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(* $Id: num.ml,v 4.1 2001/04/19 12:34:57 ddr Exp $ *)
(* Copyright (c) 2001 INRIA *)
type t = array int;
value base = 0x1000000;
value max_mul_base = max_int / base;
value zero = [| |];
value one = [| 1 |];
value eq x y = x = y;
value gt x y =
if Array.length x > Array.length y then True
else if Array.length x < Array.length y then False
else
loop (Array.length x - 1) where rec loop i =
if i < 0 then False
else if x.(i) > y.(i) then True
else if x.(i) < y.(i) then False
else loop (i - 1)
;
value twice x =
let l =
loop 0 0 where rec loop i r =
if i == Array.length x then
if r == 0 then [] else [r]
else
let v = x.(i) lsl 1 + r in
[v land (base - 1) :: loop (i + 1) (if v >= base then 1 else 0)]
in
Array.of_list l
;
value half x =
let l =
loop (Array.length x - 1) 0 [] where rec loop i r v =
if i < 0 then v
else
let rd = if x.(i) land 1 == 0 then 0 else base / 2 in
let v =
let d = r + x.(i) / 2 in
if d = 0 && v = [] then v else [d :: v]
in
loop (i - 1) rd v
in
Array.of_list l
;
value even x =
if Array.length x == 0 then True
else x.(0) land 1 == 0
;
value inc x n =
let l =
loop 0 n where rec loop i r =
if i == Array.length x then
if r == 0 then [] else [r]
else
let d = x.(i) + r in
[d mod base :: loop (i + 1) (d / base)]
in
Array.of_list l
;
value add x y =
let l =
loop 0 0 where rec loop i r =
if i >= Array.length x && i >= Array.length y then
if r == 0 then [] else [r]
else
let (d, r) =
let xi = if i >= Array.length x then 0 else x.(i) in
let yi = if i >= Array.length y then 0 else y.(i) in
let s = xi + yi + r in
(s mod base, s / base)
in
[d :: loop (i + 1) r]
in
Array.of_list l
;
value normalize =
loop where rec loop =
fun
[ [] -> []
| [x :: l] ->
let r = loop l in
if x == 0 && r = [] then r else [x :: r] ]
;
value sub x y =
let l =
loop 0 0 where rec loop i r =
if i >= Array.length x && i >= Array.length y then
if r == 0 then []
else invalid_arg "Num.sub"
else
let (d, r) =
let xi = if i >= Array.length x then 0 else x.(i) in
let yi = if i >= Array.length y then 0 else y.(i) in
if yi + r <= xi then (xi - (yi + r), 0)
else (base + xi - (yi + r), 1)
in
[d :: loop (i + 1) r]
in
Array.of_list (normalize l)
;
value mul0 x n =
if n > max_mul_base then invalid_arg "Num.mul"
else
let l =
loop 0 0 where rec loop i r =
if i == Array.length x then
if r == 0 then [] else [r]
else
let d = x.(i) * n + r in
[d mod base :: loop (i + 1) (d / base)]
in
Array.of_list l
;
value mul x n =
if n < max_mul_base then mul0 x n
else
loop zero x n where rec loop r x n =
if n < max_mul_base then add r (mul0 x n)
else
loop (add r (mul0 x (n mod max_mul_base)))
(mul0 x max_mul_base) (n / max_mul_base)
;
value div x n =
if n > max_mul_base then invalid_arg "Num.div"
else
let l =
loop (Array.length x - 1) [] 0 where rec loop i l r =
if i < 0 then l
else
let r = r mod n * base + x.(i) in
let d = r / n in
loop (i - 1) [d :: l] r
in
Array.of_list (normalize l)
;
value modl x n =
let r = sub x (mul0 (div x n) n) in
if Array.length r == 0 then 0 else r.(0)
;
value of_int i =
if i < 0 then invalid_arg "Num.of_int"
else if i == 0 then zero
else if i < base then [| i |]
else [| i mod base; i / base |]
;
value print f sep x =
if eq x zero then f "0"
else
let digits = loop [] x
where rec loop d x =
if eq x zero then d
else loop [modl x 10 :: d] (div x 10)
in
let _ =
List.fold_left
(fun n d ->
do {
f (string_of_int d);
if n > 0 && n mod 3 = 0 then f sep else ();
n - 1;
})
(List.length digits - 1) digits
in ()
;
value to_string x =
let digits = loop [] x
where rec loop d x =
if eq x zero then d
else loop [modl x 10 :: d] (div x 10)
in
let s = String.create (List.length digits) in
let _ =
List.fold_left
(fun i d -> do { s.[i] := Char.chr (Char.code '0' + d); (i + 1) })
0 digits
in
s
;
value of_string s =
loop zero 0 where rec loop n i =
if i == String.length s then n
else
match s.[i] with
[ '0'..'9' ->
loop (inc (mul0 n 10) (Char.code s.[i] - Char.code '0')) (i + 1)
| _ -> failwith "Num.of_string" ]
;
|
