pslp: padded slp automatic vectorization€¦ · slp vectorization algorithm • input is scalar ir...

PSLP: Padded SLP

Automatic Vectorization

Vasileios Porpodas†, Alberto Magni‡

and Timothy M. Jones†

University of Cambridge†

University of Edinburgh‡

EuroLLVM APR 2015

slide 1 of 17 www.cl.cam.ac.uk/ ∼vp331/

www.cl.cam.ac.uk/~vp331/

Why SIMD Vectorization?

• Scalable parallelism

Scalar Func. Units

Scalar Reg. File

a. ILP

FUFUFUFU





0 1 2 3

Vector Reg. File

b. Vector ParallelismScalar Func. Units

Scalar Reg. File

a. ILP

FUFUFUFU

Vector Unit





• High Performance0 1 2 3

Vector Reg. File


Scalar Reg. File

a. ILP

FUFUFUFU

Vector Unit





• High Performance

• Energy efficiency0 1 2 3

Vector Reg. File


Scalar Reg. File

a. ILP

FUFUFUFU

Vector Unit






• Energy efficiency

• Supported since mid 90’s

• Frequent updates of vectorISAs

0 1 2 3

Vector Reg. File


Scalar Reg. File

a. ILP

FUFUFUFU

Vector Unit

AVX2

SSE4






• Energy efficiency

• Supported since mid 90’s

• Frequent updates of vectorISAs

• Vector generation notdone in hardware

• Low-level programming orcapable compiler

0 1 2 3

Vector Reg. File


Scalar Reg. File

a. ILP

FUFUFUFU

Vector Unit

AVX2

SSE4



SLP Straight-Line Code Vectorizer

• Superword Level Parallelism [Larsen PLDI’00]


http://dx.doi.org/10.1145/349299.349320




• State-of-the-art straight-line code vectorizer


http://dx.doi.org/10.1145/349299.349320





• Implemented in most compilers (including GCC andLLVM)


http://dx.doi.org/10.1145/349299.349320






• In theory it should be a superset of loop-vectorizer


http://dx.doi.org/10.1145/349299.349320






• In theory it should be a superset of loop-vectorizer• Unroll loop and vectorize with SLP• Even if loop-vectorizer fails, SLP could partly succeed


http://dx.doi.org/10.1145/349299.349320






• In theory it should be a superset of loop-vectorizer• Unroll loop and vectorize with SLP• Even if loop-vectorizer fails, SLP could partly succeed

• In practice it is missing features present in the Loopvectorizer (Interleaved Loads, Predication)


http://dx.doi.org/10.1145/349299.349320


SLP Vectorization Algorithm

• Input is scalar IR

Scalar Code




• Input is scalar IR• Seed instructions are:

1 Consecutive Stores2 Reductions

Find vectorizationseed instructions1.

Scalar Code






• Graph contains vectorizableisomorphic instructions


Scalar Code

2.Generate graph of

isomorphic scalar groups







• Cost: weighted instr. count


CalculateVector Cost

CalculateScalar Cost3.

Scalar Code

2.Generate graph of









• Check vectorization profitability




4.If<Vector Cost

Scalar Cost

Scalar Code

2.Generate graph of










• Emit vectors only if profitable




4.If<Vector Cost

Scalar Cost

Vectorize groups& emit vectors

YES

5.

DONE

Scalar Code

2.Generate graph of










• Emit vectors only if profitable




4.If<Vector Cost

Scalar Cost

Vectorize groups& emit vectors

YES

5.

NO

DONE

Scalar Code

2.Generate graph of




When SLP Fails

1 Data DependenciesADD3ADD1 ADD2

ADD4



When SLP Fails

1 Data Dependencies

2 Too manygather/scatterinstructions. Costsoutweigh benefits.

ADD3ADD1 ADD2ADD4

ADD1ADD2ADD3ADD4

Original Vectorized

ADD1 ADD2 ADD3 ADD4

Insert1Insert2Insert3Insert4

Extract1Extract2Extract3Extract4



When SLP Fails

1 Data Dependencies

2 Too manygather/scatterinstructions. Costsoutweigh benefits.

3 Non-isomorphism

ADD3ADD1 ADD2ADD4

ADD1ADD2ADD3ADD4

Original Vectorized

ADD1 ADD2 ADD3 ADD4

Insert1Insert2Insert3Insert4

Extract1Extract2Extract3Extract4

ADD1 ADD2 ADD4MUL



SLP Fails due to non-isomorphism

X Instruction Node or Constant Data Flow Edge

a. Input C code

...

...

B[i] = A[i] * 7.0 + 1.0;B[i+1]= A[i+1] + 5.0;





S S

L

L

+

*

+

a. Input C code

...

...

7.

1. 5.

B[i] = A[i] * 7.0 + 1.0;B[i+1]= A[i+1] + 5.0;

b. DFG





S S

L

L

SS

+

*

+

a. Input C code

...

...

7.

1. 5.

S S 0

B[i] = A[i] * 7.0 + 1.0;B[i+1]= A[i+1] + 5.0;

b. DFG c. SLP internal graph d. SLP vectorized groups





S S

L

L

SS

+

*

+

a. Input C code

...

...

7.

1. 5.

S S

+ +

0

1

B[i] = A[i] * 7.0 + 1.0;B[i+1]= A[i+1] + 5.0;


++





S S

L

L

SS

+

*

+

a. Input C code

STOP !NON−ISOMORPHIC

* L

...

...

L

1. 5.

7.

1. 5.

7.

S S

+ +

0

1

2 L*

B[i] = A[i] * 7.0 + 1.0;B[i+1]= A[i+1] + 5.0;


++





S S

L

L

SS

+

S

+

*

*

+

a. Input C code


* L

...

...

L

1. 5.

7.

1. 5.

7.

S S

+ +

0

1

2 L*

B[i] = A[i] * 7.0 + 1.0;B[i+1]= A[i+1] + 5.0;

Scalar Cost


LL

S

+

++

7





S S

L

L

SS

SS

LL

+

S

+

*

*

+

a. Input C code


* L

...

...

L

1. 5.

7.

1. 5.

7.

S S

+ +

0

1

2 L*

B[i] = A[i] * 7.0 + 1.0;B[i+1]= A[i+1] + 5.0;

Vector CostScalar Cost


NoBenefit

LL

S

+

++

7 7*

ii++



PSLP fixes Non-Isomorphism

S

L

+

S

*

7.

1.

a. PSLP graphs

+

L 5.

Data Flow EdgeInstruction or ConstantX




S

L

S

L

S

L

+

S

+ +

*

*7.

1.

b. PSLP padded graphsa. PSLP graphs

7.

1. 5.

+

L 5.





S

L

S

L

S

L

+

S

+ +

*

* *7.

1.


7.

1.

7.

5.

+

L 5.





S

L

S

L

S

L

+

S

+ +

*

* *7.

1.


7.

1.

7.

5.Left Right

+

L 5.

Select Instruction Data Flow EdgeInstruction or ConstantX




S

L

S

L

S

L

+

S

+ +

*

* *7.

1.

c. PSLP groupsb. PSLP padded graphsa. PSLP graphs

7.

1.

7.

5.

1

2

0 S S

++

3 **

4 L L

Left Right+

L 5.





S

L

S

L

S

L

+

S

+ +

*

* *7.

1.

c. PSLP groupsb. PSLP padded graphsa. PSLP graphs

7.

1.

7.

5.

1

2

0 S S

++

3 **

4 L L

Left Right 5+

L 5.




PSLP Algorithm

• Extension to SLP



PSLP Algorithm


1. Find vectorization seed instructions



PSLP Algorithm


• Generate multiplegraphs (unlike SLP)

Generate a graph for each seed2.




PSLP Algorithm



• Minimal Padding

3. Perform minimal Padding of graphs





PSLP Algorithm



• Minimal Padding

• Cost estimation

CalculateScalar Cost



4.Calculate PaddedVector Cost





PSLP Algorithm



• Minimal Padding

• Cost estimation



IfPadded Cost

is best5.







PSLP Algorithm



• Minimal Padding

• Cost estimation

• Emit redundant codeto createisomorphism



IfPadded Cost

is best5.



Emit Padded Scalars

YES

6.





PSLP Algorithm



• Minimal Padding

• Cost estimation


7.If<Vector Cost

Scalar Cost

NO



IfPadded Cost

is best5.



Emit Padded Scalars

YES

6.





PSLP Algorithm



• Minimal Padding

• Cost estimation


• Code vectorized byoriginal SLP

YES

7.If<Vector Cost

Scalar Cost

NO



IfPadded Cost

is best5.

8.



Emit Padded Scalars

YES

6.

} Vanilla SLP

Generate a graph for each seed

9.

Generate SLP graph containinggroups of isomorphic scalars

Vectorize groups & emit vectors

2.




PSLP Algorithm



• Minimal Padding

• Cost estimation


• Code vectorized byoriginal SLP

YES

7.If<Vector Cost

Scalar Cost

NO



IfPadded Cost

is best5.

8.



Emit Padded Scalars

YES

6.

} Vanilla SLP

Generate a graph for each seed

9.

Generate SLP graph containinggroups of isomorphic scalars

Vectorize groups & emit vectors

NO

DONE

2.




Minimal Padding Algorithm

S

+*

7L

1

+

L

S

5

g1g2

Non−Isomorphic




S

+*

7L

1

+

L

S

5

g1g2

Non−Isomorphic

MCS1MCS2




S

+*

7L

1

+

L

S

5

+

L

S

1

+

L

S

5

g1g2

Non−Isomorphic

g1

g2

MCS1 MCS2MCS1MCS2




diff1

diff2

S

+*

7L

1

+

L

S

5

+

L

S

1

+

L

S

5

*

7

g1g2

Non−Isomorphic

g1

g2

L

+

L

+

MCS1 MCS2MCS1MCS2




diff1

diff2

S

+

L

1

S

5

+

L

S

+*

7L

1

+

L

S

5

+

L

S

1

+

L

S

5

*

7

g1g2

MinCS2MinCS1

Non−Isomorphic

g1

g2

L

+

L

+

MCS1 MCS2MCS1 MCS1 MCS2MCS2




diff1

diff2

S

+

L 7

*

1

S

5

+

L 7

*

S

+*

7L

1

+

L

S

5

+

L

S

1

+

L

S

5

*

7

g1g2

MinCS2MinCS1

Non−Isomorphic

g1

g2diff1diff1

L

+

L

+





diff1

diff2

S

+

L 7

*

1

S

5

+

L 7

*

S

+*

7L

1

+

L

S

5

+

L

S

1

+

L

S

5

*

7

g1g2

MinCS2MinCS1

Isomorphic !Non−Isomorphic

g1

g2diff1diff1

diff2diff2

L

+

L

+





diff1

diff2 SELECTSELECT

S

+

L 7

*

1

S

5

+

L 7

*

S

+*

7L

1

+

L

S

5

+

L

S

1

+

L

S

5

*

7

g1g2

MinCS2MinCS1

Isomorphic !Non−Isomorphic

g1

g2diff1diff1

diff2diff2

L

+

L

+

LeftRight




We can do better: Remove redundant Selects

S

L

+

S

*

EXAMPLE: Instruction acting as Select

7.

1.

+

L 5.




S

L

+

*

S

L

+

S

*

S

L

+

*

Left

7

1


7.

1.

+

L 5.

7

5

Right




S

L

+

*

S

L

+*

S

L

+

S

*

S

L

+

*

S

L

+*Left

7

17

1


7.

1.

+

L 5.

7

5

Right

1

1




S

L

+

*

S

L

+*

S

L

+

S

*

S

L

+

*

S

L

+*Left

7

17

1


7.

1.

+

L 5.

7

5

Right

1

1

1

+

C

A

a. Instruction acting as Selectslide 10 of 17 www.cl.cam.ac.uk/ ∼vp331/



S

L

+

*

S

L

+*

S

L

+

S

*

S

L

+

*

S

L

+*Left

7

17

1


7.

1.

+

L 5.

7

5

Right

1

1

A

+

0C

1

+

C

A

a. Instruction acting as Selectslide 10 of 17 www.cl.cam.ac.uk/ ∼vp331/



S

L

+

*

S

L

+*

S

L

+

S

*

S

L

+

*

S

L

+*Left

7

17

1


7.

1.

+

L 5.

7

5

Right

1

1

A

+

0C

A

72

1

+

C

A

a. Instruction acting as Select b. Select constantsslide 10 of 17 www.cl.cam.ac.uk/ ∼vp331/



S

L

+

*

S

L

+*

S

L

+

S

*

S

L

+

*

S

L

+*Left

7

17

1


7.

1.

+

L 5.

7

5

Right

1

1

A

+

0C

A

2

A

72

1

+

C

A

a. Instruction acting as Select b. Select constantsslide 10 of 17 www.cl.cam.ac.uk/ ∼vp331/



S

L

+

*

S

L

+*

S

L

+

S

*

S

L

+

*

S

L

+*Left

7

17

1


7.

1.

+

L 5.

7

5

Right

1

1

A

+

0C

A

2

A

72

A

B1

+

C

A

a. Instruction acting as Select b. Select constants c. Select same nodeslide 10 of 17 www.cl.cam.ac.uk/ ∼vp331/



S

L

+

*

S

L

+*

S

L

+

S

*

S

L

+

*

S

L

+*Left

7

17

1


7.

1.

+

L 5.

7

5

Right

1

1

A

+

0C

A

2

A

72

A

B

A

B

1

+

C

A

a. Instruction acting as Select b. Select constants c. Select same nodeslide 10 of 17 www.cl.cam.ac.uk/ ∼vp331/


Opportunities for PSLP in real-life applications

1 Non-isomorphic source code (e.g. computingconjugates in 433.milc)

a[0].reala[0].imaga[1].reala[1].imag

...

...

b[0].imag = − a[0].imag


b[0].real = a[0].real


Memory






...

...





Memory

2 Isomorphic source code but non-isomorphic IR dueto high-level optimizations (jdct of cjpeg)

tmp1 = quantval[0]*16384tmp2 = quantval[1]*22725tmp3 = quantval[2]*21407tmp4 = quantval[3]*19266






...

...





Memory

2 Isomorphic source code but non-isomorphic IR dueto high-level optimizations (jdct of cjpeg)

tmp1 = quantval[0]<<14tmp2 = quantval[1]*22725tmp3 = quantval[2]*21407tmp4 = quantval[3]*19266

tmp1 = quantval[0]*16384tmp2 = quantval[1]*22725tmp3 = quantval[2]*21407tmp4 = quantval[3]*19266

opt



Experimental Setup

• Implemented PSLP in the trunk version of theLLVM 3.6 compiler.



Experimental Setup


• Target: Intel Core i5-4570 @ 3.2Ghz



Experimental Setup



• Compiler flags: -O3 -allow-partial-unroll-march=core-avx2 -mtune-core-i7 -ffast-math



Experimental Setup




• Kernels, SPEC 2006 and Mediabench II• We evaluated the following cases:



Experimental Setup





1 All loop, SLP and PSLP vectorizers disabled (O3)



Experimental Setup





1 All loop, SLP and PSLP vectorizers disabled (O3)2 O3 + SLP enabled (SLP)



Experimental Setup





1 All loop, SLP and PSLP vectorizers disabled (O3)2 O3 + SLP enabled (SLP)3 O3 + PSLP enabled (PSLP)



PSLP increases performance

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

conjugates

su3-adjoint

make-ahmat-slow

jdct-ifastfloyd-warshall

GMean

Nor

mal

ized

Tim

e

Performance of Kernels (Execution Time)

O3 SLP PSLP

0.97

0.98

0.99

1.00

1.01

cjpegmpeg2dec

433.milc473.astar

GMean

Whole Benchmarks (Execution Time)

O3 SLP PSLP



PSLP enables or extends vectorization

0

10

20

30

40

50

conjugates

su3-adjoint

make-ahmat-slow


cjpegmpeg2dec

433.milc473.astar

Tim

es T

echn

ique

Suc

ceed

s

Vectorization Coverage Breakdown163

SLP-onlyPSLP-extends-SLP

PSLP-only

SLPonly

• SLP is adequate




0

10

20

30

40

50

conjugates

su3-adjoint

make-ahmat-slow


cjpegmpeg2dec

433.milc473.astar

Tim

es T

echn

ique

Suc

ceed

s



PSLP-only

SLPonly

PSLP extends SLP • SLP is adequate

• SLP stops at non-isomorphiccode. PSLP extends it.




0

10

20

30

40

50

conjugates

su3-adjoint

make-ahmat-slow


cjpegmpeg2dec

433.milc473.astar

Tim

es T

echn

ique

Suc

ceed

s



PSLP-only

PSLPonly

SLPonly

PSLP extends SLP • SLP is adequate

• SLP stops at non-isomorphiccode. PSLP extends it.

• SLP fails completely. PSLP

succeeds.slide 15 of 17 www.cl.cam.ac.uk/ ∼vp331/


Optimizing away redundant Selects

• Select-removal

optimizations

remove about 21%

of the Selects

0%

5%

10%

15%

20%

25%

30%

35%

conjugates

su3-adjoint

make-ahmat-slow


cjpegmpeg2dec

433.milc473.astar

GMean

Per

cent

age

of S

elec

ts

Percentage of Selects per region before and after Optimizations

Original-Selects Optimized-Selects



Conclusion

• PSLP improves vectorization coverage compared tothe state-of-the-art



Conclusion


• Converts non-isomorphic code into isomorphic by:



Conclusion


• Converts non-isomorphic code into isomorphic by:• Relying on the Min Common Supergraph for minimal

injection of redundant code



Conclusion



injection of redundant code• Emitting Select instructions to guarantee correctness



Conclusion



injection of redundant code• Emitting Select instructions to guarantee correctness• Optimizing away redundant Selects



Conclusion



injection of redundant code• Emitting Select instructions to guarantee correctness• Optimizing away redundant Selects

• PSLP performs better compared to SLP oncommodity SIMD-capable hardware



pslp: padded slp automatic vectorization€¦ · slp vectorization algorithm • input is scalar ir...

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