Initial data commit

Task/Arithmetic-Rational/OCaml/arithmetic-rational-4.ocaml

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+(* implementation conforming to signature *)
+module Frac : RATIO =
+   struct
+      open Big_int
+
+      type t = { num : big_int; den : big_int }
+
+      (* short aliases for big_int values and functions *)
+      let zero, one = zero_big_int, unit_big_int
+      let big, to_int, eq = big_int_of_int, int_of_big_int, eq_big_int
+      let (+~), (-~), ( *~) = add_big_int, sub_big_int, mult_big_int
+
+      (* helper function *)
+      let rec norm ({num=n;den=d} as k) =
+         if lt_big_int d zero then
+           norm {num=minus_big_int n;den=minus_big_int d}
+         else
+         let rec hcf a b =
+           let q,r = quomod_big_int a b in
+           if eq r zero then b else hcf b r in
+         let f = hcf n d in
+         if eq f one then k else
+            let div = div_big_int in
+            { num=div n f; den = div d f } (* inefficient *)
+
+      (* public functions *)
+      let frac a b = norm { num=big a; den=big b }
+
+      let from_int a = norm { num=big a; den=one }
+
+      let is_int {num=n; den=d} =
+         eq d one ||
+         eq (mod_big_int n d) zero
+
+      let to_string ({num=n; den=d} as r) =
+         let r1 = norm r in
+         let str = string_of_big_int in
+         if is_int r1 then
+            str (r1.num)
+         else
+            str (r1.num) ^ "/" ^ str (r1.den)
+
+      let cmp a b =
+         let a1 = norm a and b1 = norm b in
+         compare_big_int (a1.num*~b1.den) (b1.num*~a1.den)
+
+      let ( */ ) {num=n1; den=d1} {num=n2; den=d2} =
+         norm { num = n1*~n2; den = d1*~d2 }
+
+      let ( // ) {num=n1; den=d1} {num=n2; den=d2} =
+         norm { num = n1*~d2; den = d1*~n2 }
+
+      let ( +/ ) {num=n1; den=d1} {num=n2; den=d2} =
+         norm { num = n1*~d2 +~ n2*~d1; den = d1*~d2 }
+
+      let ( -/ ) {num=n1; den=d1} {num=n2; den=d2} =
+         norm { num = n1*~d2 -~ n2*~d1; den = d1*~d2 }
+   end