Chris@10: (*
Chris@10:  * Copyright (c) 1997-1999 Massachusetts Institute of Technology
Chris@10:  * Copyright (c) 2003, 2007-11 Matteo Frigo
Chris@10:  * Copyright (c) 2003, 2007-11 Massachusetts Institute of Technology
Chris@10:  *
Chris@10:  * This program is free software; you can redistribute it and/or modify
Chris@10:  * it under the terms of the GNU General Public License as published by
Chris@10:  * the Free Software Foundation; either version 2 of the License, or
Chris@10:  * (at your option) any later version.
Chris@10:  *
Chris@10:  * This program is distributed in the hope that it will be useful,
Chris@10:  * but WITHOUT ANY WARRANTY; without even the implied warranty of
Chris@10:  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
Chris@10:  * GNU General Public License for more details.
Chris@10:  *
Chris@10:  * You should have received a copy of the GNU General Public License
Chris@10:  * along with this program; if not, write to the Free Software
Chris@10:  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
Chris@10:  *
Chris@10:  *)
Chris@10: 
Chris@10: (* various utility functions *)
Chris@10: open List
Chris@10: open Unix 
Chris@10: 
Chris@10: (*****************************************
Chris@10:  * Integer operations
Chris@10:  *****************************************)
Chris@10: (* fint the inverse of n modulo m *)
Chris@10: let invmod n m =
Chris@10:     let rec loop i =
Chris@10: 	if ((i * n) mod m == 1) then i
Chris@10: 	else loop (i + 1)
Chris@10:     in
Chris@10: 	loop 1
Chris@10: 
Chris@10: (* Yooklid's algorithm *)
Chris@10: let rec gcd n m =
Chris@10:     if (n > m)
Chris@10:       then gcd m n
Chris@10:     else
Chris@10:       let r = m mod n
Chris@10:       in
Chris@10: 	  if (r == 0) then n
Chris@10: 	  else gcd r n
Chris@10: 
Chris@10: (* reduce the fraction m/n to lowest terms, modulo factors of n/n *)
Chris@10: let lowest_terms n m =
Chris@10:     if (m mod n == 0) then
Chris@10:       (1,0)
Chris@10:     else
Chris@10:       let nn = (abs n) in let mm = m * (n / nn)
Chris@10:       in let mpos = 
Chris@10: 	  if (mm > 0) then (mm mod nn)
Chris@10: 	  else (mm + (1 + (abs mm) / nn) * nn) mod nn
Chris@10:       and d = gcd nn (abs mm)
Chris@10:       in (nn / d, mpos / d)
Chris@10: 
Chris@10: (* find a generator for the multiplicative group mod p
Chris@10:    (where p must be prime for a generator to exist!!) *)
Chris@10: 
Chris@10: exception No_Generator
Chris@10: 
Chris@10: let find_generator p =
Chris@10:     let rec period x prod =
Chris@10:  	if (prod == 1) then 1
Chris@10: 	else 1 + (period x (prod * x mod p))
Chris@10:     in let rec findgen x =
Chris@10: 	if (x == 0) then raise No_Generator
Chris@10: 	else if ((period x x) == (p - 1)) then x
Chris@10: 	else findgen ((x + 1) mod p)
Chris@10:     in findgen 1
Chris@10: 
Chris@10: (* raise x to a power n modulo p (requires n > 0) (in principle,
Chris@10:    negative powers would be fine, provided that x and p are relatively
Chris@10:    prime...we don't need this functionality, though) *)
Chris@10: 
Chris@10: exception Negative_Power
Chris@10: 
Chris@10: let rec pow_mod x n p =
Chris@10:     if (n == 0) then 1
Chris@10:     else if (n < 0) then raise Negative_Power
Chris@10:     else if (n mod 2 == 0) then pow_mod (x * x mod p) (n / 2) p
Chris@10:     else x * (pow_mod x (n - 1) p) mod p
Chris@10: 
Chris@10: (******************************************
Chris@10:  * auxiliary functions 
Chris@10:  ******************************************)
Chris@10: let rec forall id combiner a b f =
Chris@10:     if (a >= b) then id
Chris@10:     else combiner (f a) (forall id combiner (a + 1) b f)
Chris@10: 
Chris@10: let sum_list l = fold_right (+) l 0
Chris@10: let max_list l = fold_right (max) l (-999999)
Chris@10: let min_list l = fold_right (min) l 999999
Chris@10: let count pred = fold_left 
Chris@10:     (fun a elem -> if (pred elem) then 1 + a else a) 0
Chris@10: let remove elem = List.filter (fun e -> (e != elem))
Chris@10: let cons a b = a :: b
Chris@10: let null = function 
Chris@10:     [] -> true
Chris@10:   | _ -> false
Chris@10: let for_list l f = List.iter f l
Chris@10: let rmap l f = List.map f l
Chris@10: 
Chris@10: (* functional composition *)
Chris@10: let (@@) f g x = f (g x)
Chris@10: 
Chris@10: let forall_flat a b = forall [] (@) a b
Chris@10: 
Chris@10: let identity x = x
Chris@10: 
Chris@10: let rec minimize f = function
Chris@10:     [] -> None
Chris@10:   | elem :: rest ->
Chris@10:       match minimize f rest with
Chris@10: 	None -> Some elem
Chris@10:       |	Some x -> if (f x) >= (f elem) then Some elem else Some x
Chris@10: 
Chris@10: 
Chris@10: let rec find_elem condition = function
Chris@10:     [] -> None
Chris@10:   | elem :: rest ->
Chris@10:       if condition elem then
Chris@10: 	Some elem
Chris@10:       else
Chris@10: 	find_elem condition rest
Chris@10: 
Chris@10: 
Chris@10: (* find x, x >= a, such that (p x) is true *)
Chris@10: let rec suchthat a pred =
Chris@10:   if (pred a) then a else suchthat (a + 1) pred
Chris@10: 
Chris@10: (* print an information message *)
Chris@10: let info string =
Chris@10:   if !Magic.verbose then begin
Chris@10:     let now = Unix.times () 
Chris@10:     and pid = Unix.getpid () in
Chris@10:     prerr_string ((string_of_int pid) ^ ": " ^
Chris@10: 		  "at t = " ^  (string_of_float now.tms_utime) ^ " : ");
Chris@10:     prerr_string (string ^ "\n");
Chris@10:     flush Pervasives.stderr;
Chris@10:   end
Chris@10: 
Chris@10: (* iota n produces the list [0; 1; ...; n - 1] *)
Chris@10: let iota n = forall [] cons 0 n identity
Chris@10: 
Chris@10: (* interval a b produces the list [a; 1; ...; b - 1] *)
Chris@10: let interval a b = List.map ((+) a) (iota (b - a))
Chris@10: 
Chris@10: (*
Chris@10:  * freeze a function, i.e., compute it only once on demand, and
Chris@10:  * cache it into an array.
Chris@10:  *)
Chris@10: let array n f =
Chris@10:   let a = Array.init n (fun i -> lazy (f i))
Chris@10:   in fun i -> Lazy.force a.(i)
Chris@10: 
Chris@10: 
Chris@10: let rec take n l =
Chris@10:   match (n, l) with
Chris@10:     (0, _) -> []
Chris@10:   | (n, (a :: b)) -> a :: (take (n - 1) b)
Chris@10:   | _ -> failwith "take"
Chris@10: 
Chris@10: let rec drop n l =
Chris@10:   match (n, l) with
Chris@10:     (0, _) -> l
Chris@10:   | (n, (_ :: b)) -> drop (n - 1) b
Chris@10:   | _ -> failwith "drop"
Chris@10: 
Chris@10: 
Chris@10: let either a b =
Chris@10:   match a with
Chris@10:     Some x -> x
Chris@10:   | _ -> b