Euler problem #53 in OCaml

euler53.ml

(* taking out the big guns, yes... size matters *)
open Num

open Printf

(* a throw away helper function just like pred but works with Nums, ought to give it a better name *)
let pred' n = Int (pred (int_of_num n))

(* field test *)
let rec fact x = if x =/ Int 0 then Int 1 else x */ fact (pred' x)

(* our weapon *)
let c n r = 
  if r <= n then
    let n' = fact (Int n) in
    let r' = fact (Int r) in 
    n' // (r' */ fact (Int n -/ Int r))
  else 
    raise (Failure "r > n")

(* our hero *)
let count_combinatorics =
  let r = ref 100 in
  let rec count_combinatorics' n count =
    match n with
    | 22 -> count
    | _ ->
      match !r with
      | 2 -> 
        let combinatorics = c n !r in (
          r := (pred n);
          if combinatorics >/ Int 1_000_000 then count_combinatorics' (pred n) (succ count)
          else count_combinatorics' (pred n) count
        )
      | _ -> 
        let combinatorics = c n !r in (
          r := pred !r;
          if combinatorics >/ Int 1_000_000 then count_combinatorics' n (succ count)
          else count_combinatorics' n count
        )
  in
  count_combinatorics' 100 0

(* le hero's boss *)
let () = printf "Count of values above 1m = %d\n" count_combinatorics


(* 
 * Compile it
 * $ ocamlbuild -libs nums euler53.native && mv euler53.native euler53
 * Then run it
 * $ ./euler53
*)