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BigPixel.cpp
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BigPixel.cpp
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/*
BigPixel.cpp a module for the per pixel calculations of fractals using BigNums.
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 <stdio.h>
#include "manp.h"
#include "colour.h"
#include "big.h"
#include "fractype.h"
#include "fractalp.h"
#include "complex.h"
#include "filter.h"
#include "BigDouble.h"
#include "BigComplex.h"
#include "pixel.h"
#include "Potential.h"
/**************************************************************************
Initialise fractal
**************************************************************************/
int CPixel::init_big_fractal(void)
{
BOOL IsBig = FALSE;
int i;
for (i = 0; BigFractalSpecific[i].big_calctype; i++)
if (type == BigFractalSpecific[i].type) // check the list of "allowed" fractals.
{
BigFractPtr = i;
IsBig = TRUE;
break;
}
if (!IsBig)
return -1;
if (type == EXPFRACTAL) // there's no initialisation for exp()
return 0;
if (fractalspecific[type].flags & FUNCTIONINPIXEL)
return(BigInitFunctions(type, zBig, qBig));
else if (BigFractalSpecific[BigFractPtr].big_per_pixel() < 0)
return -1;
return 0;
}
/**************************************************************************
Run fractal
**************************************************************************/
int CPixel::run_big_fractal(void)
{
if (fractalspecific[type].flags & FUNCTIONINPIXEL)
return(BigRunFunctions(type, zBig, qBig, &SpecialFlag, iteration));
else
return BigFractalSpecific[BigFractPtr].big_calctype();
}
/**************************************************************************
Filter
**************************************************************************/
int CPixel::DoBigFilter(int method, int hooper)
{
double magnitude = 0.0;
BigDouble temp;
CPotential Pot;
if (colours == 256 && decomp > 0)
*iteration = BigDecomposition(zBig->x, zBig->y);
else if (logval)
*iteration = (BYTE) (*(logtable + (*iteration % MAXTHRESHOLD)));
else
{
switch (method)
{
case EPSCROSS:
if (hooper == 1)
*iteration = special;
else if (hooper == 2)
*iteration = (special << 1);
break;
// these options by Richard Hughes modified by TW
// Add 7 to overcome negative values on the MANDEL
case REAL: // "real"
*iteration += zBig->x.BigDoubleToInt() + 7L;
break;
case IMAG: // "imag"
*iteration += zBig->y.BigDoubleToInt() + 7L;
break;
case MULT: // "mult"
temp = 0.0;
if (!(temp == zBig->y))
{
temp = zBig->x / zBig->y;
*iteration = (long)((double)(*iteration) * temp.BigDoubleToDouble());
}
break;
case SUM: // "sum"
temp = zBig->x + zBig->y;
*iteration += temp.BigDoubleToInt();
break;
case ATAN: // "atan"
mpfr_atan2(temp.x, zBig->y.x, zBig->x.x, MPFR_RNDN);
*iteration = (long)fabs(temp.BigDoubleToDouble()*180.0 / PI);
break;
case POTENTIAL:
magnitude = zBig->CSumSqr();
*iteration = Pot.potential(magnitude, *iteration, threshold, TrueCol, colors, potparam);
break;
}
}
return 0;
}
/**************************************************************************
Get Float Iteration per pixel
**************************************************************************/
void CPixel::CalcBigFloatIteration(double error, double *wpixels, int row, int col, BigComplex z, BigComplex OldZ, BigComplex OlderZ)
{
double log_zn, nu, t;
int SlopeDegree, BailoutType;
BigDouble BigTemp, BigTemp1, LogA, LogB;
if (FloatIteration < threshold)
{
DWORD index;
BigComplex a, b;
if (type == 204) // Tierazon
{
SlopeDegree = (TierazonSpecific[subtype].SlopeDegree == -1) ? *degree : TierazonSpecific[subtype].SlopeDegree;
BailoutType = TierazonSpecific[subtype].BailoutType;
}
else if (type == 228) // Mandel derivatives
{
SlopeDegree = (MandelDerivSpecific[subtype].SlopeDegree == -1) ? *degree : MandelDerivSpecific[subtype].SlopeDegree;
BailoutType = MandelDerivSpecific[subtype].BailoutType;
}
else
{
SlopeDegree = (fractalspecific[type].SlopeDegree == -1) ? *degree : fractalspecific[type].SlopeDegree;
BailoutType = fractalspecific[type].BailoutType;
}
switch (BailoutType)
{
case ESCAPING:
{
BigTemp = zBig->x * zBig->x + zBig->y * zBig->y;
// BigTemp1 = BigTemp.BigLog();
// log_zn = mpfr_get_d(BigTemp1.x, MPFR_RNDN) / SlopeDegree;
double t = mpfr_get_d(BigTemp.x, MPFR_RNDN);
log_zn = log(t) / SlopeDegree;
nu = log(log_zn / log(SlopeDegree)) / log(SlopeDegree);
FloatIteration = FloatIteration + 1 - nu;
}
break;
/*
case ESCAPING1:
log_zn = log(sqr(rqlim)) - log(OldZ.x * OldZ.x + OldZ.y * OldZ.y); // escape method 1 (page 24 Fractal-Zoomer Algorithms.docx)
t = log(z.x * z.x + z.y * z.y) - log(OldZ.x * OldZ.x + OldZ.y * OldZ.y);
nu = log_zn / t;
FloatIteration = FloatIteration + nu;
break;
case ESCAPING2:
log_zn = log(z.x * z.x + z.y * z.y) / log(sqr(rqlim)); // escape method 2 (page 24 Fractal-Zoomer Algorithms.docx)
t = log(z.x * z.x + z.y * z.y) / log(OldZ.x * OldZ.x + OldZ.y * OldZ.y);
nu = log_zn / t;
FloatIteration = FloatIteration + 1 - nu;
break;
*/
case CONVERGING:
a = OldZ - OlderZ;
b = *zBig - OldZ;
BigTemp = a.x * a.x + a.y * a.y;
LogA = BigTemp.BigLog();
log_zn = log(error) - mpfr_get_d(LogA.x, MPFR_RNDN);
// log_zn = log(error) - log(a.x * a.x + a.y * a.y); // convergence method 1 (page 25 Fractal-Zoomer Algorithms.docx)
BigTemp = b.x * b.x + b.y * b.y;
LogB = BigTemp.BigLog();
BigTemp1 = LogB - LogA;
t = mpfr_get_d(BigTemp1.x, MPFR_RNDN);
// t = log(b.x * b.x + b.y * b.y) - log(a.x * a.x + a.y * a.y);
nu = log_zn / t;
FloatIteration = FloatIteration + nu;
break;
/*
case CONVERGING1:
a = OldZ - OlderZ;
b = z - OldZ;
log_zn = log(error) / log(b.x * b.x + b.y * b.y); // convergence method 2 (page 25 Fractal-Zoomer Algorithms.docx)
t = log(b.x * b.x + b.y * b.y) / log(a.x * a.x + a.y * a.y);
nu = log_zn / t;
FloatIteration = FloatIteration + nu;
break;
case CONVERGINGMAG:
a = OldZ - root;
b = z - root;
log_zn = log(error) - log(a.x * a.x + a.y * a.y); // convergence method 1 (page 25 Fractal-Zoomer Algorithms.docx)
t = log(b.x * b.x + b.y * b.y) - log(a.x * a.x + a.y * a.y);
nu = log_zn / t;
FloatIteration = FloatIteration + nu;
break;
case CONVERGINGMAG1:
a = OldZ - root;
b = z - root;
log_zn = log(error) / log(b.x * b.x + b.y * b.y); // convergence method 2 (page 26 Fractal-Zoomer Algorithms.docx)
t = log(b.x * b.x + b.y * b.y) - log(a.x * a.x + a.y * a.y);
nu = log_zn / t;
FloatIteration = FloatIteration + nu;
break;
*/
default:
BigTemp = zBig->x * zBig->x + zBig->y * zBig->y;
BigTemp1 = BigTemp.BigLog();
log_zn = mpfr_get_d(BigTemp1.x, MPFR_RNDN) / SlopeDegree;
nu = log(log_zn / log(SlopeDegree)) / log(SlopeDegree);
FloatIteration = FloatIteration + 1 - nu;
break;
}
if ((long)FloatIteration >= threshold)
FloatIteration = (double)threshold;
else if (SpecialFlag)
FloatIteration = (double)special;
index = ((DWORD)row * (DWORD)width) + (DWORD)col;
if (col >= 0 && col < xdots - 1 && row >= 0 && row < ydots - 1)
*(wpixels + index) = FloatIteration;
}
}
/**************************************************************************
Run fractal
**************************************************************************/
//extern void ShowBignum(BigDouble x, char *Location); // use for debugging
long CPixel::DoBigFract(HWND hwnd, int row, int col)
{
long real_iteration; // actual count for orbit deletion
BigComplex bigTemp;
Complex tempComplex;
BigDouble magnitude;
BigDouble min_orbit; // orbit value closest to origin
long min_index; // iteration of min_orbit
// double tantable[16]; // used for Star Trails
BigDouble close = 0.01;
magnitude = 0.0;
min_orbit = 100000.0;
/* No point, it doesn't have a fractal nature
if (method == STARTRAIL)
{
int i;
for (i = 0; i < 16; i++)
tantable[i] = 0.0;
}
*/
int savedand, savedincr; // for periodicity checking
int result;
BigComplex BigSaved = 0.0;
BigDouble BioMorphTest = 0.5;
double temp;
int hooper = 0;
if (period_level == 0)
oldcolour = 32767; // don't check periodicity at all
else //if (reset_period)
oldcolour = 240; // don't check periodicity 1st n iterations
// BioFlag = FALSE; // no biomorph colour yet
SpecialFlag = FALSE; // no special colour yet. Use for decomp etc
savedand = 1; // begin checking every other cycle
savedincr = 1; // start checking the very first time
*iteration = 0L;
real_iteration = 0;
phaseflag = 0; // assume all type 5, 9 fractals same colour
if (InsideMethod >= TIERAZONFILTERS)
{
bigTemp = *qBig;
tempComplex = bigTemp.CBig2Double();
TZfilter->InitFilter(InsideMethod, threshold, dStrands, nFDOption, UseCurrentPalette); // initialise the constants used by Tierazon fractals
TZfilter->LoadFilterQ(tempComplex);
}
if (juliaflag)
{
qBig->x = j.x;
qBig->y = j.y;
*zBig = (invert) ? BigInvertz2(*cBig) : *cBig;
}
else
{
*qBig = (invert) ? BigInvertz2(*cBig) : *cBig;
*zBig = 0.0;
}
// ShowBignum(zBig->x, "x before init");
// ShowBignum(zBig->y, "y before init");
if (init_big_fractal() < 0)
return(BLUE);
// ShowBignum(zBig->x, "x after init");
// ShowBignum(zBig->y, "y after init");
if (InsideMethod == BOF60 || InsideMethod == BOF61)
{
magnitude = 0.0;
min_orbit = 100000.0;
}
if (InsideMethod == POTENTIAL)
BigBailout = potparam[2];
FloatIteration = 0.0;
for EVER
{
if (calcmode == 'F')
{
BigOlderZ = BigOldZ;
BigOldZ = *zBig;
}
if (FloatIteration >= threshold)
break;
(*iteration)++;
FloatIteration++;
result = run_big_fractal();
if (result < 0)
return(BLUE); // division by zero (Was Blue)
else if (result == 1) // escape time
break;
if (type == RATIONALMAP)
return(*iteration);
/* No point, it doesn't have a fractal nature
if (method == STARTRAIL)
{
if (0 < iteration && iteration < 16)
tantable[iteration - 1] = z->y / (z->x + 0.000001);
}
else
*/
if (InsideMethod == EPSCROSS)
{
hooper = 0;
if (zBig->x.BigAbs() < close)
{
hooper = 1; // close to y axis
break;
}
else if (zBig->y.BigAbs() < close)
{
hooper = 2; // close to x axis
break;
}
}
else if (InsideMethod == BOF60 || InsideMethod == BOF61)
{
magnitude = zBig->CSumSqr();
if (magnitude < min_orbit)
{
min_orbit = magnitude;
min_index = (long)*iteration + 1L;
}
}
else if (InsideMethod >= TIERAZONFILTERS)
{
bigTemp = *zBig;
tempComplex = bigTemp.CBig2Double();
TZfilter->DoTierazonFilter(tempComplex, iteration);
}
if (*iteration > oldcolour) // check periodicity
{
if ((*iteration & savedand) == 0) // time to save a new value
{
BigSaved = *zBig;
if (--savedincr == 0) // time to lengthen the periodicity?
{
savedand = (savedand << 1) + 1; // longer periodicity
savedincr = 4; // restart counter
}
}
else // check against an old save
{
BigDouble xAbs = BigSaved.x - zBig->x;
BigDouble yAbs = BigSaved.y - zBig->y;
if (xAbs.BigAbs() < BigCloseEnough)
if (yAbs.BigAbs() < BigCloseEnough)
*iteration = threshold;
}
}
}
if (calcmode == 'F')
{
SlopeError = 1.0e-9;
CalcBigFloatIteration(SlopeError, wpixels, row, col, *zBig, BigOldZ, BigOlderZ);
}
if (*iteration >= threshold && period_level)
oldcolour = 0; // check periodicity immediately next time
else
oldcolour = *iteration + 10; // check when past this+10 next time
if (*iteration >= threshold)
{
BigDouble t = min_orbit.BigSqrt() * 75.0;
if (InsideMethod == BOF60)
*iteration = (int)(t.BigDoubleToDouble());
else if (InsideMethod == BOF61)
*iteration = min_index;
}
if (SpecialFlag)
return(special); // flag for special colour
if (*iteration < threshold)
{
if (biomorph >= 0)
{
if (zBig->x.BigAbs() < BioMorphTest || zBig->y.BigAbs() < BioMorphTest)
{
*iteration = biomorph;
// BioFlag = TRUE;
}
}
DoBigFilter(InsideMethod, hooper);
DoBigFilter(OutsideMethod, hooper);
// eliminate negative colors & wrap arounds
if (*iteration < 0)
*iteration = 0;
if (*iteration > threshold && decomp <= threshold) // for small thresholds, we can still have higher decomp levels
*iteration = threshold;
// else if (colours == 256 && decomp > 0)
// iteration = float_decomposition(z.x, z.y);
// else if (logval)
// iteration = (BYTE) (*(logtable + iteration));
}
else
{
if (InsideMethod == ZMAG)
{
temp = zBig->CSumSqr();
*iteration = (long)(temp * double(threshold >> 1) + 1.0);
}
else
*iteration = threshold;
}
if (InsideMethod >= TIERAZONFILTERS)
{
BigComplex bigTemp;
Complex tempComplex;
bigTemp = *zBig;
tempComplex = bigTemp.CBig2Double();
TZfilter->EndTierazonFilter(tempComplex, iteration, TrueCol);
return *iteration;
}
if (type == NEWTON && subtype != 'N')
return (*color); // Newton root colour
return(*iteration);
}
/**************************************************************************
Invert fractal
**************************************************************************/
BigComplex CPixel::BigInvertz2(BigComplex & Cmplx1)
{
BigComplex temp;
BigDouble tempsqrx, BigRadius = f_radius;
temp.x = Cmplx1.x;
temp.y = Cmplx1.y;
temp.x -= f_xcenter; temp.y -= f_ycenter; // Normalize values to center of circle
tempsqrx = temp.x.BigSqr() + temp.y.BigSqr(); // Get old radius
if (tempsqrx.BigAbs() > (BigDouble)FLT_MIN)
tempsqrx = BigRadius / tempsqrx;
else
tempsqrx = FLT_MAX; // a big number, but not TOO big
temp.x *= tempsqrx;
temp.y *= tempsqrx; // Perform inversion
temp.x += f_xcenter;
temp.y += f_ycenter; // Renormalize
return temp;
}
/************************************************************************
Calculate Big Fractal
************************************************************************/
long CPixel::BigCalcFrac(HWND hwnd, int row, int col, int user_data(HWND hwnd))
{
// FloatCornerstoBig(var);
if (pairflag) // half size screens: only do every second row / col
if (row % pairflag || col % pairflag)
if (row != (int)ydots - 1) // must trigger for last line
return(threshold);
if (RotationAngle == 0 || RotationAngle == 90 || RotationAngle == 180 || RotationAngle == 270) // save calcs in rotating, just remap
{
if (row != *oldrow)
{
if (pairflag && row) // draw row for right hand image
draw_right_image((short)(*oldrow));
switch (RotationAngle)
{
case NORMAL: // normal
cBig->y = *Big_yymax - Big_ygap * (double)row;
break;
case 90: // 90 degrees
cBig->x = *Big_yymax - Big_xgap * (double)row;
break;
case 180: // 180 degrees
cBig->y = -(*Big_yymax - Big_ygap * (double)row);
break;
case 270: // 270 degrees
cBig->x = -(*Big_yymax - Big_xgap * (double)row);
break;
}
*oldrow = row;
}
if (col != *oldcol)
{
switch (RotationAngle)
{
case NORMAL: // normal
cBig->x = Big_xgap * (double)col + BigHor;
break;
case 90: // 90 degrees
cBig->y = Big_ygap * (double)col + BigHor;
break;
case 180: // 180 degrees
cBig->x = -(Big_xgap * (double)col + BigHor);
break;
case 270: // 270 degrees
cBig->y = -(Big_ygap * (double)col + BigHor);
break;
}
*oldcol = col;
}
}
else
{
BigDouble zero = 0.0;
BigMat->DoTransformation(&cBig->x, &cBig->y, &zero, Big_xgap * (double)col + BigHor, *Big_yymax - Big_xgap * (double)row, 0.0);
}
if (user_data(hwnd) == -1)
return(-1);
*color = DoBigFract(hwnd, row, col);
reset_period = 0;
if (*color >= threshold)
*color = threshold;
/*
else if (logval && logflag == TRUE)
color = (BYTE) (*(logtable + color));
*/
if (calcmode == 'B')
{
if (*color >= colours) /* don't use color 0 unless from inside */
if (colours < 16)
*color &= *andcolor;
else
*color = ((*color - 1) % *andcolor) + 1; /* skip color zero */
}
if ((type == SPECIALNEWT || type == MATEIN) && special != 15) // split colours
{
if (phaseflag == 1) // second phase
*color += special;
else if (phaseflag == 2) // third phase
*color += (special << 1);
} // default first phase
if (_3dflag)
projection(col, row, *color);
else if (pairflag)
do_stereo_pairs(col, row, *color);
else
plot((WORD)col, (WORD)row, *color);
return(*color);
}