ocaml: phase 5.1 newton_sqrt.ml baseline (Newton's method, sqrt(2)*1000 = 1414)

Newton's method for square root:

  let sqrt_newton x =
    let g = ref 1.0 in
    for _ = 1 to 20 do
      g := (!g +. x /. !g) /. 2.0
    done;
    !g

20 iterations is more than enough to converge for x=2 — result is
~1.414213562. Multiplied by 1000 and int_of_float'd: 1414.

First baseline exercising:
  - for _ = 1 to N do ... done (wildcard loop variable)
  - pure float arithmetic with +. /.
  - the int_of_float truncate-toward-zero fix from iter 117

38 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -23,6 +23,7 @@
   "memo_fib.ml": 75025,
   "merge_sort.ml": 44,
   "module_use.ml": 3,
+  "newton_sqrt.ml": 1414,
   "mutable_record.ml": 10,
   "option_match.ml": 5,
   "pi_leibniz.ml": 314,

lib/ocaml/baseline/newton_sqrt.ml

@@ -0,0 +1,10 @@
+let sqrt_newton x =
+  let g = ref 1.0 in
+  for _ = 1 to 20 do
+    g := (!g +. x /. !g) /. 2.0
+  done;
+  !g
+
+;;
+
+int_of_float (sqrt_newton 2.0 *. 1000.0)

plans/ocaml-on-sx.md

@@ -407,6 +407,13 @@ _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 — newton_sqrt.ml baseline (Newton's method
+  for sqrt, sqrt(2)*1000 truncated → 1414). 20 iterations of
+  `g := (g + x/g) / 2` converges to ~1.414213562 for x=2. Multiplied
+  by 1000 and int_of_float'd gives 1414. First baseline that
+  exercises `for _ = 1 to N do ... done` (wildcard loop variable),
+  pure float arithmetic with `+.` `/.`, and the `int_of_float` fix
+  from iteration 117. 38 baseline programs total.
 - 2026-05-09 Phase 5.1 — hanoi.ml baseline (Tower of Hanoi move
   count, n=10 → 1023). Classic doubly-recursive solution returning
   the number of moves: `hanoi n from to via = hanoi (n-1) from via