{-# 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
data Sign = SignNegative | SignZero | SignPositive
deriving (Sign -> Sign -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: Sign -> Sign -> Bool
$c/= :: Sign -> Sign -> Bool
== :: Sign -> Sign -> Bool
$c== :: Sign -> Sign -> Bool
Eq)
orderingToSign :: Ordering -> Sign
orderingToSign :: Ordering -> Sign
orderingToSign Ordering
EQ = Sign
SignZero
orderingToSign Ordering
GT = Sign
SignNegative
orderingToSign Ordering
LT = Sign
SignPositive
class Signed a where
{-# MINIMAL abs, signum #-}
abs :: a -> a
signum :: a -> Sign
instance Signed Integer where
abs :: Integer -> Integer
abs = forall a. Num a => a -> a
Prelude.abs
signum :: Integer -> Sign
signum = Ordering -> Sign
orderingToSign forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. forall a. Ord a => a -> a -> Ordering
compare Integer
0
instance Signed Int where
abs :: Int -> Int
abs = forall a. Num a => a -> a
Prelude.abs
signum :: Int -> Sign
signum = Ordering -> Sign
orderingToSign forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. forall a. Ord a => a -> a -> Ordering
compare Int
0
instance Signed Int8 where
abs :: Int8 -> Int8
abs = forall a. Num a => a -> a
Prelude.abs
signum :: Int8 -> Sign
signum = Ordering -> Sign
orderingToSign forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. forall a. Ord a => a -> a -> Ordering
compare Int8
0
instance Signed Int16 where
abs :: Int16 -> Int16
abs = forall a. Num a => a -> a
Prelude.abs
signum :: Int16 -> Sign
signum = Ordering -> Sign
orderingToSign forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. forall a. Ord a => a -> a -> Ordering
compare Int16
0
instance Signed Int32 where
abs :: Int32 -> Int32
abs = forall a. Num a => a -> a
Prelude.abs
signum :: Int32 -> Sign
signum = Ordering -> Sign
orderingToSign forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. forall a. Ord a => a -> a -> Ordering
compare Int32
0
instance Signed Int64 where
abs :: Int64 -> Int64
abs = forall a. Num a => a -> a
Prelude.abs
signum :: Int64 -> Sign
signum = Ordering -> Sign
orderingToSign forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. forall a. Ord a => a -> a -> Ordering
compare Int64
0
instance Signed Float where
abs :: Float -> Float
abs = forall a. Num a => a -> a
Prelude.abs
signum :: Float -> Sign
signum = Ordering -> Sign
orderingToSign forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. forall a. Ord a => a -> a -> Ordering
compare Float
0
instance Signed Double where
abs :: Double -> Double
abs = forall a. Num a => a -> a
Prelude.abs
signum :: Double -> Sign
signum = Ordering -> Sign
orderingToSign forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. forall a. Ord a => a -> a -> Ordering
compare Double
0
class IntegralRounding a where
roundUp :: Integral n => a -> n
roundDown :: Integral n => a -> n
roundTruncate :: Integral n => a -> n
roundNearest :: Integral n => a -> n
instance IntegralRounding Prelude.Rational where
roundUp :: forall n. Integral n => Rational -> n
roundUp = forall a. Integral a => Integer -> a
fromInteger forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. forall a b. (RealFrac a, Integral b) => a -> b
Prelude.ceiling
roundDown :: forall n. Integral n => Rational -> n
roundDown = forall a. Integral a => Integer -> a
fromInteger forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. forall a b. (RealFrac a, Integral b) => a -> b
Prelude.floor
roundTruncate :: forall n. Integral n => Rational -> n
roundTruncate = forall a. Integral a => Integer -> a
fromInteger forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. forall a b. (RealFrac a, Integral b) => a -> b
Prelude.truncate
roundNearest :: forall n. Integral n => Rational -> n
roundNearest = forall a. Integral a => Integer -> a
fromInteger forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. forall a b. (RealFrac a, Integral b) => a -> b
Prelude.round
instance IntegralRounding Prelude.Double where
roundUp :: forall n. Integral n => Double -> n
roundUp = forall a. Integral a => Integer -> a
fromInteger forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. forall a b. (RealFrac a, Integral b) => a -> b
Prelude.ceiling
roundDown :: forall n. Integral n => Double -> n
roundDown = forall a. Integral a => Integer -> a
fromInteger forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. forall a b. (RealFrac a, Integral b) => a -> b
Prelude.floor
roundTruncate :: forall n. Integral n => Double -> n
roundTruncate = forall a. Integral a => Integer -> a
fromInteger forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. forall a b. (RealFrac a, Integral b) => a -> b
Prelude.truncate
roundNearest :: forall n. Integral n => Double -> n
roundNearest = forall a. Integral a => Integer -> a
fromInteger forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. forall a b. (RealFrac a, Integral b) => a -> b
Prelude.round
instance IntegralRounding Prelude.Float where
roundUp :: forall n. Integral n => Float -> n
roundUp = forall a. Integral a => Integer -> a
fromInteger forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. forall a b. (RealFrac a, Integral b) => a -> b
Prelude.ceiling
roundDown :: forall n. Integral n => Float -> n
roundDown = forall a. Integral a => Integer -> a
fromInteger forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. forall a b. (RealFrac a, Integral b) => a -> b
Prelude.floor
roundTruncate :: forall n. Integral n => Float -> n
roundTruncate = forall a. Integral a => Integer -> a
fromInteger forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. forall a b. (RealFrac a, Integral b) => a -> b
Prelude.truncate
roundNearest :: forall n. Integral n => Float -> n
roundNearest = forall a. Integral a => Integer -> a
fromInteger forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. forall a b. (RealFrac a, Integral b) => a -> b
Prelude.round