first

sqrt.c

@@ -0,0 +1,87 @@
+#include <stdio.h>
+#include <math.h>
+#include <stdint.h>
+
+/*
+ *        s   1
+ *         \ /
+ *          +
+ *          |   1
+ *          \  /
+ *           >>
+ *           |
+ *       s   x
+ *        \ / \
+ *        (/) |\
+ *         |  | \
+ *         \ /   \
+ *          +     \
+ *          |  1  |
+ *          \  /  |
+ *           >>   |
+ *            |  /
+ *            \ /
+ *             -
+ */
+typedef uint32_t u32;
+
+u32 heron_sqrt(u32 s, int* iterations) {
+  // x_0 = (s + 1) / 2
+  // without increment to avoid overflow for 0xffffffff
+  u32 x = s >> 1;
+  u32 old_x = x;
+
+  *iterations = 0; // statistic
+
+  if (x == 0) return 0;
+  while(1) {
+    (*iterations)++; // statistic
+    // x_{n + 1} = (x_n + (s / x_n)) / 2
+    x = (x >> 1) + ((s/x) >> 1);
+    if (old_x  <= x) {
+      return x;
+    }
+    old_x = x;
+  }
+}
+
+int main() {
+  u32 data[] = {0, 2, 4,
+    1<<2,
+    1<<3,
+    1<<4,
+    1<<5,
+    1<<6,
+    1<<7,
+    1<<8,
+    1<<16,
+    1<<17,
+    1<<18,
+    1<<19,
+    1<<20, // 32 - 14 = 20
+    1<<24, // 32 -  8 = 24
+    1<<30,
+    0xffffffff};
+  int iter = 0, i = 0;
+  for (i = 0; i < sizeof(data)/sizeof(int); i++) {
+    if (i != 0) printf("------\n");
+    printf("s = %u\n", data[i]);
+
+    printf("sqrt(s)      = %f\n", sqrt(data[i]));
+    printf("heron_sqrt(s)   = %d (%d iterations)\n",
+        heron_sqrt(data[i], &iter), iter);
+
+    // 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;
+}

sqrt.v

@@ -0,0 +1 @@
+module incrementor()