rockbox/firmware/common/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 <stdlib.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 highest bit of u to
                                              highest bit of v */

static unsigned int state[N+1]; /* state vector + 1 to not violate ANSI C */
static unsigned int *next;     /* next random value is computed from here */
static int left = -1;     /* can *next++ this many times before reloading */

void srand(unsigned int 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.
     */

    unsigned int x = (seed | 1U) & 0xFFFFFFFFU, *s = state;
    int j;

    for(left=0, *s++=x, j=N; --j;
        *s++ = (x*=69069U) & 0xFFFFFFFFU);
}

static int rand_reload(void)
{
    unsigned int *p0=state, *p2=state+2, *pM=state+M, s0, s1;
    int j;
  
    if(left < -1)
        srand(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 (int)s1 ^ (s1 >> 18);
}

int rand(void)
{
    int y;
  
    if(--left < 0) {
        y = rand_reload();
    }
    else {
        y  = *next++;
        y ^= (y >> 11);
        y ^= (y <<  7) & 0x9D2C5680U;
        y ^= (y << 15) & 0xEFC60000U;
        y ^= (y >> 18);
    }

    return (y & 0xfffffffe) >> 1; /* 31-bit limit by Bj<42>rn Stenberg*/
}