{-# OPTIONS_GHC -Wall #-}

module Casadi.Overloading
       ( Fmod(..)
       , ArcTan2(..)
       , SymOrd(..)
       , Erf(..)
       ) where

import Data.Fixed ( mod' )

-- | doesn't require Real, used for overloading symbolics
class Fmod a where
  fmod :: a -> a -> a

instance Fmod Double where fmod = mod'
instance Fmod Float where fmod = mod'

-- | doesn't require RealFloat, used for overloading symbolics
class ArcTan2 a where
  arctan2 :: a -> a -> a

instance ArcTan2 Double where arctan2 = atan2
instance ArcTan2 Float where arctan2 = atan2

-- | Ord, but returns a 1 or a 0 instead of True or False
class SymOrd a where
  leq :: a -> a -> a
  geq :: a -> a -> a
  eq :: a -> a -> a

instance SymOrd Double where
  x `leq` y = if x <= y then 1 else 0
  x `geq` y = if x >= y then 1 else 0
  x  `eq` y = if x == y then 1 else 0
instance SymOrd Float where
  x `leq` y = if x <= y then 1 else 0
  x `geq` y = if x >= y then 1 else 0
  x  `eq` y = if x == y then 1 else 0

-- | error function
class Erf a where
  erf :: a -> a
  erfinv :: a -> a