(* Title: Pure/General/float.ML
ID: $Id$
Author: Steven Obua, Florian Haftmann, TU Muenchen
Implementation of real numbers as mantisse-exponent pairs.
*)
signature FLOAT =
sig
type float = Intt.int * Intt.int
val zero: float
val eq: float * float -> bool
val cmp: float * float -> order
val cmp_zero: float -> order
val min: float -> float -> float
val max: float -> float -> float
val add: float -> float -> float
val sub: float -> float -> float
val neg: float -> float
val mult: float -> float -> float
val positive_part: float -> float
val negative_part: float -> float
end;
structure Float : FLOAT =
struct
type float = Intt.int * Intt.int;
val zero = (Intt.zero, Intt.zero);
fun add (a1, b1) (a2, b2) =
if Intt.cmp (b1, b2) = LESS then
(Intt.add a1 (Intt.mult a2 (Intt.exp (Intt.sub b2 b1))), b1)
else
(Intt.add (Intt.mult a1 (Intt.exp (Intt.sub b1 b2))) a2, b2);
fun sub (a1, b1) (a2, b2) =
if Intt.cmp (b1, b2) = LESS then
(Intt.sub a1 (Intt.mult a2 (Intt.exp (Intt.sub b2 b1))), b1)
else
(Intt.sub (Intt.mult a1 (Intt.exp (Intt.sub b1 b2))) a2, b2);
fun neg (a, b) = (Intt.neg a, b);
fun mult (a1, b1) (a2, b2) = (Intt.mult a1 a2, Intt.add b1 b2);
fun cmp_zero (a, b) = Intt.cmp_zero a;
fun cmp (r, s) = cmp_zero (sub r s);
fun eq (r, s) = cmp (r, s) = EQUAL;
fun min r s = case cmp (r, s) of LESS => r | _ => s;
fun max r s = case cmp (r, s) of LESS => s | _ => r;
fun positive_part (a, b) = (Intt.max Intt.zero a, b);
fun negative_part (a, b) = (Intt.min Intt.zero a, b);
end;