93 lines
1.6 KiB
C
93 lines
1.6 KiB
C
#include <stdio.h>
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#include <math.h>
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#include <stdint.h>
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#include <stdlib.h>
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typedef uint32_t u32;
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// have to a multiply of 2
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#define COMMA 8
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#define COMMA_FIX (COMMA >> 1)
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void heron_sqrt(u32 *mem) {
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int i = mem[0];
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while (i > 0) {
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u32 s = mem[i];
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u32 x = s;
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if (s > 1) {
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// x_0 = (s + 1) / 2
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// without increment to avoid overflow for 0xffffffff
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x = x >> 1;
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u32 old_x = x;
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while(1) {
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// x_{n + 1} = (x_n + (s / x_n)) / 2
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x = (x >> 1) + ((s/x) >> 1);
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if (old_x <= x) {
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break;
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}
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old_x = x;
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}
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}
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mem[i] = x << COMMA_FIX;
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i--;
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}
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}
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int main() {
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float data[] = {
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0,
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//0.5,
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1.0 / (1 << COMMA),
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1.0 / (1 << (COMMA - 1)),
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1,
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2,
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2.5,
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2.25,
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2.125,
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2.0625,
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2.03125, // precision test
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3<<2,
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1<<3,
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1<<4,
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1<<5,
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1<<6,
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5<<2,
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11<<7,
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1<<7,
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1<<8,
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1<<16,
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1<<17,
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1<<18,
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1<<19,
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1<<20, // 32 - 14 = 20
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1<<24, // 32 - 8 = 24
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1<<30,
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0xffffffff
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};
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const int length = sizeof(data)/sizeof(float);
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int i;
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u32* mem = malloc((length + 1) * sizeof(u32));
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mem[0] = length;
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for (i = 1; i <= length; i++) {
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// float to fixed point
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mem[i] = (u32) (data[i] * (1 << COMMA));
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}
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heron_sqrt(mem);
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for (i = 0; i < length; i++) {
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// out-range-check
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if (data[i] <= (0xffffffff >> COMMA)) {
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printf("s = %10.10f\n", data[i]);
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printf("sqrt(s) = %10.10f\n", sqrt(data[i]));
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// fixed point to float
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printf("heron_sqrt(s) = %10.10f\n", ((float) mem[i]) / (1 << COMMA));
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}
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puts("\n");
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}
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return 0;
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}
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