module Field.Class where

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import Data.Proxy

import System.Random

import qualified Field.Goldilocks           as Goldi   
import qualified Field.Goldilocks.Extension as GoldiExt

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class (Show a, Eq a, Num a, Fractional a) => Field a where
  fieldSize :: Proxy a -> Integer
  zero      :: a
  one       :: a
  isZero    :: a -> Bool
  isOne     :: a -> Bool
  square    :: a -> a
  power     :: a -> Integer -> a
  power_    :: a -> Int     -> a
  rndIO     :: IO a

inverse :: Field a => a -> a
inverse = recip

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instance Field Goldi.F where
  fieldSize _ = Goldi.goldilocksPrime
  zero        = Goldi.zero
  one         = Goldi.one
  isZero      = Goldi.isZero
  isOne       = Goldi.isOne
  square      = Goldi.sqr
  power       = Goldi.pow
  power_      = Goldi.pow_
  rndIO       = randomIO

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instance Field GoldiExt.FExt where
  fieldSize _ = (Goldi.goldilocksPrime ^ 2)
  zero        = GoldiExt.zero
  one         = GoldiExt.one
  isZero      = GoldiExt.isZero
  isOne       = GoldiExt.isOne
  square      = GoldiExt.sqr
  power       = GoldiExt.pow
  power_      = GoldiExt.pow_
  rndIO       = randomIO

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