MersenneTwister.cpp

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

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#include "MersenneTwister.hpp"
#include <cstring>
using namespace cat;
using namespace std;


MersenneTwister::MersenneTwister()
{
    state32 = &state[0].u[0];
}

// fix the initial state to ensure that the full generator period will occur
void MersenneTwister::enforcePeriod()
{
    static const u32 PARITY[4] = {0x00000001U, 0x00000000U, 0x00000000U, 0x13c9e684U};

    u32 inner = 0;

    // An odd number of parity bits set is OK
    inner ^= state32[0] & PARITY[0];
    inner ^= state32[1] & PARITY[1];
    inner ^= state32[2] & PARITY[2];
    inner ^= state32[3] & PARITY[3];
    inner ^= inner >> 16;
    inner ^= inner >> 8;
    inner ^= inner >> 4;
    inner ^= inner >> 2;
    inner ^= inner >> 1;
    if ((inner & 1)) return;

    // Otherwise, flip the lowest parity bit to make it odd
    for (u32 ii = 0; ii < 4; ++ii)
    {
        if (PARITY[ii])
        {
            state32[ii] ^= CAT_LSB32(PARITY[ii]);
            break;
        }
    }
}

// initialize the generator with a 32-bit seed
bool MersenneTwister::Initialize(u32 seed)
{
    state32[0] = seed;

    for (u32 ii = 1; ii < N32; ++ii)
        state32[ii] = 1812433253UL * (state32[ii-1] ^ (state32[ii-1] >> 30)) + ii;

    enforcePeriod();
    used = N32;

    return true;
}

// initialize with an array of seeds
bool MersenneTwister::Initialize(u32 *seeds, u32 words)
{
    u32 ii, jj, r, count, mid, lag, size = N32;

    if (size >= 623)        lag = 11;
    else if (size >= 68)    lag = 7;
    else if (size >= 39)    lag = 5;
    else                    lag = 3;

    mid = (size - lag) / 2;

    memset(state, 0x8b, sizeof(state));

    if (words+1 > N32)    count = words+1;
    else                count = N32;

#define FUNC1(x) ( ((x) ^ ((x) >> 27)) * (u32)1664525UL )
#define FUNC2(x) ( ((x) ^ ((x) >> 27)) * (u32)1566083941UL )

    r = FUNC1(state32[0]);
    state32[mid] += r;
    r += words;
    state32[mid + lag] += r;
    state32[0] = r;

    --count;
    for (ii = 1, jj = 0; (jj < count) && (jj < words); ++jj)
    {
        r = FUNC1(state32[ii] ^ state32[(ii + mid) % N32] ^ state32[(ii + N32 - 1) % N32]);
        state32[(ii + mid) % N32] += r;
        r += seeds[jj] + ii;
        state32[(ii + mid + lag) % N32] += r;
        state32[ii] = r;
        ++ii;
        ii %= N32;
    }
    for (; jj < count; ++jj)
    {
        r = FUNC1(state32[ii] ^ state32[(ii + mid) % N32] ^ state32[(ii + N32 - 1) % N32]);
        state32[(ii + mid) % N32] += r;
        r += ii;
        state32[(ii + mid + lag) % N32] += r;
        state32[ii] = r;
        ++ii;
        ii %= N32;
    }
    for (jj = 0; jj < N32; ++jj)
    {
        r = FUNC2(state32[ii] + state32[(ii + mid) % N32] + state32[(ii + N32 - 1) % N32]);
        state32[(ii + mid) % N32] ^= r;
        r -= ii;
        state32[(ii + mid + lag) % N32] ^= r;
        state32[ii] = r;
        ++ii;
        ii %= N32;
    }

#undef FUNC1
#undef FUNC2

    enforcePeriod();
    used = N32;

    return true;
}

// r != n, 0 < bits < 32
void MersenneTwister::shiftLeft128(MT128 *r, MT128 *n, u32 bits)
{
    r->u[0] = n->u[0] << bits;
    r->u[1] = (n->u[1] << bits) | (n->u[0] >> (32 - bits)); 
    r->u[2] = (n->u[2] << bits) | (n->u[1] >> (32 - bits)); 
    r->u[3] = (n->u[3] << bits) | (n->u[2] >> (32 - bits)); 
}

// r != n, 0 < bits < 32
void MersenneTwister::shiftRight128(MT128 *r, MT128 *n, u32 bits)
{
    r->u[0] = (n->u[0] >> bits) | (n->u[1] << (32 - bits));
    r->u[1] = (n->u[1] >> bits) | (n->u[2] << (32 - bits));
    r->u[2] = (n->u[2] >> bits) | (n->u[3] << (32 - bits));
    r->u[3] = n->u[3] >> bits; 
}

// a ^= (a << SL2BITS) ^ ((b >> SR1) & MSK) ^ (c >> SR2BITS) ^ (d{0..3} << SL1)
void MersenneTwister::round(MT128 *a, MT128 *b, MT128 *c, MT128 *d)
{
    MT128 x, y;

    shiftLeft128(&x, a, SL2BITS);
    shiftRight128(&y, c, SR2BITS);

    a->u[0] ^= x.u[0] ^ ((b->u[0] >> SR1) & MSK1) ^ y.u[0] ^ (d->u[0] << SL1);
    a->u[1] ^= x.u[1] ^ ((b->u[1] >> SR1) & MSK2) ^ y.u[1] ^ (d->u[1] << SL1);
    a->u[2] ^= x.u[2] ^ ((b->u[2] >> SR1) & MSK3) ^ y.u[2] ^ (d->u[2] << SL1);
    a->u[3] ^= x.u[3] ^ ((b->u[3] >> SR1) & MSK4) ^ y.u[3] ^ (d->u[3] << SL1);
}

// permute the existing state into a new one
void MersenneTwister::update()
{
    MT128 *r1 = state + N128 - 2;
    MT128 *r2 = state + N128 - 1;
    u32 ii;

    for (ii = 0; ii < N128 - POS1; ++ii)
    {
        round(state + ii, state + ii + POS1, r1, r2);
        r1 = r2;
        r2 = state + ii;
    }

    for (; ii < N128; ++ii)
    {
        round(state + ii, state + ii + POS1 - N128, r1, r2);
        r1 = r2;
        r2 = state + ii;
    }

    used = 0;
}

// generate a 32-bit random number
u32 MersenneTwister::Generate()
{
    if (used >= N32)
        update();

    return state32[used++];
}

// generate a series of random numbers to fill a buffer of any size
void MersenneTwister::Generate(void *buffer, int bytes)
{
    u8 *buffer8 = (u8 *)buffer;
    u32 words = bytes / 4;

    while (words > 0)
    {
        if (used >= N32)
            update();

        u32 remaining = N32 - used;
        u32 copying = words;
        if (copying > remaining) copying = remaining;

        memcpy(buffer8, state32 + used, copying*4);
        used += copying;
        words -= copying;
        buffer8 += copying*4;
    }

    switch (bytes % 4)
    {
    case 1:
        buffer8[0] = (u8)Generate();
        break;
    case 2:
        *(u16*)buffer8 = (u16)Generate();
        break;
    case 3:
        words = Generate();
        buffer8[0] = (u8)words;
        *(u16*)(buffer8+1) = (u16)(words >> 8);
        break;
    }
}


#include <cmath>
using namespace std;



#define ZIGNOR_C 128			       /* number of blocks */
#define ZIGNOR_R 3.442619855899	/* start of the right tail */
				   /* (R * phi(R) + Pr(X>=R)) * sqrt(2\pi) */
#define ZIGNOR_V 9.91256303526217e-3
#define M_RAN_INVM32	2.32830643653869628906e-010			  /* 1.0 / 2^32 */
#define ZIGNOR_INVM	M_RAN_INVM32

static u32 s_aiZigRm[ZIGNOR_C];
static double s_adZigXm[ZIGNOR_C + 1];

static void zig32NorInit(s32 iC, double dR, double dV)
{
	s32 i;
	double f, m31 = ZIGNOR_INVM * 2;

	f = exp(-0.5 * dR * dR);
	s_adZigXm[0] = dV / f; /* [0] is bottom block: V / f(R) */
	s_adZigXm[1] = dR;
	s_adZigXm[iC] = 0;

	for (i = 2; i < iC; ++i)
	{
		s_adZigXm[i] = sqrt(-2 * log(dV / s_adZigXm[i - 1] + f));
		f = exp(-0.5 * s_adZigXm[i] * s_adZigXm[i]);
	}
	/* compute ratio and implement scaling */
	for (i = 0; i < iC; ++i)
		s_aiZigRm[i] = (unsigned int)
			( (s_adZigXm[i + 1] / s_adZigXm[i]) / m31 );
	for (i = 0; i <= iC; ++i)
		s_adZigXm[i] *= m31;
}

void MersenneTwister::InitializeNor() {
	zig32NorInit(ZIGNOR_C, ZIGNOR_R, ZIGNOR_V);
}



static unsigned long ke[256];
static float we[256],fe[256];

void MersenneTwister::InitializeExp() {
	const double m2 = 4294967296.;
	double q, de=7.697117470131487, te=de, ve=3.949659822581572e-3;
	int i;

	/* Set up tables for REXP */
	q = ve/exp(-de);
	ke[0]=(de/q)*m2;
	ke[1]=0;

	we[0]=q/m2;
	we[255]=de/m2;

	fe[0]=1.;
	fe[255]=exp(-de);

	for(i=254;i>=1;i--)
	{
		de=-log(ve/de+exp(-de));
		ke[i+1]= (de/te)*m2;
		te=de;
		fe[i]=exp(-de);
		we[i]=de/m2;
	}
}

float MersenneTwister::Nor() {
	u32 i;
	s32 u;
	double x, y, f0, f1;
	
	for (;;)
	{
		u = (s32)Generate();
		i = Generate() & 0x7F;
		s32 abs_u = u < 0 ? -u : u;
		if ((unsigned int)abs_u < s_aiZigRm[i])/* first try the rectangles */
		{
			return u * s_adZigXm[i];
		}
		
		if (i == 0)									/* sample from the tail */
		{
			double x, y;
			do
			{	x = log(Uni()) / ZIGNOR_R;
				y = log(Uni());
			} while (-2 * y < x * x);

			return u < 0 ? x - ZIGNOR_R : ZIGNOR_R - x;
		}

		x = u * s_adZigXm[i];		   /* is this a sample from the wedges? */
		y = 0.5 * s_adZigXm[i] / ZIGNOR_INVM;      f0 = exp(-0.5 * (y * y - x * x) );
		y = 0.5 * s_adZigXm[i + 1] / ZIGNOR_INVM;  f1 = exp(-0.5 * (y * y - x * x) );
      	if (f1 + Generate() * ZIGNOR_INVM * (f0 - f1) < 1.0) {
			return x;
		}
	}
}

float MersenneTwister::Exp() {
	float x;
	u32 jz = Generate();
	u32 iz = jz & 255;

	if (jz < ke[iz]) {
		return jz * we[iz];
	}

	for(;;)
	{
		if(iz==0) {
			return (7.69711-log(Uni()));          /* iz==0 */
		}

		u32 jz = Generate();

		x=jz*we[iz];
		if( fe[iz]+Uni()*(fe[iz-1]-fe[iz]) < exp(-x) ) {
			return x;
		}

		/* initiate, try to exit for(;;) loop */
		jz=Generate();
		iz=(jz&255);
		if(jz<ke[iz]) return (jz*we[iz]);
	}
}