A Language for the Compact Representation of Multiple Program Versions

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A Language for the Compact Representation of
Multiple Program Versions

• Sébastien Donadio1,2, James Brodman3, Thomas
  Roeder4,
• Kamen Yotov4, Denis Barthou2, Albert Cohen5,
• María Jesús Garzarán3, David Padua3, and Keshav
  Pingali4

1 BULL S.A. 2 University of Versailles 3
University of Illinois at Urbana-Champaign 4
Cornell University 5 INRIA Futurs
International Workshop LCPC 2005
2
Outline

• Context in optimization for high performance
• Goals of this language
• Features of this language
• Examples (Daxpy Dgemm)
• Conclusion

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Context

• Complex architecture and fragile optimizations
• Unpredictable performance
• Architecture, domain-specific optimizations
• Resort to empirical search
• Complement general-purpose optimizations with
  user-driven ones

4
Example FFT performance
best available implementation (FFTW, Intel IPP,
Spiral)
Reasonable implementation (Numerical recipes. GNU
scientific library)
5
Goals of X-Language

• Tool to help programmers generate and evaluate
  multiple versions of their programs
• Applying control and data structure
  transformations
• Trying multiple transformation sequences and
  parameters
• Evaluating performance of each version and taking
  decisions about which transformation variants to
  try

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Goals of X-Language (cont.)

• The code must be portable accross ISO-C
  compilers
• Use pragma annotations for the above tasks
• Observable program semantics not altered by the
  interpretation of these pragmas (assuming
  transformation legality)

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Comparaison with related works
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Features of the language

• Elementary transformations (fission, stripmining,
  interchanging, unrolling,)
• Composition of transformations
• Conditional transformations (versioning)
• Procedural abstraction of transformations
• A mechanism to define new transformations
• No validity check is performed for the
  transformation

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General schema of X-Language
Code with Pragmas
Transformation Descriptions
search
Different versions
Compile
Execute and measure performance
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X-Language

• Naming loops or scopes
• pragma xlang name loop1
• for(i0ilt10i) ai4
• Format of transformation
• pragma xlang stripmine loop1 4 ii

Transformation name
Loop name
Name of additional loops generated by
transformations
pragma xlang
parameters
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Elementary transformations implemented in
X-language

• Full unrolling
• Partial unrolling
• Scalar promote
• Interchange
• Loop fission
• Loop fusion
• Strip mining
• Lifting
• Sofware pipelining

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Applying transformation

• pragma xlang loop1
• for(iminilt4maxi)
• aibi
• pragma xlang stripmine loop1 4 ii

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How to search the value of parameters ?

• Using multistage evaluation
• External script
• for(k1klt16k2k)
• pragma xlang loop1
• for(iminiltmaxi)
• aibi
• pragma xlang stripmine loop1 d(k) ii

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Composing transformations

• pragma xlang loop1
• for(i0ilt4i)
• pragma xlang loop2
• for(jmin2jltmax2j)
• aibj
• pragma xlang interchange loop1 loop2
• pragma xlang fullunroll loop1

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Analyses and Transformations

• Static analyses should also enable the design of
  smarter (higher level) transformation primitives
• External tool to find information

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Example with analysis
for(i2ilt2Ni2) uiui-1ui-2 ui1
uiui-1
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Extending the X-Language
Rewriting rule pragma xlang name iloop for (i
0 i lt N i) ltbodygt
pragma xlang name iiloop1 for (ii 0 ii lt
(N/4)4 ii 4) pragma xlang name
iloop1 for (i ii i lt ii4 i)
ltbodygt pragma xlang name iloop2 for (i
(N/4)4 i lt N i) f ltbodygt
Pattern before ? Pattern after transformation
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Daxpy Example

• pragma xlang name loop1
• for(k0klt2000k)
• YkalphaXkYk
• We can modify values of N
• / A few values tested for unrolling factor
  Different generated version /
• pragma xlang transform stripmine loop1 k N
• pragma xlang transform scalarize-in X in loop1
• pragma xlang transform lift l1.loads before
  loop1
• pragma xlang transform scalarize-out Y in loop1
• pragma xlang transform lift loop1.loads before
  loop1
• pragma xlang transform lift loop1.stores after
  loop1
• pragma xlang transform fullunroll loop1.loads
• pragma xlang transform fullunroll loop1.stores
• pragma xlang transform fullunroll loop1

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Daxpy Example Different generated versions
Unrolling factor 8 for(k0klt2000kk16)
double x_0 Xk0 double x_1 Xk1
double x_2 Xk2 y_0alphax_0y_0
y_1alphax_1y_1 y_2alphax_2y_2
y_3alphax_3y_3 Yk0 y_0 Yk1
y_1 Yk2 y_2 Yk3 y_3

• Unrolling factor 2
• for(k0klt2000kk2)
• double x_0 Xk0
• double x_1 Xk1
• double y_0 Yk0
• double y_1 Yk1
• y_0alphax_0y_0
• y_1alphax_1y_1
• Yk0 y_0
• Yk1 y_1

Unrolling factor 4 for(k0klt2000kk4)
double x_0 Xk0 double x_1 Xk1
double x_2 Xk2 double x_3 Xk3
double y_0 Yk0 double y_1 Yk1
double y_2 Yk2 double y_3 Yk3
y_0alphax_0y_0 y_1alphax_1y_1
y_2alphax_2y_2 y_3alphax_3y_3
Yk0 y_0 Yk1 y_1 Yk2 y_2
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Matrix Multiply(Loop Declaration)

• The DGEMM example
• Matrix Multiplication
• Problems
• Data locality
• Scheduling

• pragma xlang name iloop
• for (i 0 i lt NB i)
• pragma xlang name jloop
• for (j 0 j lt NB j)
• pragma xlang name kloop
• for (k 0 k lt NB k)
• cijcijaikbkj

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Matrix Multiply(Transformation Declaration)
Sequence of transformations for Itanium

• pragma xlang transform stripmine iloop NU NUloop
• pragma xlang transform stripmine jloop MU MUloop
• pragma xlang transform interchange kloop MUloop
• pragma xlang transform interchange jloop NUloop
• pragma xlang transform interchange kloop NUloop
• pragma xlang transform fullunroll NUloop
• pragma xlang transform fullunroll MUloop
• pragma xlang transform scalarize_in b in kloop
• pragma xlang transform scalarize_in a in kloop
• pragma xlang transform scalarize_inout c in
  kloop
• pragma xlang transform lift kloop.loads before
  kloop
• pragma xlang transform lift kloop.stores after
  kloop

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Matrix Multiply(Transformation Sequence)
pragma xlang name iloop for(i 0 i lt NB
i) pragma xlang name jloop for(j 0 j lt NB
j 4) pragma xlang name kloop.loads c_0_0
ci0j0 c_0_1 ci0j1 c_0_2
ci0j2 c_0_3 ci0j3 pragma xlang
name kloop for(k 0 k lt NB k) a_0
ai0k a_1 ai0k a_2 ai0k a_3
ai0k

• b_0 bkj0
• b_1 bkj1
• b_2 bkj2
• b_3 bkj3
• c_0_0c_0_0a_0b_0
• c_0_1c_0_1a_1b_1
• c_0_2c_0_2a_2b_2
• c_0_3c_0_3a_3b_3
• ...
• pragma xlang name kloop.stores
• ci0j0 c_0_0
• ci0j1 c_0_1
• ci0j2 c_0_2
• ci0j3 c_0_3
• ... // Remainder code

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Block copies

• Block Matrix Multiplication better performance
  if matrices are contiguous in memory (TLB)
• Poor performance of C copy
• Resort to a tool generating specific asm code
• Tool generating a good code with search (XLG is
  an asm search)

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Matrix Multiply(Results)
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Conclusion

• Describe transformations with reuse, procedures,
  conditionals
• X-Language
• language designed to generate multiversion
  programs
• Multistage language with a flexible
  pattern-matching and rewriting language
• Experts can describe specific application
  transformation optimizations

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Future works

• Dependence analysis
• Going further searching asm code transformation
• More transformations vectorization, alignment,