From a07504ab09e4c63e7ef25c13e4e97466c36a651a Mon Sep 17 00:00:00 2001 From: Ian Lynagh Date: Sat, 30 Apr 2011 15:52:57 +0100 Subject: [PATCH] Add a note about the definition of quot etc Based on Simon PJ's text in #5161. --- GHC/Int.hs | 197 +++++++++++++++++++++++++++++++++++++++++++++++----------- GHC/Real.lhs | 18 ++++-- 2 files changed, 173 insertions(+), 42 deletions(-) diff --git a/GHC/Int.hs b/GHC/Int.hs index 3746d3d..7a42bb3 100644 --- a/GHC/Int.hs +++ b/GHC/Int.hs @@ -88,28 +88,28 @@ instance Enum Int8 where instance Integral Int8 where quot x@(I8# x#) y@(I8# y#) | y == 0 = divZeroError - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = 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# @@ -230,28 +230,28 @@ instance Enum Int16 where instance Integral Int16 where quot x@(I16# x#) y@(I16# y#) | y == 0 = divZeroError - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = 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# @@ -384,28 +384,28 @@ instance Enum Int32 where instance Integral Int32 where quot x@(I32# x#) y@(I32# y#) | y == 0 = divZeroError - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = overflowError + | y == (-1) && x == minBound = overflowError -- Note [Order of tests] | otherwise = (I32# (x# `divInt32#` y#), I32# (x# `modInt32#` y#)) toInteger x@(I32# x#) @@ -513,28 +513,28 @@ instance Enum Int32 where instance Integral Int32 where quot x@(I32# x#) y@(I32# y#) | y == 0 = divZeroError - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = 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# @@ -672,28 +672,28 @@ instance Enum Int64 where instance Integral Int64 where quot x@(I64# x#) y@(I64# y#) | y == 0 = divZeroError - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = overflowError + | y == (-1) && x == minBound = overflowError -- Note [Order of tests] | otherwise = (I64# (x# `divInt64#` y#), I64# (x# `modInt64#` y#)) toInteger (I64# x) = int64ToInteger x @@ -805,27 +805,27 @@ instance Enum Int64 where instance Integral Int64 where quot x@(I64# x#) y@(I64# y#) | y == 0 = divZeroError - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = 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 - | y == (-1) && x == minBound = overflowError + | y == (-1) && x == minBound = overflowError -- Note [Order of tests] | otherwise = (I64# (x# `divInt#` y#), I64# (x# `modInt#` y#)) toInteger (I64# x#) = smallInteger x# @@ -907,3 +907,128 @@ instance Ix Int64 where range (m,n) = [m..n] unsafeIndex (m,_) i = fromIntegral i - fromIntegral m inRange (m,n) i = m <= i && i <= n + +{- +Note [Order of tests] + +Suppose we had a definition like: + + quot x y + | y == 0 = divZeroError + | x == minBound && y == (-1) = overflowError + | otherwise = x `primQuot` y + +Note in particular that the + x == minBound +test comes before the + y == (-1) +test. + +this expands to something like: + + case y of + 0 -> divZeroError + _ -> case x of + -9223372036854775808 -> + case y of + -1 -> overflowError + _ -> x `primQuot` y + _ -> x `primQuot` y + +Now if we have the call (x `quot` 2), and quot gets inlined, then we get: + + case 2 of + 0 -> divZeroError + _ -> case x of + -9223372036854775808 -> + case 2 of + -1 -> overflowError + _ -> x `primQuot` 2 + _ -> x `primQuot` 2 + +which simplifies to: + + case x of + -9223372036854775808 -> x `primQuot` 2 + _ -> x `primQuot` 2 + +Now we have a case with two identical branches, which would be +eliminated (assuming it doesn't affect strictness, which it doesn't in +this case), leaving the desired: + + x `primQuot` 2 + +except in the minBound branch we know what x is, and GHC cleverly does +the division at compile time, giving: + + case x of + -9223372036854775808 -> -4611686018427387904 + _ -> x `primQuot` 2 + +So instead we use a definition like: + + quot x y + | y == 0 = divZeroError + | y == (-1) && x == minBound = overflowError + | otherwise = x `primQuot` y + +which gives us: + + case y of + 0 -> divZeroError + -1 -> + case x of + -9223372036854775808 -> overflowError + _ -> x `primQuot` y + _ -> x `primQuot` y + +for which our call (x `quot` 2) expands to: + + case 2 of + 0 -> divZeroError + -1 -> + case x of + -9223372036854775808 -> overflowError + _ -> x `primQuot` 2 + _ -> x `primQuot` 2 + +which simplifies to: + + x `primQuot` 2 + +as required. + + + +But we now have the same problem with a constant numerator: the call +(2 `quot` y) expands to + + case y of + 0 -> divZeroError + -1 -> + case 2 of + -9223372036854775808 -> overflowError + _ -> 2 `primQuot` y + _ -> 2 `primQuot` y + +which simplifies to: + + case y of + 0 -> divZeroError + -1 -> 2 `primQuot` y + _ -> 2 `primQuot` y + +which simplifies to: + + case y of + 0 -> divZeroError + -1 -> -2 + _ -> 2 `primQuot` y + + +However, constant denominators are more common than constant numerators, +so the + y == (-1) && x == minBound +order gives us better code in the common case. +-} + diff --git a/GHC/Real.lhs b/GHC/Real.lhs index fa70ded..17d0452 100644 --- a/GHC/Real.lhs +++ b/GHC/Real.lhs @@ -245,32 +245,38 @@ instance Integral Int where a `quot` b | b == 0 = divZeroError - | b == (-1) && a == minBound = overflowError + | b == (-1) && a == minBound = overflowError -- Note [Order of tests] + -- in GHC.Int | otherwise = a `quotInt` b a `rem` b | b == 0 = divZeroError - | b == (-1) && a == minBound = overflowError + | b == (-1) && a == minBound = overflowError -- Note [Order of tests] + -- in GHC.Int | otherwise = a `remInt` b a `div` b | b == 0 = divZeroError - | b == (-1) && a == minBound = overflowError + | b == (-1) && a == minBound = overflowError -- Note [Order of tests] + -- in GHC.Int | otherwise = a `divInt` b a `mod` b | b == 0 = divZeroError - | b == (-1) && a == minBound = overflowError + | b == (-1) && a == minBound = overflowError -- Note [Order of tests] + -- in GHC.Int | otherwise = a `modInt` b a `quotRem` b | b == 0 = divZeroError - | b == (-1) && a == minBound = overflowError + | b == (-1) && a == minBound = overflowError -- Note [Order of tests] + -- in GHC.Int | otherwise = a `quotRemInt` b a `divMod` b | b == 0 = divZeroError - | b == (-1) && a == minBound = overflowError + | b == (-1) && a == minBound = overflowError -- Note [Order of tests] + -- in GHC.Int | otherwise = a `divModInt` b \end{code} -- 1.7.10.4