419 lines
12 KiB
C++
419 lines
12 KiB
C++
/****************************************************************************
|
|
* VCGLib o o *
|
|
* Visual and Computer Graphics Library o o *
|
|
* _ O _ *
|
|
* Copyright(C) 2004 \/)\/ *
|
|
* Visual Computing Lab /\/| *
|
|
* ISTI - Italian National Research Council | *
|
|
* \ *
|
|
* All rights reserved. *
|
|
* *
|
|
* 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 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 (http://www.gnu.org/licenses/gpl.txt) *
|
|
* for more details. *
|
|
* *
|
|
****************************************************************************/
|
|
|
|
#ifndef __VCG_RandomGenerator
|
|
#define __VCG_RandomGenerator
|
|
|
|
#include <vcg/math/base.h>
|
|
|
|
namespace vcg {
|
|
namespace math {
|
|
|
|
/**
|
|
* Common interface for random generation (with uniform distribution).
|
|
*
|
|
* Two RNGs are available: Subtractive Ring and an improved Marsenne-Twister.
|
|
*/
|
|
class RandomGenerator
|
|
{
|
|
|
|
// construction
|
|
public:
|
|
|
|
RandomGenerator(){}
|
|
|
|
virtual ~RandomGenerator()
|
|
{}
|
|
|
|
// public methods
|
|
public:
|
|
|
|
/// (Re-)initialize with a given seed.
|
|
virtual void initialize(unsigned int seed)=0;
|
|
|
|
/// Return a random number in the given range (note that not all the RNG can handle a given limit).
|
|
virtual unsigned int generate(unsigned int limit)=0;
|
|
|
|
/// Return a random number in the [0,1) real interval.
|
|
virtual double generate01()=0;
|
|
|
|
/// Returns a random number in the [0,1] real interval.
|
|
virtual double generate01closed()=0;
|
|
|
|
/// Generates a random number in the (0,1) real interval.
|
|
virtual double generate01open()=0;
|
|
virtual double generateRange(double minV, double maxV) { return minV+(maxV-minV)*generate01(); }
|
|
};
|
|
|
|
/**
|
|
* Uniform RNG derived from a STL extension of sgi.
|
|
*
|
|
* It is based on the Subtractive Ring method.
|
|
* This implementation assumes that int is 32 bits.
|
|
*
|
|
* References
|
|
*
|
|
* D. E. Knuth, The Art of Computer Programming. Volume 2: Seminumerical Algorithms, 2nd Edition. Addison-Wesley, 1981.
|
|
* (section 3.6 of Knuth for an implementation of the subtractive method in FORTRAN)
|
|
* (section 3.2.2 of Knuth analyzes this class of algorithms)
|
|
*/
|
|
class SubtractiveRingRNG : public RandomGenerator
|
|
{
|
|
|
|
// private data member
|
|
private:
|
|
|
|
// Subtractive Ring RNG status variables
|
|
unsigned int _M_table[55];
|
|
size_t _M_index1;
|
|
size_t _M_index2;
|
|
|
|
// construction
|
|
public:
|
|
|
|
// ctor
|
|
SubtractiveRingRNG(int default_seed=161803398u)
|
|
{
|
|
initialize(default_seed);
|
|
}
|
|
|
|
virtual ~SubtractiveRingRNG()
|
|
{}
|
|
|
|
// public methods
|
|
public:
|
|
|
|
/// (Re-)initialize with a given seed.
|
|
void initialize(unsigned int seed)
|
|
{
|
|
unsigned int __k = 1;
|
|
_M_table[54] = seed;
|
|
size_t __i;
|
|
for (__i = 0; __i < 54; __i++)
|
|
{
|
|
size_t __ii = (21 * (__i + 1) % 55) - 1;
|
|
_M_table[__ii] = __k;
|
|
__k = seed - __k;
|
|
seed = _M_table[__ii];
|
|
}
|
|
for (int __loop = 0; __loop < 4; __loop++)
|
|
{
|
|
for (__i = 0; __i < 55; __i++)
|
|
_M_table[__i] = _M_table[__i] - _M_table[(1 + __i + 30) % 55];
|
|
}
|
|
_M_index1 = 0;
|
|
_M_index2 = 31;
|
|
}
|
|
|
|
/// Return a random number in the given range (limit) using the Subtractive Ring method.
|
|
unsigned int generate(unsigned int limit= 0xffffffffu)
|
|
{
|
|
_M_index1 = (_M_index1 + 1) % 55;
|
|
_M_index2 = (_M_index2 + 1) % 55;
|
|
_M_table[_M_index1] = _M_table[_M_index1] - _M_table[_M_index2];
|
|
return _M_table[_M_index1] % limit;
|
|
}
|
|
|
|
/// Return a random number in the [0,1) real interval using the Subtractive Ring method.
|
|
double generate01()
|
|
{
|
|
const unsigned int lmt = 0xffffffffu;
|
|
unsigned int number = generate(lmt);
|
|
return static_cast<double>(number) / static_cast<double>(lmt);
|
|
}
|
|
|
|
/// Returns a random number in the [0,1] real interval using the Subtractive Ring method.
|
|
double generate01closed()
|
|
{
|
|
const unsigned int lmt = 0xffffffffu;
|
|
unsigned int number = generate(lmt);
|
|
return static_cast<double>(number) / static_cast<double>(0xfffffffEu);
|
|
}
|
|
|
|
/// Generates a random number in the (0,1) real interval using the Subtractive Ring method.
|
|
double generate01open()
|
|
{
|
|
const unsigned int lmt = 0xffffffffu;
|
|
unsigned int number = generate(lmt);
|
|
return (static_cast<double>(number) + 0.5) * (1.0/static_cast<double>(lmt));
|
|
}
|
|
|
|
};
|
|
|
|
/**
|
|
* The second one is an improved Marsenne-Twister algorithm (MT19937)
|
|
* Coded by Takuji Nishimura and Makoto Matsumoto (see copyright note below)
|
|
* and successively modified to be a C++ class by Daniel Dunbar.
|
|
*
|
|
*
|
|
* References for improved Marsenne-Twister:
|
|
*
|
|
* http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
|
|
*
|
|
*/
|
|
class MarsenneTwisterRNG : public RandomGenerator
|
|
{
|
|
|
|
// definitions
|
|
private:
|
|
|
|
static const int N = 624;
|
|
static const int M = 397;
|
|
static const unsigned int MATRIX_A = 0x9908b0dfu; // constant vector a
|
|
static const unsigned int UPPER_MASK = 0x80000000u; // most significant w-r bits
|
|
static const unsigned int LOWER_MASK = 0x7fffffffu; // least significant r bits
|
|
|
|
// private data member
|
|
private:
|
|
|
|
// Improved Marsenne-Twister RNG status variables
|
|
unsigned int mt[N]; // the array for the state vector
|
|
int mti;
|
|
|
|
// construction
|
|
public:
|
|
|
|
// ctor
|
|
MarsenneTwisterRNG()
|
|
{
|
|
initialize(5489u);
|
|
}
|
|
|
|
MarsenneTwisterRNG(unsigned int seed)
|
|
{
|
|
initialize(seed);
|
|
}
|
|
|
|
virtual ~MarsenneTwisterRNG()
|
|
{}
|
|
|
|
|
|
// public methods
|
|
public:
|
|
|
|
/// (Re-)initialize with the given seed.
|
|
void initialize(unsigned int seed)
|
|
{
|
|
mt[0]= seed & 0xffffffffu;
|
|
for (mti=1; mti<N; mti++)
|
|
{
|
|
mt[mti] = (1812433253u * (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] &= 0xffffffffu;
|
|
/* for >32 bit machines */
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Initialize by an array with array-length.
|
|
*
|
|
* init_key is the array for initializing keys
|
|
* key_length is its length
|
|
*/
|
|
void initializeByArray(unsigned int init_key[], int key_length)
|
|
{
|
|
int i, j, k;
|
|
initialize(19650218u);
|
|
i=1; j=0;
|
|
k = (N>key_length ? N : key_length);
|
|
for (; k; k--)
|
|
{
|
|
mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) * 1664525u)) + init_key[j] + j; /* non linear */
|
|
mt[i] &= 0xffffffffu; /* for WORDSIZE > 32 machines */
|
|
i++; j++;
|
|
|
|
if (i>=N)
|
|
{
|
|
mt[0] = mt[N-1];
|
|
i=1;
|
|
}
|
|
|
|
if (j>=key_length) j=0;
|
|
}
|
|
|
|
for (k=N-1; k; k--)
|
|
{
|
|
mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) * 1566083941u)) - i; /* non linear */
|
|
mt[i] &= 0xffffffffu; /* for WORDSIZE > 32 machines */
|
|
i++;
|
|
if (i>=N)
|
|
{
|
|
mt[0] = mt[N-1];
|
|
i=1;
|
|
}
|
|
}
|
|
|
|
mt[0] = 0x80000000u; /* MSB is 1; assuring non-zero initial array */
|
|
}
|
|
|
|
/**
|
|
* Return a random number in the [0,0xffffffff] interval using the improved Marsenne Twister algorithm.
|
|
*
|
|
* NOTE: Limit is not considered, the interval is fixed.
|
|
*/
|
|
unsigned int generate(unsigned int /*limit*/)
|
|
{
|
|
unsigned int y;
|
|
static unsigned int mag01[2]={0x0u, MATRIX_A};
|
|
/* mag01[x] = x * MATRIX_A for x=0,1 */
|
|
|
|
if (mti >= N) // generate N words at one time
|
|
{
|
|
int kk;
|
|
|
|
for (kk=0;kk<N-M;kk++)
|
|
{
|
|
y = (mt[kk]&UPPER_MASK)|(mt[kk+1]&LOWER_MASK);
|
|
mt[kk] = mt[kk+M] ^ (y >> 1) ^ mag01[y & 0x1u];
|
|
}
|
|
|
|
for (;kk<N-1;kk++)
|
|
{
|
|
y = (mt[kk]&UPPER_MASK)|(mt[kk+1]&LOWER_MASK);
|
|
mt[kk] = mt[kk+(M-N)] ^ (y >> 1) ^ mag01[y & 0x1u];
|
|
}
|
|
|
|
y = (mt[N-1]&UPPER_MASK)|(mt[0]&LOWER_MASK);
|
|
mt[N-1] = mt[M-1] ^ (y >> 1) ^ mag01[y & 0x1u];
|
|
|
|
mti = 0;
|
|
}
|
|
|
|
y = mt[mti++];
|
|
|
|
/* Tempering */
|
|
y ^= (y >> 11);
|
|
y ^= (y << 7) & 0x9d2c5680u;
|
|
y ^= (y << 15) & 0xefc60000u;
|
|
y ^= (y >> 18);
|
|
|
|
return y;
|
|
}
|
|
|
|
/// Returns a random number in the [0,1] real interval using the improved Marsenne-Twister.
|
|
double generate01closed()
|
|
{
|
|
return generate(0)*(1.0/4294967295.0);
|
|
}
|
|
|
|
/// Returns a random number in the [0,1) real interval using the improved Marsenne-Twister.
|
|
double generate01()
|
|
{
|
|
return generate(0)*(1.0/4294967296.0);
|
|
}
|
|
|
|
/// Generates a random number in the (0,1) real interval using the improved Marsenne-Twister.
|
|
double generate01open()
|
|
{
|
|
return (((double)generate(0)) + 0.5)*(1.0/4294967296.0);
|
|
}
|
|
|
|
/// Generate a random triple of baricentric coords
|
|
template <class PointType>
|
|
void generateBarycentric(PointType &p){
|
|
p[1] = this->generate01();
|
|
p[2] = this->generate01();
|
|
|
|
if(p[1] + p[2] > 1.0){
|
|
p[1] = 1.0 - p[1];
|
|
p[2] = 1.0 - p[2];
|
|
}
|
|
p[0]=1.0-(p[1] + p[2]);
|
|
}
|
|
};
|
|
|
|
|
|
/* boxmuller
|
|
* Implements the Polar form of the Box-Muller Transformation
|
|
* (c) Copyright 1994, Everett F. Carter Jr.
|
|
* Permission is granted by the author to use this software for any
|
|
* application provided this copyright notice is preserved.
|
|
*/
|
|
inline double box_muller(RandomGenerator &generator, double m, double s) /* normal random variate generator */
|
|
{ /* mean m, standard deviation s */
|
|
double x1, x2, w, y1;
|
|
static double y2;
|
|
static int use_last = 0;
|
|
static RandomGenerator *last_generator = 0;
|
|
if(last_generator != &generator)
|
|
use_last = 0;
|
|
last_generator = &generator;
|
|
if (use_last){ /* use value from previous call */
|
|
y1 = y2;
|
|
use_last = 0;
|
|
} else {
|
|
do {
|
|
x1 = 2.0 * generator.generate01closed() - 1.0;
|
|
x2 = 2.0 * generator.generate01closed() - 1.0;
|
|
w = x1 * x1 + x2 * x2;
|
|
} while ( w >= 1.0 );
|
|
w = sqrt( (-2.0 * log( w ) ) / w );
|
|
y1 = x1 * w;
|
|
y2 = x2 * w;
|
|
use_last = 1;
|
|
}
|
|
return( m + y1 * s );
|
|
}
|
|
} // end namespace math
|
|
} // end namespace vcg
|
|
|
|
|
|
|
|
/*
|
|
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.
|
|
*/
|
|
|
|
|
|
#endif /* __VCG_RandomGenerator */
|