Handling overflow and division by zero

[Nikita Karetnikov]

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

-- http://git.haskell.org/ghc.git/blob/HEAD:/compiler/codeGen/StgCmmPrim.hs#l930
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)

-- http://git.haskell.org/ghc.git/blob/HEAD:/compiler/codeGen/StgCmmPrim.hs#l966
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. :\