--- a/src/Tools/rat.ML Tue Jun 05 18:36:10 2007 +0200
+++ b/src/Tools/rat.ML Tue Jun 05 19:19:30 2007 +0200
@@ -12,9 +12,9 @@
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 rat_of_int: integer -> rat
+ val rat_of_quotient: integer * integer -> rat
+ val quotient_of_rat: rat -> integer * integer
val string_of_rat: rat -> string
val eq: rat * rat -> bool
val cmp: rat * rat -> order
@@ -32,53 +32,59 @@
structure Rat : RAT =
struct
-datatype rat = Rat of bool * Intt.int * Intt.int;
+datatype rat = Rat of bool * integer * integer;
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);
+val zero = Rat (true, Integer.zero, Integer.one);
+val one = Rat (true, Integer.one, Integer.one);
+val two = Rat (true, Integer.two, Integer.one);
fun rat_of_int i =
- if i < Intt.int 0
- then Rat (false, ~i, Intt.int 1)
- else Rat (true, i, Intt.int 1);
+ let
+ val (a, p) = Integer.signabs i
+ in Rat (a, p, Integer.one) end;
fun norm (a, p, q) =
- if p = Intt.int 0 then Rat (true, Intt.int 0, Intt.int 1)
+ if Integer.cmp_zero p = EQUAL then Rat (true, Integer.zero, Integer.one)
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;
+ val (b, absp) = Integer.signabs p;
+ val m = Integer.gcd absp q;
+ in Rat (a = b, Integer.div absp m, Integer.div q 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
+ let
+ val q' = Integer.lcm q1 q2;
+ in (p1 *% (Integer.div q' q1), p2 *% (Integer.div q' 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);
+ let
+ val (a, absq) = Integer.signabs q;
+ in
+ if Integer.cmp_zero absq = EQUAL then raise DIVZERO
+ else norm (a, p, absq)
+ end;
-fun quotient_of_rat (Rat (a, p, q)) = (if a then p else ~p, q);
+fun quotient_of_rat (Rat (a, p, q)) = (if a then p else Integer.neg 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;
+ let
+ val (p, q) = quotient_of_rat r;
+ in Integer.string_of_int p ^ "/" ^ Integer.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
+ | 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;
+ in if a then Integer.cmp (r1, r2) else Integer.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 lt a b = (cmp (a, b) = LESS);
fun cmp_zero (Rat (false, _, _)) = LESS
| cmp_zero (Rat (_, 0, _)) = EQUAL
@@ -86,53 +92,50 @@
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)
+ val (r1, r2, den) = common (p1, q1, p2, q2);
+ val num = (if a1 then r1 else Integer.neg r1)
+ +% (if a2 then r2 else Integer.neg r2);
in norm (true, num, den) end;
fun mult (Rat (a1, p1, q1)) (Rat (a2, p2, q2)) =
- norm (a1=a2, p1*p2, q1*q2);
+ norm (a1 = a2, p1 *% p2, q1 *% q2);
fun neg (r as Rat (b, p, q)) =
- if p = Intt.int 0 then r
+ if Integer.cmp_zero p = EQUAL then r
else Rat (not b, p, q);
fun inv (Rat (a, p, q)) =
- if p = Intt.int 0 then raise DIVZERO
+ if Integer.cmp_zero q = EQUAL then raise DIVZERO
else Rat (a, q, p);
fun roundup (r as Rat (a, p, q)) =
- if q = Intt.int 1 then r
+ if q = Integer.one then r
else
let
- fun round true q = Rat (true, q + Intt.int 1, Intt.int 1)
+ fun round true q = Rat (true, Integer.inc q, Integer.one)
| 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;
+ Rat (Integer.cmp_zero q = EQUAL, Integer.int 0, Integer.int 1);
+ in round a (Integer.div p q) end;
fun rounddown (r as Rat (a, p, q)) =
- if q = Intt.int 1 then r
+ if q = Integer.one 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;
+ fun round true q = Rat (true, q, Integer.one)
+ | round false q = Rat (false, Integer.inc q, Integer.one)
+ in round a (Integer.div p q) end;
end;
-infix 5 +/;
-infix 5 -/;
-infix 7 */;
-infix 7 //;
+infix 7 */ //;
+infix 6 +/ -/;
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.eq (a, b);
fun a </ b = Rat.lt a b;
fun a <=/ b = Rat.le a b;
fun a >/ b = b </ a;