| Pedro Melo <melo@ip.pt> |
| Sterling Hughes <sterling@php.net> |
| |
- | Based on code from: Shawn Cokus <Cokus@math.washington.edu> |
+ | Based on code from: Richard J. Wagner <rjwagner@writeme.com> |
+ | Makoto Matsumoto <matumoto@math.keio.ac.jp> |
+ | Takuji Nishimura |
+ | Shawn Cokus <Cokus@math.washington.edu> |
+----------------------------------------------------------------------+
*/
/* $Id$ */
/* MT RAND FUNCTIONS */
/*
- 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...
+ The following php_mt_...() functions are based on a C++ class MTRand by
+ Richard J. Wagner. For more information see the web page at
+ http://www-personal.engin.umich.edu/~wagnerr/MersenneTwister.html
+
+ Mersenne Twister random number generator -- a C++ class MTRand
+ Based on code by Makoto Matsumoto, Takuji Nishimura, and Shawn Cokus
+ Richard J. Wagner v1.0 15 May 2003 rjwagner@writeme.com
+
+ The Mersenne Twister is an algorithm for generating random numbers. It
+ was designed with consideration of the flaws in various other generators.
+ The period, 2^19937-1, and the order of equidistribution, 623 dimensions,
+ are far greater. The generator is also fast; it avoids multiplication and
+ division, and it benefits from caches and pipelines. For more information
+ see the inventors' web page at http://www.math.keio.ac.jp/~matumoto/emt.html
+
+ Reference
+ M. Matsumoto and T. Nishimura, "Mersenne Twister: A 623-Dimensionally
+ Equidistributed Uniform Pseudo-Random Number Generator", ACM Transactions on
+ Modeling and Computer Simulation, Vol. 8, No. 1, January 1998, pp 3-30.
+
+ Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
+ Copyright (C) 2000 - 2003, Richard J. Wagner
+ All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without
+ modification, are permitted provided that the following conditions
+ are met:
+
+ 1. Redistributions of source code must retain the above copyright
+ notice, this list of conditions and the following disclaimer.
+
+ 2. Redistributions in binary form must reproduce the above copyright
+ notice, this list of conditions and the following disclaimer in the
+ documentation and/or other materials provided with the distribution.
+
+ 3. The names of its contributors may not be used to endorse or promote
+ products derived from this software without specific prior written
+ permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ The original code included the following notice:
+
+ When you use this, send an email to: matumoto@math.keio.ac.jp
+ with an appropriate reference to your work.
+
+ It would be nice to CC: rjwagner@writeme.com and Cokus@math.washington.edu
+ when you write.
*/
+
#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 */
-/* {{{ php_mt_srand
+#define twist(m,u,v) (m ^ (mixBits(u,v)>>1) ^ ((php_uint32)(-(php_int32)(loBit(u))) & 0x9908b0dfU))
+
+/* {{{ php_mt_initialize
*/
-PHPAPI void php_mt_srand(php_uint32 seed TSRMLS_DC)
+static inline void php_mt_initialize(php_uint32 seed, php_uint32 *state)
{
- /*
- 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 = (seed | 1U) & 0xFFFFFFFFU, *s = BG(state);
- register int j;
-
- for (BG(left) = 0, *s++ = x, j = N; --j;
- *s++ = (x *= 69069U) & 0xFFFFFFFFU);
-
- /* Seed only once */
- BG(mt_rand_is_seeded) = 1;
+ /* Initialize generator state with seed
+ See Knuth TAOCP Vol 2, 3rd Ed, p.106 for multiplier.
+ In previous versions, most significant bits (MSBs) of the seed affect
+ only MSBs of the state array. Modified 9 Jan 2002 by Makoto Matsumoto. */
+
+ register php_uint32 *s = state;
+ register php_uint32 *r = state;
+ register int i = 1;
+
+ *s++ = seed & 0xffffffffU;
+ for( ; i < N; ++i ) {
+ *s++ = ( 1812433253U * ( *r ^ (*r >> 30) ) + i ) & 0xffffffffU;
+ r++;
+ }
}
/* }}} */
/* {{{ php_mt_reload
*/
-static php_uint32 php_mt_reload(TSRMLS_D)
+static inline void php_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_mt_srand(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);
+ /* Generate N new values in state
+ Made clearer and faster by Matthew Bellew (matthew.bellew@home.com) */
+
+ register php_uint32 *state = BG(state);
+ register php_uint32 *p = state;
+ register int i;
+
+ for (i = N - M; i--; ++p)
+ *p = twist(p[M], p[0], p[1]);
+ for (i = M; --i; ++p)
+ *p = twist(p[M-N], p[0], p[1]);
+ *p = twist(p[M-N], p[0], state[0]);
+ BG(left) = N;
+ BG(next) = state;
+}
+/* }}} */
- s1 = BG(state)[0], *p0 = *pM ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0U);
- s1 ^= (s1 >> 11);
- s1 ^= (s1 << 7) & 0x9D2C5680U;
- s1 ^= (s1 << 15) & 0xEFC60000U;
+/* {{{ php_mt_srand
+ */
+PHPAPI void php_mt_srand(php_uint32 seed TSRMLS_DC)
+{
+ /* Seed the generator with a simple uint32 */
+ php_mt_initialize(seed, BG(state));
+ php_mt_reload(TSRMLS_C);
- return s1 ^ (s1 >> 18);
+ /* Seed only once */
+ BG(mt_rand_is_seeded) = 1;
}
/* }}} */
*/
PHPAPI php_uint32 php_mt_rand(TSRMLS_D)
{
- php_uint32 y;
-
- if (--BG(left) < 0)
- return php_mt_reload(TSRMLS_C);
-
- y = *BG(next)++;
- y ^= (y >> 11);
- y ^= (y << 7) & 0x9D2C5680U;
- y ^= (y << 15) & 0xEFC60000U;
+ /* Pull a 32-bit integer from the generator state
+ Every other access function simply transforms the numbers extracted here */
+
+ register php_uint32 s1;
- return y ^ (y >> 18);
+ if (BG(left) == 0) {
+ php_mt_reload(TSRMLS_C);
+ }
+ --BG(left);
+
+ s1 = *BG(next)++;
+ s1 ^= (s1 >> 11);
+ s1 ^= (s1 << 7) & 0x9d2c5680U;
+ s1 ^= (s1 << 15) & 0xefc60000U;
+ return ( s1 ^ (s1 >> 18) );
}
/* }}} */
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