<div dir="ltr"><div class="gmail_extra"><div class="gmail_quote">On 20 February 2015 at 17:49, Nick Lewycky <span dir="ltr"><<a href="mailto:nlewycky@google.com" target="_blank">nlewycky@google.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div class="gmail_extra"><div class="gmail_quote"><span class="">On 20 February 2015 at 17:41, Sanjoy Das <span dir="ltr"><<a href="mailto:sanjoy@playingwithpointers.com" target="_blank">sanjoy@playingwithpointers.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><span>> It's hard to do multiplication of ConstantRanges precisely, and multiply<br>
> does have a TODO requesting improvement. The problems start once you have<br>
> multiplies that can wrap. What you need to solve for is the max and min of<br>
> each of the multiplies (cartesian product) in modulo 2^n space. Because we<br>
> need to push the resulting set into a constant range, what it looks like is<br>
> "how far > 0 is the lowest value" and "how far < UINT_MAX is the highest<br>
> value", with no interesting information about the values in the middle.<br>
<br>
</span>Just to make sure I understand you: this problem isn't really limited<br>
to cases that actually wrap -- i32 [1, 4) * i32 [3, 4) == i32 {3, 6,<br>
9} and this structure is lost when we coerce the result to [3, 10).<br></blockquote><div><br></div></span><div>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.</div><div><br></div><div>Consider i8 [1, 4) * i8 [9, 10).</div></div></div></div></blockquote><div><br></div><div>Uhm, I meant to say "i8 [1, 86) * i8 [9, 10)". That's quite a typo.</div><div><br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div class="gmail_extra"><div class="gmail_quote"><div> 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.</div><span class="HOEnZb"><font color="#888888"><div><br></div><div>Nick</div></font></span><div><div class="h5"><div><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">
I wonder how crazy it is to have the notion of a first-class<br>
ConstantRange "expression" (i.e. remembering that a ConstantRange is<br>
i32 [1, 4) * i32 [3, 4) and not eagerly flattening it).<br></blockquote><div> <br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><span><font color="#888888">-- Sanjoy<br>
</font></span><div><div><br>
><br>
> Nick<br>
><br>
>><br>
>> > On 20 Feb 2015, at 23:48, Sanjoy Das <<a href="mailto:sanjoy@playingwithpointers.com" target="_blank">sanjoy@playingwithpointers.com</a>><br>
>> > wrote:<br>
>> ><br>
>> >> Actually, I don't think there is any need for a separate smultiply<br>
>> >> when we're working on two's complement. IMHO, the right solution is<br>
>> >> to just make ConstantRange::multiply smarter about handing cases like<br>
>> >> [-1,2) * [-1,2) etc.<br>
>> >><br>
>> >> -- Sanjoy<br>
>> >><br>
>> >> On Fri, Feb 20, 2015 at 3:40 PM, Sanjoy Das<br>
>> >> <<a href="mailto:sanjoy@playingwithpointers.com" target="_blank">sanjoy@playingwithpointers.com</a>> wrote:<br>
>> >>> I don't think so:<br>
>> >>><br>
>> >>> [-3,0) * [-3, 0) should be [1, 10) but using your formula I get [3,<br>
>> >>> <something>).<br>
>> >>><br>
>> >>> On Fri, Feb 20, 2015 at 3:31 PM, Hal Finkel <<a href="mailto:hfinkel@anl.gov" target="_blank">hfinkel@anl.gov</a>> wrote:<br>
>> >>>> ----- Original Message -----<br>
>> >>>>> From: "Sanjoy Das" <<a href="mailto:sanjoy@playingwithpointers.com" target="_blank">sanjoy@playingwithpointers.com</a>><br>
>> >>>>> To: <a href="mailto:reviews%2BD7789%2Bpublic%2Bffa7549bb8a7b441@reviews.llvm.org" target="_blank">reviews+D7789+public+ffa7549bb8a7b441@reviews.llvm.org</a><br>
>> >>>>> Cc: "james molloy" <<a href="mailto:james.molloy@arm.com" target="_blank">james.molloy@arm.com</a>>, "Hal Finkel"<br>
>> >>>>> <<a href="mailto:hfinkel@anl.gov" target="_blank">hfinkel@anl.gov</a>>, "Commit Messages and Patches for LLVM"<br>
>> >>>>> <<a href="mailto:llvm-commits@cs.uiuc.edu" target="_blank">llvm-commits@cs.uiuc.edu</a>><br>
>> >>>>> Sent: Friday, February 20, 2015 5:11:46 PM<br>
>> >>>>> Subject: Re: [PATCH] [ConstantRange] Add a smultiply method for<br>
>> >>>>> signed multiply<br>
>> >>>>><br>
>> >>>>>> ConstantRange<br>
>> >>>>>> +ConstantRange::smultiply(const ConstantRange &Other) const {<br>
>> >>>>>> + // TODO: If either operand is a single element and the multiply<br>
>> >>>>>> is known to<br>
>> >>>>>> + // be non-wrapping, round the result min and max value to the<br>
>> >>>>>> appropriate<br>
>> >>>>>> + // multiple of that element. If wrapping is possible, at least<br>
>> >>>>>> adjust the<br>
>> >>>>>> + // range according to the greatest power-of-two factor of the<br>
>> >>>>>> single element.<br>
>> >>>>>> +<br>
>> >>>>>> + if (isEmptySet() || Other.isEmptySet())<br>
>> >>>>>> + return ConstantRange(getBitWidth(), /*isFullSet=*/false);<br>
>> >>>>>> +<br>
>> >>>>>> + APInt this_min = getSignedMin().sext(getBitWidth() * 2);<br>
>> >>>>>> + APInt this_max = getSignedMax().sext(getBitWidth() * 2);<br>
>> >>>>>> + APInt Other_min = Other.getSignedMin().sext(getBitWidth() * 2);<br>
>> >>>>>> + APInt Other_max = Other.getSignedMax().sext(getBitWidth() * 2);<br>
>> >>>>>> +<br>
>> >>>>>> + ConstantRange Result_zext = ConstantRange(this_min * Other_min,<br>
>> >>>>>> + this_max * Other_max +<br>
>> >>>>>> 1);<br>
>> >>>>>> + return Result_zext.truncate(getBitWidth());<br>
>> >>>>><br>
>> >>>>> I'm not sure if this is correct: if we multiply [-1, 2) with<br>
>> >>>>> itself,<br>
>> >>>>> won't this return [1, 2)? Shouldn't [-1,2) * [-1,2) be [-1,2)?<br>
>> >>>><br>
>> >>>> Indeed. The minimum should not be this_min * Other_min, but rather<br>
>> >>>> min(this_min * Other_max, this_max * Other_min), right?<br>
>> >>>><br>
>> >>>> -Hal<br>
>> >>>><br>
>> >>>>><br>
>> >>>>> -- Sanjoy<br>
>> >>>>><br>
>> >>>><br>
>> >>>> --<br>
>> >>>> Hal Finkel<br>
>> >>>> Assistant Computational Scientist<br>
>> >>>> Leadership Computing Facility<br>
>> >>>> Argonne National Laboratory<br>
>> >><br>
>> ><br>
>> ><br>
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