/* -*- Mode:C++; c-file-style:"gnu"; indent-tabs-mode:nil; -*- */
//
// Copyright (C) 2001 Pierre L'Ecuyer (lecuyer@iro.umontreal.ca)
//
// This program is free software; you can redistribute it and/or modify
// it under the terms of the GNU General Public License version 2 as
// published by the Free Software Foundation;
//
// 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
//
// Modified for ns-3 by:
// - Rajib Bhattacharjea<raj.b@gatech.edu>
// - Mathieu Lacage <mathieu.lacage@gmail.com>
//
#include <cstdlib>
#include <iostream>
#include "rng-stream.h"
#include "fatal-error.h"
#include "log.h"
/// \file
/// \ingroup rngimpl
/// Class RngStream and MRG32k3a implementation.
namespace ns3 {
// Note: Logging in this file is largely avoided due to the
// number of calls that are made to these functions and the possibility
// of causing recursions leading to stack overflow
NS_LOG_COMPONENT_DEFINE ("RngStream");
} // namespace ns3
/// \ingroup rngimpl
/// Unnamed namespace for MRG32k3a implementation details.
namespace
{
/// \ingroup rngimpl
/// Type for 3x3 matrix of doubles.
typedef double Matrix[3][3];
/// \ingroup rngimpl
/// First component modulus, 2<sup>32</sup> - 209.
const double m1 = 4294967087.0;
/// \ingroup rngimpl
/// Second component modulus, 2<sup>32</sup> - 22853.
const double m2 = 4294944443.0;
/// \ingroup rngimpl
/// Normalization to obtain randoms on [0,1).
const double norm = 1.0 / (m1 + 1.0);
/// \ingroup rngimpl
/// First component multiplier of <i>n</i> - 2 value.
const double a12 = 1403580.0;
/// \ingroup rngimpl
/// First component multiplier of <i>n</i> - 3 value.
const double a13n = 810728.0;
/// \ingroup rngimpl
/// Second component multiplier of <i>n</i> - 1 value.
const double a21 = 527612.0;
/// \ingroup rngimpl
/// Second component multiplier of <i>n</i> - 3 value.
const double a23n = 1370589.0;
/// \ingroup rngimpl
/// Decomposition factor for computing a*s in less than 53 bits, 2<sup>17</sup>
const double two17 = 131072.0;
/// \ingroup rngimpl
/// IEEE-754 floating point precision, 2<sup>53</sup>
const double two53 = 9007199254740992.0;
/// \ingroup rngimpl
/// First component transition matrix.
const Matrix A1p0 = {
{ 0.0, 1.0, 0.0 },
{ 0.0, 0.0, 1.0 },
{ -810728.0, 1403580.0, 0.0 }
};
/// \ingroup rngimpl
/// Second component transition matrix.
const Matrix A2p0 = {
{ 0.0, 1.0, 0.0 },
{ 0.0, 0.0, 1.0 },
{ -1370589.0, 0.0, 527612.0 }
};
//-------------------------------------------------------------------------
/// \ingroup rngimpl
/// Return (a*s + c) MOD m; a, s, c and m must be < 2^35
///
/// This computes the result exactly, without exceeding the 53 bit
/// precision of doubles.
///
/// \param [in] a First multiplicative argument.
/// \param [in] s Second multiplicative argument.
/// \param [in] c Additive argument.
/// \param [in] m Modulus.
/// \returns <tt>(a*s +c) MOD m</tt>
//
double MultModM (double a, double s, double c, double m)
{
double v;
int32_t a1;
v = a * s + c;
if (v >= two53 || v <= -two53)
{
a1 = static_cast<int32_t> (a / two17);
a -= a1 * two17;
v = a1 * s;
a1 = static_cast<int32_t> (v / m);
v -= a1 * m;
v = v * two17 + a * s + c;
}
a1 = static_cast<int32_t> (v / m);
/* in case v < 0)*/
if ((v -= a1 * m) < 0.0)
{
return v += m;
}
else
{
return v;
}
}
//-------------------------------------------------------------------------
/// \ingroup rngimpl
/// Compute the vector v = A*s MOD m. Assume that -m < s[i] < m.
/// Works also when v = s.
///
/// \param [in] A Matrix argument, 3x3.
/// \param [in] s Three component input vector.
/// \param [out] v Three component output vector.
/// \param [in] m Modulus.
//
void MatVecModM (const Matrix A, 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];
}
}
//-------------------------------------------------------------------------
/// \ingroup rngimpl
/// 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.
///
/// \param [in] A First matrix argument.
/// \param [in] B Second matrix argument.
/// \param [out] C Result matrix.
/// \param [in] m Modulus.
//
void MatMatModM (const Matrix A, const Matrix B,
Matrix C, double m)
{
int i, j;
double V[3];
Matrix W;
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];
}
}
}
//-------------------------------------------------------------------------
/// \ingroup rngimpl
/// Compute the matrix B = (A^(2^e) Mod m); works also if A = B.
///
/// \param [in] src Matrix input argument \c A.
/// \param [out] dst Matrix output \c B.
/// \param [in] m Modulus.
/// \param [in] e The exponent.
//
void MatTwoPowModM (const Matrix src, Matrix dst, double m, int32_t e)
{
int i, j;
/* initialize: dst = src */
for (i = 0; i < 3; ++i)
{
for (j = 0; j < 3; ++j)
{
dst[i][j] = src[i][j];
}
}
/* Compute dst = src^(2^e) mod m */
for (i = 0; i < e; i++)
{
MatMatModM (dst, dst, dst, m);
}
}
//-------------------------------------------------------------------------
/*
/// \ingroup rngimpl
/// Compute the matrix B = (A^n Mod m); works even if A = B.
///
/// \param [in] A Matrix input argument.
/// \param [out] B Matrix output.
/// \param [in] m Modulus.
/// \param [in] n Exponent.
//
void MatPowModM (const double A[3][3], double B[3][3], double m, int32_t n)
{
NS_LOG_FUNCTION (A << B << m << 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;
}
}
*/
/// The transition matrices of the two MRG components
/// (in matrix form), raised to all powers of 2 from 1 to 191
//
struct Precalculated
{
Matrix a1[190]; //!< First component transition matrix powers.
Matrix a2[190]; //!< Second component transition matrix powers.
};
/// Compute the transition matrices of the two MRG components
// raised to all powers of 2 from 1 to 191.
///
/// \returns The precalculated powers of the transition matrices.
//
struct Precalculated PowerOfTwoConstants (void)
{
struct Precalculated precalculated;
for (int i = 0; i < 190; i++)
{
int power = i + 1;
MatTwoPowModM (A1p0, precalculated.a1[i], m1, power);
MatTwoPowModM (A2p0, precalculated.a2[i], m2, power);
}
return precalculated;
}
/// Get the transition matrices raised to a power of 2.
///
/// \param [in] n The power of 2.
/// \param [out] a1p The first transition matrix power.
/// \param [out] a2p The second transition matrix power.
//
void PowerOfTwoMatrix (int n, Matrix a1p, Matrix a2p)
{
static struct Precalculated constants = PowerOfTwoConstants ();
for (int i = 0; i < 3; i ++)
{
for (int j = 0; j < 3; j++)
{
a1p[i][j] = constants.a1[n-1][i][j];
a2p[i][j] = constants.a2[n-1][i][j];
}
}
}
} // end of anonymous namespace
namespace ns3 {
//-------------------------------------------------------------------------
// Generate the next random number.
//
double RngStream::RandU01 ()
{
int32_t k;
double p1, p2, u;
/* Component 1 */
p1 = a12 * m_currentState[1] - a13n * m_currentState[0];
k = static_cast<int32_t> (p1 / m1);
p1 -= k * m1;
if (p1 < 0.0)
{
p1 += m1;
}
m_currentState[0] = m_currentState[1]; m_currentState[1] = m_currentState[2]; m_currentState[2] = p1;
/* Component 2 */
p2 = a21 * m_currentState[5] - a23n * m_currentState[3];
k = static_cast<int32_t> (p2 / m2);
p2 -= k * m2;
if (p2 < 0.0)
{
p2 += m2;
}
m_currentState[3] = m_currentState[4]; m_currentState[4] = m_currentState[5]; m_currentState[5] = p2;
/* Combination */
u = ((p1 > p2) ? (p1 - p2) * norm : (p1 - p2 + m1) * norm);
return u;
}
RngStream::RngStream (uint32_t seedNumber, uint64_t stream, uint64_t substream)
{
if (seedNumber >= m1 || seedNumber >= m2 || seedNumber == 0)
{
NS_FATAL_ERROR ("invalid Seed " << seedNumber);
}
for (int i = 0; i < 6; ++i)
{
m_currentState[i] = seedNumber;
}
AdvanceNthBy (stream, 127, m_currentState);
AdvanceNthBy (substream, 76, m_currentState);
}
RngStream::RngStream(const RngStream& r)
{
for (int i = 0; i < 6; ++i)
{
m_currentState[i] = r.m_currentState[i];
}
}
void
RngStream::AdvanceNthBy (uint64_t nth, int by, double state[6])
{
Matrix matrix1,matrix2;
for (int i = 0; i < 64; i++)
{
int nbit = 63 - i;
int bit = (nth >> nbit) & 0x1;
if (bit)
{
PowerOfTwoMatrix(by + nbit, matrix1, matrix2);
MatVecModM (matrix1, state, state, m1);
MatVecModM (matrix2, &state[3], &state[3], m2);
}
}
}
} // namespace ns3