cockus.c

稀疏矩阵、链表、图、队列、二叉树、多叉树、排序、遗传算法等的实现

/*
** This is the home page of the Mersenne Twister PRNG:
** http://www.math.keio.ac.jp/~matumoto/emt.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 ([e-mail]) 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 <[e-mail]> with
** an appropriate reference to your work.
**
** It would be nice to CC: <[e-mail]> when you write.
**
*/

#include <stdio.h>
#include <stdlib.h>
#include "mtrand.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;

/* length of state vector */
#define N             (624)

/* a period parameter */
#define M             (397)

/* a magic constant */
#define K             (0x9908B0DFU)

/* mask all but highest   bit of u */
#define hiBit(u)      ((u) & 0x80000000U)

/* mask all but lowest    bit of u */
#define loBit(u)       ((u) & 0x00000001U)

/* mask     the highest   bit of u */
#define loBits(u)      ((u) & 0x7FFFFFFFU)

/* move hi bit of u to hi bit of v */
#define mixBits(u, v)  (hiBit(u)|loBits(v))

/* state vector + 1 extra to not violate ANSI C */
static uint32   state[N + 1];

/* next random value is computed from here */
static uint32  *next;

/* can *next++ this many times before reloading */
static int      left = -1;


/*
**
**  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.
*/

void            mtsrand(uint32 seed)
{
    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)
        mtsrand(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 mtrand(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 UNIT_TEST
int main(void)
{
    int             j;

    /* you can seed with any uint32, but the best are odds in 0..(2^32 - 1) */
    mtsrand(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) mtrand(), (j % 7) == 6 ? "\n" : "");

    return (EXIT_SUCCESS);
}
#endif