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A Probabilistic Pointer Analysis for Speculative Optimizations

Electrical and Computer Engineering University of Toronto. A Probabilistic Pointer Analysis for Speculative Optimizations. Jeff DaSilva Greg Steffan. ASPLOS XII. foo(int *a) { … while(…) { x = *a; … } } . Pointers Impede Optimization. Loop Invariant Code Motion.

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A Probabilistic Pointer Analysis for Speculative Optimizations

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  1. Electrical and Computer Engineering University of Toronto A Probabilistic Pointer Analysis for Speculative Optimizations Jeff DaSilva Greg Steffan ASPLOS XII

  2. foo(int *a) { … while(…) { x = *a; … } } Pointers Impede Optimization Loop Invariant Code Motion Parallelize Can pointer analysis help? ASPLOS XII

  3. optimize Definitely Pointer Analysis Definitely Not Maybe *a = ~ ~ = *b How can we optimize cases? Maybe Pointer Analysis • Do pointers a and b point to the same location? • Repeat for every pair of pointers at every program point *a = ~ ~ = *b ASPLOS XII

  4. int *a, x; … while(…) { x = *a; … } int *a, x, tmp; … tmp = *a; while(…) { x = tmp; … } <verify, recover?> a is probably loop invariant Lets Speculate • Implement a potentially unsafe optimization • Verify and Recover if necessary ASPLOS XII

  5. Data Speculative Optimizations • EPIC Instruction sets • Support for speculative load/store instructions (eg. Itanium) • Speculative compiler optimizations • Dead store elimination, redundancy elimination, copy propagation, strength reduction, register promotion • Thread-level speculation (TLS) • Hardware and compiler support for speculative parallel threads • Transactional programming • Hardware and software support for speculative parallel transactions Heavy reliance on detailed profile feedback ASPLOS XII

  6. Maybe Recovery penalty (if unsuccessful) Overhead for verify Probability of success Expected speedup (if successful) Speculate? Ideally would be a probability Maybe Can We Quantify ? Maybe • Estimate the potential benefit for speculating: ASPLOS XII

  7. optimize optimize p = 1.0 Definitely Pointer Analysis PPA p = 0.0 Definitely Not 0.0 < p < 1.0 Maybe *a = ~ ~ = *b Probabilistic Pointer Analysis (PPA) Conventional Pointer Analysis • Do pointers a and b point to the same location? • Do this for every pair of pointers at every program point *a = ~ ~ = *b • With what probability p, do pointers a and b point to the same location? • Repeat for every pair of pointers at every program point Potential bonus: PPA doesn’t have to be safe ASPLOS XII

  8. PPA Research Objectives • Accurate points-to probability information • at every static pointer dereference • Scalable analysis • Goal: entire SPEC integer benchmark suite • Understand scalability/accuracytradeoff • through flexible static memory model Improve our understanding of programs ASPLOS XII

  9. Related Work ASPLOS XII

  10. Algorithm Design Choices • Fixed • Bottom Up / Top Down Approach • Linear transfer functions (for scalability) • One-level context and flow sensitive • Flexible • Edge profiling (or static prediction) • Safe (or unsafe) • Field sensitive (or field insensitive) ASPLOS XII

  11. int x, y, z, *b = &x; void foo(int *a) { if(…) b = &y; if(…) a = &z; else(…) a = b; while(…) { x = *a; … } } = Definitely = pointer = = pointed at Maybe Traditional Points-To Graph b a x y z UND Results are inconclusive ASPLOS XII

  12. int x, y, z, *b = &x; void foo(int *a) { if(…) b = &y; if(…) a = &z; else a = b; while(…) { x = *a; … } } = p = 1.0 = pointer p = = pointed at 0.0<p< 1.0 Probabilistic Points-To Graph 0.1 taken(edge profile) b a 0.2 taken(edge profile) 0.72 0.9 0.1 0.2 0.08 x y z UND Results provide more information ASPLOS XII

  13. Linear One - Level Interprocedural Probabilistic Pointer Analysis LOLLIPOPOur PPA Algorithm ASPLOS XII

  14. Fundamentals • Location sets (Wilson & Lam) • One or more mem locations • Classified as pointer, pointer target, or both • Matrix-based approach • Nice properties, optimized implementations • Two key matrices: • Points-to matrix • Linear transformation matrix ASPLOS XII

  15. Points-To Matrix Location Sets M-1 M Area Of Interest 1 2 … Pointer Sets … N-1 N I Location Sets All matrix rows sum to 1.0 ASPLOS XII

  16. x y z UND a b a b 0.72 0.9 0.1 0.2 x 0.08 y x y z UND z UND Points-To Matrix Example 0.72 0.08 0.20 0.90 0.10 1.0 1.0 1.0 1.0 I ASPLOS XII

  17. I I Computing New Points-To Matrices Points-To Matrix In Any Instruction Points-To Matrix Out ASPLOS XII

  18. The Fundamental PPA Equation Transformation Matrix Points-To Matrix In Points-To Matrix Out = This can be applied to any instruction(incl. function calls) ASPLOS XII

  19. Transformation Matrix Location Sets Pointer Sets 1 2 3 … N-1 N 1 2 Area of Interest … Pointer Sets ø I Location Sets … N-1 N All matrix rows sum to 1.0 ASPLOS XII

  20. a b x y z UND Transformation Matrix Example a b x y z UND S1:a = &z; 1.0 1.0 TS1 1.0 1.0 1.0 1.0 = ASPLOS XII

  21. PTout TS1 PTin = x y z UND a 1.0 1.0 0.72 0.08 0.20 0.90 0.10 b a b 0.72 0.9 0.1 0.2 x 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.08 y x y z UND z UND Example - The PPA Equation S1:a = &z; PTout = ASPLOS XII

  22. PTout TS1 PTin = x y z UND a b b a 0.9 0.1 x y x y z UND z UND Example - The PPA Equation S1:a = &z; 1.0 0.90 0.10 PTout = 1.0 1.0 1.0 1.0 I ASPLOS XII

  23. Basic Block S1: Instr S2: Instr S3: Instr I I Combining Transformation Matrices PTout TS2 TS3 TS1 PTin PTin TS1 PTin = PTout TBB PTin = ASPLOS XII

  24. Control flow - if/else p + q = 1.0 X Y p p q q TX TY + = ASPLOS XII

  25. N <L,U> X Y i 1 TY = U-L+1 Control flow - loops N TX = Both operations can be implemented efficiently <L,U>  <min,max> ASPLOS XII

  26.   Safe vs. Unsafe Pointer Assignment Instructions Safe?   Shadow/invisible vars: non-linear to handle ASPLOS XII

  27. Steensgaard FICI PA for shadow vars p p Safe q p_1 p_1 q + = p_1 q p_1 and q are considered aliased Safety for Shadow Variables Unsafe q q = pointer = shadow ptr = pointed at ASPLOS XII

  28. LOLLIPOP Implementation .spd SUIF Infrastructure Static Memory Model TF-Matrix Collector Points-To Matrix Propagator ICFG SMM BU TD Edge Profile .spx • Implementation details: • Sparse matrices • Efficient matrix algorithms • Result memoization Results Stats MATLAB C Library ASPLOS XII

  29. Measuring LOLLIPOP’s Efficiency and Accuracy ASPLOS XII

  30. SPEC2000 Benchmark Data Experimental Framework: 3GHz P4 with 1GB of RAM Scales to all of SPECint ASPLOS XII

  31. Reduced Input Set SPEC2000 Benchmark Data Experimental Framework: 3GHz P4 with 1GB of RAM More efficient than points-to profiling ASPLOS XII

  32. Average Dereference Size more accurate Easy SPEC2000 Benchmarks A one-level Analysis is often adequate (i.e. safe~=unsafe) ASPLOS XII

  33. Average Dereference Size more accurate Challenging SPEC 95/2000 Benchmarks Many improbable points-to relations can be pruned away ASPLOS XII

  34. while(…) { x = *a; … } { (0.72, ), (0.08, ), (0.2, ) } x y z Σ (max probability value) = Avg Certainty (num of loads & stores) Metric: Average Max Certainty Max probability value = 0.72 ASPLOS XII

  35. Probabilistic Certainty more accurate SPEC2000 Average Certainty On average, LOLLIPOP can predict a single likely points-to relation ASPLOS XII

  36. while(…) { x = *a; … } { (0.72, ), (0.08, ), (0.2, ) } { (0.88, ), (0.02, ), (0.1, ) } x x y y z z Pd Ps Σ ║Ps – Pd ║ 1 = NAED √2 (num of loads & stores) Metric: NAED • Normalized Average Euclidean Distance LOLIPoP’s Static prediction Pts-to Profiler’s Dynamic freq vector ASPLOS XII

  37. more accurate NAED Norm Avg Euclidean Dist (NAED) ASPLOS XII

  38. Summary • A novel matrix-based PPA algorithm • Scales to the SPECint 95/2000 benchmarks • One level context and flow sensitive • Future Work • Applying LOLLIPOP to TLS/TM • Further optimize LOLLIPOP’s implementation ASPLOS XII

  39. ASPLOS XII

  40. References • Manuvir Das, Ben Liblit, Manuel Fahndrich, and Jakob Rehof. Estimating the Impact of Scalable Pointer Analysis on Optimization. SAS 2001, 260-278. • Peng-Sheng Chen, Ming-Yu Hung, Yuan-Shin Hwang, Roy Dz-Ching Ju, and Jenq Kuen Lee. Compiler support for speculative multithreading architecture with probabilistic points-to analysis. PPOPP 2003, 25-36. • Jin Lin, Tong Chen, Wei-Chung Hsu, Peng-Chung Yew, Roy Dz-Ching Ju, Tin-Fook Ngai and Sun Chan, A Compiler Framework for Speculative Analysis and Optimizations. PLDI 2003, 289-299. • R.D. Ju, J. Collard, and K. Oukbir. Probabilistic Memory Disambiguation and its Application to Data Speculation. SIGARCH Comput. Archit. News 27 1999, 27-30. • Manel Fernandez and Roger Espasa. Speculative Alias Analysis for Executable Code. PACT 2002, 221-231. ASPLOS XII

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