#define evenize(x) ((x) & (MM - 2))     /* make x even */
#define is_odd(x) ((x) & 1)     /* the units bit of x */
#define mod_diff(x, y) (((x) - (y)) & (MM - 1)) /* (x - y) mod MM */

static inline void ran_array (unsigned long int aa[], unsigned int n,
                              unsigned long int ran_x[]);
static inline unsigned long int ran_get (void *vstate);
static double ran_get_double (void *vstate);
static void ran_set (void *state, unsigned long int s);

typedef struct
{
  unsigned int i;
  unsigned long int aa[BUFLEN]; /* [Carlo]: I can't pass n to ran_array like
                                   Knuth does */
  unsigned long int ran_x[KK];  /* the generator state */
}
ran_state_t;

static inline void
ran_array (unsigned long int aa[], unsigned int n, unsigned long int ran_x[])
{
  unsigned int i;
  unsigned int j;

  for (j = 0; j < KK; j++)
    aa[j] = ran_x[j];

  for (; j < n; j++)
    aa[j] = mod_diff (aa[j - KK], aa[j - LL]);

  for (i = 0; i < LL; i++, j++)
    ran_x[i] = mod_diff (aa[j - KK], aa[j - LL]);

  for (; i < KK; i++, j++)
    ran_x[i] = mod_diff (aa[j - KK], ran_x[i - LL]);
}

static inline unsigned long int
ran_get (void *vstate)
{
  ran_state_t *state = (ran_state_t *) vstate;

  unsigned int i = state->i;

  if (i == 0)
    {
      /* fill buffer with new random numbers */
      ran_array (state->aa, BUFLEN, state->ran_x);
    }

  state->i = (i + 1) % BUFLEN;

  return state->aa[i];
}

static double
ran_get_double (void *vstate)
{
  ran_state_t *state = (ran_state_t *) vstate;

  return ran_get (state) / 1073741824.0;        /* [Carlo]: RAND_MAX + 1 */
}

static void
ran_set (void *vstate, unsigned long int s)
{
  ran_state_t *state = (ran_state_t *) vstate;

  long x[KK + KK - 1];          /* the preparation buffer */

  register int j;
  register int t;
  register long ss = evenize (s + 2);

  for (j = 0; j < KK; j++)
    {
      x[j] = ss;                /* bootstrap the buffer */
      ss <<= 1;
      if (ss >= MM)             /* cyclic shift 29 bits */
        ss -= MM - 2;
    }
  for (; j < KK + KK - 1; j++)
    x[j] = 0;
  x[1]++;                       /* make x[1] (and only x[1]) odd */
  ss = s & (MM - 1);
  t = TT - 1;
  while (t)
    {
      for (j = KK - 1; j > 0; j--)      /* square */
        x[j + j] = x[j];
      for (j = KK + KK - 2; j > KK - LL; j -= 2)
        x[KK + KK - 1 - j] = evenize (x[j]);
      for (j = KK + KK - 2; j >= KK; j--)
        if (is_odd (x[j]))
          {
            x[j - (KK - LL)] = mod_diff (x[j - (KK - LL)], x[j]);
            x[j - KK] = mod_diff (x[j - KK], x[j]);
          }
      if (is_odd (ss))
        {                       /* multiply by "z" */
          for (j = KK; j > 0; j--)
            x[j] = x[j - 1];
          x[0] = x[KK];         /* shift the buffer cyclically */
          if (is_odd (x[KK]))
            x[LL] = mod_diff (x[LL], x[KK]);
        }
      if (ss)
        ss >>= 1;
      else
        t--;
    }

  state->i = 0;

  for (j = 0; j < LL; j++)
    state->ran_x[j + KK - LL] = x[j];
  for (; j < KK; j++)
    state->ran_x[j - LL] = x[j];

  return;
}

static const gsl_rng_type ran_type = {
  "knuthran",                   /* name */
  0x3fffffffUL,                 /* RAND_MAX *//* [Carlo]: (2 ^ 30) - 1 */
  0,                            /* RAND_MIN */
  sizeof (ran_state_t),
  &ran_set,
  &ran_get,
  &ran_get_double
};

const gsl_rng_type *gsl_rng_knuthran = &ran_type;