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(* 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 quot_rem: int -> int -> int * int
val square: int -> int
val pow: int -> int -> int (* exponent -> base -> result *)
val log2: int -> int
val gcd: int -> int -> int
val lcm: int -> int -> int
val gcds: int list -> int
val lcms: int list -> int
val radicify: int -> int -> int -> int list (* base -> number of positions -> value -> coefficients *)
val eval_radix: int -> int list -> int (* base -> coefficients -> value *)
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 quot_rem x y = IntInf.quotRem (x, y);
fun square x = x * x;
fun pow k l = IntInf.pow (l, k);
val log2 = IntInf.log2;
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));
fun radicify base len k =
let
val _ = if base < 2
then error ("Bad radix base: " ^ string_of_int base) else ();
fun shift i = swap (div_mod i base);
in funpow_yield len shift k |> fst end;
fun eval_radix base ks =
fold_rev (fn k => fn i => k + i * base) ks 0;
end;
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