content: -----------------------------------------------------------------------------
  -- |
  -- 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
  