planet-mitchell-0.1.0: Planet Mitchell

Safe HaskellSafe
LanguageHaskell2010

Num.Num

Contents

Synopsis

Documentation

class Num a where #

Basic numeric class.

Minimal complete definition

(+), (*), abs, signum, fromInteger, (negate | (-))

Methods

(+) :: a -> a -> a infixl 6 #

(-) :: a -> a -> a infixl 6 #

(*) :: a -> a -> a infixl 7 #

negate :: a -> a #

Unary negation.

abs :: a -> a #

Absolute value.

signum :: a -> a #

Sign of a number. The functions abs and signum should satisfy the law:

abs x * signum x == x

For real numbers, the signum is either -1 (negative), 0 (zero) or 1 (positive).

fromInteger :: Integer -> a #

Conversion from an Integer. An integer literal represents the application of the function fromInteger to the appropriate value of type Integer, so such literals have type (Num a) => a.

Instances
Num Int

Since: base-2.1

Instance details

Defined in GHC.Num

Methods

(+) :: Int -> Int -> Int #

(-) :: Int -> Int -> Int #

(*) :: Int -> Int -> Int #

negate :: Int -> Int #

abs :: Int -> Int #

signum :: Int -> Int #

fromInteger :: Integer -> Int #

Num Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

(+) :: Int8 -> Int8 -> Int8 #

(-) :: Int8 -> Int8 -> Int8 #

(*) :: Int8 -> Int8 -> Int8 #

negate :: Int8 -> Int8 #

abs :: Int8 -> Int8 #

signum :: Int8 -> Int8 #

fromInteger :: Integer -> Int8 #

Num Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Num Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Num Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Num Integer

Since: base-2.1

Instance details

Defined in GHC.Num

Num Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Natural

Num Word

Since: base-2.1

Instance details

Defined in GHC.Num

Methods

(+) :: Word -> Word -> Word #

(-) :: Word -> Word -> Word #

(*) :: Word -> Word -> Word #

negate :: Word -> Word #

abs :: Word -> Word #

signum :: Word -> Word #

fromInteger :: Integer -> Word #

Num Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Num Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Num Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Num Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Num Scientific

WARNING: + and - compute the Integer magnitude: 10^e where e is the difference between the base10Exponents of the arguments. If these methods are applied to arguments which have huge exponents this could fill up all space and crash your program! So don't apply these methods to scientific numbers coming from untrusted sources. The other methods can be used safely.

Instance details

Defined in Data.Scientific

Num Unique 
Instance details

Defined in GHC.Event.Unique

Methods

(+) :: Unique -> Unique -> Unique #

(-) :: Unique -> Unique -> Unique #

(*) :: Unique -> Unique -> Unique #

negate :: Unique -> Unique #

abs :: Unique -> Unique #

signum :: Unique -> Unique #

fromInteger :: Integer -> Unique #

Num CDev 
Instance details

Defined in System.Posix.Types

Methods

(+) :: CDev -> CDev -> CDev #

(-) :: CDev -> CDev -> CDev #

(*) :: CDev -> CDev -> CDev #

negate :: CDev -> CDev #

abs :: CDev -> CDev #

signum :: CDev -> CDev #

fromInteger :: Integer -> CDev #

Num CIno 
Instance details

Defined in System.Posix.Types

Methods

(+) :: CIno -> CIno -> CIno #

(-) :: CIno -> CIno -> CIno #

(*) :: CIno -> CIno -> CIno #

negate :: CIno -> CIno #

abs :: CIno -> CIno #

signum :: CIno -> CIno #

fromInteger :: Integer -> CIno #

Num CMode 
Instance details

Defined in System.Posix.Types

Num COff 
Instance details

Defined in System.Posix.Types

Methods

(+) :: COff -> COff -> COff #

(-) :: COff -> COff -> COff #

(*) :: COff -> COff -> COff #

negate :: COff -> COff #

abs :: COff -> COff #

signum :: COff -> COff #

fromInteger :: Integer -> COff #

Num CPid 
Instance details

Defined in System.Posix.Types

Methods

(+) :: CPid -> CPid -> CPid #

(-) :: CPid -> CPid -> CPid #

(*) :: CPid -> CPid -> CPid #

negate :: CPid -> CPid #

abs :: CPid -> CPid #

signum :: CPid -> CPid #

fromInteger :: Integer -> CPid #

Num CSsize 
Instance details

Defined in System.Posix.Types

Num CGid 
Instance details

Defined in System.Posix.Types

Methods

(+) :: CGid -> CGid -> CGid #

(-) :: CGid -> CGid -> CGid #

(*) :: CGid -> CGid -> CGid #

negate :: CGid -> CGid #

abs :: CGid -> CGid #

signum :: CGid -> CGid #

fromInteger :: Integer -> CGid #

Num CNlink 
Instance details

Defined in System.Posix.Types

Num CUid 
Instance details

Defined in System.Posix.Types

Methods

(+) :: CUid -> CUid -> CUid #

(-) :: CUid -> CUid -> CUid #

(*) :: CUid -> CUid -> CUid #

negate :: CUid -> CUid #

abs :: CUid -> CUid #

signum :: CUid -> CUid #

fromInteger :: Integer -> CUid #

Num CCc 
Instance details

Defined in System.Posix.Types

Methods

(+) :: CCc -> CCc -> CCc #

(-) :: CCc -> CCc -> CCc #

(*) :: CCc -> CCc -> CCc #

negate :: CCc -> CCc #

abs :: CCc -> CCc #

signum :: CCc -> CCc #

fromInteger :: Integer -> CCc #

Num CSpeed 
Instance details

Defined in System.Posix.Types

Num CTcflag 
Instance details

Defined in System.Posix.Types

Num CRLim 
Instance details

Defined in System.Posix.Types

Num CBlkSize 
Instance details

Defined in System.Posix.Types

Num CBlkCnt 
Instance details

Defined in System.Posix.Types

Num CClockId 
Instance details

Defined in System.Posix.Types

Num CFsBlkCnt 
Instance details

Defined in System.Posix.Types

Num CFsFilCnt 
Instance details

Defined in System.Posix.Types

Num CId 
Instance details

Defined in System.Posix.Types

Methods

(+) :: CId -> CId -> CId #

(-) :: CId -> CId -> CId #

(*) :: CId -> CId -> CId #

negate :: CId -> CId #

abs :: CId -> CId #

signum :: CId -> CId #

fromInteger :: Integer -> CId #

Num CKey 
Instance details

Defined in System.Posix.Types

Methods

(+) :: CKey -> CKey -> CKey #

(-) :: CKey -> CKey -> CKey #

(*) :: CKey -> CKey -> CKey #

negate :: CKey -> CKey #

abs :: CKey -> CKey #

signum :: CKey -> CKey #

fromInteger :: Integer -> CKey #

Num Fd 
Instance details

Defined in System.Posix.Types

Methods

(+) :: Fd -> Fd -> Fd #

(-) :: Fd -> Fd -> Fd #

(*) :: Fd -> Fd -> Fd #

negate :: Fd -> Fd #

abs :: Fd -> Fd #

signum :: Fd -> Fd #

fromInteger :: Integer -> Fd #

Num CChar 
Instance details

Defined in Foreign.C.Types

Num CSChar 
Instance details

Defined in Foreign.C.Types

Num CUChar 
Instance details

Defined in Foreign.C.Types

Num CShort 
Instance details

Defined in Foreign.C.Types

Num CUShort 
Instance details

Defined in Foreign.C.Types

Num CInt 
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CInt -> CInt -> CInt #

(-) :: CInt -> CInt -> CInt #

(*) :: CInt -> CInt -> CInt #

negate :: CInt -> CInt #

abs :: CInt -> CInt #

signum :: CInt -> CInt #

fromInteger :: Integer -> CInt #

Num CUInt 
Instance details

Defined in Foreign.C.Types

Num CLong 
Instance details

Defined in Foreign.C.Types

Num CULong 
Instance details

Defined in Foreign.C.Types

Num CLLong 
Instance details

Defined in Foreign.C.Types

Num CULLong 
Instance details

Defined in Foreign.C.Types

Num CBool 
Instance details

Defined in Foreign.C.Types

Num CFloat 
Instance details

Defined in Foreign.C.Types

Num CDouble 
Instance details

Defined in Foreign.C.Types

Num CPtrdiff 
Instance details

Defined in Foreign.C.Types

Num CSize 
Instance details

Defined in Foreign.C.Types

Num CWchar 
Instance details

Defined in Foreign.C.Types

Num CSigAtomic 
Instance details

Defined in Foreign.C.Types

Num CClock 
Instance details

Defined in Foreign.C.Types

Num CTime 
Instance details

Defined in Foreign.C.Types

Num CUSeconds 
Instance details

Defined in Foreign.C.Types

Num CSUSeconds 
Instance details

Defined in Foreign.C.Types

Num CIntPtr 
Instance details

Defined in Foreign.C.Types

Num CUIntPtr 
Instance details

Defined in Foreign.C.Types

Num CIntMax 
Instance details

Defined in Foreign.C.Types

Num CUIntMax 
Instance details

Defined in Foreign.C.Types

Num WordPtr 
Instance details

Defined in Foreign.Ptr

Num IntPtr 
Instance details

Defined in Foreign.Ptr

Num ExactPi 
Instance details

Defined in Data.ExactPi

Num Half 
Instance details

Defined in Numeric.Half

Methods

(+) :: Half -> Half -> Half #

(-) :: Half -> Half -> Half #

(*) :: Half -> Half -> Half #

negate :: Half -> Half #

abs :: Half -> Half #

signum :: Half -> Half #

fromInteger :: Integer -> Half #

Num PortNumber 
Instance details

Defined in Network.Socket.Types

Num B 
Instance details

Defined in Data.Text.Short.Internal

Methods

(+) :: B -> B -> B #

(-) :: B -> B -> B #

(*) :: B -> B -> B #

negate :: B -> B #

abs :: B -> B #

signum :: B -> B #

fromInteger :: Integer -> B #

Num NominalDiffTime 
Instance details

Defined in Data.Time.Clock.Internal.NominalDiffTime

Num DiffTime 
Instance details

Defined in Data.Time.Clock.Internal.DiffTime

Num CodePoint 
Instance details

Defined in Data.Text.Encoding

Methods

(+) :: CodePoint -> CodePoint -> CodePoint #

(-) :: CodePoint -> CodePoint -> CodePoint #

(*) :: CodePoint -> CodePoint -> CodePoint #

negate :: CodePoint -> CodePoint #

abs :: CodePoint -> CodePoint #

signum :: CodePoint -> CodePoint #

fromInteger :: Integer -> CodePoint #

Num DecoderState 
Instance details

Defined in Data.Text.Encoding

Methods

(+) :: DecoderState -> DecoderState -> DecoderState #

(-) :: DecoderState -> DecoderState -> DecoderState #

(*) :: DecoderState -> DecoderState -> DecoderState #

negate :: DecoderState -> DecoderState #

abs :: DecoderState -> DecoderState #

signum :: DecoderState -> DecoderState #

fromInteger :: Integer -> DecoderState #

Class () (Num a) 
Instance details

Defined in Data.Constraint

Methods

cls :: Num a :- () #

() :=> (Num Double) 
Instance details

Defined in Data.Constraint

Methods

ins :: () :- Num Double #

() :=> (Num Float) 
Instance details

Defined in Data.Constraint

Methods

ins :: () :- Num Float #

() :=> (Num Int) 
Instance details

Defined in Data.Constraint

Methods

ins :: () :- Num Int #

() :=> (Num Integer) 
Instance details

Defined in Data.Constraint

Methods

ins :: () :- Num Integer #

() :=> (Num Natural) 
Instance details

Defined in Data.Constraint

Methods

ins :: () :- Num Natural #

() :=> (Num Word) 
Instance details

Defined in Data.Constraint

Methods

ins :: () :- Num Word #

Integral a => Num (Ratio a)

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

(+) :: Ratio a -> Ratio a -> Ratio a #

(-) :: Ratio a -> Ratio a -> Ratio a #

(*) :: Ratio a -> Ratio a -> Ratio a #

negate :: Ratio a -> Ratio a #

abs :: Ratio a -> Ratio a #

signum :: Ratio a -> Ratio a #

fromInteger :: Integer -> Ratio a #

(Ord a, Num a) => Num (Approximate a) 
Instance details

Defined in Data.Approximate.Type

RealFloat a => Num (Complex a)

Since: base-2.1

Instance details

Defined in Data.Complex

Methods

(+) :: Complex a -> Complex a -> Complex a #

(-) :: Complex a -> Complex a -> Complex a #

(*) :: Complex a -> Complex a -> Complex a #

negate :: Complex a -> Complex a #

abs :: Complex a -> Complex a #

signum :: Complex a -> Complex a #

fromInteger :: Integer -> Complex a #

HasResolution a => Num (Fixed a)

Since: base-2.1

Instance details

Defined in Data.Fixed

Methods

(+) :: Fixed a -> Fixed a -> Fixed a #

(-) :: Fixed a -> Fixed a -> Fixed a #

(*) :: Fixed a -> Fixed a -> Fixed a #

negate :: Fixed a -> Fixed a #

abs :: Fixed a -> Fixed a #

signum :: Fixed a -> Fixed a #

fromInteger :: Integer -> Fixed a #

Num a => Num (Min a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(+) :: Min a -> Min a -> Min a #

(-) :: Min a -> Min a -> Min a #

(*) :: Min a -> Min a -> Min a #

negate :: Min a -> Min a #

abs :: Min a -> Min a #

signum :: Min a -> Min a #

fromInteger :: Integer -> Min a #

Num a => Num (Max a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(+) :: Max a -> Max a -> Max a #

(-) :: Max a -> Max a -> Max a #

(*) :: Max a -> Max a -> Max a #

negate :: Max a -> Max a #

abs :: Max a -> Max a #

signum :: Max a -> Max a #

fromInteger :: Integer -> Max a #

Num a => Num (Identity a) 
Instance details

Defined in Data.Functor.Identity

Num a => Num (Sum a) 
Instance details

Defined in Data.Semigroup.Internal

Methods

(+) :: Sum a -> Sum a -> Sum a #

(-) :: Sum a -> Sum a -> Sum a #

(*) :: Sum a -> Sum a -> Sum a #

negate :: Sum a -> Sum a #

abs :: Sum a -> Sum a #

signum :: Sum a -> Sum a #

fromInteger :: Integer -> Sum a #

Num a => Num (Product a) 
Instance details

Defined in Data.Semigroup.Internal

Methods

(+) :: Product a -> Product a -> Product a #

(-) :: Product a -> Product a -> Product a #

(*) :: Product a -> Product a -> Product a #

negate :: Product a -> Product a #

abs :: Product a -> Product a #

signum :: Product a -> Product a #

fromInteger :: Integer -> Product a #

Num a => Num (Down a)

Since: base-4.11.0.0

Instance details

Defined in Data.Ord

Methods

(+) :: Down a -> Down a -> Down a #

(-) :: Down a -> Down a -> Down a #

(*) :: Down a -> Down a -> Down a #

negate :: Down a -> Down a #

abs :: Down a -> Down a #

signum :: Down a -> Down a #

fromInteger :: Integer -> Down a #

(Precise a, RealFloat a) => Num (Log a) 
Instance details

Defined in Numeric.Log

Methods

(+) :: Log a -> Log a -> Log a #

(-) :: Log a -> Log a -> Log a #

(*) :: Log a -> Log a -> Log a #

negate :: Log a -> Log a #

abs :: Log a -> Log a #

signum :: Log a -> Log a #

fromInteger :: Integer -> Log a #

Num a => Num (Managed a) 
Instance details

Defined in Control.Monad.Managed

Methods

(+) :: Managed a -> Managed a -> Managed a #

(-) :: Managed a -> Managed a -> Managed a #

(*) :: Managed a -> Managed a -> Managed a #

negate :: Managed a -> Managed a #

abs :: Managed a -> Managed a #

signum :: Managed a -> Managed a #

fromInteger :: Integer -> Managed a #

Num a => Num (Bound a) 
Instance details

Defined in Data.Semilattice.Bound

Methods

(+) :: Bound a -> Bound a -> Bound a #

(-) :: Bound a -> Bound a -> Bound a #

(*) :: Bound a -> Bound a -> Bound a #

negate :: Bound a -> Bound a #

abs :: Bound a -> Bound a #

signum :: Bound a -> Bound a #

fromInteger :: Integer -> Bound a #

Num a => Num (Order a) 
Instance details

Defined in Data.Semilattice.Order

Methods

(+) :: Order a -> Order a -> Order a #

(-) :: Order a -> Order a -> Order a #

(*) :: Order a -> Order a -> Order a #

negate :: Order a -> Order a #

abs :: Order a -> Order a #

signum :: Order a -> Order a #

fromInteger :: Integer -> Order a #

Num a => Num (Meeting a) 
Instance details

Defined in Data.Semilattice.Meet

Methods

(+) :: Meeting a -> Meeting a -> Meeting a #

(-) :: Meeting a -> Meeting a -> Meeting a #

(*) :: Meeting a -> Meeting a -> Meeting a #

negate :: Meeting a -> Meeting a #

abs :: Meeting a -> Meeting a #

signum :: Meeting a -> Meeting a #

fromInteger :: Integer -> Meeting a #

Num a => Num (GreaterThan a) 
Instance details

Defined in Data.Semilattice.Meet

Num a => Num (Joining a) 
Instance details

Defined in Data.Semilattice.Join

Methods

(+) :: Joining a -> Joining a -> Joining a #

(-) :: Joining a -> Joining a -> Joining a #

(*) :: Joining a -> Joining a -> Joining a #

negate :: Joining a -> Joining a #

abs :: Joining a -> Joining a #

signum :: Joining a -> Joining a #

fromInteger :: Integer -> Joining a #

Num a => Num (LessThan a) 
Instance details

Defined in Data.Semilattice.Join

Class (Num a) (Fractional a) 
Instance details

Defined in Data.Constraint

Methods

cls :: Fractional a :- Num a #

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

Defined in Data.Constraint

Methods

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

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

Defined in Data.Constraint

Methods

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

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

Defined in Data.Constraint

Methods

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

(RealFloat a) :=> (Num (Complex a)) 
Instance details

Defined in Data.Constraint

Methods

ins :: RealFloat a :- Num (Complex a) #

Num a => Num (Op a b) 
Instance details

Defined in Data.Functor.Contravariant

Methods

(+) :: Op a b -> Op a b -> Op a b #

(-) :: Op a b -> Op a b -> Op a b #

(*) :: Op a b -> Op a b -> Op a b #

negate :: Op a b -> Op a b #

abs :: Op a b -> Op a b #

signum :: Op a b -> Op a b #

fromInteger :: Integer -> Op a b #

Num b => Num (Fold a b) 
Instance details

Defined in Control.Foldl

Methods

(+) :: Fold a b -> Fold a b -> Fold a b #

(-) :: Fold a b -> Fold a b -> Fold a b #

(*) :: Fold a b -> Fold a b -> Fold a b #

negate :: Fold a b -> Fold a b #

abs :: Fold a b -> Fold a b #

signum :: Fold a b -> Fold a b #

fromInteger :: Integer -> Fold a b #

(Monad m, Num a) => Num (ListT m a) 
Instance details

Defined in List.Transformer

Methods

(+) :: ListT m a -> ListT m a -> ListT m a #

(-) :: ListT m a -> ListT m a -> ListT m a #

(*) :: ListT m a -> ListT m a -> ListT m a #

negate :: ListT m a -> ListT m a #

abs :: ListT m a -> ListT m a #

signum :: ListT m a -> ListT m a #

fromInteger :: Integer -> ListT m a #

Class (Num a, Ord a) (Real a) 
Instance details

Defined in Data.Constraint

Methods

cls :: Real a :- (Num a, Ord a) #

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

Defined in Data.Functor.Const

Methods

(+) :: Const a b -> Const a b -> Const a b #

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

(*) :: Const a b -> Const a b -> Const a b #

negate :: Const a b -> Const a b #

abs :: Const a b -> Const a b #

signum :: Const a b -> Const a b #

fromInteger :: Integer -> Const a b #

Num (f a) => Num (Alt f a) 
Instance details

Defined in Data.Semigroup.Internal

Methods

(+) :: Alt f a -> Alt f a -> Alt f a #

(-) :: Alt f a -> Alt f a -> Alt f a #

(*) :: Alt f a -> Alt f a -> Alt f a #

negate :: Alt f a -> Alt f a #

abs :: Alt f a -> Alt f a #

signum :: Alt f a -> Alt f a #

fromInteger :: Integer -> Alt f a #

(Monad m, Num b) => Num (FoldM m a b) 
Instance details

Defined in Control.Foldl

Methods

(+) :: FoldM m a b -> FoldM m a b -> FoldM m a b #

(-) :: FoldM m a b -> FoldM m a b -> FoldM m a b #

(*) :: FoldM m a b -> FoldM m a b -> FoldM m a b #

negate :: FoldM m a b -> FoldM m a b #

abs :: FoldM m a b -> FoldM m a b #

signum :: FoldM m a b -> FoldM m a b #

fromInteger :: Integer -> FoldM m a b #

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

Defined in Data.Tagged

Methods

(+) :: Tagged s a -> Tagged s a -> Tagged s a #

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

(*) :: Tagged s a -> Tagged s a -> Tagged s a #

negate :: Tagged s a -> Tagged s a #

abs :: Tagged s a -> Tagged s a #

signum :: Tagged s a -> Tagged s a #

fromInteger :: Integer -> Tagged s a #

(^) :: (Num a, Integral b) => a -> b -> a infixr 8 #

raise a number to a non-negative integral power

subtract :: Num a => a -> a -> a #

the same as flip (-).

Because - is treated specially in the Haskell grammar, (- e) is not a section, but an application of prefix negation. However, (subtract exp) is equivalent to the disallowed section.

Read

readInt #

Arguments

:: Num a 
=> a

the base

-> (Char -> Bool)

a predicate distinguishing valid digits in this base

-> (Char -> Int)

a function converting a valid digit character to an Int

-> ReadS a 

Reads an unsigned Integral value in an arbitrary base.

readDec :: (Eq a, Num a) => ReadS a #

Read an unsigned number in decimal notation.

>>> readDec "0644"
[(644,"")]

readOct :: (Eq a, Num a) => ReadS a #

Read an unsigned number in octal notation.

>>> readOct "0644"
[(420,"")]

readHex :: (Eq a, Num a) => ReadS a #

Read an unsigned number in hexadecimal notation. Both upper or lower case letters are allowed.

>>> readHex "deadbeef"
[(3735928559,"")]