ocaml: phase 5.1 count_bits.ml baseline (sum popcount 0..100 = 319)

DP recurrence for popcount that avoids host bitwise operations:

  result[i] = result[i / 2] + (i mod 2)

Drops the low bit (i / 2 stands in for i lsr 1) and adds it back
if it was 1 (i mod 2 stands in for i land 1).

  sum over 0..100 of popcount(i) = 319

Tests pure-arithmetic popcount, accumulating ref + DP array,
classic look-back to half-index pattern.

197 baseline programs total.

lib/ocaml/baseline/count_bits.ml

@@ -0,0 +1,14 @@
+let count_bits n =
+  let result = Array.make (n + 1) 0 in
+  for i = 1 to n do
+    result.(i) <- result.(i / 2) + (i mod 2)
+  done;
+  let sum = ref 0 in
+  for i = 0 to n do
+    sum := !sum + result.(i)
+  done;
+  !sum
+
+;;
+
+count_bits 100

lib/ocaml/baseline/expected.json

@@ -32,6 +32,7 @@
   "convex_hull.ml": 5,
   "coin_change.ml": 6,
   "coin_min.ml": 6,
+  "count_bits.ml": 319,
   "count_change.ml": 406,
   "count_paths_dag.ml": 3,
   "count_inversions.ml": 12,