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Better random number generator: Mersenne twiser with improved initialisation. BSD-style license.
git-svn-id: svn://svn.rockbox.org/rockbox/trunk@8396 a1c6a512-1295-4272-9138-f99709370657
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Jens Arnold
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2 changed files with 132 additions and 137 deletions
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@ -34,3 +34,38 @@ LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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SUCH DAMAGE.
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@(#)gmon.c 5.3 (Berkeley) 5/22/91
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*************************************************************************
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In: random.c
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From: http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/emt19937ar.html
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mt19937ar-cok.c
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*************************************************************************
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Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
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All rights reserved.
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions
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are met:
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1. Redistributions of source code must retain the above copyright
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notice, this list of conditions and the following disclaimer.
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2. Redistributions in binary form must reproduce the above copyright
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notice, this list of conditions and the following disclaimer in the
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documentation and/or other materials provided with the distribution.
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3. The names of its contributors may not be used to endorse or promote
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products derived from this software without specific prior written
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permission.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
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CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
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LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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@ -1,159 +1,119 @@
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/*
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* This is the ``Mersenne Twister'' random number generator MT19937, which
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* generates pseudorandom integers uniformly distributed in 0..(2^32 - 1)
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* starting from any odd seed in 0..(2^32 - 1). This version is a recode
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* by Shawn Cokus (Cokus@math.washington.edu) on March 8, 1998 of a version by
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* Takuji Nishimura (who had suggestions from Topher Cooper and Marc Rieffel in
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* July-August 1997).
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*
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* Effectiveness of the recoding (on Goedel2.math.washington.edu, a DEC Alpha
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* running OSF/1) using GCC -O3 as a compiler: before recoding: 51.6 sec. to
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* generate 300 million random numbers; after recoding: 24.0 sec. for the same
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* (i.e., 46.5% of original time), so speed is now about 12.5 million random
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* number generations per second on this machine.
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*
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* According to the URL <http://www.math.keio.ac.jp/~matumoto/emt.html>
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* (and paraphrasing a bit in places), the Mersenne Twister is ``designed
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* with consideration of the flaws of various existing generators,'' has
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* a period of 2^19937 - 1, gives a sequence that is 623-dimensionally
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* equidistributed, and ``has passed many stringent tests, including the
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* die-hard test of G. Marsaglia and the load test of P. Hellekalek and
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* S. Wegenkittl.'' It is efficient in memory usage (typically using 2506
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* to 5012 bytes of static data, depending on data type sizes, and the code
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* is quite short as well). It generates random numbers in batches of 624
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* at a time, so the caching and pipelining of modern systems is exploited.
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* It is also divide- and mod-free.
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*
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* This library is free software; you can redistribute it and/or modify it
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* under the terms of the GNU Library General Public License as published by
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* the Free Software Foundation (either version 2 of the License or, at your
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* option, any later version). This library is distributed in the hope that
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* it will be useful, but WITHOUT ANY WARRANTY, without even the implied
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* warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See
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* the GNU Library General Public License for more details. You should have
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* received a copy of the GNU Library General Public License along with this
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* library; if not, write to the Free Software Foundation, Inc., 59 Temple
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* Place, Suite 330, Boston, MA 02111-1307, USA.
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*
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* The code as Shawn received it included the following notice:
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*
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* Copyright (C) 1997 Makoto Matsumoto and Takuji Nishimura. When
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* you use this, send an e-mail to <matumoto@math.keio.ac.jp> with
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* an appropriate reference to your work.
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*
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* It would be nice to CC: <Cokus@math.washington.edu> when you write.
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*
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A C-program for MT19937, with initialization improved 2002/2/10.
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Coded by Takuji Nishimura and Makoto Matsumoto.
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This is a faster version by taking Shawn Cokus's optimization,
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Matthe Bellew's simplification.
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Before using, initialize the state by using srand(seed).
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Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
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All rights reserved.
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions
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are met:
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1. Redistributions of source code must retain the above copyright
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notice, this list of conditions and the following disclaimer.
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2. Redistributions in binary form must reproduce the above copyright
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notice, this list of conditions and the following disclaimer in the
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documentation and/or other materials provided with the distribution.
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3. The names of its contributors may not be used to endorse or promote
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products derived from this software without specific prior written
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permission.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
|
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CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
|
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PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
|
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PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
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LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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Any feedback is very welcome.
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http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
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email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space)
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*/
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/*
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Adapted to Rockbox by Jens Arnold
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*/
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#include <stdlib.h>
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#define N (624) /* length of state vector */
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#define M (397) /* a period parameter */
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#define K (0x9908B0DFUL) /* a magic constant */
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#define hiBit(u) ((u) & 0x80000000UL) /* mask all but highest bit of u */
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#define loBit(u) ((u) & 0x00000001UL) /* mask all but lowest bit of u */
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#define loBits(u) ((u) & 0x7FFFFFFFUL) /* mask the highest bit of u */
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#define mixBits(u, v) (hiBit(u)|loBits(v)) /* move highest bit of u to
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highest bit of v */
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/* Period parameters */
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#define N 624
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#define M 397
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#define MATRIX_A 0x9908b0dfUL /* constant vector a */
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#define UMASK 0x80000000UL /* most significant w-r bits */
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#define LMASK 0x7fffffffUL /* least significant r bits */
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#define MIXBITS(u,v) ( ((u) & UMASK) | ((v) & LMASK) )
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#define TWIST(u,v) ((MIXBITS(u,v) >> 1) ^ ((v)&1UL ? MATRIX_A : 0UL))
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static unsigned long state[N+1]; /* state vector + 1 to not violate ANSI C */
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static unsigned long *next; /* next random value is computed from here */
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static int left = -1; /* can *next++ this many times before reloading */
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static unsigned long state[N]; /* the array for the state vector */
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static int left = 0;
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static unsigned long *next;
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/* initializes state[N] with a seed */
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void srand(unsigned int seed)
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{
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/*
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* We initialize state[0..(N-1)] via the generator
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*
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* x_new = (69069 * x_old) mod 2^32
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*
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* from Line 15 of Table 1, p. 106, Sec. 3.3.4 of Knuth's
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* _The Art of Computer Programming_, Volume 2, 3rd ed.
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*
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* Notes (SJC): I do not know what the initial state requirements
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* of the Mersenne Twister are, but it seems this seeding generator
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* could be better. It achieves the maximum period for its modulus
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* (2^30) iff x_initial is odd (p. 20-21, Sec. 3.2.1.2, Knuth); if
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* x_initial can be even, you have sequences like 0, 0, 0, ...;
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* 2^31, 2^31, 2^31, ...; 2^30, 2^30, 2^30, ...; 2^29, 2^29 + 2^31,
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* 2^29, 2^29 + 2^31, ..., etc. so I force seed to be odd below.
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*
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* Even if x_initial is odd, if x_initial is 1 mod 4 then
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*
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* the lowest bit of x is always 1,
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* the next-to-lowest bit of x is always 0,
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* the 2nd-from-lowest bit of x alternates ... 0 1 0 1 0 1 0 1 ... ,
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* the 3rd-from-lowest bit of x 4-cycles ... 0 1 1 0 0 1 1 0 ... ,
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* the 4th-from-lowest bit of x has the 8-cycle ... 0 0 0 1 1 1 1 0 ... ,
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* ...
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*
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* and if x_initial is 3 mod 4 then
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*
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* the lowest bit of x is always 1,
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* the next-to-lowest bit of x is always 1,
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* the 2nd-from-lowest bit of x alternates ... 0 1 0 1 0 1 0 1 ... ,
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* the 3rd-from-lowest bit of x 4-cycles ... 0 0 1 1 0 0 1 1 ... ,
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* the 4th-from-lowest bit of x has the 8-cycle ... 0 0 1 1 1 1 0 0 ... ,
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* ...
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*
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* The generator's potency (min. s>=0 with (69069-1)^s = 0 mod 2^32) is
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* 16, which seems to be alright by p. 25, Sec. 3.2.1.3 of Knuth. It
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* also does well in the dimension 2..5 spectral tests, but it could be
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* better in dimension 6 (Line 15, Table 1, p. 106, Sec. 3.3.4, Knuth).
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*
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* Note that the random number user does not see the values generated
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* here directly since reloadMT() will always munge them first, so maybe
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* none of all of this matters. In fact, the seed values made here could
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* even be extra-special desirable if the Mersenne Twister theory says
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* so-- that's why the only change I made is to restrict to odd seeds.
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*/
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unsigned long x = (seed | 1UL) & 0xFFFFFFFFUL, *s = state;
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unsigned long x = seed & 0xffffffffUL;
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unsigned long *s = state;
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int j;
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for(left=0, *s++=x, j=N; --j;
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*s++ = (x*=69069UL) & 0xFFFFFFFFUL);
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for (*s++ = x, j = 1; j < N; j++) {
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x = (1812433253UL * (x ^ (x >> 30)) + j) & 0xffffffffUL;
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*s++ = x;
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/* See Knuth TAOCP Vol2. 3rd Ed. P.106 for multiplier. */
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/* In the previous versions, MSBs of the seed affect */
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/* only MSBs of the array state[]. */
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/* 2002/01/09 modified by Makoto Matsumoto */
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}
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left = 1;
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}
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static int rand_reload(void)
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static void next_state(void)
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{
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unsigned long *p0=state, *p2=state+2, *pM=state+M, s0, s1;
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unsigned long *p = state;
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int j;
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if(left < -1)
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srand(4357UL);
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/* if srand() has not been called, */
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/* a default initial seed is used */
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if (left < 0)
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srand(5489UL);
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left=N-1, next=state+1;
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left = N;
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next = state;
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for(s0=state[0], s1=state[1], j=N-M+1; --j; s0=s1, s1=*p2++)
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*p0++ = *pM++ ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0UL);
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for (j = N - M + 1; --j; p++)
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*p = p[M] ^ TWIST(p[0], p[1]);
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for(pM=state, j=M; --j; s0=s1, s1=*p2++)
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*p0++ = *pM++ ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0UL);
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for (j = M; --j; p++)
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*p = p[M-N] ^ TWIST(p[0], p[1]);
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s1=state[0], *p0 = *pM ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0UL);
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s1 ^= (s1 >> 11);
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s1 ^= (s1 << 7) & 0x9D2C5680UL;
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s1 ^= (s1 << 15) & 0xEFC60000UL;
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return (long)s1 ^ (s1 >> 18);
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*p = p[M-N] ^ TWIST(p[0], state[0]);
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}
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/* generates a random number on [0,RAND_MAX]-interval */
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int rand(void)
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{
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unsigned long y;
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if(--left < 0) {
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y = rand_reload();
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}
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else {
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if (--left <= 0)
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next_state();
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y = *next++;
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/* Tempering */
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y ^= (y >> 11);
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y ^= (y << 7) & 0x9D2C5680UL;
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y ^= (y << 15) & 0xEFC60000UL;
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y ^= (y << 7) & 0x9d2c5680UL;
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y ^= (y << 15) & 0xefc60000UL;
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y ^= (y >> 18);
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}
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return ((unsigned int)y) >> 1;
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/* 31-bit limit by Björn Stenberg*/
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/* 16-bit architectures compatibility by Jean-Philippe Bernardy */
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}
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