Epsilon.hs

module Math.Linear.Epsilon
  ( Epsilon(..)
  ) where
import Foreign.C.Types (CFloat, CDouble)

-- | Provides a fairly subjective test to see if a quantity is near zero.
--
-- >>> nearZero (1e-11 :: Double)
-- False
--
-- >>> nearZero (1e-17 :: Double)
-- True
--
-- >>> nearZero (1e-5 :: Float)
-- False
--
-- >>> nearZero (1e-7 :: Float)
-- True
class Num a => Epsilon a where
    -- | Determine if a quantity is near zero.
	nearZero :: a -> Bool

-- | @'abs' a '<=' 1e-6@
instance Epsilon Float where
	nearZero a = abs a <= 1e-6

-- | @'abs' a '<=' 1e-12@
instance Epsilon Double where
	nearZero a = abs a <= 1e-12

-- | @'abs' a '<=' 1e-6@
instance Epsilon CFloat where
	nearZero a = abs a <= 1e-6

-- | @'abs' a '<=' 1e-12@
instance Epsilon CDouble where
	nearZero a = abs a <= 1e-12