GHC/Int.hs

    {-# LANGUAGE Trustworthy #-}
    {-# LANGUAGE CPP, NoImplicitPrelude, BangPatterns, MagicHash, UnboxedTuples,
                 StandaloneDeriving, DeriveDataTypeable, 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 (
            Int8(..), Int16(..), Int32(..), Int64(..),
            uncheckedIShiftL64#, uncheckedIShiftRA64#
        ) 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
    import GHC.Float ()     -- for RealFrac methods
    import Data.Typeable

    ------------------------------------------------------------------------
    -- 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# deriving (Eq, Ord, Typeable)
    -- ^ 8-bit signed integer type

    instance Show Int8 where
        showsPrec p x = showsPrec p (fromIntegral x :: Int)

    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))

    instance Real Int8 where
        toRational x = toInteger x % 1

    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

    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#

    instance Bounded Int8 where
        minBound = -0x80
        maxBound =  0x7F

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

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

    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# (int2Word# x# `xor#` int2Word# (-1#)))
        (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

    instance FiniteBits Int8 where
        finiteBitSize _ = 8

    {-# 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# deriving (Eq, Ord, Typeable)
    -- ^ 16-bit signed integer type

    instance Show Int16 where
        showsPrec p x = showsPrec p (fromIntegral x :: Int)

    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))

    instance Real Int16 where
        toRational x = toInteger x % 1

    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

    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#

    instance Bounded Int16 where
        minBound = -0x8000
        maxBound =  0x7FFF

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

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

    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# (int2Word# x# `xor#` int2Word# (-1#)))
        (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

    instance FiniteBits Int16 where
        finiteBitSize _ = 16

    {-# 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# deriving (Eq, Ord, Typeable)
    -- ^ 32-bit signed integer type

    instance Show Int32 where
        showsPrec p x = showsPrec p (fromIntegral x :: Int)

    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))

    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

    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#

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

    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# (int2Word# x# `xor#` int2Word# (-1#)))
        (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

    instance FiniteBits Int32 where
        finiteBitSize _ = 32

    {-# 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)
      #-}

    instance Real Int32 where
        toRational x = toInteger x % 1

    instance Bounded Int32 where
        minBound = -0x80000000
        maxBound =  0x7FFFFFFF

    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# deriving( Typeable )
    -- ^ 64-bit signed integer type

    instance Eq Int64 where
        (I64# x#) == (I64# y#) = isTrue# (x# `eqInt64#` y#)
        (I64# x#) /= (I64# y#) = isTrue# (x# `neInt64#` y#)

    instance Ord Int64 where
        (I64# x#) <  (I64# y#) = isTrue# (x# `ltInt64#` y#)
        (I64# x#) <= (I64# y#) = isTrue# (x# `leInt64#` y#)
        (I64# x#) >  (I64# y#) = isTrue# (x# `gtInt64#` y#)
        (I64# x#) >= (I64# y#) = isTrue# (x# `geInt64#` y#)

    instance Show Int64 where
        showsPrec p x = showsPrec p (toInteger x)

    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)

    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

    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#

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

    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# deriving (Eq, Ord, Typeable)
    -- ^ 64-bit signed integer type

    instance Show Int64 where
        showsPrec p x = showsPrec p (fromIntegral x :: Int)

    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)

    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

    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#

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

    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

    instance FiniteBits Int64 where
        finiteBitSize _ = 64

    instance Real Int64 where
        toRational x = toInteger x % 1

    instance Bounded Int64 where
        minBound = -0x8000000000000000
        maxBound =  0x7FFFFFFFFFFFFFFF

    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]

    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.
    -}