From 529e166888905b6ed5998c72148904d141845863 Mon Sep 17 00:00:00 2001 From: Björn Stenberg Date: Wed, 17 Jul 2002 23:07:45 +0000 Subject: New vastly improved random algorithm: Mersenne Twister git-svn-id: svn://svn.rockbox.org/rockbox/trunk@1377 a1c6a512-1295-4272-9138-f99709370657 --- firmware/common/random.c | 153 +++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 153 insertions(+) create mode 100644 firmware/common/random.c (limited to 'firmware/common/random.c') diff --git a/firmware/common/random.c b/firmware/common/random.c new file mode 100644 index 0000000000..1e65eefaa0 --- /dev/null +++ b/firmware/common/random.c @@ -0,0 +1,153 @@ +/* + * 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 + * (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 with + * an appropriate reference to your work. + * + * It would be nice to CC: when you write. + * + */ + +#include + +#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 highest bit of u to + highest bit of v */ + +static unsigned int state[N+1]; /* state vector + 1 to not violate ANSI C */ +static unsigned int *next; /* next random value is computed from here */ +static int left = -1; /* can *next++ this many times before reloading */ + +void srand(unsigned int 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. + */ + + unsigned int x = (seed | 1U) & 0xFFFFFFFFU, *s = state; + int j; + + for(left=0, *s++=x, j=N; --j; + *s++ = (x*=69069U) & 0xFFFFFFFFU); +} + +static int rand_reload(void) +{ + unsigned int *p0=state, *p2=state+2, *pM=state+M, s0, s1; + int j; + + if(left < -1) + srand(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 (int)s1 ^ (s1 >> 18); +} + +int rand(void) +{ + int y; + + if(--left < 0) + return rand_reload(); + + y = *next++; + y ^= (y >> 11); + y ^= (y << 7) & 0x9D2C5680U; + y ^= (y << 15) & 0xEFC60000U; + return (y ^ (y >> 18)) & ((2^31)-1); /* 31-bit limit by Björn Stenberg*/ +} -- cgit v1.2.3