MersenneTwister.hpp

/*
	Copyright (c) 2009-2010 Christopher A. Taylor.  All rights reserved.

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*/

/*
    Algorithm by Makoto Matsumoto
    http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
*/

#ifndef CAT_MERSENNE_TWISTER_HPP
#define CAT_MERSENNE_TWISTER_HPP

#include "BitMath.hpp"

namespace cat {


// Noncryptographic pseudo-random number generator
class CAT_EXPORT MersenneTwister
{
    static const u32 MEXP = 19937;
    static const u32 N128 = MEXP/128 + 1;
    static const u32 N64 = N128 * 2;
    static const u32 N32 = N128 * 4;
    static const u32 POS1 = 122;
    static const u32 SL1 = 18;
    static const u32 SL2 = 1;
    static const u32 SL2BITS = SL2*8;
    static const u32 SR1 = 11;
    static const u32 SR2 = 1;
    static const u32 SR2BITS = SR2*8;
    static const u32 MSK1 = 0xdfffffefU;
    static const u32 MSK2 = 0xddfecb7fU;
    static const u32 MSK3 = 0xbffaffffU;
    static const u32 MSK4 = 0xbffffff6U;

    struct MT128 {
        u32 u[4];
    };

    MT128 state[19937/128 + 1];
    u32 *state32;
    u32 used;

    CAT_INLINE void shiftLeft128(MT128 *r, MT128 *n, u32 bits);
    CAT_INLINE void shiftRight128(MT128 *r, MT128 *n, u32 bits);

    void enforcePeriod(); // make corrections to ensure that the generator has the full period
    void round(MT128 *a, MT128 *b, MT128 *c, MT128 *d); // a = MTMIX(a,b,c,d)
    void update(); // permute the existing state into a new one

public:
    MersenneTwister();

    bool Initialize(u32 seed);
    bool Initialize(u32 *seeds, u32 words);
    bool Initialize();

    u32 Generate(); // generate a 32-bit number
    void Generate(void *buffer, int bytes); // generate a series of random numbers

	// Generate a 32-bit random number in the range [low..high] inclusive
	u32 GenerateUnbiased(u32 low, u32 high)
	{
		u32 range = high - low;
		if (range == 0) return low;

		// Round range up to the next pow(2)-1
		u32 available = BSR32(range);
		u32 v = (((1 << available) - 1) << 1) | 1;
		available = 32 - available;

		// Generate an unbiased random number in the inclusive range [0..(high-low)]
		u32 x;
		for (u32 trials = 0; trials < 16; ++trials)
		{
			x = Generate();
			u32 y = x;

			u32 count = available;
			while (count--)
			{
				u32 z = y & v;
				if (z <= range) return low + z;
				y >>= 1;
			}
		}

		// Give up on being unbiased because it is taking too long
		return low + (x % (range + 1));
	}

	// Uniform float: [0, 1]
	float Uni() {
		/* ******************************************************************
		   Generates a random floating-point number between -1.0 and
		   1.0. Not sure if this is the best precision possible, but is
		   based on bitwise operations, and I believe it should be faster
		   than using (float)rand()/RAND_MAX.

		   We pick up the number generated by rand, and leave just the bits
		   over the mantissa region. The signal and exponent part are
		   replaced to generate a number between 2.0 and 3.9999999. We
		   then subtract 3.0 to bring the range down to -1.0 and 0.9999999.

		   Coded in 2010-09-24 by Nicolau Werneck <nwerneck@gmail.com>.
		 *************************************************************** */
		static union {
			u32 i;
			f32 f;
		} num;

		num.i = (Generate() & 0x007fffff) | 0x40000000;

		return (num.f - 2.f) / 2.f;
	}

	// Call these functions before the following (not thread-safe)
	static void InitializeNor();
	static void InitializeExp();

	// X~StdNormal: Mean = 0, Var = 1, aX + b -> mean = b, var = a*a
	float Nor();

	// X~StdExp: Mean = 1, kX ~ Exp(1/k)
	float Exp();
};


} // namespace cat

#endif // CAT_MERSENNE_TWISTER_HPP