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(*
* Copyright (c) 1997-1999 Massachusetts Institute of Technology
* Copyright (c) 2003, 2007-11 Matteo Frigo
* Copyright (c) 2003, 2007-11 Massachusetts Institute of Technology
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*
*)
(* various utility functions *)
open List
open Unix
(*****************************************
* Integer operations
*****************************************)
(* fint the inverse of n modulo m *)
let invmod n m =
let rec loop i =
if ((i * n) mod m == 1) then i
else loop (i + 1)
in
loop 1
(* Yooklid's algorithm *)
let rec gcd n m =
if (n > m)
then gcd m n
else
let r = m mod n
in
if (r == 0) then n
else gcd r n
(* reduce the fraction m/n to lowest terms, modulo factors of n/n *)
let lowest_terms n m =
if (m mod n == 0) then
(1,0)
else
let nn = (abs n) in let mm = m * (n / nn)
in let mpos =
if (mm > 0) then (mm mod nn)
else (mm + (1 + (abs mm) / nn) * nn) mod nn
and d = gcd nn (abs mm)
in (nn / d, mpos / d)
(* find a generator for the multiplicative group mod p
(where p must be prime for a generator to exist!!) *)
exception No_Generator
let find_generator p =
let rec period x prod =
if (prod == 1) then 1
else 1 + (period x (prod * x mod p))
in let rec findgen x =
if (x == 0) then raise No_Generator
else if ((period x x) == (p - 1)) then x
else findgen ((x + 1) mod p)
in findgen 1
(* raise x to a power n modulo p (requires n > 0) (in principle,
negative powers would be fine, provided that x and p are relatively
prime...we don't need this functionality, though) *)
exception Negative_Power
let rec pow_mod x n p =
if (n == 0) then 1
else if (n < 0) then raise Negative_Power
else if (n mod 2 == 0) then pow_mod (x * x mod p) (n / 2) p
else x * (pow_mod x (n - 1) p) mod p
(******************************************
* auxiliary functions
******************************************)
let rec forall id combiner a b f =
if (a >= b) then id
else combiner (f a) (forall id combiner (a + 1) b f)
let sum_list l = fold_right (+) l 0
let max_list l = fold_right (max) l (-999999)
let min_list l = fold_right (min) l 999999
let count pred = fold_left
(fun a elem -> if (pred elem) then 1 + a else a) 0
let remove elem = List.filter (fun e -> (e != elem))
let cons a b = a :: b
let null = function
[] -> true
| _ -> false
let for_list l f = List.iter f l
let rmap l f = List.map f l
(* functional composition *)
let (@@) f g x = f (g x)
let forall_flat a b = forall [] (@) a b
let identity x = x
let rec minimize f = function
[] -> None
| elem :: rest ->
match minimize f rest with
None -> Some elem
| Some x -> if (f x) >= (f elem) then Some elem else Some x
let rec find_elem condition = function
[] -> None
| elem :: rest ->
if condition elem then
Some elem
else
find_elem condition rest
(* find x, x >= a, such that (p x) is true *)
let rec suchthat a pred =
if (pred a) then a else suchthat (a + 1) pred
(* print an information message *)
let info string =
if !Magic.verbose then begin
let now = Unix.times ()
and pid = Unix.getpid () in
prerr_string ((string_of_int pid) ^ ": " ^
"at t = " ^ (string_of_float now.tms_utime) ^ " : ");
prerr_string (string ^ "\n");
flush Pervasives.stderr;
end
(* iota n produces the list [0; 1; ...; n - 1] *)
let iota n = forall [] cons 0 n identity
(* interval a b produces the list [a; 1; ...; b - 1] *)
let interval a b = List.map ((+) a) (iota (b - a))
(*
* freeze a function, i.e., compute it only once on demand, and
* cache it into an array.
*)
let array n f =
let a = Array.init n (fun i -> lazy (f i))
in fun i -> Lazy.force a.(i)
let rec take n l =
match (n, l) with
(0, _) -> []
| (n, (a :: b)) -> a :: (take (n - 1) b)
| _ -> failwith "take"
let rec drop n l =
match (n, l) with
(0, _) -> l
| (n, (_ :: b)) -> drop (n - 1) b
| _ -> failwith "drop"
let either a b =
match a with
Some x -> x
| _ -> b
|
