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https://github.com/triqs/dft_tools
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246 lines
8.8 KiB
C++
246 lines
8.8 KiB
C++
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/*******************************************************************************
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*
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* TRIQS: a Toolbox for Research in Interacting Quantum Systems
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*
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* Copyright (C) 2011 by M. Ferrero, O. Parcollet
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*
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* TRIQS is free software: you can redistribute it and/or modify it under the
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* terms of the GNU General Public License as published by the Free Software
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* Foundation, either version 3 of the License, or (at your option) any later
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* version.
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*
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* TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
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* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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* FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
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* details.
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*
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* You should have received a copy of the GNU General Public License along with
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* TRIQS. If not, see <http://www.gnu.org/licenses/>.
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*
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******************************************************************************/
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#ifndef MERSENNE_RNG_H
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#define MERSENNE_RNG_H
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#include <iostream>
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#include <cstdlib>
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#include <cstdio>
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#include <float.h>
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//#include <gsl/gsl_rng.h>
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namespace triqs {
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namespace mc_tools {
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namespace RandomGenerators{
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// This is the ``Mersenne Twister'' random number generator MT19937, which
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// generates pseudorandom integers uniformly distributed in 0..(2^32 - 1)
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// starting from any odd seed in 0..(2^32 - 1). This version is a recode
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// by Shawn Cokus (Cokus@math.washington.edu) on March 8, 1998 of a version by
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// Takuji Nishimura (who had suggestions from Topher Cooper and Marc Rieffel in
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// July-August 1997).
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//
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// Effectiveness of the recoding (on Goedel2.math.washington.edu, a DEC Alpha
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// running OSF/1) using GCC -O3 as a compiler: before recoding: 51.6 sec. to
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// generate 300 million random numbers; after recoding: 24.0 sec. for the same
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// (i.e., 46.5% of original time), so speed is now about 12.5 million random
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// number generations per second on this machine.
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//
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// According to the URL <http://www.math.keio.ac.jp/~matumoto/emt.html>
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// (and paraphrasing a bit in places), the Mersenne Twister is ``designed
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// with consideration of the flaws of various existing generators,'' has
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// a period of 2^19937 - 1, gives a sequence that is 623-dimensionally
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// equidistributed, and ``has passed many stringent tests, including the
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// die-hard test of G. Marsaglia and the load test of P. Hellekalek and
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// S. Wegenkittl.'' It is efficient in memory usage (typically using 2506
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// to 5012 bytes of static data, depending on data type sizes, and the code
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// is quite short as well). It generates random numbers in batches of 624
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// at a time, so the caching and pipelining of modern systems is exploited.
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// It is also divide- and mod-free.
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//
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// This library is free software; you can redistribute it and/or modify it
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// under the terms of the GNU Library General Public License as published by
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// the Free Software Foundation (either version 2 of the License or, at your
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// option, any later version). This library is distributed in the hope that
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// it will be useful, but WITHOUT ANY WARRANTY, without even the implied
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// warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See
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// the GNU Library General Public License for more details. You should have
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// received a copy of the GNU Library General Public License along with this
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// library; if not, write to the Free Software Foundation, Inc., 59 Temple
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// Place, Suite 330, Boston, MA 02111-1307, USA.
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//
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// The code as Shawn received it included the following notice:
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//
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// Copyright (C) 1997 Makoto Matsumoto and Takuji Nishimura. When
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// you use this, send an e-mail to <matumoto@math.keio.ac.jp> with
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// an appropriate reference to your work.
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//
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// It would be nice to CC: <Cokus@math.washington.edu> when you write.
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//
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// RandMT class created by Paul Gresham <gresham@mediavisual.com>
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// There seems to be a slight performance deficit in process creation
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// however I've not profiled the class to compare it with the straight
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// C code.
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//
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// Use of a class removes many C nasties and also allows you to easily
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// create multiple generators.
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// To compile on GNU a simple line is:
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// g++ -O3 RandMT.cc -o RandMT
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//
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typedef unsigned long uint32;
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class RandMT {
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static const int N = 624; // length of state vector
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static const int M = 397; // a period parameter
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static const uint32 K = 0x9908B0DFU; // a magic constant
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// If you want a single generator, consider using a singleton class
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// instead of trying to make these static.
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uint32 state[N+1]; // state vector + 1 extra to not violate ANSI C
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uint32 *next; // next random value is computed from here
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uint32 initseed; //
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int left; // can *next++ this many times before reloading
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inline uint32 hiBit(uint32 u) {
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return u & 0x80000000U; // mask all but highest bit of u
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}
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inline uint32 loBit(uint32 u) {
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return u & 0x00000001U; // mask all but lowest bit of u
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}
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inline uint32 loBits(uint32 u) {
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return u & 0x7FFFFFFFU; // mask the highest bit of u
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}
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inline uint32 mixBits(uint32 u, uint32 v) {
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return hiBit(u)|loBits(v); // move hi bit of u to hi bit of v
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}
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uint32 reloadMT(void) {
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uint32 *p0=state, *p2=state+2, *pM=state+M, s0, s1;
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int j;
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if(left < -1)
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seedMT(initseed);
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left=N-1, next=state+1;
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for(s0=state[0], s1=state[1], j=N-M+1; --j; s0=s1, s1=*p2++)
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*p0++ = *pM++ ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0U);
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for(pM=state, j=M; --j; s0=s1, s1=*p2++)
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*p0++ = *pM++ ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0U);
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s1=state[0], *p0 = *pM ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0U);
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s1 ^= (s1 >> 11);
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s1 ^= (s1 << 7) & 0x9D2C5680U;
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s1 ^= (s1 << 15) & 0xEFC60000U;
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return(s1 ^ (s1 >> 18));
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}
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uint32 seed_save;
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public:
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RandMT() {
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seedMT(1U);
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}
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RandMT(uint32 seed) {
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seedMT(seed);
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}
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RandMT( RandMT const & R) {
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seedMT(R.seed_save);
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}
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void seedMT(uint32 seed) {
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seed_save = seed;
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//
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// We initialize state[0..(N-1)] via the generator
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//
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// x_new = (69069 * x_old) mod 2^32
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//
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// from Line 15 of Table 1, p. 106, Sec. 3.3.4 of Knuth's
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// _The Art of Computer Programming_, Volume 2, 3rd ed.
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//
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// Notes (SJC): I do not know what the initial state requirements
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// of the Mersenne Twister are, but it seems this seeding generator
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// could be better. It achieves the maximum period for its modulus
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// (2^30) iff x_initial is odd (p. 20-21, Sec. 3.2.1.2, Knuth); if
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// x_initial can be even, you have sequences like 0, 0, 0, ...;
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// 2^31, 2^31, 2^31, ...; 2^30, 2^30, 2^30, ...; 2^29, 2^29 + 2^31,
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// 2^29, 2^29 + 2^31, ..., etc. so I force seed to be odd below.
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//
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// Even if x_initial is odd, if x_initial is 1 mod 4 then
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//
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// the lowest bit of x is always 1,
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// the next-to-lowest bit of x is always 0,
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// the 2nd-from-lowest bit of x alternates ... 0 1 0 1 0 1 0 1 ... ,
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// the 3rd-from-lowest bit of x 4-cycles ... 0 1 1 0 0 1 1 0 ... ,
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// the 4th-from-lowest bit of x has the 8-cycle ... 0 0 0 1 1 1 1 0 ... ,
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// ...
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//
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// and if x_initial is 3 mod 4 then
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//
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// the lowest bit of x is always 1,
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// the next-to-lowest bit of x is always 1,
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// the 2nd-from-lowest bit of x alternates ... 0 1 0 1 0 1 0 1 ... ,
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// the 3rd-from-lowest bit of x 4-cycles ... 0 0 1 1 0 0 1 1 ... ,
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// the 4th-from-lowest bit of x has the 8-cycle ... 0 0 1 1 1 1 0 0 ... ,
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// ...
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//
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// The generator's potency (min. s>=0 with (69069-1)^s = 0 mod 2^32) is
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// 16, which seems to be alright by p. 25, Sec. 3.2.1.3 of Knuth. It
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// also does well in the dimension 2..5 spectral tests, but it could be
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// better in dimension 6 (Line 15, Table 1, p. 106, Sec. 3.3.4, Knuth).
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//
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// Note that the random number user does not see the values generated
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// here directly since reloadMT() will always munge them first, so maybe
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// none of all of this matters. In fact, the seed values made here could
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// even be extra-special desirable if the Mersenne Twister theory says
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// so-- that's why the only change I made is to restrict to odd seeds.
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//
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initseed = seed;
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uint32 x = (seed | 1U) & 0xFFFFFFFFU, *s = state;
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int j;
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left = 0;
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for(*s++=x, j=N; --j; *s++ = (x*=69069U) & 0xFFFFFFFFU);
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}
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inline uint32 randomMT(void) {
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uint32 y;
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if(--left < 0)
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return(reloadMT());
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y = *next++;
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y ^= (y >> 11);
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y ^= (y << 7) & 0x9D2C5680U;
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y ^= (y << 15) & 0xEFC60000U;
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return(y ^ (y >> 18));
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}
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double operator()() { return DBL_EPSILON+eval()*(1-2*DBL_EPSILON);}
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double eval();
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// inline of this causes a BIG pb with g++ 4.1.2. WHY ?????
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// inline double operator()() {
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// return ((double)(randomMT())/0xFFFFFFFFU);
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// }
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};
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}}}
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#endif
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