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bundled/Basement/Numerical/Multiplicative.hs
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331
bundled/Basement/Numerical/Multiplicative.hs
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{-# LANGUAGE BangPatterns #-}
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{-# LANGUAGE DeriveDataTypeable #-}
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{-# LANGUAGE TypeFamilies #-}
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{-# LANGUAGE RebindableSyntax #-}
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{-# LANGUAGE NoImplicitPrelude #-}
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{-# LANGUAGE FlexibleInstances #-}
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{-# LANGUAGE TypeSynonymInstances #-}
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{-# LANGUAGE DefaultSignatures #-}
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module Basement.Numerical.Multiplicative
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( Multiplicative(..)
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, IDivisible(..)
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, Divisible(..)
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, recip
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) where
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import Basement.Compat.Base
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import Basement.Compat.C.Types
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import Basement.Compat.Natural
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import Basement.Compat.NumLiteral
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import Basement.Numerical.Number
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import Basement.Numerical.Additive
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import Basement.Types.Word128 (Word128)
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import Basement.Types.Word256 (Word256)
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import qualified Basement.Types.Word128 as Word128
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import qualified Basement.Types.Word256 as Word256
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import qualified Prelude
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-- | Represent class of things that can be multiplied together
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--
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-- > x * midentity = x
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-- > midentity * x = x
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class Multiplicative a where
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{-# MINIMAL midentity, (*) #-}
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-- | Identity element over multiplication
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midentity :: a
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-- | Multiplication of 2 elements that result in another element
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(*) :: a -> a -> a
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-- | Raise to power, repeated multiplication
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-- e.g.
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-- > a ^ 2 = a * a
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-- > a ^ 10 = (a ^ 5) * (a ^ 5) ..
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--(^) :: (IsNatural n) => a -> n -> a
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(^) :: (IsNatural n, Enum n, IDivisible n) => a -> n -> a
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(^) = power
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-- | Represent types that supports an euclidian division
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--
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-- > (x ‘div‘ y) * y + (x ‘mod‘ y) == x
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class (Additive a, Multiplicative a) => IDivisible a where
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{-# MINIMAL (div, mod) | divMod #-}
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div :: a -> a -> a
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div a b = fst $ divMod a b
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mod :: a -> a -> a
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mod a b = snd $ divMod a b
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divMod :: a -> a -> (a, a)
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divMod a b = (div a b, mod a b)
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-- | Support for division between same types
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--
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-- This is likely to change to represent specific mathematic divisions
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class Multiplicative a => Divisible a where
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{-# MINIMAL (/) #-}
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(/) :: a -> a -> a
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infixl 7 *, /
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infixr 8 ^
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instance Multiplicative Integer where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative Int where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative Int8 where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative Int16 where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative Int32 where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative Int64 where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative Natural where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative Word where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative Word8 where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative Word16 where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative Word32 where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative Word64 where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative Word128 where
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midentity = 1
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(*) = (Word128.*)
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instance Multiplicative Word256 where
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midentity = 1
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(*) = (Word256.*)
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instance Multiplicative Prelude.Float where
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midentity = 1.0
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(*) = (Prelude.*)
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instance Multiplicative Prelude.Double where
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midentity = 1.0
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(*) = (Prelude.*)
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instance Multiplicative Prelude.Rational where
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midentity = 1.0
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(*) = (Prelude.*)
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instance Multiplicative CChar where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative CSChar where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative CUChar where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative CShort where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative CUShort where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative CInt where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative CUInt where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative CLong where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative CULong where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative CPtrdiff where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative CSize where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative CWchar where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative CSigAtomic where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative CLLong where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative CULLong where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative CIntPtr where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative CUIntPtr where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative CIntMax where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative CUIntMax where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative CClock where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative CTime where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative CUSeconds where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative CSUSeconds where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative COff where
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midentity = 1
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(*) = (Prelude.*)
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instance Multiplicative CFloat where
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midentity = 1.0
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(*) = (Prelude.*)
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instance Multiplicative CDouble where
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midentity = 1.0
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(*) = (Prelude.*)
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instance IDivisible Integer where
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div = Prelude.div
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mod = Prelude.mod
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instance IDivisible Int where
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div = Prelude.div
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mod = Prelude.mod
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instance IDivisible Int8 where
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div = Prelude.div
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mod = Prelude.mod
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instance IDivisible Int16 where
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div = Prelude.div
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mod = Prelude.mod
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instance IDivisible Int32 where
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div = Prelude.div
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mod = Prelude.mod
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instance IDivisible Int64 where
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div = Prelude.div
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mod = Prelude.mod
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instance IDivisible Natural where
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div = Prelude.quot
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mod = Prelude.rem
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instance IDivisible Word where
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div = Prelude.quot
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mod = Prelude.rem
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instance IDivisible Word8 where
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div = Prelude.quot
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mod = Prelude.rem
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instance IDivisible Word16 where
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div = Prelude.quot
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mod = Prelude.rem
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instance IDivisible Word32 where
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div = Prelude.quot
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mod = Prelude.rem
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instance IDivisible Word64 where
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div = Prelude.quot
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mod = Prelude.rem
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instance IDivisible Word128 where
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div = Word128.quot
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mod = Word128.rem
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instance IDivisible Word256 where
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div = Word256.quot
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mod = Word256.rem
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instance IDivisible CChar where
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div = Prelude.quot
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mod = Prelude.rem
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instance IDivisible CSChar where
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div = Prelude.quot
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mod = Prelude.rem
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instance IDivisible CUChar where
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div = Prelude.quot
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mod = Prelude.rem
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instance IDivisible CShort where
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div = Prelude.quot
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mod = Prelude.rem
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instance IDivisible CUShort where
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div = Prelude.quot
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mod = Prelude.rem
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instance IDivisible CInt where
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div = Prelude.quot
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mod = Prelude.rem
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instance IDivisible CUInt where
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div = Prelude.quot
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mod = Prelude.rem
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instance IDivisible CLong where
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div = Prelude.quot
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mod = Prelude.rem
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instance IDivisible CULong where
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div = Prelude.quot
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mod = Prelude.rem
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instance IDivisible CPtrdiff where
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div = Prelude.quot
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mod = Prelude.rem
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instance IDivisible CSize where
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div = Prelude.quot
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mod = Prelude.rem
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instance IDivisible CWchar where
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div = Prelude.quot
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mod = Prelude.rem
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instance IDivisible CSigAtomic where
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div = Prelude.quot
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mod = Prelude.rem
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instance IDivisible CLLong where
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div = Prelude.quot
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mod = Prelude.rem
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instance IDivisible CULLong where
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div = Prelude.quot
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mod = Prelude.rem
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instance IDivisible CIntPtr where
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div = Prelude.quot
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mod = Prelude.rem
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instance IDivisible CUIntPtr where
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div = Prelude.quot
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mod = Prelude.rem
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instance IDivisible CIntMax where
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div = Prelude.quot
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mod = Prelude.rem
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instance IDivisible CUIntMax where
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div = Prelude.quot
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mod = Prelude.rem
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instance Divisible Prelude.Rational where
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(/) = (Prelude./)
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instance Divisible Float where
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(/) = (Prelude./)
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instance Divisible Double where
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(/) = (Prelude./)
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instance Divisible CFloat where
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(/) = (Prelude./)
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instance Divisible CDouble where
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(/) = (Prelude./)
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recip :: Divisible a => a -> a
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recip x = midentity / x
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power :: (Enum n, IsNatural n, IDivisible n, Multiplicative a) => a -> n -> a
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power a n
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| n == 0 = midentity
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| otherwise = squaring midentity a n
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where
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squaring y x i
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| i == 0 = y
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| i == 1 = x * y
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| even i = squaring y (x*x) (i`div`2)
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| otherwise = squaring (x*y) (x*x) (pred i`div` 2)
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even :: (IDivisible n, IsIntegral n) => n -> Bool
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even n = (n `mod` 2) == 0
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