GHC/Int.hs

    {-# LANGUAGE Trustworthy #-}
    {-# LANGUAGE CPP, NoImplicitPrelude, BangPatterns, MagicHash, UnboxedTuples,
                 StandaloneDeriving, NegativeLiterals #-}
    {-# OPTIONS_HADDOCK hide #-}

    -----------------------------------------------------------------------------
    -- |
    -- Module      :  GHC.Int
    -- Copyright   :  (c) The University of Glasgow 1997-2002
    -- License     :  see libraries/base/LICENSE
    --
    -- Maintainer  :  cvs-ghc@haskell.org
    -- Stability   :  internal
    -- Portability :  non-portable (GHC Extensions)
    --
    -- The sized integral datatypes, 'Int8', 'Int16', 'Int32', and 'Int64'.
    --
    -----------------------------------------------------------------------------

    #include "MachDeps.h"

    module GHC.Int (
            Int(..), Int8(..), Int16(..), Int32(..), Int64(..),
            uncheckedIShiftL64#, uncheckedIShiftRA64#,
            -- * Equality operators
            -- | See GHC.Classes#matching_overloaded_methods_in_rules
            eqInt, neInt, gtInt, geInt, ltInt, leInt,
            eqInt8, neInt8, gtInt8, geInt8, ltInt8, leInt8,
            eqInt16, neInt16, gtInt16, geInt16, ltInt16, leInt16,
            eqInt32, neInt32, gtInt32, geInt32, ltInt32, leInt32,
            eqInt64, neInt64, gtInt64, geInt64, ltInt64, leInt64
        ) where

    import Data.Bits
    import Data.Maybe

    #if WORD_SIZE_IN_BITS < 64
    import GHC.IntWord64
    #endif

    import GHC.Base
    import GHC.Enum
    import GHC.Num
    import GHC.Real
    import GHC.Read
    import GHC.Arr
    import GHC.Word hiding (uncheckedShiftL64#, uncheckedShiftRL64#)
    import GHC.Show

    ------------------------------------------------------------------------
    -- type Int8
    ------------------------------------------------------------------------

    -- Int8 is represented in the same way as Int. Operations may assume
    -- and must ensure that it holds only values from its logical range.

    data {-# CTYPE "HsInt8" #-} Int8 = I8# Int#
    -- ^ 8-bit signed integer type

    -- See GHC.Classes#matching_overloaded_methods_in_rules
    -- | @since 2.01
    instance Eq Int8 where
        (==) = eqInt8
        (/=) = neInt8

    eqInt8, neInt8 :: Int8 -> Int8 -> Bool
    eqInt8 (I8# x) (I8# y) = isTrue# (x ==# y)
    neInt8 (I8# x) (I8# y) = isTrue# (x /=# y)
    {-# INLINE [1] eqInt8 #-}
    {-# INLINE [1] neInt8 #-}

    -- | @since 2.01
    instance Ord Int8 where
        (<)  = ltInt8
        (<=) = leInt8
        (>=) = geInt8
        (>)  = gtInt8

    {-# INLINE [1] gtInt8 #-}
    {-# INLINE [1] geInt8 #-}
    {-# INLINE [1] ltInt8 #-}
    {-# INLINE [1] leInt8 #-}
    gtInt8, geInt8, ltInt8, leInt8 :: Int8 -> Int8 -> Bool
    (I8# x) `gtInt8` (I8# y) = isTrue# (x >#  y)
    (I8# x) `geInt8` (I8# y) = isTrue# (x >=# y)
    (I8# x) `ltInt8` (I8# y) = isTrue# (x <#  y)
    (I8# x) `leInt8` (I8# y) = isTrue# (x <=# y)

    -- | @since 2.01
    instance Show Int8 where
        showsPrec p x = showsPrec p (fromIntegral x :: Int)

    -- | @since 2.01
    instance Num Int8 where
        (I8# x#) + (I8# y#)    = I8# (narrow8Int# (x# +# y#))
        (I8# x#) - (I8# y#)    = I8# (narrow8Int# (x# -# y#))
        (I8# x#) * (I8# y#)    = I8# (narrow8Int# (x# *# y#))
        negate (I8# x#)        = I8# (narrow8Int# (negateInt# x#))
        abs x | x >= 0         = x
              | otherwise      = negate x
        signum x | x > 0       = 1
        signum 0               = 0
        signum _               = -1
        fromInteger i          = I8# (narrow8Int# (integerToInt i))

    -- | @since 2.01
    instance Real Int8 where
        toRational x = toInteger x % 1

    -- | @since 2.01
    instance Enum Int8 where
        succ x
            | x /= maxBound = x + 1
            | otherwise     = succError "Int8"
        pred x
            | x /= minBound = x - 1
            | otherwise     = predError "Int8"
        toEnum i@(I# i#)
            | i >= fromIntegral (minBound::Int8) && i <= fromIntegral (maxBound::Int8)
                            = I8# i#
            | otherwise     = toEnumError "Int8" i (minBound::Int8, maxBound::Int8)
        fromEnum (I8# x#)   = I# x#
        enumFrom            = boundedEnumFrom
        enumFromThen        = boundedEnumFromThen

    -- | @since 2.01
    instance Integral Int8 where
        quot    x@(I8# x#) y@(I8# y#)
            | y == 0                     = divZeroError
            | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
            | otherwise                  = I8# (narrow8Int# (x# `quotInt#` y#))
        rem     (I8# x#) y@(I8# y#)
            | y == 0                     = divZeroError
            | otherwise                  = I8# (narrow8Int# (x# `remInt#` y#))
        div     x@(I8# x#) y@(I8# y#)
            | y == 0                     = divZeroError
            | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
            | otherwise                  = I8# (narrow8Int# (x# `divInt#` y#))
        mod       (I8# x#) y@(I8# y#)
            | y == 0                     = divZeroError
            | otherwise                  = I8# (narrow8Int# (x# `modInt#` y#))
        quotRem x@(I8# x#) y@(I8# y#)
            | y == 0                     = divZeroError
              -- Note [Order of tests]
            | y == (-1) && x == minBound = (overflowError, 0)
            | otherwise                  = case x# `quotRemInt#` y# of
                                           (# q, r #) ->
                                               (I8# (narrow8Int# q),
                                                I8# (narrow8Int# r))
        divMod  x@(I8# x#) y@(I8# y#)
            | y == 0                     = divZeroError
              -- Note [Order of tests]
            | y == (-1) && x == minBound = (overflowError, 0)
            | otherwise                  = case x# `divModInt#` y# of
                                           (# d, m #) ->
                                               (I8# (narrow8Int# d),
                                                I8# (narrow8Int# m))
        toInteger (I8# x#)               = smallInteger x#

    -- | @since 2.01
    instance Bounded Int8 where
        minBound = -0x80
        maxBound =  0x7F

    -- | @since 2.01
    instance Ix Int8 where
        range (m,n)         = [m..n]
        unsafeIndex (m,_) i = fromIntegral i - fromIntegral m
        inRange (m,n) i     = m <= i && i <= n

    -- | @since 2.01
    instance Read Int8 where
        readsPrec p s = [(fromIntegral (x::Int), r) | (x, r) <- readsPrec p s]

    -- | @since 2.01
    instance Bits Int8 where
        {-# INLINE shift #-}
        {-# INLINE bit #-}
        {-# INLINE testBit #-}

        (I8# x#) .&.   (I8# y#)   = I8# (word2Int# (int2Word# x# `and#` int2Word# y#))
        (I8# x#) .|.   (I8# y#)   = I8# (word2Int# (int2Word# x# `or#`  int2Word# y#))
        (I8# x#) `xor` (I8# y#)   = I8# (word2Int# (int2Word# x# `xor#` int2Word# y#))
        complement (I8# x#)       = I8# (word2Int# (not# (int2Word# x#)))
        (I8# x#) `shift` (I# i#)
            | isTrue# (i# >=# 0#) = I8# (narrow8Int# (x# `iShiftL#` i#))
            | otherwise           = I8# (x# `iShiftRA#` negateInt# i#)
        (I8# x#) `shiftL`       (I# i#) = I8# (narrow8Int# (x# `iShiftL#` i#))
        (I8# x#) `unsafeShiftL` (I# i#) = I8# (narrow8Int# (x# `uncheckedIShiftL#` i#))
        (I8# x#) `shiftR`       (I# i#) = I8# (x# `iShiftRA#` i#)
        (I8# x#) `unsafeShiftR` (I# i#) = I8# (x# `uncheckedIShiftRA#` i#)
        (I8# x#) `rotate` (I# i#)
            | isTrue# (i'# ==# 0#)
            = I8# x#
            | otherwise
            = I8# (narrow8Int# (word2Int# ((x'# `uncheckedShiftL#` i'#) `or#`
                                           (x'# `uncheckedShiftRL#` (8# -# i'#)))))
            where
            !x'# = narrow8Word# (int2Word# x#)
            !i'# = word2Int# (int2Word# i# `and#` 7##)
        bitSizeMaybe i            = Just (finiteBitSize i)
        bitSize i                 = finiteBitSize i
        isSigned _                = True
        popCount (I8# x#)         = I# (word2Int# (popCnt8# (int2Word# x#)))
        bit                       = bitDefault
        testBit                   = testBitDefault

    -- | @since 4.6.0.0
    instance FiniteBits Int8 where
        finiteBitSize _ = 8
        countLeadingZeros  (I8# x#) = I# (word2Int# (clz8# (int2Word# x#)))
        countTrailingZeros (I8# x#) = I# (word2Int# (ctz8# (int2Word# x#)))

    {-# RULES
    "fromIntegral/Int8->Int8" fromIntegral = id :: Int8 -> Int8
    "fromIntegral/a->Int8"    fromIntegral = \x -> case fromIntegral x of I# x# -> I8# (narrow8Int# x#)
    "fromIntegral/Int8->a"    fromIntegral = \(I8# x#) -> fromIntegral (I# x#)
      #-}

    {-# RULES
    "properFraction/Float->(Int8,Float)"
        properFraction = \x ->
                          case properFraction x of {
                            (n, y) -> ((fromIntegral :: Int -> Int8) n, y :: Float) }
    "truncate/Float->Int8"
        truncate = (fromIntegral :: Int -> Int8) . (truncate :: Float -> Int)
    "floor/Float->Int8"
        floor    = (fromIntegral :: Int -> Int8) . (floor :: Float -> Int)
    "ceiling/Float->Int8"
        ceiling  = (fromIntegral :: Int -> Int8) . (ceiling :: Float -> Int)
    "round/Float->Int8"
        round    = (fromIntegral :: Int -> Int8) . (round  :: Float -> Int)
      #-}

    {-# RULES
    "properFraction/Double->(Int8,Double)"
        properFraction = \x ->
                          case properFraction x of {
                            (n, y) -> ((fromIntegral :: Int -> Int8) n, y :: Double) }
    "truncate/Double->Int8"
        truncate = (fromIntegral :: Int -> Int8) . (truncate :: Double -> Int)
    "floor/Double->Int8"
        floor    = (fromIntegral :: Int -> Int8) . (floor :: Double -> Int)
    "ceiling/Double->Int8"
        ceiling  = (fromIntegral :: Int -> Int8) . (ceiling :: Double -> Int)
    "round/Double->Int8"
        round    = (fromIntegral :: Int -> Int8) . (round  :: Double -> Int)
      #-}

    ------------------------------------------------------------------------
    -- type Int16
    ------------------------------------------------------------------------

    -- Int16 is represented in the same way as Int. Operations may assume
    -- and must ensure that it holds only values from its logical range.

    data {-# CTYPE "HsInt16" #-} Int16 = I16# Int#
    -- ^ 16-bit signed integer type

    -- See GHC.Classes#matching_overloaded_methods_in_rules
    -- | @since 2.01
    instance Eq Int16 where
        (==) = eqInt16
        (/=) = neInt16

    eqInt16, neInt16 :: Int16 -> Int16 -> Bool
    eqInt16 (I16# x) (I16# y) = isTrue# (x ==# y)
    neInt16 (I16# x) (I16# y) = isTrue# (x /=# y)
    {-# INLINE [1] eqInt16 #-}
    {-# INLINE [1] neInt16 #-}

    -- | @since 2.01
    instance Ord Int16 where
        (<)  = ltInt16
        (<=) = leInt16
        (>=) = geInt16
        (>)  = gtInt16

    {-# INLINE [1] gtInt16 #-}
    {-# INLINE [1] geInt16 #-}
    {-# INLINE [1] ltInt16 #-}
    {-# INLINE [1] leInt16 #-}
    gtInt16, geInt16, ltInt16, leInt16 :: Int16 -> Int16 -> Bool
    (I16# x) `gtInt16` (I16# y) = isTrue# (x >#  y)
    (I16# x) `geInt16` (I16# y) = isTrue# (x >=# y)
    (I16# x) `ltInt16` (I16# y) = isTrue# (x <#  y)
    (I16# x) `leInt16` (I16# y) = isTrue# (x <=# y)

    -- | @since 2.01
    instance Show Int16 where
        showsPrec p x = showsPrec p (fromIntegral x :: Int)

    -- | @since 2.01
    instance Num Int16 where
        (I16# x#) + (I16# y#)  = I16# (narrow16Int# (x# +# y#))
        (I16# x#) - (I16# y#)  = I16# (narrow16Int# (x# -# y#))
        (I16# x#) * (I16# y#)  = I16# (narrow16Int# (x# *# y#))
        negate (I16# x#)       = I16# (narrow16Int# (negateInt# x#))
        abs x | x >= 0         = x
              | otherwise      = negate x
        signum x | x > 0       = 1
        signum 0               = 0
        signum _               = -1
        fromInteger i          = I16# (narrow16Int# (integerToInt i))

    -- | @since 2.01
    instance Real Int16 where
        toRational x = toInteger x % 1

    -- | @since 2.01
    instance Enum Int16 where
        succ x
            | x /= maxBound = x + 1
            | otherwise     = succError "Int16"
        pred x
            | x /= minBound = x - 1
            | otherwise     = predError "Int16"
        toEnum i@(I# i#)
            | i >= fromIntegral (minBound::Int16) && i <= fromIntegral (maxBound::Int16)
                            = I16# i#
            | otherwise     = toEnumError "Int16" i (minBound::Int16, maxBound::Int16)
        fromEnum (I16# x#)  = I# x#
        enumFrom            = boundedEnumFrom
        enumFromThen        = boundedEnumFromThen

    -- | @since 2.01
    instance Integral Int16 where
        quot    x@(I16# x#) y@(I16# y#)
            | y == 0                     = divZeroError
            | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
            | otherwise                  = I16# (narrow16Int# (x# `quotInt#` y#))
        rem       (I16# x#) y@(I16# y#)
            | y == 0                     = divZeroError
            | otherwise                  = I16# (narrow16Int# (x# `remInt#` y#))
        div     x@(I16# x#) y@(I16# y#)
            | y == 0                     = divZeroError
            | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
            | otherwise                  = I16# (narrow16Int# (x# `divInt#` y#))
        mod       (I16# x#) y@(I16# y#)
            | y == 0                     = divZeroError
            | otherwise                  = I16# (narrow16Int# (x# `modInt#` y#))
        quotRem x@(I16# x#) y@(I16# y#)
            | y == 0                     = divZeroError
              -- Note [Order of tests]
            | y == (-1) && x == minBound = (overflowError, 0)
            | otherwise                  = case x# `quotRemInt#` y# of
                                           (# q, r #) ->
                                               (I16# (narrow16Int# q),
                                                I16# (narrow16Int# r))
        divMod  x@(I16# x#) y@(I16# y#)
            | y == 0                     = divZeroError
              -- Note [Order of tests]
            | y == (-1) && x == minBound = (overflowError, 0)
            | otherwise                  = case x# `divModInt#` y# of
                                           (# d, m #) ->
                                               (I16# (narrow16Int# d),
                                                I16# (narrow16Int# m))
        toInteger (I16# x#)              = smallInteger x#

    -- | @since 2.01
    instance Bounded Int16 where
        minBound = -0x8000
        maxBound =  0x7FFF

    -- | @since 2.01
    instance Ix Int16 where
        range (m,n)         = [m..n]
        unsafeIndex (m,_) i = fromIntegral i - fromIntegral m
        inRange (m,n) i     = m <= i && i <= n

    -- | @since 2.01
    instance Read Int16 where
        readsPrec p s = [(fromIntegral (x::Int), r) | (x, r) <- readsPrec p s]

    -- | @since 2.01
    instance Bits Int16 where
        {-# INLINE shift #-}
        {-# INLINE bit #-}
        {-# INLINE testBit #-}

        (I16# x#) .&.   (I16# y#)  = I16# (word2Int# (int2Word# x# `and#` int2Word# y#))
        (I16# x#) .|.   (I16# y#)  = I16# (word2Int# (int2Word# x# `or#`  int2Word# y#))
        (I16# x#) `xor` (I16# y#)  = I16# (word2Int# (int2Word# x# `xor#` int2Word# y#))
        complement (I16# x#)       = I16# (word2Int# (not# (int2Word# x#)))
        (I16# x#) `shift` (I# i#)
            | isTrue# (i# >=# 0#)  = I16# (narrow16Int# (x# `iShiftL#` i#))
            | otherwise            = I16# (x# `iShiftRA#` negateInt# i#)
        (I16# x#) `shiftL`       (I# i#) = I16# (narrow16Int# (x# `iShiftL#` i#))
        (I16# x#) `unsafeShiftL` (I# i#) = I16# (narrow16Int# (x# `uncheckedIShiftL#` i#))
        (I16# x#) `shiftR`       (I# i#) = I16# (x# `iShiftRA#` i#)
        (I16# x#) `unsafeShiftR` (I# i#) = I16# (x# `uncheckedIShiftRA#` i#)
        (I16# x#) `rotate` (I# i#)
            | isTrue# (i'# ==# 0#)
            = I16# x#
            | otherwise
            = I16# (narrow16Int# (word2Int# ((x'# `uncheckedShiftL#` i'#) `or#`
                                             (x'# `uncheckedShiftRL#` (16# -# i'#)))))
            where
            !x'# = narrow16Word# (int2Word# x#)
            !i'# = word2Int# (int2Word# i# `and#` 15##)
        bitSizeMaybe i             = Just (finiteBitSize i)
        bitSize i                  = finiteBitSize i
        isSigned _                 = True
        popCount (I16# x#)         = I# (word2Int# (popCnt16# (int2Word# x#)))
        bit                        = bitDefault
        testBit                    = testBitDefault

    -- | @since 4.6.0.0
    instance FiniteBits Int16 where
        finiteBitSize _ = 16
        countLeadingZeros  (I16# x#) = I# (word2Int# (clz16# (int2Word# x#)))
        countTrailingZeros (I16# x#) = I# (word2Int# (ctz16# (int2Word# x#)))

    {-# RULES
    "fromIntegral/Word8->Int16"  fromIntegral = \(W8# x#) -> I16# (word2Int# x#)
    "fromIntegral/Int8->Int16"   fromIntegral = \(I8# x#) -> I16# x#
    "fromIntegral/Int16->Int16"  fromIntegral = id :: Int16 -> Int16
    "fromIntegral/a->Int16"      fromIntegral = \x -> case fromIntegral x of I# x# -> I16# (narrow16Int# x#)
    "fromIntegral/Int16->a"      fromIntegral = \(I16# x#) -> fromIntegral (I# x#)
      #-}

    {-# RULES
    "properFraction/Float->(Int16,Float)"
        properFraction = \x ->
                          case properFraction x of {
                            (n, y) -> ((fromIntegral :: Int -> Int16) n, y :: Float) }
    "truncate/Float->Int16"
        truncate = (fromIntegral :: Int -> Int16) . (truncate :: Float -> Int)
    "floor/Float->Int16"
        floor    = (fromIntegral :: Int -> Int16) . (floor :: Float -> Int)
    "ceiling/Float->Int16"
        ceiling  = (fromIntegral :: Int -> Int16) . (ceiling :: Float -> Int)
    "round/Float->Int16"
        round    = (fromIntegral :: Int -> Int16) . (round  :: Float -> Int)
      #-}

    {-# RULES
    "properFraction/Double->(Int16,Double)"
        properFraction = \x ->
                          case properFraction x of {
                            (n, y) -> ((fromIntegral :: Int -> Int16) n, y :: Double) }
    "truncate/Double->Int16"
        truncate = (fromIntegral :: Int -> Int16) . (truncate :: Double -> Int)
    "floor/Double->Int16"
        floor    = (fromIntegral :: Int -> Int16) . (floor :: Double -> Int)
    "ceiling/Double->Int16"
        ceiling  = (fromIntegral :: Int -> Int16) . (ceiling :: Double -> Int)
    "round/Double->Int16"
        round    = (fromIntegral :: Int -> Int16) . (round  :: Double -> Int)
      #-}

    ------------------------------------------------------------------------
    -- type Int32
    ------------------------------------------------------------------------

    -- Int32 is represented in the same way as Int.
    #if WORD_SIZE_IN_BITS > 32
    -- Operations may assume and must ensure that it holds only values
    -- from its logical range.
    #endif

    data {-# CTYPE "HsInt32" #-} Int32 = I32# Int#
    -- ^ 32-bit signed integer type

    -- See GHC.Classes#matching_overloaded_methods_in_rules
    -- | @since 2.01
    instance Eq Int32 where
        (==) = eqInt32
        (/=) = neInt32

    eqInt32, neInt32 :: Int32 -> Int32 -> Bool
    eqInt32 (I32# x) (I32# y) = isTrue# (x ==# y)
    neInt32 (I32# x) (I32# y) = isTrue# (x /=# y)
    {-# INLINE [1] eqInt32 #-}
    {-# INLINE [1] neInt32 #-}

    -- | @since 2.01
    instance Ord Int32 where
        (<)  = ltInt32
        (<=) = leInt32
        (>=) = geInt32
        (>)  = gtInt32

    {-# INLINE [1] gtInt32 #-}
    {-# INLINE [1] geInt32 #-}
    {-# INLINE [1] ltInt32 #-}
    {-# INLINE [1] leInt32 #-}
    gtInt32, geInt32, ltInt32, leInt32 :: Int32 -> Int32 -> Bool
    (I32# x) `gtInt32` (I32# y) = isTrue# (x >#  y)
    (I32# x) `geInt32` (I32# y) = isTrue# (x >=# y)
    (I32# x) `ltInt32` (I32# y) = isTrue# (x <#  y)
    (I32# x) `leInt32` (I32# y) = isTrue# (x <=# y)

    -- | @since 2.01
    instance Show Int32 where
        showsPrec p x = showsPrec p (fromIntegral x :: Int)

    -- | @since 2.01
    instance Num Int32 where
        (I32# x#) + (I32# y#)  = I32# (narrow32Int# (x# +# y#))
        (I32# x#) - (I32# y#)  = I32# (narrow32Int# (x# -# y#))
        (I32# x#) * (I32# y#)  = I32# (narrow32Int# (x# *# y#))
        negate (I32# x#)       = I32# (narrow32Int# (negateInt# x#))
        abs x | x >= 0         = x
              | otherwise      = negate x
        signum x | x > 0       = 1
        signum 0               = 0
        signum _               = -1
        fromInteger i          = I32# (narrow32Int# (integerToInt i))

    -- | @since 2.01
    instance Enum Int32 where
        succ x
            | x /= maxBound = x + 1
            | otherwise     = succError "Int32"
        pred x
            | x /= minBound = x - 1
            | otherwise     = predError "Int32"
    #if WORD_SIZE_IN_BITS == 32
        toEnum (I# i#)      = I32# i#
    #else
        toEnum i@(I# i#)
            | i >= fromIntegral (minBound::Int32) && i <= fromIntegral (maxBound::Int32)
                            = I32# i#
            | otherwise     = toEnumError "Int32" i (minBound::Int32, maxBound::Int32)
    #endif
        fromEnum (I32# x#)  = I# x#
        enumFrom            = boundedEnumFrom
        enumFromThen        = boundedEnumFromThen

    -- | @since 2.01
    instance Integral Int32 where
        quot    x@(I32# x#) y@(I32# y#)
            | y == 0                     = divZeroError
            | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
            | otherwise                  = I32# (narrow32Int# (x# `quotInt#` y#))
        rem       (I32# x#) y@(I32# y#)
            | y == 0                     = divZeroError
              -- The quotRem CPU instruction fails for minBound `quotRem` -1,
              -- but minBound `rem` -1 is well-defined (0). We therefore
              -- special-case it.
            | y == (-1)                  = 0
            | otherwise                  = I32# (narrow32Int# (x# `remInt#` y#))
        div     x@(I32# x#) y@(I32# y#)
            | y == 0                     = divZeroError
            | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
            | otherwise                  = I32# (narrow32Int# (x# `divInt#` y#))
        mod       (I32# x#) y@(I32# y#)
            | y == 0                     = divZeroError
              -- The divMod CPU instruction fails for minBound `divMod` -1,
              -- but minBound `mod` -1 is well-defined (0). We therefore
              -- special-case it.
            | y == (-1)                  = 0
            | otherwise                  = I32# (narrow32Int# (x# `modInt#` y#))
        quotRem x@(I32# x#) y@(I32# y#)
            | y == 0                     = divZeroError
              -- Note [Order of tests]
            | y == (-1) && x == minBound = (overflowError, 0)
            | otherwise                  = case x# `quotRemInt#` y# of
                                           (# q, r #) ->
                                               (I32# (narrow32Int# q),
                                                I32# (narrow32Int# r))
        divMod  x@(I32# x#) y@(I32# y#)
            | y == 0                     = divZeroError
              -- Note [Order of tests]
            | y == (-1) && x == minBound = (overflowError, 0)
            | otherwise                  = case x# `divModInt#` y# of
                                           (# d, m #) ->
                                               (I32# (narrow32Int# d),
                                                I32# (narrow32Int# m))
        toInteger (I32# x#)              = smallInteger x#

    -- | @since 2.01
    instance Read Int32 where
        readsPrec p s = [(fromIntegral (x::Int), r) | (x, r) <- readsPrec p s]

    -- | @since 2.01
    instance Bits Int32 where
        {-# INLINE shift #-}
        {-# INLINE bit #-}
        {-# INLINE testBit #-}

        (I32# x#) .&.   (I32# y#)  = I32# (word2Int# (int2Word# x# `and#` int2Word# y#))
        (I32# x#) .|.   (I32# y#)  = I32# (word2Int# (int2Word# x# `or#`  int2Word# y#))
        (I32# x#) `xor` (I32# y#)  = I32# (word2Int# (int2Word# x# `xor#` int2Word# y#))
        complement (I32# x#)       = I32# (word2Int# (not# (int2Word# x#)))
        (I32# x#) `shift` (I# i#)
            | isTrue# (i# >=# 0#)  = I32# (narrow32Int# (x# `iShiftL#` i#))
            | otherwise            = I32# (x# `iShiftRA#` negateInt# i#)
        (I32# x#) `shiftL`       (I# i#) = I32# (narrow32Int# (x# `iShiftL#` i#))
        (I32# x#) `unsafeShiftL` (I# i#) =
            I32# (narrow32Int# (x# `uncheckedIShiftL#` i#))
        (I32# x#) `shiftR`       (I# i#) = I32# (x# `iShiftRA#` i#)
        (I32# x#) `unsafeShiftR` (I# i#) = I32# (x# `uncheckedIShiftRA#` i#)
        (I32# x#) `rotate` (I# i#)
            | isTrue# (i'# ==# 0#)
            = I32# x#
            | otherwise
            = I32# (narrow32Int# (word2Int# ((x'# `uncheckedShiftL#` i'#) `or#`
                                             (x'# `uncheckedShiftRL#` (32# -# i'#)))))
            where
            !x'# = narrow32Word# (int2Word# x#)
            !i'# = word2Int# (int2Word# i# `and#` 31##)
        bitSizeMaybe i             = Just (finiteBitSize i)
        bitSize i                  = finiteBitSize i
        isSigned _                 = True
        popCount (I32# x#)         = I# (word2Int# (popCnt32# (int2Word# x#)))
        bit                        = bitDefault
        testBit                    = testBitDefault

    -- | @since 4.6.0.0
    instance FiniteBits Int32 where
        finiteBitSize _ = 32
        countLeadingZeros  (I32# x#) = I# (word2Int# (clz32# (int2Word# x#)))
        countTrailingZeros (I32# x#) = I# (word2Int# (ctz32# (int2Word# x#)))

    {-# RULES
    "fromIntegral/Word8->Int32"  fromIntegral = \(W8# x#) -> I32# (word2Int# x#)
    "fromIntegral/Word16->Int32" fromIntegral = \(W16# x#) -> I32# (word2Int# x#)
    "fromIntegral/Int8->Int32"   fromIntegral = \(I8# x#) -> I32# x#
    "fromIntegral/Int16->Int32"  fromIntegral = \(I16# x#) -> I32# x#
    "fromIntegral/Int32->Int32"  fromIntegral = id :: Int32 -> Int32
    "fromIntegral/a->Int32"      fromIntegral = \x -> case fromIntegral x of I# x# -> I32# (narrow32Int# x#)
    "fromIntegral/Int32->a"      fromIntegral = \(I32# x#) -> fromIntegral (I# x#)
      #-}

    {-# RULES
    "properFraction/Float->(Int32,Float)"
        properFraction = \x ->
                          case properFraction x of {
                            (n, y) -> ((fromIntegral :: Int -> Int32) n, y :: Float) }
    "truncate/Float->Int32"
        truncate = (fromIntegral :: Int -> Int32) . (truncate :: Float -> Int)
    "floor/Float->Int32"
        floor    = (fromIntegral :: Int -> Int32) . (floor :: Float -> Int)
    "ceiling/Float->Int32"
        ceiling  = (fromIntegral :: Int -> Int32) . (ceiling :: Float -> Int)
    "round/Float->Int32"
        round    = (fromIntegral :: Int -> Int32) . (round  :: Float -> Int)
      #-}

    {-# RULES
    "properFraction/Double->(Int32,Double)"
        properFraction = \x ->
                          case properFraction x of {
                            (n, y) -> ((fromIntegral :: Int -> Int32) n, y :: Double) }
    "truncate/Double->Int32"
        truncate = (fromIntegral :: Int -> Int32) . (truncate :: Double -> Int)
    "floor/Double->Int32"
        floor    = (fromIntegral :: Int -> Int32) . (floor :: Double -> Int)
    "ceiling/Double->Int32"
        ceiling  = (fromIntegral :: Int -> Int32) . (ceiling :: Double -> Int)
    "round/Double->Int32"
        round    = (fromIntegral :: Int -> Int32) . (round  :: Double -> Int)
      #-}

    -- | @since 2.01
    instance Real Int32 where
        toRational x = toInteger x % 1

    -- | @since 2.01
    instance Bounded Int32 where
        minBound = -0x80000000
        maxBound =  0x7FFFFFFF

    -- | @since 2.01
    instance Ix Int32 where
        range (m,n)         = [m..n]
        unsafeIndex (m,_) i = fromIntegral i - fromIntegral m
        inRange (m,n) i     = m <= i && i <= n

    ------------------------------------------------------------------------
    -- type Int64
    ------------------------------------------------------------------------

    #if WORD_SIZE_IN_BITS < 64

    data {-# CTYPE "HsInt64" #-} Int64 = I64# Int64#
    -- ^ 64-bit signed integer type

    -- See GHC.Classes#matching_overloaded_methods_in_rules
    -- | @since 2.01
    instance Eq Int64 where
        (==) = eqInt64
        (/=) = neInt64

    eqInt64, neInt64 :: Int64 -> Int64 -> Bool
    eqInt64 (I64# x) (I64# y) = isTrue# (x `eqInt64#` y)
    neInt64 (I64# x) (I64# y) = isTrue# (x `neInt64#` y)
    {-# INLINE [1] eqInt64 #-}
    {-# INLINE [1] neInt64 #-}

    -- | @since 2.01
    instance Ord Int64 where
        (<)  = ltInt64
        (<=) = leInt64
        (>=) = geInt64
        (>)  = gtInt64

    {-# INLINE [1] gtInt64 #-}
    {-# INLINE [1] geInt64 #-}
    {-# INLINE [1] ltInt64 #-}
    {-# INLINE [1] leInt64 #-}
    gtInt64, geInt64, ltInt64, leInt64 :: Int64 -> Int64 -> Bool
    (I64# x) `gtInt64` (I64# y) = isTrue# (x `gtInt64#` y)
    (I64# x) `geInt64` (I64# y) = isTrue# (x `geInt64#` y)
    (I64# x) `ltInt64` (I64# y) = isTrue# (x `ltInt64#` y)
    (I64# x) `leInt64` (I64# y) = isTrue# (x `leInt64#` y)

    -- | @since 2.01
    instance Show Int64 where
        showsPrec p x = showsPrec p (toInteger x)

    -- | @since 2.01
    instance Num Int64 where
        (I64# x#) + (I64# y#)  = I64# (x# `plusInt64#`  y#)
        (I64# x#) - (I64# y#)  = I64# (x# `minusInt64#` y#)
        (I64# x#) * (I64# y#)  = I64# (x# `timesInt64#` y#)
        negate (I64# x#)       = I64# (negateInt64# x#)
        abs x | x >= 0         = x
              | otherwise      = negate x
        signum x | x > 0       = 1
        signum 0               = 0
        signum _               = -1
        fromInteger i          = I64# (integerToInt64 i)

    -- | @since 2.01
    instance Enum Int64 where
        succ x
            | x /= maxBound = x + 1
            | otherwise     = succError "Int64"
        pred x
            | x /= minBound = x - 1
            | otherwise     = predError "Int64"
        toEnum (I# i#)      = I64# (intToInt64# i#)
        fromEnum x@(I64# x#)
            | x >= fromIntegral (minBound::Int) && x <= fromIntegral (maxBound::Int)
                            = I# (int64ToInt# x#)
            | otherwise     = fromEnumError "Int64" x
        enumFrom            = integralEnumFrom
        enumFromThen        = integralEnumFromThen
        enumFromTo          = integralEnumFromTo
        enumFromThenTo      = integralEnumFromThenTo

    -- | @since 2.01
    instance Integral Int64 where
        quot    x@(I64# x#) y@(I64# y#)
            | y == 0                     = divZeroError
            | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
            | otherwise                  = I64# (x# `quotInt64#` y#)
        rem       (I64# x#) y@(I64# y#)
            | y == 0                     = divZeroError
              -- The quotRem CPU instruction fails for minBound `quotRem` -1,
              -- but minBound `rem` -1 is well-defined (0). We therefore
              -- special-case it.
            | y == (-1)                  = 0
            | otherwise                  = I64# (x# `remInt64#` y#)
        div     x@(I64# x#) y@(I64# y#)
            | y == 0                     = divZeroError
            | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
            | otherwise                  = I64# (x# `divInt64#` y#)
        mod       (I64# x#) y@(I64# y#)
            | y == 0                     = divZeroError
              -- The divMod CPU instruction fails for minBound `divMod` -1,
              -- but minBound `mod` -1 is well-defined (0). We therefore
              -- special-case it.
            | y == (-1)                  = 0
            | otherwise                  = I64# (x# `modInt64#` y#)
        quotRem x@(I64# x#) y@(I64# y#)
            | y == 0                     = divZeroError
              -- Note [Order of tests]
            | y == (-1) && x == minBound = (overflowError, 0)
            | otherwise                  = (I64# (x# `quotInt64#` y#),
                                            I64# (x# `remInt64#` y#))
        divMod  x@(I64# x#) y@(I64# y#)
            | y == 0                     = divZeroError
              -- Note [Order of tests]
            | y == (-1) && x == minBound = (overflowError, 0)
            | otherwise                  = (I64# (x# `divInt64#` y#),
                                            I64# (x# `modInt64#` y#))
        toInteger (I64# x)               = int64ToInteger x

    divInt64#, modInt64# :: Int64# -> Int64# -> Int64#

    -- Define div in terms of quot, being careful to avoid overflow (#7233)
    x# `divInt64#` y#
        | isTrue# (x# `gtInt64#` zero) && isTrue# (y# `ltInt64#` zero)
            = ((x# `minusInt64#` one) `quotInt64#` y#) `minusInt64#` one
        | isTrue# (x# `ltInt64#` zero) && isTrue# (y# `gtInt64#` zero)
            = ((x# `plusInt64#` one)  `quotInt64#` y#) `minusInt64#` one
        | otherwise
            = x# `quotInt64#` y#
        where
        !zero = intToInt64# 0#
        !one  = intToInt64# 1#

    x# `modInt64#` y#
        | isTrue# (x# `gtInt64#` zero) && isTrue# (y# `ltInt64#` zero) ||
          isTrue# (x# `ltInt64#` zero) && isTrue# (y# `gtInt64#` zero)
            = if isTrue# (r# `neInt64#` zero) then r# `plusInt64#` y# else zero
        | otherwise = r#
        where
        !zero = intToInt64# 0#
        !r# = x# `remInt64#` y#

    -- | @since 2.01
    instance Read Int64 where
        readsPrec p s = [(fromInteger x, r) | (x, r) <- readsPrec p s]

    -- | @since 2.01
    instance Bits Int64 where
        {-# INLINE shift #-}
        {-# INLINE bit #-}
        {-# INLINE testBit #-}

        (I64# x#) .&.   (I64# y#)  = I64# (word64ToInt64# (int64ToWord64# x# `and64#` int64ToWord64# y#))
        (I64# x#) .|.   (I64# y#)  = I64# (word64ToInt64# (int64ToWord64# x# `or64#`  int64ToWord64# y#))
        (I64# x#) `xor` (I64# y#)  = I64# (word64ToInt64# (int64ToWord64# x# `xor64#` int64ToWord64# y#))
        complement (I64# x#)       = I64# (word64ToInt64# (not64# (int64ToWord64# x#)))
        (I64# x#) `shift` (I# i#)
            | isTrue# (i# >=# 0#)  = I64# (x# `iShiftL64#` i#)
            | otherwise            = I64# (x# `iShiftRA64#` negateInt# i#)
        (I64# x#) `shiftL` (I# i#) = I64# (x# `iShiftL64#` i#)
        (I64# x#) `unsafeShiftL` (I# i#) = I64# (x# `uncheckedIShiftL64#` i#)
        (I64# x#) `shiftR` (I# i#) = I64# (x# `iShiftRA64#` i#)
        (I64# x#) `unsafeShiftR` (I# i#) = I64# (x# `uncheckedIShiftRA64#` i#)
        (I64# x#) `rotate` (I# i#)
            | isTrue# (i'# ==# 0#)
            = I64# x#
            | otherwise
            = I64# (word64ToInt64# ((x'# `uncheckedShiftL64#` i'#) `or64#`
                                    (x'# `uncheckedShiftRL64#` (64# -# i'#))))
            where
            !x'# = int64ToWord64# x#
            !i'# = word2Int# (int2Word# i# `and#` 63##)
        bitSizeMaybe i             = Just (finiteBitSize i)
        bitSize i                  = finiteBitSize i
        isSigned _                 = True
        popCount (I64# x#)         =
            I# (word2Int# (popCnt64# (int64ToWord64# x#)))
        bit                        = bitDefault
        testBit                    = testBitDefault

    -- give the 64-bit shift operations the same treatment as the 32-bit
    -- ones (see GHC.Base), namely we wrap them in tests to catch the
    -- cases when we're shifting more than 64 bits to avoid unspecified
    -- behaviour in the C shift operations.

    iShiftL64#, iShiftRA64# :: Int64# -> Int# -> Int64#

    a `iShiftL64#` b  | isTrue# (b >=# 64#) = intToInt64# 0#
                      | otherwise           = a `uncheckedIShiftL64#` b

    a `iShiftRA64#` b | isTrue# (b >=# 64#) = if isTrue# (a `ltInt64#` (intToInt64# 0#))
                                              then intToInt64# (-1#)
                                              else intToInt64# 0#
                      | otherwise = a `uncheckedIShiftRA64#` b

    {-# RULES
    "fromIntegral/Int->Int64"    fromIntegral = \(I#   x#) -> I64# (intToInt64# x#)
    "fromIntegral/Word->Int64"   fromIntegral = \(W#   x#) -> I64# (word64ToInt64# (wordToWord64# x#))
    "fromIntegral/Word64->Int64" fromIntegral = \(W64# x#) -> I64# (word64ToInt64# x#)
    "fromIntegral/Int64->Int"    fromIntegral = \(I64# x#) -> I#   (int64ToInt# x#)
    "fromIntegral/Int64->Word"   fromIntegral = \(I64# x#) -> W#   (int2Word# (int64ToInt# x#))
    "fromIntegral/Int64->Word64" fromIntegral = \(I64# x#) -> W64# (int64ToWord64# x#)
    "fromIntegral/Int64->Int64"  fromIntegral = id :: Int64 -> Int64
      #-}

    -- No RULES for RealFrac methods if Int is smaller than Int64, we can't
    -- go through Int and whether going through Integer is faster is uncertain.
    #else

    -- Int64 is represented in the same way as Int.
    -- Operations may assume and must ensure that it holds only values
    -- from its logical range.

    data {-# CTYPE "HsInt64" #-} Int64 = I64# Int#
    -- ^ 64-bit signed integer type

    -- See GHC.Classes#matching_overloaded_methods_in_rules
    -- | @since 2.01
    instance Eq Int64 where
        (==) = eqInt64
        (/=) = neInt64

    eqInt64, neInt64 :: Int64 -> Int64 -> Bool
    eqInt64 (I64# x) (I64# y) = isTrue# (x ==# y)
    neInt64 (I64# x) (I64# y) = isTrue# (x /=# y)
    {-# INLINE [1] eqInt64 #-}
    {-# INLINE [1] neInt64 #-}

    -- | @since 2.01
    instance Ord Int64 where
        (<)  = ltInt64
        (<=) = leInt64
        (>=) = geInt64
        (>)  = gtInt64

    {-# INLINE [1] gtInt64 #-}
    {-# INLINE [1] geInt64 #-}
    {-# INLINE [1] ltInt64 #-}
    {-# INLINE [1] leInt64 #-}
    gtInt64, geInt64, ltInt64, leInt64 :: Int64 -> Int64 -> Bool
    (I64# x) `gtInt64` (I64# y) = isTrue# (x >#  y)
    (I64# x) `geInt64` (I64# y) = isTrue# (x >=# y)
    (I64# x) `ltInt64` (I64# y) = isTrue# (x <#  y)
    (I64# x) `leInt64` (I64# y) = isTrue# (x <=# y)

    -- | @since 2.01
    instance Show Int64 where
        showsPrec p x = showsPrec p (fromIntegral x :: Int)

    -- | @since 2.01
    instance Num Int64 where
        (I64# x#) + (I64# y#)  = I64# (x# +# y#)
        (I64# x#) - (I64# y#)  = I64# (x# -# y#)
        (I64# x#) * (I64# y#)  = I64# (x# *# y#)
        negate (I64# x#)       = I64# (negateInt# x#)
        abs x | x >= 0         = x
              | otherwise      = negate x
        signum x | x > 0       = 1
        signum 0               = 0
        signum _               = -1
        fromInteger i          = I64# (integerToInt i)

    -- | @since 2.01
    instance Enum Int64 where
        succ x
            | x /= maxBound = x + 1
            | otherwise     = succError "Int64"
        pred x
            | x /= minBound = x - 1
            | otherwise     = predError "Int64"
        toEnum (I# i#)      = I64# i#
        fromEnum (I64# x#)  = I# x#
        enumFrom            = boundedEnumFrom
        enumFromThen        = boundedEnumFromThen

    -- | @since 2.01
    instance Integral Int64 where
        quot    x@(I64# x#) y@(I64# y#)
            | y == 0                     = divZeroError
            | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
            | otherwise                  = I64# (x# `quotInt#` y#)
        rem       (I64# x#) y@(I64# y#)
            | y == 0                     = divZeroError
              -- The quotRem CPU instruction fails for minBound `quotRem` -1,
              -- but minBound `rem` -1 is well-defined (0). We therefore
              -- special-case it.
            | y == (-1)                  = 0
            | otherwise                  = I64# (x# `remInt#` y#)
        div     x@(I64# x#) y@(I64# y#)
            | y == 0                     = divZeroError
            | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
            | otherwise                  = I64# (x# `divInt#` y#)
        mod       (I64# x#) y@(I64# y#)
            | y == 0                     = divZeroError
              -- The divMod CPU instruction fails for minBound `divMod` -1,
              -- but minBound `mod` -1 is well-defined (0). We therefore
              -- special-case it.
            | y == (-1)                  = 0
            | otherwise                  = I64# (x# `modInt#` y#)
        quotRem x@(I64# x#) y@(I64# y#)
            | y == 0                     = divZeroError
              -- Note [Order of tests]
            | y == (-1) && x == minBound = (overflowError, 0)
            | otherwise                  = case x# `quotRemInt#` y# of
                                           (# q, r #) ->
                                               (I64# q, I64# r)
        divMod  x@(I64# x#) y@(I64# y#)
            | y == 0                     = divZeroError
              -- Note [Order of tests]
            | y == (-1) && x == minBound = (overflowError, 0)
            | otherwise                  = case x# `divModInt#` y# of
                                           (# d, m #) ->
                                               (I64# d, I64# m)
        toInteger (I64# x#)              = smallInteger x#

    -- | @since 2.01
    instance Read Int64 where
        readsPrec p s = [(fromIntegral (x::Int), r) | (x, r) <- readsPrec p s]

    -- | @since 2.01
    instance Bits Int64 where
        {-# INLINE shift #-}
        {-# INLINE bit #-}
        {-# INLINE testBit #-}

        (I64# x#) .&.   (I64# y#)  = I64# (word2Int# (int2Word# x# `and#` int2Word# y#))
        (I64# x#) .|.   (I64# y#)  = I64# (word2Int# (int2Word# x# `or#`  int2Word# y#))
        (I64# x#) `xor` (I64# y#)  = I64# (word2Int# (int2Word# x# `xor#` int2Word# y#))
        complement (I64# x#)       = I64# (word2Int# (int2Word# x# `xor#` int2Word# (-1#)))
        (I64# x#) `shift` (I# i#)
            | isTrue# (i# >=# 0#)  = I64# (x# `iShiftL#` i#)
            | otherwise            = I64# (x# `iShiftRA#` negateInt# i#)
        (I64# x#) `shiftL`       (I# i#) = I64# (x# `iShiftL#` i#)
        (I64# x#) `unsafeShiftL` (I# i#) = I64# (x# `uncheckedIShiftL#` i#)
        (I64# x#) `shiftR`       (I# i#) = I64# (x# `iShiftRA#` i#)
        (I64# x#) `unsafeShiftR` (I# i#) = I64# (x# `uncheckedIShiftRA#` i#)
        (I64# x#) `rotate` (I# i#)
            | isTrue# (i'# ==# 0#)
            = I64# x#
            | otherwise
            = I64# (word2Int# ((x'# `uncheckedShiftL#` i'#) `or#`
                               (x'# `uncheckedShiftRL#` (64# -# i'#))))
            where
            !x'# = int2Word# x#
            !i'# = word2Int# (int2Word# i# `and#` 63##)
        bitSizeMaybe i             = Just (finiteBitSize i)
        bitSize i                  = finiteBitSize i
        isSigned _                 = True
        popCount (I64# x#)         = I# (word2Int# (popCnt64# (int2Word# x#)))
        bit                        = bitDefault
        testBit                    = testBitDefault

    {-# RULES
    "fromIntegral/a->Int64" fromIntegral = \x -> case fromIntegral x of I# x# -> I64# x#
    "fromIntegral/Int64->a" fromIntegral = \(I64# x#) -> fromIntegral (I# x#)
      #-}

    {-# RULES
    "properFraction/Float->(Int64,Float)"
        properFraction = \x ->
                          case properFraction x of {
                            (n, y) -> ((fromIntegral :: Int -> Int64) n, y :: Float) }
    "truncate/Float->Int64"
        truncate = (fromIntegral :: Int -> Int64) . (truncate :: Float -> Int)
    "floor/Float->Int64"
        floor    = (fromIntegral :: Int -> Int64) . (floor :: Float -> Int)
    "ceiling/Float->Int64"
        ceiling  = (fromIntegral :: Int -> Int64) . (ceiling :: Float -> Int)
    "round/Float->Int64"
        round    = (fromIntegral :: Int -> Int64) . (round  :: Float -> Int)
      #-}

    {-# RULES
    "properFraction/Double->(Int64,Double)"
        properFraction = \x ->
                          case properFraction x of {
                            (n, y) -> ((fromIntegral :: Int -> Int64) n, y :: Double) }
    "truncate/Double->Int64"
        truncate = (fromIntegral :: Int -> Int64) . (truncate :: Double -> Int)
    "floor/Double->Int64"
        floor    = (fromIntegral :: Int -> Int64) . (floor :: Double -> Int)
    "ceiling/Double->Int64"
        ceiling  = (fromIntegral :: Int -> Int64) . (ceiling :: Double -> Int)
    "round/Double->Int64"
        round    = (fromIntegral :: Int -> Int64) . (round  :: Double -> Int)
      #-}

    uncheckedIShiftL64# :: Int# -> Int# -> Int#
    uncheckedIShiftL64#  = uncheckedIShiftL#

    uncheckedIShiftRA64# :: Int# -> Int# -> Int#
    uncheckedIShiftRA64# = uncheckedIShiftRA#
    #endif

    -- | @since 4.6.0.0
    instance FiniteBits Int64 where
        finiteBitSize _ = 64
    #if WORD_SIZE_IN_BITS < 64
        countLeadingZeros  (I64# x#) = I# (word2Int# (clz64# (int64ToWord64# x#)))
        countTrailingZeros (I64# x#) = I# (word2Int# (ctz64# (int64ToWord64# x#)))
    #else
        countLeadingZeros  (I64# x#) = I# (word2Int# (clz64# (int2Word# x#)))
        countTrailingZeros (I64# x#) = I# (word2Int# (ctz64# (int2Word# x#)))
    #endif

    -- | @since 2.01
    instance Real Int64 where
        toRational x = toInteger x % 1

    -- | @since 2.01
    instance Bounded Int64 where
        minBound = -0x8000000000000000
        maxBound =  0x7FFFFFFFFFFFFFFF

    -- | @since 2.01
    instance Ix Int64 where
        range (m,n)         = [m..n]
        unsafeIndex (m,_) i = fromIntegral i - fromIntegral m
        inRange (m,n) i     = m <= i && i <= n

    {- Note [Order of tests]
    ~~~~~~~~~~~~~~~~~~~~~~~~~
    (See Trac #3065, #5161.) Suppose we had a definition like:

        quot x y
         | y == 0                     = divZeroError
         | x == minBound && y == (-1) = overflowError
         | otherwise                  = x `primQuot` y

    Note in particular that the
        x == minBound
    test comes before the
        y == (-1)
    test.

    this expands to something like:

        case y of
        0 -> divZeroError
        _ -> case x of
             -9223372036854775808 ->
                 case y of
                 -1 -> overflowError
                 _ -> x `primQuot` y
             _ -> x `primQuot` y

    Now if we have the call (x `quot` 2), and quot gets inlined, then we get:

        case 2 of
        0 -> divZeroError
        _ -> case x of
             -9223372036854775808 ->
                 case 2 of
                 -1 -> overflowError
                 _ -> x `primQuot` 2
             _ -> x `primQuot` 2

    which simplifies to:

        case x of
        -9223372036854775808 -> x `primQuot` 2
        _                    -> x `primQuot` 2

    Now we have a case with two identical branches, which would be
    eliminated (assuming it doesn't affect strictness, which it doesn't in
    this case), leaving the desired:

        x `primQuot` 2

    except in the minBound branch we know what x is, and GHC cleverly does
    the division at compile time, giving:

        case x of
        -9223372036854775808 -> -4611686018427387904
        _                    -> x `primQuot` 2

    So instead we use a definition like:

        quot x y
         | y == 0                     = divZeroError
         | y == (-1) && x == minBound = overflowError
         | otherwise                  = x `primQuot` y

    which gives us:

        case y of
        0 -> divZeroError
        -1 ->
            case x of
            -9223372036854775808 -> overflowError
            _ -> x `primQuot` y
        _ -> x `primQuot` y

    for which our call (x `quot` 2) expands to:

        case 2 of
        0 -> divZeroError
        -1 ->
            case x of
            -9223372036854775808 -> overflowError
            _ -> x `primQuot` 2
        _ -> x `primQuot` 2

    which simplifies to:

        x `primQuot` 2

    as required.

    But we now have the same problem with a constant numerator: the call
    (2 `quot` y) expands to

        case y of
        0 -> divZeroError
        -1 ->
            case 2 of
            -9223372036854775808 -> overflowError
            _ -> 2 `primQuot` y
        _ -> 2 `primQuot` y

    which simplifies to:

        case y of
        0 -> divZeroError
        -1 -> 2 `primQuot` y
        _ -> 2 `primQuot` y

    which simplifies to:

        case y of
        0 -> divZeroError
        -1 -> -2
        _ -> 2 `primQuot` y

    However, constant denominators are more common than constant numerators,
    so the
        y == (-1) && x == minBound
    order gives us better code in the common case.
    -}