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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);
+ }
+
+
+
+