    -----------------------------------------------------------------------------
    -- |
    -- Copyright   :  (C) 2012-2015 Edward Kmett
    -- License     :  BSD-style (see the file LICENSE)
    -- Maintainer  :  Edward Kmett <ekmett@gmail.com>
    -- Stability   :  provisional
    -- Portability :  portable
    --
    -- Testing for values "near" zero
    -----------------------------------------------------------------------------
    module Linear.Epsilon
      ( Epsilon(..)
      ) where
    import Data.Complex (Complex, magnitude)
    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

    instance (Epsilon a, RealFloat a) => Epsilon (Complex a) where
      nearZero = nearZero . magnitude