IPSJ SIG Technical Report Vol.2014-HPC-143 No /3/3 1 1 t-fpc 1 bit SCALE t-fpc TIME-SERIES DATA COMPRESSION METHOD FOR TIME EVOLUTION SIMULATION
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1 1 1 t-fpc 1 bit SCALE t-fpc TIME-SERIES DATA COMPRESSION METHOD FOR TIME EVOLUTION SIMULATIONS Yuki Matsuo 1 Yutaka Ishikawa 1 Abstract: Time evolution simulations generate a large amount of data periodically to ouput results. Existing compression techniques reduce data size by utilizing the similarity among the neighboring values inside the data that is written at one time step. In this paper, we propose t-fpc, a time-series data compression method that adapts the existing predictor based fast floating point compression algorithm. Compared to previous compression methods, it differs in the aspect that it compresses the intermediate result of one time step utilizing the finite differences among the data of recent multiple time steps, instead of those inside the data at the same time step in order to increase the compression ratio. In t-fpc, diffs are compressed with eight kinds of bit lengths. Those are determined based on bit length distribution of diffs. Special encoding is introduced for the two cases: one is that an element at one time step is the same as the previous time step, and another is that all elements at one time step is completely the same as the previous time step. Using the SCALE weather and climate model, it is shown that t-fpc achieves better processing speed and compression ratio than other data compressors including a famous floating point compressor. 1. HPC [1] 1 [2] I/O FPC(Floating Point Compression) [3] t-fpc FPC 3 ( ) 1
2 1 FPC t-fpc 4 1) FPC t-fpc 2) FPC 1 8 t-fpc 8 FPC FPC t-fpc 8 3 3) 3 1 4) 2. FPC(Floating Point Compression) t-fpc 2.1 FPC 1 FPC a 14bit ( 1 ) a[1] a[2] a[2] a[3] a[3] a[4] ( 2 ) 3 dpred 0 2 ( 3 ) dpred a[4] a[5] ( 4 ) a[5] ( 5 ) IEEE754 14bit 7bit 6bit ( 6 ) FPC 3bit FPC 2 FPC t-fpc FPC 2.2 t-fpc FPC 3 t-fpc API 3 API 4 t-fpc FPC 3 FPC FPC 2
![typedef struct { union double_uint* prev; uint64_t* delta[3]; size_t nelm; int state; struct](/docs-images/96/127786859/images/3-0.jpg "hash_entry* ht; } struct_tfpc; 6 size_t compress(double* in, double* out, struct_tfpc* st); void")
![SCALE[5] t-fpc FPC gzip[6], bzip2[6] velocity(u, V, W) potential temperature(pt) relative humidity(rh)](/docs-images/96/127786859/images/3-2.jpg "total water(qtot) 60 600 2 9 gzip, bzip2 t-fpc FPC 60 FPC 13.5 %600 FPC 2.3 % 10 t-fpc FPC gzip 66% 3")
3 typedef struct { union double_uint* prev; uint64_t* delta[3]; size_t nelm; int state; struct hash_entry* ht; } struct_tfpc; 6 size_t compress(double* in, double* out, struct_tfpc* st); void decompress(double* in, double* out, struct_tfpc* st, int flag); 3 t-fpc API t-fpc FPC 3bit 7 t-fpc FPC 2bit 8bit 3bit 5 Sandia National Laboratory LAMMPS[4] SCALE[5] 10bit 30bit t-fpc 3. SCALE[5] t-fpc FPC gzip[6], bzip2[6] velocity(u, V, W) potential temperature(pt) relative humidity(rh) total water(qtot) gzip, bzip2 t-fpc FPC 60 FPC 13.5 %600 FPC 2.3 % 10 t-fpc FPC gzip 66% 3
![9 5. t-fpc t-fpc t-fpc [3] t-fpc FPC t-fpc I/O 10 / HPCI HPCI CREST 11 11 t-fpc 4. Hogan [7] DEFLATE [8] [9] Lorenzo [1] Dongarra, J. and Beckman, P.](/docs-images/96/127786859/images/4-0.jpg ": The International Exascale Software Roadmap, International Journal of High Performance Computer Applications, No. 1 (2011). [2] :. [3] Goeman, B., Vandierendonck, H. and De Bosschere, K.")
![(online), available from http://lammps.sandia.gov/. [5] : SCALE Scalable Computing for Advanced Library and Environment, http://www.gfd- dennou.org/arch/davis/workshop/2012-12- 12/nishizawa 20121212.](/docs-images/96/127786859/images/4-2.jpg "pdf. [6] : bzip2, http://www.bzip.org. [7] Hogan, S., Hammond, J. and Chien, A.: An evaluation of difference and threshold techniques for efficient checkpoints, DSN Workshops, IEEE (2012).")
4 9 5. t-fpc t-fpc t-fpc [3] t-fpc FPC t-fpc I/O 10 / HPCI HPCI CREST t-fpc 4. Hogan [7] DEFLATE [8] [9] Lorenzo [1] Dongarra, J. and Beckman, P.: The International Exascale Software Roadmap, International Journal of High Performance Computer Applications, No. 1 (2011). [2] :. [3] Goeman, B., Vandierendonck, H. and De Bosschere, K.: Differential FCM: increasing value prediction accuracy by improving table usage efficiency, High-Performance Computer Architecture, HPCA. The Seventh International Symposium on, pp (online), DOI: /HPCA (2001). [4] : LAMMPS Molecular Dynamics Simulator, (online), available from [5] : SCALE Scalable Computing for Advanced Library and Environment, dennou.org/arch/davis/workshop/ /nishizawa pdf. [6] : bzip2, [7] Hogan, S., Hammond, J. and Chien, A.: An evaluation of difference and threshold techniques for efficient checkpoints, DSN Workshops, IEEE (2012). [8] Gomez, L. A. and Cappello, F.: Improving foating point compression through binary masks, International Conference on Big Data, pp (2013). [9] Lindstrom, P. and Isenburg, M.: Fast and efficient compression of oatingpoint data, Vol. 12, No. 5 (2006). 4
![正誤表図 5 9 10 11 は順に次が正 参考文献 [3] は次の 2 文献の引用が正 [3-1] Burtscher, M. and Ratanaworabhan, P.](/docs-images/96/127786859/images/5-3.jpg ": FPC: A High-Speed Compressor for Double-Precision Floating-Point Data, Computers, IEEE Transactions on, Vol. 58, No. 1, pp. 18 31 (online), DOI: 10.1109/ TC.2008.")
![131(2009). [3-2] Ratanaworabhan, P., Ke, J. and Burtscher, M.: Fast lossless compression of scientific floating-point data, Data Compression Conference, 2006. DCC 2006.](/docs-images/96/127786859/images/5-5.jpg "Proceedings, pp. 133 142 (online), DOI: 10.1109/ DCC. 2006.35 (2006).")
5 正誤表図 は順に次が正 参考文献 [3] は次の 2 文献の引用が正 [3-1] Burtscher, M. and Ratanaworabhan, P.: FPC: A High-Speed Compressor for Double-Precision Floating-Point Data, Computers, IEEE Transactions on, Vol. 58, No. 1, pp (online), DOI: / TC (2009). [3-2] Ratanaworabhan, P., Ke, J. and Burtscher, M.: Fast lossless compression of scientific floating-point data, Data Compression Conference, DCC Proceedings, pp (online), DOI: / DCC (2006). 図 5 ゼロビット長出現頻度 1 章 誤 あるデータが直前に書きだしたデータと同じ値の場合には 正 同じ値が連続する場合には 正確な値予測が可能になる あるデータが予測値と同じ場合には 誤 直前のタイムステップで書きだしたデータが全部同じ値であった場合の識別子 正 あるタイムステップで書き出したデータが全部予測値と同じ値であった場合の識別子 図 9 圧縮率 2.1 節 誤 ここでは浮動小数点データは14bit で表現されている 正 ここでは浮動小数点データは13bit で表現されている 誤 図の例では 14bit 中 正 図の例では 13bit 中 図 6 の説明文誤 残余領域が少ない場合 正 データ変動が少ない場合 図 8 の説明文 図 10 圧縮 / 解凍時間 誤 残余が同じ場合 正 データが変動しない場合 節の表題誤 残余領域が少ない場合の圧縮率向上 正 データ変動が少ない場合の圧縮率向上 節の表題誤 残余が同じ場合の圧縮率向上 正 データが変動しない場合の圧縮率向上 節 図 11 圧縮方向の影響 誤 当該ステップは同じであるという識別子 正 当該ステップの値は全て予測値と同一になり そのことを表 す識別子
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Q [4] 2. [3] [5] ϵ- Q Q CO CO [4] Q Q [1] i = X ln n i + C (1) n i i n n i i i n i = n X i i C exploration exploitation [4] Q Q Q ϵ 1 ϵ 3. [3] [5] [4]
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