eoRNG.h

#ifndef EO_RANDOM_NUMBER_GENERATOR
#define EO_RANDOM_NUMBER_GENERATOR

// uint32_t is an unsigned integer type capable of holding 32 bits.
//
// In the applicatione here exactly 32 but should typically be fastest, but 64
// might be better on an Alpha with GCC at -O3 optimization so try your options
// and see what's best for you.
//
// The C99-standard defines uint32_t to be declared in stdint.h, but some
// systmes don't have that and implement it in inttypes.h.
#if (! defined __sun)
#include <stdint.h>
#else
#include <inttypes.h>
#endif

#include <vector>
#include "eoPersistent.h"
#include "eoObject.h"

class eoRng : public eoObject, public eoPersistent
{
public :

    eoRng(uint32_t s)
        : state(0), next(0), left(-1), cached(false), N(624), M(397), K(0x9908B0DFU)
        {
            state = new uint32_t[N+1];
            initialize(2*s);
        }

    ~eoRng(void)
        {
            delete [] state;
        }

    void reseed(uint32_t s)
        {
            initialize(2*s);
        }

    void oldReseed(uint32_t s)
        {
            initialize(s);
        }

    double uniform(double m = 1.0)
        { // random number between [0, m]
            return m * double(rand()) / double(1.0 + rand_max());
        }

    uint32_t random(uint32_t m)
        {
            return uint32_t(uniform() * double(m));
        }

    bool flip(float bias=0.5)
        {
            return uniform() < bias;
        }

    double normal(void);        // gaussian mutation, stdev 1

    double normal(double stdev)
        {
            return stdev * normal();
        }

    double normal(double mean, double stdev)
        {
            return mean + normal(stdev);
        }

    double negexp(double mean)
        {
            return ( -mean*log((double)rand() / rand_max()));
        }

    uint32_t rand();

    uint32_t rand_max(void) const { return uint32_t(0xffffffff); }

    template <typename TYPE>
    int roulette_wheel(const std::vector<TYPE>& vec, TYPE total = 0)
        {
            if (total == 0)
            { // count
                for (unsigned    i = 0; i < vec.size(); ++i)
                    total += vec[i];
            }
            double fortune = uniform() * total;
            int i = 0;
            while (fortune > 0)
            {
                fortune -= vec[i++];
            }
            return --i;
        }


    template <typename TYPE>
    const TYPE& choice(const std::vector<TYPE>& vec) const
        { return vec[random(vec.size())]; }


    template <typename TYPE>
    TYPE& choice(std::vector<TYPE>& vec)
        { return vec[random(vec.size())]; }

    void printOn(std::ostream& _os) const
        {
            for (int i = 0; i < N; ++i)
            {
                _os << state[i] << ' ';
            }
            _os << int(next - state) << ' ';
            _os << left << ' ' << cached << ' ' << cacheValue;
        }

    void readFrom(std::istream& _is)
        {
            for (int i = 0; i < N; ++i)
            {
                _is >> state[i];
            }

            int n;
            _is >> n;
            next = state + n;

            _is >> left;
            _is >> cached;
            _is >> cacheValue;
        }

    std::string className(void) const { return "Mersenne-Twister"; }

private:

    uint32_t restart(void);


    /* @brief Initialize state

    We initialize state[0..(N-1)] via the generator

    <tt>x_new = (69069 * x_old) mod 2^32</tt>

    from Line 15 of Table 1, p. 106, Sec. 3.3.4 of Knuth's _The Art of Computer
    Programming_, Volume 2, 3rd ed.

    Notes (SJC): I do not know what the initial state requirements of the
    Mersenne Twister are, but it seems this seeding generator could be better.
    It achieves the maximum period for its modulus (2^30) iff x_initial is odd
    (p. 20-21, Sec. 3.2.1.2, Knuth); if x_initial can be even, you have
    sequences like 0, 0, 0, ...; 2^31, 2^31, 2^31, ...; 2^30, 2^30, 2^30, ...;
    2^29, 2^29 + 2^31, 2^29, 2^29 + 2^31, ..., etc. so I force seed to be odd
    below.

    Even if x_initial is odd, if x_initial is 1 mod 4 then

    the          lowest bit of x is always 1,
    the  next-to-lowest bit of x is always 0,
    the 2nd-from-lowest bit of x alternates      ... 0 1 0 1 0 1 0 1 ... ,
    the 3rd-from-lowest bit of x 4-cycles        ... 0 1 1 0 0 1 1 0 ... ,
    the 4th-from-lowest bit of x has the 8-cycle ... 0 0 0 1 1 1 1 0 ... ,
    ...

    and if x_initial is 3 mod 4 then

    the          lowest bit of x is always 1,
    the  next-to-lowest bit of x is always 1,
    the 2nd-from-lowest bit of x alternates      ... 0 1 0 1 0 1 0 1 ... ,
    the 3rd-from-lowest bit of x 4-cycles        ... 0 0 1 1 0 0 1 1 ... ,
    the 4th-from-lowest bit of x has the 8-cycle ... 0 0 1 1 1 1 0 0 ... ,
    ...

    The generator's potency (min. s>=0 with (69069-1)^s = 0 mod 2^32) is 16,
    which seems to be alright by p. 25, Sec. 3.2.1.3 of Knuth. It also does well
    in the dimension 2..5 spectral tests, but it could be better in dimension 6
    (Line 15, Table 1, p. 106, Sec. 3.3.4, Knuth).

    Note that the random number user does not see the values generated here
    directly since restart() will always munge them first, so maybe none of all
    of this matters. In fact, the seed values made here could even be
    extra-special desirable if the Mersenne Twister theory says so-- that's why
    the only change I made is to restrict to odd seeds.
    */
    void initialize(uint32_t seed);

    uint32_t* state;

    uint32_t* next;

    int left;

    // for normal distribution
    bool cached;

    float cacheValue;

    const int N;

    const int M;

    const uint32_t K;


    eoRng(const eoRng&);

    eoRng& operator=(const eoRng&);
};



namespace eo
{
    extern eoRng rng;
}
using eo::rng;





// Implementation of some eoRng members.... Don't mind the mess, it does work.


#define hiBit(u)       ((u) & 0x80000000U)   // mask all but highest   bit of u
#define loBit(u)       ((u) & 0x00000001U)   // mask all but lowest    bit of u
#define loBits(u)      ((u) & 0x7FFFFFFFU)   // mask     the highest   bit of u
#define mixBits(u, v)  (hiBit(u)|loBits(v))  // move hi bit of u to hi bit of v

inline void eoRng::initialize(uint32_t seed)
{
    left = -1;

    register uint32_t x = (seed | 1U) & 0xFFFFFFFFU, *s = state;
    register int    j;

    for(left=0, *s++=x, j=N; --j;
        *s++ = (x*=69069U) & 0xFFFFFFFFU);
}



inline uint32_t eoRng::restart(void)
{
    register uint32_t *p0=state, *p2=state+2, *pM=state+M, s0, s1;
    register int    j;

    left=N-1, next=state+1;

    for(s0=state[0], s1=state[1], j=N-M+1; --j; s0=s1, s1=*p2++)
        *p0++ = *pM++ ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0U);

    for(pM=state, j=M; --j; s0=s1, s1=*p2++)
        *p0++ = *pM++ ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0U);

    s1=state[0], *p0 = *pM ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0U);
    s1 ^= (s1 >> 11);
    s1 ^= (s1 <<  7) & 0x9D2C5680U;
    s1 ^= (s1 << 15) & 0xEFC60000U;
    return(s1 ^ (s1 >> 18));
}



inline uint32_t eoRng::rand(void)
{

    uint32_t y;

    if(--left < 0)
        return(restart());

    y  = *next++;
    y ^= (y >> 11);
    y ^= (y <<  7) & 0x9D2C5680U;
    y ^= (y << 15) & 0xEFC60000U;
    return(y ^ (y >> 18));
}



inline double eoRng::normal(void)
{
    if (cached)
    {
        cached = false;
        return cacheValue;
    }

    float rSquare, factor, var1, var2;

    do
    {
        var1 = 2.0 * uniform() - 1.0;
        var2 = 2.0 * uniform() - 1.0;

        rSquare = var1 * var1 + var2 * var2;
    }
    while (rSquare >= 1.0 || rSquare == 0.0);

    factor = sqrt(-2.0 * log(rSquare) / rSquare);

    cacheValue = var1 * factor;
    cached = true;

    return (var2 * factor);
}



namespace eo {
    // a few convenience functions for generating numbers

    template <typename T>
    inline T random(const T& max) {
        return static_cast<T>(rng.uniform() * max); }

    template <typename T>
    inline T random(const T& min, const T& max) {
        return static_cast<T>(rng.uniform() * (max-min)) + min; }

    inline double normal() { return rng.normal(); }
}


#endif


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