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|
-- |
-- Module : Foundation.Numerical
-- License : BSD-style
-- Maintainer : Vincent Hanquez <vincent@snarc.org>
-- Stability : experimental
-- Portability : portable
--
-- Compared to the Haskell hierarchy of number classes
-- this provide a more flexible approach that is closer to the
-- mathematical foundation (group, field, etc)
--
-- This try to only provide one feature per class, at the expense of
-- the number of classes.
--
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE TypeSynonymInstances #-}
module Foundation.Numerical
( IsIntegral(..)
, IsNatural(..)
, Signed(..)
, Additive(..)
, Subtractive(..)
, Multiplicative(..)
, IDivisible(..)
, Divisible(..)
, Sign(..)
, recip
, IntegralRounding(..)
, FloatingPoint(..)
) where
import Basement.Compat.Base
import Basement.Numerical.Number
import Basement.Numerical.Additive
import Basement.Numerical.Subtractive
import Basement.Numerical.Multiplicative
import Foundation.Numerical.Floating
import qualified Prelude
-- | Sign of a signed number
data Sign = SignNegative | SignZero | SignPositive
deriving (Eq)
orderingToSign :: Ordering -> Sign
orderingToSign EQ = SignZero
orderingToSign GT = SignNegative
orderingToSign LT = SignPositive
-- | types that have sign and can be made absolute
class Signed a where
{-# MINIMAL abs, signum #-}
abs :: a -> a
signum :: a -> Sign
instance Signed Integer where
abs = Prelude.abs
signum = orderingToSign . compare 0
instance Signed Int where
abs = Prelude.abs
signum = orderingToSign . compare 0
instance Signed Int8 where
abs = Prelude.abs
signum = orderingToSign . compare 0
instance Signed Int16 where
abs = Prelude.abs
signum = orderingToSign . compare 0
instance Signed Int32 where
abs = Prelude.abs
signum = orderingToSign . compare 0
instance Signed Int64 where
abs = Prelude.abs
signum = orderingToSign . compare 0
instance Signed Float where
abs = Prelude.abs
signum = orderingToSign . compare 0
instance Signed Double where
abs = Prelude.abs
signum = orderingToSign . compare 0
class IntegralRounding a where
-- | Round up, to the next integral.
--
-- Also known as 'ceiling'
roundUp :: Integral n => a -> n
-- | Round down, to the previous integral
--
-- Also known as 'floor'
roundDown :: Integral n => a -> n
-- | Truncate to the closest integral to the fractional number
-- closer to 0.
--
-- This is equivalent to roundUp for negative Number
-- and roundDown for positive Number
roundTruncate :: Integral n => a -> n
-- | Round to the nearest integral
--
-- > roundNearest 3.6
-- 4
-- > roundNearest 3.4
-- 3
roundNearest :: Integral n => a -> n
instance IntegralRounding Prelude.Rational where
roundUp = fromInteger . Prelude.ceiling
roundDown = fromInteger . Prelude.floor
roundTruncate = fromInteger . Prelude.truncate
roundNearest = fromInteger . Prelude.round
instance IntegralRounding Prelude.Double where
roundUp = fromInteger . Prelude.ceiling
roundDown = fromInteger . Prelude.floor
roundTruncate = fromInteger . Prelude.truncate
roundNearest = fromInteger . Prelude.round
instance IntegralRounding Prelude.Float where
roundUp = fromInteger . Prelude.ceiling
roundDown = fromInteger . Prelude.floor
roundTruncate = fromInteger . Prelude.truncate
roundNearest = fromInteger . Prelude.round
|
