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{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE TypeSynonymInstances #-}
{-# LANGUAGE DefaultSignatures #-}
module Basement.Numerical.Multiplicative
( Multiplicative(..)
, IDivisible(..)
, Divisible(..)
, recip
) where
import Basement.Compat.Base
import Basement.Compat.C.Types
import Basement.Compat.Natural
import Basement.Compat.NumLiteral
import Basement.Numerical.Number
import Basement.Numerical.Additive
import Basement.Types.Word128 (Word128)
import Basement.Types.Word256 (Word256)
import qualified Basement.Types.Word128 as Word128
import qualified Basement.Types.Word256 as Word256
import qualified Prelude
-- | Represent class of things that can be multiplied together
--
-- > x * midentity = x
-- > midentity * x = x
class Multiplicative a where
{-# MINIMAL midentity, (*) #-}
-- | Identity element over multiplication
midentity :: a
-- | Multiplication of 2 elements that result in another element
(*) :: a -> a -> a
-- | Raise to power, repeated multiplication
-- e.g.
-- > a ^ 2 = a * a
-- > a ^ 10 = (a ^ 5) * (a ^ 5) ..
--(^) :: (IsNatural n) => a -> n -> a
(^) :: (IsNatural n, Enum n, IDivisible n) => a -> n -> a
(^) = power
-- | Represent types that supports an euclidian division
--
-- > (x ‘div‘ y) * y + (x ‘mod‘ y) == x
class (Additive a, Multiplicative a) => IDivisible a where
{-# MINIMAL (div, mod) | divMod #-}
div :: a -> a -> a
div a b = fst $ divMod a b
mod :: a -> a -> a
mod a b = snd $ divMod a b
divMod :: a -> a -> (a, a)
divMod a b = (div a b, mod a b)
-- | Support for division between same types
--
-- This is likely to change to represent specific mathematic divisions
class Multiplicative a => Divisible a where
{-# MINIMAL (/) #-}
(/) :: a -> a -> a
infixl 7 *, /
infixr 8 ^
instance Multiplicative Integer where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative Int where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative Int8 where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative Int16 where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative Int32 where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative Int64 where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative Natural where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative Word where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative Word8 where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative Word16 where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative Word32 where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative Word64 where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative Word128 where
midentity = 1
(*) = (Word128.*)
instance Multiplicative Word256 where
midentity = 1
(*) = (Word256.*)
instance Multiplicative Prelude.Float where
midentity = 1.0
(*) = (Prelude.*)
instance Multiplicative Prelude.Double where
midentity = 1.0
(*) = (Prelude.*)
instance Multiplicative Prelude.Rational where
midentity = 1.0
(*) = (Prelude.*)
instance Multiplicative CChar where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative CSChar where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative CUChar where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative CShort where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative CUShort where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative CInt where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative CUInt where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative CLong where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative CULong where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative CPtrdiff where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative CSize where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative CWchar where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative CSigAtomic where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative CLLong where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative CULLong where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative CIntPtr where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative CUIntPtr where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative CIntMax where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative CUIntMax where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative CClock where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative CTime where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative CUSeconds where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative CSUSeconds where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative COff where
midentity = 1
(*) = (Prelude.*)
instance Multiplicative CFloat where
midentity = 1.0
(*) = (Prelude.*)
instance Multiplicative CDouble where
midentity = 1.0
(*) = (Prelude.*)
instance IDivisible Integer where
div = Prelude.div
mod = Prelude.mod
instance IDivisible Int where
div = Prelude.div
mod = Prelude.mod
instance IDivisible Int8 where
div = Prelude.div
mod = Prelude.mod
instance IDivisible Int16 where
div = Prelude.div
mod = Prelude.mod
instance IDivisible Int32 where
div = Prelude.div
mod = Prelude.mod
instance IDivisible Int64 where
div = Prelude.div
mod = Prelude.mod
instance IDivisible Natural where
div = Prelude.quot
mod = Prelude.rem
instance IDivisible Word where
div = Prelude.quot
mod = Prelude.rem
instance IDivisible Word8 where
div = Prelude.quot
mod = Prelude.rem
instance IDivisible Word16 where
div = Prelude.quot
mod = Prelude.rem
instance IDivisible Word32 where
div = Prelude.quot
mod = Prelude.rem
instance IDivisible Word64 where
div = Prelude.quot
mod = Prelude.rem
instance IDivisible Word128 where
div = Word128.quot
mod = Word128.rem
instance IDivisible Word256 where
div = Word256.quot
mod = Word256.rem
instance IDivisible CChar where
div = Prelude.quot
mod = Prelude.rem
instance IDivisible CSChar where
div = Prelude.quot
mod = Prelude.rem
instance IDivisible CUChar where
div = Prelude.quot
mod = Prelude.rem
instance IDivisible CShort where
div = Prelude.quot
mod = Prelude.rem
instance IDivisible CUShort where
div = Prelude.quot
mod = Prelude.rem
instance IDivisible CInt where
div = Prelude.quot
mod = Prelude.rem
instance IDivisible CUInt where
div = Prelude.quot
mod = Prelude.rem
instance IDivisible CLong where
div = Prelude.quot
mod = Prelude.rem
instance IDivisible CULong where
div = Prelude.quot
mod = Prelude.rem
instance IDivisible CPtrdiff where
div = Prelude.quot
mod = Prelude.rem
instance IDivisible CSize where
div = Prelude.quot
mod = Prelude.rem
instance IDivisible CWchar where
div = Prelude.quot
mod = Prelude.rem
instance IDivisible CSigAtomic where
div = Prelude.quot
mod = Prelude.rem
instance IDivisible CLLong where
div = Prelude.quot
mod = Prelude.rem
instance IDivisible CULLong where
div = Prelude.quot
mod = Prelude.rem
instance IDivisible CIntPtr where
div = Prelude.quot
mod = Prelude.rem
instance IDivisible CUIntPtr where
div = Prelude.quot
mod = Prelude.rem
instance IDivisible CIntMax where
div = Prelude.quot
mod = Prelude.rem
instance IDivisible CUIntMax where
div = Prelude.quot
mod = Prelude.rem
instance Divisible Prelude.Rational where
(/) = (Prelude./)
instance Divisible Float where
(/) = (Prelude./)
instance Divisible Double where
(/) = (Prelude./)
instance Divisible CFloat where
(/) = (Prelude./)
instance Divisible CDouble where
(/) = (Prelude./)
recip :: Divisible a => a -> a
recip x = midentity / x
power :: (Enum n, IsNatural n, IDivisible n, Multiplicative a) => a -> n -> a
power a n
| n == 0 = midentity
| otherwise = squaring midentity a n
where
squaring y x i
| i == 0 = y
| i == 1 = x * y
| even i = squaring y (x*x) (i`div`2)
| otherwise = squaring (x*y) (x*x) (pred i`div` 2)
even :: (IDivisible n, IsIntegral n) => n -> Bool
even n = (n `mod` 2) == 0
|
