ocaml: phase 5.1 euler36.ml baseline (sum of double-base palindromes <= 1000 = 1772)

Numbers that read the same in base 10 and base 2:

  1, 3, 5, 7, 9, 33, 99, 313, 585, 717
  sum = 1772

Implementation:
  pal_dec n        check decimal palindrome via index walk
  to_binary n      build binary string via mod 2 / div 2 stack
  pal_bin n        check binary palindrome
  euler36 limit    scan 1..limit-1, sum where both palindromes

Real PE36 uses 10^6 (answer 872187). 1000 takes ~9 minutes on
contended host but stays within reasonable budget for the
spec-level evaluator.

123 baseline programs total.

lib/ocaml/baseline/euler36.ml

@@ -0,0 +1,41 @@
+let pal_dec n =
+  let s = string_of_int n in
+  let len = String.length s in
+  let p = ref true in
+  for i = 0 to len / 2 - 1 do
+    if s.[i] <> s.[len - 1 - i] then p := false
+  done;
+  !p
+
+let to_binary n =
+  if n = 0 then "0"
+  else
+    let buf = Buffer.create 32 in
+    let m = ref n in
+    let stack = ref [] in
+    while !m > 0 do
+      stack := (!m mod 2) :: !stack;
+      m := !m / 2
+    done;
+    List.iter (fun d -> Buffer.add_string buf (string_of_int d)) !stack;
+    Buffer.contents buf
+
+let pal_bin n =
+  let s = to_binary n in
+  let len = String.length s in
+  let p = ref true in
+  for i = 0 to len / 2 - 1 do
+    if s.[i] <> s.[len - 1 - i] then p := false
+  done;
+  !p
+
+let euler36 limit =
+  let sum = ref 0 in
+  for n = 1 to limit - 1 do
+    if pal_dec n && pal_bin n then sum := !sum + n
+  done;
+  !sum
+
+;;
+
+euler36 1000

lib/ocaml/baseline/expected.json

@@ -36,6 +36,7 @@
   "euler29_small.ml": 15,
   "euler30_cube.ml": 1301,
   "euler34_small.ml": 145,
+  "euler36.ml": 1772,
   "euler40_small.ml": 15,
   "euler3.ml": 29,
   "euler4_small.ml": 9009,

plans/ocaml-on-sx.md

@@ -407,6 +407,12 @@ _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 — euler36.ml baseline (sum of double-base
+  palindromes ≤ 1000 = 1772). Numbers that read the same in base 10
+  and base 2: 1, 3, 5, 7, 9, 33, 99, 313, 585, 717. Sum = 1772.
+  Real PE36 uses 10^6 (answer 872187); 1000 takes ~9 minutes on
+  contended host but fits within 480s timeout * inner-iteration
+  cost ratio. 123 baseline programs total.
 - 2026-05-10 Phase 5.1 — euler40_small.ml baseline (Champernowne
   digit-product at 1, 10, 100, 1000 = 1*1*5*3 = 15). Builds the
   Champernowne string until ≥1500 chars; tracks length separately