低周波成分高周波成分量子化適用データ符号化適用データ 元データ ウェーブレット変換量子化符号化 gzip 1 A [] [1] [2] [3] A[2i]+ A[2i +1] L[i] = 2 [2i] [2i+1] [2n] [2n+1] L [] [1] [i] [n] H [] [1] [i]
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- そよ わくや
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1 HPC NICAM 5% 7% 1. HPC HPC [1], [2], [3] 22 MTBF( ) 3 HPC [4], [5] MTBF MTBF [6] gzip 1 NICAM[7] 5% 7% I/O N I/O T C N > T + C (1) 2.2 [8] c 214 Information Processing Society of Japan 1
2 低周波成分高周波成分量子化適用データ符号化適用データ 元データ ウェーブレット変換量子化符号化 gzip 1 A [] [1] [2] [3] A[2i]+ A[2i +1] L[i] = 2 [2i] [2i+1] [2n] [2n+1] L [] [1] [i] [n] H [] [1] [i] [n] A[] A[1] A[2] A[3] A[4] A[5] A[6] A[7] A[8] 2 A[9] A[1] A[11] A[12] A[13] A[14] A[15] 3 1 L[] L[2] L[4] L[6] L[1] L[3] L[5] L[7] H[] H[2] H[4] H[6] H[1] H[3] H[5] H[7] 2 A[2i] A[2i +1] H[i] = 2 LL[] LL[1] LL[2] LL[3] LH[] LH[1] LH[2] LH[3] HL[] HL[1] HL[2] HL[3] HH[] HH[1] HH[2] HH[3] A[] A[1] A[2] A[3] A[4] A[5] A[6] A[7] A[8] A[9] A[1] A[11] A[12] A[13] A[14] A[15] 2.3 メモリ A[] A[1] A[2] A[3] LL[] LL[1] HL[] HL[1] JPEG2 JPEG [9] 3. gzip 1 O(n) A[4] A[5] A[6] A[7] LL[2] LL[3] HL[2] HL[3] A[8] A[9] A[1] A[11] LH[] LH[1] HH[] HH[1] A[12] A[13] A[14] A[15] LH[2] LH[3] HH[2] HH[3] LL[] LH[] HL[] HH[] LL[2] LH[2] HL[2] HH[2] LL[1] LH[1] HL[1] HH[1] LL[3] LH[3] HL[3] HH[3] メモリ 4 float double 1,2, c 214 Information Processing Society of Japan 2
![単純な量子化手法 2,3 1 個数 3 値高周波成分の分布 (double) average [] [1] [2] [3] n = 4 符号化 (char) 1 2 3 4 提案する量子化手法 2 3 LH, HL, HH 4 個数 1 3 3 8 値高周波成分の分布 d =1 n = 4 1 7 各分割のすべての値をその分割の平均値に置き換える 3.2 5 3.2.1 5 n n 5 n = 4 n 3.](/docs-images/92/109634269/images/3-0.jpg "2.2 5 ( d ) 5 d = 1 N high N div 5 (double) average [][1] [2] [3] 符号化 (char) 1 2 3 ビットマップ平均値の対応表低周波成分と高周波成分 (double, char 混在 ) 1 1 1 1 1 1 1 ave[] ave[n- 1] double char char double double char N div")
3 単純な量子化手法 2,3 1 個数 3 値高周波成分の分布 (double) average [] [1] [2] [3] n = 4 符号化 (char) 提案する量子化手法 2 3 LH, HL, HH 4 個数 値高周波成分の分布 d =1 n = 各分割のすべての値をその分割の平均値に置き換える n n 5 n = 4 n ( d ) 5 d = 1 N high N div 5 (double) average [][1] [2] [3] 符号化 (char) ビットマップ平均値の対応表低周波成分と高周波成分 (double, char 混在 ) ave[] ave[n- 1] double char char double double char N div N high d 6 (2) n 3.3 n double(float) n char 5i char i float 1/4 double 1/8 char bit k float k/32 double k/ double(float) double(float) char char c 214 Information Processing Society of Japan 3
4 1 12 CPU Intel Core i7-393k 6 cores 3.2GHz 1 RAID 16GB Network File System (NFS) v3 1.5TB Broadcom bnx2 Dell PERC H7 (RAID6) Western Digital WD (model:wd22faex) 圧縮時間 [usec] 圧縮時 I/O gzip その他符号化量子化ウェーブレット malloc 未圧縮時 I/O 並列数 double(float) char 6 bit double *64 bit float *32 bit char bit 4. NICAM[7] NICAM x,y,z NFS 2 ~2 7 1~128 2 cr cs orig cs comp 7 cr = cs comp cs orig 1 (3) re i X = {x i } X = { x i } re i = x i x i max j {x j } min j {x j } (4) 5 d I/O I/O 7 I/O 1.5MB I/O 2GB/s 2 I/O c 214 Information Processing Society of Japan 4
5 gzipのみウェーブレット +gzip 単純量子化 ( 符号化なし, n=1) 圧縮率 [%] 単純な手法 提案手法 圧縮率 [%] 各種圧縮手法 単純量子化 ( 符号化あり, n=1) 単純量子化 ( 符号化なし, n=128) 単純量子化 ( 符号化あり, n=128) 提案量子化 ( 符号化なし, n=1) 提案量子化 ( 符号化あり, n=1) 提案量子化 ( 符号化なし, n=128) 提案量子化 ( 符号化あり, n=128) 分割数 I/O I/O MB I/O I/O 29% 7% 3 I/O O(n) % % % % 3% 11~13% 13~29% 9 相対誤差 [%] 分割数 単純な手法提案手法 1 gzip gzip n = 1 gzip n = 1 n = 128 gzip n = 128 n = 1 gzip n = 1 n = 128 gzip n = 128 gzip 86.78% gzip 85.56% 18.92% 1% % % 1.49% % 67%.48~56.84% c 214 Information Processing Society of Japan 5
6 .53~14.56%.22~5.94%.4~1.19% [1] 5. [11], [12] [13], [14], [15], [16] [11] 3 [17], [18] [12] 3 [19] 2 1 [13], [14], [15] [13] [16] 87% 62% I/O [2], [21] [1] 6. NICAM 5% 7% c 214 Information Processing Society of Japan 6
7 相対誤差 [%] タイムステップ (1 ステップは 12 秒 ) 単純な手法 提案手法 11 S JST-CREST [1] Liang, Y., Zhang, Y., Jette, M., Sivasubramaniam, A. and Sahoo, R.: BlueGene/L Failure Analysis and Prediction Models, International Conference on Dependable Systems and Networks(DSN 26), pp (online), DOI: 1.119/DSN (26). [2] Sato, K., Maruyama, N., Mohror, K., Moody, A., Gamblin, T., de Supinski, B. R. and Matsuoka, S.: Design and Modeling of a Non-blocking Checkpointing System, Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, SC 12, Salt Lake City, UT, USA, IEEE Computer Society Press, pp. 19:1 19:1 (online), available from (212). [3] Moody, A., Bronevetsky, G., Mohror, K. and De Supinski, B.: Design, Modeling, and Evaluation of a Scalable Multi-level Checkpointing System, 21 International Conference for High Performance Computing, Networking, Storage and Analysis (SC), pp (online), DOI: 1.119/SC (21). [4] Bautista-Gomez, L., Tsuboi, S., Komatitsch, D., Cappello, F., Maruyama, N. and Matsuoka, S.: FTI: High Performance Fault Tolerance Interface for Hybrid Systems, Proceedings of 211 International Conference for High Performance Computing, Networking, Storage and Analysis, SC 11, New York, NY, USA, ACM, pp. 32:1 32:32 (online), DOI: / (211). [5] Nagarajan, A. B., Mueller, F., Engelmann, C. and Scott, S. L.: Proactive Fault Tolerance for HPC with Xen Virtualization, Proceedings of the 21st Annual International Conference on Supercomputing, ICS 7, New York, NY, USA, ACM, pp (online), DOI: / (27). [6] Graps, A.: An introduction to wavelets, Computational Science Engineering, IEEE, Vol. 2, No. 2, pp (online), DOI: 1.119/ (1995). [7] Satoh, M., Matsuno, T., Tomita, H., Miura, H., Nasuno, T. and Iga, S.: Nonhydrostatic icosahedral atmospheric model (NICAM) for global cloud resolving simulations, Journal of Computational Physics, Vol. 227, No. 7, pp (online), DOI: (28). [8] Said, A. and Pearlman, W.: An image multiresolution representation for lossless and lossy compression, IEEE Transactions on Image Processing, Vol. 5, No. 9, pp (online), DOI: 1.119/ (1996). [9] Ahmed, N., Natarajan, T. and Rao, K.: Discrete Cosine Transform, IEEE Transactions on Computers, Vol. C-23, No. 1, pp (online), DOI: 1.119/T- C (1974). [1] Baker, A. H., Xu, H., Dennis, J. M., Levy, M. N., Nychka, D., Mickelson, S. A., Edwards, J., Vertenstein, M. and Wegener, A.: A Methodology for Evaluating the Impact of Data Compression on Climate Simulation Data, Proceedings of the 23rd International Symposium on High-performance Parallel and Distributed Computing, HPDC 14, New York, NY, USA, ACM, pp (online), DOI: / (214). [11] Vaidya, N.: On Checkpoint Latency, In Proceedings of the Pacific Rim International Symposium on Fault- Tolerant Systems, pp (1995). [12] Plank, J. and Li, K.: ickp: a consistent checkpointer for multicomputers, Parallel Distributed Technology: Systems Applications, IEEE, Vol. 2, No. 2, pp (online), DOI: 1.119/ (1994). [13] Naksinehaboon, N., Liu, Y., Leangsuksun, C., Nassar, R., Paun, M. and Scott, S.: Reliability-Aware Approach: An Incremental Checkpoint/Restart Model in HPC Environments, 8th IEEE International Sympoc 214 Information Processing Society of Japan 7
8 sium on Cluster Computing and the Grid, 28. CC- GRID 8, pp (online), DOI: 1.119/CC- GRID (28). [14] Plank, J. S., Xu, J. and Netzer, R. H. B.: Compressed Differences: An Algorithm for Fast Incremental Checkpointing, Technical Report CS-95-32, University of Tennessee (1995). [15] Sancho, J., Petrini, F., Johnson, G. and Frachtenberg, E.: On the feasibility of incremental checkpointing for scientific computing, 18th International Parallel and Distributed Processing Symposium, 24. Proceedings, pp. 58 (online), DOI: 1.119/IPDPS (24). [16] Islam, T., Mohror, K., Bagchi, S., Moody, A., De Supinski, B. and Eigenmann, R.: MCREngine: A scalable checkpointing system using data-aware aggregation and compression, High Performance Computing, Networking, Storage and Analysis (SC), 212 International Conference for, pp (online), DOI: 1.119/SC (212). [17] Trivedi, K. S.: Probability and Statistics with Reliability, Queuing and Computer Science Applications, John Wiley and Sons Ltd., Chichester, UK, 2nd edition edition (22). [18] Ziv, A. and Bruck, J.: Analysis of Checkpointing Schemes for Multiprocessor Systems, Tech. Rep. RJ 9593, IBM Almaden Research Center, pp (1993). [19] Chandy, K. M. and Lamport, L.: Distributed Snapshots: Determining Global States of Distributed Systems, ACM Trans. Comput. Syst., Vol. 3, No. 1, pp (online), DOI: / (1985). [2] Woodring, J., Mniszewski, S., Brislawn, C., DeMarle, D. and Ahrens, J.: Revisiting wavelet compression for large-scale climate data using JPEG 2 and ensuring data precision, 211 IEEE Symposium on Large Data Analysis and Visualization (LDAV), pp (online), DOI: 1.119/LDAV (211). [21] Lakshminarasimhan, S., Shah, N., Ethier, S., Klasky, S., Latham, R., Ross, R. and Samatova, N. F.: Compressing the Incompressible with ISABELA: In-situ Reduction of Spatio-temporal Data, Proceedings of the 17th International Conference on Parallel Processing - Volume Part I, Euro-Par 11, Berlin, Heidelberg, Springer-Verlag, pp (online), available from (211). c 214 Information Processing Society of Japan 8
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