mirror of
https://github.com/triqs/dft_tools
synced 2024-12-26 14:23:38 +01:00
246 lines
8.8 KiB
C++
246 lines
8.8 KiB
C++
|
|
/*******************************************************************************
|
|
*
|
|
* TRIQS: a Toolbox for Research in Interacting Quantum Systems
|
|
*
|
|
* Copyright (C) 2011 by M. Ferrero, O. Parcollet
|
|
*
|
|
* TRIQS is free software: you can redistribute it and/or modify it under the
|
|
* terms of the GNU General Public License as published by the Free Software
|
|
* Foundation, either version 3 of the License, or (at your option) any later
|
|
* version.
|
|
*
|
|
* TRIQS 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 General Public License for more
|
|
* details.
|
|
*
|
|
* You should have received a copy of the GNU General Public License along with
|
|
* TRIQS. If not, see <http://www.gnu.org/licenses/>.
|
|
*
|
|
******************************************************************************/
|
|
|
|
#ifndef MERSENNE_RNG_H
|
|
#define MERSENNE_RNG_H
|
|
|
|
#include <iostream>
|
|
#include <cstdlib>
|
|
#include <cstdio>
|
|
#include <float.h>
|
|
|
|
//#include <gsl/gsl_rng.h>
|
|
namespace triqs {
|
|
namespace mc_tools {
|
|
namespace RandomGenerators{
|
|
|
|
|
|
// 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.
|
|
//
|
|
// RandMT class created by Paul Gresham <gresham@mediavisual.com>
|
|
// There seems to be a slight performance deficit in process creation
|
|
// however I've not profiled the class to compare it with the straight
|
|
// C code.
|
|
//
|
|
// Use of a class removes many C nasties and also allows you to easily
|
|
// create multiple generators.
|
|
// To compile on GNU a simple line is:
|
|
// g++ -O3 RandMT.cc -o RandMT
|
|
//
|
|
|
|
typedef unsigned long uint32;
|
|
|
|
class RandMT {
|
|
|
|
static const int N = 624; // length of state vector
|
|
static const int M = 397; // a period parameter
|
|
static const uint32 K = 0x9908B0DFU; // a magic constant
|
|
|
|
// If you want a single generator, consider using a singleton class
|
|
// instead of trying to make these static.
|
|
uint32 state[N+1]; // state vector + 1 extra to not violate ANSI C
|
|
uint32 *next; // next random value is computed from here
|
|
uint32 initseed; //
|
|
int left; // can *next++ this many times before reloading
|
|
|
|
inline uint32 hiBit(uint32 u) {
|
|
return u & 0x80000000U; // mask all but highest bit of u
|
|
}
|
|
|
|
inline uint32 loBit(uint32 u) {
|
|
return u & 0x00000001U; // mask all but lowest bit of u
|
|
}
|
|
|
|
inline uint32 loBits(uint32 u) {
|
|
return u & 0x7FFFFFFFU; // mask the highest bit of u
|
|
}
|
|
|
|
inline uint32 mixBits(uint32 u, uint32 v) {
|
|
return hiBit(u)|loBits(v); // move hi bit of u to hi bit of v
|
|
}
|
|
|
|
uint32 reloadMT(void) {
|
|
uint32 *p0=state, *p2=state+2, *pM=state+M, s0, s1;
|
|
int j;
|
|
|
|
if(left < -1)
|
|
seedMT(initseed);
|
|
|
|
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(s1 ^ (s1 >> 18));
|
|
}
|
|
|
|
uint32 seed_save;
|
|
|
|
public:
|
|
|
|
RandMT() {
|
|
seedMT(1U);
|
|
}
|
|
|
|
RandMT(uint32 seed) {
|
|
seedMT(seed);
|
|
}
|
|
|
|
RandMT( RandMT const & R) {
|
|
seedMT(R.seed_save);
|
|
}
|
|
|
|
void seedMT(uint32 seed) {
|
|
|
|
seed_save = 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.
|
|
//
|
|
initseed = seed;
|
|
|
|
uint32 x = (seed | 1U) & 0xFFFFFFFFU, *s = state;
|
|
int j;
|
|
left = 0;
|
|
for(*s++=x, j=N; --j; *s++ = (x*=69069U) & 0xFFFFFFFFU);
|
|
}
|
|
|
|
|
|
|
|
inline uint32 randomMT(void) {
|
|
uint32 y;
|
|
|
|
if(--left < 0)
|
|
return(reloadMT());
|
|
|
|
y = *next++;
|
|
y ^= (y >> 11);
|
|
y ^= (y << 7) & 0x9D2C5680U;
|
|
y ^= (y << 15) & 0xEFC60000U;
|
|
return(y ^ (y >> 18));
|
|
}
|
|
|
|
double operator()() { return DBL_EPSILON+eval()*(1-2*DBL_EPSILON);}
|
|
|
|
double eval();
|
|
// inline of this causes a BIG pb with g++ 4.1.2. WHY ?????
|
|
// inline double operator()() {
|
|
// return ((double)(randomMT())/0xFFFFFFFFU);
|
|
// }
|
|
|
|
};
|
|
|
|
}}}
|
|
|
|
#endif
|