Category : C Source Code
Archive   : FRASRC18.ZIP
Filename : MPMATH_C.C

 
Output of file : MPMATH_C.C contained in archive : FRASRC18.ZIP
/* MPMath_c.c (C) 1989, Mark C. Peterson, CompuServe [70441,3353]
All rights reserved.

Code may be used in any program provided the author is credited
either during program execution or in the documentation. Source
code may be distributed only in combination with public domain or
shareware source code. Source code may be modified provided the
copyright notice and this message is left unchanged and all
modifications are clearly documented.

I would appreciate a copy of any work which incorporates this code,
however this is optional.

Mark C. Peterson
405-C Queen St. Suite #181
Southington, CT 06489
(203) 276-9721
*/

#include
#include "mpmath.h"
#include "prototyp.h"

#ifndef XFRACT

int MPaccuracy = 32;

struct MP *MPsub(struct MP x, struct MP y) {
y.Exp ^= 0x8000;
return(MPadd(x, y));
}

/* added by TW */
struct MP *MPsub086(struct MP x, struct MP y) {
y.Exp ^= 0x8000;
return(MPadd086(x, y));
}

/* added by TW */
struct MP *MPsub386(struct MP x, struct MP y) {
y.Exp ^= 0x8000;
return(MPadd386(x, y));
}

struct MP *MPabs(struct MP x) {
x.Exp &= 0x7fff;
return(&x);
}

struct MPC MPCsqr(struct MPC x) {
struct MPC z;

z.x = *pMPsub(*pMPmul(x.x, x.x), *pMPmul(x.y, x.y));
z.y = *pMPmul(x.x, x.y);
z.y.Exp++;
return(z);
}

struct MP MPCmod(struct MPC x) {
return(*pMPadd(*pMPmul(x.x, x.x), *pMPmul(x.y, x.y)));
}

struct MPC MPCmul(struct MPC x, struct MPC y) {
struct MPC z;

z.x = *pMPsub(*pMPmul(x.x, y.x), *pMPmul(x.y, y.y));
z.y = *pMPadd(*pMPmul(x.x, y.y), *pMPmul(x.y, y.x));
return(z);
}

struct MPC MPCdiv(struct MPC x, struct MPC y) {
struct MP mod;

mod = MPCmod(y);
y.y.Exp ^= 0x8000;
y.x = *pMPdiv(y.x, mod);
y.y = *pMPdiv(y.y, mod);
return(MPCmul(x, y));
}

struct MPC MPCadd(struct MPC x, struct MPC y) {
struct MPC z;

z.x = *pMPadd(x.x, y.x);
z.y = *pMPadd(x.y, y.y);
return(z);
}

struct MPC MPCsub(struct MPC x, struct MPC y) {
struct MPC z;

z.x = *pMPsub(x.x, y.x);
z.y = *pMPsub(x.y, y.y);
return(z);
}

struct MPC MPCone = { 0x3fff, 0x80000000l, 0, 0l };

struct MPC MPCpow(struct MPC x, int exp) {
struct MPC z;
struct MPC zz;

if(exp & 1)
z = x;
else
z = MPCone;
exp >>= 1;
while(exp) {
zz.x = *pMPsub(*pMPmul(x.x, x.x), *pMPmul(x.y, x.y));
zz.y = *pMPmul(x.x, x.y);
zz.y.Exp++;
x = zz;
if(exp & 1) {
zz.x = *pMPsub(*pMPmul(z.x, x.x), *pMPmul(z.y, x.y));
zz.y = *pMPadd(*pMPmul(z.x, x.y), *pMPmul(z.y, x.x));
z = zz;
}
exp >>= 1;
}
return(z);
}

int MPCcmp(struct MPC x, struct MPC y) {
struct MPC z;

if(pMPcmp(x.x, y.x) || pMPcmp(x.y, y.y)) {
z.x = MPCmod(x);
z.y = MPCmod(y);
return(pMPcmp(z.x, z.y));
}
else
return(0);
}

_CMPLX MPC2cmplx(struct MPC x) {
_CMPLX z;

z.x = *pMP2d(x.x);
z.y = *pMP2d(x.y);
return(z);
}

struct MPC cmplx2MPC(_CMPLX z) {
struct MPC x;

x.x = *pd2MP(z.x);
x.y = *pd2MP(z.y);
return(x);
}

/* function pointer versions added by Tim Wegner 12/07/89 */
int (*ppMPcmp)() = MPcmp086;
int (*pMPcmp)(struct MP x, struct MP y) = MPcmp086;
struct MP *(*pMPmul)(struct MP x, struct MP y)= MPmul086;
struct MP *(*pMPdiv)(struct MP x, struct MP y)= MPdiv086;
struct MP *(*pMPadd)(struct MP x, struct MP y)= MPadd086;
struct MP *(*pMPsub)(struct MP x, struct MP y)= MPsub086;
struct MP *(*pd2MP)(double x) = d2MP086 ;
double *(*pMP2d)(struct MP m) = MP2d086 ;
struct MP *(*pfg2MP)(long x, int fg) = fg2MP086;

void setMPfunctions(void) {
if(cpu == 386)
{
pMPmul = MPmul386;
pMPdiv = MPdiv386;
pMPadd = MPadd386;
pMPsub = MPsub386;
pMPcmp = MPcmp386;
pd2MP = d2MP386 ;
pMP2d = MP2d386 ;
pfg2MP = fg2MP386;
}
else
{
pMPmul = MPmul086;
pMPdiv = MPdiv086;
pMPadd = MPadd086;
pMPsub = MPsub086;
pMPcmp = MPcmp086;
pd2MP = d2MP086 ;
pMP2d = MP2d086 ;
pfg2MP = fg2MP086;
}
}

#endif /* XFRACT */

#ifndef sqr
#define sqr(x) ((x)*(x))
#endif

extern int debugflag, fpu;

_CMPLX ComplexPower(_CMPLX xx, _CMPLX yy) {
_CMPLX z, cLog, t;
double e2x, siny, cosy;

FPUcplxlog(&xx, &cLog);
FPUcplxmul(&cLog, &yy, &t);

if(fpu == 387)
FPUcplxexp387(&t, &z);
else {
if(t.x < -690)
e2x = 0;
else
e2x = exp(t.x);
FPUsincos(&t.y, &siny, &cosy);
z.x = e2x * cosy;
z.y = e2x * siny;
}
return(z);
}

/***** FRACTINT specific routines and variables *****/

#ifndef TESTING_MATH

#include

#include "fractint.h"

extern double param[];
extern _CMPLX old, new, init;
extern double threshold, roverd, d1overd, dx0[], dy0[];
extern int periodicitycheck, row, col, debugflag;


#include

extern int xdots, ydots; /* coordinates of dots on the screen */
extern int colors; /* maximum colors available */
extern int maxit;

BYTE far *LogTable = (BYTE far *)0;
extern int LogFlag;
/* LogFlag == 1 -- standard log palettes
LogFlag == -1 -- 'old' log palettes
LogFlag > 1 -- compress counts < LogFlag into color #1
LogFlag < -1 -- use quadratic palettes based on square roots && compress
*/

void SetupLogTable(void) {
float l, f, c, m;
unsigned n, prev, limit, lf;

if (LogFlag > -2) {
lf = (LogFlag > 1) ? LogFlag : 0;
if (lf >= maxit)
lf = maxit - 1;
Fg2Float((long)(maxit-lf), 0, m);
fLog14(m, m);
Fg2Float((long)(colors-(lf?2:1)), 0, c);
fDiv(m, c, m);
for (prev = 1; prev <= lf; prev++)
LogTable[prev] = 1;
for (n = (lf?2:1); n < colors; n++) {
Fg2Float((long)n, 0, f);
fMul16(f, m, f);
fExp14(f, l);
limit = Float2Fg(l, 0) + lf;
if (limit > maxit || n == colors-1)
limit = maxit;
while (prev <= limit)
LogTable[prev++] = n;
}
} else {
if ((lf = 0 - LogFlag) >= maxit)
lf = maxit - 1;
Fg2Float((long)(maxit-lf), 0, m);
fSqrt14(m, m);
Fg2Float((long)(colors-2), 0, c);
fDiv(m, c, m);
for (prev = 1; prev <= lf; prev++)
LogTable[prev] = 1;
for (n = 2; n < colors; n++) {
Fg2Float((long)n, 0, f);
fMul16(f, m, f);
fMul16(f, f, l);
limit = Float2Fg(l, 0) + lf;
if (limit > maxit || n == colors-1)
limit = maxit;
while (prev <= limit)
LogTable[prev++] = n;
}
}
LogTable[0] = 0;
if (LogFlag != -1)
for (n = 1; n < maxit; n++) /* spread top to incl unused colors */
if (LogTable[n] > LogTable[n-1])
LogTable[n] = LogTable[n-1]+1;
}

long far ExpFloat14(long xx) {
static float fLogTwo = (float)0.6931472;
int f;
long Ans;

f = 23 - (int)RegFloat2Fg(RegDivFloat(xx, *(long*)&fLogTwo), 0);
Ans = ExpFudged(RegFloat2Fg(xx, 16), f);
return(RegFg2Float(Ans, (char)f));
}

extern _CMPLX tmp;
extern int color, colors;
double TwoPi;
_CMPLX temp, t2, BaseLog;
_CMPLX cdegree = { 3.0, 0.0 },
croot = { 1.0, 0.0 };

int ComplexNewtonSetup(void) {
threshold = .001;
periodicitycheck = 0;
if(param[0] != 0.0 || param[1] != 0.0 || param[2] != 0.0 ||
param[3] != 0.0) {
croot.x = param[2];
croot.y = param[3];
cdegree.x = param[0];
cdegree.y = param[1];
FPUcplxlog(&croot, &BaseLog);
TwoPi = asin(1.0) * 4;
}
return(1);
}

int ComplexNewton(void) {
_CMPLX cd1;

/* new = ((cdegree-1) * old**cdegree) + croot
----------------------------------
cdegree * old**(cdegree-1) */

cd1.x = cdegree.x - 1.0;
cd1.y = cdegree.y;

temp = ComplexPower(old, cd1);
FPUcplxmul(&temp, &old, &new);

tmp.x = new.x - croot.x;
tmp.y = new.y - croot.y;
if((sqr(tmp.x) + sqr(tmp.y)) < threshold)
return(1);

FPUcplxmul(&new, &cd1, &tmp);
tmp.x += croot.x;
tmp.y += croot.y;

FPUcplxmul(&temp, &cdegree, &t2);
FPUcplxdiv(&tmp, &t2, &old);
if(DivideOverflow)
{
DivideOverflow = 0;
return(1);
}
new = old;
return(0);
}

int ComplexBasin(void) {
_CMPLX cd1;
double mod;

/* new = ((cdegree-1) * old**cdegree) + croot
----------------------------------
cdegree * old**(cdegree-1) */

cd1.x = cdegree.x - 1.0;
cd1.y = cdegree.y;

temp = ComplexPower(old, cd1);
FPUcplxmul(&temp, &old, &new);

tmp.x = new.x - croot.x;
tmp.y = new.y - croot.y;
if((sqr(tmp.x) + sqr(tmp.y)) < threshold) {
if(fabs(old.y) < .01)
old.y = 0.0;
FPUcplxlog(&old, &temp);
FPUcplxmul(&temp, &cdegree, &tmp);
mod = tmp.y/TwoPi;
color = (int)mod;
if(fabs(mod - color) > 0.5) {
if(mod < 0.0)
color--;
else
color++;
}
color += 2;
if(color < 0)
color += 128;
return(1);
}

FPUcplxmul(&new, &cd1, &tmp);
tmp.x += croot.x;
tmp.y += croot.y;

FPUcplxmul(&temp, &cdegree, &t2);
FPUcplxdiv(&tmp, &t2, &old);
if(DivideOverflow)
{
DivideOverflow = 0;
return(1);
}
new = old;
return(0);
}

extern int Distribution, Offset, Slope;
extern long con;

/*** PB, commented this out, it was unused, actual work is in prompts.c
int Starfield(void) {
int c;

plasma();
Distribution = (int)param[1];
con = (long)(param[2] / 100 * (1L << 16));
Slope = (int)param[3];
for(row = 0; row < ydots; row++) {
for(col = 0; col < xdots; col++) {
if(check_key())
return(-1);
c = getcolor(col, row);
putcolor(col, row, GausianNumber(c, colors));
}
}
return(0);
}
***/

/*
* Generate a gaussian distributed number.
* The right half of the distribution is folded onto the lower half.
* That is, the curve slopes up to the peak and then drops to 0.
* The larger slope is, the smaller the standard deviation.
* The values vary from 0+offset to range+offset, with the peak
* at range+offset.
* To make this more complicated, you only have a
* 1 in Distribution*(1-Probability/Range*con)+1 chance of getting a
* Gaussian; otherwise you just get offset.
*/
int GausianNumber(int Probability, int Range) {
int n, r;
long Accum = 0, p;

p = divide((long)Probability << 16, (long)Range << 16, 16);
p = multiply(p, con, 16);
p = multiply((long)Distribution << 16, p, 16);
if(!(rand15() % (Distribution - (int)(p >> 16) + 1))) {
for(n = 0; n < Slope; n++)
Accum += rand15();
Accum /= Slope;
r = (int)(multiply((long)Range << 15, Accum, 15) >> 14);
r = r - Range;
if(r < 0)
r = -r;
return(Range - r + Offset);
}
return(Offset);
}

#endif


  3 Responses to “Category : C Source Code
Archive   : FRASRC18.ZIP
Filename : MPMATH_C.C

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