(* Title: Pure/General/integer.ML
Author: Florian Haftmann, TU Muenchen
Auxiliary operations on (unbounded) integers.
*)
signature INTEGER =
sig
val min: int -> int -> int
val max: int -> int -> int
val add: int -> int -> int
val mult: int -> int -> int
val sum: int list -> int
val prod: int list -> int
val sign: int -> order
val div_mod: int -> int -> int * int
val square: int -> int
val pow: int -> int -> int (* exponent -> base -> result *)
val gcd: int -> int -> int
val lcm: int -> int -> int
val gcds: int list -> int
val lcms: int list -> int
end;
structure Integer : INTEGER =
struct
fun min x y = Int.min (x, y);
fun max x y = Int.max (x, y);
fun add x y = x + y;
fun mult x y = x * y;
fun sum xs = fold add xs 0;
fun prod xs = fold mult xs 1;
fun sign x = int_ord (x, 0);
fun div_mod x y = IntInf.divMod (x, y);
fun square x = x * x;
fun pow k l =
let
fun pw 0 _ = 1
| pw 1 l = l
| pw k l =
let
val (k', r) = div_mod k 2;
val l' = pw k' (l * l);
in if r = 0 then l' else l' * l end;
in
if k < 0
then error "pow: negative exponent"
else pw k l
end;
fun gcd x y = PolyML.IntInf.gcd (x, y);
fun lcm x y = abs (PolyML.IntInf.lcm (x, y));
fun gcds [] = 0
| gcds (x :: xs) = fold gcd xs x;
fun lcms [] = 1
| lcms (x :: xs) = abs (Library.foldl PolyML.IntInf.lcm (x, xs));
end;