PHP Code:
#ifndef RNG_H
#define RNG_H
/***********************************************************************\
*
* File: RngStream.cpp for multiple streams of Random Numbers
* Language: C++
* Copyright: Pierre L’Ecuyer, University of Montreal
* Notice: This code can be used freely for personnal, academic,
* or non-commercial purposes. For commercial purposes,
* please contact P. L’Ecuyer at: [email]lecuyer@iro.umontreal.ca[/email]
* Date: 14 August 2001
*
\***********************************************************************/
#include <cstdlib>
#include <iostream>
#include "RngStream.h"
using namespace std;
namespace
{
const double m1 = 4294967087.0;
const double m2 = 4294944443.0;
const double norm = 1.0 / (m1 + 1.0);
const double a12 = 1403580.0;
const double a13n = 810728.0;
const double a21 = 527612.0;
const double a23n = 1370589.0;
const double two17 = 131072.0;
const double two53 = 9007199254740992.0;
const double fact = 5.9604644775390625e-8; /* 1 / 2^24 */
// 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.
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 }
};
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 }
};
const double A1p0[3][3] = {
{ 0.0, 1.0, 0.0 },
{ 0.0, 0.0, 1.0 },
{ -810728.0, 1403580.0, 0.0 }
};
const double A2p0[3][3] = {
{ 0.0, 1.0, 0.0 },
{ 0.0, 0.0, 1.0 },
{ -1370589.0, 0.0, 527612.0 }
};
const double A1p76[3][3] = {
{ 82758667.0, 1871391091.0, 4127413238.0 },
{ 3672831523.0, 69195019.0, 1871391091.0 },
{ 3672091415.0, 3528743235.0, 69195019.0 }
};
const double A2p76[3][3] = {
{ 1511326704.0, 3759209742.0, 1610795712.0 },
{ 4292754251.0, 1511326704.0, 3889917532.0 },
{ 3859662829.0, 4292754251.0, 3708466080.0 }
};
const double A1p127[3][3] = {
{ 2427906178.0, 3580155704.0, 949770784.0 },
{ 226153695.0, 1230515664.0, 3580155704.0 },
{ 1988835001.0, 986791581.0, 1230515664.0 }
};
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
//
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.
//
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.
//
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.
//
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.
//
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.
//
int CheckSeed (const unsigned long seed[6])
{
int i;
for (i =0;i <3; ++i) {
if (seed[i] >= m1) {
cerr << "****************************************\n\n"
<< "ERROR: Seed[" << i << "] >= 4294967087, Seed is not set."
<< "\n\n****************************************\n\n";
return (-1);
}
}
for (i =3;i <6; ++i) {
if (seed[i] >= m2) {
cerr << "*****************************************\n\n"
<< "ERROR: Seed[" << i << "] >= 4294944443, Seed is not set."
<< "\n\n*****************************************\n\n";
return (-1);
}
}
if (seed[0] == 0 && seed[1] == 0 && seed[2] == 0) {
cerr << "****************************\n\n"
<< "ERROR: First 3 seeds = 0.\n\n"
<< "****************************\n\n";
return (-1);
}
if (seed[3] == 0 && seed[4] == 0 && seed[5] == 0) {
cerr << "****************************\n\n"
<< "ERROR: Last 3 seeds = 0.\n\n"
<< "****************************\n\n";
return (-1);
}
return 0;
}
} // end of anonymous namespace
//-------------------------------------------------------------------------
// Generate the next random number.
//
double RngStream::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 RngStream::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.
//
double RngStream::nextSeed[6] =
{
12345.0, 12345.0, 12345.0, 12345.0, 12345.0, 12345.0
};
//-------------------------------------------------------------------------
// constructor
//
RngStream::RngStream (const char *s) : name (s)
{
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);
}
//-------------------------------------------------------------------------
// Reset Stream to beginning of Stream.
//
void RngStream::ResetStartStream ()
{
for (int i = 0; i < 6; ++i)
Cg[i] = Bg[i] = Ig[i];
}
//-------------------------------------------------------------------------
// Reset Stream to beginning of SubStream.
//
void RngStream::ResetStartSubstream ()
{
for (int i = 0; i < 6; ++i)
Cg[i] = Bg[i];
}
//-------------------------------------------------------------------------
// Reset Stream to NextSubStream.
//
void RngStream::ResetNextSubstream ()
{
MatVecModM(A1p76, Bg, Bg, m1);
MatVecModM(A2p76, &Bg[3], &Bg[3], m2);
for (int i = 0; i < 6; ++i)
Cg[i] = Bg[i];
}
//-------------------------------------------------------------------------
void RngStream::SetPackageSeed (const unsigned long seed[6])
{
if (CheckSeed (seed)) exit (EXIT_FAILURE);
for (int i = 0; i < 6; ++i)
nextSeed[i] = seed[i];
}
//-------------------------------------------------------------------------
void RngStream::SetSeed (const unsigned long seed[6])
{
if (CheckSeed (seed)) exit (EXIT_FAILURE);
for (int i = 0; i < 6; ++i)
Cg[i] = Bg[i] = Ig[i] = seed[i];
}
//-------------------------------------------------------------------------
// if e > 0, let n = 2^e + c;
// if e < 0, let n = -2^(-e) + c;
// if e = 0, let n = c.
// Jump n steps forward if n >0, backwards if n <0.
//
void RngStream::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 RngStream::GetState (unsigned long seed[6]) const
{
for (int i = 0; i < 6; ++i)
seed[i] = static_cast<unsigned long> (Cg[i]);
}
//-------------------------------------------------------------------------
void RngStream::WriteState () const
{
cout << "The current state of the Rngstream";
if (name.size() > 0)
cout <<""<< name;
cout << ":\n Cg ={";
for (int i = 0;i <5; i++) {
cout << static_cast<unsigned long> (Cg [i]) << ", ";
}
cout << static_cast<unsigned long> (Cg [5]) << " }\n\n";
}
//-------------------------------------------------------------------------
void RngStream::WriteStateFull () const
{
int i;
cout << "The RngStream";
if (name.size() > 0)
cout <<""<< name;
cout << ":\n anti = " << (anti ? "true" : "false") << "\n";
cout << " incPrec = " << (incPrec ? "true" : "false") << "\n";
cout << " Ig = { ";
for (i =0;i <5; i++) {
cout << static_cast<unsigned long> (Ig [i]) << ", ";
}
cout << static_cast<unsigned long> (Ig [5]) << " }\n";
cout << " Bg = { ";
for (i =0;i <5; i++) {
cout << static_cast<unsigned long> (Bg [i]) << ", ";
}
cout << static_cast<unsigned long> (Bg [5]) << " }\n";
cout << " Cg = { ";
for (i =0;i <5; i++) {
cout << static_cast<unsigned long> (Cg [i]) << ", ";
}
cout << static_cast<unsigned long> (Cg [5]) << " }\n\n";
}
//-------------------------------------------------------------------------
void RngStream::IncreasedPrecis (bool incp)
{
incPrec = incp;
}
//-------------------------------------------------------------------------
void RngStream::SetAntithetic (bool a)
{
anti = a;
}
//-------------------------------------------------------------------------
// Generate the next random number.
//
double RngStream::RandU01 ()
{
if (incPrec)
return U01d();
else
return U01();
}
//-------------------------------------------------------------------------
// Generate the next random integer.
//
long RngStream::RandInt (long low, long high)
{
return low + static_cast<long> ((high - low + 1) * RandU01 ());
};
//--End of Class Implementation-------------------------------
#endif