GHC/Int.hs

{-# 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.
-}