src/Tools/float.ML
 author wenzelm Fri, 02 Oct 2009 22:15:08 +0200 changeset 32861 105f40051387 parent 30161 c26e515f1c29 child 67560 0fa87bd86566 permissions -rw-r--r--
```
(*  Title:      Tools/float.ML
Author:     Steven Obua, Florian Haftmann, TU Muenchen

Implementation of real numbers as mantisse-exponent pairs.
*)

signature FLOAT =
sig
type float = int * int
val zero: float
val eq: float * float -> bool
val ord: float * float -> order
val sign: 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 = int * int;

val zero: float = (0, 0);

fun add (a1, b1) (a2, b2) =
if b1 < b2 then
(a1 + a2 * Integer.square (b2 - b1), b1)
else
(a1 * Integer.square (b1 - b2) + a2, b2);

fun sub (a1, b1) (a2, b2) =
if b1 < b2 then
(a1 - a2 * Integer.square (b2 - b1), b1)
else
(a1 * Integer.square (b1 - b2) - a2, b2);

fun neg (a, b) = (~ a, b);

fun mult (a1, b1) (a2, b2) = (a1 * a2, b1 + b2);

fun sign (a, b) = Integer.sign a;

fun ord (r, s) = sign (sub r s);

fun eq (r, s) = ord (r, s) = EQUAL;

fun min r s = case ord (r, s) of LESS => r | _ => s;
fun max r s = case ord (r, s) of LESS => s | _ => r;

fun positive_part (a, b) = (Int.max (0, a), b);
fun negative_part (a, b) = (Int.min (0, a), b);

end;
```