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.

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]