wta: Implement Probability in terms of Data.Scientific

This already does all we need, so instead of duplicating the whole
implementation, just use it.

copar.cabal

@@ -302,4 +302,5 @@ executable random-wta
                      , text
                      , random >= 1.1 && <1.2
                      , mtl >= 2.2 && <2.3
-                     , megaparsec >= 7
+                     , megaparsec >= 7 && <8
+                     , scientific >= 0.3 && <0.4

src/random-wta/Probability.hs

+{-# LANGUAGE DerivingStrategies #-}
 {-# LANGUAGE GeneralizedNewtypeDeriving #-}
 
 module Probability (Probability(..), readProbability, decide) where
 
 import           System.Random
-import           Text.Printf
+import           Data.Scientific
 
-data Probability = Probability Integer Int
+newtype Probability = Probability Scientific
+  deriving newtype (Show)
 
 readProbability :: String -> Either String Probability
-readProbability input = case input of
-  "0" -> Right (Probability 0 0)
+readProbability input = Probability <$> case input of
+  "0" -> Right (scientific 0 0)
   ('0':'.':rest) -> case reads rest of
-    [(digits, "")] -> Right (Probability digits (length rest))
+    [(digits, "")] -> Right (scientific digits (negate (length rest)))
     _ -> failure
-  "1" -> Right (Probability 1 0)
+  "1" -> Right (scientific 1 0)
   ('1':'.':rest)
-    | all (=='0') rest -> Right (Probability 1 0)
+    | all (=='0') rest -> Right (scientific 1 0)
     | otherwise -> failure
   _ -> failure
 
   where failure = Left "Could not parse probability"
 
-instance Show Probability where
-  show (Probability digits 0) = show digits
-  show (Probability digits exp) = "0." ++ printf "%0*d" exp digits
-
 decide :: Probability -> IO Bool
-decide (Probability digits exp) = do
+decide (Probability science) = do
+  let digits = coefficient science
+  let exp  = negate (base10Exponent science)
   randomNumber <- randomRIO (0, (10^exp)-1)
   return $ randomNumber < digits