ocaml: phase 5.1 euler16.ml baseline (digit sum of 2^15 = 26)

Computes 2^n via for-loop multiplication, then walks the digits via
mod 10 / div 10:

  let euler16 n =
    let p = ref 1 in
    for _ = 1 to n do p := !p * 2 done;
    let sum = ref 0 in
    let m = ref !p in
    while !m > 0 do
      sum := !sum + !m mod 10;
      m := !m / 10
    done;
    !sum

  euler16 15 = 3 + 2 + 7 + 6 + 8 = 26  (= digit sum of 32768)

Real PE16 asks for 2^1000 which exceeds float precision; 2^15 stays
safe and exercises the same digit-decomposition pattern.

115 baseline programs total.

lib/ocaml/baseline/euler16.ml

@@ -0,0 +1,14 @@
+let euler16 n =
+  let p = ref 1 in
+  for _ = 1 to n do p := !p * 2 done;
+  let sum = ref 0 in
+  let m = ref !p in
+  while !m > 0 do
+    sum := !sum + !m mod 10;
+    m := !m / 10
+  done;
+  !sum
+
+;;
+
+euler16 15

lib/ocaml/baseline/expected.json

@@ -26,6 +26,7 @@
   "exception_handle.ml": 4,
   "exception_user.ml": 26,
   "euler1.ml": 233168,
+  "euler16.ml": 26,
   "euler10.ml": 1060,
   "euler2.ml": 4613732,
   "euler25.ml": 55,

plans/ocaml-on-sx.md

@@ -407,6 +407,11 @@ _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 — euler16.ml baseline (digit sum of 2^15 =
+  26). Computes 2^n via for-loop accumulation, then walks the digits
+  via mod 10 / div 10 to sum them. Real PE16 asks for 2^1000 which
+  exceeds float precision; 2^15 = 32768 stays safe and exercises the
+  same digit-decomposition pattern. 115 baseline programs total.
 - 2026-05-09 Phase 5.1 — euler25.ml baseline (first Fibonacci index
   with 12 digits = 55). Iteratively grows two refs while the larger
   is below `10^(n-1)`, counting iterations. Real PE25 asks for 1000