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BigFunctions.cpp
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BigFunctions.cpp
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/*
BIGFUNCTIONS.CPP a module for the per pixel calculations of Bignum fractals.
Written in Microsoft Visual 'C++' by Paul de Leeuw.
This program is written in "standard" C. Hardware dependant code
(console drivers & serial I/O) is in separate machine libraries.
*/
#include <math.h>
#include "manp.h"
#include "fractype.h"
#include "Complex.h"
#include "big.h"
#include "BigDouble.h"
#include "BigComplex.h"
#include "pixel.h"
/**************************************************************************
Initialise functions for each pixel
**************************************************************************/
int CPixel::BigInitFunctions(WORD type, BigComplex *zBig, BigComplex *qBig)
{
switch (type)
{
case MANDELFP: // Mandelbrot
case MANDEL: // to handle fractint par files
case JULIA: // to handle fractint par files
case BURNINGSHIP: // Burning Ship
if (!juliaflag)
{
zBig->x = qBig->x + param[0];
zBig->y = qBig->y + param[1];
}
break;
case BURNINGSHIPPOWER: // Burning Ship to higher power
case POWER: // Power
*degree = (int)param[0];
if (*degree < 1)
*degree = 1;
if (!juliaflag)
{
zBig->x = qBig->x + param[1];
zBig->y = qBig->y + param[2];
}
break;
case CUBIC: // Art Matrix Cubic
{
BigComplex tempBig;
switch ((int)param[0])
{
case 0:
subtype = 'B';
break;
case 1:
subtype = 'C';
break;
case 2:
subtype = 'F';
break;
case 3:
subtype = 'K';
break;
default:
subtype = 'B';
break;
}
if ((int)param[1] < 0)
special = 0;
else
special = (int)param[1];
period_level = FALSE; // no periodicity checking
if (subtype == 'B') // CBIN
{
t3Big = *qBig * 3.0; // T3 = 3*T
t2Big = qBig->CSqr(); // T2 = T*T
aBig = (t2Big + 1.0) / t3Big; // A = (T2 + 1)/T3
// B = 2*A*A*A + (T2 - 2)/T3
tempBig = aBig.CCube(); // A*A*A
tempBig = tempBig.CDouble(); // 2*A*A*A
bBig = (t2Big - 2.0) / t3Big + tempBig; // B = 2*A*A*A + (T2 - 2)/T3
}
else if (subtype == 'C' || subtype == 'F') // CCIN or CFIN
{
aBig = *qBig; // A = T
// find B = T + 2*T*T*T
tempBig = qBig->CCube(); // B = T*T*T
if (subtype == 'C')
bBig = tempBig.CDouble() + *qBig; // B = B * 2 + T
else
{
bBig = (tempBig - *qBig); // B = B - T
bBig = bBig.CDouble(); // B = B * 2 - 2 * T
a2Big = aBig.CDouble();
}
}
else if (subtype == 'K') // CKIN
{
aBig = 0;
vBig = 0;
bBig = *qBig; // B = T
}
aa3Big = aBig.CSqr()*3.0; // AA3 = A*A*3
if (!juliaflag)
*zBig = -aBig; // Z = -A
}
break;
case SPECIALNEWT: // Art Matrix Newton
l2Big = qBig->CSqr();
aBig = -l2Big + 0.25;
bBig = -(l2Big + 0.75);
lm5Big = *qBig - 0.5;
lp5Big = *qBig + 0.5;
break;
case MATEIN: // Art Matriuc Matein fractal
{
period_level = FALSE; // no periodicity checking
double one = 1.0;
if ((absolute = qBig->CSumSqr()) > one)
return(-1); // not inside set
zBig->x = 1.0;
zBig->y = 0.0;
/* DO 300 I = 1,100 */
/* 300 Z = L*(Z + 1/Z) */
for (int i = 0; i < 100; ++i)
*zBig = (*zBig + zBig->CInvert()) * *qBig;
distance = 1.0; // D = 1
ozBig = zBig->CInvert(); // OZ = 1/Z
break;
}
case SINFRACTAL: // Sine
if (!juliaflag)
{
BigDouble BigPi;
mpfr_const_pi(BigPi.x, MPFR_RNDN);
// zBig.x = PI / 2.0; // dz_real = HALF_PI;
// zBig->x = BigPi / 2.0; // dz_real = HALF_PI;
zBig->x = param[3];
zBig->y = 0.0;
}
break;
case REDSHIFTRIDER: // RedShiftRider a*z^2 +/- z^n + c
aBig.x = param[0];
aBig.y = param[1];
*degree = (WORD)param[2];
if (!juliaflag)
{
zBig->x = qBig->x + param[3];
zBig->y = qBig->y + param[4];
}
break;
case TALIS: // Talis Power Z = Z^N/(M + Z^(N-1)) + C
*degree = (int)param[0];
if (*degree < 1)
*degree = 1;
if (!juliaflag)
{
zBig->x = qBig->x + param[2];
zBig->y = qBig->y + param[3];
}
break;
case POLYNOMIAL:
if (!juliaflag)
{
zBig->x = qBig->x + param[0];
zBig->y = qBig->y + param[1];
}
for (int i = 0; i < MAXPOLYDEG; i++) // find highest order of polynomial for use with fwd diff calcs
{
if (param[2 + i] != 0.0)
{
fractalspecific[type].SlopeDegree = MAXPOLYDEG - i;
break;
}
}
break;
case MANDELDERIVATIVES: // a group of Mandelbrot Derivatives
BigInitManDerFunctions(subtype, zBig, qBig);
break;
case TIERAZON: // a group of Mandelbrot Derivatives
BigInitTierazonFunctions(subtype, zBig, qBig);
break;
}
return 0;
}
/**************************************************************************
Run functions for each iteration
**************************************************************************/
int CPixel::BigRunFunctions(WORD type, BigComplex *zBig, BigComplex *qBig, BYTE *SpecialFlag, long *iteration)
{
switch (type)
{
case MANDELFP: // Mandelbrot
case MANDEL: // to handle fractint par files
case JULIA: // to handle fractint par files
{
BigDouble t, realimagBig;
BigComplex sqrBig;
// use direct function calls for Mandelbrot for speed. Approx 10 - 15 % faster.
mpfr_mul(realimagBig.x, zBig->x.x, zBig->y.x, MPFR_RNDN);
mpfr_mul(sqrBig.x.x, zBig->x.x, zBig->x.x, MPFR_RNDN);
mpfr_mul(sqrBig.y.x, zBig->y.x, zBig->y.x, MPFR_RNDN);
mpfr_sub(t.x, sqrBig.x.x, sqrBig.y.x, MPFR_RNDN);
mpfr_add(zBig->x.x, qBig->x.x, t.x, MPFR_RNDN);
mpfr_add(t.x, realimagBig.x, qBig->y.x, MPFR_RNDN);
mpfr_add(zBig->y.x, realimagBig.x, t.x, MPFR_RNDN);
mpfr_add(t.x, sqrBig.x.x, sqrBig.y.x, MPFR_RNDN);
return (mpfr_cmp(t.x, BigBailout.x) > 0);
}
case BURNINGSHIP: // Burning Ship
{
BigDouble t, realimagBig;
BigComplex sqrBig;
sqrBig.x = zBig->x.BigSqr();
sqrBig.y = zBig->y.BigSqr();
t = zBig->x * zBig->y;
realimagBig = t.BigAbs();
zBig->x = qBig->x + sqrBig.x - sqrBig.y;
zBig->y = realimagBig + realimagBig - qBig->y;
return (sqrBig.x + sqrBig.y > BigBailout);
}
case BURNINGSHIPPOWER: // Burning Ship to higher power
zBig->x = zBig->x.BigAbs();
zBig->y = -zBig->y.BigAbs();
*zBig = *qBig + zBig->CPolynomial(*degree);
return (zBig->x.BigSqr() + zBig->y.BigSqr() > BigBailout);
case POWER: // Power
*zBig = *qBig + zBig->CPolynomial(*degree);
return (zBig->CSumSqr() > rqlim);
// return (zBig->x.BigSqr() + zBig->y.BigSqr() > BigBailout);
case CUBIC: // Art Matrix Cubic
{
BigComplex tempBig;
if (subtype == 'K') // CKIN
*zBig = zBig->CCube() + bBig; // Z = Z*Z*Z + B
else // Z = Z*Z*Z - AA3*Z + B
{
tempBig = zBig->CCube() + bBig; // Z = Z*Z*Z + B
*zBig = tempBig - aa3Big * *zBig; // Z = Z*Z*Z - AA3*Z + B
}
if (zBig->CSumSqr() >= 100.0)
return (TRUE);
else
{
if (subtype == 'F')
{
if (qBig->CSumSqr() <= 0.111111)
{
*iteration = special;
*SpecialFlag = TRUE; // for decomp and biomorph
return (TRUE);
}
vBig = *zBig + a2Big;
}
else if (subtype == 'K')
vBig = *zBig - vBig;
else
vBig = *zBig - aBig;
if (vBig.CSumSqr() <= 0.000001)
{
*iteration = special;
*SpecialFlag = TRUE; // for decomp and biomorph
return (TRUE);
}
}
return(FALSE);
}
case SPECIALNEWT: // Art Matrix Newton
{
BigComplex z2Big;
z2Big = zBig->CSqr();
temp1Big = z2Big * zBig->CDouble() + aBig;
temp2Big = z2Big * 3.0 + bBig;
*zBig = temp1Big / temp2Big;
vBig = *zBig - 1.0;
if (vBig.CSumSqr() <= 0.000001)
{
phaseflag = 0; // first phase
return(TRUE);
}
// v_real = dz_real - lm5_real;
vBig = *zBig - lm5Big; // v_imag = dz_imag - lm5_imag;
if (vBig.CSumSqr() <= 0.000001)
{
phaseflag = 1; // second phase
return(TRUE);
}
// v_real = dz_real + lp5_real;
vBig = *zBig + lp5Big; // v_imag = dz_imag + lp5_imag;
if (vBig.CSumSqr() <= 0.000001)
{
phaseflag = 2; // third phase
return(TRUE);
}
return(FALSE);
}
case MATEIN: // Art Matriuc Matein fractal
{
double epsilon = 0.01;
double escape = 10.0E20;
BigComplex t;
*zBig = *qBig * (*zBig + ozBig); // Z = L*(Z + OZ)
ozBig = zBig->CInvert(); // OZ = 1/Z
t = -ozBig / *zBig; // T = 1 - OZ/Z
t.x = t.x + 1.0;
// D = D*ABSL*(REAL(T)*REAL(T) + IMAG(T)*IMAG(T))
distance = distance * absolute * t.CSumSqr();
if (distance <= epsilon)
{
phaseflag = 0; // first phase
return(TRUE);
}
if (distance > escape)
{
phaseflag = 1; // second phase
return(TRUE);
}
return(FALSE);
}
case SINFRACTAL: // Sine
{
BigDouble a, b;
if (param[2] == 0.0)
*zBig = *qBig * zBig->CSin();
else
*zBig = *qBig + zBig->CSin();
a = 80.0;
b = -80.0;
if (zBig->x > a || zBig->x < b || zBig->y > a || zBig->y < b)
return(TRUE);
return(FALSE);
}
case EXPFRACTAL: // Exponential
{
int compare;
BigDouble a, b;
*zBig = *qBig * zBig->CExp(); // Z = L*EXP(Z)
a = 10.0;
b = -10.0;
switch (subtype)
{
case 'R':
compare = (zBig->x > a);
break;
case 'I':
compare = (zBig->y > a);
break;
case 'M':
compare = (zBig->x > a || zBig->x < b || zBig->y > a || zBig->y < b);
break;
default:
compare = (zBig->x > a);
break;
}
if (compare)
return(TRUE);
return(FALSE);
}
case REDSHIFTRIDER: // RedShiftRider a*z^2 +/- z^n + c
*zBig = aBig * *zBig * *zBig + zBig->CPolynomial(*degree) * ((param[5] == 1.0) ? 1.0 : -1.0);
*zBig = *zBig + *qBig;
return (zBig->CSumSqr() > rqlim);
case TALIS: // Talis Power Z = Z^N/(M + Z^(N-1)) + C
{
double m;
BigComplex z1;
m = param[1];
z1 = zBig->CPolynomial(*degree - 1);
*zBig = (z1 * *zBig) / (z1 + m) + *qBig;
return (zBig->CSumSqr() > rqlim);
}
case POLYNOMIAL: // Polynomial
{
BigComplex InitialZ = *zBig;
BigComplex FinalZ = { 0.0, 0.0 };
for (int m = 0; m < MAXPOLYDEG; m++)
{
BigComplex BigComplexTemp = InitialZ;
if (param[2 + m] != 0.0)
{
for (int k = 0; k < MAXPOLYDEG - m - 1; k++)
BigComplexTemp *= InitialZ;
FinalZ += (BigComplexTemp * param[2 + m]);
}
}
*zBig = FinalZ + *qBig;
return (zBig->CSumSqr() >= rqlim);
}
case MANDELDERIVATIVES: // a group of Mandelbrot Derivatives
return (BigRunManDerFunctions(subtype, zBig, qBig, SpecialFlag, iteration));
case TIERAZON: // a group of Mandelbrot Derivatives
return (BigRunTierazonFunctions(subtype, zBig, qBig, SpecialFlag, iteration));
}
return 0;
}