Copyright	(c) The University of Glasgow 1994-2002
License	see libraries/base/LICENSE
Maintainer	ghc-devs@haskell.org
Stability	internal
Portability	non-portable (GHC Extensions)
Safe Haskell	None
Language	Haskell2010

GHC.Num

Description

The Num class and the Integer type.

Synopsis

class Num a where
- (+) :: a -> a -> a
- (-) :: a -> a -> a
- (*) :: a -> a -> a
- negate :: a -> a
- abs :: a -> a
- signum :: a -> a
- fromInteger :: Integer -> a
subtract :: Num a => a -> a -> a
quotRemInteger :: Integer -> Integer -> (# Integer, Integer #)
data Integer
- = IS Int#
- | IP ByteArray#
- | IN ByteArray#
integerToInt :: Integer -> Int
integerToWord :: Integer -> Word
integerLog2# :: Integer -> Word#
integerLogBase# :: Integer -> Integer -> Word#
integerAbs :: Integer -> Integer
integerAdd :: Integer -> Integer -> Integer
integerAnd :: Integer -> Integer -> Integer
integerBit :: Word -> Integer
integerBit# :: Word# -> Integer
integerCheck :: Integer -> Bool
integerCheck# :: Integer -> Bool#
integerCompare :: Integer -> Integer -> Ordering
integerComplement :: Integer -> Integer
integerDecodeDouble# :: Double# -> (# Integer, Int# #)
integerDiv :: Integer -> Integer -> Integer
integerDivMod :: Integer -> Integer -> (Integer, Integer)
integerDivMod# :: Integer -> Integer -> (# Integer, Integer #)
integerEncodeDouble :: Integer -> Int -> Double
integerEncodeDouble# :: Integer -> Int# -> Double#
integerEncodeFloat# :: Integer -> Int# -> Float#
integerEq :: Integer -> Integer -> Bool
integerEq# :: Integer -> Integer -> Bool#
integerFromAddr :: Word# -> Addr# -> Bool# -> IO Integer
integerFromAddr# :: Word# -> Addr# -> Bool# -> State# s -> (# State# s, Integer #)
integerFromBigNat# :: BigNat# -> Integer
integerFromBigNatNeg# :: BigNat# -> Integer
integerFromBigNatSign# :: Int# -> BigNat# -> Integer
integerFromByteArray :: Word# -> ByteArray# -> Word# -> Bool# -> Integer
integerFromByteArray# :: Word# -> ByteArray# -> Word# -> Bool# -> State# s -> (# State# s, Integer #)
integerFromInt :: Int -> Integer
integerFromInt# :: Int# -> Integer
integerFromInt64# :: Int64# -> Integer
integerFromNatural :: Natural -> Integer
integerFromWord :: Word -> Integer
integerFromWord# :: Word# -> Integer
integerFromWord64# :: Word64# -> Integer
integerFromWordList :: Bool -> [Word] -> Integer
integerFromWordNeg# :: Word# -> Integer
integerFromWordSign# :: Int# -> Word# -> Integer
integerGcd :: Integer -> Integer -> Integer
integerGcde :: Integer -> Integer -> (Integer, Integer, Integer)
integerGcde# :: Integer -> Integer -> (# Integer, Integer, Integer #)
integerGe :: Integer -> Integer -> Bool
integerGe# :: Integer -> Integer -> Bool#
integerGt :: Integer -> Integer -> Bool
integerGt# :: Integer -> Integer -> Bool#
integerIsNegative :: Integer -> Bool
integerIsNegative# :: Integer -> Bool#
integerIsOne :: Integer -> Bool
integerIsPowerOf2# :: Integer -> (# (# #) | Word# #)
integerIsZero :: Integer -> Bool
integerLcm :: Integer -> Integer -> Integer
integerLe :: Integer -> Integer -> Bool
integerLe# :: Integer -> Integer -> Bool#
integerLog2 :: Integer -> Word
integerLogBase :: Integer -> Integer -> Word
integerLogBaseWord :: Word -> Integer -> Word
integerLogBaseWord# :: Word# -> Integer -> Word#
integerLt :: Integer -> Integer -> Bool
integerLt# :: Integer -> Integer -> Bool#
integerMod :: Integer -> Integer -> Integer
integerMul :: Integer -> Integer -> Integer
integerNe :: Integer -> Integer -> Bool
integerNe# :: Integer -> Integer -> Bool#
integerNegate :: Integer -> Integer
integerOne :: Integer
integerOr :: Integer -> Integer -> Integer
integerPopCount# :: Integer -> Int#
integerPowMod# :: Integer -> Integer -> Natural -> (# Natural | () #)
integerQuot :: Integer -> Integer -> Integer
integerQuotRem :: Integer -> Integer -> (Integer, Integer)
integerQuotRem# :: Integer -> Integer -> (# Integer, Integer #)
integerRecipMod# :: Integer -> Natural -> (# Natural | () #)
integerRem :: Integer -> Integer -> Integer
integerShiftL :: Integer -> Word -> Integer
integerShiftL# :: Integer -> Word# -> Integer
integerShiftR :: Integer -> Word -> Integer
integerShiftR# :: Integer -> Word# -> Integer
integerSignum :: Integer -> Integer
integerSignum# :: Integer -> Int#
integerSizeInBase# :: Word# -> Integer -> Word#
integerSqr :: Integer -> Integer
integerSub :: Integer -> Integer -> Integer
integerTestBit :: Integer -> Word -> Bool
integerTestBit# :: Integer -> Word# -> Bool#
integerToAddr :: Integer -> Addr# -> Bool# -> IO Word
integerToAddr# :: Integer -> Addr# -> Bool# -> State# s -> (# State# s, Word# #)
integerToBigNatClamp# :: Integer -> BigNat#
integerToBigNatSign# :: Integer -> (# Int#, BigNat# #)
integerToInt# :: Integer -> Int#
integerToInt64# :: Integer -> Int64#
integerToMutableByteArray :: Integer -> MutableByteArray# RealWorld -> Word# -> Bool# -> IO Word
integerToMutableByteArray# :: Integer -> MutableByteArray# s -> Word# -> Bool# -> State# s -> (# State# s, Word# #)
integerToNatural :: Integer -> Natural
integerToNaturalClamp :: Integer -> Natural
integerToNaturalThrow :: Integer -> Natural
integerToWord# :: Integer -> Word#
integerToWord64# :: Integer -> Word64#
integerXor :: Integer -> Integer -> Integer
integerZero :: Integer
data Natural
- = NS Word#
- | NB ByteArray#
naturalToWord :: Natural -> Word
naturalAdd :: Natural -> Natural -> Natural
naturalAnd :: Natural -> Natural -> Natural
naturalAndNot :: Natural -> Natural -> Natural
naturalBit :: Word -> Natural
naturalBit# :: Word# -> Natural
naturalCheck :: Natural -> Bool
naturalCheck# :: Natural -> Bool#
naturalClearBit :: Natural -> Word -> Natural
naturalClearBit# :: Natural -> Word# -> Natural
naturalCompare :: Natural -> Natural -> Ordering
naturalComplementBit :: Natural -> Word -> Natural
naturalComplementBit# :: Natural -> Word# -> Natural
naturalEncodeDouble# :: Natural -> Int# -> Double#
naturalEncodeFloat# :: Natural -> Int# -> Float#
naturalEq :: Natural -> Natural -> Bool
naturalEq# :: Natural -> Natural -> Bool#
naturalFromAddr :: Word# -> Addr# -> Bool# -> IO Natural
naturalFromAddr# :: Word# -> Addr# -> Bool# -> State# s -> (# State# s, Natural #)
naturalFromBigNat# :: BigNat# -> Natural
naturalFromByteArray# :: Word# -> ByteArray# -> Word# -> Bool# -> State# s -> (# State# s, Natural #)
naturalFromWord :: Word -> Natural
naturalFromWord# :: Word# -> Natural
naturalFromWord2# :: Word# -> Word# -> Natural
naturalFromWordList :: [Word] -> Natural
naturalGcd :: Natural -> Natural -> Natural
naturalGe :: Natural -> Natural -> Bool
naturalGe# :: Natural -> Natural -> Bool#
naturalGt :: Natural -> Natural -> Bool
naturalGt# :: Natural -> Natural -> Bool#
naturalIsOne :: Natural -> Bool
naturalIsPowerOf2# :: Natural -> (# (# #) | Word# #)
naturalIsZero :: Natural -> Bool
naturalLcm :: Natural -> Natural -> Natural
naturalLe :: Natural -> Natural -> Bool
naturalLe# :: Natural -> Natural -> Bool#
naturalLog2 :: Natural -> Word
naturalLog2# :: Natural -> Word#
naturalLogBase :: Natural -> Natural -> Word
naturalLogBase# :: Natural -> Natural -> Word#
naturalLogBaseWord :: Word -> Natural -> Word
naturalLogBaseWord# :: Word# -> Natural -> Word#
naturalLt :: Natural -> Natural -> Bool
naturalLt# :: Natural -> Natural -> Bool#
naturalMul :: Natural -> Natural -> Natural
naturalNe :: Natural -> Natural -> Bool
naturalNe# :: Natural -> Natural -> Bool#
naturalNegate :: Natural -> Natural
naturalOne :: Natural
naturalOr :: Natural -> Natural -> Natural
naturalPopCount :: Natural -> Word
naturalPopCount# :: Natural -> Word#
naturalPowMod :: Natural -> Natural -> Natural -> Natural
naturalQuot :: Natural -> Natural -> Natural
naturalQuotRem :: Natural -> Natural -> (Natural, Natural)
naturalQuotRem# :: Natural -> Natural -> (# Natural, Natural #)
naturalRem :: Natural -> Natural -> Natural
naturalSetBit :: Natural -> Word -> Natural
naturalSetBit# :: Natural -> Word# -> Natural
naturalShiftL :: Natural -> Word -> Natural
naturalShiftL# :: Natural -> Word# -> Natural
naturalShiftR :: Natural -> Word -> Natural
naturalShiftR# :: Natural -> Word# -> Natural
naturalSignum :: Natural -> Natural
naturalSizeInBase# :: Word# -> Natural -> Word#
naturalSqr :: Natural -> Natural
naturalSub :: Natural -> Natural -> (# (# #) | Natural #)
naturalSubThrow :: Natural -> Natural -> Natural
naturalSubUnsafe :: Natural -> Natural -> Natural
naturalTestBit :: Natural -> Word -> Bool
naturalTestBit# :: Natural -> Word# -> Bool#
naturalToAddr :: Natural -> Addr# -> Bool# -> IO Word
naturalToAddr# :: Natural -> Addr# -> Bool# -> State# s -> (# State# s, Word# #)
naturalToBigNat# :: Natural -> BigNat#
naturalToMutableByteArray# :: Natural -> MutableByteArray# s -> Word# -> Bool# -> State# s -> (# State# s, Word# #)
naturalToWord# :: Natural -> Word#
naturalToWordClamp :: Natural -> Word
naturalToWordClamp# :: Natural -> Word#
naturalToWordMaybe# :: Natural -> (# (# #) | Word# #)
naturalXor :: Natural -> Natural -> Natural
naturalZero :: Natural

Documentation

class Num a where Source #

Basic numeric class.

The Haskell Report defines no laws for Num. However, (+) and (*) are customarily expected to define a ring and have the following properties:

Associativity of (+): (x + y) + z = x + (y + z)
Commutativity of (+): x + y = y + x
fromInteger 0 is the additive identity: x + fromInteger 0 = x
negate gives the additive inverse: x + negate x = fromInteger 0
Associativity of (*): (x * y) * z = x * (y * z)
fromInteger 1 is the multiplicative identity: x * fromInteger 1 = x and fromInteger 1 * x = x
Distributivity of (*) with respect to (+): a * (b + c) = (a * b) + (a * c) and (b + c) * a = (b * a) + (c * a)
Coherence with toInteger: if the type also implements Integral, then fromInteger is a left inverse for toInteger, i.e. fromInteger (toInteger i) == i

Note that it isn't customarily expected that a type instance of both Num and Ord implement an ordered ring. Indeed, in base only Integer and Rational do.

Minimal complete definition

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

Methods

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

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

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

negate :: a -> a Source #

Unary negation.

abs :: a -> a Source #

Absolute value.

signum :: a -> a Source #

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 Source #

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

Instances details

Num Unique	@since base-4.4.0.0
Instance details Defined in GHC.Internal.Event.Unique Methods (+) :: Unique -> Unique -> Unique Source # (-) :: Unique -> Unique -> Unique Source # (*) :: Unique -> Unique -> Unique Source # negate :: Unique -> Unique Source # abs :: Unique -> Unique Source # signum :: Unique -> Unique Source # fromInteger :: Integer -> Unique Source #
Num CBool
Instance details Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CBool -> CBool -> CBool Source # (-) :: CBool -> CBool -> CBool Source # (*) :: CBool -> CBool -> CBool Source # negate :: CBool -> CBool Source # abs :: CBool -> CBool Source # signum :: CBool -> CBool Source # fromInteger :: Integer -> CBool Source #
Num CChar
Instance details Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CChar -> CChar -> CChar Source # (-) :: CChar -> CChar -> CChar Source # (*) :: CChar -> CChar -> CChar Source # negate :: CChar -> CChar Source # abs :: CChar -> CChar Source # signum :: CChar -> CChar Source # fromInteger :: Integer -> CChar Source #
Num CClock
Instance details Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CClock -> CClock -> CClock Source # (-) :: CClock -> CClock -> CClock Source # (*) :: CClock -> CClock -> CClock Source # negate :: CClock -> CClock Source # abs :: CClock -> CClock Source # signum :: CClock -> CClock Source # fromInteger :: Integer -> CClock Source #
Num CDouble
Instance details Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CDouble -> CDouble -> CDouble Source # (-) :: CDouble -> CDouble -> CDouble Source # (*) :: CDouble -> CDouble -> CDouble Source # negate :: CDouble -> CDouble Source # abs :: CDouble -> CDouble Source # signum :: CDouble -> CDouble Source # fromInteger :: Integer -> CDouble Source #
Num CFloat
Instance details Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CFloat -> CFloat -> CFloat Source # (-) :: CFloat -> CFloat -> CFloat Source # (*) :: CFloat -> CFloat -> CFloat Source # negate :: CFloat -> CFloat Source # abs :: CFloat -> CFloat Source # signum :: CFloat -> CFloat Source # fromInteger :: Integer -> CFloat Source #
Num CInt
Instance details Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CInt -> CInt -> CInt Source # (-) :: CInt -> CInt -> CInt Source # (*) :: CInt -> CInt -> CInt Source # negate :: CInt -> CInt Source # abs :: CInt -> CInt Source # signum :: CInt -> CInt Source # fromInteger :: Integer -> CInt Source #
Num CIntMax
Instance details Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CIntMax -> CIntMax -> CIntMax Source # (-) :: CIntMax -> CIntMax -> CIntMax Source # (*) :: CIntMax -> CIntMax -> CIntMax Source # negate :: CIntMax -> CIntMax Source # abs :: CIntMax -> CIntMax Source # signum :: CIntMax -> CIntMax Source # fromInteger :: Integer -> CIntMax Source #
Num CIntPtr
Instance details Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CIntPtr -> CIntPtr -> CIntPtr Source # (-) :: CIntPtr -> CIntPtr -> CIntPtr Source # (*) :: CIntPtr -> CIntPtr -> CIntPtr Source # negate :: CIntPtr -> CIntPtr Source # abs :: CIntPtr -> CIntPtr Source # signum :: CIntPtr -> CIntPtr Source # fromInteger :: Integer -> CIntPtr Source #
Num CLLong
Instance details Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CLLong -> CLLong -> CLLong Source # (-) :: CLLong -> CLLong -> CLLong Source # (*) :: CLLong -> CLLong -> CLLong Source # negate :: CLLong -> CLLong Source # abs :: CLLong -> CLLong Source # signum :: CLLong -> CLLong Source # fromInteger :: Integer -> CLLong Source #
Num CLong
Instance details Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CLong -> CLong -> CLong Source # (-) :: CLong -> CLong -> CLong Source # (*) :: CLong -> CLong -> CLong Source # negate :: CLong -> CLong Source # abs :: CLong -> CLong Source # signum :: CLong -> CLong Source # fromInteger :: Integer -> CLong Source #
Num CPtrdiff
Instance details Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CPtrdiff -> CPtrdiff -> CPtrdiff Source # (-) :: CPtrdiff -> CPtrdiff -> CPtrdiff Source # (*) :: CPtrdiff -> CPtrdiff -> CPtrdiff Source # negate :: CPtrdiff -> CPtrdiff Source # abs :: CPtrdiff -> CPtrdiff Source # signum :: CPtrdiff -> CPtrdiff Source # fromInteger :: Integer -> CPtrdiff Source #
Num CSChar
Instance details Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CSChar -> CSChar -> CSChar Source # (-) :: CSChar -> CSChar -> CSChar Source # (*) :: CSChar -> CSChar -> CSChar Source # negate :: CSChar -> CSChar Source # abs :: CSChar -> CSChar Source # signum :: CSChar -> CSChar Source # fromInteger :: Integer -> CSChar Source #
Num CSUSeconds
Instance details Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CSUSeconds -> CSUSeconds -> CSUSeconds Source # (-) :: CSUSeconds -> CSUSeconds -> CSUSeconds Source # (*) :: CSUSeconds -> CSUSeconds -> CSUSeconds Source # negate :: CSUSeconds -> CSUSeconds Source # abs :: CSUSeconds -> CSUSeconds Source # signum :: CSUSeconds -> CSUSeconds Source # fromInteger :: Integer -> CSUSeconds Source #
Num CShort
Instance details Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CShort -> CShort -> CShort Source # (-) :: CShort -> CShort -> CShort Source # (*) :: CShort -> CShort -> CShort Source # negate :: CShort -> CShort Source # abs :: CShort -> CShort Source # signum :: CShort -> CShort Source # fromInteger :: Integer -> CShort Source #
Num CSigAtomic
Instance details Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CSigAtomic -> CSigAtomic -> CSigAtomic Source # (-) :: CSigAtomic -> CSigAtomic -> CSigAtomic Source # (*) :: CSigAtomic -> CSigAtomic -> CSigAtomic Source # negate :: CSigAtomic -> CSigAtomic Source # abs :: CSigAtomic -> CSigAtomic Source # signum :: CSigAtomic -> CSigAtomic Source # fromInteger :: Integer -> CSigAtomic Source #
Num CSize
Instance details Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CSize -> CSize -> CSize Source # (-) :: CSize -> CSize -> CSize Source # (*) :: CSize -> CSize -> CSize Source # negate :: CSize -> CSize Source # abs :: CSize -> CSize Source # signum :: CSize -> CSize Source # fromInteger :: Integer -> CSize Source #
Num CTime
Instance details Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CTime -> CTime -> CTime Source # (-) :: CTime -> CTime -> CTime Source # (*) :: CTime -> CTime -> CTime Source # negate :: CTime -> CTime Source # abs :: CTime -> CTime Source # signum :: CTime -> CTime Source # fromInteger :: Integer -> CTime Source #
Num CUChar
Instance details Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CUChar -> CUChar -> CUChar Source # (-) :: CUChar -> CUChar -> CUChar Source # (*) :: CUChar -> CUChar -> CUChar Source # negate :: CUChar -> CUChar Source # abs :: CUChar -> CUChar Source # signum :: CUChar -> CUChar Source # fromInteger :: Integer -> CUChar Source #
Num CUInt
Instance details Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CUInt -> CUInt -> CUInt Source # (-) :: CUInt -> CUInt -> CUInt Source # (*) :: CUInt -> CUInt -> CUInt Source # negate :: CUInt -> CUInt Source # abs :: CUInt -> CUInt Source # signum :: CUInt -> CUInt Source # fromInteger :: Integer -> CUInt Source #
Num CUIntMax
Instance details Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CUIntMax -> CUIntMax -> CUIntMax Source # (-) :: CUIntMax -> CUIntMax -> CUIntMax Source # (*) :: CUIntMax -> CUIntMax -> CUIntMax Source # negate :: CUIntMax -> CUIntMax Source # abs :: CUIntMax -> CUIntMax Source # signum :: CUIntMax -> CUIntMax Source # fromInteger :: Integer -> CUIntMax Source #
Num CUIntPtr
Instance details Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CUIntPtr -> CUIntPtr -> CUIntPtr Source # (-) :: CUIntPtr -> CUIntPtr -> CUIntPtr Source # (*) :: CUIntPtr -> CUIntPtr -> CUIntPtr Source # negate :: CUIntPtr -> CUIntPtr Source # abs :: CUIntPtr -> CUIntPtr Source # signum :: CUIntPtr -> CUIntPtr Source # fromInteger :: Integer -> CUIntPtr Source #
Num CULLong
Instance details Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CULLong -> CULLong -> CULLong Source # (-) :: CULLong -> CULLong -> CULLong Source # (*) :: CULLong -> CULLong -> CULLong Source # negate :: CULLong -> CULLong Source # abs :: CULLong -> CULLong Source # signum :: CULLong -> CULLong Source # fromInteger :: Integer -> CULLong Source #
Num CULong
Instance details Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CULong -> CULong -> CULong Source # (-) :: CULong -> CULong -> CULong Source # (*) :: CULong -> CULong -> CULong Source # negate :: CULong -> CULong Source # abs :: CULong -> CULong Source # signum :: CULong -> CULong Source # fromInteger :: Integer -> CULong Source #
Num CUSeconds
Instance details Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CUSeconds -> CUSeconds -> CUSeconds Source # (-) :: CUSeconds -> CUSeconds -> CUSeconds Source # (*) :: CUSeconds -> CUSeconds -> CUSeconds Source # negate :: CUSeconds -> CUSeconds Source # abs :: CUSeconds -> CUSeconds Source # signum :: CUSeconds -> CUSeconds Source # fromInteger :: Integer -> CUSeconds Source #
Num CUShort
Instance details Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CUShort -> CUShort -> CUShort Source # (-) :: CUShort -> CUShort -> CUShort Source # (*) :: CUShort -> CUShort -> CUShort Source # negate :: CUShort -> CUShort Source # abs :: CUShort -> CUShort Source # signum :: CUShort -> CUShort Source # fromInteger :: Integer -> CUShort Source #
Num CWchar
Instance details Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CWchar -> CWchar -> CWchar Source # (-) :: CWchar -> CWchar -> CWchar Source # (*) :: CWchar -> CWchar -> CWchar Source # negate :: CWchar -> CWchar Source # abs :: CWchar -> CWchar Source # signum :: CWchar -> CWchar Source # fromInteger :: Integer -> CWchar Source #
Num IntPtr
Instance details Defined in GHC.Internal.Foreign.Ptr Methods (+) :: IntPtr -> IntPtr -> IntPtr Source # (-) :: IntPtr -> IntPtr -> IntPtr Source # (*) :: IntPtr -> IntPtr -> IntPtr Source # negate :: IntPtr -> IntPtr Source # abs :: IntPtr -> IntPtr Source # signum :: IntPtr -> IntPtr Source # fromInteger :: Integer -> IntPtr Source #
Num WordPtr
Instance details Defined in GHC.Internal.Foreign.Ptr Methods (+) :: WordPtr -> WordPtr -> WordPtr Source # (-) :: WordPtr -> WordPtr -> WordPtr Source # (*) :: WordPtr -> WordPtr -> WordPtr Source # negate :: WordPtr -> WordPtr Source # abs :: WordPtr -> WordPtr Source # signum :: WordPtr -> WordPtr Source # fromInteger :: Integer -> WordPtr Source #
Num Int16	@since base-2.01
Instance details Defined in GHC.Internal.Int Methods (+) :: Int16 -> Int16 -> Int16 Source # (-) :: Int16 -> Int16 -> Int16 Source # (*) :: Int16 -> Int16 -> Int16 Source # negate :: Int16 -> Int16 Source # abs :: Int16 -> Int16 Source # signum :: Int16 -> Int16 Source # fromInteger :: Integer -> Int16 Source #
Num Int32	@since base-2.01
Instance details Defined in GHC.Internal.Int Methods (+) :: Int32 -> Int32 -> Int32 Source # (-) :: Int32 -> Int32 -> Int32 Source # (*) :: Int32 -> Int32 -> Int32 Source # negate :: Int32 -> Int32 Source # abs :: Int32 -> Int32 Source # signum :: Int32 -> Int32 Source # fromInteger :: Integer -> Int32 Source #
Num Int64	@since base-2.01
Instance details Defined in GHC.Internal.Int Methods (+) :: Int64 -> Int64 -> Int64 Source # (-) :: Int64 -> Int64 -> Int64 Source # (*) :: Int64 -> Int64 -> Int64 Source # negate :: Int64 -> Int64 Source # abs :: Int64 -> Int64 Source # signum :: Int64 -> Int64 Source # fromInteger :: Integer -> Int64 Source #
Num Int8	@since base-2.01
Instance details Defined in GHC.Internal.Int Methods (+) :: Int8 -> Int8 -> Int8 Source # (-) :: Int8 -> Int8 -> Int8 Source # (*) :: Int8 -> Int8 -> Int8 Source # negate :: Int8 -> Int8 Source # abs :: Int8 -> Int8 Source # signum :: Int8 -> Int8 Source # fromInteger :: Integer -> Int8 Source #
Num CBlkCnt
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CBlkCnt -> CBlkCnt -> CBlkCnt Source # (-) :: CBlkCnt -> CBlkCnt -> CBlkCnt Source # (*) :: CBlkCnt -> CBlkCnt -> CBlkCnt Source # negate :: CBlkCnt -> CBlkCnt Source # abs :: CBlkCnt -> CBlkCnt Source # signum :: CBlkCnt -> CBlkCnt Source # fromInteger :: Integer -> CBlkCnt Source #
Num CBlkSize
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CBlkSize -> CBlkSize -> CBlkSize Source # (-) :: CBlkSize -> CBlkSize -> CBlkSize Source # (*) :: CBlkSize -> CBlkSize -> CBlkSize Source # negate :: CBlkSize -> CBlkSize Source # abs :: CBlkSize -> CBlkSize Source # signum :: CBlkSize -> CBlkSize Source # fromInteger :: Integer -> CBlkSize Source #
Num CCc
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CCc -> CCc -> CCc Source # (-) :: CCc -> CCc -> CCc Source # (*) :: CCc -> CCc -> CCc Source # negate :: CCc -> CCc Source # abs :: CCc -> CCc Source # signum :: CCc -> CCc Source # fromInteger :: Integer -> CCc Source #
Num CClockId
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CClockId -> CClockId -> CClockId Source # (-) :: CClockId -> CClockId -> CClockId Source # (*) :: CClockId -> CClockId -> CClockId Source # negate :: CClockId -> CClockId Source # abs :: CClockId -> CClockId Source # signum :: CClockId -> CClockId Source # fromInteger :: Integer -> CClockId Source #
Num CDev
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CDev -> CDev -> CDev Source # (-) :: CDev -> CDev -> CDev Source # (*) :: CDev -> CDev -> CDev Source # negate :: CDev -> CDev Source # abs :: CDev -> CDev Source # signum :: CDev -> CDev Source # fromInteger :: Integer -> CDev Source #
Num CFsBlkCnt
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CFsBlkCnt -> CFsBlkCnt -> CFsBlkCnt Source # (-) :: CFsBlkCnt -> CFsBlkCnt -> CFsBlkCnt Source # (*) :: CFsBlkCnt -> CFsBlkCnt -> CFsBlkCnt Source # negate :: CFsBlkCnt -> CFsBlkCnt Source # abs :: CFsBlkCnt -> CFsBlkCnt Source # signum :: CFsBlkCnt -> CFsBlkCnt Source # fromInteger :: Integer -> CFsBlkCnt Source #
Num CFsFilCnt
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CFsFilCnt -> CFsFilCnt -> CFsFilCnt Source # (-) :: CFsFilCnt -> CFsFilCnt -> CFsFilCnt Source # (*) :: CFsFilCnt -> CFsFilCnt -> CFsFilCnt Source # negate :: CFsFilCnt -> CFsFilCnt Source # abs :: CFsFilCnt -> CFsFilCnt Source # signum :: CFsFilCnt -> CFsFilCnt Source # fromInteger :: Integer -> CFsFilCnt Source #
Num CGid
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CGid -> CGid -> CGid Source # (-) :: CGid -> CGid -> CGid Source # (*) :: CGid -> CGid -> CGid Source # negate :: CGid -> CGid Source # abs :: CGid -> CGid Source # signum :: CGid -> CGid Source # fromInteger :: Integer -> CGid Source #
Num CId
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CId -> CId -> CId Source # (-) :: CId -> CId -> CId Source # (*) :: CId -> CId -> CId Source # negate :: CId -> CId Source # abs :: CId -> CId Source # signum :: CId -> CId Source # fromInteger :: Integer -> CId Source #
Num CIno
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CIno -> CIno -> CIno Source # (-) :: CIno -> CIno -> CIno Source # (*) :: CIno -> CIno -> CIno Source # negate :: CIno -> CIno Source # abs :: CIno -> CIno Source # signum :: CIno -> CIno Source # fromInteger :: Integer -> CIno Source #
Num CKey
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CKey -> CKey -> CKey Source # (-) :: CKey -> CKey -> CKey Source # (*) :: CKey -> CKey -> CKey Source # negate :: CKey -> CKey Source # abs :: CKey -> CKey Source # signum :: CKey -> CKey Source # fromInteger :: Integer -> CKey Source #
Num CMode
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CMode -> CMode -> CMode Source # (-) :: CMode -> CMode -> CMode Source # (*) :: CMode -> CMode -> CMode Source # negate :: CMode -> CMode Source # abs :: CMode -> CMode Source # signum :: CMode -> CMode Source # fromInteger :: Integer -> CMode Source #
Num CNfds
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CNfds -> CNfds -> CNfds Source # (-) :: CNfds -> CNfds -> CNfds Source # (*) :: CNfds -> CNfds -> CNfds Source # negate :: CNfds -> CNfds Source # abs :: CNfds -> CNfds Source # signum :: CNfds -> CNfds Source # fromInteger :: Integer -> CNfds Source #
Num CNlink
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CNlink -> CNlink -> CNlink Source # (-) :: CNlink -> CNlink -> CNlink Source # (*) :: CNlink -> CNlink -> CNlink Source # negate :: CNlink -> CNlink Source # abs :: CNlink -> CNlink Source # signum :: CNlink -> CNlink Source # fromInteger :: Integer -> CNlink Source #
Num COff
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: COff -> COff -> COff Source # (-) :: COff -> COff -> COff Source # (*) :: COff -> COff -> COff Source # negate :: COff -> COff Source # abs :: COff -> COff Source # signum :: COff -> COff Source # fromInteger :: Integer -> COff Source #
Num CPid
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CPid -> CPid -> CPid Source # (-) :: CPid -> CPid -> CPid Source # (*) :: CPid -> CPid -> CPid Source # negate :: CPid -> CPid Source # abs :: CPid -> CPid Source # signum :: CPid -> CPid Source # fromInteger :: Integer -> CPid Source #
Num CRLim
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CRLim -> CRLim -> CRLim Source # (-) :: CRLim -> CRLim -> CRLim Source # (*) :: CRLim -> CRLim -> CRLim Source # negate :: CRLim -> CRLim Source # abs :: CRLim -> CRLim Source # signum :: CRLim -> CRLim Source # fromInteger :: Integer -> CRLim Source #
Num CSocklen
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CSocklen -> CSocklen -> CSocklen Source # (-) :: CSocklen -> CSocklen -> CSocklen Source # (*) :: CSocklen -> CSocklen -> CSocklen Source # negate :: CSocklen -> CSocklen Source # abs :: CSocklen -> CSocklen Source # signum :: CSocklen -> CSocklen Source # fromInteger :: Integer -> CSocklen Source #
Num CSpeed
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CSpeed -> CSpeed -> CSpeed Source # (-) :: CSpeed -> CSpeed -> CSpeed Source # (*) :: CSpeed -> CSpeed -> CSpeed Source # negate :: CSpeed -> CSpeed Source # abs :: CSpeed -> CSpeed Source # signum :: CSpeed -> CSpeed Source # fromInteger :: Integer -> CSpeed Source #
Num CSsize
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CSsize -> CSsize -> CSsize Source # (-) :: CSsize -> CSsize -> CSsize Source # (*) :: CSsize -> CSsize -> CSsize Source # negate :: CSsize -> CSsize Source # abs :: CSsize -> CSsize Source # signum :: CSsize -> CSsize Source # fromInteger :: Integer -> CSsize Source #
Num CTcflag
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CTcflag -> CTcflag -> CTcflag Source # (-) :: CTcflag -> CTcflag -> CTcflag Source # (*) :: CTcflag -> CTcflag -> CTcflag Source # negate :: CTcflag -> CTcflag Source # abs :: CTcflag -> CTcflag Source # signum :: CTcflag -> CTcflag Source # fromInteger :: Integer -> CTcflag Source #
Num CUid
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CUid -> CUid -> CUid Source # (-) :: CUid -> CUid -> CUid Source # (*) :: CUid -> CUid -> CUid Source # negate :: CUid -> CUid Source # abs :: CUid -> CUid Source # signum :: CUid -> CUid Source # fromInteger :: Integer -> CUid Source #
Num Fd
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: Fd -> Fd -> Fd Source # (-) :: Fd -> Fd -> Fd Source # (*) :: Fd -> Fd -> Fd Source # negate :: Fd -> Fd Source # abs :: Fd -> Fd Source # signum :: Fd -> Fd Source # fromInteger :: Integer -> Fd Source #
Num Word16	@since base-2.01
Instance details Defined in GHC.Internal.Word Methods (+) :: Word16 -> Word16 -> Word16 Source # (-) :: Word16 -> Word16 -> Word16 Source # (*) :: Word16 -> Word16 -> Word16 Source # negate :: Word16 -> Word16 Source # abs :: Word16 -> Word16 Source # signum :: Word16 -> Word16 Source # fromInteger :: Integer -> Word16 Source #
Num Word32	@since base-2.01
Instance details Defined in GHC.Internal.Word Methods (+) :: Word32 -> Word32 -> Word32 Source # (-) :: Word32 -> Word32 -> Word32 Source # (*) :: Word32 -> Word32 -> Word32 Source # negate :: Word32 -> Word32 Source # abs :: Word32 -> Word32 Source # signum :: Word32 -> Word32 Source # fromInteger :: Integer -> Word32 Source #
Num Word64	@since base-2.01
Instance details Defined in GHC.Internal.Word Methods (+) :: Word64 -> Word64 -> Word64 Source # (-) :: Word64 -> Word64 -> Word64 Source # (*) :: Word64 -> Word64 -> Word64 Source # negate :: Word64 -> Word64 Source # abs :: Word64 -> Word64 Source # signum :: Word64 -> Word64 Source # fromInteger :: Integer -> Word64 Source #
Num Word8	@since base-2.01
Instance details Defined in GHC.Internal.Word Methods (+) :: Word8 -> Word8 -> Word8 Source # (-) :: Word8 -> Word8 -> Word8 Source # (*) :: Word8 -> Word8 -> Word8 Source # negate :: Word8 -> Word8 Source # abs :: Word8 -> Word8 Source # signum :: Word8 -> Word8 Source # fromInteger :: Integer -> Word8 Source #
Num Integer	@since base-2.01
Instance details Defined in GHC.Internal.Num Methods (+) :: Integer -> Integer -> Integer Source # (-) :: Integer -> Integer -> Integer Source # (*) :: Integer -> Integer -> Integer Source # negate :: Integer -> Integer Source # abs :: Integer -> Integer Source # signum :: Integer -> Integer Source # fromInteger :: Integer -> Integer Source #
Num Natural	Note that `Natural`'s `Num` instance isn't a ring: no element but 0 has an additive inverse. It is a semiring though. @since base-4.8.0.0
Instance details Defined in GHC.Internal.Num Methods (+) :: Natural -> Natural -> Natural Source # (-) :: Natural -> Natural -> Natural Source # (*) :: Natural -> Natural -> Natural Source # negate :: Natural -> Natural Source # abs :: Natural -> Natural Source # signum :: Natural -> Natural Source # fromInteger :: Integer -> Natural Source #
Num Int	@since base-2.01
Instance details Defined in GHC.Internal.Num Methods (+) :: Int -> Int -> Int Source # (-) :: Int -> Int -> Int Source # (*) :: Int -> Int -> Int Source # negate :: Int -> Int Source # abs :: Int -> Int Source # signum :: Int -> Int Source # fromInteger :: Integer -> Int Source #
Num Word	@since base-2.01
Instance details Defined in GHC.Internal.Num Methods (+) :: Word -> Word -> Word Source # (-) :: Word -> Word -> Word Source # (*) :: Word -> Word -> Word Source # negate :: Word -> Word Source # abs :: Word -> Word Source # signum :: Word -> Word Source # fromInteger :: Integer -> Word Source #
RealFloat a => Num (Complex a) Source #	Since: base-2.1
Instance details Defined in Data.Complex Methods (+) :: Complex a -> Complex a -> Complex a Source # (-) :: Complex a -> Complex a -> Complex a Source # (*) :: Complex a -> Complex a -> Complex a Source # negate :: Complex a -> Complex a Source # abs :: Complex a -> Complex a Source # signum :: Complex a -> Complex a Source # fromInteger :: Integer -> Complex a Source #
Num a => Num (Max a) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (+) :: Max a -> Max a -> Max a Source # (-) :: Max a -> Max a -> Max a Source # (*) :: Max a -> Max a -> Max a Source # negate :: Max a -> Max a Source # abs :: Max a -> Max a Source # signum :: Max a -> Max a Source # fromInteger :: Integer -> Max a Source #
Num a => Num (Min a) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (+) :: Min a -> Min a -> Min a Source # (-) :: Min a -> Min a -> Min a Source # (*) :: Min a -> Min a -> Min a Source # negate :: Min a -> Min a Source # abs :: Min a -> Min a Source # signum :: Min a -> Min a Source # fromInteger :: Integer -> Min a Source #
Num a => Num (Identity a)	@since base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Functor.Identity Methods (+) :: Identity a -> Identity a -> Identity a Source # (-) :: Identity a -> Identity a -> Identity a Source # (*) :: Identity a -> Identity a -> Identity a Source # negate :: Identity a -> Identity a Source # abs :: Identity a -> Identity a Source # signum :: Identity a -> Identity a Source # fromInteger :: Integer -> Identity a Source #
Num a => Num (Down a)	@since base-4.11.0.0
Instance details Defined in GHC.Internal.Data.Ord Methods (+) :: Down a -> Down a -> Down a Source # (-) :: Down a -> Down a -> Down a Source # (*) :: Down a -> Down a -> Down a Source # negate :: Down a -> Down a Source # abs :: Down a -> Down a Source # signum :: Down a -> Down a Source # fromInteger :: Integer -> Down a Source #
Num a => Num (Product a)	@since base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods (+) :: Product a -> Product a -> Product a Source # (-) :: Product a -> Product a -> Product a Source # (*) :: Product a -> Product a -> Product a Source # negate :: Product a -> Product a Source # abs :: Product a -> Product a Source # signum :: Product a -> Product a Source # fromInteger :: Integer -> Product a Source #
Num a => Num (Sum a)	@since base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods (+) :: Sum a -> Sum a -> Sum a Source # (-) :: Sum a -> Sum a -> Sum a Source # (*) :: Sum a -> Sum a -> Sum a Source # negate :: Sum a -> Sum a Source # abs :: Sum a -> Sum a Source # signum :: Sum a -> Sum a Source # fromInteger :: Integer -> Sum a Source #
Integral a => Num (Ratio a)	@since base-2.0.1
Instance details Defined in GHC.Internal.Real Methods (+) :: Ratio a -> Ratio a -> Ratio a Source # (-) :: Ratio a -> Ratio a -> Ratio a Source # (*) :: Ratio a -> Ratio a -> Ratio a Source # negate :: Ratio a -> Ratio a Source # abs :: Ratio a -> Ratio a Source # signum :: Ratio a -> Ratio a Source # fromInteger :: Integer -> Ratio a Source #
HasResolution a => Num (Fixed a) Source #	Multiplication is not associative or distributive: `>>>` *`(0.2 0.6 :: Deci) * 0.9 == 0.2 * (0.6 * 0.9)`False `>>>` `(0.1 + 0.1 :: Deci) * 0.5 == 0.1 * 0.5 + 0.1 * 0.5`*False Since: base-2.1*
Instance details Defined in Data.Fixed Methods (+) :: Fixed a -> Fixed a -> Fixed a Source # (-) :: Fixed a -> Fixed a -> Fixed a Source # (*) :: Fixed a -> Fixed a -> Fixed a Source # negate :: Fixed a -> Fixed a Source # abs :: Fixed a -> Fixed a Source # signum :: Fixed a -> Fixed a Source # fromInteger :: Integer -> Fixed a Source #
Num a => Num (Op a b) Source #
Instance details Defined in Data.Functor.Contravariant Methods (+) :: Op a b -> Op a b -> Op a b Source # (-) :: Op a b -> Op a b -> Op a b Source # (*) :: Op a b -> Op a b -> Op a b Source # negate :: Op a b -> Op a b Source # abs :: Op a b -> Op a b Source # signum :: Op a b -> Op a b Source # fromInteger :: Integer -> Op a b Source #
Num a => Num (Const a b)	@since base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Functor.Const Methods (+) :: Const a b -> Const a b -> Const a b Source # (-) :: Const a b -> Const a b -> Const a b Source # (*) :: Const a b -> Const a b -> Const a b Source # negate :: Const a b -> Const a b Source # abs :: Const a b -> Const a b Source # signum :: Const a b -> Const a b Source # fromInteger :: Integer -> Const a b Source #
(Applicative f, Num a) => Num (Ap f a)	Note that even if the underlying `Num` and `Applicative` instances are lawful, for most `Applicative`s, this instance will not be lawful. If you use this instance with the list `Applicative`, the following customary laws will not hold: Commutativity: `>>>` `Ap [10,20] + Ap [1,2]`Ap {getAp = [11,12,21,22]} `>>>` `Ap [1,2] + Ap [10,20]`Ap {getAp = [11,21,12,22]} Additive inverse: `>>>` `Ap [] + negate (Ap [])`Ap {getAp = []} `>>>` `fromInteger 0 :: Ap [] Int`Ap {getAp = [0]} Distributivity: `>>>` *`Ap [1,2] (3 + 4)`Ap {getAp = [7,14]} `>>>` `(Ap [1,2] * 3) + (Ap [1,2] * 4)`**Ap {getAp = [7,11,10,14]} @since base-4.12.0.0
Instance details Defined in GHC.Internal.Data.Monoid Methods (+) :: Ap f a -> Ap f a -> Ap f a Source # (-) :: Ap f a -> Ap f a -> Ap f a Source # (*) :: Ap f a -> Ap f a -> Ap f a Source # negate :: Ap f a -> Ap f a Source # abs :: Ap f a -> Ap f a Source # signum :: Ap f a -> Ap f a Source # fromInteger :: Integer -> Ap f a Source #
Num (f a) => Num (Alt f a)	@since base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods (+) :: Alt f a -> Alt f a -> Alt f a Source # (-) :: Alt f a -> Alt f a -> Alt f a Source # (*) :: Alt f a -> Alt f a -> Alt f a Source # negate :: Alt f a -> Alt f a Source # abs :: Alt f a -> Alt f a Source # signum :: Alt f a -> Alt f a Source # fromInteger :: Integer -> Alt f a Source #
Num (f (g a)) => Num (Compose f g a) Source #	Since: base-4.19.0.0
Instance details Defined in Data.Functor.Compose Methods (+) :: Compose f g a -> Compose f g a -> Compose f g a Source # (-) :: Compose f g a -> Compose f g a -> Compose f g a Source # (*) :: Compose f g a -> Compose f g a -> Compose f g a Source # negate :: Compose f g a -> Compose f g a Source # abs :: Compose f g a -> Compose f g a Source # signum :: Compose f g a -> Compose f g a Source # fromInteger :: Integer -> Compose f g a Source #

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

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.

quotRemInteger :: Integer -> Integer -> (# Integer, Integer #) Source #

data Integer #

Constructors

IS Int#
IP ByteArray#
IN ByteArray#

Instances

Instances details

PrintfArg Integer Source #	Since: base-2.1
Instance details Defined in Text.Printf Methods formatArg :: Integer -> FieldFormatter Source # parseFormat :: Integer -> ModifierParser Source #
Bits Integer	@since base-2.01
Instance details Defined in GHC.Internal.Bits Methods (.&.) :: Integer -> Integer -> Integer Source # (.\|.) :: Integer -> Integer -> Integer Source # xor :: Integer -> Integer -> Integer Source # complement :: Integer -> Integer Source # shift :: Integer -> Int -> Integer Source # rotate :: Integer -> Int -> Integer Source # zeroBits :: Integer Source # bit :: Int -> Integer Source # setBit :: Integer -> Int -> Integer Source # clearBit :: Integer -> Int -> Integer Source # complementBit :: Integer -> Int -> Integer Source # testBit :: Integer -> Int -> Bool Source # bitSizeMaybe :: Integer -> Maybe Int Source # bitSize :: Integer -> Int Source # isSigned :: Integer -> Bool Source # shiftL :: Integer -> Int -> Integer Source # unsafeShiftL :: Integer -> Int -> Integer Source # shiftR :: Integer -> Int -> Integer Source # unsafeShiftR :: Integer -> Int -> Integer Source # rotateL :: Integer -> Int -> Integer Source # rotateR :: Integer -> Int -> Integer Source # popCount :: Integer -> Int Source #
Data Integer	@since base-4.0.0.0
Instance details Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Integer -> c Integer Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Integer Source # toConstr :: Integer -> Constr Source # dataTypeOf :: Integer -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Integer) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Integer) Source # gmapT :: (forall b. Data b => b -> b) -> Integer -> Integer Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Integer -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Integer -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Integer -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Integer -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Integer -> m Integer Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Integer -> m Integer Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Integer -> m Integer Source #
Enum Integer	@since base-2.01
Instance details Defined in GHC.Internal.Enum Methods succ :: Integer -> Integer Source # pred :: Integer -> Integer Source # toEnum :: Int -> Integer Source # fromEnum :: Integer -> Int Source # enumFrom :: Integer -> [Integer] Source # enumFromThen :: Integer -> Integer -> [Integer] Source # enumFromTo :: Integer -> Integer -> [Integer] Source # enumFromThenTo :: Integer -> Integer -> Integer -> [Integer] Source #
Ix Integer	@since base-2.01
Instance details Defined in GHC.Internal.Ix Methods range :: (Integer, Integer) -> [Integer] Source # index :: (Integer, Integer) -> Integer -> Int Source # unsafeIndex :: (Integer, Integer) -> Integer -> Int Source # inRange :: (Integer, Integer) -> Integer -> Bool Source # rangeSize :: (Integer, Integer) -> Int Source # unsafeRangeSize :: (Integer, Integer) -> Int Source #
Num Integer	@since base-2.01
Instance details Defined in GHC.Internal.Num Methods (+) :: Integer -> Integer -> Integer Source # (-) :: Integer -> Integer -> Integer Source # (*) :: Integer -> Integer -> Integer Source # negate :: Integer -> Integer Source # abs :: Integer -> Integer Source # signum :: Integer -> Integer Source # fromInteger :: Integer -> Integer Source #
Read Integer	@since base-2.01
Instance details Defined in GHC.Internal.Read Methods readsPrec :: Int -> ReadS Integer Source # readList :: ReadS [Integer] Source # readPrec :: ReadPrec Integer Source # readListPrec :: ReadPrec [Integer] Source #
Integral Integer	@since base-2.0.1
Instance details Defined in GHC.Internal.Real Methods quot :: Integer -> Integer -> Integer Source # rem :: Integer -> Integer -> Integer Source # div :: Integer -> Integer -> Integer Source # mod :: Integer -> Integer -> Integer Source # quotRem :: Integer -> Integer -> (Integer, Integer) Source # divMod :: Integer -> Integer -> (Integer, Integer) Source # toInteger :: Integer -> Integer Source #
Real Integer	@since base-2.0.1
Instance details Defined in GHC.Internal.Real Methods toRational :: Integer -> Rational Source #
Show Integer	@since base-2.01
Instance details Defined in GHC.Internal.Show Methods showsPrec :: Int -> Integer -> ShowS Source # show :: Integer -> String Source # showList :: [Integer] -> ShowS Source #
Eq Integer
Instance details Defined in GHC.Num.Integer Methods (==) :: Integer -> Integer -> Bool Source # (/=) :: Integer -> Integer -> Bool Source #
Ord Integer
Instance details Defined in GHC.Num.Integer Methods compare :: Integer -> Integer -> Ordering Source # (<) :: Integer -> Integer -> Bool Source # (<=) :: Integer -> Integer -> Bool Source # (>) :: Integer -> Integer -> Bool Source # (>=) :: Integer -> Integer -> Bool Source # max :: Integer -> Integer -> Integer Source # min :: Integer -> Integer -> Integer Source #

integerToInt :: Integer -> Int #

integerToWord :: Integer -> Word #

integerLog2# :: Integer -> Word# #

integerLogBase# :: Integer -> Integer -> Word# #

integerAbs :: Integer -> Integer #

integerAdd :: Integer -> Integer -> Integer #

integerAnd :: Integer -> Integer -> Integer #

integerBit :: Word -> Integer #

integerBit# :: Word# -> Integer #

integerCheck :: Integer -> Bool #

integerCheck# :: Integer -> Bool# #

integerCompare :: Integer -> Integer -> Ordering #

integerComplement :: Integer -> Integer #

integerDecodeDouble# :: Double# -> (# Integer, Int# #) #

integerDiv :: Integer -> Integer -> Integer #

integerDivMod :: Integer -> Integer -> (Integer, Integer) #

integerDivMod# :: Integer -> Integer -> (# Integer, Integer #) #

integerEncodeDouble :: Integer -> Int -> Double #

integerEncodeDouble# :: Integer -> Int# -> Double# #

integerEncodeFloat# :: Integer -> Int# -> Float# #

integerEq :: Integer -> Integer -> Bool #

integerEq# :: Integer -> Integer -> Bool# #

integerFromAddr :: Word# -> Addr# -> Bool# -> IO Integer #

integerFromAddr# :: Word# -> Addr# -> Bool# -> State# s -> (# State# s, Integer #) #

integerFromBigNat# :: BigNat# -> Integer #

integerFromBigNatNeg# :: BigNat# -> Integer #

integerFromBigNatSign# :: Int# -> BigNat# -> Integer #

integerFromByteArray :: Word# -> ByteArray# -> Word# -> Bool# -> Integer #

integerFromByteArray# :: Word# -> ByteArray# -> Word# -> Bool# -> State# s -> (# State# s, Integer #) #

integerFromInt :: Int -> Integer #

integerFromInt# :: Int# -> Integer #

integerFromInt64# :: Int64# -> Integer #

integerFromNatural :: Natural -> Integer #

integerFromWord :: Word -> Integer #

integerFromWord# :: Word# -> Integer #

integerFromWord64# :: Word64# -> Integer #

integerFromWordList :: Bool -> [Word] -> Integer #

integerFromWordNeg# :: Word# -> Integer #

integerFromWordSign# :: Int# -> Word# -> Integer #

integerGcd :: Integer -> Integer -> Integer #

integerGcde :: Integer -> Integer -> (Integer, Integer, Integer) #

integerGcde# :: Integer -> Integer -> (# Integer, Integer, Integer #) #

integerGe :: Integer -> Integer -> Bool #

integerGe# :: Integer -> Integer -> Bool# #

integerGt :: Integer -> Integer -> Bool #

integerGt# :: Integer -> Integer -> Bool# #

integerIsNegative :: Integer -> Bool #

integerIsNegative# :: Integer -> Bool# #

integerIsOne :: Integer -> Bool #

integerIsPowerOf2# :: Integer -> (# (# #) | Word# #) #

integerIsZero :: Integer -> Bool #

integerLcm :: Integer -> Integer -> Integer #

integerLe :: Integer -> Integer -> Bool #

integerLe# :: Integer -> Integer -> Bool# #

integerLog2 :: Integer -> Word #

integerLogBase :: Integer -> Integer -> Word #

integerLogBaseWord :: Word -> Integer -> Word #

integerLogBaseWord# :: Word# -> Integer -> Word# #

integerLt :: Integer -> Integer -> Bool #

integerLt# :: Integer -> Integer -> Bool# #

integerMod :: Integer -> Integer -> Integer #

integerMul :: Integer -> Integer -> Integer #

integerNe :: Integer -> Integer -> Bool #

integerNe# :: Integer -> Integer -> Bool# #

integerNegate :: Integer -> Integer #

integerOne :: Integer #

integerOr :: Integer -> Integer -> Integer #

integerPopCount# :: Integer -> Int# #

integerPowMod# :: Integer -> Integer -> Natural -> (# Natural | () #) #

integerQuot :: Integer -> Integer -> Integer #

integerQuotRem :: Integer -> Integer -> (Integer, Integer) #

integerQuotRem# :: Integer -> Integer -> (# Integer, Integer #) #

integerRecipMod# :: Integer -> Natural -> (# Natural | () #) #

integerRem :: Integer -> Integer -> Integer #

integerShiftL :: Integer -> Word -> Integer #

integerShiftL# :: Integer -> Word# -> Integer #

integerShiftR :: Integer -> Word -> Integer #

integerShiftR# :: Integer -> Word# -> Integer #

integerSignum :: Integer -> Integer #

integerSignum# :: Integer -> Int# #

integerSizeInBase# :: Word# -> Integer -> Word# #

integerSqr :: Integer -> Integer #

integerSub :: Integer -> Integer -> Integer #

integerTestBit :: Integer -> Word -> Bool #

integerTestBit# :: Integer -> Word# -> Bool# #

integerToAddr :: Integer -> Addr# -> Bool# -> IO Word #

integerToAddr# :: Integer -> Addr# -> Bool# -> State# s -> (# State# s, Word# #) #

integerToBigNatClamp# :: Integer -> BigNat# #

integerToBigNatSign# :: Integer -> (# Int#, BigNat# #) #

integerToInt# :: Integer -> Int# #

integerToInt64# :: Integer -> Int64# #

integerToMutableByteArray :: Integer -> MutableByteArray# RealWorld -> Word# -> Bool# -> IO Word #

integerToMutableByteArray# :: Integer -> MutableByteArray# s -> Word# -> Bool# -> State# s -> (# State# s, Word# #) #

integerToNatural :: Integer -> Natural #

integerToNaturalClamp :: Integer -> Natural #

integerToNaturalThrow :: Integer -> Natural #

integerToWord# :: Integer -> Word# #

integerToWord64# :: Integer -> Word64# #

integerXor :: Integer -> Integer -> Integer #

integerZero :: Integer #

data Natural #

Constructors

NS Word#
NB ByteArray#

Instances

Instances details

PrintfArg Natural Source #	Since: base-4.8.0.0
Instance details Defined in Text.Printf Methods formatArg :: Natural -> FieldFormatter Source # parseFormat :: Natural -> ModifierParser Source #
Bits Natural	@since base-4.8.0
Instance details Defined in GHC.Internal.Bits Methods (.&.) :: Natural -> Natural -> Natural Source # (.\|.) :: Natural -> Natural -> Natural Source # xor :: Natural -> Natural -> Natural Source # complement :: Natural -> Natural Source # shift :: Natural -> Int -> Natural Source # rotate :: Natural -> Int -> Natural Source # zeroBits :: Natural Source # bit :: Int -> Natural Source # setBit :: Natural -> Int -> Natural Source # clearBit :: Natural -> Int -> Natural Source # complementBit :: Natural -> Int -> Natural Source # testBit :: Natural -> Int -> Bool Source # bitSizeMaybe :: Natural -> Maybe Int Source # bitSize :: Natural -> Int Source # isSigned :: Natural -> Bool Source # shiftL :: Natural -> Int -> Natural Source # unsafeShiftL :: Natural -> Int -> Natural Source # shiftR :: Natural -> Int -> Natural Source # unsafeShiftR :: Natural -> Int -> Natural Source # rotateL :: Natural -> Int -> Natural Source # rotateR :: Natural -> Int -> Natural Source # popCount :: Natural -> Int Source #
Data Natural	@since base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Natural -> c Natural Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Natural Source # toConstr :: Natural -> Constr Source # dataTypeOf :: Natural -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Natural) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Natural) Source # gmapT :: (forall b. Data b => b -> b) -> Natural -> Natural Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Natural -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Natural -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Natural -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Natural -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Natural -> m Natural Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Natural -> m Natural Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Natural -> m Natural Source #
Enum Natural	@since base-4.8.0.0
Instance details Defined in GHC.Internal.Enum Methods succ :: Natural -> Natural Source # pred :: Natural -> Natural Source # toEnum :: Int -> Natural Source # fromEnum :: Natural -> Int Source # enumFrom :: Natural -> [Natural] Source # enumFromThen :: Natural -> Natural -> [Natural] Source # enumFromTo :: Natural -> Natural -> [Natural] Source # enumFromThenTo :: Natural -> Natural -> Natural -> [Natural] Source #
Ix Natural	@since base-4.8.0.0
Instance details Defined in GHC.Internal.Ix Methods range :: (Natural, Natural) -> [Natural] Source # index :: (Natural, Natural) -> Natural -> Int Source # unsafeIndex :: (Natural, Natural) -> Natural -> Int Source # inRange :: (Natural, Natural) -> Natural -> Bool Source # rangeSize :: (Natural, Natural) -> Int Source # unsafeRangeSize :: (Natural, Natural) -> Int Source #
Num Natural	Note that `Natural`'s `Num` instance isn't a ring: no element but 0 has an additive inverse. It is a semiring though. @since base-4.8.0.0
Instance details Defined in GHC.Internal.Num Methods (+) :: Natural -> Natural -> Natural Source # (-) :: Natural -> Natural -> Natural Source # (*) :: Natural -> Natural -> Natural Source # negate :: Natural -> Natural Source # abs :: Natural -> Natural Source # signum :: Natural -> Natural Source # fromInteger :: Integer -> Natural Source #
Read Natural	@since base-4.8.0.0
Instance details Defined in GHC.Internal.Read Methods readsPrec :: Int -> ReadS Natural Source # readList :: ReadS [Natural] Source # readPrec :: ReadPrec Natural Source # readListPrec :: ReadPrec [Natural] Source #
Integral Natural	@since base-4.8.0.0
Instance details Defined in GHC.Internal.Real Methods quot :: Natural -> Natural -> Natural Source # rem :: Natural -> Natural -> Natural Source # div :: Natural -> Natural -> Natural Source # mod :: Natural -> Natural -> Natural Source # quotRem :: Natural -> Natural -> (Natural, Natural) Source # divMod :: Natural -> Natural -> (Natural, Natural) Source # toInteger :: Natural -> Integer Source #
Real Natural	@since base-4.8.0.0
Instance details Defined in GHC.Internal.Real Methods toRational :: Natural -> Rational Source #
Show Natural	@since base-4.8.0.0
Instance details Defined in GHC.Internal.Show Methods showsPrec :: Int -> Natural -> ShowS Source # show :: Natural -> String Source # showList :: [Natural] -> ShowS Source #
Eq Natural
Instance details Defined in GHC.Num.Natural Methods (==) :: Natural -> Natural -> Bool Source # (/=) :: Natural -> Natural -> Bool Source #
Ord Natural
Instance details Defined in GHC.Num.Natural Methods compare :: Natural -> Natural -> Ordering Source # (<) :: Natural -> Natural -> Bool Source # (<=) :: Natural -> Natural -> Bool Source # (>) :: Natural -> Natural -> Bool Source # (>=) :: Natural -> Natural -> Bool Source # max :: Natural -> Natural -> Natural Source # min :: Natural -> Natural -> Natural Source #
KnownNat n => HasResolution (n :: Nat) Source #	For example, `Fixed 1000` will give you a `Fixed` with a resolution of 1000.
Instance details Defined in Data.Fixed Methods resolution :: p n -> Integer Source #
TestCoercion SNat	@since base-4.18.0.0
Instance details Defined in GHC.Internal.TypeNats Methods testCoercion :: forall (a :: Nat) (b :: Nat). SNat a -> SNat b -> Maybe (Coercion a b) Source #
TestEquality SNat	@since base-4.18.0.0
Instance details Defined in GHC.Internal.TypeNats Methods testEquality :: forall (a :: Nat) (b :: Nat). SNat a -> SNat b -> Maybe (a :~: b) Source #
type Compare (a :: Natural) (b :: Natural)
Instance details Defined in GHC.Internal.Data.Type.Ord type Compare (a :: Natural) (b :: Natural) = CmpNat a b