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1/*
2 * This is the ``Mersenne Twister'' random number generator MT19937, which
3 * generates pseudorandom integers uniformly distributed in 0..(2^32 - 1)
4 * starting from any odd seed in 0..(2^32 - 1). This version is a recode
5 * by Shawn Cokus (Cokus@math.washington.edu) on March 8, 1998 of a version by
6 * Takuji Nishimura (who had suggestions from Topher Cooper and Marc Rieffel in
7 * July-August 1997).
8 *
9 * Effectiveness of the recoding (on Goedel2.math.washington.edu, a DEC Alpha
10 * running OSF/1) using GCC -O3 as a compiler: before recoding: 51.6 sec. to
11 * generate 300 million random numbers; after recoding: 24.0 sec. for the same
12 * (i.e., 46.5% of original time), so speed is now about 12.5 million random
13 * number generations per second on this machine.
14 *
15 * According to the URL <http://www.math.keio.ac.jp/~matumoto/emt.html>
16 * (and paraphrasing a bit in places), the Mersenne Twister is ``designed
17 * with consideration of the flaws of various existing generators,'' has
18 * a period of 2^19937 - 1, gives a sequence that is 623-dimensionally
19 * equidistributed, and ``has passed many stringent tests, including the
20 * die-hard test of G. Marsaglia and the load test of P. Hellekalek and
21 * S. Wegenkittl.'' It is efficient in memory usage (typically using 2506
22 * to 5012 bytes of static data, depending on data type sizes, and the code
23 * is quite short as well). It generates random numbers in batches of 624
24 * at a time, so the caching and pipelining of modern systems is exploited.
25 * It is also divide- and mod-free.
26 *
27 * This library is free software; you can redistribute it and/or modify it
28 * under the terms of the GNU Library General Public License as published by
29 * the Free Software Foundation (either version 2 of the License or, at your
30 * option, any later version). This library is distributed in the hope that
31 * it will be useful, but WITHOUT ANY WARRANTY, without even the implied
32 * warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See
33 * the GNU Library General Public License for more details. You should have
34 * received a copy of the GNU Library General Public License along with this
35 * library; if not, write to the Free Software Foundation, Inc., 59 Temple
36 * Place, Suite 330, Boston, MA 02111-1307, USA.
37 *
38 * The code as Shawn received it included the following notice:
39 *
40 * Copyright (C) 1997 Makoto Matsumoto and Takuji Nishimura. When
41 * you use this, send an e-mail to <matumoto@math.keio.ac.jp> with
42 * an appropriate reference to your work.
43 *
44 * It would be nice to CC: <Cokus@math.washington.edu> when you write.
45 *
46 */
47
48#include <stdlib.h>
49
50#define N (624) /* length of state vector */
51#define M (397) /* a period parameter */
52#define K (0x9908B0DFU) /* a magic constant */
53#define hiBit(u) ((u) & 0x80000000U) /* mask all but highest bit of u */
54#define loBit(u) ((u) & 0x00000001U) /* mask all but lowest bit of u */
55#define loBits(u) ((u) & 0x7FFFFFFFU) /* mask the highest bit of u */
56#define mixBits(u, v) (hiBit(u)|loBits(v)) /* move highest bit of u to
57 highest bit of v */
58
59static unsigned int state[N+1]; /* state vector + 1 to not violate ANSI C */
60static unsigned int *next; /* next random value is computed from here */
61static int left = -1; /* can *next++ this many times before reloading */
62
63void srand(unsigned int seed)
64{
65 /*
66 * We initialize state[0..(N-1)] via the generator
67 *
68 * x_new = (69069 * x_old) mod 2^32
69 *
70 * from Line 15 of Table 1, p. 106, Sec. 3.3.4 of Knuth's
71 * _The Art of Computer Programming_, Volume 2, 3rd ed.
72 *
73 * Notes (SJC): I do not know what the initial state requirements
74 * of the Mersenne Twister are, but it seems this seeding generator
75 * could be better. It achieves the maximum period for its modulus
76 * (2^30) iff x_initial is odd (p. 20-21, Sec. 3.2.1.2, Knuth); if
77 * x_initial can be even, you have sequences like 0, 0, 0, ...;
78 * 2^31, 2^31, 2^31, ...; 2^30, 2^30, 2^30, ...; 2^29, 2^29 + 2^31,
79 * 2^29, 2^29 + 2^31, ..., etc. so I force seed to be odd below.
80 *
81 * Even if x_initial is odd, if x_initial is 1 mod 4 then
82 *
83 * the lowest bit of x is always 1,
84 * the next-to-lowest bit of x is always 0,
85 * the 2nd-from-lowest bit of x alternates ... 0 1 0 1 0 1 0 1 ... ,
86 * the 3rd-from-lowest bit of x 4-cycles ... 0 1 1 0 0 1 1 0 ... ,
87 * the 4th-from-lowest bit of x has the 8-cycle ... 0 0 0 1 1 1 1 0 ... ,
88 * ...
89 *
90 * and if x_initial is 3 mod 4 then
91 *
92 * the lowest bit of x is always 1,
93 * the next-to-lowest bit of x is always 1,
94 * the 2nd-from-lowest bit of x alternates ... 0 1 0 1 0 1 0 1 ... ,
95 * the 3rd-from-lowest bit of x 4-cycles ... 0 0 1 1 0 0 1 1 ... ,
96 * the 4th-from-lowest bit of x has the 8-cycle ... 0 0 1 1 1 1 0 0 ... ,
97 * ...
98 *
99 * The generator's potency (min. s>=0 with (69069-1)^s = 0 mod 2^32) is
100 * 16, which seems to be alright by p. 25, Sec. 3.2.1.3 of Knuth. It
101 * also does well in the dimension 2..5 spectral tests, but it could be
102 * better in dimension 6 (Line 15, Table 1, p. 106, Sec. 3.3.4, Knuth).
103 *
104 * Note that the random number user does not see the values generated
105 * here directly since reloadMT() will always munge them first, so maybe
106 * none of all of this matters. In fact, the seed values made here could
107 * even be extra-special desirable if the Mersenne Twister theory says
108 * so-- that's why the only change I made is to restrict to odd seeds.
109 */
110
111 unsigned int x = (seed | 1U) & 0xFFFFFFFFU, *s = state;
112 int j;
113
114 for(left=0, *s++=x, j=N; --j;
115 *s++ = (x*=69069U) & 0xFFFFFFFFU);
116}
117
118static int rand_reload(void)
119{
120 unsigned int *p0=state, *p2=state+2, *pM=state+M, s0, s1;
121 int j;
122
123 if(left < -1)
124 srand(4357U);
125
126 left=N-1, next=state+1;
127
128 for(s0=state[0], s1=state[1], j=N-M+1; --j; s0=s1, s1=*p2++)
129 *p0++ = *pM++ ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0U);
130
131 for(pM=state, j=M; --j; s0=s1, s1=*p2++)
132 *p0++ = *pM++ ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0U);
133
134 s1=state[0], *p0 = *pM ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0U);
135 s1 ^= (s1 >> 11);
136 s1 ^= (s1 << 7) & 0x9D2C5680U;
137 s1 ^= (s1 << 15) & 0xEFC60000U;
138 return (int)s1 ^ (s1 >> 18);
139}
140
141int rand(void)
142{
143 int y;
144
145 if(--left < 0)
146 return rand_reload();
147
148 y = *next++;
149 y ^= (y >> 11);
150 y ^= (y << 7) & 0x9D2C5680U;
151 y ^= (y << 15) & 0xEFC60000U;
152 return (y ^ (y >> 18)) & ((2^31)-1); /* 31-bit limit by Björn Stenberg*/
153}