Chris@82: (*
Chris@82:  * Copyright (c) 1997-1999 Massachusetts Institute of Technology
Chris@82:  * Copyright (c) 2003, 2007-14 Matteo Frigo
Chris@82:  * Copyright (c) 2003, 2007-14 Massachusetts Institute of Technology
Chris@82:  *
Chris@82:  * This program is free software; you can redistribute it and/or modify
Chris@82:  * it under the terms of the GNU General Public License as published by
Chris@82:  * the Free Software Foundation; either version 2 of the License, or
Chris@82:  * (at your option) any later version.
Chris@82:  *
Chris@82:  * This program is distributed in the hope that it will be useful,
Chris@82:  * but WITHOUT ANY WARRANTY; without even the implied warranty of
Chris@82:  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
Chris@82:  * GNU General Public License for more details.
Chris@82:  *
Chris@82:  * You should have received a copy of the GNU General Public License
Chris@82:  * along with this program; if not, write to the Free Software
Chris@82:  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
Chris@82:  *
Chris@82:  *)
Chris@82: 
Chris@82: (* 
Chris@82:  * The LittleSimplifier module implements a subset of the simplifications
Chris@82:  * of the AlgSimp module.  These simplifications can be executed
Chris@82:  * quickly here, while they would take a long time using the heavy
Chris@82:  * machinery of AlgSimp.  
Chris@82:  * 
Chris@82:  * For example, 0 * x is simplified to 0 tout court by the LittleSimplifier.
Chris@82:  * On the other hand, AlgSimp would first simplify x, generating lots
Chris@82:  * of common subexpressions, storing them in a table etc, just to
Chris@82:  * discard all the work later.  Similarly, the LittleSimplifier
Chris@82:  * reduces the constant FFT in Rader's algorithm to a constant sequence.
Chris@82:  *)
Chris@82: 
Chris@82: open Expr
Chris@82: 
Chris@82: let rec makeNum = function
Chris@82:   | n -> Num n
Chris@82: 
Chris@82: and makeUminus = function
Chris@82:   | Uminus a -> a 
Chris@82:   | Num a -> makeNum (Number.negate a)
Chris@82:   | a -> Uminus a
Chris@82: 
Chris@82: and makeTimes = function
Chris@82:   | (Num a, Num b) -> makeNum (Number.mul a b)
Chris@82:   | (Num a, Times (Num b, c)) -> makeTimes (makeNum (Number.mul a b), c)
Chris@82:   | (Num a, b) when Number.is_zero a -> makeNum (Number.zero)
Chris@82:   | (Num a, b) when Number.is_one a -> b
Chris@82:   | (Num a, b) when Number.is_mone a -> makeUminus b
Chris@82:   | (Num a, Uminus b) -> Times (makeUminus (Num a), b)
Chris@82:   | (a, (Num b as b')) -> makeTimes (b', a)
Chris@82:   | (a, b) -> Times (a, b)
Chris@82: 
Chris@82: and makePlus l = 
Chris@82:   let rec reduceSum x = match x with
Chris@82:     [] -> []
Chris@82:   | [Num a] -> if Number.is_zero a then [] else x
Chris@82:   | (Num a) :: (Num b) :: c -> 
Chris@82:       reduceSum ((makeNum (Number.add a b)) :: c)
Chris@82:   | ((Num _) as a') :: b :: c -> b :: reduceSum (a' :: c)
Chris@82:   | a :: s -> a :: reduceSum s
Chris@82: 
Chris@82:   in match reduceSum l with
Chris@82:     [] -> makeNum (Number.zero)
Chris@82:   | [a] -> a 
Chris@82:   | [a; b] when a == b -> makeTimes (Num Number.two, a)
Chris@82:   | [Times (Num a, b); Times (Num c, d)] when b == d ->
Chris@82:       makeTimes (makePlus [Num a; Num c], b)
Chris@82:   | a -> Plus a
Chris@82: