add doubledouble version
This commit is contained in:
josch
parent
be7342b0cf
commit
63b7a4d02a
5 changed files with 308 additions and 14 deletions
7
Makefile
7
Makefile
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@ -1,4 +1,5 @@
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all:
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gcc -Ofast -Wall -lquadmath mandel_quad.c -o mandel_quad
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gcc -Ofast -Wall -lmpfr mandel_mpfr.c -o mandel_mpfr
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gcc -Ofast -Wall -lm mandel.c -o mandel
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gcc -O3 -Wall -lquadmath mandel_quad.c -o mandel_quad
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gcc -O3 -Wall -lmpfr -lm mandel_mpfr.c -o mandel_mpfr
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gcc -O3 -Wall -lm mandel.c -o mandel
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gcc -O3 -Wall -lm mandel_dd.c -o mandel_dd
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143
doubledouble.h
Normal file
143
doubledouble.h
Normal file
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@ -0,0 +1,143 @@
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#include <math.h>
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typedef struct {
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double hi;
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double lo;
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} DoubleDouble;
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inline DoubleDouble dd_new(double hi, double lo) {
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DoubleDouble num;
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num.hi = hi;
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num.lo = lo;
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return num;
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}
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unsigned int dd_get_ui(DoubleDouble num) {
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return num.hi;
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}
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inline DoubleDouble dd_sqrt(DoubleDouble num) {
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double a, b, c, d, e;
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d = 1 / sqrt(num.hi);
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e = num.hi * d;
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a = 0x08000001 * e;
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a += e - a;
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b = e - a;
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c = e * e;
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b = ((a * a - c) + a * b * 2) + b * b;
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a = num.hi - c;
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c = num.hi - a;
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c = (a + ((((num.hi - (c + a)) + (c - c)) + num.lo) - b)) * d * 0.5;
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a = e + c;
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b = e - a;
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return dd_new(a, (e - (b + a)) + (b + c));
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}
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inline DoubleDouble dd_div(DoubleDouble num1, DoubleDouble num2) {
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double a, b, c, d, e, f, g;
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f = num1.hi / num2.hi;
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a = 0x08000001 * num2.hi;
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a += num2.hi - a;
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b = num2.hi - a;
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c = 0x08000001 * f;
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c += f - c;
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d = f - c;
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e = num2.hi * f;
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c = (((a * c - e) + (a * d + b * c)) + b * d) + num2.lo * f;
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b = num1.lo - c;
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d = num1.lo - b;
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a = num1.hi - e;
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e = (num1.hi - ((num1.hi - a) + a)) + b;
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g = a + e;
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e += (a - g) + ((num1.lo - (d + b)) + (d - c));
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a = g + e;
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b = a / num2.hi;
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f += (e + (g - a)) / num2.hi;
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a = f + b;
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return dd_new(a, b + (f - a));
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}
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inline DoubleDouble dd_ui_div(unsigned int num1, DoubleDouble num2) {
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return dd_div(dd_new(num1, 0), num2);
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}
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inline DoubleDouble dd_div_ui(DoubleDouble num1, unsigned int num2) {
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return dd_div(num1, dd_new(num2, 0));
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}
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inline DoubleDouble dd_si_div(signed int num1, DoubleDouble num2) {
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return dd_div(dd_new(num1, 0), num2);
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}
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inline DoubleDouble dd_div_si(DoubleDouble num1, signed int num2) {
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return dd_div(num1, dd_new(num2, 0));
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}
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inline DoubleDouble dd_add(DoubleDouble num1, DoubleDouble num2) {
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double a, b, c, d, e, f;
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e = num1.hi + num2.hi;
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d = num1.hi - e;
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a = num1.lo + num2.lo;
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f = num1.lo - a;
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d = ((num1.hi - (d + e)) + (d + num2.hi)) + a;
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b = e + d;
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c = ((num1.lo - (f + a)) + (f + num2.lo)) + (d + (e - b));
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a = b + c;
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return dd_new(a, c + (b - a));
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}
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inline DoubleDouble dd_mul(DoubleDouble num1, DoubleDouble num2) {
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double a, b, c, d, e;
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a = 0x08000001 * num1.hi;
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a += num1.hi - a;
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b = num1.hi - a;
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c = 0x08000001 * num2.hi;
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c += num2.hi - c;
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d = num2.hi - c;
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e = num1.hi * num2.hi;
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c = (((a * c - e) + (a * d + b * c)) + b * d) + (num1.lo * num2.hi + num1.hi * num2.lo);
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a = e + c;
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return dd_new(a, c + (e - a));
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}
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inline DoubleDouble dd_mul2(DoubleDouble num1, DoubleDouble num2) {
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double a, b, c, d, e;
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a = 0x08000001 * num1.hi;
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a += num1.hi - a;
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b = num1.hi - a;
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c = 0x08000001 * num2.hi;
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c += num2.hi - c;
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d = num2.hi - c;
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e = num1.hi * num2.hi;
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c = 2*((((a * c - e) + (a * d + b * c)) + b * d) + (num1.lo * num2.hi + num1.hi * num2.lo));
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a = 2*e + c;
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return dd_new(a, c + (2*e - a));
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}
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inline DoubleDouble dd_mul_ui(DoubleDouble num1, unsigned int num2) {
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return dd_mul(num1, dd_new(num2, 0));
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}
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inline DoubleDouble dd_sub(DoubleDouble num1, DoubleDouble num2) {
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double a, b, c, d, e, f, g;
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g = num1.lo - num2.lo;
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f = num1.lo - g;
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e = num1.hi - num2.hi;
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d = num1.hi - e;
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d = ((num1.hi - (d + e)) + (d - num2.hi)) + g;
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b = e + d;
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c = (d + (e - b)) + ((num1.lo - (f + g)) + (f - num2.lo));
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a = b + c;
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return dd_new(a, c + (b - a));
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}
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inline DoubleDouble dd_sqr(DoubleDouble num) {
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double a, b, c;
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a = 0x08000001 * num.hi;
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a += num.hi - a;
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b = num.hi - a;
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c = num.hi * num.hi;
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b = ((((a * a - c) + a * b * 2) + b * b) + num.hi * num.lo * 2) + num.lo * num.lo;
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a = b + c;
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return dd_new(a, b + (c - a));
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}
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16
mandel.c
16
mandel.c
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@ -4,20 +4,24 @@
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#include <stdlib.h>
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#include <stdbool.h>
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int main() {
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int main(int argc, char **argv) {
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if (argc != 6) {
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fprintf(stderr, "usage: %s width height centerx centery magnification", argv[0]);
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return 1;
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}
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long double eps = 1e-17;
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long double Q1LOG2 = 1.44269504088896340735992468100189213742664595415299;
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long double LOG2 = 0.69314718055994530941723212145817656807550013436026;
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int width = 640;
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int height = 480;
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int width = atoi(argv[1]);
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int height = atoi(argv[2]);
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char* image = malloc(width*height*3);
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int x, y;
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long double centerx = -0.743643887037158704752191506114774;
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long double centery = 0.131825904205311970493132056385139;
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long double centerx = strtold(argv[3], NULL);
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long double centery = strtold(argv[4], NULL);
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long double bailout = 128;
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long double logLogBailout = log(log(bailout));
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int foundperiods = 0;
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long double magn = 1e18;
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long double magn = strtold(argv[5], NULL);
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long maxiter = width * sqrt(magn);
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long double x0d = 4 / magn / width;
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long double x2 = -2 / magn + centerx;
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139
mandel_dd.c
Normal file
139
mandel_dd.c
Normal file
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@ -0,0 +1,139 @@
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#include "colors.h"
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#include <stdio.h>
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#include <stdlib.h>
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#include <stdbool.h>
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#include <math.h>
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#include <gmp.h>
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#include "doubledouble.h"
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int main(int argc, char **argv) {
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if (argc != 6) {
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fprintf(stderr, "usage: %s width height centerx centery magnification", argv[0]);
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return 1;
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}
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DoubleDouble temp1;
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double eps = 1e-17;
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double Q1LOG2 = 1.44269504088896340735992468100189213742664595415299;
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double LOG2 = 0.69314718055994530941723212145817656807550013436026;
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unsigned int width = atoi(argv[1]);
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unsigned int height = atoi(argv[2]);
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char* image = malloc(width*height*3);
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unsigned int x, y;
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DoubleDouble centerx, centery;
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centerx = dd_new(-0.7436438870371587, -3.628952515063387E-17);
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centery = dd_new(0.13182590420531198, -1.2892807754956678E-17);
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double bailout = 4; // the distance must not be greater than 2 (4 = 2*2)
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double logLogBailout = log(log(bailout));
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DoubleDouble magn = dd_new(strtod(argv[5], NULL), 0);
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// maxiter = width * sqrt(magn);
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temp1 = dd_sqrt(magn);
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unsigned long maxiter = width * dd_get_ui(temp1);
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DoubleDouble x2, y2, x0d, y1d;
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// x0d = 4 / magn / width;
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x0d = dd_ui_div(4, magn);
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x0d = dd_div_ui(x0d, width);
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// x2 = -2 / magn + centerx;
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x2 = dd_si_div(-2, magn);
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x2 = dd_add(x2, centerx);
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// y1d = -4 / magn / width;
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y1d = dd_si_div(-4, magn);
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y1d = dd_div_ui(y1d, width);
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// y2 = 2 / magn * height / width + centery;
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y2 = dd_ui_div(2, magn);
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temp1 = dd_new(height, 0);
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temp1 = dd_div_ui(temp1, width);
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y2 = dd_mul(y2, temp1);
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y2 = dd_add(y2, centery);
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DoubleDouble px, py, zx, zy, xx, yy;
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unsigned int idx;
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unsigned int imgidx = 0;
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double hx, hy, d;
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int foundperiods = 0;
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/*fprintf(stderr, "centerx: %E\n", centerx.hi);
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fprintf(stderr, "centery: %E\n", centery.hi);
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fprintf(stderr, "magn: %E\n", magn.hi);
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fprintf(stderr, "x2: %E\n", x2.hi);
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fprintf(stderr, "y2: %E\n", y2.hi);
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fprintf(stderr, "x0d: %E\n", x0d.hi);
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fprintf(stderr, "y1d: %E\n", y1d.hi);*/
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for (y = 0; y < height; y++) {
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for (x = 0; x < width; x++) {
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fprintf(stderr, "\r%f %%", (float)imgidx/(width*height*3)*100);
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//px = x*x0d + x2;
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px = dd_mul_ui(x0d, x);
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px = dd_add(px, x2);
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//py = y*y1d + y2;
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py = dd_mul_ui(y1d, y);
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py = dd_add(py, y2);
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// no Main bulb or Cardoid check to be faster
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zx = dd_new(px.hi, px.lo);
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zy = dd_new(py.hi, py.lo);
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unsigned long i;
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bool inside = true;
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int check = 3;
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int whenupdate = 10;
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hx = 0;
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hy = 0;
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//for (i = 1; i <= maxiter; i++) {
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for (i = 1; i <= 50000; i++) {
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//xx = zx * zx;
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xx = dd_sqr(zx);
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//yy = zy * zy;
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yy = dd_sqr(zy);
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//if (xx + yy > bailout) {
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if (xx.hi + yy.hi > bailout) {
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inside = false;
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break;
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}
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// iterate
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//zy = 2 * zx * zy + py;
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//zx = dd_mul_ui(zx, 2);
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//zy = dd_mul(zx, zy);
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zy = dd_add(dd_mul2(zx, zy), py);
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//zx = xx - yy + px;
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zx = dd_add(dd_sub(xx, yy), px);
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// period checking
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d = zx.hi - hx;
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if (d > 0.0 ? d < eps : d > -eps) {
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d = zy.hi - hy;
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if (d > 0.0 ? d < eps : d > -eps) {
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// Period found.
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foundperiods++;
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break;
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}
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}
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if ((i & check) == 0) {
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if (--whenupdate == 0) {
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whenupdate = 10;
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check <<= 1;
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check++;
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}
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// period = 0;
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hx = zx.hi;
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hy = zy.hi;
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}
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}
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if (inside) {
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image[imgidx++] = 0;
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image[imgidx++] = 0;
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image[imgidx++] = 0;
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} else {
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double r = sqrt(zx.hi*zx.hi + zy.hi*zy.hi);
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double c = i - 1.28 + (logLogBailout - log(log(r))) * Q1LOG2;
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idx = fmod((log(c/64+1)/LOG2+0.45), 1)*GRADIENTLENGTH + 0.5;
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image[imgidx++] = colors[idx][0];
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image[imgidx++] = colors[idx][1];
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image[imgidx++] = colors[idx][2];
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}
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}
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}
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// write out image
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printf("P6 %d %d 255\n", width, height);
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fwrite(image, 1, width*height*3, stdout);
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//fprintf(stderr, "\r%d found periods", foundperiods);
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fprintf(stderr, "\n");
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return 0;
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}
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17
run.sh
17
run.sh
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#!/bin/sh
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start="1.0"
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end="1.0e+32"
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frames="100"
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end="1.0e+30"
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frames="14400"
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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)])"`
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@ -11,8 +11,15 @@ centery="0.131825904205311970493132056385139"
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i=0
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for mag in $magn; do
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echo $mag
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fname=`printf "out_%04d_%s.ppm" $i $mag`
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./a.out 320 240 $centerx $centery $mag > "$fname"
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pngname=`printf "out_%05d_%s.png" $i $mag`
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if [ -s "$pngname" ]; then
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i=$((i+1))
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continue
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fi
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echo $i $mag
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fname=`printf "out_%05d_%s.ppm" $i $mag`
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/usr/bin/time -f "%e s" ./mandel_dd 320 240 $centerx $centery $mag > "$fname"
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convert "$fname" -format png "$pngname"
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rm "$fname"
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i=$((i+1))
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done
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