src/Tools/rat.ML

--- a/src/Tools/rat.ML	Tue Sep 18 11:06:22 2007 +0200
+++ b/src/Tools/rat.ML	Tue Sep 18 16:08:00 2007 +0200
@@ -12,15 +12,14 @@
   val zero: rat
   val one: rat
   val two: rat
-  val rat_of_int: integer -> rat
-  val rat_of_quotient: integer * integer -> rat
-  val quotient_of_rat: rat -> integer * integer
+  val rat_of_int: int -> rat
+  val rat_of_quotient: int * int -> rat
+  val quotient_of_rat: rat -> int * int
   val string_of_rat: rat -> string
   val eq: rat * rat -> bool
   val ord: rat * rat -> order
   val le: rat -> rat -> bool
   val lt: rat -> rat -> bool
-  val signabs: rat -> order * rat
   val sign: rat -> order
   val abs: rat -> rat
   val add: rat -> rat -> rat
@@ -37,16 +36,16 @@
 fun common (p1, q1) (p2, q2) =
   let
     val m = Integer.lcm q1 q2;
-  in ((Integer.mult p1 (Integer.div m q1), Integer.mult p2 (Integer.div m q2)), m) end;
+  in ((p1 * (m div q1), p2 * (m div q2)), m) end;
 
-datatype rat = Rat of integer * integer; (* nominator, denominator (positive!) *)
+datatype rat = Rat of int * int;  (*nominator, denominator (positive!)*)
 
 exception DIVZERO;
 
 fun rat_of_quotient (p, q) =
   let
-    val m = Integer.gcd (Integer.abs p) q
-  in Rat (Integer.div p m, Integer.div q m) end handle Div => raise DIVZERO;
+    val m = Integer.gcd (Int.abs p) q
+  in Rat (p div m, q div m) end handle Div => raise DIVZERO;
 
 fun quotient_of_rat (Rat r) = r;
 
@@ -57,11 +56,12 @@
 val two = rat_of_int 2;
 
 fun string_of_rat (Rat (p, q)) =
-  Integer.string_of_int p ^ "/" ^ Integer.string_of_int q;
+  string_of_int p ^ "/" ^ string_of_int q;
 
 fun eq (Rat (p1, q1), Rat (p2, q2)) = (p1 = p2 andalso q1 = q2);
 
-fun ord (Rat (p1, q1), Rat (p2, q2)) = case (Integer.sign p1, Integer.sign p2)
+fun ord (Rat (p1, q1), Rat (p2, q2)) =
+ case (Integer.sign p1, Integer.sign p2)
  of (LESS, EQUAL) => LESS
   | (LESS, GREATER) => LESS
   | (EQUAL, LESS) => GREATER
@@ -69,38 +69,35 @@
   | (EQUAL, GREATER) => LESS
   | (GREATER, LESS) => GREATER
   | (GREATER, EQUAL) => GREATER
-  | _ => Integer.ord (fst (common (p1, q1) (p2, q2)));
+  | _ => int_ord (fst (common (p1, q1) (p2, q2)));
 
 fun le a b = not (ord (a, b) = GREATER);
 fun lt a b = (ord (a, b) = LESS);
 
 fun sign (Rat (p, _)) = Integer.sign p;
 
-fun abs (Rat (p, q)) = Rat (Integer.abs p, q);
-
-fun signabs (Rat (p, q)) =
-  let
-    val (s, p') = Integer.signabs p;
-  in (s, Rat (p', q)) end;
+fun abs (Rat (p, q)) = Rat (Int.abs p, q);
 
 fun add (Rat (p1, q1)) (Rat (p2, q2)) =
   let
     val ((m1, m2), n) = common (p1, q1) (p2, q2);
-  in rat_of_quotient (Integer.add m1 m2, n) end;
+  in rat_of_quotient (m1 + m2, n) end;
 
 fun mult (Rat (p1, q1)) (Rat (p2, q2)) =
-  rat_of_quotient (Integer.mult p1 p2, Integer.mult q1 q2);
+  rat_of_quotient (p1 * p2, q1 * q2);
+
+fun neg (Rat (p, q)) = Rat (~ p, q);
 
-fun neg (Rat (p, q)) = Rat (Integer.neg p, q);
-
-fun inv (Rat (p, q)) = case Integer.sign p
- of LESS => Rat (Integer.neg q, Integer.neg p)
+fun inv (Rat (p, q)) =
+ case Integer.sign p
+ of LESS => Rat (~ q, ~ p)
   | EQUAL => raise DIVZERO
   | GREATER => Rat (q, p);
 
-fun rounddown (Rat (p, q)) = Rat (Integer.div p q, 1);
+fun rounddown (Rat (p, q)) = Rat (p div q, 1);
 
-fun roundup (Rat (p, q)) = case Integer.divmod p q
+fun roundup (Rat (p, q)) =
+ case Integer.div_mod p q
  of (m, 0) => Rat (m, 1)
   | (m, _) => Rat (m + 1, 1);