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josch 11 years ago
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98
mandel.c
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#include "colors.h"
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>
int main() {
long double eps = 1e-17;
long double Q1LOG2 = 1.44269504088896340735992468100189213742664595415299;
long double LOG2 = 0.69314718055994530941723212145817656807550013436026;
int width = 640;
int height = 480;
char* image = malloc(width*height*3);
int x, y;
long double centerx = -0.743643887037158704752191506114774;
long double centery = 0.131825904205311970493132056385139;
long double bailout = 128;
long double logLogBailout = log(log(bailout));
int foundperiods = 0;
long double magn = 1e18;
long maxiter = width * sqrt(magn);
long double x0d = 4 / magn / width;
long double x2 = -2 / magn + centerx;
long double y1d = -4 / magn / width;
long double y2 = 2 / magn * height / width + centery;
int imgidx = 0;
for (y = 0; y < height; y++) {
fprintf(stderr, "\r%f %%", (float)imgidx/(width*height*3)*100);
for (x = 0; x < width; x++) {
long double px = x*x0d + x2;
long double py = y*y1d + y2;
// no Main bulb or Cardoid check to be faster
long double zx = px;
long double zy = py;
long i;
// Initial maximum period to detect.
int check = 3;
// Maximum period doubles every iterations:
int whenupdate = 10;
// Period history registers.
long double hx = 0;
long double hy = 0;
long double xx, yy;
bool inside = true;
for (i = 1; i <= maxiter; i++) {
xx = zx * zx;
yy = zy * zy;
if (xx + yy > bailout) {
inside = false;
break;
}
// iterate
zy = 2 * zx * zy + py;
zx = xx - yy + px;
// periodicity check
long double d = zx - hx;
if (d > 0.0 ? d < eps : d > -eps) {
d = zy - hy;
if (d > 0.0 ? d < eps : d > -eps) {
// Period found.
foundperiods++;
break;
}
}
if ((i & check) == 0) {
if (--whenupdate == 0) {
whenupdate = 10;
check <<= 1;
check++;
}
// period = 0;
hx = zx;
hy = zy;
}
}
if (inside) {
image[imgidx++] = 0;
image[imgidx++] = 0;
image[imgidx++] = 0;
} else {
long double r = sqrtl(zx*zx + zy*zy);
long double c = i - 1.28 + (logLogBailout - logl(logl(r))) * Q1LOG2;
int idx = fmodl((logl(c/64+1)/LOG2+0.45), 1)*GRADIENTLENGTH + 0.5;
image[imgidx++] = colors[idx][0];
image[imgidx++] = colors[idx][1];
image[imgidx++] = colors[idx][2];
}
}
}
// write out image
printf("P6 %d %d 255\n", width, height);
fwrite(image, 1, width*height*3, stdout);
fprintf(stderr, "%d periods found\n", foundperiods);
return 0;
}

180
mandel_mpfr.c
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#include "colors.h"
#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>
#include <math.h>
#include <gmp.h>
#include <mpfr.h>
int main(int argc, char **argv) {
if (argc != 6) {
fprintf(stderr, "usage: %s width height centerx centery magnification", argv[0]);
return 1;
}
mpfr_t temp1, temp2;
mpfr_init2(temp1, 300);
mpfr_init2(temp2, 300);
//long double eps = 1e-17;
mpfr_t Q1LOG2, LOG2;
mpfr_init_set_str(Q1LOG2, "1.44269504088896340735992468100189213742664595415299", 10, MPFR_RNDN);
mpfr_init_set_str(LOG2, "0.69314718055994530941723212145817656807550013436026", 10, MPFR_RNDN);
unsigned int width = atoi(argv[1]);
unsigned int height = atoi(argv[2]);
char* image = malloc(width*height*3);
unsigned int x, y;
mpfr_t centerx, centery;
mpfr_init_set_str(centerx, argv[3], 10, MPFR_RNDN);
mpfr_init_set_str(centery, argv[4], 10, MPFR_RNDN);
double bailout = 4; // the distance must not be greater than 2 (4 = 2*2)
mpfr_t logLogBailout;
mpfr_init2(logLogBailout, 300);
// logLogBailout = log(log(bailout));
mpfr_set_d(logLogBailout, bailout, MPFR_RNDN);
mpfr_log(logLogBailout, logLogBailout, MPFR_RNDN);
mpfr_log(logLogBailout, logLogBailout, MPFR_RNDN);
mpfr_t magn;
mpfr_init_set_str(magn, argv[5], 10, MPFR_RNDN);
// maxiter = width * sqrt(magn);
mpfr_sqrt(temp1, magn, MPFR_RNDN);
unsigned long maxiter = width * mpfr_get_ui(temp1, MPFR_RNDN);
mpfr_t x2, y2, x0d, y1d;
mpfr_init2(x2, 300);
mpfr_init2(y2, 300);
mpfr_init2(x0d, 300);
mpfr_init2(y1d, 300);
// x0d = 4 / magn / width;
mpfr_ui_div(x0d, 4, magn, MPFR_RNDN);
mpfr_div_ui(x0d, x0d, width, MPFR_RNDN);
// x2 = -2 / magn + centerx;
mpfr_si_div(x2, -2, magn, MPFR_RNDN);
mpfr_add(x2, x2, centerx, MPFR_RNDN);
// y1d = -4 / magn / width;
mpfr_si_div(y1d, -4, magn, MPFR_RNDN);
mpfr_div_ui(y1d, y1d, width, MPFR_RNDN);
// y2 = 2 / magn * height / width + centery;
mpfr_ui_div(y2, 2, magn, MPFR_RNDN);
mpfr_set_ui(temp1, height, MPFR_RNDN);
mpfr_div_ui(temp1, temp1, width, MPFR_RNDN);
mpfr_mul(y2, y2, temp1, MPFR_RNDN);
mpfr_add(y2, y2, centery, MPFR_RNDN);
mpfr_t px, py, zx, zy, xx, yy, r, c;
mpfr_init2(px, 300);
mpfr_init2(py, 300);
mpfr_init2(zx, 300);
mpfr_init2(zy, 300);
mpfr_init2(xx, 300);
mpfr_init2(yy, 300);
mpfr_init2(r, 300);
mpfr_init2(c, 300);
int idx;
int imgidx = 0;
mpfr_t hx, hy, d;
mpfr_init2(hx, 300);
mpfr_init2(hy, 300);
mpfr_init2(d, 300);
int foundperiods = 0;
for (y = 0; y < height; y++) {
for (x = 0; x < width; x++) {
fprintf(stderr, "\r%f %%", (float)imgidx/(width*height*3)*100);
//px = x*x0d + x2;
mpfr_mul_ui(px, x0d, x, MPFR_RNDN);
mpfr_add(px, px, x2, MPFR_RNDN);
//py = y*y1d + y2;
mpfr_mul_ui(py, y1d, y, MPFR_RNDN);
mpfr_add(py, py, y2, MPFR_RNDN);
// no Main bulb or Cardoid check to be faster
//zx = px;
mpfr_set(zx, px, MPFR_RNDN);
//zy = py;
mpfr_set(zy, py, MPFR_RNDN);
unsigned long i;
bool inside = true;
/*int check = 3;
int whenupdate = 10;*/
mpfr_set_d(hx, 0, MPFR_RNDN);
mpfr_set_d(hy, 0, MPFR_RNDN);
for (i = 1; i <= maxiter; i++) {
//xx = zx * zx;
mpfr_mul(xx, zx, zx, MPFR_RNDN);
//yy = zy * zy;
mpfr_mul(yy, zy, zy, MPFR_RNDN);
//if (xx + yy > bailout) {
mpfr_add(temp1, xx, yy, MPFR_RNDN);
if (mpfr_cmp_ld(temp1, bailout) > 0) {
inside = false;
break;
}
// iterate
//zy = 2 * zx * zy + py;
mpfr_mul_ui(zx, zx, 2, MPFR_RNDN);
mpfr_mul(zy, zx, zy, MPFR_RNDN);
mpfr_add(zy, zy, py, MPFR_RNDN);
//zx = xx - yy + px;
mpfr_sub(zx, xx, yy, MPFR_RNDN);
mpfr_add(zx, zx, px, MPFR_RNDN);
// period checking
// d = zx - hx;
/*mpfr_sub(d, zx, hx, MPFR_RNDN);
mpfr_abs(d, d, MPFR_RNDN);
if (mpfr_cmp_d(d, eps) < 0) {
// d = zy - hy;
mpfr_sub(d, zy, hy, MPFR_RNDN);
mpfr_abs(d, d, MPFR_RNDN);
if (mpfr_cmp_d(d, eps) < 0) {
// Period found.
foundperiods++;
break;
}
}
if ((i & check) == 0) {
if (--whenupdate == 0) {
whenupdate = 10;
check <<= 1;
check++;
}
// period = 0;
mpfr_set(hx, zx, MPFR_RNDN);
mpfr_set(hy, zy, MPFR_RNDN);
}*/
}
if (inside) {
image[imgidx++] = 0;
image[imgidx++] = 0;
image[imgidx++] = 0;
} else {
//r = sqrtl(zx*zx + zy*zy);
mpfr_mul(temp1, zx, zx, MPFR_RNDN);
mpfr_mul(temp2, zy, zy, MPFR_RNDN);
mpfr_add(temp1, temp1, temp2, MPFR_RNDN);
mpfr_sqrt(r, temp1, MPFR_RNDN);
//c = i - 1.28 + (logLogBailout - logl(logl(r))) * Q1LOG2;
mpfr_log(r, r, MPFR_RNDN);
mpfr_log(r, r, MPFR_RNDN);
mpfr_sub(c, logLogBailout, r, MPFR_RNDN);
mpfr_mul(c, c, Q1LOG2, MPFR_RNDN);
mpfr_add_d(c, c, i - 1.28, MPFR_RNDN);
//idx = fmodl((logl(c/64+1)/LOG2+0.45), 1)*GRADIENTLENGTH + 0.5;
mpfr_div_ui(c, c, 64, MPFR_RNDN);
mpfr_add_ui(c, c, 1, MPFR_RNDN);
mpfr_log(c, c, MPFR_RNDN);
mpfr_div(c, c, LOG2, MPFR_RNDN);
mpfr_add_d(c, c, 0.45, MPFR_RNDN);
mpfr_frac(c, c, MPFR_RNDN);
mpfr_mul_d(c, c, GRADIENTLENGTH, MPFR_RNDN);
idx = mpfr_get_ui(c, MPFR_RNDN);
image[imgidx++] = colors[idx][0];
image[imgidx++] = colors[idx][1];
image[imgidx++] = colors[idx][2];
}
}
}
// write out image
printf("P6 %d %d 255\n", width, height);
fwrite(image, 1, width*height*3, stdout);
//fprintf(stderr, "\r%d found periods", foundperiods);
fprintf(stderr, "\n");
return 0;
}
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