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FRACTALS.C
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1992-02-19
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/*
FRACTALS.C, FRACTALP.C and CALCFRAC.C actually calculate the fractal
images (well, SOMEBODY had to do it!). The modules are set up so that
all logic that is independent of any fractal-specific code is in
CALCFRAC.C, the code that IS fractal-specific is in FRACTALS.C, and the
struscture that ties (we hope!) everything together is in FRACTALP.C.
Original author Tim Wegner, but just about ALL the authors have
contributed SOME code to this routine at one time or another, or
contributed to one of the many massive restructurings.
The Fractal-specific routines are divided into three categories:
1. Routines that are called once-per-orbit to calculate the orbit
value. These have names like "XxxxFractal", and their function
pointers are stored in fractalspecific[fractype].orbitcalc. EVERY
new fractal type needs one of these. Return 0 to continue iterations,
1 if we're done. Results for integer fractals are left in 'lnew.x' and
'lnew.y', for floating point fractals in 'new.x' and 'new.y'.
2. Routines that are called once per pixel to set various variables
prior to the orbit calculation. These have names like xxx_per_pixel
and are fairly generic - chances are one is right for your new type.
They are stored in fractalspecific[fractype].per_pixel.
3. Routines that are called once per screen to set various variables.
These have names like XxxxSetup, and are stored in
fractalspecific[fractype].per_image.
4. The main fractal routine. Usually this will be StandardFractal(),
but if you have written a stand-alone fractal routine independent
of the StandardFractal mechanisms, your routine name goes here,
stored in fractalspecific[fractype].calctype.per_image.
Adding a new fractal type should be simply a matter of adding an item
to the 'fractalspecific' structure, writing (or re-using one of the existing)
an appropriate setup, per_image, per_pixel, and orbit routines.
-------------------------------------------------------------------- */
#include <stdio.h>
#include <stdlib.h>
#include <float.h>
#include <limits.h>
#include <string.h>
#ifdef __TURBOC__
#include <alloc.h>
#else
#include <malloc.h>
#endif
#include "fractint.h"
#include "mpmath.h"
#include "helpdefs.h"
#include "fractype.h"
#define NEWTONDEGREELIMIT 100
extern struct complex initorbit;
extern struct lcomplex linitorbit;
extern char useinitorbit;
extern double fgLimit;
extern int distest;
extern void (*ltrig0)();
extern void (*ltrig1)();
extern void (*ltrig2)();
extern void (*ltrig3)();
extern void (*dtrig0)();
extern void (*dtrig1)();
extern void (*dtrig2)();
extern void (*dtrig3)();
/* -------------------------------------------------------------------- */
/* The following #defines allow the complex transcendental functions */
/* in parser.c to be used here thus avoiding duplicated code. */
/* -------------------------------------------------------------------- */
#define CMPLXmod(z) (sqr((z).x)+sqr((z).y))
#define CMPLXconj(z) ((z).y = -((z).y))
#define LCMPLXmod(z) (lsqr((z).x)+lsqr((z).y))
#define LCMPLXconj(z) ((z).y = -((z).y))
#define LCMPLXtrig0(arg,out) Arg1->l = (arg); ltrig0(); (out)=Arg1->l
#define LCMPLXtrig1(arg,out) Arg1->l = (arg); ltrig1(); (out)=Arg1->l
#define LCMPLXtrig2(arg,out) Arg1->l = (arg); ltrig2(); (out)=Arg1->l
#define LCMPLXtrig3(arg,out) Arg1->l = (arg); ltrig3(); (out)=Arg1->l
#define CMPLXtrig0(arg,out) Arg1->d = (arg); dtrig0(); (out)=Arg1->d
#define CMPLXtrig1(arg,out) Arg1->d = (arg); dtrig1(); (out)=Arg1->d
#define CMPLXtrig2(arg,out) Arg1->d = (arg); dtrig2(); (out)=Arg1->d
#define CMPLXtrig3(arg,out) Arg1->d = (arg); dtrig3(); (out)=Arg1->d
#define LCMPLXsin(arg,out) Arg1->l = (arg); lStkSin(); (out) = Arg1->l
#define LCMPLXcos(arg,out) Arg1->l = (arg); lStkCos(); (out) = Arg1->l
#define LCMPLXsinh(arg,out) Arg1->l = (arg); lStkSinh(); (out) = Arg1->l
#define LCMPLXcosh(arg,out) Arg1->l = (arg); lStkCosh(); (out) = Arg1->l
#define LCMPLXlog(arg,out) Arg1->l = (arg); lStkLog(); (out) = Arg1->l
#define LCMPLXexp(arg,out) Arg1->l = (arg); lStkExp(); (out) = Arg1->l
/*
#define LCMPLXsqr(arg,out) Arg1->l = (arg); lStkSqr(); (out) = Arg1->l
*/
#define LCMPLXsqr(arg,out) \
(out).x = lsqr((arg).x) - lsqr((arg).y);\
(out).y = multiply((arg).x, (arg).y, bitshiftless1)
#define LCMPLXsqr_old(out) \
(out).y = multiply(lold.x, lold.y, bitshiftless1);\
(out).x = ltempsqrx - ltempsqry\
#define LCMPLXpwr(arg1,arg2,out) Arg2->l = (arg1); Arg1->l = (arg2);\
lStkPwr(); Arg1++; Arg2++; (out) = Arg2->l
#define LCMPLXmult(arg1,arg2,out) Arg2->l = (arg1); Arg1->l = (arg2);\
lStkMul(); Arg1++; Arg2++; (out) = Arg2->l
#define LCMPLXadd(arg1,arg2,out) \
(out).x = (arg1).x + (arg2).x; (out).y = (arg1).y + (arg2).y
#define LCMPLXsub(arg1,arg2,out) \
(out).x = (arg1).x - (arg2).x; (out).y = (arg1).y - (arg2).y
#define LCMPLXtimesreal(arg,real,out) \
(out).x = multiply((arg).x,(real),bitshift);\
(out).y = multiply((arg).y,(real),bitshift)
#define LCMPLXrecip(arg,out) \
{ long denom; denom = lsqr((arg).x) + lsqr((arg).y);\
if(denom==0L) overflow=1; else {(out).x = divide((arg).x,denom,bitshift);\
(out).y = -divide((arg).y,denom,bitshift);}}
#define CMPLXsin(arg,out) Arg1->d = (arg); dStkSin(); (out) = Arg1->d
#define CMPLXcos(arg,out) Arg1->d = (arg); dStkCos(); (out) = Arg1->d
#define CMPLXsinh(arg,out) Arg1->d = (arg); dStkSinh(); (out) = Arg1->d
#define CMPLXcosh(arg,out) Arg1->d = (arg); dStkCosh(); (out) = Arg1->d
#define CMPLXlog(arg,out) Arg1->d = (arg); dStkLog(); (out) = Arg1->d
#define CMPLXexp(arg,out) FPUcplxexp(&(arg), &(out))
/*
#define CMPLXsqr(arg,out) Arg1->d = (arg); dStkSqr(); (out) = Arg1->d
*/
#define CMPLXsqr(arg,out) \
(out).x = sqr((arg).x) - sqr((arg).y);\
(out).y = ((arg).x+(arg).x) * (arg).y
#define CMPLXsqr_old(out) \
(out).y = (old.x+old.x) * old.y;\
(out).x = tempsqrx - tempsqry
#define CMPLXpwr(arg1,arg2,out) (out)= ComplexPower((arg1), (arg2))
#define CMPLXmult1(arg1,arg2,out) Arg2->d = (arg1); Arg1->d = (arg2);\
dStkMul(); Arg1++; Arg2++; (out) = Arg2->d
#define CMPLXmult(arg1,arg2,out) \
{\
CMPLX TmP;\
TmP.x = (arg1).x*(arg2).x - (arg1).y*(arg2).y;\
TmP.y = (arg1).x*(arg2).y + (arg1).y*(arg2).x;\
(out) = TmP;\
}
#define CMPLXadd(arg1,arg2,out) \
(out).x = (arg1).x + (arg2).x; (out).y = (arg1).y + (arg2).y
#define CMPLXsub(arg1,arg2,out) \
(out).x = (arg1).x - (arg2).x; (out).y = (arg1).y - (arg2).y
#define CMPLXtimesreal(arg,real,out) \
(out).x = (arg).x*(real);\
(out).y = (arg).y*(real)
#define CMPLXrecip(arg,out) \
{ double denom; denom = sqr((arg).x) + sqr((arg).y);\
if(denom==0.0) {(out).x = 1.0e10;(out).y = 1.0e10;}else\
{ (out).x = (arg).x/denom;\
(out).y = -(arg).y/denom;}}
extern int xshift, yshift;
long Exp086(long);
double fmod(double,double);
extern int biomorph;
extern int forcesymmetry;
extern int symmetry;
LCMPLX lcoefficient,lold,lnew,lparm, linit,ltmp,ltmp2,lparm2;
long ltempsqrx,ltempsqry;
extern int decomp[];
extern double param[];
extern int potflag; /* potential enabled? */
extern double f_radius,f_xcenter,f_ycenter; /* inversion radius, center */
extern double xxmin,xxmax,yymin,yymax; /* corners */
extern int overflow;
extern int integerfractal; /* TRUE if fractal uses integer math */
int maxcolor;
int root, degree,basin;
double floatmin,floatmax;
double roverd, d1overd, threshold;
CMPLX tmp2;
extern CMPLX init,tmp,old,new,saved,ComplexPower();
CMPLX staticroots[16]; /* roots array for degree 16 or less */
CMPLX *roots = staticroots;
struct MPC *MPCroots;
extern int color, row, col;
extern int invert;
extern double far *dx0, far *dy0;
extern double far *dx1, far *dy1;
long FgHalf;
CMPLX one;
CMPLX pwr;
CMPLX Coefficient;
extern int colors; /* maximum colors available */
extern int inside; /* "inside" color to use */
extern int outside; /* "outside" color to use */
extern int finattract;
extern int fractype; /* fractal type */
extern int debugflag; /* for debugging purposes */
extern double param[]; /* parameters */
extern long far *lx0, far *ly0; /* X, Y points */
extern long far *lx1, far *ly1; /* X, Y points */
extern long delx,dely; /* X, Y increments */
extern long delmin; /* min(max(dx),max(dy) */
extern double ddelmin; /* min(max(dx),max(dy) */
extern long fudge; /* fudge factor (2**n) */
extern int bitshift; /* bit shift for fudge */
int bitshiftless1; /* bit shift less 1 */
#ifndef sqr
#define sqr(x) ((x)*(x))
#endif
#ifndef lsqr
#define lsqr(x) (multiply((x),(x),bitshift))
#endif
#define modulus(z) (sqr((z).x)+sqr((z).y))
#define conjugate(pz) ((pz)->y = 0.0 - (pz)->y)
#define distance(z1,z2) (sqr((z1).x-(z2).x)+sqr((z1).y-(z2).y))
#define pMPsqr(z) (*pMPmul((z),(z)))
#define MPdistance(z1,z2) (*pMPadd(pMPsqr(*pMPsub((z1).x,(z2).x)),pMPsqr(*pMPsub((z1).y,(z2).y))))
double twopi = PI*2.0;
static int c_exp;
/* These are local but I don't want to pass them as parameters */
CMPLX lambda;
extern double magnitude, rqlim, rqlim2;
CMPLX parm,parm2;
CMPLX *floatparm;
LCMPLX *longparm; /* used here and in jb.c */
extern int (*calctype)();
extern unsigned long lm; /* magnitude limit (CALCMAND) */
/* -------------------------------------------------------------------- */
/* These variables are external for speed's sake only */
/* -------------------------------------------------------------------- */
double sinx,cosx,sinhx,coshx;
double siny,cosy,sinhy,coshy;
double tmpexp;
double tempsqrx,tempsqry;
double foldxinitx,foldyinity,foldxinity,foldyinitx;
long oldxinitx,oldyinity,oldxinity,oldyinitx;
long longtmp;
extern long lmagnitud, llimit, llimit2, l16triglim;
extern periodicitycheck;
extern char floatflag;
extern int StandardFractal();
extern int NewtonFractal2(); /* Lee Crocker's Newton code */
/* these are in mpmath_c.c */
extern int ComplexNewtonSetup(void);
extern int ComplexNewton(void), ComplexBasin(void), MarksCplxMand(void);
extern int MarksCplxMandperp(void);
/* these are in (I think) JB.C */
extern int Std4dFractal(), JulibrotSetup(), jb_per_pixel();
extern int Lsystem();
extern int lya_setup(void);
extern int lyapunov(void);
/* temporary variables for trig use */
long lcosx, lcoshx, lsinx, lsinhx;
long lcosy, lcoshy, lsiny, lsinhy;
/*
** details of finite attractors (required for Magnet Fractals)
** (can also be used in "coloring in" the lakes of Julia types)
*/
extern int attractors; /* number of finite attractors */
extern CMPLX attr[]; /* finite attractor values (f.p) */
extern LCMPLX lattr[]; /* finite attractor values (int) */
/*
** pre-calculated values for fractal types Magnet2M & Magnet2J
*/
CMPLX T_Cm1; /* 3 * (floatparm - 1) */
CMPLX T_Cm2; /* 3 * (floatparm - 2) */
CMPLX T_Cm1Cm2; /* (floatparm - 1) * (floatparm - 2) */
void FloatPreCalcMagnet2() /* precalculation for Magnet2 (M & J) for speed */
{
T_Cm1.x = floatparm->x - 1.0; T_Cm1.y = floatparm->y;
T_Cm2.x = floatparm->x - 2.0; T_Cm2.y = floatparm->y;
T_Cm1Cm2.x = (T_Cm1.x * T_Cm2.x) - (T_Cm1.y * T_Cm2.y);
T_Cm1Cm2.y = (T_Cm1.x * T_Cm2.y) + (T_Cm1.y * T_Cm2.x);
T_Cm1.x += T_Cm1.x + T_Cm1.x; T_Cm1.y += T_Cm1.y + T_Cm1.y;
T_Cm2.x += T_Cm2.x + T_Cm2.x; T_Cm2.y += T_Cm2.y + T_Cm2.y;
}
/* -------------------------------------------------------------------- */
/* Stand-alone routines */
/* -------------------------------------------------------------------- */
extern int orbit2dfloat();
extern int orbit2dlong();
extern int kamtorusfloatorbit();
extern int kamtoruslongorbit();
/* functions defined elswhere needed for fractalspecific */
extern int hopalong2dfloatorbit();
extern int martin2dfloatorbit();
extern int orbit3dfloat();
extern int orbit3dlong();
extern int lorenz3dlongorbit();
extern int orbit3dlongsetup();
extern int lorenz3dfloatorbit();
extern int lorenz3d1floatorbit();
extern int lorenz3d3floatorbit();
extern int lorenz3d4floatorbit();
extern int orbit3dfloatsetup();
extern int rosslerfloatorbit();
extern int rosslerlongorbit();
extern int henonfloatorbit();
extern int henonlongorbit();
extern int pickoverfloatorbit();
extern int gingerbreadfloatorbit();
extern int diffusion();
extern int plasma();
extern int test();
extern int ifs();
extern int Bifurcation(void);
extern int BifurcVerhulst(void);
extern int LongBifurcVerhulst(void);
extern int BifurcLambda(void);
extern int LongBifurcLambda(void);
extern int BifurcAddSinPi(void);
extern int LongBifurcAddSinPi(void);
extern int BifurcSetSinPi(void);
extern int LongBifurcSetSinPi(void);
extern int BifurcStewart(void);
extern int LongBifurcStewart(void);
extern int popcorn(void);
/* -------------------------------------------------------------------- */
/* Bailout Routines Macros */
/* -------------------------------------------------------------------- */
static int near floatbailout()
{
if ( ( magnitude = ( tempsqrx=sqr(new.x) )
+ ( tempsqry=sqr(new.y) ) ) >= rqlim ) return(1);
old = new;
return(0);
}
/* longbailout() is equivalent to next */
#define LONGBAILOUT() \
ltempsqrx = lsqr(lnew.x); ltempsqry = lsqr(lnew.y);\
lmagnitud = ltempsqrx + ltempsqry;\
if (lmagnitud >= llimit || lmagnitud < 0 || labs(lnew.x) > llimit2\
|| labs(lnew.y) > llimit2 || overflow) \
{ overflow=0;return(1);}\
lold = lnew;
#define FLOATTRIGBAILOUT() \
if (fabs(old.y) >= rqlim2) return(1);
#define LONGTRIGBAILOUT() \
if(labs(lold.y) >= llimit2 || overflow) { overflow=0;return(1);}
#define LONGXYTRIGBAILOUT() \
if(labs(lold.x) >= llimit2 || labs(lold.y) >= llimit2 || overflow)\
{ overflow=0;return(1);}
#define FLOATXYTRIGBAILOUT() \
if (fabs(old.x) >= rqlim2 || fabs(old.y) >= rqlim2) return(1);
#define FLOATHTRIGBAILOUT() \
if (fabs(old.x) >= rqlim2) return(1);
#define LONGHTRIGBAILOUT() \
if(labs(lold.x) >= llimit2 || overflow) { overflow=0;return(1);}
#define TRIG16CHECK(X) \
if(labs((X)) > l16triglim || overflow) { overflow=0;return(1);}
#define FLOATEXPBAILOUT() \
if (fabs(old.y) >= 1.0e8) return(1);\
if (fabs(old.x) >= 6.4e2) return(1);
#define LONGEXPBAILOUT() \
if (labs(lold.y) >= (1000L<<bitshift)) return(1);\
if (labs(lold.x) >= (8L<<bitshift)) return(1);
#if 0
/* this define uses usual trig instead of fast trig */
#define FPUsincos(px,psinx,pcosx) \
*(psinx) = sin(*(px));\
*(pcosx) = cos(*(px));
#define FPUsinhcosh(px,psinhx,pcoshx) \
*(psinhx) = sinh(*(px));\
*(pcoshx) = cosh(*(px));
#endif
#define LTRIGARG(X) \
if(labs((X)) > l16triglim)\
{\
double tmp;\
tmp = (X);\
tmp /= fudge;\
tmp = fmod(tmp,twopi);\
tmp *= fudge;\
(X) = tmp;\
}\
/* -------------------------------------------------------------------- */
/* Fractal (once per iteration) routines */
/* -------------------------------------------------------------------- */
static double xt, yt, t2;
/* Raise complex number (base) to the (exp) power, storing the result
** in complex (result).
*/
void cpower(CMPLX *base, int exp, CMPLX *result)
{
xt = base->x; yt = base->y;
if (exp & 1)
{
result->x = xt;
result->y = yt;
}
else
{
result->x = 1.0;
result->y = 0.0;
}
exp >>= 1;
while (exp)
{
t2 = xt * xt - yt * yt;
yt = 2 * xt * yt;
xt = t2;
if (exp & 1)
{
t2 = xt * result->x - yt * result->y;
result->y = result->y * xt + yt * result->x;
result->x = t2;
}
exp >>= 1;
}
}
/* long version */
static long lxt, lyt, lt2;
lcpower(LCMPLX *base, int exp, LCMPLX *result, int bitshift)
{
static long maxarg;
maxarg = 64L<<bitshift;
overflow = 0;
lxt = base->x; lyt = base->y;
if (exp & 1)
{
result->x = lxt;
result->y = lyt;
}
else
{
result->x = 1L<<bitshift;
result->y = 0L;
}
exp >>= 1;
while (exp)
{
/*
if(labs(lxt) >= maxarg || labs(lyt) >= maxarg)
return(-1);
*/
lt2 = multiply(lxt, lxt, bitshift) - multiply(lyt,lyt,bitshift);
lyt = multiply(lxt,lyt,bitshiftless1);
if(overflow)
return(overflow);
lxt = lt2;
if (exp & 1)
{
lt2 = multiply(lxt,result->x, bitshift) - multiply(lyt,result->y,bitshift);
result->y = multiply(result->y,lxt,bitshift) + multiply(lyt,result->x,bitshift);
result->x = lt2;
}
exp >>= 1;
}
if(result->x == 0 && result->y == 0)
overflow = 1;
return(overflow);
}
#if 0
z_to_the_z(CMPLX *z, CMPLX *out)
{
static CMPLX tmp1,tmp2;
/* raises complex z to the z power */
int errno_xxx;
errno_xxx = 0;
if(fabs(z->x) < DBL_EPSILON) return(-1);
/* log(x + iy) = 1/2(log(x*x + y*y) + i(arc_tan(y/x)) */
tmp1.x = .5*log(sqr(z->x)+sqr(z->y));
/* the fabs in next line added to prevent discontinuity in image */
tmp1.y = atan(fabs(z->y/z->x));
/* log(z)*z */
tmp2.x = tmp1.x * z->x - tmp1.y * z->y;
tmp2.y = tmp1.x * z->y + tmp1.y * z->x;
/* z*z = e**(log(z)*z) */
/* e**(x + iy) = e**x * (cos(y) + isin(y)) */
tmpexp = exp(tmp2.x);
FPUsincos(&tmp2.y,&siny,&cosy);
out->x = tmpexp*cosy;
out->y = tmpexp*siny;
return(errno_xxx);
}
#endif
/* Distance of complex z from unit circle */
#define DIST1(z) (((z).x-1.0)*((z).x-1.0)+((z).y)*((z).y))
#define LDIST1(z) (lsqr((((z).x)-fudge)) + lsqr(((z).y)))
#ifdef NEWTON
int complex_mult(CMPLX arg1,CMPLX arg2,CMPLX *pz);
int complex_div(CMPLX arg1,CMPLX arg2,CMPLX *pz);
int NewtonFractal()
{
static char start=1;
if(start)
{
start = 0;
}
cpower(&old, degree-1, &tmp);
complex_mult(tmp, old, &new);
if (DIST1(new) < threshold)
{
if(fractype==NEWTBASIN)
{
int tmpcolor;
int i;
tmpcolor = -1;
/* this code determines which degree-th root of root the
Newton formula converges to. The roots of a 1 are
distributed on a circle of radius 1 about the origin. */
for(i=0;i<degree;i++)
/* color in alternating shades with iteration according to
which root of 1 it converged to */
if(distance(roots[i],old) < threshold)
{
/* tmpcolor = 1+(i&7)+((color&1)<<3); */
tmpcolor = 1+i;
break;
}
if(tmpcolor == -1)
color = maxcolor;
else
color = tmpcolor;
}
return(1);
}
new.x = d1overd * new.x + roverd;
new.y *= d1overd;
/* Watch for divide underflow */
if ((t2 = tmp.x * tmp.x + tmp.y * tmp.y) < FLT_MIN)
return(1);
else
{
t2 = 1.0 / t2;
old.x = t2 * (new.x * tmp.x + new.y * tmp.y);
old.y = t2 * (new.y * tmp.x - new.x * tmp.y);
}
return(0);
}
complex_mult(arg1,arg2,pz)
CMPLX arg1,arg2,*pz;
{
pz->x = arg1.x*arg2.x - arg1.y*arg2.y;
pz->y = arg1.x*arg2.y+arg1.y*arg2.x;
return(0);
}
complex_div(numerator,denominator,pout)
CMPLX numerator,denominator,*pout;
{
double mod;
if((mod = modulus(denominator)) < FLT_MIN)
return(1);
conjugate(&denominator);
complex_mult(numerator,denominator,pout);
pout->x = pout->x/mod;
pout->y = pout->y/mod;
return(0);
}
lcomplex_mult(arg1,arg2,pz,bitshift)
LCMPLX arg1,arg2,*pz;
int bitshift;
{
overflow = 0;
pz->x = multiply(arg1.x,arg2.x,bitshift) - multiply(arg1.y,arg2.y,bitshift);
pz->y = multiply(arg1.x,arg2.y,bitshift) + multiply(arg1.y,arg2.x,bitshift);
return(overflow);
}
#endif
#define MPCmod(m) (*pMPadd(*pMPmul((m).x, (m).x), *pMPmul((m).y, (m).y)))
struct MPC mpcold, mpcnew, mpctmp, mpctmp1;
struct MP mproverd, mpd1overd, mpthreshold,sqrmpthreshold;
struct MP mpt2;
struct MP mpone;
extern struct MPC MPCone;
extern int MPOverflow;
int MPCNewtonFractal()
{
MPOverflow = 0;
mpctmp = MPCpow(mpcold,degree-1);
#ifndef XFRACT
mpcnew.x = *pMPsub(*pMPmul(mpctmp.x,mpcold.x),*pMPmul(mpctmp.y,mpcold.y));
mpcnew.y = *pMPadd(*pMPmul(mpctmp.x,mpcold.y),*pMPmul(mpctmp.y,mpcold.x));
mpctmp1.x = *pMPsub(mpcnew.x, MPCone.x);
mpctmp1.y = *pMPsub(mpcnew.y, MPCone.y);
if(pMPcmp(MPCmod(mpctmp1),mpthreshold)< 0)
#else
mpcnew.x.val = mpctmp.x.val*mpcold.x.val-mpctmp.y.val*mpcold.y.val;
mpcnew.y.val = mpctmp.x.val*mpcold.y.val+mpctmp.y.val*mpcold.x.val;
mpctmp1.x.val = mpcnew.x.val-1;
mpctmp1.y.val = mpcnew.y.val;
if (mpctmp1.x.val*mpctmp1.x.val+mpctmp1.y.val*mpctmp1.y.val<mpthreshold.val)
#endif
{
if(fractype==MPNEWTBASIN)
{
int tmpcolor;
int i;
tmpcolor = -1;
for(i=0;i<degree;i++)
if(pMPcmp(MPdistance(MPCroots[i],mpcold),mpthreshold) < 0)
{
if(basin==2)
tmpcolor = 1+(i&7) + ((color&1)<<3);
else
tmpcolor = 1+i;
break;
}
if(tmpcolor == -1)
color = maxcolor;
else
color = tmpcolor;
}
return(1);
}
#ifndef XFRACT
mpcnew.x = *pMPadd(*pMPmul(mpd1overd,mpcnew.x),mproverd);
mpcnew.y = *pMPmul(mpcnew.y,mpd1overd);
mpt2 = MPCmod(mpctmp);
mpt2 = *pMPdiv(mpone,mpt2);
mpcold.x = *pMPmul(mpt2,(*pMPadd(*pMPmul(mpcnew.x,mpctmp.x),*pMPmul(mpcnew.y,mpctmp.y))));
mpcold.y = *pMPmul(mpt2,(*pMPsub(*pMPmul(mpcnew.y,mpctmp.x),*pMPmul(mpcnew.x,mpctmp.y))));
#else
mpcnew.x.val = mpd1overd.val*mpcnew.x.val+mproverd.val;
mpcnew.y.val= mpcnew.y.val*mpd1overd.val;
mpt2.val = mpctmp.x.val*mpctmp.x.val+mpctmp.y.val*mpctmp.y.val;
mpt2.val = 1./mpt2.val;
mpcold.x.val = mpt2.val*(mpcnew.x.val*mpctmp.x.val+mpcnew.y.val*mpctmp.y.val);
mpcold.y.val = mpt2.val*(mpcnew.y.val*mpctmp.x.val-mpcnew.x.val*mpctmp.y.val);
#endif
new.x = *pMP2d(mpcold.x);
new.y = *pMP2d(mpcold.y);
return(MPOverflow);
}
Barnsley1Fractal()
{
/* Barnsley's Mandelbrot type M1 from "Fractals
Everywhere" by Michael Barnsley, p. 322 */
/* calculate intermediate products */
oldxinitx = multiply(lold.x, longparm->x, bitshift);
oldyinity = multiply(lold.y, longparm->y, bitshift);
oldxinity = multiply(lold.x, longparm->y, bitshift);
oldyinitx = multiply(lold.y, longparm->x, bitshift);
/* orbit calculation */
if(lold.x >= 0)
{
lnew.x = (oldxinitx - longparm->x - oldyinity);
lnew.y = (oldyinitx - longparm->y + oldxinity);
}
else
{
lnew.x = (oldxinitx + longparm->x - oldyinity);
lnew.y = (oldyinitx + longparm->y + oldxinity);
}
return(longbailout());
}
Barnsley1FPFractal()
{
/* Barnsley's Mandelbrot type M1 from "Fractals
Everywhere" by Michael Barnsley, p. 322 */
/* note that fast >= 287 equiv in fracsuba.asm must be kept in step */
/* calculate intermediate products */
foldxinitx = old.x * floatparm->x;
foldyinity = old.y * floatparm->y;
foldxinity = old.x * floatparm->y;
foldyinitx = old.y * floatparm->x;
/* orbit calculation */
if(old.x >= 0)
{
new.x = (foldxinitx - floatparm->x - foldyinity);
new.y = (foldyinitx - floatparm->y + foldxinity);
}
else
{
new.x = (foldxinitx + floatparm->x - foldyinity);
new.y = (foldyinitx + floatparm->y + foldxinity);
}
return(floatbailout());
}
Barnsley2Fractal()
{
/* An unnamed Mandelbrot/Julia function from "Fractals
Everywhere" by Michael Barnsley, p. 331, example 4.2 */
/* note that fast >= 287 equiv in fracsuba.asm must be kept in step */
/* calculate intermediate products */
oldxinitx = multiply(lold.x, longparm->x, bitshift);
oldyinity = multiply(lold.y, longparm->y, bitshift);
oldxinity = multiply(lold.x, longparm->y, bitshift);
oldyinitx = multiply(lold.y, longparm->x, bitshift);
/* orbit calculation */
if(oldxinity + oldyinitx >= 0)
{
lnew.x = oldxinitx - longparm->x - oldyinity;
lnew.y = oldyinitx - longparm->y + oldxinity;
}
else
{
lnew.x = oldxinitx + longparm->x - oldyinity;
lnew.y = oldyinitx + longparm->y + oldxinity;
}
return(longbailout());
}
Barnsley2FPFractal()
{
/* An unnamed Mandelbrot/Julia function from "Fractals
Everywhere" by Michael Barnsley, p. 331, example 4.2 */
/* calculate intermediate products */
foldxinitx = old.x * floatparm->x;
foldyinity = old.y * floatparm->y;
foldxinity = old.x * floatparm->y;
foldyinitx = old.y * floatparm->x;
/* orbit calculation */
if(foldxinity + foldyinitx >= 0)
{
new.x = foldxinitx - floatparm->x - foldyinity;
new.y = foldyinitx - floatparm->y + foldxinity;
}
else
{
new.x = foldxinitx + floatparm->x - foldyinity;
new.y = foldyinitx + floatparm->y + foldxinity;
}
return(floatbailout());
}
JuliaFractal()
{
/* used for C prototype of fast integer math routines for classic
Mandelbrot and Julia */
lnew.x = ltempsqrx - ltempsqry + longparm->x;
lnew.y = multiply(lold.x, lold.y, bitshiftless1) + longparm->y;
return(longbailout());
}
JuliafpFractal()
{
/* floating point version of classical Mandelbrot/Julia */
/* note that fast >= 287 equiv in fracsuba.asm must be kept in step */
new.x = tempsqrx - tempsqry + floatparm->x;
new.y = 2.0 * old.x * old.y + floatparm->y;
return(floatbailout());
}
static double f(double x, double y)
{
return(x - x*y);
}
static double g(double x, double y)
{
return(-y + x*y);
}
LambdaFPFractal()
{
/* variation of classical Mandelbrot/Julia */
/* note that fast >= 287 equiv in fracsuba.asm must be kept in step */
tempsqrx = old.x - tempsqrx + tempsqry;
tempsqry = -(old.y * old.x);
tempsqry += tempsqry + old.y;
new.x = floatparm->x * tempsqrx - floatparm->y * tempsqry;
new.y = floatparm->x * tempsqry + floatparm->y * tempsqrx;
return(floatbailout());
}
LambdaFractal()
{
/* variation of classical Mandelbrot/Julia */
/* in complex math) temp = Z * (1-Z) */
ltempsqrx = lold.x - ltempsqrx + ltempsqry;
ltempsqry = lold.y
- multiply(lold.y, lold.x, bitshiftless1);
/* (in complex math) Z = Lambda * Z */
lnew.x = multiply(longparm->x, ltempsqrx, bitshift)
- multiply(longparm->y, ltempsqry, bitshift);
lnew.y = multiply(longparm->x, ltempsqry, bitshift)
+ multiply(longparm->y, ltempsqrx, bitshift);
return(longbailout());
}
SierpinskiFractal()
{
/* following code translated from basic - see "Fractals
Everywhere" by Michael Barnsley, p. 251, Program 7.1.1 */
lnew.x = (lold.x << 1); /* new.x = 2 * old.x */
lnew.y = (lold.y << 1); /* new.y = 2 * old.y */
if(lold.y > ltmp.y) /* if old.y > .5 */
lnew.y = lnew.y - ltmp.x; /* new.y = 2 * old.y - 1 */
else if(lold.x > ltmp.y) /* if old.x > .5 */
lnew.x = lnew.x - ltmp.x; /* new.x = 2 * old.x - 1 */
/* end barnsley code */
return(longbailout());
}
SierpinskiFPFractal()
{
/* following code translated from basic - see "Fractals
Everywhere" by Michael Barnsley, p. 251, Program 7.1.1 */
new.x = old.x + old.x;
new.y = old.y + old.y;
if(old.y > .5)
new.y = new.y - 1;
else if (old.x > .5)
new.x = new.x - 1;
/* end barnsley code */
return(floatbailout());
}
LambdaexponentFractal()
{
/* found this in "Science of Fractal Images" */
FLOATEXPBAILOUT();
FPUsincos (&old.y,&siny,&cosy);
if (old.x >= rqlim && cosy >= 0.0) return(1);
tmpexp = exp(old.x);
tmp.x = tmpexp*cosy;
tmp.y = tmpexp*siny;
/*multiply by lamda */
new.x = floatparm->x*tmp.x - floatparm->y*tmp.y;
new.y = floatparm->y*tmp.x + floatparm->x*tmp.y;
old = new;
return(0);
}
LongLambdaexponentFractal()
{
/* found this in "Science of Fractal Images" */
LONGEXPBAILOUT();
SinCos086 (lold.y, &lsiny, &lcosy);
if (lold.x >= llimit && lcosy >= 0L) return(1);
longtmp = Exp086(lold.x);
ltmp.x = multiply(longtmp, lcosy, bitshift);
ltmp.y = multiply(longtmp, lsiny, bitshift);
lnew.x = multiply(longparm->x, ltmp.x, bitshift)
- multiply(longparm->y, ltmp.y, bitshift);
lnew.y = multiply(longparm->x, ltmp.y, bitshift)
+ multiply(longparm->y, ltmp.x, bitshift);
lold = lnew;
return(0);
}
FloatTrigPlusExponentFractal()
{
/* another Scientific American biomorph type */
/* z(n+1) = e**z(n) + trig(z(n)) + C */
if (fabs(old.x) >= 6.4e2) return(1); /* DOMAIN errors */
tmpexp = exp(old.x);
FPUsincos (&old.y,&siny,&cosy);
CMPLXtrig0(old,new);
/*new = trig(old) + e**old + C */
new.x += tmpexp*cosy + floatparm->x;
new.y += tmpexp*siny + floatparm->y;
return(floatbailout());
}
LongTrigPlusExponentFractal()
{
/* calculate exp(z) */
/* domain check for fast transcendental functions */
TRIG16CHECK(lold.x);
TRIG16CHECK(lold.y);
longtmp = Exp086(lold.x);
SinCos086 (lold.y, &lsiny, &lcosy);
LCMPLXtrig0(lold,lnew);
lnew.x += multiply(longtmp, lcosy, bitshift) + longparm->x;
lnew.y += multiply(longtmp, lsiny, bitshift) + longparm->y;
return(longbailout());
}
MarksLambdaFractal()
{
/* Mark Peterson's variation of "lambda" function */
/* Z1 = (C^(exp-1) * Z**2) + C */
ltmp.x = ltempsqrx - ltempsqry;
ltmp.y = multiply(lold.x ,lold.y ,bitshiftless1);
lnew.x = multiply(lcoefficient.x, ltmp.x, bitshift)
- multiply(lcoefficient.y, ltmp.y, bitshift) + longparm->x;
lnew.y = multiply(lcoefficient.x, ltmp.y, bitshift)
+ multiply(lcoefficient.y, ltmp.x, bitshift) + longparm->y;
return(longbailout());
}
long XXOne, FgOne, FgTwo;
UnityFractal()
{
/* brought to you by Mark Peterson - you won't find this in any fractal
books unless they saw it here first - Mark invented it! */
XXOne = multiply(lold.x, lold.x, bitshift) + multiply(lold.y, lold.y, bitshift);
if((XXOne > FgTwo) || (labs(XXOne - FgOne) < delmin))
return(1);
lold.y = multiply(FgTwo - XXOne, lold.x, bitshift);
lold.x = multiply(FgTwo - XXOne, lold.y, bitshift);
lnew=lold; /* TW added this line */
return(0);
}
#define XXOne new.x
UnityfpFractal()
{
/* brought to you by Mark Peterson - you won't find this in any fractal
books unless they saw it here first - Mark invented it! */
XXOne = sqr(old.x) + sqr(old.y);
if((XXOne > 2.0) || (fabs(XXOne - 1.0) < ddelmin))
return(1);
old.y = (2.0 - XXOne)* old.x;
old.x = (2.0 - XXOne)* old.y;
new=old; /* TW added this line */
return(0);
}
#undef XXOne
Mandel4Fractal()
{
/* By writing this code, Bert has left behind the excuse "don't
know what a fractal is, just know how to make'em go fast".
Bert is hereby declared a bonafide fractal expert! Supposedly
this routine calculates the Mandelbrot/Julia set based on the
polynomial z**4 + lambda, but I wouldn't know -- can't follow
all that integer math speedup stuff - Tim */
/* first, compute (x + iy)**2 */
lnew.x = ltempsqrx - ltempsqry;
lnew.y = multiply(lold.x, lold.y, bitshiftless1);
if (longbailout()) return(1);
/* then, compute ((x + iy)**2)**2 + lambda */
lnew.x = ltempsqrx - ltempsqry + longparm->x;
lnew.y = multiply(lold.x, lold.y, bitshiftless1) + longparm->y;
return(longbailout());
}
floatZtozPluszpwrFractal()
{
cpower(&old,(int)param[2],&new);
old = ComplexPower(old,old);
new.x = new.x + old.x +floatparm->x;
new.y = new.y + old.y +floatparm->y;
return(floatbailout());
}
longZpowerFractal()
{
if(lcpower(&lold,c_exp,&lnew,bitshift))
lnew.x = lnew.y = 8L<<bitshift;
lnew.x += longparm->x;
lnew.y += longparm->y;
return(longbailout());
}
longCmplxZpowerFractal()
{
struct complex x, y;
x.x = (double)lold.x / fudge;
x.y = (double)lold.y / fudge;
y.x = (double)lparm2.x / fudge;
y.y = (double)lparm2.y / fudge;
x = ComplexPower(x, y);
if(fabs(x.x) < fgLimit && fabs(x.y) < fgLimit) {
lnew.x = (long)(x.x * fudge);
lnew.y = (long)(x.y * fudge);
}
else
overflow = 1;
lnew.x += longparm->x;
lnew.y += longparm->y;
return(longbailout());
}
floatZpowerFractal()
{
cpower(&old,c_exp,&new);
new.x += floatparm->x;
new.y += floatparm->y;
return(floatbailout());
}
floatCmplxZpowerFractal()
{
new = ComplexPower(old, parm2);
new.x += floatparm->x;
new.y += floatparm->y;
return(floatbailout());
}
Barnsley3Fractal()
{
/* An unnamed Mandelbrot/Julia function from "Fractals
Everywhere" by Michael Barnsley, p. 292, example 4.1 */
/* calculate intermediate products */
oldxinitx = multiply(lold.x, lold.x, bitshift);
oldyinity = multiply(lold.y, lold.y, bitshift);
oldxinity = multiply(lold.x, lold.y, bitshift);
/* orbit calculation */
if(lold.x > 0)
{
lnew.x = oldxinitx - oldyinity - fudge;
lnew.y = oldxinity << 1;
}
else
{
lnew.x = oldxinitx - oldyinity - fudge
+ multiply(longparm->x,lold.x,bitshift);
lnew.y = oldxinity <<1;
/* This term added by Tim Wegner to make dependent on the
imaginary part of the parameter. (Otherwise Mandelbrot
is uninteresting. */
lnew.y += multiply(longparm->y,lold.x,bitshift);
}
return(longbailout());
}
Barnsley3FPFractal()
{
/* An unnamed Mandelbrot/Julia function from "Fractals
Everywhere" by Michael Barnsley, p. 292, example 4.1 */
/* calculate intermediate products */
foldxinitx = old.x * old.x;
foldyinity = old.y * old.y;
foldxinity = old.x * old.y;
/* orbit calculation */
if(old.x > 0)
{
new.x = foldxinitx - foldyinity - 1.0;
new.y = foldxinity * 2;
}
else
{
new.x = foldxinitx - foldyinity -1.0 + floatparm->x * old.x;
new.y = foldxinity * 2;
/* This term added by Tim Wegner to make dependent on the
imaginary part of the parameter. (Otherwise Mandelbrot
is uninteresting. */
new.y += floatparm->y * old.x;
}
return(floatbailout());
}
TrigPlusZsquaredFractal()
{
/* From Scientific American, July 1989 */
/* A Biomorph */
/* z(n+1) = trig(z(n))+z(n)**2+C */
LCMPLXtrig0(lold,lnew);
lnew.x += ltempsqrx - ltempsqry + longparm->x;
lnew.y += multiply(lold.x, lold.y, bitshiftless1) + longparm->y;
return(longbailout());
}
TrigPlusZsquaredfpFractal()
{
/* From Scientific American, July 1989 */
/* A Biomorph */
/* z(n+1) = trig(z(n))+z(n)**2+C */
CMPLXtrig0(old,new);
new.x += tempsqrx - tempsqry + floatparm->x;
new.y += 2.0 * old.x * old.y + floatparm->y;
return(floatbailout());
}
Richard8fpFractal()
{
/* Richard8 {c = z = pixel: z=sin(z)+sin(pixel),|z|<=50} */
CMPLXtrig0(old,new);
/* CMPLXtrig1(*floatparm,tmp); */
new.x += tmp.x;
new.y += tmp.y;
return(floatbailout());
}
Richard8Fractal()
{
/* Richard8 {c = z = pixel: z=sin(z)+sin(pixel),|z|<=50} */
LCMPLXtrig0(lold,lnew);
/* LCMPLXtrig1(*longparm,ltmp); */
lnew.x += ltmp.x;
lnew.y += ltmp.y;
return(longbailout());
}
PopcornFractal()
{
extern int row;
tmp = old;
tmp.x *= 3.0;
tmp.y *= 3.0;
FPUsincos(&tmp.x,&sinx,&cosx);
FPUsincos(&tmp.y,&siny,&cosy);
tmp.x = sinx/cosx + old.x;
tmp.y = siny/cosy + old.y;
FPUsincos(&tmp.x,&sinx,&cosx);
FPUsincos(&tmp.y,&siny,&cosy);
new.x = old.x - parm.x*siny;
new.y = old.y - parm.x*sinx;
/*
new.x = old.x - parm.x*sin(old.y+tan(3*old.y));
new.y = old.y - parm.x*sin(old.x+tan(3*old.x));
*/
if(plot == noplot)
{
plot_orbit(new.x,new.y,1+row%colors);
old = new;
}
else
/* FLOATBAILOUT(); */
/* PB The above line was weird, not what it seems to be! But, bracketing
it or always doing it (either of which seem more likely to be what
was intended) changes the image for the worse, so I'm not touching it.
Same applies to int form in next routine. */
/* PB later: recoded inline, still leaving it weird */
tempsqrx = sqr(new.x);
tempsqry = sqr(new.y);
if((magnitude = tempsqrx + tempsqry) >= rqlim) return(1);
old = new;
return(0);
}
LPopcornFractal()
{
extern int row;
ltmp = lold;
ltmp.x *= 3L;
ltmp.y *= 3L;
LTRIGARG(ltmp.x);
LTRIGARG(ltmp.y);
SinCos086(ltmp.x,&lsinx,&lcosx);
SinCos086(ltmp.y,&lsiny,&lcosy);
ltmp.x = divide(lsinx,lcosx,bitshift) + lold.x;
ltmp.y = divide(lsiny,lcosy,bitshift) + lold.y;
LTRIGARG(ltmp.x);
LTRIGARG(ltmp.y);
SinCos086(ltmp.x,&lsinx,&lcosx);
SinCos086(ltmp.y,&lsiny,&lcosy);
lnew.x = lold.x - multiply(lparm.x,lsiny,bitshift);
lnew.y = lold.y - multiply(lparm.x,lsinx,bitshift);
if(plot == noplot)
{
iplot_orbit(lnew.x,lnew.y,1+row%colors);
lold = lnew;
}
else
LONGBAILOUT();
/* PB above still the old way, is weird, see notes in FP popcorn case */
return(0);
}
int MarksCplxMand(void)
{
tmp.x = tempsqrx - tempsqry;
tmp.y = 2*old.x*old.y;
FPUcplxmul(&tmp, &Coefficient, &new);
new.x += floatparm->x;
new.y += floatparm->y;
return(floatbailout());
}
int SpiderfpFractal(void)
{
/* Spider(XAXIS) { c=z=pixel: z=z*z+c; c=c/2+z, |z|<=4 } */
new.x = tempsqrx - tempsqry + tmp.x;
new.y = 2 * old.x * old.y + tmp.y;
tmp.x = tmp.x/2 + new.x;
tmp.y = tmp.y/2 + new.y;
return(floatbailout());
}
SpiderFractal(void)
{
/* Spider(XAXIS) { c=z=pixel: z=z*z+c; c=c/2+z, |z|<=4 } */
lnew.x = ltempsqrx - ltempsqry + ltmp.x;
lnew.y = multiply(lold.x, lold.y, bitshiftless1) + ltmp.y;
ltmp.x = (ltmp.x >> 1) + lnew.x;
ltmp.y = (ltmp.y >> 1) + lnew.y;
return(longbailout());
}
TetratefpFractal()
{
/* Tetrate(XAXIS) { c=z=pixel: z=c^z, |z|<=(P1+3) } */
new = ComplexPower(*floatparm,old);
return(floatbailout());
}
ZXTrigPlusZFractal()
{
/* z = (p1*z*trig(z))+p2*z */
LCMPLXtrig0(lold,ltmp); /* ltmp = trig(old) */
LCMPLXmult(lparm,ltmp,ltmp); /* ltmp = p1*trig(old) */
LCMPLXmult(lold,ltmp,ltmp2); /* ltmp2 = p1*old*trig(old) */
LCMPLXmult(lparm2,lold,ltmp); /* ltmp = p2*old */
LCMPLXadd(ltmp2,ltmp,lnew); /* lnew = p1*trig(old) + p2*old */
return(longbailout());
}
ScottZXTrigPlusZFractal()
{
/* z = (z*trig(z))+z */
LCMPLXtrig0(lold,ltmp); /* ltmp = trig(old) */
LCMPLXmult(lold,ltmp,lnew); /* lnew = old*trig(old) */
LCMPLXadd(lnew,lold,lnew); /* lnew = trig(old) + old */
return(longbailout());
}
SkinnerZXTrigSubZFractal()
{
/* z = (z*trig(z))-z */
LCMPLXtrig0(lold,ltmp); /* ltmp = trig(old) */
LCMPLXmult(lold,ltmp,lnew); /* lnew = old*trig(old) */
LCMPLXsub(lnew,lold,lnew); /* lnew = trig(old) - old */
return(longbailout());
}
ZXTrigPlusZfpFractal()
{
/* z = (p1*z*trig(z))+p2*z */
CMPLXtrig0(old,tmp); /* tmp = trig(old) */
CMPLXmult(parm,tmp,tmp); /* tmp = p1*trig(old) */
CMPLXmult(old,tmp,tmp2); /* tmp2 = p1*old*trig(old) */
CMPLXmult(parm2,old,tmp); /* tmp = p2*old */
CMPLXadd(tmp2,tmp,new); /* new = p1*trig(old) + p2*old */
return(floatbailout());
}
ScottZXTrigPlusZfpFractal()
{
/* z = (z*trig(z))+z */
CMPLXtrig0(old,tmp); /* tmp = trig(old) */
CMPLXmult(old,tmp,new); /* new = old*trig(old) */
CMPLXadd(new,old,new); /* new = trig(old) + old */
return(floatbailout());
}
SkinnerZXTrigSubZfpFractal()
{
/* z = (z*trig(z))-z */
CMPLXtrig0(old,tmp); /* tmp = trig(old) */
CMPLXmult(old,tmp,new); /* new = old*trig(old) */
CMPLXsub(new,old,new); /* new = trig(old) - old */
return(floatbailout());
}
Sqr1overTrigFractal()
{
/* z = sqr(1/trig(z)) */
LCMPLXtrig0(lold,lold);
LCMPLXrecip(lold,lold);
LCMPLXsqr(lold,lnew);
return(longbailout());
}
Sqr1overTrigfpFractal()
{
/* z = sqr(1/trig(z)) */
CMPLXtrig0(old,old);
CMPLXrecip(old,old);
CMPLXsqr(old,new);
return(floatbailout());
}
TrigPlusTrigFractal()
{
/* z = trig(0,z)*p1+trig1(z)*p2 */
LCMPLXtrig0(lold,ltmp);
LCMPLXmult(lparm,ltmp,ltmp);
LCMPLXtrig1(lold,ltmp2);
LCMPLXmult(lparm2,ltmp2,lold);
LCMPLXadd(ltmp,lold,lnew);
return(longbailout());
}
TrigPlusTrigfpFractal()
{
/* z = trig0(z)*p1+trig1(z)*p2 */
CMPLXtrig0(old,tmp);
CMPLXmult(parm,tmp,tmp);
CMPLXtrig1(old,old);
CMPLXmult(parm2,old,old);
CMPLXadd(tmp,old,new);
return(floatbailout());
}
ScottTrigPlusTrigFractal()
{
/* z = trig0(z)+trig1(z) */
LCMPLXtrig0(lold,ltmp);
LCMPLXtrig1(lold,lold);
LCMPLXadd(ltmp,lold,lnew);
return(longbailout());
}
ScottTrigPlusTrigfpFractal()
{
/* z = trig0(z)+trig1(z) */
CMPLXtrig0(old,tmp);
CMPLXtrig1(old,tmp2);
CMPLXadd(tmp,tmp2,new);
return(floatbailout());
}
SkinnerTrigSubTrigFractal()
{
/* z = trig(0,z)-trig1(z) */
LCMPLXtrig0(lold,ltmp);
LCMPLXtrig1(lold,ltmp2);
LCMPLXsub(ltmp,ltmp2,lnew);
return(longbailout());
}
SkinnerTrigSubTrigfpFractal()
{
/* z = trig0(z)-trig1(z) */
CMPLXtrig0(old,tmp);
CMPLXtrig1(old,tmp2);
CMPLXsub(tmp,tmp2,new);
return(floatbailout());
}
TrigXTrigfpFractal()
{
/* z = trig0(z)*trig1(z) */
CMPLXtrig0(old,tmp);
CMPLXtrig1(old,old);
CMPLXmult(tmp,old,new);
return(floatbailout());
}
TrigXTrigFractal()
{
LCMPLX ltmp2;
/* z = trig0(z)*trig1(z) */
LCMPLXtrig0(lold,ltmp);
LCMPLXtrig1(lold,ltmp2);
LCMPLXmult(ltmp,ltmp2,lnew);
if(overflow)
TryFloatFractal(TrigXTrigfpFractal);
return(longbailout());
}
/* call float version of fractal if integer math overflow */
TryFloatFractal(int (*fpFractal)())
{
overflow=0;
/* lold had better not be changed! */
old.x = lold.x; old.x /= fudge;
old.y = lold.y; old.y /= fudge;
tempsqrx = sqr(old.x);
tempsqry = sqr(old.y);
fpFractal();
lnew.x = new.x/fudge;
lnew.y = new.y/fudge;
return(0);
}
/********************************************************************/
/* Next six orbit functions are one type - extra functions are */
/* special cases written for speed. */
/********************************************************************/
TrigPlusSqrFractal() /* generalization of Scott and Skinner types */
{
/* { z=pixel: z=(p1,p2)*trig(z)+(p3,p4)*sqr(z), |z|<BAILOUT } */
LCMPLXtrig0(lold,ltmp); /* ltmp = trig(lold) */
LCMPLXmult(lparm,ltmp,lnew); /* lnew = lparm*trig(lold) */
LCMPLXsqr_old(ltmp); /* ltmp = sqr(lold) */
LCMPLXmult(lparm2,ltmp,ltmp);/* ltmp = lparm2*sqr(lold) */
LCMPLXadd(lnew,ltmp,lnew); /* lnew = lparm*trig(lold)+lparm2*sqr(lold) */
return(longbailout());
}
TrigPlusSqrfpFractal() /* generalization of Scott and Skinner types */
{
/* { z=pixel: z=(p1,p2)*trig(z)+(p3,p4)*sqr(z), |z|<BAILOUT } */
CMPLXtrig0(old,tmp); /* tmp = trig(old) */
CMPLXmult(parm,tmp,new); /* new = parm*trig(old) */
CMPLXsqr_old(tmp); /* tmp = sqr(old) */
CMPLXmult(parm2,tmp,tmp2); /* tmp = parm2*sqr(old) */
CMPLXadd(new,tmp2,new); /* new = parm*trig(old)+parm2*sqr(old) */
return(floatbailout());
}
ScottTrigPlusSqrFractal()
{
/* { z=pixel: z=trig(z)+sqr(z), |z|<BAILOUT } */
LCMPLXtrig0(lold,lnew); /* lnew = trig(lold) */
LCMPLXsqr_old(ltmp); /* lold = sqr(lold) */
LCMPLXadd(ltmp,lnew,lnew); /* lnew = trig(lold)+sqr(lold) */
return(longbailout());
}
ScottTrigPlusSqrfpFractal() /* float version */
{
/* { z=pixel: z=sin(z)+sqr(z), |z|<BAILOUT } */
CMPLXtrig0(old,new); /* new = trig(old) */
CMPLXsqr_old(tmp); /* tmp = sqr(old) */
CMPLXadd(new,tmp,new); /* new = trig(old)+sqr(old) */
return(floatbailout());
}
SkinnerTrigSubSqrFractal()
{
/* { z=pixel: z=sin(z)-sqr(z), |z|<BAILOUT } */
LCMPLXtrig0(lold,lnew); /* lnew = trig(lold) */
LCMPLXsqr_old(ltmp); /* lold = sqr(lold) */
LCMPLXsub(lnew,ltmp,lnew); /* lnew = trig(lold)-sqr(lold) */
return(longbailout());
}
SkinnerTrigSubSqrfpFractal()
{
/* { z=pixel: z=sin(z)-sqr(z), |z|<BAILOUT } */
CMPLXtrig0(old,new); /* new = trig(old) */
CMPLXsqr_old(tmp); /* old = sqr(old) */
CMPLXsub(new,tmp,new); /* new = trig(old)-sqr(old) */
return(floatbailout());
}
TrigZsqrdfpFractal()
{
/* { z=pixel: z=trig(z*z), |z|<TEST } */
CMPLXsqr_old(tmp);
CMPLXtrig0(tmp,new);
return(floatbailout());
}
TrigZsqrdFractal() /* this doesn't work very well */
{
/* { z=pixel: z=trig(z*z), |z|<TEST } */
LCMPLXsqr_old(ltmp);
LCMPLXtrig0(ltmp,lnew);
if(overflow)
TryFloatFractal(TrigZsqrdfpFractal);
return(longbailout());
}
SqrTrigFractal()
{
/* { z=pixel: z=sqr(trig(z)), |z|<TEST} */
LCMPLXtrig0(lold,ltmp);
LCMPLXsqr(ltmp,lnew);
return(longbailout());
}
SqrTrigfpFractal()
{
/* SZSB(XYAXIS) { z=pixel, TEST=(p1+3): z=sin(z)*sin(z), |z|<TEST} */
CMPLXtrig0(old,tmp);
CMPLXsqr(tmp,new);
return(floatbailout());
}
Magnet1Fractal() /* Z = ((Z**2 + C - 1)/(2Z + C - 2))**2 */
{ /* In "Beauty of Fractals", code by Kev Allen. */
CMPLX top, bot, tmp;
double div;
top.x = tempsqrx - tempsqry + floatparm->x - 1; /* top = Z**2+C-1 */
top.y = old.x * old.y;
top.y = top.y + top.y + floatparm->y;
bot.x = old.x + old.x + floatparm->x - 2; /* bot = 2*Z+C-2 */
bot.y = old.y + old.y + floatparm->y;
div = bot.x*bot.x + bot.y*bot.y; /* tmp = top/bot */
if (div < FLT_MIN) return(1);
tmp.x = (top.x*bot.x + top.y*bot.y)/div;
tmp.y = (top.y*bot.x - top.x*bot.y)/div;
new.x = (tmp.x + tmp.y) * (tmp.x - tmp.y); /* Z = tmp**2 */
new.y = tmp.x * tmp.y;
new.y += new.y;
return(floatbailout());
}
Magnet2Fractal() /* Z = ((Z**3 + 3(C-1)Z + (C-1)(C-2) ) / */
/* (3Z**2 + 3(C-2)Z + (C-1)(C-2)+1) )**2 */
{ /* In "Beauty of Fractals", code by Kev Allen. */
CMPLX top, bot, tmp;
double div;
top.x = old.x * (tempsqrx-tempsqry-tempsqry-tempsqry + T_Cm1.x)
- old.y * T_Cm1.y + T_Cm1Cm2.x;
top.y = old.y * (tempsqrx+tempsqrx+tempsqrx-tempsqry + T_Cm1.x)
+ old.x * T_Cm1.y + T_Cm1Cm2.y;
bot.x = tempsqrx - tempsqry;
bot.x = bot.x + bot.x + bot.x
+ old.x * T_Cm2.x - old.y * T_Cm2.y
+ T_Cm1Cm2.x + 1.0;
bot.y = old.x * old.y;
bot.y += bot.y;
bot.y = bot.y + bot.y + bot.y
+ old.x * T_Cm2.y + old.y * T_Cm2.x
+ T_Cm1Cm2.y;
div = bot.x*bot.x + bot.y*bot.y; /* tmp = top/bot */
if (div < FLT_MIN) return(1);
tmp.x = (top.x*bot.x + top.y*bot.y)/div;
tmp.y = (top.y*bot.x - top.x*bot.y)/div;
new.x = (tmp.x + tmp.y) * (tmp.x - tmp.y); /* Z = tmp**2 */
new.y = tmp.x * tmp.y;
new.y += new.y;
return(floatbailout());
}
LambdaTrigFractal()
{
LONGXYTRIGBAILOUT();
LCMPLXtrig0(lold,ltmp); /* ltmp = trig(lold) */
LCMPLXmult(*longparm,ltmp,lnew); /* lnew = longparm*trig(lold) */
lold = lnew;
return(0);
}
LambdaTrigfpFractal()
{
FLOATXYTRIGBAILOUT();
CMPLXtrig0(old,tmp); /* tmp = trig(old) */
CMPLXmult(*floatparm,tmp,new); /* new = longparm*trig(old) */
old = new;
return(0);
}
/* bailouts are different for different trig functions */
LambdaTrigFractal1()
{
LONGTRIGBAILOUT(); /* sin,cos */
LCMPLXtrig0(lold,ltmp); /* ltmp = trig(lold) */
LCMPLXmult(*longparm,ltmp,lnew); /* lnew = longparm*trig(lold) */
lold = lnew;
return(0);
}
LambdaTrigfpFractal1()
{
FLOATTRIGBAILOUT(); /* sin,cos */
CMPLXtrig0(old,tmp); /* tmp = trig(old) */
CMPLXmult(*floatparm,tmp,new); /* new = longparm*trig(old) */
old = new;
return(0);
}
LambdaTrigFractal2()
{
LONGHTRIGBAILOUT(); /* sinh,cosh */
LCMPLXtrig0(lold,ltmp); /* ltmp = trig(lold) */
LCMPLXmult(*longparm,ltmp,lnew); /* lnew = longparm*trig(lold) */
lold = lnew;
return(0);
}
LambdaTrigfpFractal2()
{
FLOATHTRIGBAILOUT(); /* sinh,cosh */
CMPLXtrig0(old,tmp); /* tmp = trig(old) */
CMPLXmult(*floatparm,tmp,new); /* new = longparm*trig(old) */
old = new;
return(0);
}
ManOWarFractal()
{
/* From Art Matrix via Lee Skinner */
lnew.x = ltempsqrx - ltempsqry + ltmp.x + longparm->x;
lnew.y = multiply(lold.x, lold.y, bitshiftless1) + ltmp.y + longparm->y;
ltmp = lold;
return(longbailout());
}
ManOWarfpFractal()
{
/* From Art Matrix via Lee Skinner */
/* note that fast >= 287 equiv in fracsuba.asm must be kept in step */
new.x = tempsqrx - tempsqry + tmp.x + floatparm->x;
new.y = 2.0 * old.x * old.y + tmp.y + floatparm->y;
tmp = old;
return(floatbailout());
}
/*
MarksMandelPwr (XAXIS) {
z = pixel, c = z ^ (z - 1):
z = c * sqr(z) + pixel,
|z| <= 4
}
*/
MarksMandelPwrfpFractal()
{
CMPLXtrig0(old,new);
CMPLXmult(tmp,new,new);
new.x += floatparm->x;
new.y += floatparm->y;
return(floatbailout());
}
MarksMandelPwrFractal()
{
LCMPLXtrig0(lold,lnew);
LCMPLXmult(ltmp,lnew,lnew);
lnew.x += longparm->x;
lnew.y += longparm->y;
return(longbailout());
}
/* I was coding Marksmandelpower and failed to use some temporary
variables. The result was nice, and since my name is not on any fractal,
I thought I would immortalize myself with this error!
Tim Wegner */
TimsErrorfpFractal()
{
CMPLXtrig0(old,new);
new.x = new.x * tmp.x - new.y * tmp.y;
new.y = new.x * tmp.y - new.y * tmp.x;
new.x += floatparm->x;
new.y += floatparm->y;
return(floatbailout());
}
TimsErrorFractal()
{
LCMPLXtrig0(lold,lnew);
lnew.x = multiply(lnew.x,ltmp.x,bitshift)-multiply(lnew.y,ltmp.y,bitshift);
lnew.y = multiply(lnew.x,ltmp.y,bitshift)-multiply(lnew.y,ltmp.x,bitshift);
lnew.x += longparm->x;
lnew.y += longparm->y;
return(longbailout());
}
CirclefpFractal()
{
extern int colors;
extern int color;
int i;
i = param[0]*(tempsqrx+tempsqry);
color = i&(colors-1);
return(1);
}
/*
CirclelongFractal()
{
extern int colors;
extern int color;
long i;
i = multiply(lparm.x,(ltempsqrx+ltempsqry),bitshift);
i = i >> bitshift;
color = i&(colors-1);
return(1);
}
*/
/* -------------------------------------------------------------------- */
/* Initialization (once per pixel) routines */
/* -------------------------------------------------------------------- */
#ifdef XFRACT
/* this code translated to asm - lives in newton.asm */
/* transform points with reciprocal function */
void invertz2(CMPLX *z)
{
z->x = dx0[col]+dx1[row];
z->y = dy0[row]+dy1[col];
z->x -= f_xcenter; z->y -= f_ycenter; /* Normalize values to center of circle */
tempsqrx = sqr(z->x) + sqr(z->y); /* Get old radius */
if(fabs(tempsqrx) > FLT_MIN)
tempsqrx = f_radius / tempsqrx;
else
tempsqrx = FLT_MAX; /* a big number, but not TOO big */
z->x *= tempsqrx; z->y *= tempsqrx; /* Perform inversion */
z->x += f_xcenter; z->y += f_ycenter; /* Renormalize */
}
#endif
int long_julia_per_pixel()
{
/* integer julia types */
/* lambda */
/* barnsleyj1 */
/* barnsleyj2 */
/* sierpinski */
if(invert)
{
/* invert */
invertz2(&old);
/* watch out for overflow */
if(sqr(old.x)+sqr(old.y) >= 127)
{
old.x = 8; /* value to bail out in one iteration */
old.y = 8;
}
/* convert to fudged longs */
lold.x = old.x*fudge;
lold.y = old.y*fudge;
}
else
{
lold.x = lx0[col]+lx1[row];
lold.y = ly0[row]+ly1[col];
}
return(0);
}
int long_richard8_per_pixel()
{
long_mandel_per_pixel();
LCMPLXtrig1(*longparm,ltmp);
LCMPLXmult(ltmp,lparm2,ltmp);
return(1);
}
int long_mandel_per_pixel()
{
/* integer mandel types */
/* barnsleym1 */
/* barnsleym2 */
linit.x = lx0[col]+lx1[row];
if(invert)
{
/* invert */
invertz2(&init);
/* watch out for overflow */
if(sqr(init.x)+sqr(init.y) >= 127)
{
init.x = 8; /* value to bail out in one iteration */
init.y = 8;
}
/* convert to fudged longs */
linit.x = init.x*fudge;
linit.y = init.y*fudge;
}
if(useinitorbit == 1)
lold = linitorbit;
else
lold = linit;
lold.x += lparm.x; /* initial pertubation of parameters set */
lold.y += lparm.y;
return(1); /* 1st iteration has been done */
}
int julia_per_pixel()
{
/* julia */
if(invert)
{
/* invert */
invertz2(&old);
/* watch out for overflow */
if(bitshift <= 24)
if (sqr(old.x)+sqr(old.y) >= 127)
{
old.x = 8; /* value to bail out in one iteration */
old.y = 8;
}
if(bitshift > 24)
if (sqr(old.x)+sqr(old.y) >= 4.0)
{
old.x = 2; /* value to bail out in one iteration */
old.y = 2;
}
/* convert to fudged longs */
lold.x = old.x*fudge;
lold.y = old.y*fudge;
}
else
{
lold.x = lx0[col]+lx1[row];
lold.y = ly0[row]+ly1[col];
}
ltempsqrx = multiply(lold.x, lold.x, bitshift);
ltempsqry = multiply(lold.y, lold.y, bitshift);
ltmp = lold;
return(0);
}
marks_mandelpwr_per_pixel()
{
mandel_per_pixel();
ltmp = lold;
ltmp.x -= fudge;
LCMPLXpwr(lold,ltmp,ltmp);
return(1);
}
int mandel_per_pixel()
{
/* mandel */
if(invert)
{
invertz2(&init);
/* watch out for overflow */
if(bitshift <= 24)
if (sqr(init.x)+sqr(init.y) >= 127)
{
init.x = 8; /* value to bail out in one iteration */
init.y = 8;
}
if(bitshift > 24)
if (sqr(init.x)+sqr(init.y) >= 4)
{
init.x = 2; /* value to bail out in one iteration */
init.y = 2;
}
/* convert to fudged longs */
linit.x = init.x*fudge;
linit.y = init.y*fudge;
}
else
linit.x = lx0[col]+lx1[row];
switch (fractype)
{
case MANDELLAMBDA: /* Critical Value 0.5 + 0.0i */
lold.x = FgHalf;
lold.y = 0;
break;
default:
lold = linit;
break;
}
/* alter init value */
if(useinitorbit == 1)
lold = linitorbit;
else if(useinitorbit == 2)
lold = linit;
if(inside == -60 || inside == -61)
{
/* kludge to match "Beauty of Fractals" picture since we start
Mandelbrot iteration with init rather than 0 */
lold.x = lparm.x; /* initial pertubation of parameters set */
lold.y = lparm.y;
color = -1;
}
else
{
lold.x += lparm.x; /* initial pertubation of parameters set */
lold.y += lparm.y;
}
ltmp = linit; /* for spider */
ltempsqrx = multiply(lold.x, lold.x, bitshift);
ltempsqry = multiply(lold.y, lold.y, bitshift);
return(1); /* 1st iteration has been done */
}
int marksmandel_per_pixel()
{
/* marksmandel */
if(invert)
{
invertz2(&init);
/* watch out for overflow */
if(sqr(init.x)+sqr(init.y) >= 127)
{
init.x = 8; /* value to bail out in one iteration */
init.y = 8;
}
/* convert to fudged longs */
linit.x = init.x*fudge;
linit.y = init.y*fudge;
}
else
linit.x = lx0[col]+lx1[row];
if(useinitorbit == 1)
lold = linitorbit;
else
lold = linit;
lold.x += lparm.x; /* initial pertubation of parameters set */
lold.y += lparm.y;
if(c_exp > 3)
lcpower(&lold,c_exp-1,&lcoefficient,bitshift);
else if(c_exp == 3) {
lcoefficient.x = multiply(lold.x, lold.x, bitshift)
- multiply(lold.y, lold.y, bitshift);
lcoefficient.y = multiply(lold.x, lold.y, bitshiftless1);
}
else if(c_exp == 2)
lcoefficient = lold;
else if(c_exp < 2) {
lcoefficient.x = 1L << bitshift;
lcoefficient.y = 0L;
}
ltempsqrx = multiply(lold.x, lold.x, bitshift);
ltempsqry = multiply(lold.y, lold.y, bitshift);
return(1); /* 1st iteration has been done */
}
marks_mandelpwrfp_per_pixel()
{
mandelfp_per_pixel();
tmp = old;
tmp.x -= 1;
CMPLXpwr(old,tmp,tmp);
return(1);
}
int mandelfp_per_pixel()
{
/* floating point mandelbrot */
/* mandelfp */
if(invert)
invertz2(&init);
else
init.x = dx0[col]+dx1[row];
switch (fractype)
{
case MAGNET2M:
FloatPreCalcMagnet2();
case MAGNET1M: /* Crit Val Zero both, but neither */
old.x = old.y = 0.0; /* is of the form f(Z,C) = Z*g(Z)+C */
break;
case MANDELLAMBDAFP: /* Critical Value 0.5 + 0.0i */
old.x = 0.5;
old.y = 0.0;
break;
default:
old = init;
break;
}
/* alter init value */
if(useinitorbit == 1)
old = initorbit;
else if(useinitorbit == 2)
old = init;
if(inside == -60 || inside == -61)
{
/* kludge to match "Beauty of Fractals" picture since we start
Mandelbrot iteration with init rather than 0 */
old.x = parm.x; /* initial pertubation of parameters set */
old.y = parm.y;
color = -1;
}
else
{
old.x += parm.x;
old.y += parm.y;
}
tmp = init; /* for spider */
tempsqrx = sqr(old.x); /* precalculated value for regular Mandelbrot */
tempsqry = sqr(old.y);
return(1); /* 1st iteration has been done */
}
int juliafp_per_pixel()
{
/* floating point julia */
/* juliafp */
if(invert)
invertz2(&old);
else
{
old.x = dx0[col]+dx1[row];
old.y = dy0[row]+dy1[col];
}
tempsqrx = sqr(old.x); /* precalculated value for regular Julia */
tempsqry = sqr(old.y);
tmp = old;
return(0);
}
int MPCjulia_per_pixel()
{
/* floating point julia */
/* juliafp */
if(invert)
invertz2(&old);
else
{
old.x = dx0[col]+dx1[row];
old.y = dy0[row]+dy1[col];
}
mpcold.x = *pd2MP(old.x);
mpcold.y = *pd2MP(old.y);
return(0);
}
otherrichard8fp_per_pixel()
{
othermandelfp_per_pixel();
CMPLXtrig1(*floatparm,tmp);
CMPLXmult(tmp,parm2,tmp);
return(1);
}
int othermandelfp_per_pixel()
{
if(invert)
invertz2(&init);
else
init.x = dx0[col]+dx1[row];
if(useinitorbit == 1)
old = initorbit;
else
old = init;
old.x += parm.x; /* initial pertubation of parameters set */
old.y += parm.y;
return(1); /* 1st iteration has been done */
}
int otherjuliafp_per_pixel()
{
if(invert)
invertz2(&old);
else
{
old.x = dx0[col]+dx1[row];
old.y = dy0[row]+dy1[col];
}
return(0);
}
int trigmandelfp_per_pixel()
{
if(invert)
invertz2(&init);
else
init.x = dx0[col]+dx1[row];
if(useinitorbit == 1)
old = initorbit;
else
old = init;
old.x += parm.x; /* initial pertubation of parameters set */
old.y += parm.y;
CMPLXtrig0(old,old);
return(1); /* 1st iteration has been done */
}
int trigjuliafp_per_pixel()
{
/* for tetrated types */
if(invert)
invertz2(&old);
else
{
old.x = dx0[col]+dx1[row];
old.y = dy0[row]+dy1[col];
}
CMPLXtrig0(old,old);
return(0);
}
int trigXtrigmandelfp_per_pixel()
{
if(invert)
invertz2(&init);
else
init.x = dx0[col]+dx1[row];
if(useinitorbit == 1)
old = initorbit;
else
old = init;
old.x += parm.x; /* initial pertubation of parameters set */
old.y += parm.y;
CMPLXtrig0(old,tmp);
CMPLXtrig1(old,tmp2);
CMPLXmult(tmp,tmp2,old);
return(1); /* 1st iteration has been done */
}
int trigXtrigjuliafp_per_pixel()
{
if(invert)
invertz2(&old);
else
{
old.x = dx0[col]+dx1[row];
old.y = dy0[row]+dy1[col];
}
CMPLXtrig0(old,tmp);
CMPLXtrig1(old,tmp2);
CMPLXmult(tmp,tmp2,old);
return(0);
}
int MarksCplxMandperp(void)
{
if(invert)
invertz2(&init);
else
init.x = dx0[col]+dx1[row];
old.x = init.x + parm.x; /* initial pertubation of parameters set */
old.y = init.y + parm.y;
tempsqrx = sqr(old.x); /* precalculated value */
tempsqry = sqr(old.y);
Coefficient = ComplexPower(init, pwr);
return(1);
}
/* -------------------------------------------------------------------- */
/* Setup (once per fractal image) routines */
/* -------------------------------------------------------------------- */
MandelSetup() /* Mandelbrot Routine */
{
#ifndef XFRACT
if (debugflag != 90 && ! invert && decomp[0] == 0 && rqlim <= 4.0
&& bitshift == 29 && potflag == 0
&& biomorph == -1 && inside > -59 && outside == -1
&& useinitorbit != 1)
calctype = calcmand; /* the normal case - use CALCMAND */
else
#endif
{
/* special case: use the main processing loop */
calctype = StandardFractal;
longparm = &linit;
}
return(1);
}
JuliaSetup() /* Julia Routine */
{
if (debugflag != 90 && ! invert && decomp[0] == 0 && rqlim <= 4.0
&& bitshift == 29 && potflag == 0
&& biomorph == -1 && inside > -59 && outside == -1
&& !finattract)
calctype = calcmand; /* the normal case - use CALCMAND */
else
{
/* special case: use the main processing loop */
calctype = StandardFractal;
longparm = &lparm;
get_julia_attractor (0.0, 0.0); /* another attractor? */
}
return(1);
}
NewtonSetup() /* Newton/NewtBasin Routines */
{
int i;
extern int basin;
extern int fpu;
if (debugflag != 1010)
{
if(fpu != 0)
{
if(fractype == MPNEWTON)
fractype = NEWTON;
else if(fractype == MPNEWTBASIN)
fractype = NEWTBASIN;
}
else
{
if(fractype == NEWTON)
fractype = MPNEWTON;
else if(fractype == NEWTBASIN)
fractype = MPNEWTBASIN;
}
curfractalspecific = &fractalspecific[fractype];
}
/* set up table of roots of 1 along unit circle */
degree = (int)parm.x;
if(degree < 2)
degree = 3; /* defaults to 3, but 2 is possible */
root = 1;
/* precalculated values */
roverd = (double)root / (double)degree;
d1overd = (double)(degree - 1) / (double)degree;
maxcolor = 0;
threshold = .3*PI/degree; /* less than half distance between roots */
if (fractype == MPNEWTON || fractype == MPNEWTBASIN) {
mproverd = *pd2MP(roverd);
mpd1overd = *pd2MP(d1overd);
mpthreshold = *pd2MP(threshold);
mpone = *pd2MP(1.0);
}
floatmin = FLT_MIN;
floatmax = FLT_MAX;
basin = 0;
if(roots != staticroots) {
free(roots);
roots = staticroots;
}
if (fractype==NEWTBASIN)
{
if(parm.y)
basin = 2; /*stripes */
else
basin = 1;
if(degree > 16)
{
if((roots=(CMPLX *)malloc(degree*sizeof(CMPLX)))==NULL)
{
roots = staticroots;
degree = 16;
}
}
else
roots = staticroots;
/* list of roots to discover where we converged for newtbasin */
for(i=0;i<degree;i++)
{
roots[i].x = cos(i*PI*2.0/(double)degree);
roots[i].y = sin(i*PI*2.0/(double)degree);
}
}
else if (fractype==MPNEWTBASIN)
{
if(parm.y)
basin = 2; /*stripes */
else
basin = 1;
if(degree > 16)
{
if((MPCroots=(struct MPC *)malloc(degree*sizeof(struct MPC)))==NULL)
{
MPCroots = (struct MPC *)staticroots;
degree = 16;
}
}
else
MPCroots = (struct MPC *)staticroots;
/* list of roots to discover where we converged for newtbasin */
for(i=0;i<degree;i++)
{
MPCroots[i].x = *pd2MP(cos(i*PI*2.0/(double)degree));
MPCroots[i].y = *pd2MP(sin(i*PI*2.0/(double)degree));
}
}
if (degree%4 == 0)
symmetry = XYAXIS;
else
symmetry = XAXIS;
calctype=StandardFractal;
if (fractype == MPNEWTON || fractype == MPNEWTBASIN)
setMPfunctions();
return(1);
}
StandaloneSetup()
{
timer(0,curfractalspecific->calctype);
return(0); /* effectively disable solid-guessing */
}
UnitySetup()
{
periodicitycheck = 0;
FgOne = (1L << bitshift);
FgTwo = FgOne + FgOne;
return(1);
}
MandelfpSetup()
{
c_exp = param[2];
pwr.x = param[2] - 1.0;
pwr.y = param[3];
floatparm = &init;
switch (fractype)
{
case MANDELFP:
/*
floating point code could probably be altered to handle many of
the situations that otherwise are using StandardFractal().
calcmandfp() can currently handle invert, any rqlim, potflag
zmag, epsilon cross, and all the current outside options
Wes Loewer 11/03/91
*/
if (debugflag != 90
&& !distest
&& decomp[0] == 0
&& biomorph == -1
&& (inside >= -1 || inside == -59 || inside == -100)
/* uncomment this next line if more outside options are added */
/* && outside >= -5 */
&& useinitorbit != 1)
{
calctype = calcmandfp; /* the normal case - use calcmandfp */
calcmandfpasmstart();
}
else
{
/* special case: use the main processing loop */
calctype = StandardFractal;
}
break;
case FPMANDELZPOWER:
if(c_exp < 1)
c_exp = 1;
if(c_exp & 1) /* odd exponents */
symmetry = XYAXIS_NOPARM;
if(param[3] != 0 || (double)c_exp != param[2])
symmetry = NOSYM;
if(param[4] == 0.0 && debugflag != 6000 && (double)c_exp == param[2])
fractalspecific[fractype].orbitcalc = floatZpowerFractal;
else
fractalspecific[fractype].orbitcalc = floatCmplxZpowerFractal;
break;
case MAGNET1M:
case MAGNET2M:
attr[0].x = 1.0; /* 1.0 + 0.0i always attracts */
attr[0].y = 0.0; /* - both MAGNET1 and MAGNET2 */
attractors = 1;
break;
case SPIDERFP:
if(periodicitycheck==1) /* if not user set */
periodicitycheck=4;
break;
case MANDELEXP:
symmetry = XAXIS_NOPARM;
break;
default:
break;
}
return(1);
}
JuliafpSetup()
{
c_exp = param[2];
floatparm = &parm;
if(fractype==COMPLEXMARKSJUL)
{
pwr.x = param[2] - 1.0;
pwr.y = param[3];
Coefficient = ComplexPower(*floatparm, pwr);
}
switch (fractype)
{
case JULIAFP:
/*
floating point code could probably be altered to handle many of
the situations that otherwise are using StandardFractal().
calcmandfp() can currently handle invert, any rqlim, potflag
zmag, epsilon cross, and all the current outside options
Wes Loewer 11/03/91
*/
if (debugflag != 90
&& !distest
&& decomp[0] == 0
&& biomorph == -1
&& (inside >= -1 || inside == -59 || inside == -100)
/* uncomment this next line if more outside options are added */
/* && outside >= -5 */
&& useinitorbit != 1
&& !finattract)
{
calctype = calcmandfp; /* the normal case - use calcmandfp */
calcmandfpasmstart();
}
else
{
/* special case: use the main processing loop */
calctype = StandardFractal;
get_julia_attractor (0.0, 0.0); /* another attractor? */
}
break;
case FPJULIAZPOWER:
if((c_exp & 1) || param[3] != 0.0 || (double)c_exp != param[2] )
symmetry = NOSYM;
else if(c_exp < 1)
c_exp = 1;
if(param[4] == 0.0 && debugflag != 6000 && (double)c_exp == param[2])
fractalspecific[fractype].orbitcalc = floatZpowerFractal;
else
fractalspecific[fractype].orbitcalc = floatCmplxZpowerFractal;
break;
case MAGNET2J:
FloatPreCalcMagnet2();
case MAGNET1J:
attr[0].x = 1.0; /* 1.0 + 0.0i always attracts */
attr[0].y = 0.0; /* - both MAGNET1 and MAGNET2 */
attractors = 1;
get_julia_attractor (0.0, 0.0); /* another attractor? */
break;
case LAMBDAFP:
get_julia_attractor (0.0, 0.0); /* another attractor? */
get_julia_attractor (0.5, 0.0); /* another attractor? */
break;
case LAMBDAEXP:
if(parm.y == 0.0)
symmetry=XAXIS;
get_julia_attractor (0.0, 0.0); /* another attractor? */
break;
default:
get_julia_attractor (0.0, 0.0); /* another attractor? */
break;
}
return(1);
}
MandellongSetup()
{
FgHalf = fudge >> 1;
c_exp = param[2];
if(fractype==MARKSMANDEL && c_exp < 1)
c_exp = 1;
if(fractype==LMANDELZPOWER && c_exp < 1)
c_exp = 1;
if((fractype==MARKSMANDEL && !(c_exp & 1)) ||
(fractype==LMANDELZPOWER && c_exp & 1))
symmetry = XYAXIS_NOPARM; /* odd exponents */
if((fractype==MARKSMANDEL && (c_exp & 1)) || fractype==LMANDELEXP)
symmetry = XAXIS_NOPARM;
if(fractype==SPIDER && periodicitycheck==1)
periodicitycheck=4;
longparm = &linit;
if(fractype==LMANDELZPOWER)
{
if(param[4] == 0.0 && debugflag != 6000 && (double)c_exp == param[2])
fractalspecific[fractype].orbitcalc = longZpowerFractal;
else
fractalspecific[fractype].orbitcalc = longCmplxZpowerFractal;
if(param[3] != 0 || (double)c_exp != param[2] )
symmetry = NOSYM;
}
return(1);
}
JulialongSetup()
{
c_exp = param[2];
longparm = &lparm;
switch (fractype)
{
case LJULIAZPOWER:
if((c_exp & 1) || param[3] != 0.0 || (double)c_exp != param[2])
symmetry = NOSYM;
else if(c_exp < 1)
c_exp = 1;
if(param[4] == 0.0 && debugflag != 6000 && (double)c_exp == param[2])
fractalspecific[fractype].orbitcalc = longZpowerFractal;
else
fractalspecific[fractype].orbitcalc = longCmplxZpowerFractal;
break;
case LAMBDA:
get_julia_attractor (0.0, 0.0); /* another attractor? */
get_julia_attractor (0.5, 0.0); /* another attractor? */
break;
case LLAMBDAEXP:
if(lparm.y == 0)
symmetry = XAXIS;
break;
default:
get_julia_attractor (0.0, 0.0); /* another attractor? */
break;
}
return(1);
}
TrigPlusSqrlongSetup()
{
curfractalspecific->per_pixel = julia_per_pixel;
curfractalspecific->orbitcalc = TrigPlusSqrFractal;
if(lparm.x == fudge && lparm.y == 0L && lparm2.y == 0L && debugflag != 90)
{
if(lparm2.x == fudge) /* Scott variant */
curfractalspecific->orbitcalc = ScottTrigPlusSqrFractal;
else if(lparm2.x == -fudge) /* Skinner variant */
curfractalspecific->orbitcalc = SkinnerTrigSubSqrFractal;
}
return(JulialongSetup());
}
TrigPlusSqrfpSetup()
{
curfractalspecific->per_pixel = juliafp_per_pixel;
curfractalspecific->orbitcalc = TrigPlusSqrfpFractal;
if(parm.x == 1.0 && parm.y == 0.0 && parm2.y == 0.0 && debugflag != 90)
{
if(parm2.x == 1.0) /* Scott variant */
curfractalspecific->orbitcalc = ScottTrigPlusSqrfpFractal;
else if(parm2.x == -1.0) /* Skinner variant */
curfractalspecific->orbitcalc = SkinnerTrigSubSqrfpFractal;
}
return(JuliafpSetup());
}
TrigPlusTriglongSetup()
{
FnPlusFnSym();
if(trigndx[1] == SQR)
return(TrigPlusSqrlongSetup());
curfractalspecific->per_pixel = long_julia_per_pixel;
curfractalspecific->orbitcalc = TrigPlusTrigFractal;
if(lparm.x == fudge && lparm.y == 0L && lparm2.y == 0L && debugflag != 90)
{
if(lparm2.x == fudge) /* Scott variant */
curfractalspecific->orbitcalc = ScottTrigPlusTrigFractal;
else if(lparm2.x == -fudge) /* Skinner variant */
curfractalspecific->orbitcalc = SkinnerTrigSubTrigFractal;
}
return(JulialongSetup());
}
TrigPlusTrigfpSetup()
{
FnPlusFnSym();
if(trigndx[1] == SQR)
return(TrigPlusSqrfpSetup());
curfractalspecific->per_pixel = otherjuliafp_per_pixel;
curfractalspecific->orbitcalc = TrigPlusTrigfpFractal;
if(parm.x == 1.0 && parm.y == 0.0 && parm2.y == 0.0 && debugflag != 90)
{
if(parm2.x == 1.0) /* Scott variant */
curfractalspecific->orbitcalc = ScottTrigPlusTrigfpFractal;
else if(parm2.x == -1.0) /* Skinner variant */
curfractalspecific->orbitcalc = SkinnerTrigSubTrigfpFractal;
}
return(JuliafpSetup());
}
FnPlusFnSym() /* set symmetry matrix for fn+fn type */
{
static char far fnplusfn[7][7] =
{/* fn2 ->sin cos sinh cosh sqr exp log */
/* fn1 */
/* sin */ {PI_SYM,XAXIS, XYAXIS, XAXIS, XAXIS, XAXIS, XAXIS},
/* cos */ {XAXIS, PI_SYM,XAXIS, XYAXIS,XAXIS, XAXIS, XAXIS},
/* sinh*/ {XYAXIS,XAXIS, XYAXIS, XAXIS, XAXIS, XAXIS, XAXIS},
/* cosh*/ {XAXIS, XYAXIS,XAXIS, XYAXIS,XAXIS, XAXIS, XAXIS},
/* sqr */ {XAXIS, XYAXIS,XAXIS, XAXIS, XYAXIS,XAXIS, XAXIS},
/* exp */ {XAXIS, XAXIS, XAXIS, XAXIS, XAXIS, XAXIS, XAXIS},
/* log */ {XAXIS, XAXIS, XAXIS, XAXIS, XAXIS, XAXIS, XYAXIS}
};
if(parm.y == 0.0 && parm2.y == 0.0)
symmetry = fnplusfn[trigndx[0]][trigndx[1]];
else
symmetry = NOSYM;
return(0);
}
ZXTrigPlusZSetup()
{
static char far ZXTrigPlusZSym1[] =
/* fn1 -> sin cos sinh cosh sqr exp log */
{XAXIS,XYAXIS,XAXIS,XYAXIS,XYAXIS,XAXIS,XAXIS};
static char far ZXTrigPlusZSym2[] =
/* fn1 -> sin cos sinh cosh sqr exp log */
{NOSYM,ORIGIN,NOSYM,ORIGIN,XYAXIS,NOSYM,NOSYM};
if(param[1] == 0.0 && param[3] == 0.0)
symmetry = ZXTrigPlusZSym1[trigndx[0]];
else
symmetry = ZXTrigPlusZSym2[trigndx[0]];
if(curfractalspecific->isinteger)
{
curfractalspecific->orbitcalc = ZXTrigPlusZFractal;
if(lparm.x == fudge && lparm.y == 0L && lparm2.y == 0L && debugflag != 90)
{
if(lparm2.x == fudge) /* Scott variant */
curfractalspecific->orbitcalc = ScottZXTrigPlusZFractal;
else if(lparm2.x == -fudge) /* Skinner variant */
curfractalspecific->orbitcalc = SkinnerZXTrigSubZFractal;
}
return(JulialongSetup());
}
else
{
curfractalspecific->orbitcalc = ZXTrigPlusZfpFractal;
if(parm.x == 1.0 && parm.y == 0.0 && parm2.y == 0.0 && debugflag != 90)
{
if(parm2.x == 1.0) /* Scott variant */
curfractalspecific->orbitcalc = ScottZXTrigPlusZfpFractal;
else if(parm2.x == -1.0) /* Skinner variant */
curfractalspecific->orbitcalc = SkinnerZXTrigSubZfpFractal;
}
}
return(JuliafpSetup());
}
LambdaTrigSetup()
{
int isinteger;
if((isinteger = curfractalspecific->isinteger))
curfractalspecific->orbitcalc = LambdaTrigFractal;
else
curfractalspecific->orbitcalc = LambdaTrigfpFractal;
switch(trigndx[0])
{
case SIN:
case COS:
symmetry = PI_SYM;
if(isinteger)
curfractalspecific->orbitcalc = LambdaTrigFractal1;
else
curfractalspecific->orbitcalc = LambdaTrigfpFractal1;
break;
case SINH:
case COSH:
symmetry = ORIGIN;
if(isinteger)
curfractalspecific->orbitcalc = LambdaTrigFractal2;
else
curfractalspecific->orbitcalc = LambdaTrigfpFractal2;
break;
case SQR:
symmetry = ORIGIN;
break;
case EXP:
if(isinteger)
curfractalspecific->orbitcalc = LongLambdaexponentFractal;
else
curfractalspecific->orbitcalc = LambdaexponentFractal;
symmetry = XAXIS;
break;
case LOG:
symmetry = NOSYM;
break;
}
if(isinteger)
return(JulialongSetup());
else
return(JuliafpSetup());
}
JuliafnPlusZsqrdSetup()
{
static char far fnpluszsqrd[] =
/* fn1 -> sin cos sinh cosh sqr exp log */
/* sin */ {NOSYM,ORIGIN,NOSYM,ORIGIN,ORIGIN,NOSYM,NOSYM};
symmetry = fnpluszsqrd[trigndx[0]];
if(curfractalspecific->isinteger)
return(JulialongSetup());
else
return(JuliafpSetup());
}
SqrTrigSetup()
{
static char far SqrTrigSym[] =
/* fn1 -> sin cos sinh cosh sqr exp log */
{PI_SYM,PI_SYM,XYAXIS,XYAXIS,XYAXIS,XAXIS,XAXIS};
symmetry = SqrTrigSym[trigndx[0]];
if(curfractalspecific->isinteger)
return(JulialongSetup());
else
return(JuliafpSetup());
}
FnXFnSetup()
{
static char far fnxfn[7][7] =
{/* fn2 ->sin cos sinh cosh sqr exp log */
/* fn1 */
/* sin */ {PI_SYM,YAXIS, XYAXIS,XYAXIS,XYAXIS,XAXIS, XAXIS},
/* cos */ {YAXIS, PI_SYM,XYAXIS,XYAXIS,XYAXIS,XAXIS, XAXIS},
/* sinh*/ {XYAXIS,XYAXIS,XYAXIS,XYAXIS,XYAXIS,XAXIS, XAXIS},
/* cosh*/ {XYAXIS,XYAXIS,XYAXIS,XYAXIS,XYAXIS,XAXIS, XAXIS},
/* sqr */ {XYAXIS,XYAXIS,XYAXIS,XYAXIS,XYAXIS,XAXIS, XAXIS},
/* exp */ {XAXIS, XAXIS, XAXIS, XAXIS, XAXIS, XAXIS, XAXIS},
/* log */ {XAXIS, XAXIS, XAXIS, XAXIS, XAXIS, XAXIS, XAXIS},
};
/*
if(trigndx[0]==EXP || trigndx[0]==LOG || trigndx[1]==EXP || trigndx[1]==LOG)
symmetry = XAXIS;
else if((trigndx[0]==SIN && trigndx[1]==SIN)||(trigndx[0]==COS && trigndx[1]==COS))
symmetry = PI_SYM;
else if((trigndx[0]==SIN && trigndx[1]==COS)||(trigndx[0]==COS && trigndx[1]==SIN))
symmetry = YAXIS;
else
symmetry = XYAXIS;
*/
symmetry = fnxfn[trigndx[0]][trigndx[1]];
if(curfractalspecific->isinteger)
return(JulialongSetup());
else
return(JuliafpSetup());
}
MandelTrigSetup()
{
int isinteger;
if((isinteger = curfractalspecific->isinteger))
curfractalspecific->orbitcalc = LambdaTrigFractal;
else
curfractalspecific->orbitcalc = LambdaTrigfpFractal;
symmetry = XYAXIS_NOPARM;
switch(trigndx[0])
{
case SIN:
case COS:
if(isinteger)
curfractalspecific->orbitcalc = LambdaTrigFractal1;
else
curfractalspecific->orbitcalc = LambdaTrigfpFractal1;
break;
case SINH:
case COSH:
if(isinteger)
curfractalspecific->orbitcalc = LambdaTrigFractal2;
else
curfractalspecific->orbitcalc = LambdaTrigfpFractal2;
break;
case EXP:
symmetry = XAXIS_NOPARM;
if(isinteger)
curfractalspecific->orbitcalc = LongLambdaexponentFractal;
else
curfractalspecific->orbitcalc = LambdaexponentFractal;
break;
case LOG:
symmetry = XAXIS_NOPARM;
break;
}
if(isinteger)
return(MandellongSetup());
else
return(MandelfpSetup());
}
MarksJuliaSetup()
{
c_exp = param[2];
longparm = &lparm;
lold = *longparm;
if(c_exp > 2)
lcpower(&lold,c_exp,&lcoefficient,bitshift);
else if(c_exp == 2)
{
lcoefficient.x = multiply(lold.x,lold.x,bitshift) - multiply(lold.y,lold.y,bitshift);
lcoefficient.y = multiply(lold.x,lold.y,bitshiftless1);
}
else if(c_exp < 2)
lcoefficient = lold;
return(1);
}
SierpinskiSetup()
{
/* sierpinski */
periodicitycheck = 0; /* disable periodicity checks */
ltmp.x = 1;
ltmp.x = ltmp.x << bitshift; /* ltmp.x = 1 */
ltmp.y = ltmp.x >> 1; /* ltmp.y = .5 */
return(1);
}
SierpinskiFPSetup()
{
/* sierpinski */
periodicitycheck = 0; /* disable periodicity checks */
tmp.x = 1;
tmp.y = 0.5;
return(1);
}
StandardSetup()
{
if(fractype==UNITYFP)
periodicitycheck=0;
return(1);
}