Updates

fftw-3.3.10/genfft/littlesimp.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
+ *
+ *)
+
+(* 
+ * The LittleSimplifier module implements a subset of the simplifications
+ * of the AlgSimp module.  These simplifications can be executed
+ * quickly here, while they would take a long time using the heavy
+ * machinery of AlgSimp.  
+ * 
+ * For example, 0 * x is simplified to 0 tout court by the LittleSimplifier.
+ * On the other hand, AlgSimp would first simplify x, generating lots
+ * of common subexpressions, storing them in a table etc, just to
+ * discard all the work later.  Similarly, the LittleSimplifier
+ * reduces the constant FFT in Rader's algorithm to a constant sequence.
+ *)
+
+open Expr
+
+let rec makeNum = function
+  | n -> Num n
+
+and makeUminus = function
+  | Uminus a -> a 
+  | Num a -> makeNum (Number.negate a)
+  | a -> Uminus a
+
+and makeTimes = function
+  | (Num a, Num b) -> makeNum (Number.mul a b)
+  | (Num a, Times (Num b, c)) -> makeTimes (makeNum (Number.mul a b), c)
+  | (Num a, b) when Number.is_zero a -> makeNum (Number.zero)
+  | (Num a, b) when Number.is_one a -> b
+  | (Num a, b) when Number.is_mone a -> makeUminus b
+  | (Num a, Uminus b) -> Times (makeUminus (Num a), b)
+  | (a, (Num b as b')) -> makeTimes (b', a)
+  | (a, b) -> Times (a, b)
+
+and makePlus l = 
+  let rec reduceSum x = match x with
+    [] -> []
+  | [Num a] -> if Number.is_zero a then [] else x
+  | (Num a) :: (Num b) :: c -> 
+      reduceSum ((makeNum (Number.add a b)) :: c)
+  | ((Num _) as a') :: b :: c -> b :: reduceSum (a' :: c)
+  | a :: s -> a :: reduceSum s
+
+  in match reduceSum l with
+    [] -> makeNum (Number.zero)
+  | [a] -> a 
+  | [a; b] when a == b -> makeTimes (Num Number.two, a)
+  | [Times (Num a, b); Times (Num c, d)] when b == d ->
+      makeTimes (makePlus [Num a; Num c], b)
+  | a -> Plus a
+