[PATCH] [ConstantRange] Add a smultiply method for signed multiply

[James Molloy]

Hi Sanjoy,

OK, I agree with you that abstractly the resulting range is sign independent. However, the algorithm to calculate the range isn’t; further up the thread we suggested that the lower bound of the resulting range is the minimum of the cartesian product of the lowers and uppers of the inputs:

lower_multiply(a, b)  = min(
  [a.lower * b.lower, a.lower * b.upper, a.upper * b.lower, a.upper * b.upper]
);

Similarly for the upper bound substituting min with max. Surely here a signed minimum would produce a different value to an unsigned minimum?

Thanks for bearing with me, I feel like I’m being rather slow on the uptake here.

Cheers,

James


On 21 Feb 2015, at 19:22, Sanjoy Das <sanjoy at playingwithpointers.com> wrote:

>> [-2,0) * [-4,4)
>> Consider the trivial case: i8 [254,0) * i8 [252,4). In signed arithmetic,we
>> get:
>> a[0] * b[0] = 8
>> a[1] * b[1] = 0
>> a[0] * b[1] = -8
>> a[1] * b[0] = 0
>
> I'm not sure this is correct -- a[0]*b[1] == 254 * 253 == i8 6 no?
> Maybe I misunderstood the subscript notation?
>
>> So depending on the signedness of the minimum/maximum operation, we get
>> different results. Therefore, we do need a signed version of multiply.
>
> The max and min operations are already signedness-dependent
> (ConstantRange has getSignedMax and getUnsignedMax as you know); but
> computing the resulting range shouldn't be.
>
> "i8 [254,0) * i8 [252,4)" is "i8 [250, 9)".  The signed max of the
> result range is 8 while the unsigned max of that same range is 255.
> Similar story for min.
>
> Now it is possible that due to some reason the result for i8 [254,0) *
> i8 [252,4) computed by ::multiply is more conservative than [250,9).
> In that case, it is ::multiply that should be fixed since we have a
> case where it can be taught to be compute a better result.
>
> -- Sanjoy
>


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