wta: Don't use floats for probability

This switches from floats to a sort of arbitrary precision base10 floating point
implementation where we can easily generate uniform random numbers.

The problem with floats is that they aren't distributed equally across the whole
range and thus a random number in [0, 1) is not uniform.

copar.cabal

@@ -289,6 +289,7 @@ executable random-wta
   other-modules:       Types
                      , Generator
                      , Output
+                     , Probability
   default-language:    Haskell2010
   default-extensions:  OverloadedStrings
                      , LambdaCase

src/random-wta/Generator.hs

@@ -13,10 +13,11 @@ import           Data.Maybe
 import           Data.Foldable
 
 import           Types hiding (spec)
+import           Probability
 
 data GeneratorConfig m = GeneratorConfig
    { spec :: WTASpec m
-   , zeroFreq :: Double
+   , zeroFreq :: Probability
    }
 
 type Generator m = ReaderT (GeneratorConfig m) IO
@@ -42,9 +43,7 @@ aritySummand arity = do
 
 decideZero :: Generator m Bool
 decideZero = do
-  freq <- asks zeroFreq
-  randomValue :: Double <- liftIO (randomRIO (0.0, 1.0))
-  return $ randomValue < freq
+  asks zeroFreq >>= liftIO . decide
 
 -- Generates Nothing, when it decides that a zero value would be in order
 genTransition :: Int -> Int -> [State] -> Generator m (Maybe (Transition m))

src/random-wta/Main.hs

@@ -22,6 +22,7 @@ import           System.IO
 import           Types
 import           Generator
 import           Output
+import           Probability
 
 data SomeMonoid = forall m. SomeMonoid (MonoidType m)
 
@@ -29,7 +30,7 @@ data Opts = Opts
   { optMonoid :: SomeMonoid
   , optStates :: Int
   , optSymbols :: SymbolSpec
-  , optZeroFrequency :: Double
+  , optZeroFrequency :: Probability
   , optRandomState :: Maybe StdGen
   }
 
@@ -82,10 +83,10 @@ parseOpts =
                "Comma separated list of symbols per arity. E.g. 2,0,1 means two symbols with arity 0, non with arity 1 and one with arity two"
           )
     <*> Options.option
-          Options.auto
+          (Options.eitherReader readProbability)
           (  Options.long "zero-frequency"
           <> Options.showDefault
-          <> Options.value 0.7
+          <> Options.value (Probability 7 1)
           <> Options.metavar "FREQ"
           <> Options.help
                "Frequency of edges with zero weight as number between 0 and 1."

src/random-wta/Probability.hs

+{-# LANGUAGE GeneralizedNewtypeDeriving #-}
+
+module Probability (Probability(..), readProbability, decide) where
+
+import           System.Random
+import           Text.Printf
+
+data Probability = Probability Integer Int
+
+readProbability :: String -> Either String Probability
+readProbability input = case input of
+  "0" -> Right (Probability 0 0)
+  ('0':'.':rest) -> case reads rest of
+    [(digits, "")] -> Right (Probability digits (length rest))
+    _ -> failure
+  "1" -> Right (Probability 1 0)
+  ('1':'.':rest)
+    | all (=='0') rest -> Right (Probability 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
+  randomNumber <- randomRIO (0, (10^exp)-1)
+  return $ randomNumber < digits