-----------------------------------------------------------------------------

-- |

-- 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 :: Float -> Bool
nearZero Float
a = forall a. Num a => a -> a
abs Float
a forall a. Ord a => a -> a -> Bool
<= Float
1e-6

-- | @'abs' a '<=' 1e-12@

instance Epsilon Double where
  nearZero :: Double -> Bool
nearZero Double
a = forall a. Num a => a -> a
abs Double
a forall a. Ord a => a -> a -> Bool
<= Double
1e-12

-- | @'abs' a '<=' 1e-6@

instance Epsilon CFloat where
  nearZero :: CFloat -> Bool
nearZero CFloat
a = forall a. Num a => a -> a
abs CFloat
a forall a. Ord a => a -> a -> Bool
<= CFloat
1e-6

-- | @'abs' a '<=' 1e-12@

instance Epsilon CDouble where
  nearZero :: CDouble -> Bool
nearZero CDouble
a = forall a. Num a => a -> a
abs CDouble
a forall a. Ord a => a -> a -> Bool
<= CDouble
1e-12

instance (Epsilon a, RealFloat a) => Epsilon (Complex a) where
  nearZero :: Complex a -> Bool
nearZero = forall a. Epsilon a => a -> Bool
nearZero forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. RealFloat a => Complex a -> a
magnitude