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|
{-# LANGUAGE RankNTypes #-}
{-
- Copyright 2018 Raymond Hogenson
-
- This file is part of HSC.
- HSC 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 3 of the License, or
- (at your option) any later version.
-
- HSC 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 HSC. If not, see <http://www.gnu.org/licenses/>.
-}
module RealCalc (calculate) where
import qualified Expr
import qualified Data.Ratio
data Result = RInt Integer | RFloat Double | RRatio Rational
data ResultPair = RInts Integer Integer | RFloats Double Double | RRatios Rational Rational
instance Show Result where
show (RInt i) = show i
show (RFloat d) = show d
show (RRatio r) = show (Data.Ratio.numerator r) ++ "/" ++ show (Data.Ratio.denominator r)
rToDouble :: Result -> Double
rToDouble (RInt i) = fromIntegral i
rToDouble (RFloat d) = d
rToDouble (RRatio r) = fromIntegral (Data.Ratio.numerator r) / fromIntegral (Data.Ratio.denominator r)
castSame :: Result -> Result -> ResultPair
castSame a (RFloat b) = RFloats (rToDouble a) b
castSame (RFloat a) b = RFloats a (rToDouble b)
castSame (RRatio a) (RRatio b) = RRatios a b
castSame (RInt a) (RRatio b) = RRatios (fromIntegral a) b
castSame (RInt a) (RInt b) = RInts a b
castSame (RRatio a) (RInt b) = RRatios a (fromIntegral b)
genericCombine :: (forall a. Num a => a -> a -> a) -> Result
-> Result -> Result
genericCombine f i j =
case castSame i j of
RInts a b -> RInt (f a b)
RFloats a b -> RFloat (f a b)
RRatios a b -> RRatio (f a b)
genericInner :: (forall a. Num a => a -> a) -> Result -> Result
genericInner f (RInt i) = RInt (f i)
genericInner f (RFloat d) = RFloat (f d)
genericInner f (RRatio r) = RRatio (f r)
simplify :: Expr.Expr -> Result
simplify (Expr.Plus e1 e2) =
genericCombine (+) (simplify e1) (simplify e2)
simplify (Expr.Negate e) = genericInner negate (simplify e)
simplify (Expr.Minus e1 e2) =
genericCombine (-) (simplify e1) (simplify e2)
simplify (Expr.Times e1 e2) =
genericCombine (*) (simplify e1) (simplify e2)
simplify (Expr.Div e1 e2) =
case castSame (simplify e1) (simplify e2) of
RInts a b -> RRatio (a Data.Ratio.% b)
RRatios a b -> RRatio (a / b)
RFloats a b -> RFloat (a / b)
simplify (Expr.Pow e1 e2) =
case (simplify e1, simplify e2) of
(RInt a, RInt b)
| b >= 0 -> RInt (a ^ b)
(RRatio a, RInt b) -> RRatio (a ^^ b)
(RFloat a, RInt b) -> RFloat (a ^^ b)
(a, b) -> RFloat (rToDouble a ** rToDouble b)
simplify (Expr.EInt i) = RInt i
simplify (Expr.EFloat d) = RFloat d
simplify Expr.E = RFloat (exp 1)
simplify Expr.Pi = RFloat pi
simplify (Expr.Log e) = RFloat . log . rToDouble $ simplify e
simplify (Expr.Sin e) = RFloat . sin . rToDouble $ simplify e
simplify (Expr.Cos e) = RFloat . cos . rToDouble $ simplify e
simplify (Expr.Sqrt e) = RFloat . sqrt . rToDouble $ simplify e
calculate :: String -> Maybe String
calculate s = case Expr.parseE s of
Left _ -> Nothing
Right e -> Just . show $ simplify e
|
