ocaml: phase 5.1 bs_bounds.ml baseline (lower/upper bound, fingerprint 3211)

C++-style lower_bound / upper_bound on a sorted array:

  lower_bound — first index >= x  (loop uses arr.(mid) < x)
  upper_bound — first index >  x  (loop uses arr.(mid) <= x)

  a = [|1; 2; 2; 3; 3; 3; 5; 7; 9|]

  upper(x) - lower(x) gives the count of x in a:
    cnt3 = 3   cnt2 = 2   cnt5 = 1   cnt9 = 1   cnt4 = 0

  fingerprint = 3*1000 + 2*100 + 1*10 + 1 + 0 = 3211

Tests parallel while loops with bisection on ref, mixed strict
and non-strict comparison branches, count-via-subtraction idiom.

176 baseline programs total.

lib/ocaml/baseline/bs_bounds.ml

@@ -0,0 +1,27 @@
+let lower_bound arr x =
+  let lo = ref 0 and hi = ref (Array.length arr) in
+  while !lo < !hi do
+    let mid = (!lo + !hi) / 2 in
+    if arr.(mid) < x then lo := mid + 1
+    else hi := mid
+  done;
+  !lo
+
+let upper_bound arr x =
+  let lo = ref 0 and hi = ref (Array.length arr) in
+  while !lo < !hi do
+    let mid = (!lo + !hi) / 2 in
+    if arr.(mid) <= x then lo := mid + 1
+    else hi := mid
+  done;
+  !lo
+
+;;
+
+let a = [| 1; 2; 2; 3; 3; 3; 5; 7; 9 |] in
+let cnt3 = upper_bound a 3 - lower_bound a 3 in
+let cnt2 = upper_bound a 2 - lower_bound a 2 in
+let cnt5 = upper_bound a 5 - lower_bound a 5 in
+let cnt9 = upper_bound a 9 - lower_bound a 9 in
+let cnt4 = upper_bound a 4 - lower_bound a 4 in
+cnt3 * 1000 + cnt2 * 100 + cnt5 * 10 + cnt9 + cnt4

lib/ocaml/baseline/expected.json

@@ -21,6 +21,7 @@
   "bfs_grid.ml": 8,
   "btree.ml": 39,
   "brainfuck.ml": 75,
+  "bs_bounds.ml": 3211,
   "bsearch.ml": 7,
   "caesar.ml": 215,
   "calc.ml": 13,

plans/ocaml-on-sx.md

@@ -407,6 +407,15 @@ _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.
+- 2026-05-11 Phase 5.1 — bs_bounds.ml baseline (lower_bound /
+  upper_bound binary search; counts of {3,2,5,9,4} in
+  [1;2;2;3;3;3;5;7;9] encoded as 3211). Standard half-open
+  variants: lower_bound returns the first index ≥ x (using `<`),
+  upper_bound returns the first index > x (using `≤`). Counts:
+  3→3, 2→2, 5→1, 9→1, 4→0 → 3*1000+2*100+1*10+1+0 = 3211. Tests
+  parallel while loops with bisection on ref, mixed strict and
+  non-strict comparisons, computing counts via subtraction.
+  176 baseline programs total.
 - 2026-05-11 Phase 5.1 — distinct_subseq.ml baseline (count
   distinct subsequences of "rabbbit" that equal "rabbit" = 3).
   Classic 2D DP: dp[i][j] = dp[i-1][j] + (s[i-1]=t[j-1] ? dp[i-1][j-1]