{-# 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
(Sign -> Sign -> Bool) -> (Sign -> Sign -> Bool) -> Eq Sign
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 = Integer -> Integer
forall a. Num a => a -> a
Prelude.abs
signum :: Integer -> Sign
signum = Ordering -> Sign
orderingToSign (Ordering -> Sign) -> (Integer -> Ordering) -> Integer -> Sign
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Integer -> Integer -> Ordering
forall a. Ord a => a -> a -> Ordering
compare Integer
0
instance Signed Int where
abs :: Int -> Int
abs = Int -> Int
forall a. Num a => a -> a
Prelude.abs
signum :: Int -> Sign
signum = Ordering -> Sign
orderingToSign (Ordering -> Sign) -> (Int -> Ordering) -> Int -> Sign
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Int -> Int -> Ordering
forall a. Ord a => a -> a -> Ordering
compare Int
0
instance Signed Int8 where
abs :: Int8 -> Int8
abs = Int8 -> Int8
forall a. Num a => a -> a
Prelude.abs
signum :: Int8 -> Sign
signum = Ordering -> Sign
orderingToSign (Ordering -> Sign) -> (Int8 -> Ordering) -> Int8 -> Sign
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Int8 -> Int8 -> Ordering
forall a. Ord a => a -> a -> Ordering
compare Int8
0
instance Signed Int16 where
abs :: Int16 -> Int16
abs = Int16 -> Int16
forall a. Num a => a -> a
Prelude.abs
signum :: Int16 -> Sign
signum = Ordering -> Sign
orderingToSign (Ordering -> Sign) -> (Int16 -> Ordering) -> Int16 -> Sign
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Int16 -> Int16 -> Ordering
forall a. Ord a => a -> a -> Ordering
compare Int16
0
instance Signed Int32 where
abs :: Int32 -> Int32
abs = Int32 -> Int32
forall a. Num a => a -> a
Prelude.abs
signum :: Int32 -> Sign
signum = Ordering -> Sign
orderingToSign (Ordering -> Sign) -> (Int32 -> Ordering) -> Int32 -> Sign
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Int32 -> Int32 -> Ordering
forall a. Ord a => a -> a -> Ordering
compare Int32
0
instance Signed Int64 where
abs :: Int64 -> Int64
abs = Int64 -> Int64
forall a. Num a => a -> a
Prelude.abs
signum :: Int64 -> Sign
signum = Ordering -> Sign
orderingToSign (Ordering -> Sign) -> (Int64 -> Ordering) -> Int64 -> Sign
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Int64 -> Int64 -> Ordering
forall a. Ord a => a -> a -> Ordering
compare Int64
0
instance Signed Float where
abs :: Float -> Float
abs = Float -> Float
forall a. Num a => a -> a
Prelude.abs
signum :: Float -> Sign
signum = Ordering -> Sign
orderingToSign (Ordering -> Sign) -> (Float -> Ordering) -> Float -> Sign
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Float -> Float -> Ordering
forall a. Ord a => a -> a -> Ordering
compare Float
0
instance Signed Double where
abs :: Double -> Double
abs = Double -> Double
forall a. Num a => a -> a
Prelude.abs
signum :: Double -> Sign
signum = Ordering -> Sign
orderingToSign (Ordering -> Sign) -> (Double -> Ordering) -> Double -> Sign
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Double -> Double -> Ordering
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 :: Rational -> n
roundUp = Integer -> n
forall a. Integral a => Integer -> a
fromInteger (Integer -> n) -> (Rational -> Integer) -> Rational -> n
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Rational -> Integer
forall a b. (RealFrac a, Integral b) => a -> b
Prelude.ceiling
roundDown :: Rational -> n
roundDown = Integer -> n
forall a. Integral a => Integer -> a
fromInteger (Integer -> n) -> (Rational -> Integer) -> Rational -> n
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Rational -> Integer
forall a b. (RealFrac a, Integral b) => a -> b
Prelude.floor
roundTruncate :: Rational -> n
roundTruncate = Integer -> n
forall a. Integral a => Integer -> a
fromInteger (Integer -> n) -> (Rational -> Integer) -> Rational -> n
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Rational -> Integer
forall a b. (RealFrac a, Integral b) => a -> b
Prelude.truncate
roundNearest :: Rational -> n
roundNearest = Integer -> n
forall a. Integral a => Integer -> a
fromInteger (Integer -> n) -> (Rational -> Integer) -> Rational -> n
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Rational -> Integer
forall a b. (RealFrac a, Integral b) => a -> b
Prelude.round
instance IntegralRounding Prelude.Double where
roundUp :: Double -> n
roundUp = Integer -> n
forall a. Integral a => Integer -> a
fromInteger (Integer -> n) -> (Double -> Integer) -> Double -> n
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Double -> Integer
forall a b. (RealFrac a, Integral b) => a -> b
Prelude.ceiling
roundDown :: Double -> n
roundDown = Integer -> n
forall a. Integral a => Integer -> a
fromInteger (Integer -> n) -> (Double -> Integer) -> Double -> n
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Double -> Integer
forall a b. (RealFrac a, Integral b) => a -> b
Prelude.floor
roundTruncate :: Double -> n
roundTruncate = Integer -> n
forall a. Integral a => Integer -> a
fromInteger (Integer -> n) -> (Double -> Integer) -> Double -> n
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Double -> Integer
forall a b. (RealFrac a, Integral b) => a -> b
Prelude.truncate
roundNearest :: Double -> n
roundNearest = Integer -> n
forall a. Integral a => Integer -> a
fromInteger (Integer -> n) -> (Double -> Integer) -> Double -> n
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Double -> Integer
forall a b. (RealFrac a, Integral b) => a -> b
Prelude.round
instance IntegralRounding Prelude.Float where
roundUp :: Float -> n
roundUp = Integer -> n
forall a. Integral a => Integer -> a
fromInteger (Integer -> n) -> (Float -> Integer) -> Float -> n
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Float -> Integer
forall a b. (RealFrac a, Integral b) => a -> b
Prelude.ceiling
roundDown :: Float -> n
roundDown = Integer -> n
forall a. Integral a => Integer -> a
fromInteger (Integer -> n) -> (Float -> Integer) -> Float -> n
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Float -> Integer
forall a b. (RealFrac a, Integral b) => a -> b
Prelude.floor
roundTruncate :: Float -> n
roundTruncate = Integer -> n
forall a. Integral a => Integer -> a
fromInteger (Integer -> n) -> (Float -> Integer) -> Float -> n
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Float -> Integer
forall a b. (RealFrac a, Integral b) => a -> b
Prelude.truncate
roundNearest :: Float -> n
roundNearest = Integer -> n
forall a. Integral a => Integer -> a
fromInteger (Integer -> n) -> (Float -> Integer) -> Float -> n
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Float -> Integer
forall a b. (RealFrac a, Integral b) => a -> b
Prelude.round