Liang Yuan
Peter Denning
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Abstract
In many areas of program and system analysis and optimization, locality is a common concept and has been defined and measured in many ways. This article aims to formally establish relations between these previously disparate types of locality. It categorizes locality definitions in three groups and shows whether and how they can be interconverted. For the footprint, a recent metric, it gives a new measurement algorithm that is asymptotically more time/space efficient than previous approaches. Using the conversion relations, the new algorithm derives with the same efficiency different locality metrics developed and used in program analysis, memory management, and cache design.
- Alfred V. Aho, Monica S. Lam, Ravi Sethi, and Jeffrey D. Ullman. 2006. Compilers: Principles, Techniques, and Tools (2nd ed.). Addison-Wesley. Google Scholar
Digital Library
- Randy Allen and Ken Kennedy. 2001. Optimizing Compilers for Modern Architectures: A Dependence-based Approach. Morgan Kaufmann Publishers.Google Scholar
- Ganesh Balakrishnan and Yan Solihin. 2012. WEST: Cloning data cache behavior using stochastic traces. In Proceedings of the International Symposium on High-Performance Computer Architecture. 387--398. Google ScholarDigital Library
- Kristof Beyls and Erik H. D’Hollander. 2006. Discovery of locality-improving refactoring by reuse path analysis. In Proceedings of High Performance Computing and Communications, Lecture Notes in Computer Science, Vol. 4208. Springer, 220--229. Google ScholarDigital Library
- Jacob Brock, Chen Ding, Rahman Lavaee, Fangzhou Liu, and Liang Yuan. 2018. Prediction and bounds on shared cache demand from memory access interleaving. In Proceedings of the International Symposium on Memory Management. 96--108. Google ScholarDigital Library
- Jeffrey P. Buzen. 2015. Rethinking Randomness: A New Foundation for Stochastic Modeling.Google Scholar
- Daniel Byrne, Nilufer Onder, and Zhenlin Wang. 2018. mPart: Miss-ratio curve guided partitioning in key-value stores. In Proceedings of the International Symposium on Memory Management. 84--95. Google ScholarDigital Library
- Dhruba Chandra, Fei Guo, Seongbeom Kim, and Yan Solihin. 2005. Predicting inter-thread cache contention on a chip multi-processor architecture. In Proceedings of the International Symposium on High-Performance Computer Architecture. 340--351. Google ScholarDigital Library
- Dong Chen, Fangzhou Liu, Chen Ding, and Sreepathi Pai. 2018. Locality analysis through static parallel sampling. In Proceedings of the ACM SIGPLAN Conference on Programming Language Design and Implementation. 557--570. Google ScholarDigital Library
- Xi E. Chen and Tor M. Aamodt. 2009. A first-order fine-grained multithreaded throughput model. In Proceedings of the International Symposium on High-Performance Computer Architecture. 329--340.Google Scholar
- Trishul M. Chilimbi, Bob Davidson, and James R. Larus. 1999. Cache-conscious structure definition. In Proceedings of the ACM SIGPLAN Conference on Programming Language Design and Implementation. 13--24. Google ScholarDigital Library
- Edward G. Coffman Jr. and Peter J. Denning. 1973. Operating Systems Theory. Prentice-Hall. Google ScholarDigital Library
- Keith Cooper and Linda Torczon. 2010. Engineering a Compiler (2nd ed.). Morgan Kaufmann.Google Scholar
- Peter J. Denning. 1968. The working set model for program behaviour. Commun. ACM 11, 5 (1968), 323--333. Google ScholarDigital Library
- Peter J. Denning and Jeffrey P. Buzen. 1978. The operational analysis of queueing network models. Comput. Surv. 10, 3 (1978), 225--261. Google ScholarDigital Library
- Peter J. Denning and Kevin C. Kahn. 1975. A study of program locality and lifetime functions. In Proceedings of the ACM Symposium on Operating System Principles. 207--216. Google ScholarDigital Library
- Peter J. Denning and Craig H. Martell. 2015. Great Principles of Computing. MIT Press. Google ScholarDigital Library
- Peter J. Denning and Stuart C. Schwartz. 1972. Properties of the working set model. Commun. ACM 15, 3 (1972), 191--198. Google ScholarDigital Library
- Peter J. Denning and Donald R. Slutz. 1978. Generalized working sets for segment reference strings. Commun. ACM 21, 9 (1978), 750--759. Google ScholarDigital Library
- C. Ding and K. Kennedy. 2004. Improving effective bandwidth through compiler enhancement of global cache reuse. J. Parallel Distrib. Comput. 64, 1 (2004), 108--134. Google ScholarDigital Library
- Chen Ding, Xiaoya Xiang, Bin Bao, Hao Luo, Ying-Wei Luo, and Xiao-lin Wang. 2014. Performance metrics and models for shared cache. J. Comput. Sci. Technol. 29, 4 (2014), 692--712.Google ScholarCross Ref
- Malcolm C. Easton and Ronald Fagin. 1978. Cold-start vs. Warm-start miss ratios. Commun. ACM 21, 10 (1978), 866--872. Google ScholarDigital Library
- David Eklov, David Black-Schaffer, and Erik Hagersten. 2011. Fast modeling of shared caches in multicore systems. In Proceedings of the International Conference on High Performance Embedded Architectures and Compilers. 147--157. Google ScholarDigital Library
- David Eklov and Erik Hagersten. 2010. StatStack: Efficient modeling of LRU caches. In Proceedings of the IEEE International Symposium on Performance Analysis of Systems and Software. 55--65.Google ScholarCross Ref
- Venmugil Elango, Fabrice Rastello, Louis-Noël Pouchet, J. Ramanujam, and P. Sadayappan. 2015. On characterizing the data access complexity of programs. In Proceedings of the ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages. 567--580. Google ScholarDigital Library
- Changpeng Fang, Steve Carr, Soner Önder, and Zhenlin Wang. 2005. Instruction based memory distance analysis and its application. In Proceedings of the International Conference on Parallel Architecture and Compilation Techniques. 27--37. Google ScholarDigital Library
- Xiaoming Gu, Ian Christopher, Tongxin Bai, Chengliang Zhang, and Chen Ding. 2009. A component model of spatial locality. In Proceedings of the International Symposium on Memory Management. 99--108. Google ScholarDigital Library
- Saurabh Gupta, Ping Xiang, Yi Yang, and Huiyang Zhou. 2013. Locality principle revisited: A probability-based quantitative approach. J. Parallel Distrib. Comput. 73, 7 (2013), 1011--1027.Google ScholarCross Ref
- J. Hong and H. T. Kung. 1981. I/O complexity: The red-blue pebble game. In Proceedings of the ACM Conference on Theory of Computing. Google ScholarDigital Library
- Xiameng Hu, Xiaolin Wang, Lan Zhou, Yingwei Luo, Chen Ding, and Zhenlin Wang. 2016. Kinetic modeling of data eviction in cache. In Proceedings of USENIX Annual Technical Conference. 351--364. Google ScholarDigital Library
- Xiameng Hu, Xiaolin Wang, Lan Zhou, Yingwei Luo, Zhenlin Wang, Chen Ding, and Chencheng Ye. 2018. Fast miss ratio curve modeling for storage cache. ACM Trans. Stor. 14, 2 (2018), 12:1--12:34. Google ScholarDigital Library
- Khaled Z. Ibrahim and Erich Strohmaier. 2010. Characterizing the relation between Apex-Map synthetic probes and reuse distance distributions. In Proceedings of the International Conference on Parallel Processing. 0 (2010), 353--362. Google ScholarDigital Library
- Bruce Jacob, Spencer W. Ng, and David T. Wang. 2010. Memory Systems: Cache, DRAM, Disk. Morgan Kaufmann. Google ScholarDigital Library
- S. Jiang and X. Zhang. 2002. LIRS: An efficient low inter-reference recency set replacement to improve buffer cache performance. In Proceedings of the International Conference on Measurement and Modeling of Computer Systems. Google ScholarDigital Library
- Rahman Lavaee. 2016. The hardness of data packing. In Proceedings of the ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages. 232--242. Google ScholarDigital Library
- Pengcheng Li, Colin Pronovost, William Wilson, Benjamin Tait, Jie Zhou, Chen Ding, and John Criswell. 2019. Beating OPT with statistical clairvoyance and variable size caching. In Proceedings of the International Conference on Architectural Support for Programming Languages and Operating Systems. 243--256. Google ScholarDigital Library
- Yumeng (Lucinda) Liu, Daniel Busaba, Chen Ding, and Daniel Gildea. 2018. All timescale window co-occurrence: Efficient analysis and a possible use. In Proceedings of the 28th Annual International Conference on Computer Science and Software Engineering. 289--292. http://dl.acm.org/citation.cfm?id=3291291.3291322. Google ScholarDigital Library
- Li Lu and Michael L. Scott. 2011. Toward a formal semantic framework for deterministic parallel programming. In Proceedings of the International Conference on Distributed Computing. 460--474. Google ScholarDigital Library
- Hao Luo, Guoyang Chen, Fangzhou Liu, Pengcheng Li, Chen Ding, and Xipeng Shen. 2018. Footprint modeling of cache associativity and granularity. In Proceedings of the International Symposium on Memory Systems (MEMSYS’18). 232--242. Google ScholarDigital Library
- Hao Luo, Pengcheng Li, and Chen Ding. 2017. Thread data sharing in cache: Theory and measurement. In Proceedings of the ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming. 103--115. Google ScholarDigital Library
- Rafael K. V. Maeda, Qiong Cai, Jiang Xu, Zhe Wang, and Zhongyuan Tian. 2017. Fast and accurate exploration of multi-level caches using hierarchical reuse distance. In Proceedings of the International Symposium on High-Performance Computer Architecture. 145--156.Google ScholarCross Ref
- G. Marin and J. Mellor-Crummey. 2004. Cross architecture performance predictions for scientific applications using parameterized models. In Proceedings of the International Conference on Measurement and Modeling of Computer Systems. 2--13. Google ScholarDigital Library
- R. L. Mattson, J. Gecsei, D. Slutz, and I. L. Traiger. 1970. Evaluation techniques for storage hierarchies. IBM Syst. J. 9, 2 (1970), 78--117. Google ScholarDigital Library
- Ulrich Meyer, Peter Sanders, and Jop F. Sibeyn (Eds.). 2003. Algorithms for Memory Hierarchies, Advanced Lectures. Lecture Notes in Computer Science, Vol. 2625. Springer. Google ScholarDigital Library
- Cedric Nugteren, Gert-Jan van den Braak, Henk Corporaal, and Henri E. Bal. 2014. A detailed GPU cache model based on reuse distance theory. In Proceedings of the International Symposium on High-Performance Computer Architecture.Google Scholar
- E. Petrank and D. Rawitz. 2002. The hardness of cache conscious data placement. In Proceedings of the ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages. Google ScholarDigital Library
- Apan Qasem and Ken Kennedy. 2005. Evaluating a Model for Cache Conflict Miss Prediction. Technical Report CS-TR05-457. Rice University.Google Scholar
- S. Rubin, R. Bodik, and T. Chilimbi. 2002. An efficient profile-analysis framework for data layout optimizations. In Proceedings of the ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages. Portland, Oregon. Google ScholarDigital Library
- Derek L. Schuff, Milind Kulkarni, and Vijay S. Pai. 2010. Accelerating multicore reuse distance analysis with sampling and parallelization. In Proceedings of the International Conference on Parallel Architecture and Compilation Techniques. 53--64. Google ScholarDigital Library
- Rathijit Sen and David A. Wood. 2013. Reuse-based online models for caches. In Proceedings of the International Conference on Measurement and Modeling of Computer Systems. 279--292. Google ScholarDigital Library
- Xipeng Shen and Jonathan Shaw. 2008. Scalable implementation of efficient locality approximation. In Proceedings of the Workshop on Languages and Compilers for Parallel Computing. 202--216. Google ScholarDigital Library
- Xipeng Shen, Jonathan Shaw, Brian Meeker, and Chen Ding. 2007. Locality approximation using time. In Proceedings of the ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages. 55--61. Google ScholarDigital Library
- Donald R. Slutz and Irving L. Traiger. 1974. A note on the calculation working set size. Commun. ACM 17, 10 (1974), 563--565. Google ScholarDigital Library
- A. J. Smith. 1976. On the effectiveness of set associative page mapping and its applications in main memory management. In Proceedings of the International Conference on Software Engineering. Google ScholarDigital Library
- M. Snir and J. Yu. 2005. On the Theory of Spatial and Temporal Locality. Technical Report DCS-R-2005-2564. Computer Science Deptartment, University of Illinois at Urbana--Champaign.Google Scholar
- G. Edward Suh, Srinivas Devadas, and Larry Rudolph. 2001. Analytical cache models with applications to cache partitioning. In Proceedings of the International Conference on Supercomputing. 1--12. Google ScholarDigital Library
- David K. Tam, Reza Azimi, Livio Soares, and Michael Stumm. 2009. RapidMRC: Approximating L2 miss rate curves on commodity systems for online optimizations. In Proceedings of the International Conference on Architectural Support for Programming Languages and Operating Systems. 121--132. Google ScholarDigital Library
- Qingsen Wang, Xu Liu, and Milind Chabbi. 2019. Featherlight reuse-distance measurement. In Proceedings of the International Symposium on High-Performance Computer Architecture. 440--453.Google ScholarCross Ref
- Jake Wires, Stephen Ingram, Zachary Drudi, Nicholas JA Harvey, Andrew Warfield, and Coho Data. 2014. Characterizing storage workloads with counter stacks. In Proceedings of the Symposium on Operating Systems Design and Implementation. USENIX Association, 335--349. Google ScholarDigital Library
- M. J. Wolfe. 1996. High Performance Compilers for Parallel Computing. Addison-Wesley, Redwood City, CA. Google ScholarDigital Library
- Meng-Ju Wu and Donald Yeung. 2013. Efficient reuse distance analysis of multicore scaling for loop-based parallel programs. ACM Trans. Comput. Syst. 31, 1 (2013), 1. Google ScholarDigital Library
- Meng-Ju Wu and Donald Yeung. 2011. Coherent profiles: Enabling efficient reuse distance analysis of multicore scaling for loop-based parallel programs. In Proceedings of the International Conference on Parallel Architecture and Compilation Techniques. 264--275. Google ScholarDigital Library
- Meng-Ju Wu, Minshu Zhao, and Donald Yeung. 2013. Studying multicore processor scaling via reuse distance analysis. In Proceedings of the International Symposium on Computer Architecture. 499--510. Google ScholarDigital Library
- Xiaoya Xiang, Bin Bao, Tongxin Bai, Chen Ding, and Trishul M. Chilimbi. 2011a. All-window profiling and composable models of cache sharing. In Proceedings of the ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming. 91--102. Google ScholarDigital Library
- Xiaoya Xiang, Bin Bao, Chen Ding, and Yaoqing Gao. 2011b. Linear-time modeling of program working set in shared cache. In Proceedings of the International Conference on Parallel Architecture and Compilation Techniques. 350--360. Google ScholarDigital Library
- Xiaoya Xiang, Chen Ding, Hao Luo, and Bin Bao. 2013. HOTL: A higher order theory of locality. In Proceedings of the International Conference on Architectural Support for Programming Languages and Operating Systems. 343--356. Google ScholarDigital Library
- Yaocheng Xiang, Xiaolin Wang, Zihui Huang, Zeyu Wang, Yingwei Luo, and Zhenlin Wang. 2018. DCAPS: Dynamic cache allocation with partial sharing. In Proceedings of the EuroSys Conference. 13:1--13:15. Google ScholarDigital Library
- Chencheng Ye, Chen Ding, Hao Luo, Jacob Brock, Dong Chen, and Hai Jin. 2017. Cache exclusivity and sharing: Theory and optimization. ACM Trans. Arch. Code Optimiz. 14, 4, 34:1--34:26. Google ScholarDigital Library
- Liang Yuan, Wesley Smith, Chen Ding, Sicong Fan, Zixu Chen, and Yunquan Zhang. 2018. Footmark: A new formulation for working set statistics. In Proceedings of the Workshop on Languages and Compilers for Parallel Computing.Google Scholar
- Chengliang Zhang, Chen Ding, Mitsunori Ogihara, Yutao Zhong, and Youfeng Wu. 2006. A hierarchical model of data locality. In Proceedings of the ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages. 16--29. Google ScholarDigital Library
- Y. Zhong, S. G. Dropsho, X. Shen, A. Studer, and C. Ding. 2007. Miss rate prediction across program inputs and cache configurations. IEEE Trans. Comput. 56, 3 (Mar. 2007), 328--343. Google ScholarDigital Library
- Yutao Zhong, Xipeng Shen, and Chen Ding. 2009. Program locality analysis using reuse distance. ACM Trans. Program. Lang. Syst. 31, 6 (Aug. 2009), 1--39. Google ScholarDigital Library
Index Terms
- A Relational Theory of Locality
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