MersenneRNG.hpp

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// Copyright (c) 2013-2018 Commissariat à l'énergie atomique et aux énergies alternatives (CEA)
// Copyright (c) 2013-2018 Centre national de la recherche scientifique (CNRS)
// Copyright (c) 2018-2020 Simons Foundation
//
// This program 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.
//
// This program 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 may obtain a copy of the License at
//     https://www.gnu.org/licenses/gpl-3.0.txt
//
// Authors: Michel Ferrero, Olivier Parcollet, Nils Wentzell

 
#ifndef MERSENNE_RNG_H
#define MERSENNE_RNG_H
 
#include <cstdlib>
#include <float.h>
#include <iostream>
#include <iterator>
#include <stdexcept>
 
namespace triqs::mc_tools::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 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);
    //   }
 
    // Same interface as boost::variate_generator.
    [[nodiscard]] RandMT &engine() { return *this; }
    [[nodiscard]] RandMT const &engine() const { return *this; }
 
    // Write a textual representation of a RandMT object to `std::ostream`.
    friend std::ostream &operator<<(std::ostream &os, const RandMT &rng) {
      for (uint32 i = 0; i < std::size(rng.state); ++i) os << rng.state[i] << ' ';
      long distance = rng.next - rng.state; // NOLINT
      os << distance << ' ' << rng.left << ' ' << rng.initseed << ' ' << rng.seed_save;
      if (!os) throw std::runtime_error("Error writing a triqs::mc_tools::RandomGenerators::RandMT to ostream.");
      return os;
    }
 
    // Read a textual representation of a RandMT object from `std::istream`.
    friend std::istream &operator>>(std::istream &is, RandMT &rng) {
      for (uint32 i = 0; i < std::size(rng.state); ++i) { is >> rng.state[i] >> std::ws; }
      long distance = 0;
      is >> distance >> std::ws >> rng.left >> std::ws >> rng.initseed >> std::ws >> rng.seed_save;
      rng.next = rng.state + distance; // NOLINT
      if (!is) throw std::runtime_error("Error reading a triqs::mc_tools::RandomGenerators::RandMT from istream.");
      return is;
    };
  };
 
} // namespace triqs::mc_tools::RandomGenerators
 
#endif