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