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rand_mt.c
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rand_mt.c
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/*
+----------------------------------------------------------------------+
| PHP version 4.0 |
+----------------------------------------------------------------------+
| Copyright (c) 1997-2001 The PHP Group |
+----------------------------------------------------------------------+
| This source file is subject to version 2.02 of the PHP license, |
| that is bundled with this package in the file LICENSE, and is |
| available at through the world-wide-web at |
| http://www.php.net/license/2_02.txt. |
| If you did not receive a copy of the PHP license and are unable to |
| obtain it through the world-wide-web, please send a note to |
| license@php.net so we can mail you a copy immediately. |
+----------------------------------------------------------------------+
| Authors: Rasmus Lerdorf <rasmus@lerdorf.on.ca> |
| Zeev Suraski <zeev@zend.com> |
| Pedro Melo <melo@ip.pt> |
| |
| Based on code from: Shawn Cokus <Cokus@math.washington.edu> |
+----------------------------------------------------------------------+
*/
/* $Id$ */
#include <stdlib.h>
#include "php.h"
#include "php_rand.h"
#include "basic_functions.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.
php_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
Melo: we should put some ifdefs here to catch those alphas...
*/
static void _php_srand_mt(long seed TSRMLS_DC);
static inline long _php_rand_mt_reload(TSRMLS_D);
static long _php_rand_mt(void);
/*
* Melo: it could be 2^^32 but we only use 2^^31 to maintain
* compatibility with the previous php_rand
*/
#define PHP_RANDMAX_MT ((long)(0x7FFFFFFF)) /* 2^^31 - 1 */
PHP_MINIT_FUNCTION(rand_mt)
{
PHP_RANDGEN_ENTRY(PHP_RAND_MT,
_php_srand_mt, /* void srand(long seed) */
_php_rand_mt, /* long rand(void) */
PHP_RANDMAX_MT, /* long randmax */
"mt" /* char *ini_str */
);
}
#define N MT_N /* 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 */
#define MIX_AND_RETURN(var) { \
(var) ^= ((var) >> 11); \
(var) ^= ((var) << 7) & 0x9D2C5680U; \
(var) ^= ((var) << 15) & 0xEFC60000U; \
(var) ^= ((var) >> 18); \
/*
* Melo: hmms.. these are 32 random bits...
* Yet, the previous php_rand only returns 31 at most.
* So I put a right shift to loose the lsb. It *seems*
* better than clearing the msb.
* Update:
* I talked with Cokus via email and it won't ruin the algorithm
*
* Jeroen: moved this to end of php_rand_mt and php_rand_mt_reload
*/ \
return (long)((var) >> 1); \
}
/* {{{ void _php_srand_mt(long seed)
*/
static void _php_srand_mt(long seed TSRMLS_DC)
{
/*
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 php_uint32 x = ((php_uint32)seed | 1U) & 0xFFFFFFFFU, *s = BG(state);
register int j;
for(BG(left)=0, *s++=x, j=N; --j;
*s++ = (x*=69069U) & 0xFFFFFFFFU);
}
/* }}} */
/* {{{ long _php_rand_mt_reload(void) [internal function]
* Generates a new batch of random numbers, and returns the first of it */
static inline long _php_rand_mt_reload(TSRMLS_D)
{
register php_uint32 *p0=BG(state), *p2=BG(state)+2, *pM=BG(state)+M, s0, s1;
register int j;
if(BG(left) < -1)
_php_srand_mt(4357U TSRMLS_CC);
BG(left)=N-1, BG(next)=BG(state)+1;
for(s0=BG(state)[0], s1=BG(state)[1], j=N-M+1; --j; s0=s1, s1=*p2++)
*p0++ = *pM++ ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0U);
for(pM=BG(state), j=M; --j; s0=s1, s1=*p2++)
*p0++ = *pM++ ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0U);
s1=BG(state)[0], *p0 = *pM ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0U);
MIX_AND_RETURN(s1);
}
/*}}}*/
/* {{{ long _php_rand_mt(void) */
static long _php_rand_mt(void)
{
php_uint32 y;
TSRMLS_FETCH();
if(--BG(left) < 0)
return(_php_rand_mt_reload(TSRMLS_C));
y = *BG(next)++;
MIX_AND_RETURN(y);
}
/* }}} */
/*
* Local variables:
* tab-width: 4
* c-basic-offset: 4
* End:
* vim600: sw=4 ts=4 tw=78 fdm=marker
* vim<600: sw=4 ts=4 tw=78
*/