ocaml: phase 5.1 int_sqrt.ml baseline (Newton integer sqrt, 12+14+1000+1 = 1027)

Newton's method on integers, converging when y >= x:

  let isqrt n =
    if n < 2 then n
    else
      let x = ref n in
      let y = ref ((!x + 1) / 2) in
      while !y < !x do
        x := !y;
        y := (!x + n / !x) / 2
      done;
      !x

Test cases:
  isqrt 144      = 12     (perfect square)
  isqrt 200      = 14     (floor of sqrt(200) ~= 14.14)
  isqrt 1000000  = 1000
  isqrt 2        = 1
  sum            = 1027

Companion to newton_sqrt.ml (iter 124, float Newton). Tests integer
division semantics from iter 94 and a while-until-convergence loop.

88 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -36,6 +36,7 @@
   "hailstone.ml": 111,
   "hanoi.ml": 1023,
   "hist.ml": 75,
+  "int_sqrt.ml": 1027,
   "fizzbuzz.ml": 57,
   "flatten_tree.ml": 28,
   "list_ops.ml": 30,

lib/ocaml/baseline/int_sqrt.ml

@@ -0,0 +1,14 @@
+let isqrt n =
+  if n < 2 then n
+  else
+    let x = ref n in
+    let y = ref ((!x + 1) / 2) in
+    while !y < !x do
+      x := !y;
+      y := (!x + n / !x) / 2
+    done;
+    !x
+
+;;
+
+isqrt 144 + isqrt 200 + isqrt 1000000 + isqrt 2

plans/ocaml-on-sx.md

@@ -407,6 +407,16 @@ _Newest first._
   binary search tree (`type 'a tree = Leaf | Node of 'a * 'a tree *
   'a tree`) with insert + in-order traversal. Tests parametric ADT,
   recursive match, List.append, List.fold_left.
+- 2026-05-09 Phase 5.1 — int_sqrt.ml baseline (integer Newton sqrt,
+  12+14+1000+1 = 1027). Newton's method on integers using `(x +
+  n/x) / 2` until convergence (`y >= x`). Tests:
+    isqrt 144     = 12
+    isqrt 200     = 14   (floor of sqrt(200) = 14.14...)
+    isqrt 1000000 = 1000
+    isqrt 2       = 1
+  Sum = 1027. Companion to newton_sqrt.ml (iter 124, float Newton).
+  Tests integer division semantics + while convergence loop. 88
+  baseline programs total.
 - 2026-05-09 Phase 5.1 — grid_paths.ml baseline (count distinct
   paths in (4+1)x(6+1) grid = C(10,4) = 210). DP fills a flattened
   2D array: `dp.(0,0) = 1`, others `dp.(i,j) = dp.(i-1,j) + dp.(i,