spolly speculative optimizations in the polyhedral model
play

SPolly: Speculative Optimizations in the Polyhedral Model Johannes - PowerPoint PPT Presentation

Jan 12, 2024 •178 likes •876 views

SPolly: Speculative Optimizations in the Polyhedral Model Johannes Doerfert, Clemens Hammacher, Kevin Streit, Sebastian Hack Saarland University, Germany January 21, 2013 The Problem int A[256][256], B[256][256], C[256][256]; void matmul() {

  1. SPolly: Speculative Optimizations in the Polyhedral Model Johannes Doerfert, Clemens Hammacher, Kevin Streit, Sebastian Hack Saarland University, Germany January 21, 2013

  2. The Problem int A[256][256], B[256][256], C[256][256]; void matmul() { for (int i=0; i<256; i++) for (int j=0; j<256; j++) for (int k=0; k<256; k++) C[i][j] += A[k][i] * B[j][k]; } 2/16

  3. The Problem int A[65536], B[65536], C[65536]; void matmul() { for (int i=0; i<256; i++) for (int j=0; j<256; j++) for (int k=0; k<256; k++) C[i*256+j] += A[k*256+i] * B[j*256+k]; } 2/16

  4. The Problem void matmul(int* A, int* B, int* C) { for (int i=0; i<256; i++) for (int j=0; j<256; j++) for (int k=0; k<256; k++) C[i*256+j] += A[k*256+i] * B[j*256+k]; } 2/16

  5. The Problem void matmul(int* A, int* B, int* C, int N) { for (int i=0; i<N; i++) for (int j=0; j<N; j++) for (int k=0; k<N; k++) C[i*N+j] += A[k*N+i] * B[j*N+k]; } 2/16

  6. 14.8% 85.2% Valid Regions Invalid Regions How urgent is this problem? 3/16

  7. How urgent is this problem? 14.8% 85.2% Valid Regions Invalid Regions 3/16

  8. How urgent is this problem? Setup ◮ Polly ◮ state-of-the-art polyhedral optimizer integrated in LLVM ◮ SPEC 2000 ◮ industry standard benchmark suite ◮ nine real world programs: ammp, art, bzip2, crafty, equake, gzip, mcf, mesa, twolf 4/16

  9. How urgent is this problem? Setup ◮ Polly ◮ state-of-the-art polyhedral optimizer integrated in LLVM ◮ SPEC 2000 ◮ industry standard benchmark suite ◮ nine real world programs: ammp, art, bzip2, crafty, equake, gzip, mcf, mesa, twolf ◮ Research questions ◮ number of Static Control Parts (SCoPs := code regions amenable to polyhedral optimizations) ◮ impact of individual rejection causes 4/16

  10. How urgent is this problem? SCoP rejection causes found in 1862 regions Rejection cause A B C i 0 Non-affine expressions 1 Aliasing 2 Non-affine loop bounds 3 Function call 4 Non-canonical indvars 5 Complex CFG 6 Unsigned comparison 7 Others 5/16

  11. How urgent is this problem? SCoP rejection causes found in 1862 regions Rejection cause A B C i 0 Non-affine expressions 1 Aliasing 2 Non-affine loop bounds 3 Function call 4 Non-canonical indvars 5 Complex CFG 6 Unsigned comparison 7 Others for (i = 0; i < N; i++) A[ ] += B[i]; i*N 5/16

  12. How urgent is this problem? SCoP rejection causes found in 1862 regions Rejection cause A B C i 0 Non-affine expressions 1 Aliasing 2 Non-affine loop bounds 3 Function call 4 Non-canonical indvars 5 Complex CFG 6 Unsigned comparison 7 Others void f( , ){ int* A int* B A[0] = B[5]; 5/16

  13. How urgent is this problem? SCoP rejection causes found in 1862 regions Rejection cause A B C i 0 Non-affine expressions 1 Aliasing 2 Non-affine loop bounds 3 Function call 4 Non-canonical indvars 5 Complex CFG 6 Unsigned comparison 7 Others for (i = 0; i < ; i++) N*M A[i] += B[i]; 5/16

  14. How urgent is this problem? SCoP rejection causes found in 1862 regions Rejection cause A B C i 0 Non-affine expressions 1 Aliasing 2 Non-affine loop bounds 3 Function call 4 Non-canonical indvars 5 Complex CFG 6 Unsigned comparison 7 Others for (i = 0; i < N; i++) g(i) A[i] += ; 5/16

  15. How urgent is this problem? SCoP rejection causes found in 1862 regions Rejection cause A B C i 0 Non-affine expressions 1 Aliasing 2 Non-affine loop bounds 3 Function call 4 Non-canonical indvars 5 Complex CFG 6 Unsigned comparison 7 Others for (i=0; i<N; ) i+=i/2+1 A[i] += A[i+1]; 5/16

  16. How urgent is this problem? SCoP rejection causes found in 1862 regions Rejection cause A B C i 0 Non-affine expressions 1 Aliasing 2 Non-affine loop bounds 3 Function call 4 Non-canonical indvars 5 Complex CFG 6 Unsigned comparison 7 Others 5/16

  17. How urgent is this problem? SCoP rejection causes found in 1862 regions Rejection cause A B C i 0 Non-affine expressions 1230 (66%) 1 Aliasing 1093 (59%) 2 Non-affine loop bounds 840 (45%) 3 Function call 532 (29%) 4 Non-canonical indvars 384 (21%) 5 Complex CFG 253 (14%) 6 Unsigned comparison 199 (11%) 7 Others 1 ( 0%) A #regions where condition i is violated. 5/16

  18. How urgent is this problem? SCoP rejection causes found in 1862 regions Rejection cause A B C i 0 Non-affine expressions 1230 (66%) 1 Aliasing 1093 (59%) 2 Non-affine loop bounds 840 (45%) 3 Function call 532 (29%) 4 Non-canonical indvars 384 (21%) 5 Complex CFG 253 (14%) 6 Unsigned comparison 199 (11%) 7 Others 1 ( 0%) A #regions where condition i is violated. 5/16

  19. How urgent is this problem? SCoP rejection causes found in 1862 regions Rejection cause A B C i 0 Non-affine expressions 1230 (66%) 84 ( 5%) 1 Aliasing 1093 (59%) 207 (11%) 2 Non-affine loop bounds 840 (45%) 6 ( 0%) 3 Function call 532 (29%) 72 ( 4%) 4 Non-canonical indvars 384 (21%) 0 ( 0%) 5 Complex CFG 253 (14%) 31 ( 2%) 6 Unsigned comparison 199 (11%) 0 ( 0%) 7 Others 1 ( 0%) 0 ( 0%) A #regions where condition i is violated. B #regions where only condition i is violated. 5/16

  20. How urgent is this problem? SCoP rejection causes found in 1862 regions Rejection cause A B C i 0 Non-affine expressions 1230 (66%) 84 ( 5%) 1 Aliasing 1093 (59%) 207 (11%) 2 Non-affine loop bounds 840 (45%) 6 ( 0%) 3 Function call 532 (29%) 72 ( 4%) 4 Non-canonical indvars 384 (21%) 0 ( 0%) 5 Complex CFG 253 (14%) 31 ( 2%) 6 Unsigned comparison 199 (11%) 0 ( 0%) 7 Others 1 ( 0%) 0 ( 0%) A #regions where condition i is violated. B #regions where only condition i is violated. 5/16

  21. How urgent is this problem? SCoP rejection causes found in 1862 regions Rejection cause A B C i 0 Non-affine expressions 1230 (66%) 84 ( 5%) 84 ( 5%) 1 Aliasing 1093 (59%) 207 (11%) 510 (27%) 2 Non-affine loop bounds 840 (45%) 6 ( 0%) 660 (35%) 3 Function call 532 (29%) 72 ( 4%) 928 (50%) 4 Non-canonical indvars 384 (21%) 0 ( 0%) 1174 (63%) 5 Complex CFG 253 (14%) 31 ( 2%) 1387 (74%) 6 Unsigned comparison 199 (11%) 0 ( 0%) 1586 (85%) 7 Others 1 ( 0%) 0 ( 0%) 1587 (85%) A #regions where condition i is violated. B #regions where only condition i is violated. C #regions where only conditions 0 to i are violated. 5/16

  22. How urgent is this problem? SCoP rejection causes found in 1862 regions Rejection cause A B C i 0 Non-affine expressions 1230 (66%) 84 ( 5%) 84 ( 5%) 1 Aliasing 1093 (59%) 207 (11%) 510 (27%) 2 Non-affine loop bounds 840 (45%) 6 ( 0%) 660 (35%) 3 Function call 532 (29%) 72 ( 4%) 928 (50%) 4 Non-canonical indvars 384 (21%) 0 ( 0%) 1174 (63%) 5 Complex CFG 253 (14%) 31 ( 2%) 1387 (74%) 6 Unsigned comparison 199 (11%) 0 ( 0%) 1586 (85%) 7 Others 1 ( 0%) 0 ( 0%) 1587 (85%) A #regions where condition i is violated. B #regions where only condition i is violated. C #regions where only conditions 0 to i are violated. 5/16

  23. How urgent is this problem? SCoP rejection causes found in 1862 regions Rejection cause A B C i 0 Non-affine expressions 1230 (66%) 84 ( 5%) 84 ( 5%) 1 Aliasing 1093 (59%) 207 (11%) 510 (27%) 2 Non-affine loop bounds 840 (45%) 6 ( 0%) 660 (35%) 3 Function call 532 (29%) 72 ( 4%) 928 (50%) 4 Non-canonical indvars 384 (21%) 0 ( 0%) 1174 (63%) 5 Complex CFG 253 (14%) 31 ( 2%) 1387 (74%) 6 Unsigned comparison 199 (11%) 0 ( 0%) 1586 (85%) 7 Others 1 ( 0%) 0 ( 0%) 1587 (85%) A #regions where condition i is violated. B #regions where only condition i is violated. C #regions where only conditions 0 to i are violated. 5/16

  24. How urgent is this problem? Conclusion 14.8% 49.8% 35.4% Valid Regions Targeted Regions Invalid Regions 6/16

  25. How to allow more polyhedral optimizations? Example void f(int* A, int* B) { for (int i=0; i < 2048; i++) A[i] += B[i]; } 7/16

  26. How to allow more polyhedral optimizations? Example 1. speculatively assume properties (e.g., constant parameters) void f(int* A, int* B) { for (int i=0; i < 2048; i++) A[i] += B[i]; } 7/16

  27. How to allow more polyhedral optimizations? Example 1. speculatively assume properties (e.g., constant parameters) 2. derive specialized versions void f_spec(int* restrict A, int* restrict B) { for (int i=0; i < 2048; i++) A[i] += B[i]; } 7/16

  28. How to allow more polyhedral optimizations? Example 1. speculatively assume properties (e.g., constant parameters) 2. derive specialized versions 3. apply polyhedral optimizations void f_opt(int* restrict A, int* restrict B) { parfor (int j=0; j < 2048; j+=32) for (int i=j; i < 32 + j; i++) A[i] += B[i]; } 7/16

  29. How to allow more polyhedral optimizations? Example 1. speculatively assume properties (e.g., constant parameters) 2. derive specialized versions 3. apply polyhedral optimizations 4. add runtime dispatcher void f_dispatcher(int* A, int* B) { if (overlap(A, B, 2048)) f(A, B); else f_opt(A, B); } 7/16

  30. How to allow more polyhedral optimizations? Implementation 8/16

  31. How to allow more polyhedral optimizations? Implementation Polly LLVM-IR SPolly SCoP Detection Valid SCoPs Polyhedral Optimizations Code Generation Program 8/16

  32. How to allow more polyhedral optimizations? Implementation Polly LLVM-IR SPolly Invalid SCoPs SCoP Detection sSCoP Detection Valid SCoPs Polyhedral Optimizations Code Generation Program 8/16

Recommend

Polly Polyhedral Optimizations for LLVM Tobias Grosser - Hongbin Zheng - Raghesh Aloor Andreas

Polly Polyhedral Optimizations for LLVM Tobias Grosser - Hongbin Zheng - Raghesh Aloor Andreas

Polly Polyhedral Optimizations for LLVM Tobias Grosser - Hongbin Zheng - Raghesh Aloor Andreas Simb urger - Armin Gr osslinger - Louis-No el Pouchet April 03, 2011 Polly - Polyhedral Optimizations for LLVM April 03, 2011 1 / 27

564 views • 27 slides
GRAPHITE: Polyhedral Analyses and Optimizations for GCC Sebastian Pop 1 , Albert Cohen 2 , edric

GRAPHITE: Polyhedral Analyses and Optimizations for GCC Sebastian Pop 1 , Albert Cohen 2 , edric

GRAPHITE: Polyhedral Analyses and Optimizations for GCC Sebastian Pop 1 , Albert Cohen 2 , edric Bastoul 2 , Sylvain Girbal 2 , C e Silber 1 , Nicolas Vasilache 2 Georges-Andr 1 CRI/ENSMP 2 Alchemy/INRIA, LRI/Paris Sud 11 University June,

845 views • 29 slides
The Polyhedral Model Beyond Loops Recursion Optimization and Parallelization Through Polyhedral

The Polyhedral Model Beyond Loops Recursion Optimization and Parallelization Through Polyhedral

The Polyhedral Model Beyond Loops Recursion Optimization and Parallelization Through Polyhedral Modeling Salwa Kobeissi &amp; Philippe Clauss CAMUS team - Inria, University of Strasbourg, ICPS team - ICube Laboratory IMPACT - HIPEAC 2019,

620 views • 35 slides
AlphaZ: A System for Design Space Exploration in the Polyhedral Model Tomofumi Yuki, Gautam

AlphaZ: A System for Design Space Exploration in the Polyhedral Model Tomofumi Yuki, Gautam

AlphaZ: A System for Design Space Exploration in the Polyhedral Model Tomofumi Yuki, Gautam Gupta, DaeGon Kim, Tanveer Pathan, and Sanjay Rajopadhye Polyhedral Compilation n The Polyhedral Model n Now a well established approach for

722 views • 19 slides
Optimization Through Recomputation in the Polyhedral Model By Mike Jongen, Luc Waeijen, Roel

Optimization Through Recomputation in the Polyhedral Model By Mike Jongen, Luc Waeijen, Roel

Optimization Through Recomputation in the Polyhedral Model By Mike Jongen, Luc Waeijen, Roel Jordans, Lech Jwiak , Henk Corporaal. 1 Contents Introduction Related work Optimizing Through Recompute Polyhedral

863 views • 60 slides
FRACTAL AN EXECUTION MODEL FOR FINE-GRAIN NESTED SPECULATIVE PARALLELISM SU SUVINAY Y SU

FRACTAL AN EXECUTION MODEL FOR FINE-GRAIN NESTED SPECULATIVE PARALLELISM SU SUVINAY Y SU

FRACTAL AN EXECUTION MODEL FOR FINE-GRAIN NESTED SPECULATIVE PARALLELISM SU SUVINAY Y SU SUBRAMANIAN , MARK C. JEFFREY, MALEEN ABEYDEERA, HYUN RYONG LEE, VICTOR A. YING, JOEL EMER, DANIEL SANCHEZ IS ISCA 2017 Current speculative systems

984 views • 47 slides
A Model of Rational Speculative Trade Dmitry Lubensky 1 Doug Smith 2 1 Kelley School of Business

A Model of Rational Speculative Trade Dmitry Lubensky 1 Doug Smith 2 1 Kelley School of Business

A Model of Rational Speculative Trade Dmitry Lubensky 1 Doug Smith 2 1 Kelley School of Business Indiana University 2 Federal Trade Commission January 21, 2014 Speculative Trade Example: suckers in poker; origination of CDS contracts

523 views • 17 slides
Loop Optimizations Important because lots of execution Loop Optimizations Loop Optimizations

Loop Optimizations Important because lots of execution Loop Optimizations Loop Optimizations

Loop Optimizations Important because lots of execution Loop Optimizations Loop Optimizations time occurs in loops First, we will identify loops We will study three optimizations Loop-invariant code motion This lecture is

249 views • 5 slides
Speculative Defragmentation Speculative Defragmentation A Technique to Improve the

Speculative Defragmentation Speculative Defragmentation A Technique to Improve the

Ninth IEEE International Symposium on High Performance Distributed Computing, Pittsburgh, Pennsylvania, August 1-4, 2000 Speculative Defragmentation Speculative Defragmentation A Technique to Improve the Communication A Technique to

237 views • 22 slides
Harmonizing Speculative and Non-Speculative Execution in Architectures for Ordered Parallelism

Harmonizing Speculative and Non-Speculative Execution in Architectures for Ordered Parallelism

Harmonizing Speculative and Non-Speculative Execution in Architectures for Ordered Parallelism MA MARK C. JEFFR FFREY , VICTOR A. YING, SUVINAY SUBRAMANIAN, HYUN RYONG LEE, JOEL EMER, DANIEL SANCHEZ MI MICRO 2018 There is a (false)

1.48k views • 130 slides
The Polyhedral Model Is More Widely Applicable Than You Think Mohamed-Walid Benabderrahmane 1

The Polyhedral Model Is More Widely Applicable Than You Think Mohamed-Walid Benabderrahmane 1

The Polyhedral Model Is More Widely Applicable Than You Think Mohamed-Walid Benabderrahmane 1 Louis-Nol Pouchet 1 , 2 Albert Cohen 1 Cdric Bastoul 1 1 ALCHEMY group, INRIA Saclay / University of Paris-Sud 11, France 2 The Ohio State University,

359 views • 24 slides
Iterative Optimization in the Polyhedral Model: One-Dimensional Affine Schedules Louis-Nol

Iterative Optimization in the Polyhedral Model: One-Dimensional Affine Schedules Louis-Nol

Iterative Optimization in the Polyhedral Model: One-Dimensional Affine Schedules Louis-Nol Pouchet , Cdric Bastoul and Albert Cohen ALCHEMY, LRI - INRIA Futurs October 17, 2006 2nd HiPEAC Industrial Workshop, Eindhoven, NL Outline: 2nd

1.09k views • 70 slides
A study of some pitfalls preventing peak performance in polyhedral compilation using a polyhedral

A study of some pitfalls preventing peak performance in polyhedral compilation using a polyhedral

Mind the Gap! A study of some pitfalls preventing peak performance in polyhedral compilation using a polyhedral antidote Philippe Clauss Team CAMUS, INRIA, ICube Lab., CNRS, University of Strasbourg, France IMPACT - January 19, 2015 The

417 views • 26 slides
Iterative Optimization in the Polyhedral Model: Part I, One-Dimensional Time Louis-Nol Pouchet ,

Iterative Optimization in the Polyhedral Model: Part I, One-Dimensional Time Louis-Nol Pouchet ,

Iterative Optimization in the Polyhedral Model: Part I, One-Dimensional Time Louis-Nol Pouchet , Cdric Bastoul, Albert Cohen and Nicolas Vasilache ALCHEMY, INRIA Futurs / University of Paris-Sud XI March 12, 2007 Fifth International

864 views • 47 slides
Iterative Optimization in the Polyhedral Model: Part II, Multidimensional Time Louis-Nol Pouchet

Iterative Optimization in the Polyhedral Model: Part II, Multidimensional Time Louis-Nol Pouchet

Iterative Optimization in the Polyhedral Model: Part II, Multidimensional Time Louis-Nol Pouchet 1 Cdric Bastoul 1 Albert Cohen 1 John Cavazos 2 1 ALCHEMY group, INRIA Saclay / University of Paris-Sud 11, France 2 Dept. of Computer &amp;

771 views • 34 slides
Extending the Polyhedral Compilation Model for Debugging and Optimization of SPMD-style Explicitly

Extending the Polyhedral Compilation Model for Debugging and Optimization of SPMD-style Explicitly

Extending the Polyhedral Compilation Model for Debugging and Optimization of SPMD-style Explicitly Parallel Programs Prasanth Chatarasi Masters Thesis Defense Habanero Extreme Scale Software Research Group Department of Computer Science Rice

429 views • 42 slides
Speculative Concurrent Processing with Transactional Memory in the Actor Model OPODIS 2013

Speculative Concurrent Processing with Transactional Memory in the Actor Model OPODIS 2013

Speculative Concurrent Processing with Transactional Memory in the Actor Model OPODIS 2013 Yaroslav Hayduk, Anita Sobe, Derin Harmanci, Patrick December 17, 2013 Marlier and Pascal Felber University of Neuchatel,

354 views • 20 slides
Iterative Optimization in the Polyhedral Model: Part I, One-Dimensional Time Louis-Noel Pouchet,

Iterative Optimization in the Polyhedral Model: Part I, One-Dimensional Time Louis-Noel Pouchet,

Iterative Optimization in the Polyhedral Model: Part I, One-Dimensional Time Louis-Noel Pouchet, Cedric Bastoul, Albert Cohen and Nicolas Vasilache Presented by: Tom St. John Dept of Computer &amp; Information Sciences University of Delaware

702 views • 41 slides
When Iterative Optimization Meets the Polyhedral Model: One-Dimensional Date Louis-Nol Pouchet

When Iterative Optimization Meets the Polyhedral Model: One-Dimensional Date Louis-Nol Pouchet

When Iterative Optimization Meets the Polyhedral Model: One-Dimensional Date Louis-Nol Pouchet ALCHEMY, LRI - INRIA Futurs Under the direction of A. Cohen &amp; C. Bastoul October 9, 2006 EPITA final internship defense, CSI 2006 Situation:

802 views • 59 slides
Computing the Cohomology Ring of a Polyhedral Complex Joint work with D. Kravatz, R.

Computing the Cohomology Ring of a Polyhedral Complex Joint work with D. Kravatz, R.

Computing the Cohomology Ring of a Polyhedral Complex Joint work with D. Kravatz, R. Gonzalez-Diaz &amp; J. Lamar Ron Umble Millersville Univiversity TGTS September 15, 2017 Polyhedral Complexes A polyhedral complex X is a regular cell

725 views • 51 slides
Polyhedral Loop Optimization (Part I) Armin Grlinger SPPEXA Doctoral Retreat 2015 September

Polyhedral Loop Optimization (Part I) Armin Grlinger SPPEXA Doctoral Retreat 2015 September

Polyhedral Loop Optimization (Part I) Armin Grlinger SPPEXA Doctoral Retreat 2015 September 14, 2015 Overview Monday: Basics of the polyhedral model Modeling Transformation Code generation Wednesday: Practice

823 views • 36 slides
Task Coarsening Through Polyhedral Compilation for a Macro-Dataflow Programming Model Alina

Task Coarsening Through Polyhedral Compilation for a Macro-Dataflow Programming Model Alina

Task Coarsening Through Polyhedral Compilation for a Macro-Dataflow Programming Model Alina Sbirlea, Louis-Nol Pouchet, Vivek Sarkar Rice University Ohio State University January 19, 2014 IMPACT15 Amsterdam Overview: IMPACT15 DFGR

294 views • 3 slides
Iterative Optimization in the Polyhedral Model Louis-Nol Pouchet ALCHEMY group, INRIA Saclay /

Iterative Optimization in the Polyhedral Model Louis-Nol Pouchet ALCHEMY group, INRIA Saclay /

Iterative Optimization in the Polyhedral Model Louis-Nol Pouchet ALCHEMY group, INRIA Saclay / University of Paris-Sud 11, France January 18th, 2010 Ph.D Defense Introduction: ALCHEMY group A Brief History... A Quick look backward:

1.2k views • 95 slides
Computing the Cohomology Algebra of a Polyhedral Complex Joint work with R. Gonzalez-Diaz &amp;

Computing the Cohomology Algebra of a Polyhedral Complex Joint work with R. Gonzalez-Diaz &amp;

Computing the Cohomology Algebra of a Polyhedral Complex Joint work with R. Gonzalez-Diaz &amp; J. Lamar Ron Umble Millersville Univiversity Escuela de Ingeniera Informatica 27 March 2018 Polyhedral Complexes A polyhedral complex X is a

1.38k views • 98 slides

More recommend