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add doubledouble version

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josch 11 years ago
parent be7342b0cf
commit 63b7a4d02a
5 changed files with 308 additions and 14 deletions
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7
Makefile
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all:
gcc -Ofast -Wall -lquadmath mandel_quad.c -o mandel_quad
gcc -Ofast -Wall -lmpfr mandel_mpfr.c -o mandel_mpfr
gcc -Ofast -Wall -lm mandel.c -o mandel
gcc -O3 -Wall -lquadmath mandel_quad.c -o mandel_quad
gcc -O3 -Wall -lmpfr -lm mandel_mpfr.c -o mandel_mpfr
gcc -O3 -Wall -lm mandel.c -o mandel
gcc -O3 -Wall -lm mandel_dd.c -o mandel_dd

143
doubledouble.h
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#include <math.h>
typedef struct {
double hi;
double lo;
} DoubleDouble;
inline DoubleDouble dd_new(double hi, double lo) {
DoubleDouble num;
num.hi = hi;
num.lo = lo;
return num;
}
unsigned int dd_get_ui(DoubleDouble num) {
return num.hi;
}
inline DoubleDouble dd_sqrt(DoubleDouble num) {
double a, b, c, d, e;
d = 1 / sqrt(num.hi);
e = num.hi * d;
a = 0x08000001 * e;
a += e - a;
b = e - a;
c = e * e;
b = ((a * a - c) + a * b * 2) + b * b;
a = num.hi - c;
c = num.hi - a;
c = (a + ((((num.hi - (c + a)) + (c - c)) + num.lo) - b)) * d * 0.5;
a = e + c;
b = e - a;
return dd_new(a, (e - (b + a)) + (b + c));
}
inline DoubleDouble dd_div(DoubleDouble num1, DoubleDouble num2) {
double a, b, c, d, e, f, g;
f = num1.hi / num2.hi;
a = 0x08000001 * num2.hi;
a += num2.hi - a;
b = num2.hi - a;
c = 0x08000001 * f;
c += f - c;
d = f - c;
e = num2.hi * f;
c = (((a * c - e) + (a * d + b * c)) + b * d) + num2.lo * f;
b = num1.lo - c;
d = num1.lo - b;
a = num1.hi - e;
e = (num1.hi - ((num1.hi - a) + a)) + b;
g = a + e;
e += (a - g) + ((num1.lo - (d + b)) + (d - c));
a = g + e;
b = a / num2.hi;
f += (e + (g - a)) / num2.hi;
a = f + b;
return dd_new(a, b + (f - a));
}
inline DoubleDouble dd_ui_div(unsigned int num1, DoubleDouble num2) {
return dd_div(dd_new(num1, 0), num2);
}
inline DoubleDouble dd_div_ui(DoubleDouble num1, unsigned int num2) {
return dd_div(num1, dd_new(num2, 0));
}
inline DoubleDouble dd_si_div(signed int num1, DoubleDouble num2) {
return dd_div(dd_new(num1, 0), num2);
}
inline DoubleDouble dd_div_si(DoubleDouble num1, signed int num2) {
return dd_div(num1, dd_new(num2, 0));
}
inline DoubleDouble dd_add(DoubleDouble num1, DoubleDouble num2) {
double a, b, c, d, e, f;
e = num1.hi + num2.hi;
d = num1.hi - e;
a = num1.lo + num2.lo;
f = num1.lo - a;
d = ((num1.hi - (d + e)) + (d + num2.hi)) + a;
b = e + d;
c = ((num1.lo - (f + a)) + (f + num2.lo)) + (d + (e - b));
a = b + c;
return dd_new(a, c + (b - a));
}
inline DoubleDouble dd_mul(DoubleDouble num1, DoubleDouble num2) {
double a, b, c, d, e;
a = 0x08000001 * num1.hi;
a += num1.hi - a;
b = num1.hi - a;
c = 0x08000001 * num2.hi;
c += num2.hi - c;
d = num2.hi - c;
e = num1.hi * num2.hi;
c = (((a * c - e) + (a * d + b * c)) + b * d) + (num1.lo * num2.hi + num1.hi * num2.lo);
a = e + c;
return dd_new(a, c + (e - a));
}
inline DoubleDouble dd_mul2(DoubleDouble num1, DoubleDouble num2) {
double a, b, c, d, e;
a = 0x08000001 * num1.hi;
a += num1.hi - a;
b = num1.hi - a;
c = 0x08000001 * num2.hi;
c += num2.hi - c;
d = num2.hi - c;
e = num1.hi * num2.hi;
c = 2*((((a * c - e) + (a * d + b * c)) + b * d) + (num1.lo * num2.hi + num1.hi * num2.lo));
a = 2*e + c;
return dd_new(a, c + (2*e - a));
}
inline DoubleDouble dd_mul_ui(DoubleDouble num1, unsigned int num2) {
return dd_mul(num1, dd_new(num2, 0));
}
inline DoubleDouble dd_sub(DoubleDouble num1, DoubleDouble num2) {
double a, b, c, d, e, f, g;
g = num1.lo - num2.lo;
f = num1.lo - g;
e = num1.hi - num2.hi;
d = num1.hi - e;
d = ((num1.hi - (d + e)) + (d - num2.hi)) + g;
b = e + d;
c = (d + (e - b)) + ((num1.lo - (f + g)) + (f - num2.lo));
a = b + c;
return dd_new(a, c + (b - a));
}
inline DoubleDouble dd_sqr(DoubleDouble num) {
double a, b, c;
a = 0x08000001 * num.hi;
a += num.hi - a;
b = num.hi - a;
c = num.hi * num.hi;
b = ((((a * a - c) + a * b * 2) + b * b) + num.hi * num.lo * 2) + num.lo * num.lo;
a = b + c;
return dd_new(a, b + (c - a));
}

16
mandel.c
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#include <stdlib.h>
#include <stdbool.h>
int main() {
int main(int argc, char **argv) {
if (argc != 6) {
fprintf(stderr, "usage: %s width height centerx centery magnification", argv[0]);
return 1;
}
long double eps = 1e-17;
long double Q1LOG2 = 1.44269504088896340735992468100189213742664595415299;
long double LOG2 = 0.69314718055994530941723212145817656807550013436026;
int width = 640;
int height = 480;
int width = atoi(argv[1]);
int height = atoi(argv[2]);
char* image = malloc(width*height*3);
int x, y;
long double centerx = -0.743643887037158704752191506114774;
long double centery = 0.131825904205311970493132056385139;
long double centerx = strtold(argv[3], NULL);
long double centery = strtold(argv[4], NULL);
long double bailout = 128;
long double logLogBailout = log(log(bailout));
int foundperiods = 0;
long double magn = 1e18;
long double magn = strtold(argv[5], NULL);
long maxiter = width * sqrt(magn);
long double x0d = 4 / magn / width;
long double x2 = -2 / magn + centerx;

139
mandel_dd.c
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#include "colors.h"
#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>
#include <math.h>
#include <gmp.h>
#include "doubledouble.h"
int main(int argc, char **argv) {
if (argc != 6) {
fprintf(stderr, "usage: %s width height centerx centery magnification", argv[0]);
return 1;
}
DoubleDouble temp1;
double eps = 1e-17;
double Q1LOG2 = 1.44269504088896340735992468100189213742664595415299;
double LOG2 = 0.69314718055994530941723212145817656807550013436026;
unsigned int width = atoi(argv[1]);
unsigned int height = atoi(argv[2]);
char* image = malloc(width*height*3);
unsigned int x, y;
DoubleDouble centerx, centery;
centerx = dd_new(-0.7436438870371587, -3.628952515063387E-17);
centery = dd_new(0.13182590420531198, -1.2892807754956678E-17);
double bailout = 4; // the distance must not be greater than 2 (4 = 2*2)
double logLogBailout = log(log(bailout));
DoubleDouble magn = dd_new(strtod(argv[5], NULL), 0);
// maxiter = width * sqrt(magn);
temp1 = dd_sqrt(magn);
unsigned long maxiter = width * dd_get_ui(temp1);
DoubleDouble x2, y2, x0d, y1d;
// x0d = 4 / magn / width;
x0d = dd_ui_div(4, magn);
x0d = dd_div_ui(x0d, width);
// x2 = -2 / magn + centerx;
x2 = dd_si_div(-2, magn);
x2 = dd_add(x2, centerx);
// y1d = -4 / magn / width;
y1d = dd_si_div(-4, magn);
y1d = dd_div_ui(y1d, width);
// y2 = 2 / magn * height / width + centery;
y2 = dd_ui_div(2, magn);
temp1 = dd_new(height, 0);
temp1 = dd_div_ui(temp1, width);
y2 = dd_mul(y2, temp1);
y2 = dd_add(y2, centery);
DoubleDouble px, py, zx, zy, xx, yy;
unsigned int idx;
unsigned int imgidx = 0;
double hx, hy, d;
int foundperiods = 0;
/*fprintf(stderr, "centerx: %E\n", centerx.hi);
fprintf(stderr, "centery: %E\n", centery.hi);
fprintf(stderr, "magn: %E\n", magn.hi);
fprintf(stderr, "x2: %E\n", x2.hi);
fprintf(stderr, "y2: %E\n", y2.hi);
fprintf(stderr, "x0d: %E\n", x0d.hi);
fprintf(stderr, "y1d: %E\n", y1d.hi);*/
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;
px = dd_mul_ui(x0d, x);
px = dd_add(px, x2);
//py = y*y1d + y2;
py = dd_mul_ui(y1d, y);
py = dd_add(py, y2);
// no Main bulb or Cardoid check to be faster
zx = dd_new(px.hi, px.lo);
zy = dd_new(py.hi, py.lo);
unsigned long i;
bool inside = true;
int check = 3;
int whenupdate = 10;
hx = 0;
hy = 0;
//for (i = 1; i <= maxiter; i++) {
for (i = 1; i <= 50000; i++) {
//xx = zx * zx;
xx = dd_sqr(zx);
//yy = zy * zy;
yy = dd_sqr(zy);
//if (xx + yy > bailout) {
if (xx.hi + yy.hi > bailout) {
inside = false;
break;
}
// iterate
//zy = 2 * zx * zy + py;
//zx = dd_mul_ui(zx, 2);
//zy = dd_mul(zx, zy);
zy = dd_add(dd_mul2(zx, zy), py);
//zx = xx - yy + px;
zx = dd_add(dd_sub(xx, yy), px);
// period checking
d = zx.hi - hx;
if (d > 0.0 ? d < eps : d > -eps) {
d = zy.hi - 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.hi;
hy = zy.hi;
}
}
if (inside) {
image[imgidx++] = 0;
image[imgidx++] = 0;
image[imgidx++] = 0;
} else {
double r = sqrt(zx.hi*zx.hi + zy.hi*zy.hi);
double c = i - 1.28 + (logLogBailout - log(log(r))) * Q1LOG2;
idx = fmod((log(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, "\r%d found periods", foundperiods);
fprintf(stderr, "\n");
return 0;
}

17
run.sh
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#!/bin/sh
start="1.0"
end="1.0e+32"
frames="100"
end="1.0e+30"
frames="14400"
magn=`python -c "from math import pow; fac = pow($end / $start, 1.0 / ($frames - 1)); print \"\\n\".join([ str($start * pow(fac, i-1)) for i in range(1, $frames + 1)])"`
@ -11,8 +11,15 @@ centery="0.131825904205311970493132056385139"
i=0
for mag in $magn; do
echo $mag
fname=`printf "out_%04d_%s.ppm" $i $mag`
./a.out 320 240 $centerx $centery $mag > "$fname"
pngname=`printf "out_%05d_%s.png" $i $mag`
if [ -s "$pngname" ]; then
i=$((i+1))
continue
fi
echo $i $mag
fname=`printf "out_%05d_%s.ppm" $i $mag`
/usr/bin/time -f "%e s" ./mandel_dd 320 240 $centerx $centery $mag > "$fname"
convert "$fname" -format png "$pngname"
rm "$fname"
i=$((i+1))
done

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