Random.h

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// Copyright © 2008-2023 Pioneer Developers. See AUTHORS.txt for details
// Licensed under the terms of the GPL v3. See licenses/GPL-3.txt
 
// A deterministic random number generator for use by the rest of the
// engine. It *should* give the same output for a given input regardless
// of the processor architecture. If it doesn't then it needs to be fixed!
 
// Based on: http://www.javamex.com/tutorials/random_numbers/xorshift.shtml
 
#ifndef RAND_H
#define RAND_H
 
#include <assert.h>
#include <cmath>
 
#include "RefCounted.h"
#include "fixed.h"
 
extern "C" {
#include "jenkins/lookup3.h"
}
 
#define PCG_LITTLE_ENDIAN 1
#include "pcg-cpp/pcg_random.hpp"
 
// A deterministic random number generator
class Random : public RefCounted {
    pcg32 mPCG;
 
    // For storing second rand from Normal
    bool cached;
    double z1;
 
public:
    //
    // Constructors
    //
 
    // Construct a new random generator using the given seed
    Random(const Uint32 initialSeed = 0xabcd1234)
    {
        seed(initialSeed);
    }
 
    // Construct a new generator given an array of 32-bit seeds.
    Random(const Uint32 *const seeds, size_t length)
    {
        seed(seeds, length);
    }
 
    // Construct a new random generator from an array of 64-bit
    // seeds.
    Random(const Uint64 *const seeds, size_t length)
    {
        seed(reinterpret_cast<const Uint32 *>(seeds), length * 2);
    }
 
    //
    // Seed functions
    //
 
    // Seed the RNG using the hash of the given array of seeds.
    void seed(const Uint32 *const seeds, size_t length)
    {
        const Uint32 hash = lookup3_hashword(seeds, length, 0);
        mPCG.seed(hash);
        cached = false;
    }
 
    // Seed using an array of 64-bit integers
    void seed(const Uint64 *const seeds, size_t length)
    {
        seed(reinterpret_cast<const Uint32 *>(seeds), length * 2);
    }
 
    // Seed using a single 32-bit integer
    void seed(const Uint32 value)
    {
        seed(&value, 1);
    }
 
    //
    // Number generators.
    //
    // Starting from a given seed value the generator will return the
    // same sequence of numbers. Unless otherwise stated the numbers
    // are 32-bit and each call consumes one
    //
 
    // Get the next integer from the sequence
    // interval [0, 2**32)
    inline Uint32 Int32()
    {
        return mPCG();
    }
 
    // Pick an integer like you're rolling a "choices" sided die,
    // a 6 sided die would return a number between 0 and 5.
    // interval [0, choices)
    inline Uint32 Int32(const int choices)
    {
        return Int32() % choices;
    }
 
    // Pick a number between min and max, inclusive.
    // interval [min, max]
    inline int Int32(const int min, const int max)
    {
        return (Int32() % (1 + max - min)) + min;
    }
 
    // Pick a number in the half open interval [0, 1)
    inline double Double()
    {
        return double(Int32()) * (1. / 4294967296.); // divided by 2^32
    }
 
    // Pick a number in the closed interval [0, 1]
    inline double Double_closed()
    {
        return double(Int32()) * (1. / 4294967295.); // divided by 2^32 - 1
    }
 
    // Pick a number in the open interval (0, 1)
    inline double Double_open()
    {
        return (double(Int32()) + .5) * (1. / 4294967296.); // divided by 2^32
    }
 
    // Pick a 53-bit resolution double in the half open interval [0, 1)
    // This method consumes two 32-bit numbers from the sequence.
    inline double Double53()
    {
        return (double(Int32() >> 5) * 67108864. + double(Int32() >> 6)) * (1. / 9007199254740992.);
    }
 
    // Pick a number in the half-open interval [min, limit)
    inline double Double(double min, double limit)
    {
        return Double(limit - min) + min;
    }
 
    // Pick a number in the half-open interval [0, limit)
    inline double Double(double limit)
    {
        return limit * Double();
    }
 
    // Pick a number between 0 and max inclusive
    // interval [0, max]
    inline double Double_closed(double max)
    {
        return max * Double_closed();
    }
 
    // Pick a number between min and max inclusive
    // interval [min, max]
    inline double Double_closed(double min, double max)
    {
        return Double_closed(max - min) + min;
    }
 
    // interval [0,1)
    inline double NDouble(int p)
    {
        double o = Double(1.0);
        while (--p > 0)
            o *= Double(1.0);
        return o;
    }
 
    // Normal distribution with zero mean, and unit variance
    inline double Normal()
    {
        return Normal(0.0, 1.0);
    }
 
    // Normal distribution with unit variance
    inline double Normal(const double mean)
    {
        return Normal(mean, 1.0);
    }
 
    //Normal (Gauss) distribution
    inline double Normal(const double mean, const double stddev)
    {
        //https://en.wikipedia.org/wiki/Box-Muller_transform#Polar_form
        double u, v, s, z0;
 
        if (cached) {
            z0 = z1;
            cached = false;
        } else {
            do {
                u = Double_closed(-1, 1);
                v = Double_closed(-1, 1);
                s = u * u + v * v;
            } while (s >= 1.0);
 
            s = sqrt((-2.0 * log(s)) / s);
            z0 = u * s;
            z1 = v * s;
            cached = true;
        }
 
        return mean + z0 * stddev;
    }
 
    inline int Poisson(const double lambda)
    {
        int k = 0;
        double p = Double();
        const double target = exp(-lambda);
        while (p > target) {
            k += 1;
            p *= Double();
        }
        return k;
    }
 
    // Pick a fixed-point integer half open interval [0,1)
    inline fixed Fixed()
    {
        return fixed(Int32());
    }
 
    // interval [0,1)
    inline fixed NFixed(int p)
    {
        fixed o = Fixed();
        while (--p > 0)
            o *= Fixed();
        return o;
    }
 
    const pcg32 &GetPCG() const { return mPCG; }
 
private:
    Random(const Random &); // copy constructor not defined
    void operator=(const Random &); // assignment operator not defined
};
 
#endif // RAND_H