ocaml: phase 5.1 bisect.ml baseline (root-finding, sqrt(2)*100 = 141)

Bisection method searching for f(x) = 0 in [lo, hi] over 50
iterations:

  let bisect f lo hi =
    let lo = ref lo and hi = ref hi in
    for _ = 1 to 50 do
      let mid = (!lo +. !hi) /. 2.0 in
      if f mid = 0.0 || f !lo *. f mid < 0.0 then hi := mid
      else lo := mid
    done;
    !lo

Solving x^2 - 2 = 0 in [1, 2] via 'bisect (fun x -> x *. x -. 2.0)
1.0 2.0' converges to ~1.41421356... -> int_of_float (r *. 100) =
141.

Tests:
  - higher-order function passing
  - multi-let 'let lo = ref ... and hi = ref ...'
  - float arithmetic
  - int_of_float truncate-toward-zero (iter 117)

62 baseline programs total.

lib/ocaml/baseline/bisect.ml

@@ -0,0 +1,13 @@
+let bisect f lo hi =
+  let lo = ref lo and hi = ref hi in
+  for _ = 1 to 50 do
+    let mid = (!lo +. !hi) /. 2.0 in
+    if f mid = 0.0 || f !lo *. f mid < 0.0 then hi := mid
+    else lo := mid
+  done;
+  !lo
+
+;;
+
+let r = bisect (fun x -> x *. x -. 2.0) 1.0 2.0 in
+int_of_float (r *. 100.0)

lib/ocaml/baseline/expected.json

@@ -5,6 +5,7 @@
   "atm.ml": 120,
   "bag.ml": 3,
   "bf_full.ml": 6,
+  "bisect.ml": 141,
   "bigint_add.ml": 28,
   "bits.ml": 21,
   "balance.ml": 3,

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 — bisect.ml baseline (root-finding via
+  bisection, sqrt(2) * 100 = 141). 50 iterations of bisection
+  searching for x^2 - 2 = 0 in [1, 2]. Tests higher-order function
+  passing (the function-to-zero is `(fun x -> x *. x -. 2.0)`),
+  multi-let `let lo = ref ... and hi = ref ...`, float arithmetic,
+  and the int_of_float truncate-toward-zero from iteration 117. 62
+  baseline programs total.
 - 2026-05-09 Phase 5.1 — base_n.ml baseline (int -> base-N string,
   length sum 2+11+3+1 = 17). 36-character digit alphabet supports up
   to base 36. Loop divides quotient by base, prepends digit. Tests: