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204 lines
7.3 KiB
C++
204 lines
7.3 KiB
C++
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/**
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*
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* Grabbed by Kevin from http://www.math.keio.ac.jp/~matumoto/cokus.c
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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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#include <stdio.h>
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#include <stdlib.h>
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//
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// uint32 must be an unsigned integer type capable of holding at least 32
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// bits; exactly 32 should be fastest, but 64 is better on an Alpha with
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// GCC at -O3 optimization so try your options and see what's best for you
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//
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//typedef unsigned int uint32;
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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 (0x9908B0DFU) // a magic constant
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#define hiBit(u) ((u) & 0x80000000U) // mask all but highest bit of u
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#define loBit(u) ((u) & 0x00000001U) // mask all but lowest bit of u
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#define loBits(u) ((u) & 0x7FFFFFFFU) // mask the highest bit of u
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#define mixBits(u, v) (hiBit(u)|loBits(v)) // move hi bit of u to hi bit of v
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static unsigned int state[ N + 1 ]; // state vector + 1 extra to not violate ANSI C
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static unsigned int *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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void seedMT( unsigned int seed ) // Defined in cokus_c.c
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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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register unsigned int x = ( seed | 1U ) & 0xFFFFFFFFU, *s = state;
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register int j;
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for ( left = 0, *s++ = x, j = N; --j;
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*s++ = ( x *= 69069U ) & 0xFFFFFFFFU )
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;
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}
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unsigned int reloadMT( void )
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{
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register unsigned int * p0 = state, *p2 = state + 2, *pM = state + M, s0, s1;
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register int j;
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if ( left < -1 )
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seedMT( 4357U );
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left = N - 1, next = state + 1;
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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 : 0U );
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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 : 0U );
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s1 = state[ 0 ], *p0 = *pM ^ ( mixBits( s0, s1 ) >> 1 ) ^ ( loBit( s1 ) ? K : 0U );
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s1 ^= ( s1 >> 11 );
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s1 ^= ( s1 << 7 ) & 0x9D2C5680U;
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s1 ^= ( s1 << 15 ) & 0xEFC60000U;
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return ( s1 ^ ( s1 >> 18 ) );
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}
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unsigned int randomMT( void )
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{
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unsigned int y;
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if ( --left < 0 )
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return ( reloadMT() );
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y = *next++;
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y ^= ( y >> 11 );
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y ^= ( y << 7 ) & 0x9D2C5680U;
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y ^= ( y << 15 ) & 0xEFC60000U;
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return ( y ^ ( y >> 18 ) );
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// This change made so the value returned is in the same range as what rand() returns
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// return(y ^ (y >> 18)) % 32767;
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}
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float frandomMT( void )
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{
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return ( float ) ( ( double ) randomMT() / 4294967296.0 );
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}
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/*
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int main(void)
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{
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int j;
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// you can seed with any uint32, but the best are odds in 0..(2^32 - 1)
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seedMT(4357U);
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// print the first 2,002 random numbers seven to a line as an example
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for(j=0; j<2002; j++)
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printf(" %10lu%s", (unsigned int) randomMT(), (j%7)==6 ? "\n" : "");
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return(EXIT_SUCCESS);
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}
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*/
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