ocaml: phase 5.1 mod_inverse.ml baseline (extended Euclidean, inverse sum = 27)

Extended Euclidean returns a triple (gcd, x, y) such that
a*x + b*y = gcd:

  let rec ext_gcd a b =
    if b = 0 then (a, 1, 0)
    else
      let (g, x1, y1) = ext_gcd b (a mod b) in
      (g, y1, x1 - (a / b) * y1)

  let mod_inverse a m =
    let (_, x, _) = ext_gcd a m in
    ((x mod m) + m) mod m

Three invariants checked:

  inv(3, 11)  = 4      (3*4  = 12  = 1 mod 11)
  inv(5, 26)  = 21     (5*21 = 105 = 1 mod 26)
  inv(7, 13)  = 2      (7*2  = 14  = 1 mod 13)
  sum         = 27

Tests recursive triple-tuple return, tuple-pattern destructuring on
let-binding (with wildcard for unused fields), and nested
let-binding inside the recursive call site.

72 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -36,6 +36,7 @@
   "flatten_tree.ml": 28,
   "list_ops.ml": 30,
   "mat_mul.ml": 621,
+  "mod_inverse.ml": 27,
   "json_pretty.ml": 24,
   "kadane.ml": 6,
   "lambda_calc.ml": 7,

lib/ocaml/baseline/mod_inverse.ml

@@ -0,0 +1,13 @@
+let rec ext_gcd a b =
+  if b = 0 then (a, 1, 0)
+  else
+    let (g, x1, y1) = ext_gcd b (a mod b) in
+    (g, y1, x1 - (a / b) * y1)
+
+let mod_inverse a m =
+  let (_, x, _) = ext_gcd a m in
+  ((x mod m) + m) mod m
+
+;;
+
+mod_inverse 3 11 + mod_inverse 5 26 + mod_inverse 7 13

plans/ocaml-on-sx.md

@@ -407,6 +407,15 @@ _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 — mod_inverse.ml baseline (extended Euclidean
+  + modular inverse, sum 4+21+2 = 27). ext_gcd returns a triple
+  (gcd, x, y) such that ax + by = gcd. mod_inverse extracts x and
+  reduces mod m to a positive representative. Three checks:
+    inv(3, 11) = 4   (3*4 = 12 ≡ 1)
+    inv(5, 26) = 21  (5*21 = 105 ≡ 1)
+    inv(7, 13) = 2   (7*2 = 14 ≡ 1)
+  Sum = 27. Tests recursive triple-tuple return + tuple-pattern
+  destructuring + nested let-binding. 72 baseline programs total.
 - 2026-05-09 Phase 5.1 — hist.ml baseline (Hashtbl-based int
   histogram, total * max = 75). Three small functions: hist builds
   the count table, max_value finds the maximum bin, total sums all