ocaml: phase 5.1 fib_mod.ml baseline (Fibonacci mod prime, fib(100) mod 1000003 = 391360)

Iterative two-ref Fibonacci with modular reduction every step:

  let fib_mod n m =
    let a = ref 0 in
    let b = ref 1 in
    for _ = 1 to n do
      let c = (!a + !b) mod m in
      a := !b;
      b := c
    done;
    !a

The 100th Fibonacci is 354_224_848_179_261_915_075, well past JS
safe-int (2^53). Modular reduction every step keeps intermediate
values within int53 precision so the answer is exact in our
runtime. fib(100) mod 1000003 = 391360.

76 baseline programs total.

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.
+- 2026-05-09 Phase 5.1 — fib_mod.ml baseline (Fibonacci mod prime,
+  fib(100) mod 1000003 = 391360). Iterative two-ref Fibonacci with
+  modular reduction at every step to keep intermediate values
+  bounded. The 100th Fibonacci is 354224848179261915075, which
+  exceeds JS safe-int range; modular arithmetic on each step keeps
+  computations within int53 precision. 76 baseline programs total.
 - 2026-05-09 Phase 5.1 — luhn.ml baseline (Luhn check digit, 2/4
   inputs valid). Walks digits right-to-left, doubles every other
   starting from the second-from-right; if doubled value > 9