From: Dmitry Stogov Date: Fri, 10 Nov 2006 10:11:05 +0000 (+0000) Subject: Faster and better licensed implementation X-Git-Tag: RELEASE_1_0_0RC1~1082 X-Git-Url: https://granicus.if.org/sourcecode?a=commitdiff_plain;h=afe251ab8d8fd62b04c3f7bb3bf923dd646e91ca;p=php Faster and better licensed implementation --- diff --git a/ext/standard/rand.c b/ext/standard/rand.c index 3bb34dd972..6db1bce97c 100644 --- a/ext/standard/rand.c +++ b/ext/standard/rand.c @@ -17,7 +17,10 @@ | Pedro Melo | | Sterling Hughes | | | - | Based on code from: Shawn Cokus | + | Based on code from: Richard J. Wagner | + | Makoto Matsumoto | + | Takuji Nishimura | + | Shawn Cokus | +----------------------------------------------------------------------+ */ /* $Id$ */ @@ -85,152 +88,127 @@ PHPAPI long php_rand(TSRMLS_D) /* 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 - (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. - - - - 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; } /* }}} */ @@ -238,17 +216,21 @@ static php_uint32 php_mt_reload(TSRMLS_D) */ 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) ); } /* }}} */