--- a/src/Pure/General/rat.ML Tue Jun 05 15:16:11 2007 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,140 +0,0 @@
-(* Title: Pure/General/rat.ML
- ID: $Id$
- Author: Tobias Nipkow, TU Muenchen
-
-Canonical implementation of exact rational numbers.
-*)
-
-signature RAT =
-sig
- type rat
- exception DIVZERO
- val zero: rat
- val one: rat
- val two: rat
- val rat_of_int: Intt.int -> rat
- val rat_of_quotient: Intt.int * Intt.int -> rat
- val quotient_of_rat: rat -> Intt.int * Intt.int
- val string_of_rat: rat -> string
- val eq: rat * rat -> bool
- val cmp: rat * rat -> order
- val le: rat -> rat -> bool
- val lt: rat -> rat -> bool
- val cmp_zero: rat -> order
- val add: rat -> rat -> rat
- val mult: rat -> rat -> rat
- val neg: rat -> rat
- val inv: rat -> rat
- val roundup: rat -> rat
- val rounddown: rat -> rat
-end;
-
-structure Rat : RAT =
-struct
-
-datatype rat = Rat of bool * Intt.int * Intt.int;
-
-exception DIVZERO;
-
-val zero = Rat (true, Intt.int 0, Intt.int 1);
-val one = Rat (true, Intt.int 1, Intt.int 1);
-val two = Rat (true, Intt.int 2, Intt.int 1);
-
-fun rat_of_int i =
- if i < Intt.int 0
- then Rat (false, ~i, Intt.int 1)
- else Rat (true, i, Intt.int 1);
-
-fun norm (a, p, q) =
- if p = Intt.int 0 then Rat (true, Intt.int 0, Intt.int 1)
- else
- let
- val absp = abs p
- val m = gcd (absp, q)
- in Rat(a = (Intt.int 0 <= p), absp div m, q div m) end;
-
-fun common (p1, q1, p2, q2) =
- let val q' = lcm (q1, q2)
- in (p1 * (q' div q1), p2 * (q' div q2), q') end
-
-fun rat_of_quotient (p, q) =
- if q = Intt.int 0 then raise DIVZERO
- else norm (Intt.int 0 <= q, p, abs q);
-
-fun quotient_of_rat (Rat (a, p, q)) = (if a then p else ~p, q);
-
-fun string_of_rat r =
- let val (p, q) = quotient_of_rat r
- in Intt.string_of_int p ^ "/" ^ Intt.string_of_int q end;
-
-fun eq (Rat (false, _, _), Rat (true, _, _)) = false
- | eq (Rat (true, _, _), Rat (false, _, _)) = false
- | eq (Rat (_, p1, q1), Rat (_, p2, q2)) = p1 = p2 andalso q1 = q2
-
-fun cmp (Rat (false, _, _), Rat (true, _, _)) = LESS
- | cmp (Rat (true, _, _), Rat (false, _, _)) = GREATER
- | cmp (Rat (a, p1, q1), Rat (_, p2, q2)) =
- let val (r1, r2, _) = common (p1, q1, p2, q2)
- in if a then Intt.cmp (r1, r2) else Intt.cmp (r2, r1) end;
-
-fun le a b = let val order = cmp (a, b) in order = LESS orelse order = EQUAL end;
-fun lt a b = cmp (a, b) = LESS;
-
-fun cmp_zero (Rat (false, _, _)) = LESS
- | cmp_zero (Rat (_, 0, _)) = EQUAL
- | cmp_zero (Rat (_, _, _)) = GREATER;
-
-fun add (Rat (a1, p1, q1)) (Rat(a2, p2, q2)) =
- let
- val (r1, r2, den) = common (p1, q1, p2, q2)
- val num = (if a1 then r1 else ~r1) + (if a2 then r2 else ~r2)
- in norm (true, num, den) end;
-
-fun mult (Rat (a1, p1, q1)) (Rat (a2, p2, q2)) =
- norm (a1=a2, p1*p2, q1*q2);
-
-fun neg (r as Rat (b, p, q)) =
- if p = Intt.int 0 then r
- else Rat (not b, p, q);
-
-fun inv (Rat (a, p, q)) =
- if p = Intt.int 0 then raise DIVZERO
- else Rat (a, q, p);
-
-fun roundup (r as Rat (a, p, q)) =
- if q = Intt.int 1 then r
- else
- let
- fun round true q = Rat (true, q + Intt.int 1, Intt.int 1)
- | round false q =
- if q = Intt.int 0
- then Rat (true, Intt.int 0, Intt.int 1)
- else Rat (false, q, Intt.int 1);
- in round a (p div q) end;
-
-fun rounddown (r as Rat (a, p, q)) =
- if q = Intt.int 1 then r
- else
- let
- fun round true q = Rat (true, q, Intt.int 1)
- | round false q = Rat (false, q + Intt.int 1, Intt.int 1)
- in round a (p div q) end;
-
-end;
-
-infix 5 +/;
-infix 5 -/;
-infix 7 */;
-infix 7 //;
-infix 4 =/ </ <=/ >/ >=/ <>/;
-
-fun a +/ b = Rat.add a b;
-fun a -/ b = a +/ Rat.neg b;
-fun a */ b = Rat.mult a b;
-fun a // b = a */ Rat.inv b;
-fun a =/ b = Rat.eq (a,b);
-fun a </ b = Rat.lt a b;
-fun a <=/ b = Rat.le a b;
-fun a >/ b = b </ a;
-fun a >=/ b = b <=/ a;
-fun a <>/ b = not (a =/ b);