MT19937RNGEngine.h

#pragma once

#include <c10/util/irange.h>

// define constants like M_PI and C keywords for MSVC
#ifdef _MSC_VER
#ifndef _USE_MATH_DEFINES
#define _USE_MATH_DEFINES
#endif
#include <math.h>
#endif

#include <array>
#include <cmath>
#include <cstdint>

namespace at {

constexpr int MERSENNE_STATE_N = 624;
constexpr int MERSENNE_STATE_M = 397;
constexpr uint32_t MATRIX_A = 0x9908b0df;
constexpr uint32_t UMASK = 0x80000000;
constexpr uint32_t LMASK = 0x7fffffff;

/**
 * Note [Mt19937 Engine implementation]
 * ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 * Originally implemented in:
 * http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/CODES/MTARCOK/mt19937ar-cok.c
 * and modified with C++ constructs. Moreover the state array of the engine
 * has been modified to hold 32 bit uints instead of 64 bits.
 *
 * Note that we reimplemented mt19937 instead of using std::mt19937 because,
 * at::mt19937 turns out to be faster in the pytorch codebase. PyTorch builds with -O2
 * by default and following are the benchmark numbers (benchmark code can be found at
 * https://github.com/syed-ahmed/benchmark-rngs):
 *
 * with -O2
 * Time to get 100000000 philox randoms with at::uniform_real_distribution = 0.462759s
 * Time to get 100000000 at::mt19937 randoms with at::uniform_real_distribution = 0.39628s
 * Time to get 100000000 std::mt19937 randoms with std::uniform_real_distribution = 0.352087s
 * Time to get 100000000 std::mt19937 randoms with at::uniform_real_distribution = 0.419454s
 *
 * std::mt19937 is faster when used in conjunction with std::uniform_real_distribution,
 * however we can't use std::uniform_real_distribution because of this bug:
 * http://open-std.org/JTC1/SC22/WG21/docs/lwg-active.html#2524. Plus, even if we used
 * std::uniform_real_distribution and filtered out the 1's, it is a different algorithm
 * than what's in pytorch currently and that messes up the tests in tests_distributions.py.
 * The other option, using std::mt19937 with at::uniform_real_distribution is a tad bit slower
 * than at::mt19937 with at::uniform_real_distribution and hence, we went with the latter.
 *
 * Copyright notice:
 * A C-program for MT19937, with initialization improved 2002/2/10.
 * Coded by Takuji Nishimura and Makoto Matsumoto.
 * This is a faster version by taking Shawn Cokus's optimization,
 * Matthe Bellew's simplification, Isaku Wada's real version.
 *
 * Before using, initialize the state by using init_genrand(seed)
 * or init_by_array(init_key, key_length).
 *
 * Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
 * 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.
 *
 *
 * Any feedback is very welcome.
 * http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
 * email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space)
 */

/**
 * mt19937_data_pod is used to get POD data in and out
 * of mt19937_engine. Used in torch.get_rng_state and
 * torch.set_rng_state functions.
 */
struct mt19937_data_pod {
  uint64_t seed_;
  int left_;
  bool seeded_;
  uint32_t next_;
  std::array<uint32_t, MERSENNE_STATE_N> state_;
};

class mt19937_engine {
public:

  inline explicit mt19937_engine(uint64_t seed = 5489) {
    init_with_uint32(seed);
  }

  inline mt19937_data_pod data() const {
    return data_;
  }

  inline void set_data(const mt19937_data_pod& data) {
    data_ = data;
  }

  inline uint64_t seed() const {
    return data_.seed_;
  }

  inline bool is_valid() {
    if ((data_.seeded_ == true)
      && (data_.left_ > 0 && data_.left_ <= MERSENNE_STATE_N)
      && (data_.next_ <= MERSENNE_STATE_N)) {
      return true;
    }
    return false;
  }

  inline uint32_t operator()() {
    uint32_t y;

    if (--(data_.left_) == 0) {
        next_state();
    }
    y = *(data_.state_.data() + data_.next_++);
    y ^= (y >> 11);
    y ^= (y << 7) & 0x9d2c5680;
    y ^= (y << 15) & 0xefc60000;
    y ^= (y >> 18);

    return y;
  }

private:
  mt19937_data_pod data_;

  inline void init_with_uint32(uint64_t seed) {
    data_.seed_ = seed;
    data_.seeded_ = true;
    data_.state_[0] = seed & 0xffffffff;
    for (const auto j : c10::irange(1, MERSENNE_STATE_N)) {
      data_.state_[j] = (1812433253 * (data_.state_[j-1] ^ (data_.state_[j-1] >> 30)) + j);
    }
    data_.left_ = 1;
    data_.next_ = 0;
  }

  inline uint32_t mix_bits(uint32_t u, uint32_t v) {
    return (u & UMASK) | (v & LMASK);
  }

  inline uint32_t twist(uint32_t u, uint32_t v) {
    return (mix_bits(u,v) >> 1) ^ (v & 1 ? MATRIX_A : 0);
  }

  inline void next_state() {
    uint32_t* p = data_.state_.data();
    data_.left_ = MERSENNE_STATE_N;
    data_.next_ = 0;

    for(int j = MERSENNE_STATE_N - MERSENNE_STATE_M + 1; --j; p++) {
      *p = p[MERSENNE_STATE_M] ^ twist(p[0], p[1]);
    }

    for(int j = MERSENNE_STATE_M; --j; p++) {
      *p = p[MERSENNE_STATE_M - MERSENNE_STATE_N] ^ twist(p[0], p[1]);
    }

    *p = p[MERSENNE_STATE_M - MERSENNE_STATE_N] ^ twist(p[0], data_.state_[0]);
  }

};

typedef mt19937_engine mt19937;

} // namespace at