content: {-# LANGUAGE Trustworthy #-}
  {-# LANGUAGE CPP, NoImplicitPrelude, BangPatterns, MagicHash, UnboxedTuples,
               StandaloneDeriving, AutoDeriveTypeable, 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 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# (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
  
  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# 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# (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
  
  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# 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# (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
  
  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)
    #-}
  
  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
  #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
  
  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]
  ~~~~~~~~~~~~~~~~~~~~~~~~~
  (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.
  -}
  