/*---------------------------------------------------------------------------
* Gamedriver: Random Generator
*
* 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.
*
* High-speed implementation by Shawn J. Cokus who appreciates a copy
* of the above mail (<Cokus@math.washington.edu>).
*
* 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.
*---------------------------------------------------------------------------
* 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.
*---------------------------------------------------------------------------
*/
#include "driver.h"
#include "random.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
*/
/*-------------------------------------------------------------------------*/
#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 */
/*-------------------------------------------------------------------------*/
void
seed_random (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) NOOP;
}
/*-------------------------------------------------------------------------*/
static
mp_uint reloadMT (void)
{
register uint32 *p0=state, *p2=state+2, *pM=state+M, s0, s1;
register int j;
if(left < -1)
seed_random(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_number (uint32 n)
/* Return a random number in the range 0..n-1.
*
* The key return an evenly distributed random number in
* the given range is not to use the low bits of the raw random
* number, as these are distressingly non-random.
* The C-FAQ 13.16 gives a solution ('rc / (RANDOM_MAX / n + 1)'), which
* unfortunately doesn't work too well for large ranges.
*/
{
#define RANDOM_MAX 0xFFFFFFFFU
uint32 y, rc;
#if !defined(HAVE_LONG_LONG) || SIZEOF_CHAR_P != 4
uint32 rmax;
rmax = (RANDOM_MAX / (n+1)) * n;
/* rmax = 0 if n >= RANDOM_MAX */
do {
#endif
if(--left < 0)
rc = reloadMT();
else
{
y = *next++;
y ^= (y >> 11);
y ^= (y << 7) & 0x9D2C5680U;
y ^= (y << 15) & 0xEFC60000U;
rc = (y ^ (y >> 18));
}
#if defined(HAVE_LONG_LONG) && SIZEOF_CHAR_P == 4
return (uint32)
((unsigned long long)rc * (unsigned long long)n
>> sizeof(uint32) * CHAR_BIT);
#else
} while (rmax && rc > rmax);
if (!rmax)
return rc;
if (rmax / n < rc && rmax / n > 0)
return rc / (rmax / n);
return (rc * n) / rmax;
#endif
}
/***************************************************************************/
