planet-mitchell-0.0.0: Planet Mitchell

Safe HaskellSafe
LanguageHaskell2010

Numeric.Integral

Contents

Synopsis

Integral

class (Real a, Enum a) => Integral a where #

Integral numbers, supporting integer division.

Minimal complete definition

quotRem, toInteger

Methods

quot :: a -> a -> a infixl 7 #

integer division truncated toward zero

rem :: a -> a -> a infixl 7 #

integer remainder, satisfying

(x `quot` y)*y + (x `rem` y) == x

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

integer division truncated toward negative infinity

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

integer modulus, satisfying

(x `div` y)*y + (x `mod` y) == x

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

simultaneous quot and rem

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

simultaneous div and mod

toInteger :: a -> Integer #

conversion to Integer

Instances
Integral Int

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

quot :: Int -> Int -> Int #

rem :: Int -> Int -> Int #

div :: Int -> Int -> Int #

mod :: Int -> Int -> Int #

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

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

toInteger :: Int -> Integer #

Integral Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

quot :: Int8 -> Int8 -> Int8 #

rem :: Int8 -> Int8 -> Int8 #

div :: Int8 -> Int8 -> Int8 #

mod :: Int8 -> Int8 -> Int8 #

quotRem :: Int8 -> Int8 -> (Int8, Int8) #

divMod :: Int8 -> Int8 -> (Int8, Int8) #

toInteger :: Int8 -> Integer #

Integral Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Integral Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Integral Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Integral Integer

Since: base-2.0.1

Instance details

Defined in GHC.Real

Integral Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Natural

Integral Word

Since: base-2.1

Instance details

Defined in GHC.Real

Methods

quot :: Word -> Word -> Word #

rem :: Word -> Word -> Word #

div :: Word -> Word -> Word #

mod :: Word -> Word -> Word #

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

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

toInteger :: Word -> Integer #

Integral Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Integral Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Integral Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Integral Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Integral CDev 
Instance details

Defined in System.Posix.Types

Methods

quot :: CDev -> CDev -> CDev #

rem :: CDev -> CDev -> CDev #

div :: CDev -> CDev -> CDev #

mod :: CDev -> CDev -> CDev #

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

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

toInteger :: CDev -> Integer #

Integral CIno 
Instance details

Defined in System.Posix.Types

Methods

quot :: CIno -> CIno -> CIno #

rem :: CIno -> CIno -> CIno #

div :: CIno -> CIno -> CIno #

mod :: CIno -> CIno -> CIno #

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

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

toInteger :: CIno -> Integer #

Integral CMode 
Instance details

Defined in System.Posix.Types

Integral COff 
Instance details

Defined in System.Posix.Types

Methods

quot :: COff -> COff -> COff #

rem :: COff -> COff -> COff #

div :: COff -> COff -> COff #

mod :: COff -> COff -> COff #

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

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

toInteger :: COff -> Integer #

Integral CPid 
Instance details

Defined in System.Posix.Types

Methods

quot :: CPid -> CPid -> CPid #

rem :: CPid -> CPid -> CPid #

div :: CPid -> CPid -> CPid #

mod :: CPid -> CPid -> CPid #

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

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

toInteger :: CPid -> Integer #

Integral CSsize 
Instance details

Defined in System.Posix.Types

Integral CGid 
Instance details

Defined in System.Posix.Types

Methods

quot :: CGid -> CGid -> CGid #

rem :: CGid -> CGid -> CGid #

div :: CGid -> CGid -> CGid #

mod :: CGid -> CGid -> CGid #

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

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

toInteger :: CGid -> Integer #

Integral CNlink 
Instance details

Defined in System.Posix.Types

Integral CUid 
Instance details

Defined in System.Posix.Types

Methods

quot :: CUid -> CUid -> CUid #

rem :: CUid -> CUid -> CUid #

div :: CUid -> CUid -> CUid #

mod :: CUid -> CUid -> CUid #

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

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

toInteger :: CUid -> Integer #

Integral CTcflag 
Instance details

Defined in System.Posix.Types

Integral CRLim 
Instance details

Defined in System.Posix.Types

Integral CBlkSize 
Instance details

Defined in System.Posix.Types

Integral CBlkCnt 
Instance details

Defined in System.Posix.Types

Integral CClockId 
Instance details

Defined in System.Posix.Types

Integral CFsBlkCnt 
Instance details

Defined in System.Posix.Types

Integral CFsFilCnt 
Instance details

Defined in System.Posix.Types

Integral CId 
Instance details

Defined in System.Posix.Types

Methods

quot :: CId -> CId -> CId #

rem :: CId -> CId -> CId #

div :: CId -> CId -> CId #

mod :: CId -> CId -> CId #

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

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

toInteger :: CId -> Integer #

Integral CKey 
Instance details

Defined in System.Posix.Types

Methods

quot :: CKey -> CKey -> CKey #

rem :: CKey -> CKey -> CKey #

div :: CKey -> CKey -> CKey #

mod :: CKey -> CKey -> CKey #

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

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

toInteger :: CKey -> Integer #

Integral Fd 
Instance details

Defined in System.Posix.Types

Methods

quot :: Fd -> Fd -> Fd #

rem :: Fd -> Fd -> Fd #

div :: Fd -> Fd -> Fd #

mod :: Fd -> Fd -> Fd #

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

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

toInteger :: Fd -> Integer #

Integral CChar 
Instance details

Defined in Foreign.C.Types

Integral CSChar 
Instance details

Defined in Foreign.C.Types

Integral CUChar 
Instance details

Defined in Foreign.C.Types

Integral CShort 
Instance details

Defined in Foreign.C.Types

Integral CUShort 
Instance details

Defined in Foreign.C.Types

Integral CInt 
Instance details

Defined in Foreign.C.Types

Methods

quot :: CInt -> CInt -> CInt #

rem :: CInt -> CInt -> CInt #

div :: CInt -> CInt -> CInt #

mod :: CInt -> CInt -> CInt #

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

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

toInteger :: CInt -> Integer #

Integral CUInt 
Instance details

Defined in Foreign.C.Types

Integral CLong 
Instance details

Defined in Foreign.C.Types

Integral CULong 
Instance details

Defined in Foreign.C.Types

Integral CLLong 
Instance details

Defined in Foreign.C.Types

Integral CULLong 
Instance details

Defined in Foreign.C.Types

Integral CBool 
Instance details

Defined in Foreign.C.Types

Integral CPtrdiff 
Instance details

Defined in Foreign.C.Types

Integral CSize 
Instance details

Defined in Foreign.C.Types

Integral CWchar 
Instance details

Defined in Foreign.C.Types

Integral CSigAtomic 
Instance details

Defined in Foreign.C.Types

Integral CIntPtr 
Instance details

Defined in Foreign.C.Types

Integral CUIntPtr 
Instance details

Defined in Foreign.C.Types

Integral CIntMax 
Instance details

Defined in Foreign.C.Types

Integral CUIntMax 
Instance details

Defined in Foreign.C.Types

Integral WordPtr 
Instance details

Defined in Foreign.Ptr

Integral IntPtr 
Instance details

Defined in Foreign.Ptr

Integral TestLimit 
Instance details

Defined in Hedgehog.Internal.Property

Integral DiscardLimit 
Instance details

Defined in Hedgehog.Internal.Property

Integral ShrinkLimit 
Instance details

Defined in Hedgehog.Internal.Property

Integral ShrinkRetries 
Instance details

Defined in Hedgehog.Internal.Property

Integral Size 
Instance details

Defined in Hedgehog.Internal.Range

Methods

quot :: Size -> Size -> Size #

rem :: Size -> Size -> Size #

div :: Size -> Size -> Size #

mod :: Size -> Size -> Size #

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

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

toInteger :: Size -> Integer #

Integral PortNumber 
Instance details

Defined in Network.Socket.Types

() :=> (Integral Int) 
Instance details

Defined in Data.Constraint

Methods

ins :: () :- Integral Int #

() :=> (Integral Integer) 
Instance details

Defined in Data.Constraint

Methods

ins :: () :- Integral Integer #

() :=> (Integral Natural) 
Instance details

Defined in Data.Constraint

Methods

ins :: () :- Integral Natural #

() :=> (Integral Word) 
Instance details

Defined in Data.Constraint

Methods

ins :: () :- Integral Word #

Integral a => Integral (Identity a) 
Instance details

Defined in Data.Functor.Identity

(Integral a) :=> (RealFrac (Ratio a)) 
Instance details

Defined in Data.Constraint

Methods

ins :: Integral a :- RealFrac (Ratio a) #

(Integral a) :=> (Real (Ratio a)) 
Instance details

Defined in Data.Constraint

Methods

ins :: Integral a :- Real (Ratio a) #

(Integral a) :=> (Ord (Ratio a)) 
Instance details

Defined in Data.Constraint

Methods

ins :: Integral a :- Ord (Ratio a) #

(Integral a) :=> (Num (Ratio a)) 
Instance details

Defined in Data.Constraint

Methods

ins :: Integral a :- Num (Ratio a) #

(Integral a) :=> (Integral (Identity a)) 
Instance details

Defined in Data.Constraint

Methods

ins :: Integral a :- Integral (Identity a) #

(Integral a) :=> (Integral (Const a b)) 
Instance details

Defined in Data.Constraint

Methods

ins :: Integral a :- Integral (Const a b) #

(Integral a) :=> (Fractional (Ratio a)) 
Instance details

Defined in Data.Constraint

Methods

ins :: Integral a :- Fractional (Ratio a) #

(Integral a) :=> (Enum (Ratio a)) 
Instance details

Defined in Data.Constraint

Methods

ins :: Integral a :- Enum (Ratio a) #

Class (Real a, Enum a) (Integral a) 
Instance details

Defined in Data.Constraint

Methods

cls :: Integral a :- (Real a, Enum a) #

(Integral a, Show a) :=> (Show (Ratio a)) 
Instance details

Defined in Data.Constraint

Methods

ins :: (Integral a, Show a) :- Show (Ratio a) #

(Integral a, Read a) :=> (Read (Ratio a)) 
Instance details

Defined in Data.Constraint

Methods

ins :: (Integral a, Read a) :- Read (Ratio a) #

Integral a => Integral (Const a b) 
Instance details

Defined in Data.Functor.Const

Methods

quot :: Const a b -> Const a b -> Const a b #

rem :: Const a b -> Const a b -> Const a b #

div :: Const a b -> Const a b -> Const a b #

mod :: Const a b -> Const a b -> Const a b #

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

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

toInteger :: Const a b -> Integer #

Integral a => Integral (Tagged s a) 
Instance details

Defined in Data.Tagged

Methods

quot :: Tagged s a -> Tagged s a -> Tagged s a #

rem :: Tagged s a -> Tagged s a -> Tagged s a #

div :: Tagged s a -> Tagged s a -> Tagged s a #

mod :: Tagged s a -> Tagged s a -> Tagged s a #

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

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

toInteger :: Tagged s a -> Integer #

even :: Integral a => a -> Bool #

odd :: Integral a => a -> Bool #

gcd :: Integral a => a -> a -> a #

gcd x y is the non-negative factor of both x and y of which every common factor of x and y is also a factor; for example gcd 4 2 = 2, gcd (-4) 6 = 2, gcd 0 4 = 4. gcd 0 0 = 0. (That is, the common divisor that is "greatest" in the divisibility preordering.)

Note: Since for signed fixed-width integer types, abs minBound < 0, the result may be negative if one of the arguments is minBound (and necessarily is if the other is 0 or minBound) for such types.

lcm :: Integral a => a -> a -> a #

lcm x y is the smallest positive integer that both x and y divide.

fromIntegral :: (Integral a, Num b) => a -> b #

general coercion from integral types

Show

showInt :: Integral a => a -> ShowS #

Show non-negative Integral numbers in base 10.

showIntAtBase :: (Integral a, Show a) => a -> (Int -> Char) -> a -> ShowS #

Shows a non-negative Integral number using the base specified by the first argument, and the character representation specified by the second.

showOct :: (Integral a, Show a) => a -> ShowS #

Show non-negative Integral numbers in base 8.

showHex :: (Integral a, Show a) => a -> ShowS #

Show non-negative Integral numbers in base 16.