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

[Nick Lewycky]

On 20 February 2015 at 17:41, Sanjoy Das <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). 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>
> >> > 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> 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>
> wrote:
> >> >>>> ----- Original Message -----
> >> >>>>> From: "Sanjoy Das" <sanjoy at playingwithpointers.com>
> >> >>>>> To: reviews+D7789+public+ffa7549bb8a7b441 at reviews.llvm.org
> >> >>>>> Cc: "james molloy" <james.molloy at arm.com>, "Hal Finkel"
> >> >>>>> <hfinkel at anl.gov>, "Commit Messages and Patches for LLVM"
> >> >>>>> <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
> >> >>>>>> adjust the
> >> >>>>>> +  // 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
> >> >>>> Leadership Computing Facility
> >> >>>> Argonne National Laboratory
> >> >>
> >> >
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