randomstream.h

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/******************************************************************************
 *
 * MantaFlow fluid solver framework
 * Copyright 2011 Tobias Pfaff, Nils Thuerey 
 *
 * This program is free software, distributed under the terms of the
 * GNU General Public License (GPL) 
 * http://www.gnu.org/licenses
 *
 * Random numbers
 *
 * Based on GPL code by Makoto Matsumoto, Takuji Nishimura, and Shawn Cokus
 * Richard J. Wagner  v0.5  7 November 2000  rjwagner@writeme.com
 *
 ******************************************************************************/

#ifndef _RANDOMSTREAM_H
#define _RANDOMSTREAM_H 

namespace Manta {

#include <iostream>
#include <stdio.h>
#include <time.h>
#include "vectorbase.h"

class MTRand {
    // Data
    public:
        typedef unsigned long uint32;  // unsigned integer type, at least 32 bits

        enum { N = 624 };       // length of state vector
        enum { SAVE = N + 1 };  // length of array for save()

    protected:
        enum { M = 397 };  // period parameter

        uint32 state[N];   // internal state
        uint32 *pNext;     // next value to get from state
        int left;          // number of values left before reload needed


        //Methods
    public:
        MTRand( const uint32& oneSeed );  // initialize with a simple uint32
        MTRand( uint32 *const bigSeed, uint32 const seedLength = N );  // or an array
        MTRand();  // auto-initialize with /dev/urandom or time() and clock()

        // Do NOT use for CRYPTOGRAPHY without securely hashing several returned
        // values together, otherwise the generator state can be learned after
        // reading 624 consecutive values.

        // Access to 32-bit random numbers
        double rand();                          // real number in [0,1]
        double rand( const double& n );         // real number in [0,n]
        double randExc();                       // real number in [0,1)
        double randExc( const double& n );      // real number in [0,n)
        double randDblExc();                    // real number in (0,1)
        double randDblExc( const double& n );   // real number in (0,n)
        uint32 randInt();                       // integer in [0,2^32-1]
        uint32 randInt( const uint32& n );      // integer in [0,n] for n < 2^32
        double operator()() { return rand(); }  // same as rand()

        // Access to 53-bit random numbers (capacity of IEEE double precision)
        double rand53();  // real number in [0,1)

        // Access to nonuniform random number distributions
        double randNorm( const double& mean = 0.0, const double& variance = 1.0 );

        // Re-seeding functions with same behavior as initializers
        void seed( const uint32 oneSeed );
        void seed( uint32 *const bigSeed, const uint32 seedLength = N );
        void seed();

        // Saving and loading generator state
        void save( uint32* saveArray ) const;  // to array of size SAVE
        void load( uint32 *const loadArray );  // from such array
        friend std::ostream& operator<<( std::ostream& os, const MTRand& mtrand );
        friend std::istream& operator>>( std::istream& is, MTRand& mtrand );

    protected:
        void initialize( const uint32 oneSeed );
        void reload();
        uint32 hiBit( const uint32& u ) const { return u & 0x80000000UL; }
        uint32 loBit( const uint32& u ) const { return u & 0x00000001UL; }
        uint32 loBits( const uint32& u ) const { return u & 0x7fffffffUL; }
        uint32 mixBits( const uint32& u, const uint32& v ) const { 
            return hiBit(u) | loBits(v); 
        }
        uint32 twist( const uint32& m, const uint32& s0, const uint32& s1 ) const { 
            return m ^ (mixBits(s0,s1)>>1) ^ (-loBit(s1) & 0x9908b0dfUL); 
        }
        static uint32 hash( time_t t, clock_t c );
};


inline MTRand::MTRand( const uint32& oneSeed )
    { seed(oneSeed); }

inline MTRand::MTRand( uint32 *const bigSeed, const uint32 seedLength )
    { seed(bigSeed,seedLength); }

inline MTRand::MTRand()
    { seed(); }

inline double MTRand::rand()
    { return double(randInt()) * (1.0/4294967295.0); }

inline double MTRand::rand( const double& n )
    { return rand() * n; }

inline double MTRand::randExc()
    { return double(randInt()) * (1.0/4294967296.0); }

inline double MTRand::randExc( const double& n )
    { return randExc() * n; }

inline double MTRand::randDblExc()
    { return ( double(randInt()) + 0.5 ) * (1.0/4294967296.0); }

inline double MTRand::randDblExc( const double& n )
    { return randDblExc() * n; }

inline double MTRand::rand53()
{
    uint32 a = randInt() >> 5, b = randInt() >> 6;
    return ( a * 67108864.0 + b ) * (1.0/9007199254740992.0);  // by Isaku Wada
}

inline double MTRand::randNorm( const double& mean, const double& variance )
{
    // Return a real number from a normal (Gaussian) distribution with given
    // mean and variance by Box-Muller method
    double r = sqrt( -2.0 * log( 1.0-randDblExc()) ) * variance;
    double phi = 2.0 * 3.14159265358979323846264338328 * randExc();
    return mean + r * cos(phi);
}

inline MTRand::uint32 MTRand::randInt()
{
    // Pull a 32-bit integer from the generator state
    // Every other access function simply transforms the numbers extracted here
    
    if( left == 0 ) reload();
    --left;
        
    uint32 s1;
    s1 = *pNext++;
    s1 ^= (s1 >> 11);
    s1 ^= (s1 <<  7) & 0x9d2c5680UL;
    s1 ^= (s1 << 15) & 0xefc60000UL;
    return ( s1 ^ (s1 >> 18) );
}

inline MTRand::uint32 MTRand::randInt( const uint32& n )
{
    // Find which bits are used in n
    // Optimized by Magnus Jonsson (magnus@smartelectronix.com)
    uint32 used = n;
    used |= used >> 1;
    used |= used >> 2;
    used |= used >> 4;
    used |= used >> 8;
    used |= used >> 16;
    
    // Draw numbers until one is found in [0,n]
    uint32 i;
    do
        i = randInt() & used;  // toss unused bits to shorten search
    while( i > n );
    return i;
}


inline void MTRand::seed( const uint32 oneSeed )
{
    // Seed the generator with a simple uint32
    initialize(oneSeed);
    reload();
}


inline void MTRand::seed( uint32 *const bigSeed, const uint32 seedLength )
{
    // Seed the generator with an array of uint32's
    // There are 2^19937-1 possible initial states.  This function allows
    // all of those to be accessed by providing at least 19937 bits (with a
    // default seed length of N = 624 uint32's).  Any bits above the lower 32
    // in each element are discarded.
    // Just call seed() if you want to get array from /dev/urandom
    initialize(19650218UL);
    const unsigned int Nenum = N;
    int i = 1;
    uint32 j = 0;
    int k = ( Nenum > seedLength ? Nenum : seedLength );
    for( ; k; --k )
    {
        state[i] =
            state[i] ^ ( (state[i-1] ^ (state[i-1] >> 30)) * 1664525UL );
        state[i] += ( bigSeed[j] & 0xffffffffUL ) + j;
        state[i] &= 0xffffffffUL;
        ++i;  ++j;
        if( i >= N ) { state[0] = state[N-1];  i = 1; }
        if( j >= seedLength ) j = 0;
    }
    for( k = N - 1; k; --k )
    {
        state[i] =
            state[i] ^ ( (state[i-1] ^ (state[i-1] >> 30)) * 1566083941UL );
        state[i] -= i;
        state[i] &= 0xffffffffUL;
        ++i;
        if( i >= N ) { state[0] = state[N-1];  i = 1; }
    }
    state[0] = 0x80000000UL;  // MSB is 1, assuring non-zero initial array
    reload();
}


inline void MTRand::seed()
{
    // Seed the generator with an array from /dev/urandom if available
    // Otherwise use a hash of time() and clock() values
    
    // First try getting an array from /dev/urandom
    FILE* urandom = fopen( "/dev/urandom", "rb" );
    if( urandom )
    {
        uint32 bigSeed[N];
        uint32 *s = bigSeed;
        int i = N;
        bool success = true;
        while( success && i-- )
            success = fread( s++, sizeof(uint32), 1, urandom );
        fclose(urandom);
        if( success ) { seed( bigSeed, N );  return; }
    }
    
    // Was not successful, so use time() and clock() instead
    seed( hash( time(NULL), clock() ) );
}


inline void MTRand::initialize( const uint32 intseed )
{
    // Initialize generator state with seed
    // See Knuth TAOCP Vol 2, 3rd Ed, p.106 for multiplier.
    // In previous versions, most significant bits (MSBs) of the seed affect
    // only MSBs of the state array.  Modified 9 Jan 2002 by Makoto Matsumoto.
    uint32 *s = state;
    uint32 *r = state;
    int i = 1;
    *s++ = intseed & 0xffffffffUL;
    for( ; i < N; ++i )
    {
        *s++ = ( 1812433253UL * ( *r ^ (*r >> 30) ) + i ) & 0xffffffffUL;
        r++;
    }
}


inline void MTRand::reload()
{
    // Generate N new values in state
    // Made clearer and faster by Matthew Bellew (matthew.bellew@home.com)
    uint32 *p = state;
    int i;
    for( i = N - M; i--; ++p )
        *p = twist( p[M], p[0], p[1] );
    for( i = M; --i; ++p )
        *p = twist( p[M-N], p[0], p[1] );
    *p = twist( p[M-N], p[0], state[0] );

    left = N, pNext = state;
}


inline MTRand::uint32 MTRand::hash( time_t t, clock_t c )
{
    // Get a uint32 from t and c
    // Better than uint32(x) in case x is floating point in [0,1]
    // Based on code by Lawrence Kirby (fred@genesis.demon.co.uk)

    static uint32 differ = 0;  // guarantee time-based seeds will change

    uint32 h1 = 0;
    unsigned char *p = (unsigned char *) &t;
    for( size_t i = 0; i < sizeof(t); ++i )
    {
        h1 *= std::numeric_limits<unsigned char>::max() + 2U;
        h1 += p[i];
    }
    uint32 h2 = 0;
    p = (unsigned char *) &c;
    for( size_t j = 0; j < sizeof(c); ++j )
    {
        h2 *= std::numeric_limits<unsigned char>::max() + 2U;
        h2 += p[j];
    }
    return ( h1 + differ++ ) ^ h2;
}


inline void MTRand::save( uint32* saveArray ) const
{
    uint32 *sa = saveArray;
    const uint32 *s = state;
    int i = N;
    for( ; i--; *sa++ = *s++ ) {}
    *sa = left;
}


inline void MTRand::load( uint32 *const loadArray )
{
    uint32 *s = state;
    uint32 *la = loadArray;
    int i = N;
    for( ; i--; *s++ = *la++ ) {}
    left = *la;
    pNext = &state[N-left];
}


inline std::ostream& operator<<( std::ostream& os, const MTRand& mtrand )
{
    const MTRand::uint32 *s = mtrand.state;
    int i = mtrand.N;
    for( ; i--; os << *s++ << "\t" ) {}
    return os << mtrand.left;
}


inline std::istream& operator>>( std::istream& is, MTRand& mtrand )
{
    MTRand::uint32 *s = mtrand.state;
    int i = mtrand.N;
    for( ; i--; is >> *s++ ) {}
    is >> mtrand.left;
    mtrand.pNext = &mtrand.state[mtrand.N-mtrand.left];
    return is;
}

// simple interface to mersenne twister
class RandomStream
{
public:
    inline RandomStream(long seed) : mtr(seed) {} ;
    ~RandomStream() {}

    inline double getDouble( void ) { return mtr.rand(); };
    inline float  getFloat ( void ) { return (float)mtr.rand(); };

    inline float  getFloat( float min, float max ) { return mtr.rand(max-min) + min; };
    inline float  getRandNorm( float mean, float var) { return mtr.randNorm(mean, var); };

    #if FLOATINGPOINT_PRECISION==1
    inline Real getReal()           { return getFloat(); }

    #else
    inline Real getReal()           { return getDouble(); }
    #endif

    inline Vec3   getVec3 ()        { Real a=getReal(), b=getReal(), c=getReal(); return Vec3(a,b,c); }
    inline Vec3   getVec3Norm ()    { Vec3 a=getVec3(); normalize(a); return a; }

private: 
    MTRand mtr; 
};


} // namespace

#endif