-{-# OPTIONS_GHC -XNoImplicitPrelude #-}
+{-# LANGUAGE CPP, NoImplicitPrelude, BangPatterns, MagicHash,
+ StandaloneDeriving #-}
{-# OPTIONS_HADDOCK hide #-}
-----------------------------------------------------------------------------
-- |
import GHC.Err
import GHC.Word hiding (uncheckedShiftL64#, uncheckedShiftRL64#)
import GHC.Show
+import GHC.Float () -- for RealFrac methods
+-- For defining instances for the new generic deriving mechanism
+--import GHC.Generics (Arity(..), Associativity(..), Fixity(..))
------------------------------------------------------------------------
-- type Int8
instance Integral Int8 where
quot x@(I8# x#) y@(I8# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = I8# (narrow8Int# (x# `quotInt#` y#))
rem x@(I8# x#) y@(I8# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = I8# (narrow8Int# (x# `remInt#` y#))
div x@(I8# x#) y@(I8# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = I8# (narrow8Int# (x# `divInt#` y#))
mod x@(I8# x#) y@(I8# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = I8# (narrow8Int# (x# `modInt#` y#))
quotRem x@(I8# x#) y@(I8# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = (I8# (narrow8Int# (x# `quotInt#` y#)),
I8# (narrow8Int# (x# `remInt#` y#)))
divMod x@(I8# x#) y@(I8# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = (I8# (narrow8Int# (x# `divInt#` y#)),
I8# (narrow8Int# (x# `modInt#` y#)))
toInteger (I8# x#) = smallInteger x#
= I8# (narrow8Int# (word2Int# ((x'# `uncheckedShiftL#` i'#) `or#`
(x'# `uncheckedShiftRL#` (8# -# i'#)))))
where
- x'# = narrow8Word# (int2Word# x#)
- i'# = word2Int# (int2Word# i# `and#` int2Word# 7#)
+ !x'# = narrow8Word# (int2Word# x#)
+ !i'# = word2Int# (int2Word# i# `and#` int2Word# 7#)
bitSize _ = 8
isSigned _ = True
- {-# INLINE shiftR #-}
- -- same as the default definition, but we want it inlined (#2376)
- x `shiftR` i = x `shift` (-i)
-
{-# 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)"
+ forall x. properFraction (x :: Float) =
+ case properFraction x of {
+ (n, y) -> ((fromIntegral :: Int -> Int8) n, y) }
+"truncate/Float->Int8"
+ forall x. truncate (x :: Float) = (fromIntegral :: Int -> Int8) (truncate x)
+"floor/Float->Int8"
+ forall x. floor (x :: Float) = (fromIntegral :: Int -> Int8) (floor x)
+"ceiling/Float->Int8"
+ forall x. ceiling (x :: Float) = (fromIntegral :: Int -> Int8) (ceiling x)
+"round/Float->Int8"
+ forall x. round (x :: Float) = (fromIntegral :: Int -> Int8) (round x)
+ #-}
+
+{-# RULES
+"properFraction/Double->(Int8,Double)"
+ forall x. properFraction (x :: Double) =
+ case properFraction x of {
+ (n, y) -> ((fromIntegral :: Int -> Int8) n, y) }
+"truncate/Double->Int8"
+ forall x. truncate (x :: Double) = (fromIntegral :: Int -> Int8) (truncate x)
+"floor/Double->Int8"
+ forall x. floor (x :: Double) = (fromIntegral :: Int -> Int8) (floor x)
+"ceiling/Double->Int8"
+ forall x. ceiling (x :: Double) = (fromIntegral :: Int -> Int8) (ceiling x)
+"round/Double->Int8"
+ forall x. round (x :: Double) = (fromIntegral :: Int -> Int8) (round x)
+ #-}
+
------------------------------------------------------------------------
-- type Int16
------------------------------------------------------------------------
instance Integral Int16 where
quot x@(I16# x#) y@(I16# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = I16# (narrow16Int# (x# `quotInt#` y#))
rem x@(I16# x#) y@(I16# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = I16# (narrow16Int# (x# `remInt#` y#))
div x@(I16# x#) y@(I16# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = I16# (narrow16Int# (x# `divInt#` y#))
mod x@(I16# x#) y@(I16# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = I16# (narrow16Int# (x# `modInt#` y#))
quotRem x@(I16# x#) y@(I16# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = (I16# (narrow16Int# (x# `quotInt#` y#)),
I16# (narrow16Int# (x# `remInt#` y#)))
divMod x@(I16# x#) y@(I16# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = (I16# (narrow16Int# (x# `divInt#` y#)),
I16# (narrow16Int# (x# `modInt#` y#)))
toInteger (I16# x#) = smallInteger x#
= I16# (narrow16Int# (word2Int# ((x'# `uncheckedShiftL#` i'#) `or#`
(x'# `uncheckedShiftRL#` (16# -# i'#)))))
where
- x'# = narrow16Word# (int2Word# x#)
- i'# = word2Int# (int2Word# i# `and#` int2Word# 15#)
+ !x'# = narrow16Word# (int2Word# x#)
+ !i'# = word2Int# (int2Word# i# `and#` int2Word# 15#)
bitSize _ = 16
isSigned _ = True
- {-# INLINE shiftR #-}
- -- same as the default definition, but we want it inlined (#2376)
- x `shiftR` i = x `shift` (-i)
{-# RULES
"fromIntegral/Word8->Int16" fromIntegral = \(W8# x#) -> I16# (word2Int# x#)
"fromIntegral/Int16->a" fromIntegral = \(I16# x#) -> fromIntegral (I# x#)
#-}
+{-# RULES
+"properFraction/Float->(Int16,Float)"
+ forall x. properFraction (x :: Float) =
+ case properFraction x of {
+ (n, y) -> ((fromIntegral :: Int -> Int16) n, y) }
+"truncate/Float->Int16"
+ forall x. truncate (x :: Float) = (fromIntegral :: Int -> Int16) (truncate x)
+"floor/Float->Int16"
+ forall x. floor (x :: Float) = (fromIntegral :: Int -> Int16) (floor x)
+"ceiling/Float->Int16"
+ forall x. ceiling (x :: Float) = (fromIntegral :: Int -> Int16) (ceiling x)
+"round/Float->Int16"
+ forall x. round (x :: Float) = (fromIntegral :: Int -> Int16) (round x)
+ #-}
+
+{-# RULES
+"properFraction/Double->(Int16,Double)"
+ forall x. properFraction (x :: Double) =
+ case properFraction x of {
+ (n, y) -> ((fromIntegral :: Int -> Int16) n, y) }
+"truncate/Double->Int16"
+ forall x. truncate (x :: Double) = (fromIntegral :: Int -> Int16) (truncate x)
+"floor/Double->Int16"
+ forall x. floor (x :: Double) = (fromIntegral :: Int -> Int16) (floor x)
+"ceiling/Double->Int16"
+ forall x. ceiling (x :: Double) = (fromIntegral :: Int -> Int16) (ceiling x)
+"round/Double->Int16"
+ forall x. round (x :: Double) = (fromIntegral :: Int -> Int16) (round x)
+ #-}
+
------------------------------------------------------------------------
-- type Int32
------------------------------------------------------------------------
instance Integral Int32 where
quot x@(I32# x#) y@(I32# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = I32# (x# `quotInt32#` y#)
rem x@(I32# x#) y@(I32# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = I32# (x# `remInt32#` y#)
div x@(I32# x#) y@(I32# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = I32# (x# `divInt32#` y#)
mod x@(I32# x#) y@(I32# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = I32# (x# `modInt32#` y#)
quotRem x@(I32# x#) y@(I32# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = (I32# (x# `quotInt32#` y#),
I32# (x# `remInt32#` y#))
divMod x@(I32# x#) y@(I32# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = (I32# (x# `divInt32#` y#),
I32# (x# `modInt32#` y#))
toInteger x@(I32# x#)
bitSize _ = 32
isSigned _ = True
- {-# INLINE shiftR #-}
- -- same as the default definition, but we want it inlined (#2376)
- x `shiftR` i = x `shift` (-i)
{-# RULES
"fromIntegral/Int->Int32" fromIntegral = \(I# x#) -> I32# (intToInt32# x#)
"fromIntegral/Int32->Int32" fromIntegral = id :: Int32 -> Int32
#-}
-#else
+-- No rules for RealFrac methods if Int32 is larger than Int
+#else
-- Int32 is represented in the same way as Int.
#if WORD_SIZE_IN_BITS > 32
instance Integral Int32 where
quot x@(I32# x#) y@(I32# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = I32# (narrow32Int# (x# `quotInt#` y#))
rem x@(I32# x#) y@(I32# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = I32# (narrow32Int# (x# `remInt#` y#))
div x@(I32# x#) y@(I32# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = I32# (narrow32Int# (x# `divInt#` y#))
mod x@(I32# x#) y@(I32# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = I32# (narrow32Int# (x# `modInt#` y#))
quotRem x@(I32# x#) y@(I32# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = (I32# (narrow32Int# (x# `quotInt#` y#)),
I32# (narrow32Int# (x# `remInt#` y#)))
divMod x@(I32# x#) y@(I32# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = (I32# (narrow32Int# (x# `divInt#` y#)),
I32# (narrow32Int# (x# `modInt#` y#)))
toInteger (I32# x#) = smallInteger x#
= I32# (narrow32Int# (word2Int# ((x'# `uncheckedShiftL#` i'#) `or#`
(x'# `uncheckedShiftRL#` (32# -# i'#)))))
where
- x'# = narrow32Word# (int2Word# x#)
- i'# = word2Int# (int2Word# i# `and#` int2Word# 31#)
+ !x'# = narrow32Word# (int2Word# x#)
+ !i'# = word2Int# (int2Word# i# `and#` int2Word# 31#)
bitSize _ = 32
isSigned _ = True
- {-# INLINE shiftR #-}
- -- same as the default definition, but we want it inlined (#2376)
- x `shiftR` i = x `shift` (-i)
-
{-# RULES
"fromIntegral/Word8->Int32" fromIntegral = \(W8# x#) -> I32# (word2Int# x#)
"fromIntegral/Word16->Int32" fromIntegral = \(W16# x#) -> I32# (word2Int# x#)
"fromIntegral/Int32->a" fromIntegral = \(I32# x#) -> fromIntegral (I# x#)
#-}
-#endif
+{-# RULES
+"properFraction/Float->(Int32,Float)"
+ forall x. properFraction (x :: Float) =
+ case properFraction x of {
+ (n, y) -> ((fromIntegral :: Int -> Int32) n, y) }
+"truncate/Float->Int32"
+ forall x. truncate (x :: Float) = (fromIntegral :: Int -> Int32) (truncate x)
+"floor/Float->Int32"
+ forall x. floor (x :: Float) = (fromIntegral :: Int -> Int32) (floor x)
+"ceiling/Float->Int32"
+ forall x. ceiling (x :: Float) = (fromIntegral :: Int -> Int32) (ceiling x)
+"round/Float->Int32"
+ forall x. round (x :: Float) = (fromIntegral :: Int -> Int32) (round x)
+ #-}
+
+{-# RULES
+"properFraction/Double->(Int32,Double)"
+ forall x. properFraction (x :: Double) =
+ case properFraction x of {
+ (n, y) -> ((fromIntegral :: Int -> Int32) n, y) }
+"truncate/Double->Int32"
+ forall x. truncate (x :: Double) = (fromIntegral :: Int -> Int32) (truncate x)
+"floor/Double->Int32"
+ forall x. floor (x :: Double) = (fromIntegral :: Int -> Int32) (floor x)
+"ceiling/Double->Int32"
+ forall x. ceiling (x :: Double) = (fromIntegral :: Int -> Int32) (ceiling x)
+"round/Double->Int32"
+ forall x. round (x :: Double) = (fromIntegral :: Int -> Int32) (round x)
+ #-}
+
+#endif
instance Real Int32 where
toRational x = toInteger x % 1
instance Integral Int64 where
quot x@(I64# x#) y@(I64# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = I64# (x# `quotInt64#` y#)
rem x@(I64# x#) y@(I64# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = I64# (x# `remInt64#` y#)
div x@(I64# x#) y@(I64# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = I64# (x# `divInt64#` y#)
mod x@(I64# x#) y@(I64# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = I64# (x# `modInt64#` y#)
quotRem x@(I64# x#) y@(I64# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = (I64# (x# `quotInt64#` y#),
I64# (x# `remInt64#` y#))
divMod x@(I64# x#) y@(I64# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = (I64# (x# `divInt64#` y#),
I64# (x# `modInt64#` y#))
toInteger (I64# x) = int64ToInteger x
= if r# `neInt64#` intToInt64# 0# then r# `plusInt64#` y# else intToInt64# 0#
| otherwise = r#
where
- r# = x# `remInt64#` y#
+ !r# = x# `remInt64#` y#
instance Read Int64 where
readsPrec p s = [(fromInteger x, r) | (x, r) <- readsPrec p s]
= I64# (word64ToInt64# ((x'# `uncheckedShiftL64#` i'#) `or64#`
(x'# `uncheckedShiftRL64#` (64# -# i'#))))
where
- x'# = int64ToWord64# x#
- i'# = word2Int# (int2Word# i# `and#` int2Word# 63#)
+ !x'# = int64ToWord64# x#
+ !i'# = word2Int# (int2Word# i# `and#` int2Word# 63#)
bitSize _ = 64
isSigned _ = True
- {-# INLINE shiftR #-}
- -- same as the default definition, but we want it inlined (#2376)
- x `shiftR` i = x `shift` (-i)
-
-
-- 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
"fromIntegral/Int64->Int64" fromIntegral = id :: Int64 -> Int64
#-}
-#else
+-- 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
instance Integral Int64 where
quot x@(I64# x#) y@(I64# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = I64# (x# `quotInt#` y#)
rem x@(I64# x#) y@(I64# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = I64# (x# `remInt#` y#)
div x@(I64# x#) y@(I64# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = I64# (x# `divInt#` y#)
mod x@(I64# x#) y@(I64# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = I64# (x# `modInt#` y#)
quotRem x@(I64# x#) y@(I64# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = (I64# (x# `quotInt#` y#), I64# (x# `remInt#` y#))
divMod x@(I64# x#) y@(I64# y#)
| y == 0 = divZeroError
- | x == minBound && y == (-1) = overflowError
+ | y == (-1) && x == minBound = overflowError -- Note [Order of tests]
| otherwise = (I64# (x# `divInt#` y#), I64# (x# `modInt#` y#))
toInteger (I64# x#) = smallInteger x#
= I64# (word2Int# ((x'# `uncheckedShiftL#` i'#) `or#`
(x'# `uncheckedShiftRL#` (64# -# i'#))))
where
- x'# = int2Word# x#
- i'# = word2Int# (int2Word# i# `and#` int2Word# 63#)
+ !x'# = int2Word# x#
+ !i'# = word2Int# (int2Word# i# `and#` int2Word# 63#)
bitSize _ = 64
isSigned _ = True
- {-# INLINE shiftR #-}
- -- same as the default definition, but we want it inlined (#2376)
- x `shiftR` i = x `shift` (-i)
-
{-# 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)"
+ forall x. properFraction (x :: Float) =
+ case properFraction x of {
+ (n, y) -> ((fromIntegral :: Int -> Int64) n, y) }
+"truncate/Float->Int64"
+ forall x. truncate (x :: Float) = (fromIntegral :: Int -> Int64) (truncate x)
+"floor/Float->Int64"
+ forall x. floor (x :: Float) = (fromIntegral :: Int -> Int64) (floor x)
+"ceiling/Float->Int64"
+ forall x. ceiling (x :: Float) = (fromIntegral :: Int -> Int64) (ceiling x)
+"round/Float->Int64"
+ forall x. round (x :: Float) = (fromIntegral :: Int -> Int64) (round x)
+ #-}
+
+{-# RULES
+"properFraction/Double->(Int64,Double)"
+ forall x. properFraction (x :: Double) =
+ case properFraction x of {
+ (n, y) -> ((fromIntegral :: Int -> Int64) n, y) }
+"truncate/Double->Int64"
+ forall x. truncate (x :: Double) = (fromIntegral :: Int -> Int64) (truncate x)
+"floor/Double->Int64"
+ forall x. floor (x :: Double) = (fromIntegral :: Int -> Int64) (floor x)
+"ceiling/Double->Int64"
+ forall x. ceiling (x :: Double) = (fromIntegral :: Int -> Int64) (ceiling x)
+"round/Double->Int64"
+ forall x. round (x :: Double) = (fromIntegral :: Int -> Int64) (round x)
+ #-}
+
uncheckedIShiftL64# :: Int# -> Int# -> Int#
uncheckedIShiftL64# = uncheckedIShiftL#
range (m,n) = [m..n]
unsafeIndex (m,_) i = fromIntegral i - fromIntegral m
inRange (m,n) i = m <= i && i <= n
+
+------------------------------------------------------------------------
+-- Generic deriving
+------------------------------------------------------------------------
+
+-- We need instances for some basic datatypes, but some of those use Int,
+-- so we have to put the instances here
+{-
+deriving instance Eq Arity
+deriving instance Eq Associativity
+deriving instance Eq Fixity
+
+deriving instance Ord Arity
+deriving instance Ord Associativity
+deriving instance Ord Fixity
+
+deriving instance Read Arity
+deriving instance Read Associativity
+deriving instance Read Fixity
+
+deriving instance Show Arity
+deriving instance Show Associativity
+deriving instance Show Fixity
+-}
+
+{-
+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.
+-}
projects / ghc-base.git / blobdiff