llvm dev - Aug 2016 - SCEV LoopTripCount

Hello,

I was doing some experiments with SCEV and especially the loop trip count.
Sorry for the dumb question, what is the easiest way to dump SCEV analysis
results on a .bc file?

On a side note, I wanted to see if we could optimize this function:

unsigned long kernel(long w, long h, long d) {
unsigned long count = 0;
for(int i = 0; i < w; ++i)
for(int j = i; j < h; ++j)
for(int k = j; k < d; ++k)
++count;
return count;
}

into this (it might not take into account overflows, it was generated using
the barvinok library):

unsigned long kernel2(long w, long h, long d) {
return
(-1 + w >= 0 && -1 - w + h >= 0 && -1 - h + d >= 0)
? (((((2 * w - 3 * w*w + w*w*w) + 3 * w * h + -3 * w * h*h) + ((3 * w - 3 *
w*w) + 6 * w * h) * d))/6)
: (-1 + w >= 0 && -1 - w + d >= 0 && h - d >= 0)
? ((((2 * w - 3 * w*w + w*w*w) + (6 * w - 3 * w*w) * d + 3 * w * d*d))/6)
: (-1 + h >= 0 && w - h >= 0 && -1 - h + d >= 0)
? ((((2 * h - 2 * h*h*h) + (3 * h + 3 * h*h) * d))/6)
: (-1 + d >= 0 && h - d >= 0 && w - d >= 0)
? (((2 * d + 3 * d*d + d*d*d))/6)
: 0;
}

I am not sure how advanced are SCEV-based trip counts.

Best regards.

-- 
*Alexandre Isoard*
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Hi,
> On Aug 9, 2016, at 6:39 PM, Alexandre Isoard via llvm-dev <llvm-dev at
lists.llvm.org> wrote:
> 
> Hello,
> 
> I was doing some experiments with SCEV and especially the loop trip count.
> Sorry for the dumb question, what is the easiest way to dump SCEV analysis
results on a .bc file?
opt -analyze -scalar-evolution < file.bc
> 
> On a side note, I wanted to see if we could optimize this function:
> 
> unsigned long kernel(long w, long h, long d) {
> 	unsigned long count = 0;
> 	for(int i = 0; i < w; ++i)
> 		for(int j = i; j < h; ++j)
> 			for(int k = j; k < d; ++k)
> 				++count;
> 	return count;
> }
> 
> into this (it might not take into account overflows, it was generated using
the barvinok library):
Looks like we can not, but I haven’t examined why. Overflows might indeed get
into the way.

Michael
> unsigned long kernel2(long w, long h, long d) {
> 	return
> 		(-1 + w >= 0 && -1 - w + h >= 0 && -1 - h + d >=
0)
> 		? (((((2 * w - 3 * w*w + w*w*w) + 3 * w * h + -3 * w * h*h) + ((3 * w - 3
* w*w) + 6 * w * h) * d))/6)
> 		: (-1 + w >= 0 && -1 - w + d >= 0 && h - d >= 0)
> 		? ((((2 * w - 3 * w*w + w*w*w) + (6 * w - 3 * w*w) * d + 3 * w * d*d))/6)
> 		: (-1 + h >= 0 && w - h >= 0 && -1 - h + d >= 0)
> 		? ((((2 * h - 2 * h*h*h) + (3 * h + 3 * h*h) * d))/6)
> 		: (-1 + d >= 0 && h - d >= 0 && w - d >= 0)
> 		? (((2 * d + 3 * d*d + d*d*d))/6)
> 		: 0;
> }
> 
> I am not sure how advanced are SCEV-based trip counts.
> 
> Best regards.
> 
> -- 
> Alexandre Isoard
> _______________________________________________
> LLVM Developers mailing list
> llvm-dev at lists.llvm.org
> http://lists.llvm.org/cgi-bin/mailman/listinfo/llvm-dev
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(Hit reply-all this time :) )

I'm doing this on a old clang/llvm build (from June 29), but if I
generate IR by

clang -mllvm -unroll-threshold=0 -O3 -S -emit-llvm -fno-vectorize x.c -o 
x.ll

(loop unrolling and vectorization both tend to obscure trip count
computation)

then we are able to compute the trip counts in whatever loops that
remain:

Loop %for.cond8.preheader: backedge-taken count is {(-1 + 
%h),+,-1}<nw><%for.cond2.preheader>
Loop %for.cond8.preheader: max backedge-taken count is -1
Loop %for.cond2.preheader: backedge-taken count is (-1 + %w)
Loop %for.cond2.preheader: max backedge-taken count is -1



It isn't clear to me why indvars does not fold way all the loops out
of existence (it is "clearly profitable" in this case).  I'll try
to
take a closer look tonight.

-- Sanjoy


Michael Zolotukhin via llvm-dev wrote:
 >
 > unsigned long kernel(long w, long h, long d) {
 > unsigned long count = 0;
 > for(int i = 0; i < w; ++i)
 > for(int j = i; j < h; ++j)
 > for(int k = j; k < d; ++k)
 > ++count;
 > return count;
 > }

Michael Zolotukhin via llvm-dev wrote:
> Hi,
>
>> On Aug 9, 2016, at 6:39 PM, Alexandre Isoard via llvm-dev
>> <llvm-dev at lists.llvm.org <mailto:llvm-dev at
lists.llvm.org>> wrote:
>>
>> Hello,
>>
>> I was doing some experiments with SCEV and especially the loop trip
count.
>> Sorry for the dumb question, what is the easiest way to dump SCEV
>> analysis results on a .bc file?
> opt -analyze -scalar-evolution < file.bc
>
>>
>> On a side note, I wanted to see if we could optimize this function:
>>
>> unsigned long kernel(long w, long h, long d) {
>> unsigned long count = 0;
>> for(int i = 0; i < w; ++i)
>> for(int j = i; j < h; ++j)
>> for(int k = j; k < d; ++k)
>> ++count;
>> return count;
>> }
>>
>> into this (it might not take into account overflows, it was generated
>> using the barvinok library):
> Looks like we can not, but I haven’t examined why. Overflows might
> indeed get into the way.
>
> Michael
>
>> unsigned long kernel2(long w, long h, long d) {
>> return
>> (-1 + w >= 0 && -1 - w + h >= 0 && -1 - h + d
>= 0)
>> ? (((((2 * w - 3 * w*w + w*w*w) + 3 * w * h + -3 * w * h*h) + ((3 * w
>> - 3 * w*w) + 6 * w * h) * d))/6)
>> : (-1 + w >= 0 && -1 - w + d >= 0 && h - d >=
0)
>> ? ((((2 * w - 3 * w*w + w*w*w) + (6 * w - 3 * w*w) * d + 3 * w *
d*d))/6)
>> : (-1 + h >= 0 && w - h >= 0 && -1 - h + d >=
0)
>> ? ((((2 * h - 2 * h*h*h) + (3 * h + 3 * h*h) * d))/6)
>> : (-1 + d >= 0 && h - d >= 0 && w - d >= 0)
>> ? (((2 * d + 3 * d*d + d*d*d))/6)
>> : 0;
>> }
>>
>> I am not sure how advanced are SCEV-based trip counts.
>>
>> Best regards.
>>
>> --
>> *Alexandre Isoard*
>> _______________________________________________
>> LLVM Developers mailing list
>> llvm-dev at lists.llvm.org <mailto:llvm-dev at lists.llvm.org>
>> http://lists.llvm.org/cgi-bin/mailman/listinfo/llvm-dev
>
> _______________________________________________
> LLVM Developers mailing list
> llvm-dev at lists.llvm.org
> http://lists.llvm.org/cgi-bin/mailman/listinfo/llvm-dev

Thank you for the fast answer.

On Tue, Aug 9, 2016 at 6:51 PM, Michael Zolotukhin <mzolotukhin at
apple.com>
wrote:
> Hi,
>
> On Aug 9, 2016, at 6:39 PM, Alexandre Isoard via llvm-dev <
> llvm-dev at lists.llvm.org> wrote:
>
> Hello,
>
> I was doing some experiments with SCEV and especially the loop trip count.
> Sorry for the dumb question, what is the easiest way to dump SCEV analysis
> results on a .bc file?
>
> opt -analyze -scalar-evolution < file.bc
>
Perfect. Thank you.
>
> On a side note, I wanted to see if we could optimize this function:
>
> unsigned long kernel(long w, long h, long d) {
> unsigned long count = 0;
> for(int i = 0; i < w; ++i)
> for(int j = i; j < h; ++j)
> for(int k = j; k < d; ++k)
> ++count;
> return count;
> }
>
>
> into this (it might not take into account overflows, it was generated
> using the barvinok library):
>
> Looks like we can not, but I haven’t examined why. Overflows might indeed
> get into the way.
>
Also I wrongfully used int as induction variables instead of long.
But even after this correction, playing with unsignedness does not improve
the situation. (even with all signed or all unsigned)

However, I came to realise that the first code could be improved into:

long kernel2(long w, long h, long d) {
using std::min;
long count = 0;
for (long i = 0; i < min(min(w, h), d); ++i)
for (long j = i; j < min(h, d); ++j)
for (long k = j; k < d; ++k)
++count;
return count;
}

That is, removing dead loop iterations. Do we perform this kind of
transformation? (when we can compute SCEV)
>
> Michael
>
> unsigned long kernel2(long w, long h, long d) {
> return
> (-1 + w >= 0 && -1 - w + h >= 0 && -1 - h + d >=
0)
> ? (((((2 * w - 3 * w*w + w*w*w) + 3 * w * h + -3 * w * h*h) + ((3 * w - 3
> * w*w) + 6 * w * h) * d))/6)
> : (-1 + w >= 0 && -1 - w + d >= 0 && h - d >= 0)
> ? ((((2 * w - 3 * w*w + w*w*w) + (6 * w - 3 * w*w) * d + 3 * w * d*d))/6)
> : (-1 + h >= 0 && w - h >= 0 && -1 - h + d >= 0)
> ? ((((2 * h - 2 * h*h*h) + (3 * h + 3 * h*h) * d))/6)
> : (-1 + d >= 0 && h - d >= 0 && w - d >= 0)
> ? (((2 * d + 3 * d*d + d*d*d))/6)
> : 0;
> }
>
> I am not sure how advanced are SCEV-based trip counts.
>
> Best regards.
>
> --
> *Alexandre Isoard*
> _______________________________________________
> LLVM Developers mailing list
> llvm-dev at lists.llvm.org
> http://lists.llvm.org/cgi-bin/mailman/listinfo/llvm-dev
>
>
>
Regards.

-- 
*Alexandre Isoard*
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