/* comments are changed from C++ style to ANSI C style,   then wrappers are added by Naoki Takebayashi.   Also testing code at the bottom is changed.   Other than that the main functions are not changed at all   Jun 01, 2000*//* for RandDecimal() to return closed interval [0,1], #define MT_CLOSED_INTVL   Otherwise RandDecimal reuturns interval[0,1)*/#include "mt-rand.h"/* 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 */#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)); }uint32 randomMT(void) {    uint32 y;    if(--left < 0)        return(reloadMT());    y  = *next++;    y ^= (y >> 11);    y ^= (y <<  7) & 0x9D2C5680U;    y ^= (y << 15) & 0xEFC60000U;    return(y ^ (y >> 18)); }double MTrandDec(void) {#ifdef MT_CLOSED_INTVL  /* for reals with closed interval [0,1] */  return ( (double) randomMT() * 2.3283064370807974e-10 );#else  /* for reals: [0,1)-interval */  return ( (double) randomMT() * 2.3283064365386963e-10 );#endif}/* returns a int [0, max] both-end  inclusive */int MTrandInt(int max) {  return ( (int) (MTrandDec() * (max + 1)) );}#ifdef TEST#define MAX 200000000UL#define DM 10000int main(void) {    int j;    unsigned long k;    unsigned long dummy[DM];    /* you can seed with any uint32, but the best are odds in 0..(2^32 - 1) */    seedMT(4357U);    /* print the first 2,002 random numbers seven to a line as an example */    for(j=0; j<2002; j++)        printf(" %10lu%s", (unsigned long) randomMT(), (j%7)==6 ? "\n" : "");    /* added for bench mark */    for(k=0; k<MAX; k++) {      dummy[(k % DM)] = (unsigned long) MTrandInt(1000);    }    return(EXIT_SUCCESS); }#endif/* TEST */