Memory Access Time: In order to look at the performance of cache memories, we need to look at . 63 - 74, October 1991. Large-Scale Shared Memory Multiprocessors. Software optimizations for cache/ Virtual memory & memory hierarchy Hung-Wei Tseng. edu In Proceedings of the 4th International Conference on Architectural Support for Programming Languages and Operating Systems, pages 63-74, April 1991. 63-74, April 1991; K. Conference Paper. Google Scholar Digital Library. Finally, we consider stencil computations on a machine with an explicitly-managed memory hierarchy, the Cell processor. . Google Scholar; 7 D. Gannon, W. Jalby, and K. Gallivan. • Implementing algorithms in a more cache friendly way! Average memory access time = hit time + Miss rate x Miss Penalty. In Proceedings of the 4th International Conference on Archi-tectural Support for Programming Languages and Operating Systems, pages 63.74, April 1991. and cache/memory optimizations. Concern regarding poor performance of cache memories for processors due to the size of data sets has been studied by a number of researchers (see M. S. Lam, E. E. Rothberg, and M. E. Wolf, "The cache performance and optimizations of blocked algorithms," Proc. Instead of operating on entire rows or columns of an array, blocked algorithms operate on submatrices or blocks . Improved cache performance is crucial to improved code performance. the cache performance of cache oblivious algorithms for matrix transpose, FFT, and sorting in [9]. Multilevel Caches • Reducing Miss Rate 4. Conf. 2019. edu [email protected] berkeley. performance for many stencil kernels. One characteristic that these problems share is a very regular memory accesses that are known at compile time. As a side note, you will be required to implement several levels of cache blocking for matrix multiplication for Project 3. The Euclidean algorithm for computing the gcd of two numbers is used to predict conflicts between different array columns for linear algebra codes. 18 A. R. Lebeck and D. A. Those types of 2 sockets (56 cores) of CLX8280. computations — a class of algorithms a . berkeley. 1991 ) p. 63-74 Sys., pp. The cache performance and optimizations of blocked algorithms . Impact of modern memory subsystems on cache optimizations for stencil computations (2005) by Shoaib Kamil, Parry Husbands, Leonid Oliker, John Shalf, Katherine Yelick . For this lab, you will implement a cache blocking scheme for matrix transposition and analyze its performance. Instead of operating on entire rows or columns of an array, blocked algorithms operate on submatrices or blocks. Some research compilers do attack the problem of automatically optimizing code for particular cache organizations. Section 5 of- "The cache performance and optimizations of blocked algorithms". Where Hit Time is the time to deliver a block in the cache to the processor (includes time to determine whether the block is in the cache), Miss Rate is the fraction of memory references not found in cache (misses/references) and Miss Penalty is the . 63 -74 . Other authors have proposed similar and different techniques for accelerating the sparse matrix-vector product. Google Scholar Kun Li, Honghui Shang, Yunquan Zhang, Shigang Li, Baodong Wu, Dong Wang, Libo Zhang, Fang Li, Dexun Chen, and Zhiqiang Wei. the resulting performance numbers. of Arch, Supp. 63{74. Blocked matrix multiplication algorithms are described in detail in Lam et al., The Cache Performance and Optimizations of Blocked Algorithms, Proceedings of the Fourth International Conference on Architectural Support for Programming Languages and Operating Systems, pp. Cache oblivious optimizations optimize algorithms with-out using cache sizes as a tuning parameter. Unformatted text preview: An Overview of Cache Optimization Techniques and Cache{Aware Numerical Algorithms? Some research compilers do attack the problem of automatically optimizing code for particular cache organizations. Section 3 de- scribes some known techniques for cache optimizations. The cache performance and optimizations of blocked algorithms. 63--74. Many compilers use some of these optimizations to improve code performance. The Efficacy of Software Prefetching and Locality Optimizations on Future Memory Systems. Lam, E. E. Rothberg and M. E. Wolf, 'The cache performance and optimizations of blocked algorithms', Proc. The A100 GPU includes 40 MB of L2 cache, which is 6.7x larger than V100 L2 cache.The L2 cache is divided into two partitions to enable higher bandwidth and lower latency memory access. The Cache Performance and Optimizations of Blocked Algorithms ASPLOS 1991 — Monica S. Lam, Edward E. Rothberg, Michael E. Wolf. The influence of memory hierarchy on algorithm organization: Programming FFTs on a vector multiproeessor. Cache Performance . Lang. This paper presents cache performance data for blocked programs and evaluates several optimizations . , "The cache performance and optimizations of blocked algorithms". The cache performance and optimizations of blocked algorithms. cache performance data for blocked programs evaluates several optimizations to improve this performance data is obtained by a theoretical model of data conflicts in the cache validated by large amounts of simulation 第二段 cache缺失的程度 highly sensitive to the stride of data accesses the size of the blocks cause wide variations in machine performance conf. Larger Cache size . algorithms so to exploit locality and software portability by addressing code optimizations and compiler-driven memory-hierarchy adaptations such as data--cache-line size, data-cache mapping. Set associative mapping!less misses but more sets (slower). compilers [19], [16] and [5], or study the cache performance of particular types of algorithm, especially blocked ones [6], [20], [9], and [22]. In this paper, we focus on cache blocking (Section 2) and ask the fundamental questions of what limits exist on such performance tuning, and how close tuned code gets to these limits. . Experiments on a range of programs indicate PadLite can eliminate conflicts for benchmarks, but Pad is more effective over a range of cache and problem sizes. The cache performance and optimizations of blocked algorithms. Sec- tion 2 briefly reviews cache memories. The book ends with an overview of parallel algorithms using STL execution policies, Boost Compute, and OpenCL to utilize both the CPU and the GPU. 3 Upper Bounds on Performance We use performance upper bounds to estimate the best possible performance given a matrix and data structure but independent of any particular instruction mix or ordering. Improving the Accuracy of Dynamic Branch Prediction Using Branch Correlation ASPLOS 1992 — Shien-Tai Pan, Kimming So, Joseph T. Rahmeh. Google Scholar For The processor has an on-chip primary data cache of 8 Kbytes, and a secondary cache of 256 Kbytes. The blocked algorithm has computational intensity q » b • The larger the block size, the more efficient our algorithm will be • Limit: All three blocks from A,B,C must fit in fast memory (cache), so we cannot make these blocks arbitrarily large • Assume your fast memory has size M fast 3b2 £ M fast, so q » b £ (M fast/3)1/2 required Apr 1991; . The associativities for the L1 instruction, L1 data, unified L2, and shared L3 caches are 4-way, 8-way, 8-way, and 16-way set associative, respectively. David Patterson, John Shalf, Katherine Yelick - In (submitted to) Proc. In Proceedings of the 4th International Conference on Architectural Support for Programming Languages and Operating Systems, pp. Lam et al.4 evaluated several optimizations to improve cache performance of blocked matrix multiplication algorithms. and Opr. In: Int. 11 A. Porterfield. PhD thesis, Department of Computer Science, University of Illinois at Urbana-Champaign, May 1987. Christopher Weiss. 4th Architectural Support for Programming Languages and Operating Systems (ASPLOS-IV . CACM, 12 (3):153-165, 1969. For example, see the SUIF compiler work at Stanford, such as "The Cache Performance and Optimizations of Blocked Algorithms" by M. Lam, E. Rothberg and M. Wolf. The optimizations target cache reuse across stencil sweeps, including both an implicit cache oblivious approach and a cache-aware algorithm blocked to match the cache structure. the cache performance and optimizations of blocked algorithms Proceedings of the Fourth International Conference on Architectural Support for Programming Languages and Operating Systems ( Apr. Carnegie Mellon Blocked D&C Algorithms ♦Most matrix-computations libraries are blocked-Code legacy (Fortran)-Availability of advanced compiler optimizations Tiling (Improving cache locality) Software pipelining (hiding latency/exploit ILP) Register allocation (Reducing cache/memory accesses) This paper presents cache performance data for blocked programs and evaluates several optimizations to improve this performance. For instance, Toledo ([8] and the references therein) mentions the possibility of reordering the matrix (in particular with a bandwidth reducing algorithm) to reduce cache misses on the input vector. When Cache Blocking of Sparse Matrix Vector Multiply Works and Why By Rajesh Nishtala, Richard W. Vuduc, James W. Demmel, and Katherine A. Yelick Be. on Architectural Support for Programming Languages and Operating Systems (ASPLOS), pp. In: Proceedings of the Fourth International Conference on Architectural Support for Programming Languages and Operating System, pp. [LW91] Lam, Monica S., and Michael E Wolf. The organization of matrices and matrix operations in a paged multiprogramming environment. More recently, Frigo The optimizations target cache reuse across stencil sweeps, including both an implicit cache oblivious approach and a cache-aware algorithm blocked to match the cache structure. Strategies for cache and local memory management by global program transformation. The Cache Performance of Blocked Monica S. Lam, Edward Computer Stanford and Optimization Algorithms and Michael 94305 E. Wolf Laboratory CA E. Rothberg Systems University, Abstract Blocking is a well-known optimization technique for improving the effectiveness of memory hierarchies. Such opti-mizations have been shown to improve performance for some classes of matrix operations [8] including matrix transpose, fast fourier transform, and sorting [3]. In section 4 we present the query processing algorithms and study how cache optimization helps. ignore conflict misses) n Ignores TLB misses (Called the \tall cache assumption.") • BlockMultiply only accesses elements of A0, B0, C0. 63-74, 1991. PhD thesis, Rice University, May 1989. Park and Prasanna discuss dynamic data remapping to improve cache performance for the DFT in [13]. Gannon and Jalby8 presented an analytical model of The cache performance and optimizations of blocked algorithms. We formulate graph optimizations, including edge traversal direction, data layout, parallelization, cache, non-uniform memory access (NUMA), bucket updates, and kernel fusion optimizations, as tradeoffs between locality, parallelism, and work-efficiency. SC2008: High performance computing , networking . A core also has a unified L2 cache (same cache for instructions and data) of 256 Kibibytes. cache blocking of Sparse Matrix Vector Multiplica-tion (SpM×V) yield significant performance improve-ments. The code example below, which performs matrix multiplication, helps . The Cache Performance and Optimizations of Blocked Algorithms. Lam, M. S., Rothberg, E. E., and Wolf, M. E. April 1991. The Cache Performance and Optimizations of Blocked Algorithms, In 4th International Conference on Architectural Support for Programming Languages, held in Santa Clara, Calif., April, 1991, 63-74. Overall, results show that a cache-aware . From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop: Ten advanced optimizations of cache performance. Advanced cache memory optimizations Advanced optimizations Way prediction Way prediction Problem: Direct mapping!fast but many misses. In: Proceedings of the Fourth International Conference on Architectural Support for Programming Languages and Operating System, pp. the optimizations we propose are most suitable when SpATAmust be performed many times (e.g., in sparse iterative methods). can be done in O(T2=B + T) cache misses. Finally, we consider stencil computations on a machine with an explicitly-managed memory hierarchy, the Cell processor. 24 Cache Optimizations II. M. S. Lam, E. E. Rothberg, and M. E. Wolf. The rest of the paper is organized as follows. Berkeley Benchmarking and Optimization Group 12 Performance Models n Upper Bound on Performance n Evaluate quality of optimized code against bound n Model Characteristics and Assumptions n Considers only the cost of memory operations n Accounts for minimum effective cache and memory latencies n Considers only compulsory misses (i.e. the cache performance of cache oblivious algorithms for matrix transpose, FFT, and sorting in [9]. The optimizations target cache reuse across stencil sweeps, including both an implicit cache oblivious approach and a cache-aware algorithm blocked to match the cache structure. The cache performance and optimizations of blocked algorithms M. Lam, E. Rothberg, M. E. Wolf Published in ASPLOS IV 1 April 1991 Computer Science Blocking is a well-known optimization technique for improving the effectiveness of memory hierarchies. We also found that the optimized algorithm with the cache oblivious approach is more sensitive to conventional optimization techniques such as tiling. The 4 cores on a microprocessor share an L3 cache of 8 Mibibytes. The penalty of a primary cache miss that hits in the secondary cache is 12 cycles, and the total penalty of a miss that goes all the way to memory is 75 cycles. and algorithms community on improving memory-hierarchy performance by using techniques such as loop transformation, array padding, and cache blocking [7,8,9], and we use some of these optimizations in our optimized packing algorithms. Kim, "A new cache replacement algorithm for last-level caches by exploiting tag-distance correlation of cache lines." [11] Monica S. Lam, Edward E. Rothberg and Michael E. Wolf, "The Cache Performance and Optimizations of Blocked Algorithms." International Journal of Engineering Research & Technology (IJERT) Way prediction Additional bits stored for predicting the way to be selected in the next access. The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries = =. , "The cache performance and optimizations of blocked algorithms". For example, see the SUIF compiler work at Stanford, such as "The Cache Performance and Optimizations of Blocked Algorithms" by M. Lam, E. Rothberg and M. Wolf. Improving the Accuracy of Dynamic Branch Prediction Using Branch Correlation ASPLOS 1992 — Shien-Tai Pan, Kimming So, Joseph T. Rahmeh. • The L1 $ of intel Core i7 or AMD RyZen is 32KB, 8-way, 64-byte blocked Each L2 partition localizes and caches data for memory accesses from SMs in the GPCs directly connected to the partition. In this paper, we explore optimizations of the Blocked Compressed Sparse Row Algorithm that aim to mask the low Floating Point Operation to Memory Operation ratio that is characteristic of the SpM×V operation. The Cache Performance and Optimizations of Blocked Algorithms. Iterative algorithm. for Prog. Code optimizations, such as tile size selection, selected with the help of predicted miss ratios require a really accurate assessment of program's code behaviour. We focus strictly on sequential performance, and implement several code optimizations. Wood. Experimental results on several platforms show that the optimized algorithms improve the cache performance and achieves speedups of 2-10 times. To limit the coni- Blocking is a well-known optimization technique for improving the effectiveness of memory hierarchies. 63-74, 1991. Code optimizations, such as tile size selection, selected with the help of predicted miss ratios require a really accurate assessment of program's code behavior. What you will learn. The goal is to maximize accesses to the data loaded into the cache before the data are replaced. Value Locality and Load Value Prediction Lam M D, Rothberg E E and Wolf M E 1991 The cache performance and optimizations of blocked algorithms J. ACM SIGARCH Computer Architecture News 19 63-74 Crossref Google Scholar [5] Download to read the full article text References 1. BOP Project, U. C. Berkeley June, 2004 http: //bebop. on Architectural Support for Programming Languages and Operating Systems, Santa Clara, CA (April 1991) Google Scholar 11. Cache profiling and the SPEC benchmarks: A case study. Performance optimizations are specified using a separatescheduling language. Avoiding Address Translation during Cache Indexing • Reducing Miss Penalty 3. Park and Prasanna discuss dynamic data remapping to improve cache performance for the DFT in [13]. Instead of operating on entire rows or columns of an array, blocked algorithms operate on submatrices or blocks, so that data loaded into the faster levels of the memory hierarchy are reused. M. S. Lam, E. E. Rothberg, and M. E. Wolf, The cache performance and optimizations of blocked algorithms, in Proceedings of the Fourth International Conference on Architectural Support for Programming Languages and Operating Systems, Santa Clara, California, 1991, pp. Block prefetching and compare to single tag. One characteristic that these problems share is a very regular memory accesses that are known at compile time. Data Locality Optimizations for Iterative Numerical Algorithms and Cellular Automata on Hierarchical Memory Architectures Datenlokalit¨atsoptimierungen fur¨ iterative numerische Algorithmen und zellul¨are Automaten auf Architekturen mit hierarchischem Speicher Der Technischen Fakult¨at der Universit¨at Erlangen-Nurn¨ berg zur Erlangung . Finally, we consider stencil computations on a machine with an explicitlymanaged memory hierarchy, the Cell processor. This change improves performance by been developed for Intel Xeon CPUs with very high bandwidth 2.6× and we are now able to obtain 143.46 GB/s and 193.54 GF/s on memory subsystems, such as the Intel Xeon Phi [7]. 21 , "The Cache Performance and Optimizations of Blocked Algorithms," in Proc. Instead of operating on entire rows or columns of an array, blocked algorithms operate on submatrices or blocks, so that data loaded into the faster levels of the memory hierarchy are reused. The Cache Performance and Optimization of Blocked Algorithms The Cache Performance and Optimization of Blocked Algorithms Monica S. Lam, Edward E. Rothberg and Michael E. Wolf Computer Systems Laboratory Stanford University, CA 94305 Abstract Blocking is a well-known optimization technique for improving the effectiveness of memory hierarchies. Google Scholar Digital Library. The objectives of this module are to discuss the various factors that contribute to the average memory access time in a hierarchical memory system and discuss some of the techniques that can be adopted to improve the same. The average memory access time is calculated as follows . If B = O(M2) then we can simplify this to O(M=B). Value Locality and Load Value Prediction Since all three matrices are in cache, it requires zero additional cache misses • Therefore, our total running time is the number of loop 7 Tips of software optimizations . [11] R. This (if implemented correctly) will result in a substantial improvement in performance. Markus Kowarschik1 and Christian Wei 2 1 Lehrstuhl f ur Systemsimulation (Informatik 10) Institut f ur Informatik Friedrich{Alexander{Universit at Erlangen{N urnberg, Germany [email protected] 2 Lehrstuhl f ur Rechnertechnik und . For this reason, a combination of . 1The Roman X Legion (the tenth legion) was under the direct order of Julius Caesar during the Gaul's war. In The Characteristics of Parallel Algorithms. Giving Reads Priority over Writes • E.g., Read complete before earlier writes in write buffer 2. More on blocked algorithms • Data in the sub-blocks are contiguous within rows only • We may incur conflict cache misses • Idea: since re-use is so high… let's copy the subblocks into contiguous memory before passing to our matrix multiply routine "The Cache Performance and Optimizations of Blocked Algorithms," October 1, 2012 . Review: 6 Basic Cache Optimizations • Reducing hit time 1. 20 R. L. Lee. An overview of cache optimization techniques and cache-aware numerical algorithms . In a multiprogrammed system, when the operating system switches contexts, in addition to the cost for handling the processes being swapped out and in,… In ASPLOS4, pages 63-74, April 1991. cs. 3 Upper Bounds on Performance We use performance upper bounds to estimate the best possible performance given a matrix and data structure but independent of any particular instruction mix or ordering. the cache performance of a set of computational-intensive Fortran programs, and applied several loop transformation techniques to these programs. In Proceedings of the Fourth International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS-IV) , pages 63--74, Santa Clara, CA, April 1991. the optimizations we propose are most suitable when SpATAmust be performed many times (e.g., in sparse iterative methods). MIT Press, 1987. 63-74, April 1991, which is hereby incorporated by reference. Markus Kowarschik. The Cache Performance and Optimizations of Blocked Algorithms ASPLOS 1991 — Monica S. Lam, Edward E. Rothberg, Michael E. Wolf. compilers [6], [16] and [23], or study the cache performance of particular types of algorithm, especially blocked ones [3], [7], [10], and [22]. Software Methods for Improvement of Cache Performance on Supercomputer Applications. Cache Basics • Cache hit: in-cache memory access—cheap •C ache miss: non-cached memory access—expensive • Consider a tiny cache (for illustration only) X000 X001 X010 X011 X100 X101 X110 X111 • Cache line length: # of bytes loaded together in one entry • Associativity The authors have developed a cache visualization tool which both dynamically visualizes cache content and provides related statistics that can guide developers in making better software and hardware optimizations. Benefits of modern C++ constructs and techniques; Identify hardware bottlenecks, such as CPU cache misses, to boost performance variety of performance optimization techniques, including register blocking, cache blocking, and multiplication by multiple vectors. matrix multiply, strassen's algorithm, cache memory, data layout 1 Introduction . of the Int. An overview of cache optimization techniques and cache-aware numerical algorithms. Tuning the Matrix Multiply Algorithm Saugata Ghose, Jonathan Tse fsg532, jdt76g@cornell.edu Abstract—We implement several optimizations to improve the cache behavior of a matrix multiply algorithm on an Intel Xeon processor from the Core i7 family. We demonstrate how . Larger Block size (Compulsory misses) 5. Architectural Support for Programming Languages and Operating Systems, pages 63-74, April 1991. The Cache Performance and Optimizations of Blocked Algorithms (ASPLOS IV). Algorithms for Memory Hierarchies, 2003. Both caches are direct-mapped and use 32 byte lines. optimizations are outside the scope of this paper.
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