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

James Molloy James.Molloy at arm.com
Sat Feb 21 03:58:39 PST 2015

```Hi Nick, all,

Firstly apologies for not creating a unit test. I thought this was totally trivial and it turns out it’s completely not.

When wrapping, it is sufficient for my use case to know that we’ve wrapped. I don’t care about what we represent a wrapped value as (where we pick the gap).

Discounting wrapping for the moment, it seems to me that while multiplication is signedness-independent, minimum and maximum are not.

[-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

min: -8, max: 8

In unsigned arithmetic we get:
a[0] * b[0] = 8
a[1] * b[1] = 0
a[0] * b[1] = 248
a[1] * b[0] = 0

min: 8, max: 248 ( =-8 )

So depending on the signedness of the minimum/maximum operation, we get different results. Therefore, we do need a signed version of multiply.

That’s as far as my logic takes me, could someone please point out where I’ve gone wrong?

Cheers,

James

On 21 Feb 2015, at 02:11, Nick Lewycky <nlewycky at google.com<mailto:nlewycky at google.com>> wrote:

On 20 February 2015 at 17:49, Nick Lewycky <nlewycky at google.com<mailto:nlewycky at google.com>> wrote:
On 20 February 2015 at 17:41, Sanjoy Das <sanjoy at playingwithpointers.com<mailto:sanjoy at playingwithpointers.com>> wrote:
> It's hard to do multiplication of ConstantRanges precisely, and multiply
> does have a TODO requesting improvement. The problems start once you have
> multiplies that can wrap. What you need to solve for is the max and min of
> each of the multiplies (cartesian product) in modulo 2^n space. Because we
> need to push the resulting set into a constant range, what it looks like is
> "how far > 0 is the lowest value" and "how far < UINT_MAX is the highest
> value", with no interesting information about the values in the middle.

Just to make sure I understand you:  this problem isn't really limited
to cases that actually wrap -- i32 [1, 4) * i32 [3, 4) == i32 {3, 6,
9} and this structure is lost when we coerce the result to [3, 10).

I wasn't considering that a problem. ConstantRange::multiply today precisely produces the range [3, 10) in that case. There is no improvement to be made.

Consider i8 [1, 4) * i8 [9, 10).

Uhm, I meant to say "i8 [1, 86) * i8 [9, 10)". That's quite a typo.

The best possible range is [1, 253), but our implementation will return the full set. That's really hard to get right. We extend the bit range to twice the bit range so that we can do the multiply algebraically, then we call truncate. Truncate correctly detects that we cover the whole span of integers in the bitwidth and returns the full set.

Nick

I wonder how crazy it is to have the notion of a first-class
ConstantRange "expression" (i.e. remembering that a ConstantRange is
i32 [1, 4) * i32 [3, 4) and not eagerly flattening it).

-- Sanjoy

>
> Nick
>
>>
>> > On 20 Feb 2015, at 23:48, Sanjoy Das <sanjoy at playingwithpointers.com<mailto:sanjoy at playingwithpointers.com>>
>> > wrote:
>> >
>> >> Actually, I don't think there is any need for a separate smultiply
>> >> when we're working on two's complement.  IMHO, the right solution is
>> >> to just make ConstantRange::multiply smarter about handing cases like
>> >> [-1,2) * [-1,2) etc.
>> >>
>> >> -- Sanjoy
>> >>
>> >> On Fri, Feb 20, 2015 at 3:40 PM, Sanjoy Das
>> >> <sanjoy at playingwithpointers.com<mailto:sanjoy at playingwithpointers.com>> wrote:
>> >>> I don't think so:
>> >>>
>> >>> [-3,0) * [-3, 0) should be [1, 10) but using your formula I get [3,
>> >>> <something>).
>> >>>
>> >>> On Fri, Feb 20, 2015 at 3:31 PM, Hal Finkel <hfinkel at anl.gov<mailto:hfinkel at anl.gov>> wrote:
>> >>>> ----- Original Message -----
>> >>>>> From: "Sanjoy Das" <sanjoy at playingwithpointers.com<mailto:sanjoy at playingwithpointers.com>>
>> >>>>> To: reviews+D7789+public+ffa7549bb8a7b441 at reviews.llvm.org<mailto:reviews%2BD7789%2Bpublic%2Bffa7549bb8a7b441 at reviews.llvm.org>
>> >>>>> Cc: "james molloy" <james.molloy at arm.com<mailto:james.molloy at arm.com>>, "Hal Finkel"
>> >>>>> <hfinkel at anl.gov<mailto:hfinkel at anl.gov>>, "Commit Messages and Patches for LLVM"
>> >>>>> <llvm-commits at cs.uiuc.edu<mailto:llvm-commits at cs.uiuc.edu>>
>> >>>>> Sent: Friday, February 20, 2015 5:11:46 PM
>> >>>>> Subject: Re: [PATCH] [ConstantRange] Add a smultiply method for
>> >>>>> signed multiply
>> >>>>>
>> >>>>>> ConstantRange
>> >>>>>> +ConstantRange::smultiply(const ConstantRange &Other) const {
>> >>>>>> +  // TODO: If either operand is a single element and the multiply
>> >>>>>> is known to
>> >>>>>> +  // be non-wrapping, round the result min and max value to the
>> >>>>>> appropriate
>> >>>>>> +  // multiple of that element. If wrapping is possible, at least
>> >>>>>> +  // range according to the greatest power-of-two factor of the
>> >>>>>> single element.
>> >>>>>> +
>> >>>>>> +  if (isEmptySet() || Other.isEmptySet())
>> >>>>>> +    return ConstantRange(getBitWidth(), /*isFullSet=*/false);
>> >>>>>> +
>> >>>>>> +  APInt this_min = getSignedMin().sext(getBitWidth() * 2);
>> >>>>>> +  APInt this_max = getSignedMax().sext(getBitWidth() * 2);
>> >>>>>> +  APInt Other_min = Other.getSignedMin().sext(getBitWidth() * 2);
>> >>>>>> +  APInt Other_max = Other.getSignedMax().sext(getBitWidth() * 2);
>> >>>>>> +
>> >>>>>> +  ConstantRange Result_zext = ConstantRange(this_min * Other_min,
>> >>>>>> +                                            this_max * Other_max +
>> >>>>>> 1);
>> >>>>>> +  return Result_zext.truncate(getBitWidth());
>> >>>>>
>> >>>>> I'm not sure if this is correct:  if we multiply [-1, 2) with
>> >>>>> itself,
>> >>>>> won't this return [1, 2)?  Shouldn't [-1,2) * [-1,2) be [-1,2)?
>> >>>>
>> >>>> Indeed. The minimum should not be this_min * Other_min, but rather
>> >>>> min(this_min * Other_max, this_max * Other_min), right?
>> >>>>
>> >>>> -Hal
>> >>>>
>> >>>>>
>> >>>>> -- Sanjoy
>> >>>>>
>> >>>>
>> >>>> --
>> >>>> Hal Finkel
>> >>>> Assistant Computational Scientist
>> >>>> Argonne National Laboratory
>> >>
>> >
>> >
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