Data commit

Task/Isqrt-integer-square-root-of-X/ObjectIcon/isqrt-integer-square-root-of-x.oi

@@ -0,0 +1,61 @@
+# -*- ObjectIcon -*-
+
+import io
+import ipl.numbers              # For the "commas" procedure.
+import ipl.printf
+
+procedure main ()
+  write ("isqrt(i) for 0 <= i <= 65:")
+  write ()
+  roots_of_0_to_65()
+  write ()
+  write ()
+  write ("isqrt(7**i) for 1 <= i <= 73, i odd:")
+  write ()
+  printf ("%2s %84s %43s\n", "i", "7**i", "sqrt(7**i)")
+  write (repl("-", 131))
+  roots_of_odd_powers_of_7()
+end
+
+procedure roots_of_0_to_65 ()
+  local i
+
+  every i := 0 to 64 do writes (isqrt(i), " ")
+  write (isqrt(65))
+end
+
+procedure roots_of_odd_powers_of_7 ()
+  local i, power_of_7, root
+
+  every i := 1 to 73 by 2 do {
+    power_of_7 := 7^i
+    root := isqrt(power_of_7)
+    printf ("%2d %84s %43s\n", i, commas(power_of_7), commas(root))
+  }
+end
+
+procedure isqrt (x)
+  local q, z, r, t
+
+  q := find_a_power_of_4_greater_than_x (x)
+  z := x
+  r := 0
+  while 1 < q do {
+    q := ishift(q, -2)
+    t := z - r - q
+    r := ishift(r, -1)
+    if 0 <= t then {
+      z := t
+      r +:= q
+    }
+  }
+  return r
+end
+
+procedure find_a_power_of_4_greater_than_x (x)
+  local q
+
+  q := 1
+  while q <= x do q := ishift(q, 2)
+  return q
+end