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-// 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 <stdio.h>
-#include <stdlib.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;
-
-#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 seedMT(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);
- }
-
-
-uint32 reloadMT(void)
- {
- register uint32 *p0=state, *p2=state+2, *pM=state+M, s0, s1;
- register int j;
-
- if(left < -1)
- seedMT(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));
- }
-
-
-inline uint32 randomMT(void)
- {
- uint32 y;
-
- if(--left < 0)
- return(reloadMT());
-
- y = *next++;
- y ^= (y >> 11);
- y ^= (y << 7) & 0x9D2C5680U;
- y ^= (y << 15) & 0xEFC60000U;
- y ^= (y >> 18);
- return(y);
- }
-
-
-
-