From a619e63030316f5b16a799e1b9d43be66b77a322 Mon Sep 17 00:00:00 2001
From: Raymond Hogenson <rhogenson@posteo.net>
Date: Sun, 18 Nov 2018 00:33:43 -0500
Subject: Add rational numbers

Now calculations are done to arbitrary precision if possible.
---
 RealCalc.hs | 33 ++++++++++++++++++++++++++-------
 1 file changed, 26 insertions(+), 7 deletions(-)

(limited to 'RealCalc.hs')

diff --git a/RealCalc.hs b/RealCalc.hs
index ac8ecb5..d54cf84 100644
--- a/RealCalc.hs
+++ b/RealCalc.hs
@@ -22,27 +22,42 @@
 module RealCalc (calculate) where
 
 import qualified Expr
+import qualified Data.Ratio
 
-data Result = RInt Integer | RFloat Double
+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 (i, j) of
-    (RInt a, RInt b) -> RInt (f a b)
-    _ -> RFloat (f (rToDouble i) (rToDouble 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) =
@@ -53,13 +68,17 @@ simplify (Expr.Minus e1 e2) =
 simplify (Expr.Times e1 e2) =
   genericCombine (*) (simplify e1) (simplify e2)
 simplify (Expr.Div e1 e2) =
-  RFloat (rToDouble (simplify e1) / rToDouble (simplify 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)
-    (a, RInt b) -> RFloat (rToDouble a ^^ b)
-    (a, RFloat b) -> RFloat (rToDouble 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)
-- 
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