module Basement.Numerical.Additive
( Additive(..)
) where
#include "MachDeps.h"
import Basement.Compat.Base
import Basement.Compat.C.Types
import Basement.Compat.Natural
import Basement.Numerical.Number
import qualified Prelude
import GHC.Types
import GHC.Prim
import GHC.Int
import GHC.Word
import Basement.Bounded
import Basement.Nat
import Basement.Types.Word128 (Word128)
import Basement.Types.Word256 (Word256)
import qualified Basement.Types.Word128 as Word128
import qualified Basement.Types.Word256 as Word256
#if WORD_SIZE_IN_BITS < 64
import GHC.IntWord64
#endif
class Additive a where
azero :: a
(+) :: a -> a -> a
scale :: IsNatural n => n -> a -> a
scale 0 _ = azero
scale 1 a = a
scale 2 a = a + a
scale n a = a + scale (pred n) a
infixl 6 +
instance Additive Integer where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive Int where
azero = 0
(I# a) + (I# b) = I# (a +# b)
scale = scaleNum
instance Additive Int8 where
azero = 0
(I8# a) + (I8# b) = I8# (narrow8Int# (a +# b))
scale = scaleNum
instance Additive Int16 where
azero = 0
(I16# a) + (I16# b) = I16# (narrow16Int# (a +# b))
scale = scaleNum
instance Additive Int32 where
azero = 0
(I32# a) + (I32# b) = I32# (narrow32Int# (a +# b))
scale = scaleNum
instance Additive Int64 where
azero = 0
#if WORD_SIZE_IN_BITS == 64
(I64# a) + (I64# b) = I64# (a +# b)
#else
(I64# a) + (I64# b) = I64# (a `plusInt64#` b)
#endif
scale = scaleNum
instance Additive Word where
azero = 0
(W# a) + (W# b) = W# (a `plusWord#` b)
scale = scaleNum
instance Additive Natural where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive Word8 where
azero = 0
(W8# a) + (W8# b) = W8# (narrow8Word# (a `plusWord#` b))
scale = scaleNum
instance Additive Word16 where
azero = 0
(W16# a) + (W16# b) = W16# (narrow16Word# (a `plusWord#` b))
scale = scaleNum
instance Additive Word32 where
azero = 0
(W32# a) + (W32# b) = W32# (narrow32Word# (a `plusWord#` b))
scale = scaleNum
instance Additive Word64 where
azero = 0
#if WORD_SIZE_IN_BITS == 64
(W64# a) + (W64# b) = W64# (a `plusWord#` b)
#else
(W64# a) + (W64# b) = W64# (int64ToWord64# (word64ToInt64# a `plusInt64#` word64ToInt64# b))
#endif
scale = scaleNum
instance Additive Word128 where
azero = 0
(+) = (Word128.+)
scale = scaleNum
instance Additive Word256 where
azero = 0
(+) = (Word256.+)
scale = scaleNum
instance Additive Prelude.Float where
azero = 0.0
(F# a) + (F# b) = F# (a `plusFloat#` b)
scale = scaleNum
instance Additive Prelude.Double where
azero = 0.0
(D# a) + (D# b) = D# (a +## b)
scale = scaleNum
instance (KnownNat n, NatWithinBound Word64 n) => Additive (Zn64 n) where
azero = zn64 0
(+) = (Prelude.+)
scale = scaleNum
instance KnownNat n => Additive (Zn n) where
azero = zn 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive CChar where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive CSChar where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive CUChar where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive CShort where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive CUShort where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive CInt where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive CUInt where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive CLong where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive CULong where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive CPtrdiff where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive CSize where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive CWchar where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive CSigAtomic where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive CLLong where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive CULLong where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive CIntPtr where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive CUIntPtr where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive CIntMax where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive CUIntMax where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive CClock where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive CTime where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive CUSeconds where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive CSUSeconds where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive COff where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive CFloat where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
instance Additive CDouble where
azero = 0
(+) = (Prelude.+)
scale = scaleNum
scaleNum :: (Prelude.Num a, IsNatural n) => n -> a -> a
scaleNum n a = (Prelude.fromIntegral $ toNatural n) Prelude.* a