ocaml: phase 5.1 fenwick_tree.ml baseline (BIT over 8 elements, fingerprint 228)

Fenwick / Binary Indexed Tree for prefix sums. The classic
`i & -i` low-bit trick needs negative-aware AND, but our `land`
evaluator (iter 127, bitwise via floor/mod arithmetic) only handles
non-negative operands. Workaround: a portable lowbit helper that
finds the largest power of 2 dividing i:

  let lowbit i =
    let r = ref 1 in
    while !r * 2 <= i && i mod (!r * 2) = 0 do
      r := !r * 2
    done;
    !r

After building from [1;3;5;7;9;11;13;15]:
  total       = prefix_sum 8 = 64
  update 1 by +100
  after       = prefix_sum 8 = 164
  total + after = 228

Tests recursive update / prefix_sum chains via helper-extracted
lowbit; documents a non-obvious limit of the bitwise-emulation
layer.

168 baseline programs total.

plans/ocaml-on-sx.md

@@ -407,6 +407,17 @@ _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.
+- 2026-05-10 Phase 5.1 — fenwick_tree.ml baseline (Binary Indexed
+  Tree over [1;3;5;7;9;11;13;15], total + after = 228). Initial
+  prefix_sum n = 64; after +100 at index 1, prefix_sum n = 164;
+  64 + 164 = 228. Because our `land` evaluator implementation only
+  handles non-negative operands (iter 127 bitwise-via-arithmetic
+  workaround), and Fenwick relies on `i & -i` to extract the
+  lowest set bit, we replace `i land (-i)` with a portable
+  `lowbit` helper: largest power-of-2 dividing i. Tests recursive
+  update / prefix_sum chains using helper-extracted lowbit,
+  highlights a non-obvious tradeoff in the bitwise-emulation
+  layer. 168 baseline programs total.
 - 2026-05-10 Phase 5.1 — segment_tree.ml baseline (range-sum
   segment tree over [1;3;5;7;9;11;13;15] with one point update,
   encoded r1 + r2*100 = 4232). build/query/update use the standard