New vastly improved random algorithm: Mersenne Twister

git-svn-id: svn://svn.rockbox.org/rockbox/trunk@1377 a1c6a512-1295-4272-9138-f99709370657

3 files changed, 158 insertions, 16 deletions

diff --git a/apps/playlist.c b/apps/playlist.c
index 2d8bbd3a33..c74d643c52 100644
--- a/apps/playlist.c
+++ b/apps/playlist.c
@@ -205,20 +205,6 @@ void add_indices_to_playlist( playlist_info_t *playlist )
     close(fd);
 }
 
-static unsigned int playlist_seed = 0xdeadcafe;
-static void seedit(unsigned int seed)
-{
-    playlist_seed = seed;   
-}
-
-static int getrand(void)
-{
-    playlist_seed += 0x12345;
-
-    /* the rand is from 0 to RAND_MAX */
-    return playlist_seed;
-}
-
 /*
  * randomly rearrange the array of indices for the playlist
  */
@@ -229,14 +215,14 @@ void randomise_playlist( playlist_info_t *playlist, unsigned int seed )
     int store;
     
     /* seed with the given seed */
-    seedit( seed );
+    srand( seed );
 
     /* randomise entire indices list */
     
     while( count < playlist->amount )
     {
         /* the rand is from 0 to RAND_MAX, so adjust to our value range */
-        candidate = getrand() % ( playlist->amount );
+        candidate = rand() % playlist->amount;
 
         /* now swap the values at the 'count' and 'candidate' positions */
         store = playlist->indices[candidate];
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 <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 <stdlib.h>
+
+#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*/
+}
diff --git a/firmware/include/stdlib.h b/firmware/include/stdlib.h
index 40b5207223..9076bc25d2 100644
--- a/firmware/include/stdlib.h
+++ b/firmware/include/stdlib.h
@@ -30,6 +30,9 @@ void *calloc (size_t nmemb, size_t size);
 void free(void *);
 void *realloc(void *, size_t);
 
+void srand(unsigned int seed);
+int rand(void);
+
 #define abs(x) ((x)>0?(x):-(x))
 
 #ifdef __cplusplus