(*
* 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 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