Safe Haskell	None
Language	Haskell2010

NumHask.Algebra.Integral

Description

Integral classes

Synopsis

class Semiring a => Integral a where
class ToInteger a where
class FromInteger a where
fromIntegral :: (ToInteger a, FromInteger b) => a -> b
even :: (Eq a, Integral a) => a -> Bool
odd :: (Eq a, Integral a) => a -> Bool
(^) :: (Ord b, Integral b, Multiplicative a) => a -> b -> a
(^^) :: MultiplicativeGroup a => a -> Integer -> a

Documentation

class Semiring a => Integral a where #

Integral laws

b == zero || b * (a `div` b) + (a `mod` b) == a

Minimal complete definition

divMod, quotRem

Methods

div :: a -> a -> a infixl 7 #

mod :: a -> a -> a infixl 7 #

divMod :: a -> a -> (a, a) #

quot :: a -> a -> a #

rem :: a -> a -> a #

quotRem :: a -> a -> (a, a) #

Instances

Integral Int #
Instance details Defined in NumHask.Algebra.Integral Methods div :: Int -> Int -> Int # mod :: Int -> Int -> Int # divMod :: Int -> Int -> (Int, Int) # quot :: Int -> Int -> Int # rem :: Int -> Int -> Int # quotRem :: Int -> Int -> (Int, Int) #
Integral Int8 #
Instance details Defined in NumHask.Algebra.Integral Methods div :: Int8 -> Int8 -> Int8 # mod :: Int8 -> Int8 -> Int8 # divMod :: Int8 -> Int8 -> (Int8, Int8) # quot :: Int8 -> Int8 -> Int8 # rem :: Int8 -> Int8 -> Int8 # quotRem :: Int8 -> Int8 -> (Int8, Int8) #
Integral Int16 #
Instance details Defined in NumHask.Algebra.Integral Methods div :: Int16 -> Int16 -> Int16 # mod :: Int16 -> Int16 -> Int16 # divMod :: Int16 -> Int16 -> (Int16, Int16) # quot :: Int16 -> Int16 -> Int16 # rem :: Int16 -> Int16 -> Int16 # quotRem :: Int16 -> Int16 -> (Int16, Int16) #
Integral Int32 #
Instance details Defined in NumHask.Algebra.Integral Methods div :: Int32 -> Int32 -> Int32 # mod :: Int32 -> Int32 -> Int32 # divMod :: Int32 -> Int32 -> (Int32, Int32) # quot :: Int32 -> Int32 -> Int32 # rem :: Int32 -> Int32 -> Int32 # quotRem :: Int32 -> Int32 -> (Int32, Int32) #
Integral Int64 #
Instance details Defined in NumHask.Algebra.Integral Methods div :: Int64 -> Int64 -> Int64 # mod :: Int64 -> Int64 -> Int64 # divMod :: Int64 -> Int64 -> (Int64, Int64) # quot :: Int64 -> Int64 -> Int64 # rem :: Int64 -> Int64 -> Int64 # quotRem :: Int64 -> Int64 -> (Int64, Int64) #
Integral Integer #
Instance details Defined in NumHask.Algebra.Integral Methods div :: Integer -> Integer -> Integer # mod :: Integer -> Integer -> Integer # divMod :: Integer -> Integer -> (Integer, Integer) # quot :: Integer -> Integer -> Integer # rem :: Integer -> Integer -> Integer # quotRem :: Integer -> Integer -> (Integer, Integer) #
Integral Natural #
Instance details Defined in NumHask.Algebra.Integral Methods div :: Natural -> Natural -> Natural # mod :: Natural -> Natural -> Natural # divMod :: Natural -> Natural -> (Natural, Natural) # quot :: Natural -> Natural -> Natural # rem :: Natural -> Natural -> Natural # quotRem :: Natural -> Natural -> (Natural, Natural) #
Integral Word #
Instance details Defined in NumHask.Algebra.Integral Methods div :: Word -> Word -> Word # mod :: Word -> Word -> Word # divMod :: Word -> Word -> (Word, Word) # quot :: Word -> Word -> Word # rem :: Word -> Word -> Word # quotRem :: Word -> Word -> (Word, Word) #
Integral Word8 #
Instance details Defined in NumHask.Algebra.Integral Methods div :: Word8 -> Word8 -> Word8 # mod :: Word8 -> Word8 -> Word8 # divMod :: Word8 -> Word8 -> (Word8, Word8) # quot :: Word8 -> Word8 -> Word8 # rem :: Word8 -> Word8 -> Word8 # quotRem :: Word8 -> Word8 -> (Word8, Word8) #
Integral Word16 #
Instance details Defined in NumHask.Algebra.Integral Methods div :: Word16 -> Word16 -> Word16 # mod :: Word16 -> Word16 -> Word16 # divMod :: Word16 -> Word16 -> (Word16, Word16) # quot :: Word16 -> Word16 -> Word16 # rem :: Word16 -> Word16 -> Word16 # quotRem :: Word16 -> Word16 -> (Word16, Word16) #
Integral Word32 #
Instance details Defined in NumHask.Algebra.Integral Methods div :: Word32 -> Word32 -> Word32 # mod :: Word32 -> Word32 -> Word32 # divMod :: Word32 -> Word32 -> (Word32, Word32) # quot :: Word32 -> Word32 -> Word32 # rem :: Word32 -> Word32 -> Word32 # quotRem :: Word32 -> Word32 -> (Word32, Word32) #
Integral Word64 #
Instance details Defined in NumHask.Algebra.Integral Methods div :: Word64 -> Word64 -> Word64 # mod :: Word64 -> Word64 -> Word64 # divMod :: Word64 -> Word64 -> (Word64, Word64) # quot :: Word64 -> Word64 -> Word64 # rem :: Word64 -> Word64 -> Word64 # quotRem :: Word64 -> Word64 -> (Word64, Word64) #

class ToInteger a where #

toInteger is kept separate from Integral to help with compatability issues.

Minimal complete definition

toInteger

Methods

toInteger :: a -> Integer #

Instances

ToInteger Int #
Instance details Defined in NumHask.Algebra.Integral Methods toInteger :: Int -> Integer #
ToInteger Int8 #
Instance details Defined in NumHask.Algebra.Integral Methods toInteger :: Int8 -> Integer #
ToInteger Int16 #
Instance details Defined in NumHask.Algebra.Integral Methods toInteger :: Int16 -> Integer #
ToInteger Int32 #
Instance details Defined in NumHask.Algebra.Integral Methods toInteger :: Int32 -> Integer #
ToInteger Int64 #
Instance details Defined in NumHask.Algebra.Integral Methods toInteger :: Int64 -> Integer #
ToInteger Integer #
Instance details Defined in NumHask.Algebra.Integral Methods toInteger :: Integer -> Integer #
ToInteger Natural #
Instance details Defined in NumHask.Algebra.Integral Methods toInteger :: Natural -> Integer #
ToInteger Word #
Instance details Defined in NumHask.Algebra.Integral Methods toInteger :: Word -> Integer #
ToInteger Word8 #
Instance details Defined in NumHask.Algebra.Integral Methods toInteger :: Word8 -> Integer #
ToInteger Word16 #
Instance details Defined in NumHask.Algebra.Integral Methods toInteger :: Word16 -> Integer #
ToInteger Word32 #
Instance details Defined in NumHask.Algebra.Integral Methods toInteger :: Word32 -> Integer #
ToInteger Word64 #
Instance details Defined in NumHask.Algebra.Integral Methods toInteger :: Word64 -> Integer #
(ToInteger a, ExpField a) => ToInteger (LogField a) #
Instance details Defined in NumHask.Data.LogField Methods toInteger :: LogField a -> Integer #

class FromInteger a where #

fromInteger is the most problematic of the Num class operators. Particularly heinous, it is assumed that any number type can be constructed from an Integer, so that the broad classes of objects that are composed of multiple elements is avoided in haskell.

Minimal complete definition

fromInteger

Methods

fromInteger :: Integer -> a #

Instances

FromInteger Double #
Instance details Defined in NumHask.Algebra.Integral Methods fromInteger :: Integer -> Double #
FromInteger Float #
Instance details Defined in NumHask.Algebra.Integral Methods fromInteger :: Integer -> Float #
FromInteger Int #
Instance details Defined in NumHask.Algebra.Integral Methods fromInteger :: Integer -> Int #
FromInteger Int8 #
Instance details Defined in NumHask.Algebra.Integral Methods fromInteger :: Integer -> Int8 #
FromInteger Int16 #
Instance details Defined in NumHask.Algebra.Integral Methods fromInteger :: Integer -> Int16 #
FromInteger Int32 #
Instance details Defined in NumHask.Algebra.Integral Methods fromInteger :: Integer -> Int32 #
FromInteger Int64 #
Instance details Defined in NumHask.Algebra.Integral Methods fromInteger :: Integer -> Int64 #
FromInteger Integer #
Instance details Defined in NumHask.Algebra.Integral Methods fromInteger :: Integer -> Integer #
FromInteger Natural #
Instance details Defined in NumHask.Algebra.Integral Methods fromInteger :: Integer -> Natural #
FromInteger Word #
Instance details Defined in NumHask.Algebra.Integral Methods fromInteger :: Integer -> Word #
FromInteger Word8 #
Instance details Defined in NumHask.Algebra.Integral Methods fromInteger :: Integer -> Word8 #
FromInteger Word16 #
Instance details Defined in NumHask.Algebra.Integral Methods fromInteger :: Integer -> Word16 #
FromInteger Word32 #
Instance details Defined in NumHask.Algebra.Integral Methods fromInteger :: Integer -> Word32 #
FromInteger Word64 #
Instance details Defined in NumHask.Algebra.Integral Methods fromInteger :: Integer -> Word64 #
(FromInteger a, MultiplicativeUnital a) => FromInteger (Ratio a) #
Instance details Defined in NumHask.Algebra.Rational Methods fromInteger :: Integer -> Ratio a #
(FromInteger a, ExpField a) => FromInteger (LogField a) #
Instance details Defined in NumHask.Data.LogField Methods fromInteger :: Integer -> LogField a #

fromIntegral :: (ToInteger a, FromInteger b) => a -> b #

coercion of Integrals

fromIntegral a == a

even :: (Eq a, Integral a) => a -> Bool #

odd :: (Eq a, Integral a) => a -> Bool #

(^) :: (Ord b, Integral b, Multiplicative a) => a -> b -> a #

raise a number to a non-negative integral power

(^^) :: MultiplicativeGroup a => a -> Integer -> a #