Mic92/heron_sqrt
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This commit is contained in:
Jörg Thalheim 2013-12-04 21:32:13 +01:00
parent b0dda9aef1
commit 86396fbadb
2 changed files with 83 additions and 54 deletions
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15
Makefile Normal file
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@ -0,0 +1,15 @@
CC?=cc
all:
$(CC) -lm -o sqrt sqrt.c
check: all
./sqrt
debug:
$(CC) -g -lm -o sqrt sqrt.c
gdb ./sqrt
bericht:
latexmk -pdf bericht.tex;

104
sqrt.c
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@ -1,52 +1,68 @@
#include <stdio.h> #include <stdio.h>
#include <math.h> #include <math.h>
#include <stdint.h> #include <stdint.h>
#include <stdlib.h>
#include <string.h>
/*
* s 1
* \ /
* +
* | 1
* \ /
* >>
* |
* s x
* \ / \
* (/) |\
* | | \
* \ / \
* + \
* | 1 |
* \ / |
* >> |
* | /
* \ /
* -
*/
typedef uint32_t u32; typedef uint32_t u32;
u32 heron_sqrt(u32 s, int* iterations) { void heron_sqrt(u32 *mem) {
int i;
for (i = 1; i <= mem[0]; i++){
u32 s = mem[i];
// x_0 = (s + 1) / 2 // x_0 = (s + 1) / 2
// without increment to avoid overflow for 0xffffffff // without increment to avoid overflow for 0xffffffff
u32 x = s >> 1; u32 x = s >> 1;
u32 old_x = x; u32 old_x = x;
*iterations = 0; // statistic if (x != 0) {
if (x == 0) return 0;
while(1) { while(1) {
(*iterations)++; // statistic
// x_{n + 1} = (x_n + (s / x_n)) / 2 // x_{n + 1} = (x_n + (s / x_n)) / 2
x = (x >> 1) + ((s/x) >> 1); x = (x >> 1) + ((s/x) >> 1);
printf("%d\n", x);
if (old_x <= x) { if (old_x <= x) {
return x; mem[i] = x;
break;
} }
old_x = x; old_x = x;
} }
}
mem[i] = x;
}
} }
//void heron_sqrt2(u32 *mem) {
// int i = 1;
// while(i <= mem[0]) {
// u32 s = mem[i];
// // x_0 = (s + 1) / 2
// // without increment to avoid overflow for 0xffffffff
// u32 x = s >> 1;
// u32 old_x = x;
//
// if (x != 0) {
// while(1) {
// // x_{n + 1} = (x_n + (s / x_n)) / 2
// //x = (x >> 1) + ((s/x) >> 1);
// x = (x / 2) + ((s/x) / 2);
// printf("%d\n", x);
// if (old_x == x) {
// mem[i] = x;
// break;
// }
// old_x = x;
// }
// }
// mem[i] = x;
// i++;
// }
//}
int main() { int main() {
u32 data[] = {0, 2, 4, u32 data[] = {0,
1,
2,
4,
1<<2, 1<<2,
1<<3, 1<<3,
1<<4, 1<<4,
@ -62,26 +78,24 @@ int main() {
1<<24, // 32 - 8 = 24 1<<24, // 32 - 8 = 24
1<<30, 1<<30,
0xffffffff}; 0xffffffff};
int iter = 0, i = 0; const int length = sizeof(data)/sizeof(u32);
for (i = 0; i < sizeof(data)/sizeof(int); i++) { const int mem_size = sizeof(data) + sizeof(u32);
if (i != 0) printf("------\n"); u32* mem = malloc(mem_size);
memcpy(mem, data, mem_size);
u32* mem2 = malloc(mem_size);
memcpy(mem2, data, mem_size);
mem[0] = length;
heron_sqrt(mem);
//heron_sqrt2(mem2);
int i = 0;
for (i = 0; i < length; i++) {
printf("s = %u\n", data[i]); printf("s = %u\n", data[i]);
printf("sqrt(s) = %f\n", sqrt(data[i])); printf("sqrt(s) = %f\n", sqrt(data[i]));
printf("heron_sqrt(s) = %d (%d iterations)\n", printf("heron_sqrt(s) = %d\n", mem[i]);
heron_sqrt(data[i], &iter), iter); //printf("heron_sqrt2(s) = %d\n", mem2[i]);
// 1/16 = 0.0625
u32 s8 = data[i] << 8;
printf("heron_sqrt8(s) = %f (%d iterations)%s\n",
((double) heron_sqrt(s8, &iter)) / 16,
iter, s8 == 0 ? " Out of range!" : "");
// 1/128 = 0.0078125
u32 s14 = data[i] << 14;
printf("heron_sqrt14(s) = %f (%d iterations)%s\n",
((double) heron_sqrt(data[i]<<14, &iter)) / 128,
iter, s14 == 0 ? " Out of range!" : "");
} }
return 0; return 0;
} }