Random.cpp
/*
* Copyright (C) 2010 Regents of the University of Michigan
*
* 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 should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
//////////////////////////////////////////////////////////////////////////////
// This file includes code derived from the original Mersenne Twister Code
// by Makoto Matsumoto and Takuji Nishimura
// and is subject to their original copyright notice copied below:
//////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////
// COPYRIGHT NOTICE FOR MERSENNE TWISTER CODE
// 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.
//
///////////////////////////////////////////////////////////////////////////////
#include "Random.h"
#include "MathConstant.h"
#include "Error.h"
#include <math.h>
//Constants used internally by Mersenne random number generator
#define MERSENNE_N 624
#define MERSENNE_M 397
// constant vector a
#define MATRIX_A 0x9908b0dfUL
// most significant w-r bits
#define UPPER_MASK 0x80000000UL
// least significant r bits
#define LOWER_MASK 0x7fffffffUL
// Constants used internally by Park-Miller random generator
#define IA 16807
#define IM 2147483647
#define AM (1.0 / IM)
#define IQ 127773
#define IR 2836
#define NTAB 32
#define NDIV (1+(IM-1)/NTAB)
#define RNMX (1.0-EPS)
Random::Random(long s)
{
#ifndef __NO_MERSENNE
mt = new unsigned long [MERSENNE_N];
mti = MERSENNE_N + 1;
mersenneMult = 1.0/4294967296.0;
#else
shuffler = new long [NTAB];
#endif
Reset(s);
}
Random::~Random()
{
#ifndef __NO_MERSENNE
delete [] mt;
#else
delete [] shuffler;
#endif
}
void Random::Reset(long s)
{
normSaved = 0;
#ifndef __NO_MERSENNE
InitMersenne(s);
#else
// 'Continuous' Random Generator
if ((seed = s) < 1)
seed = s == 0 ? 1 : -s; // seed == 0 would be disastrous
for (int j=NTAB+7; j>=0; j--) // Warm up and set shuffle table
{
long k = seed / IQ;
seed = IA * (seed - k * IQ) - IR * k;
if (seed < 0) seed += IM;
if (j < NTAB) shuffler[j] = seed;
}
last=shuffler[0];
#endif
}
// initializes mt[MERSENNE_N] with a seed
void Random::InitMersenne(unsigned long s)
{
mt[0]= s & 0xffffffffUL;
for (mti = 1; mti < MERSENNE_N; mti++)
{
mt[mti] = (1812433253UL * (mt[mti-1] ^(mt[mti-1] >> 30)) + mti);
/* See Knuth TAOCP Vol2. 3rd Ed. P.106 for multiplier. */
/* In the previous versions, MSBs of the seed affect */
/* only MSBs of the array mt[]. */
/* 2002/01/09 modified by Makoto Matsumoto */
mt[mti] &= 0xffffffffUL;
}
}
int Random::Binary()
{
return Next() > 0.5 ? 1 : 0;
}
#ifndef __NO_MERSENNE
double Random::Next()
{
unsigned long y;
// mag01[x] = x * MATRIX_A for x=0,1
static unsigned long mag01[2]={0x0UL, MATRIX_A};
if (mti >= MERSENNE_N)
{
/* generate MERSENNE_N words at one time */
int kk;
// If InitMersenne() has not been called, a default initial seed is used
if (mti == MERSENNE_N+1)
InitMersenne(5489UL);
for (kk=0; kk < MERSENNE_N-MERSENNE_M; kk++)
{
y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
mt[kk] = mt[kk+MERSENNE_M] ^(y >> 1) ^ mag01[y & 0x1UL];
}
for (; kk < MERSENNE_N-1; kk++)
{
y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
mt[kk] = mt[kk+(MERSENNE_M - MERSENNE_N)] ^(y >> 1) ^ mag01[y & 0x1UL];
}
y = (mt[MERSENNE_N-1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
mt[MERSENNE_N-1] = mt[MERSENNE_M-1] ^(y >> 1) ^ mag01[y & 0x1UL];
mti = 0;
}
y = mt[mti++];
// Tempering
y ^= (y >> 11);
y ^= (y << 7) & 0x9d2c5680UL;
y ^= (y << 15) & 0xefc60000UL;
y ^= (y >> 18);
return (mersenneMult *((double) y + 0.5));
}
// Generates a random number on [0,0xffffffff]-interval
unsigned long Random::NextInt()
{
unsigned long y;
// mag01[x] = x * MATRIX_A for x=0,1
static unsigned long mag01[2]={0x0UL, MATRIX_A};
if (mti >= MERSENNE_N)
{
/* generate MERSENNE_N words at one time */
int kk;
// If InitMersenne() has not been called, a default initial seed is used
if (mti == MERSENNE_N + 1)
InitMersenne(5489UL);
for (kk= 0; kk < MERSENNE_N - MERSENNE_M; kk++)
{
y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
mt[kk] = mt[kk+MERSENNE_M] ^(y >> 1) ^ mag01[y & 0x1UL];
}
for (; kk< MERSENNE_N-1; kk++)
{
y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
mt[kk] = mt[kk+(MERSENNE_M - MERSENNE_N)] ^(y >> 1) ^ mag01[y & 0x1UL];
}
y = (mt[MERSENNE_N-1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
mt[MERSENNE_N-1] = mt[MERSENNE_M-1] ^(y >> 1) ^ mag01[y & 0x1UL];
mti = 0;
}
y = mt[mti++];
// Tempering
y ^= (y >> 11);
y ^= (y << 7) & 0x9d2c5680UL;
y ^= (y << 15) & 0xefc60000UL;
y ^= (y >> 18);
return y;
}
#else
double Random::Next()
{
// Compute seed = (IA * seed) % IM without overflows
// by Schrage's method
long k = seed / IQ;
seed = IA * (seed - k * IQ) - IR * k;
if (seed < 0) seed += IM;
// Map to 0..NTAB-1
int j = last/NDIV;
// Output value is shuffler[j], which is in turn replaced by seed
last = shuffler[j];
shuffler[j] = seed;
// Map to 0.0 .. 1.0 excluding endpoints
double temp = AM * last;
if (temp > RNMX) return RNMX;
return temp;
}
unsigned long Random::NextInt()
{
// Compute seed = (IA * seed) % IM without overflows
// by Schrage's method
long k = seed / IQ;
seed = IA * (seed - k * IQ) - IR * k;
if (seed < 0) seed += IM;
// Map to 0..NTAB-1
int j = last/NDIV;
// Output value is shuffler[j], which is in turn replaced by seed
last = shuffler[j];
shuffler[j] = seed;
return last;
}
#endif
double Random::Normal()
{
double v1, v2, fac, rsq;
if (!normSaved) // Do we need new numbers?
{
do
{
v1 = 2.0 * Next() - 1.0; // Pick two coordinates from
v2 = 2.0 * Next() - 1.0; // -1 to +1 and check if they
rsq = v1*v1 + v2*v2; // are in unit circle...
}
while (rsq >= 1.0 || rsq == 0.0);
fac = sqrt(-2.0 * log(rsq)/rsq); // Apply the Box-Muller
normStore = v1 * fac; // transformation and save
normSaved = 1; // one deviate for next time
return v2 * fac;
}
else
{
normSaved = 0;
return normStore;
}
}
void Random::Choose(int * array, int n, int k)
{
int choices = 1, others = 0;
if (k > n / 2)
{
choices = 0;
others = 1;
k = n - k;
}
for (int i = 0; i < n; i++)
array[i] = others;
while (k > 0)
{
int i = NextInt() % n;
if (array[i] == choices) continue;
array[i] = choices;
k--;
}
}
void Random::Choose(int * array, float * weights, int n, int k)
{
int choices = 1, others = 0;
if (k > n / 2)
{
choices = 0;
others = 1;
k = n - k;
}
// First calculate cumulative sums of weights ...
float * cumulative = new float [n + 1];
cumulative[0] = 0;
for (int i = 1; i <= n; i++)
cumulative[i] = cumulative[i - 1] + weights[i - 1];
float & sum = cumulative[n], reject = 0.0;
for (int i = 0; i < n; i++)
array[i] = others;
while (k > 0)
{
float weight = Next() * sum;
int hi = n, lo = 0, i = 0;
while (hi >= lo)
{
i = (hi + lo) / 2;
if (cumulative[i + 1] <= weight)
lo = i + 1;
else if (cumulative[i] >= weight)
hi = i - 1;
else break;
}
if (array[i] == choices) continue;
array[i] = choices;
reject += weights[i];
// After selecting a substantial number of elements, update the cumulative
// distribution -- to ensure that at least half of our samples produce a hit
if (reject > sum * 0.50)
{
cumulative[0] = 0;
for (int i = 1; i <= n; i++)
if (array[i] != choices)
cumulative[i] = cumulative[i - 1] + weights[i - 1];
else
cumulative[i] = cumulative[i - 1];
reject = 0.0;
sum = cumulative[n];
}
k--;
}
delete [] cumulative;
}
Random globalRandom;
Random
Definition: Random.h:73