# Handling overflow and division by zero

Edward Kmett ekmett at gmail.com
Sun Jun 28 22:30:14 UTC 2015

```You should be able to reduce the bit-twiddling a great deal IIRC in the
word case.

SW a + SW b
| c <- a + b, c >= min a b = SW c
| otherwise = throw Overflow

There is a similar trick that escapes me at the moment for the signed case.

On Sun, Jun 28, 2015 at 6:15 PM, Nikita Karetnikov <nikita at karetnikov.org>
wrote:

> Haskell is often marketed as a safe (or safer) language, but there's
> an issue that makes it less safe as it could be.  I'm talking about
> arithmetic overflows and division by zero.  The safeint package tries
> to address this, but it only supports the Int type because (as I
> understand it) there are no useful primitives for other common types
> defined in Data.Int and Data.Word.
>
> I've tried adding Int64 support to safeint just to see how it would work
> without primops.  Here's a snippet (I haven't tested this code well, so
> it may be wrong, sorry about that):
>
> shiftRUnsigned :: Word64 -> Int -> Word64
> shiftRUnsigned = shiftR
>
> --
> plusSI64 :: SafeInt64 -> SafeInt64 -> SafeInt64
> plusSI64 (SI64 a) (SI64 b) = if c == 0 then SI64 r else overflowError
>   where
>     r = a + b
>     c = (fromIntegral \$ (complement (a `xor` b)) .&. (a `xor` r))
>         `shiftRUnsigned`
>         ((finiteBitSize a) - 1)
>
> --
> minusSI64 :: SafeInt64 -> SafeInt64 -> SafeInt64
> minusSI64 (SI64 a) (SI64 b) = if c == 0 then SI64 r else overflowError
>   where
>     r = a - b
>     c = (fromIntegral \$ (a `xor` b) .&. (a `xor` r))
>         `shiftRUnsigned`
>         ((finiteBitSize a) - 1)
>
> -- https://stackoverflow.com/a/1815371
> timesSI64 :: SafeInt64 -> SafeInt64 -> SafeInt64
> timesSI64 (SI64 a) (SI64 b) =
>   let x = a * b
>   in if a /= 0 && x `div` a /= b
>      then overflowError
>      else SI64 x
>
> I may be wrong, but my understanding is that new primops could reduce
> overhead here.  If so, would a patch adding them be accepted?  Are
> there any caveats?
>
> In the safeint package, would it be reasonable to return an Either
> value instead of throwing an exception?  Or would it be too much?
>
> I haven't created a wiki page or ticket because I don't know much, so
> I want to get some feedback before doing so.  That would be my first
> patch to GHC (if ever), so maybe I'm not the best candidate, but I've
> been thinking about it for too long to ignore. :\
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