Updates

fftw-3.3.10/genfft/util.ml

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+(*
+ * Copyright (c) 1997-1999 Massachusetts Institute of Technology
+ * Copyright (c) 2003, 2007-14 Matteo Frigo
+ * Copyright (c) 2003, 2007-14 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; 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