lecuyer.h

Go to the documentation of this file.

/* 
 * Scythe Statistical Library
 * Copyright (C) 2000-2002 Andrew D. Martin and Kevin M. Quinn;
 * 2002-present Andrew D. Martin, Kevin M. Quinn, and Daniel
 * Pemstein.  All Rights Reserved.
 *
 * This program is free software; you can redistribute it and/or modify
 * under the terms of the GNU General Public License as published by
 * Free Software Foundation; either version 2 of the License, or (at
 * your option) any later version.  See the text files COPYING
 * and LICENSE, distributed with this source code, for further
 * information.
 * --------------------------------------------------------------------
 * scythestat/rng/lecuyer.h
 *
 * Provides the class definition for the L'Ecuyer random number
 * generator, a rng capable of generating many independent substreams.
 * This class extends the abstract rng class by implementing runif().
 * Based on RngStream.cpp, by Pierre L'Ecuyer.
 *
 * Pierre L'Ecuyer agreed to the following dual-licensing terms in an
 * email received 7 August 2004.  This dual-license was prompted by
 * the Debian maintainers of R and MCMCpack. 
 *
 * This software is Copyright (C) 2004 Pierre L'Ecuyer.
 *
 * License: this code can be used freely for personal, academic, or
 * non-commercial purposes.  For commercial licensing, please contact
 * P. L'Ecuyer at lecuyer@iro.umontreal.ca.
 *
 * This code may also be redistributed and modified under the terms of
 * the GNU General Public License as published by the Free Software
 * Foundation; either version 2 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 should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307,
 * USA.
 *
 */
#ifndef SCYTHE_LECUYER_H
#define SCYTHE_LECUYER_H

#include<cstdlib>
#include<iostream>
#include<string>

#ifdef SCYTHE_COMPILE_DIRECT
#include "rng.h"
#else
#include "scythestat/rng.h"
#endif

/* We want to use an anonymous namespace to make the following consts
 * and functions local to this file, but mingw doesn't play nice with
 * anonymous namespaces so we do things differently when using the
 * cross-compiler.
 */
#ifdef __MINGW32__
#define SCYTHE_MINGW32_STATIC static
#else
#define SCYTHE_MINGW32_STATIC
#endif

namespace scythe {
#ifndef __MINGW32__
  namespace {
#endif

  SCYTHE_MINGW32_STATIC const double m1   = 4294967087.0;
  SCYTHE_MINGW32_STATIC const double m2   = 4294944443.0;
  SCYTHE_MINGW32_STATIC const double norm = 1.0 / (m1 + 1.0);
  SCYTHE_MINGW32_STATIC const double a12  = 1403580.0;
  SCYTHE_MINGW32_STATIC const double a13n = 810728.0;
  SCYTHE_MINGW32_STATIC const double a21  = 527612.0;
  SCYTHE_MINGW32_STATIC const double a23n = 1370589.0;
  SCYTHE_MINGW32_STATIC const double two17 =131072.0;
  SCYTHE_MINGW32_STATIC const double two53 =9007199254740992.0;
  /* 1/2^24 */
  SCYTHE_MINGW32_STATIC const double fact = 5.9604644775390625e-8;

  // The following are the transition matrices of the two MRG
  // components (in matrix form), raised to the powers -1, 1, 2^76,
  // and 2^127, resp.

  SCYTHE_MINGW32_STATIC const double InvA1[3][3] = { // Inverse of A1p0
         { 184888585.0,   0.0,  1945170933.0 },
         {         1.0,   0.0,           0.0 },
         {         0.0,   1.0,           0.0 } };

  SCYTHE_MINGW32_STATIC const double InvA2[3][3] = { // Inverse of A2p0
         {      0.0,  360363334.0,  4225571728.0 },
         {      1.0,          0.0,           0.0 },
         {      0.0,          1.0,           0.0 } };

  SCYTHE_MINGW32_STATIC const double A1p0[3][3] = {
         {       0.0,        1.0,       0.0 },
         {       0.0,        0.0,       1.0 },
         { -810728.0,  1403580.0,       0.0 } };

  SCYTHE_MINGW32_STATIC const double A2p0[3][3] = {
         {        0.0,        1.0,       0.0 },
         {        0.0,        0.0,       1.0 },
         { -1370589.0,        0.0,  527612.0 } };

  SCYTHE_MINGW32_STATIC const double A1p76[3][3] = {
         {      82758667.0, 1871391091.0, 4127413238.0 },
         {    3672831523.0,   69195019.0, 1871391091.0 },
         {    3672091415.0, 3528743235.0,   69195019.0 } };

  SCYTHE_MINGW32_STATIC const double A2p76[3][3] = {
         {    1511326704.0, 3759209742.0, 1610795712.0 },
         {    4292754251.0, 1511326704.0, 3889917532.0 },
         {    3859662829.0, 4292754251.0, 3708466080.0 } };

  SCYTHE_MINGW32_STATIC const double A1p127[3][3] = {
         {    2427906178.0, 3580155704.0,  949770784.0 },
         {     226153695.0, 1230515664.0, 3580155704.0 },
         {    1988835001.0,  986791581.0, 1230515664.0 } };

  SCYTHE_MINGW32_STATIC const double A2p127[3][3] = {
         {    1464411153.0,  277697599.0, 1610723613.0 },
         {      32183930.0, 1464411153.0, 1022607788.0 },
         {    2824425944.0,   32183930.0, 2093834863.0 } };

  // Return (a*s + c) MOD m; a, s, c and m must be < 2^35
  SCYTHE_MINGW32_STATIC double
  MultModM (double a, double s, double c, double m)
  {
    double v;
    long a1;

    v = a * s + c;

    if (v >= two53 || v <= -two53) {
      a1 = static_cast<long> (a / two17);    a -= a1 * two17;
      v  = a1 * s;
      a1 = static_cast<long> (v / m);     v -= a1 * m;
      v = v * two17 + a * s + c;
    }

    a1 = static_cast<long> (v / m);
    /* in case v < 0)*/
    if ((v -= a1 * m) < 0.0) return v += m;   else return v;
  }

  // Compute the vector v = A*s MOD m. Assume that -m < s[i] < m.
  // Works also when v = s.
  SCYTHE_MINGW32_STATIC void
  MatVecModM (const double A[3][3], const double s[3],
              double v[3], double m)
  {
    int i;
    double x[3];               // Necessary if v = s

    for (i = 0; i < 3; ++i) {
      x[i] = MultModM (A[i][0], s[0], 0.0, m);
      x[i] = MultModM (A[i][1], s[1], x[i], m);
      x[i] = MultModM (A[i][2], s[2], x[i], m);
    }
    for (i = 0; i < 3; ++i)
      v[i] = x[i];
  }

  // Compute the matrix C = A*B MOD m. Assume that -m < s[i] < m.
  // Note: works also if A = C or B = C or A = B = C.
  SCYTHE_MINGW32_STATIC void
  MatMatModM (const double A[3][3], const double B[3][3],
              double C[3][3], double m)
  {
    int i, j;
    double V[3], W[3][3];

    for (i = 0; i < 3; ++i) {
      for (j = 0; j < 3; ++j)
        V[j] = B[j][i];
      MatVecModM (A, V, V, m);
      for (j = 0; j < 3; ++j)
        W[j][i] = V[j];
    }
    for (i = 0; i < 3; ++i)
      for (j = 0; j < 3; ++j)
        C[i][j] = W[i][j];
  }

  // Compute the matrix B = (A^(2^e) Mod m);  works also if A = B. 
  SCYTHE_MINGW32_STATIC void
  MatTwoPowModM(const double A[3][3], double B[3][3],
                double m, long e)
  {
   int i, j;

   /* initialize: B = A */
   if (A != B) {
     for (i = 0; i < 3; ++i)
       for (j = 0; j < 3; ++j)
         B[i][j] = A[i][j];
   }
   /* Compute B = A^(2^e) mod m */
   for (i = 0; i < e; i++)
     MatMatModM (B, B, B, m);
  }

  // Compute the matrix B = (A^n Mod m);  works even if A = B.
  SCYTHE_MINGW32_STATIC void
  MatPowModM (const double A[3][3], double B[3][3], double m,
              long n)
  {
    int i, j;
    double W[3][3];

    /* initialize: W = A; B = I */
    for (i = 0; i < 3; ++i)
      for (j = 0; j < 3; ++j) {
        W[i][j] = A[i][j];
        B[i][j] = 0.0;
      }
    for (j = 0; j < 3; ++j)
      B[j][j] = 1.0;

    /* Compute B = A^n mod m using the binary decomposition of n */
    while (n > 0) {
      if (n % 2) MatMatModM (W, B, B, m);
      MatMatModM (W, W, W, m);
      n /= 2;
    }
  }

  // Check that the seeds are legitimate values. Returns 0 if legal
  // seeds, -1 otherwise.
  SCYTHE_MINGW32_STATIC int
  CheckSeed (const unsigned long seed[6])
  {
    int i;

    for (i = 0; i < 3; ++i) {
      if (seed[i] >= m1) {
      SCYTHE_THROW(scythe_randseed_error,
          "Seed[" << i << "] >= 4294967087, Seed is not set");
        return -1;
      }
    }
    for (i = 3; i < 6; ++i) {
      if (seed[i] >= m2) {
      SCYTHE_THROW(scythe_randseed_error,
          "Seed[" << i << "] >= 4294944443, Seed is not set");
        return -1;
      }
    }
    if (seed[0] == 0 && seed[1] == 0 && seed[2] == 0) {
      SCYTHE_THROW(scythe_randseed_error, "First 3 seeds = 0");
      return -1;
    }
    if (seed[3] == 0 && seed[4] == 0 && seed[5] == 0) {
      SCYTHE_THROW(scythe_randseed_error, "Last 3 seeds = 0");
      return -1;
    }

    return 0;
  }
 
#ifndef __MINGW32__
  } // end anonymous namespace
#endif

  class lecuyer : public rng<lecuyer>
  {
    public:

      // Constructor
      lecuyer (std::string streamname = "")
        : rng<lecuyer> (),
          streamname_ (streamname)
      {
        anti = false;
        incPrec = false;
        
        /* Information on a stream. The arrays {Cg, Bg, Ig} contain
         * the current state of the stream, the starting state of the
         * current SubStream, and the starting state of the stream.
         * This stream generates antithetic variates if anti = true.
         * It also generates numbers with extended precision (53 bits
         * if machine follows IEEE 754 standard) if incPrec = true.
         * nextSeed will be the seed of the next declared RngStream.
         */

        for (int i = 0; i < 6; ++i) {
          Bg[i] = Cg[i] = Ig[i] = nextSeed[i];
        }

        MatVecModM (A1p127, nextSeed, nextSeed, m1);
        MatVecModM (A2p127, &nextSeed[3], &nextSeed[3], m2);
      }

      std::string
      name() const
      {
        return streamname_;
      }

      void
      ResetStartStream ()
      {
        for (int i = 0; i < 6; ++i)
          Cg[i] = Bg[i] = Ig[i];
      }

      void
      ResetStartSubstream ()
      {
        for (int i = 0; i < 6; ++i)
          Cg[i] = Bg[i];
      }

      void
      ResetNextSubstream ()
      {
        MatVecModM(A1p76, Bg, Bg, m1);
        MatVecModM(A2p76, &Bg[3], &Bg[3], m2);
        for (int i = 0; i < 6; ++i)
          Cg[i] = Bg[i];
      }

      static void
      SetPackageSeed (unsigned long seed[6])
      {
         if (CheckSeed (seed)) return;
         for (int i = 0; i < 6; ++i)
            nextSeed[i] = seed[i];
      }

      void
      SetSeed (unsigned long seed[6])
      {
        if (CheckSeed (seed)) return;
          for (int i = 0; i < 6; ++i)
            Cg[i] = Bg[i] = Ig[i] = seed[i];
      }

      // XXX: get the cases formula working!
      void
      AdvanceState (long e, long c)
      {
        double B1[3][3], C1[3][3], B2[3][3], C2[3][3];

        if (e > 0) {
          MatTwoPowModM (A1p0, B1, m1, e);
          MatTwoPowModM (A2p0, B2, m2, e);
        } else if (e < 0) {
          MatTwoPowModM (InvA1, B1, m1, -e);
          MatTwoPowModM (InvA2, B2, m2, -e);
        }

        if (c >= 0) {
          MatPowModM (A1p0, C1, m1, c);
          MatPowModM (A2p0, C2, m2, c);
        } else {
          MatPowModM (InvA1, C1, m1, -c);
          MatPowModM (InvA2, C2, m2, -c);
        }

        if (e) {
          MatMatModM (B1, C1, C1, m1);
          MatMatModM (B2, C2, C2, m2);
        }

        MatVecModM (C1, Cg, Cg, m1);
        MatVecModM (C2, &Cg[3], &Cg[3], m2);
      }

      void
      GetState (unsigned long seed[6]) const
      {
        for (int i = 0; i < 6; ++i)
          seed[i] = static_cast<unsigned long> (Cg[i]);
      }

      void
      IncreasedPrecis (bool incp)
      {
        incPrec = incp;
      }

      void
      SetAntithetic (bool a)
      {
        anti = a;
      }

      double
      runif ()
      {
        if (incPrec)
          return U01d();
        else
          return U01();
      }

      /* We have to override the overloaded form of runif because
       * overloading the no-arg runif() hides the base class
       * definition; C++ stops looking once it finds the above.
       */
      template <matrix_order O, matrix_style S>
      Matrix<double,O,S> runif(unsigned int rows, unsigned int cols)
      {
        return rng<lecuyer>::runif<O,S>(rows,cols);
      }

      Matrix<double,Col,Concrete> runif(unsigned int rows,
                                        unsigned int cols)
      {
        return rng<lecuyer>::runif<Col,Concrete>(rows, cols);
      }

      long
      RandInt (long low, long high)
      {
        return low + static_cast<long> ((high - low + 1) * runif ());
      }

    protected:
      // Generate the next random number.
      //
      double
      U01 ()
      {
        long k;
        double p1, p2, u;

        /* Component 1 */
        p1 = a12 * Cg[1] - a13n * Cg[0];
        k = static_cast<long> (p1 / m1);
        p1 -= k * m1;
        if (p1 < 0.0) p1 += m1;
        Cg[0] = Cg[1]; Cg[1] = Cg[2]; Cg[2] = p1;

        /* Component 2 */
        p2 = a21 * Cg[5] - a23n * Cg[3];
        k = static_cast<long> (p2 / m2);
        p2 -= k * m2;
        if (p2 < 0.0) p2 += m2;
        Cg[3] = Cg[4]; Cg[4] = Cg[5]; Cg[5] = p2;

        /* Combination */
        u = ((p1 > p2) ? (p1 - p2) * norm : (p1 - p2 + m1) * norm);

        return (anti == false) ? u : (1 - u);
      }

      // Generate the next random number with extended (53 bits) precision.
      double 
      U01d ()
      {
        double u;
        u = U01();
        if (anti) {
          // Don't forget that U01() returns 1 - u in the antithetic case
          u += (U01() - 1.0) * fact;
          return (u < 0.0) ? u + 1.0 : u;
        } else {
          u += U01() * fact;
          return (u < 1.0) ? u : (u - 1.0);
        }
      }


      // Public members of the class start here
      
      // The default seed of the package; will be the seed of the first
      // declared RngStream, unless SetPackageSeed is called.
      static double nextSeed[6];

      /* Instance variables */
      double Cg[6], Bg[6], Ig[6];


      bool anti, incPrec;


      std::string streamname_;

  };

  /* Default seed definition */
  double lecuyer::nextSeed[6] = 
      {
         12345.0, 12345.0, 12345.0, 12345.0, 12345.0, 12345.0
      };

}

#endif /* SCYTHE_LECUYER_H */

---