-1796254192 `div` 357566600 == 5 ??

[Dylan Thurston]

On Fri, Jun 28, 2002 at 10:24:13AM +0100, Malcolm Wallace wrote:
> Yes,    -5`div`2  ==  -(5`div`2)  ==  -2
> but   (-5)`div`2  ==  -3
> 
> Ghc 5.02.2 has the infix priority wrong, and interprets the former as the latter.
> But more bizarrely, ghc 5.02.2 gets this very wrong:
> 
>     Prelude> (-1796254192) `div` 357566600
>     5

Thanks for the clear summary.

I've investigated a little, and I think I've found the problem.  Note
that 1796254192 and 357566600 are less than 2^31, so the division is
done with short integers; however, there sum is bigger than 2^31.  Now
look at this code from PrelBase.hs:

> divInt#, modInt# :: Int# -> Int# -> Int#
> x# `divInt#` y#
>     | (x# ># 0#) && (y# <# 0#) = ((x# -# y#) -# 1#) `quotInt#` y#
>     | (x# <# 0#) && (y# ># 0#) = ((x# -# y#) +# 1#) `quotInt#` y#
>     | otherwise                = x# `quotInt#` y#
> x# `modInt#` y#
>     | (x# ># 0#) && (y# <# 0#) ||
>       (x# <# 0#) && (y# ># 0#)    = if r# /=# 0# then r# +# y# else 0#
>     | otherwise                   = r#
>     where
>     r# = x# `remInt#` y#

This was obviously written with no thought to possible overflow.  This
code is from 5.02.2, but the same code seems to be in the CVS version
(in libraries/base/GHC/Base.lhs).

Assuming that quotInt# is correct, a version of divInt# which is
correct (I believe) is

> divInt# :: Int# -> Int# -> Int#
> x# `divInt#` y#
>     | (x# ># 0#) && (y# <# 0#) = (x# -# 1#) `quotInt#` y# -# 1#
>     | (x# <# 0#) && (y# ># 0#) = (x# +# 1#) `quotInt#` y# -# 1#
>     | otherwise                = x# `quotInt#` y#

By the way, a more efficient and transparent implementation of modInt#
is

> x# `modInt#` y# = if r# <# 0# then r# +# y# else r#
>   where r# = x# `remInt#` y#

Best,
	Dylan Thurston
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