Paper Study - Incremental Data-Flow Analysis Algorithms by Ryder et al
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The document discusses incremental data-flow analysis algorithms, specifically the incremental allen-cocke interval analysis, aiming to optimize the recalculation of data-flow results affected by program changes. It presents an overview of methods and background information on conventional data-flow analysis, emphasizing the need for efficient updates after program modifications. The authors conclude that their approach maintains the same time complexity as original algorithms while providing systematic solutions and clear dependency relationships among data-flow variables.
Paper Study - Incremental Data-Flow Analysis Algorithms by Ryder et al
- 1. Incremental Data-Flow Analysis Algorithms Barbara G. Ryder et al. Published atTOPLAS 1988 (Conference version: POPL 1983) Presenter: Min-Yih Hsu
- 2. Outline • Overview • Allen-Cocke Interval Analysis • Incremental Allen-Cocke Interval Analysis (ACINCF) • Related Works • Comments
- 3. Overview
- 4. Backgrounds
- 5. Backgrounds • Data-flow analysis results will be invalidated when program changes.
- 6. Backgrounds • Data-flow analysis results will be invalidated when program changes. • Redo the entire data-flow analysis will be expensive (e.g. O(n2) for Allen-Cocke interval analysis)
- 7. Backgrounds • Data-flow analysis results will be invalidated when program changes. • Redo the entire data-flow analysis will be expensive (e.g. O(n2) for Allen-Cocke interval analysis) • What about only re-calculate the analysis results that are related to the modified part of the program?
- 8. Backgrounds • Data-flow analysis results will be invalidated when program changes. • Redo the entire data-flow analysis will be expensive (e.g. O(n2) for Allen-Cocke interval analysis) • What about only re-calculate the analysis results that are related to the modified part of the program? • Relations between the program changes and the affected analysis results are difficult to figure out.
- 9. Traditional Recalculation Upon Program Changes Original Program
- 10. Traditional Recalculation Upon Program Changes Original Program Data-Flow Analysis Result
- 11. Traditional Recalculation Upon Program Changes Original Program Data-Flow Analysis Result New Program
- 12. Traditional Recalculation Upon Program Changes Original Program Data-Flow Analysis Result New Data-Flow Analysis Result New Program
- 13. Incremental Update Upon Program Changes Original Program
- 14. Incremental Update Upon Program Changes Original Program Data-Flow Analysis Result Base Analysis
- 15. Incremental Update Upon Program Changes Original Program New Program Data-Flow Analysis Result Base Analysis
- 16. Incremental Update Upon Program Changes Original Program New Program New Data-Flow Analysis Result Small Delta Data-Flow Analysis Result Base Analysis
- 17. Incremental Update Upon Program Changes Original Program New Program New Data-Flow Analysis Result Small Delta Data-Flow Analysis Result Base Analysis
- 18. Incremental Update Upon Program Changes Original Program New Program New Data-Flow Analysis Result Small Delta Data-Flow Analysis Result Base Analysis ANALYSIS SPEED
- 19. The Base Analysis - Allen-Cocke Interval Analysis
- 21. Interval (in CFG) • Subgraph of CFG.
- 22. Interval (in CFG) • Subgraph of CFG. • Single entry.
- 23. Interval (in CFG) • Subgraph of CFG. • Single entry. • For each BB in an interval, all its predecessors are also in that interval (Except for the first BB). • The first BB is called the “interval header”.
- 24. Intervals in Reducible CFG Various Ways to Describe Reducible CFG
- 25. Intervals in Reducible CFG Various Ways to Describe Reducible CFG 1. Fore each loop in a CFG, the loop header always dominates its loop body blocks.
- 26. Intervals in Reducible CFG Various Ways to Describe Reducible CFG 1. Fore each loop in a CFG, the loop header always dominates its loop body blocks. 2. CFG without multi-entries loops.
- 27. Intervals in Reducible CFG Various Ways to Describe Reducible CFG 1. Fore each loop in a CFG, the loop header always dominates its loop body blocks. 2. CFG without multi-entries loops. 3. Formal definition by Hecht and Ullman in 1972: A CFG that can be reduced to single vertex by T1and T2 transformations.
- 28. Intervals in Reducible CFG Various Ways to Describe Reducible CFG 1. Fore each loop in a CFG, the loop header always dominates its loop body blocks. 2. CFG without multi-entries loops. 3. Formal definition by Hecht and Ullman in 1972: A CFG that can be reduced to single vertex by T1and T2 transformations. Will reduce an interval into single vertex
- 29. Intervals in Reducible CFG
- 30. Intervals in Reducible CFG interval-head-variable
- 31. Intervals in Reducible CFG interval-head-variable
- 32. Intervals in Reducible CFG interval-head-variable reduced interval-head-variable
- 33. Intervals in Reducible CFG interval-head-variable reduced interval-head-variable
- 34. Intervals in Reducible CFG interval-head-variable reduced interval-head-variable Derived Graphs
- 35. Summary: Interval in CFG • Interval is a single-entry program region. • In Gi, we can reduce one of the intervals and form Gi+1, which has a new set of intervals.
- 37. Dataflow Equations • Zm is the data flow solution of vertex m.
- 38. Dataflow Equations • Zm is the data flow solution of vertex m. • A vertex can be a BB or a reduced interval-head-variable.
- 39. Dataflow Equations • Zm is the data flow solution of vertex m. • A vertex can be a BB or a reduced interval-head-variable. • “ “can be union or intersection
- 40. Dataflow Equations • Zm is the data flow solution of vertex m. • A vertex can be a BB or a reduced interval-head-variable. • “ “can be union or intersection • Sm is the set of immediate neighbors of vertex m. (e.g. {pred(m)} for forward-analysis)
- 41. Dataflow Equations • Zm is the data flow solution of vertex m. • A vertex can be a BB or a reduced interval-head-variable. • “ “can be union or intersection • Sm is the set of immediate neighbors of vertex m. (e.g. {pred(m)} for forward-analysis) • am,k and bm,k are coefficients, and cm is the constant for this equation.
- 42. Dataflow Equations • Zm is the data flow solution of vertex m. • A vertex can be a BB or a reduced interval-head-variable. • “ “can be union or intersection • Sm is the set of immediate neighbors of vertex m. (e.g. {pred(m)} for forward-analysis) • am,k and bm,k are coefficients, and cm is the constant for this equation.
- 48. Combining Intervals and Data-flow Equations
- 49. Combining Intervals and Data-flow Equations • A program generates many data-flow equations Qi.
- 50. Combining Intervals and Data-flow Equations • A program generates many data-flow equations Qi. • Difficult to solve them at once.
- 51. Combining Intervals and Data-flow Equations • A program generates many data-flow equations Qi. • Difficult to solve them at once. • When we’re reducing an interval into single vertex, we can “merge” the associated equations into one at the same time!
- 52. Rules to combine coefficients Intervals
- 53. Rules to combine coefficients Intervals
- 54. Rules to combine coefficients Intervals
- 56. After plug-in X4 to X5
- 57. After plug-in X4 to X5 After plug-in X5 to X3
- 58. After plug-in X4 to X5 After plug-in X5 to X3 After loop-breaking
- 60. Plug-in X3 to X2
- 70. ACINCF: Incremental Allen-Cocke Interval Analysis (Forward Direction)
- 71. Recap: Backgrounds • Data-flow analysis results will be invalidated upon program changing. • Redo the entire data-flow analysis will be expensive (e.g. O(n2) for Allen-Cocke interval analysis) • Relations between the program changes and the affected analysis results are difficult to figure out.
- 72. Recap: Backgrounds • Data-flow analysis results will be invalidated upon program changing. • Redo the entire data-flow analysis will be expensive (e.g. O(n2) for Allen-Cocke interval analysis) • Relations between the program changes and the affected analysis results are difficult to figure out. When certain part of program changes, which data-flow facts should we re-calculate?
- 74. Recap: Dataflow Equations Changing Program implies Changing Coefficient Values*
- 75. Coefficient Reduction Rules At the Very End of Elimination Process…
- 76. Coefficient Reduction Rules At the Very End of Elimination Process… Changed Unchanged
- 77. Coefficient Reduction Rules At the Very End of Elimination Process… Changed Unchanged
- 78. Coefficient Reduction Rules At the Very End of Elimination Process… Changed Unchanged
- 88. Key Insights /Takeaways • Allen-Cocke data-flow analysis provided a systematic way to resolve data-flow equations.
- 89. Key Insights /Takeaways • Allen-Cocke data-flow analysis provided a systematic way to resolve data-flow equations. • Using intervals, we can have a clear view on the dependency relationships among data-flow variables.
- 90. Key Insights /Takeaways • Allen-Cocke data-flow analysis provided a systematic way to resolve data-flow equations. • Using intervals, we can have a clear view on the dependency relationships among data-flow variables. • With these relationships, we can easily figure out which data- flow variables need recalculations after certain program change.
- 91. Time Complexity
- 92. Time Complexity • Worst scenario:The program has deep nested loops (Size of O(n)).
- 93. Time Complexity • Worst scenario:The program has deep nested loops (Size of O(n)). • Has the same time complexity as the original Allen-Cocke algorithm: O(n2).
- 94. Time Complexity • Worst scenario:The program has deep nested loops (Size of O(n)). • Has the same time complexity as the original Allen-Cocke algorithm: O(n2). • However, authors argued that deep nested loops are rare.
- 95. Time Complexity • Worst scenario:The program has deep nested loops (Size of O(n)). • Has the same time complexity as the original Allen-Cocke algorithm: O(n2). • However, authors argued that deep nested loops are rare. • (After a program change) When re-doing elimination*, for each Gi, there is at most one interval got changed.
- 96. Related Works / Comparisons
- 97. IncrementalVersion of Hecht-Ullman’s Data-Flow Analysis* *Hecht, Matthew S., and Jeffrey D. Ullman. "A simple algorithm for global data flow analysis problems." SIAM Journal on Computing 4.4 (1975): 519-532.
- 98. IncrementalVersion of Hecht-Ullman’s Data-Flow Analysis* • The “normal” version of Hecht-Ullman’s data-flow analysis has time complexity of O(n log n). *Hecht, Matthew S., and Jeffrey D. Ullman. "A simple algorithm for global data flow analysis problems." SIAM Journal on Computing 4.4 (1975): 519-532.
- 99. IncrementalVersion of Hecht-Ullman’s Data-Flow Analysis* • The “normal” version of Hecht-Ullman’s data-flow analysis has time complexity of O(n log n). • However, that algorithm is really hard to make incremental update. *Hecht, Matthew S., and Jeffrey D. Ullman. "A simple algorithm for global data flow analysis problems." SIAM Journal on Computing 4.4 (1975): 519-532.
- 100. IncrementalVersion of Hecht-Ullman’s Data-Flow Analysis* • The “normal” version of Hecht-Ullman’s data-flow analysis has time complexity of O(n log n). • However, that algorithm is really hard to make incremental update. • Requires auxiliary data structures. *Hecht, Matthew S., and Jeffrey D. Ullman. "A simple algorithm for global data flow analysis problems." SIAM Journal on Computing 4.4 (1975): 519-532.
- 101. IncrementalVersion of Hecht-Ullman’s Data-Flow Analysis* • The “normal” version of Hecht-Ullman’s data-flow analysis has time complexity of O(n log n). • However, that algorithm is really hard to make incremental update. • Requires auxiliary data structures. • Storage and execution costs of maintaining those data structures during incremental updates might overshadow the speed up of the original algorithm. *Hecht, Matthew S., and Jeffrey D. Ullman. "A simple algorithm for global data flow analysis problems." SIAM Journal on Computing 4.4 (1975): 519-532.
- 102. Related Works Published After thisTranscript • Burke, Michael. "An interval-based approach to exhaustive and incremental interprocedural data-flow analysis." ACMTransactions on Programming Languages and Systems (TOPLAS) 12.3 (1990): 341-395. • Duesterwald, Evelyn, Rajiv Gupta, and Mary Lou Soffa. "Demand-driven computation of interprocedural data flow." Proceedings of the 22nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages.ACM, 1995. • Reps,Thomas, EmmaTuretsky, and Prathmesh Prabhu. "Newtonian program analysis via tensor product." ACM SIGPLAN Notices.Vol. 51. No. 1.ACM, 2016.
- 103. My Comments
- 105. • Both Allen-Cocke interval analysis and this work have been published for over 20 years.
- 106. • Both Allen-Cocke interval analysis and this work have been published for over 20 years. • Algorithms are easy (to implement)…
- 107. • Both Allen-Cocke interval analysis and this work have been published for over 20 years. • Algorithms are easy (to implement)… • They provide systematic instead of ad-hoc solutions…
- 108. • Both Allen-Cocke interval analysis and this work have been published for over 20 years. • Algorithms are easy (to implement)… • They provide systematic instead of ad-hoc solutions… • Nowadays there are more use cases that requires fast data- flow analysis (e.g. JIT Compilation, Language Server)…
- 109. • Both Allen-Cocke interval analysis and this work have been published for over 20 years. • Algorithms are easy (to implement)… • They provide systematic instead of ad-hoc solutions… • Nowadays there are more use cases that requires fast data- flow analysis (e.g. JIT Compilation, Language Server)… • But both of them seem to receive little attentions nowadays.
- 111. • Regarding time complexity: It will be better to use amortized analysis or probabilistic-based analysis.
- 112. • Regarding time complexity: It will be better to use amortized analysis or probabilistic-based analysis. • (For us) It will be cool to see if this algorithm still doing well on modern-days programs.
- 113. • Regarding time complexity: It will be better to use amortized analysis or probabilistic-based analysis. • (For us) It will be cool to see if this algorithm still doing well on modern-days programs. • And compare with recent works regarding incremental static analyses.
- 114. Summary
- 115. Summary • Allen-Cocke data-flow analysis provided a systematic way to resolve data-flow equations.
- 116. Summary • Allen-Cocke data-flow analysis provided a systematic way to resolve data-flow equations. • This work augment Allen-Cocke’s algorithm to make incremental update on data-flow facts upon program changes. • The updates are guided by program intervals, which provides dependencies among data-flow expressions.
- 117. Summary • Allen-Cocke data-flow analysis provided a systematic way to resolve data-flow equations. • This work augment Allen-Cocke’s algorithm to make incremental update on data-flow facts upon program changes. • The updates are guided by program intervals, which provides dependencies among data-flow expressions. • The time complexity of this is no-worse than the original Allen- Cocke analysis.
- 118. Backup
- 122. Gaussian Elimination
- 123. High School Math 101
- 124. High School Math 101
- 125. High School Math 101
- 126. High School Math 101
- 127. High School Math 101
- 128. High School Math 101
- 129. High School Math 101
- 130. High School Math 101
- 131. Data-Flow Equations and Gaussian Eliminations Example
- 132. Data-Flow Equations and Gaussian Eliminations + Example
- 133. Data-Flow Equations and Gaussian Eliminations + = Example
- 134. Data-Flow Equations and Gaussian Eliminations