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https://github.com/logos-storage/outsourcing-Reed-Solomon.git
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78 lines
2.2 KiB
Haskell
78 lines
2.2 KiB
Haskell
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{-# LANGUAGE TypeFamilies #-}
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module Field.Class where
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--------------------------------------------------------------------------------
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import Data.Kind
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import Data.Proxy
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import System.Random
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import qualified Field.Goldilocks as Goldi
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import qualified Field.Goldilocks.Extension as GoldiExt
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--------------------------------------------------------------------------------
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class (Show a, Eq a, Num a, Fractional a) => Field a where
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fieldSize :: Proxy a -> Integer
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zero :: a
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one :: a
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isZero :: a -> Bool
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isOne :: a -> Bool
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square :: a -> a
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power :: a -> Integer -> a
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power_ :: a -> Int -> a
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rndIO :: IO a
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inverse :: Field a => a -> a
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inverse = recip
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-- | Quadratic extensions
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class (Field (BaseField ext), Field ext) => QuadraticExt ext where
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type BaseField ext :: Type
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inject :: BaseField ext -> ext
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project :: ext -> Maybe (BaseField ext)
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scale :: BaseField ext -> ext -> ext
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quadraticPack :: (BaseField ext, BaseField ext) -> ext
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quadraticUnpack :: ext -> (BaseField ext, BaseField ext)
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--------------------------------------------------------------------------------
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instance Field Goldi.F where
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fieldSize _ = Goldi.goldilocksPrime
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zero = Goldi.zero
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one = Goldi.one
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isZero = Goldi.isZero
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isOne = Goldi.isOne
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square = Goldi.sqr
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power = Goldi.pow
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power_ = Goldi.pow_
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rndIO = randomIO
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--------------------------------------------------------------------------------
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instance Field GoldiExt.FExt where
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fieldSize _ = (Goldi.goldilocksPrime ^ 2)
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zero = GoldiExt.zero
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one = GoldiExt.one
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isZero = GoldiExt.isZero
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isOne = GoldiExt.isOne
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square = GoldiExt.sqr
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power = GoldiExt.pow
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power_ = GoldiExt.pow_
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rndIO = randomIO
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--------------------------------------------------------------------------------
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instance QuadraticExt GoldiExt.FExt where
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type BaseField GoldiExt.FExt = Goldi.F
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inject = GoldiExt.inj
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project = GoldiExt.proj
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scale = GoldiExt.scl
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quadraticPack = GoldiExt.pack
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quadraticUnpack = GoldiExt.unpack
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--------------------------------------------------------------------------------
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