{-# OPTIONS -fglasgow-exts #-}
module Fuzzy(Fuzzy, Teps5, Teps10, Teps15, Tsub1, Fuzz) where

newtype Fuzzy d a = F a deriving (Num, Fractional, Floating, Real, RealFrac, Show, Read)

class Fuzz d a {- | d -> a -} where
    eps :: d -> a

data Teps5
data Teps10
data Teps15
data Tsub1 a

instance (Fractional a, Fuzz d a) => Fuzz (Tsub1 d) a where
    eps x = eps x / 10

instance (Fractional a) => Fuzz Teps5 a where
    eps _ = 1e-5

instance (Fractional a) => Fuzz Teps10 a where
    eps _ = 1e-5

instance (Fractional a) => Fuzz Teps15 a where
    eps _ = 1e-15

fuzzyEq :: (Fuzz d a, Ord a, Num a) => Fuzzy d a -> Fuzzy d a -> Bool
fuzzyEq fx@(F x) (F y) = abs (x - y) < eps (dOf fx)
  where dOf :: Fuzzy d a -> d
        dOf _ = undefined

instance (Fuzz d a, Ord a, Num a) => Eq (Fuzzy d a) where
    x == y  =  fuzzyEq x y

{-
fuzzyCmp :: (Fuzz d, Ord a) => Fuzzy d a -> Fuzzy d a -> Ordering
fuzzyCmp fx@(F x) (F y) = abs (x - y) `compare` eps (dOf fx)
  where dOf :: Fuzzy d a -> d
        dOf _ = undefined
-}
{-
instance (Fuzz d, Ord a) => Ord (Fuzzy d a) where
    x `compare` y  = x `fuzzyCmp` y
-}