SZ-1.4: Significantly Improving Lossy Compression for Scientific Data Sets Based on Multidimensional Prediction and Error- Controlled Quantization

Transcription

1 SZ-1.4: Significantly Improving Lossy Compression for Scientific Data Sets Based on Mltidimensional Prediction and Error- Controlled Qantization Dingwen Tao (University of California, Riverside) Sheng Di (Argonne National Laboratory) Zizhong Chen (University of California, Riverside) Franck Cappello (Argonne National Laboratory & UIUC) 1

2 Introdction (1) Extremely large amont of data are prodced by scientific simlations and instrments HACC (Cosmology Simlation) ² 20 PB data: a single 1-trillion-particle simlation ² Mira at ANL: 26 PB file system storage ² 20 PB / 26 PB ~ 80% CESM/CMIP5 (Climate Simlation) ² 2.5 PB raw data prodced ² 170 TB post-processed data Two partial visalizations of HACC simlation data: coarse grain on fll volme or fll resoltion on small sb-volmes 2

3 Introdction (2) APS-U: next-generation APS (Advanced Photon Sorce) project at ANL 15 PB data for storage 35 TB post-processed floatingpoint data 100 GB/s bandwidth between APS and Mira 15 PB / 100 GB/s ~ 10 5 seconds (42 hors) Data compression provides a promising way to relieve I/O and storage pressre!! 3

4 Motivation Limitations of Existing Lossless Compressors Existing lossless compressors work not efficiently on large-scale scientific data (compression ratio p to 2) Table 1: Compression ratios for lossless compressors on large-scale simlations Compression ratio = Original data size / Compressed data size 4

5 Otline Introdction Large amont of scientific data Limitations of lossless compression Existing lossy compressors and limitations 5

6 Otline Introdction Large amont of scientific data Limitations of lossless compression Existing lossy compressors and limitations Or Designs Mltidimensional / Mltilayer Prediction Model Adaptive Error-Controlled Qantization 6

7 Otline Introdction Large amont of scientific data Limitations of lossless compression Existing lossy compressors and limitations Or Designs Mltidimensional / Mltilayer Prediction Model Adaptive Error-Controlled Qantization Metrics and Measrements 7

8 Otline Introdction Large amont of scientific data Limitations of lossless compression Existing lossy compressors and limitations Or Designs Mltidimensional / Mltilayer Prediction Model Adaptive Error-Controlled Qantization Metrics and Measrements Empirical Evalation Compression performance & Parallel evalation Conclsion 8

9 Otline Introdction Large amont of scientific data Limitations of lossless compression Existing lossy compressors and limitations Or Designs Mltidimensional / Mltilayer Prediction Model Adaptive Error-Controlled Qantization Metrics and Measrements Empirical Evalation Compression performance & Parallel evalation Conclsion 9

10 Existing Lossy Compressors Existing state-of-the-art lossy compressors ISABELA (NCSU) ² Sorting preconditioner ² B-Spline interpolation ZFP (LLNL) ² Cstomized orthogonal block transform ² Exponent alignment ² Block-wise bit-stream trncation SZ-1.1 (ANL) ² Linear and qadratic 1D crve fitting for prediction ² Binary representation analysis for npredictable data ² Others: non-competitive (as shown in SZ-1.1 paper IPDPS 16) 10

11 Limitations of Existing Lossy Compressor ISABELA ² Sorting is very time-consming ² Storing initial index extremely limits compression ratio ZFP ² Over-preserves errors in decompressed data with respect to ser-set error bond ² Might not respect strictly error bonds in some extreme cases de to exponent alignment step (see details in the paper) ² Not effective on low dimensional data sets (e.g., 1D and 2D) SZ-1.1 ² Prediction: only adopts 1D prediction model, i.e., linear / qadratic crve fitting ² Qantization: prediction-hitting rate drops qickly when data are not smooth or high-accracy reqirement 11

12 Otline Introdction Large amont of scientific data Limitations of lossless compression Existing lossy compressors and limitations Or Designs Mltidimensional / Mltilayer Prediction Model Adaptive Error-Controlled Qantization Metrics and Measrements Empirical Evalation Compression performance & Parallel evalation Conclsion 12

13 SZ-1.4: Significantly Improving Error-bonded Lossy Compressor The whole compression procedre 1. Point-wise mltidimensional / mltilayer data prediction 2. Error-bonded qantization (linear-scaling qantization) 3. Variable-length encoding (cstomized Hffman encoding) 4. Unpredictable data compression (similar to SZ-1.1) 5. Dictionary-based encoding (cstomized LZ77) (optional) 13

14 Or Designs Mltidimensional / Mltilayer Prediction Model (1) Use 2D data set as an example Sppose prple star is data point to be predicted SZ-1.1 s prediction model Only se 1D information in prediction SZ

15 Or Designs Mltidimensional / Mltilayer Prediction Model (1) Use 2D data set as an example Sppose prple star is data point to be predicted SZ-1.1 s prediction model Only se 1D information in prediction SZ-1.4 s prediction model Mltidimensional prediction se adjacent data points along mltiple directions Mltilayer prediction se adjacent data points in mltiple layers (e.g., 2-layer incldes red + ble points) SZ

16 Or Designs Mltidimensional / Mltilayer Prediction Model (2) Target: se n-layer prediction Point to be predicted: (i 0, j 0 ) Constrct a fitting srface f(x, y) based (i 0, j 0 ) s adjacent points n(2n+1) nknown coefficients Straightforward idea to get f(x, y) Choose n(2n+1) data points Assme fitting srface go throgh all n(2n+1) points Solve nknown coefficients Problem: not any n(2n+1) points can be on f(x, y) at the same time 16

17 Or Designs Mltidimensional / Mltilayer Prediction Model (3) Theorem The n(2n+1) points {(k 1,k 2 ) 0 k 1 +k 2 2n-1, k 1, k 2 0} can be sed for solving the n(2n+1) nknown coefficients in f(x, y) Fitting srface s vale on point (i 0, j 0 ), f(i 0, j 0 ), can be expressed explicitly by the n(2n+1) points vales f(i 0, j 0 ) serves as the prediction vale for point (i 0, j 0 ), i.e., Eqation (10) Note V(i, j) is the decompressed vale of point (i, j) Or model can tilize different nmber of layers (i.e., n) in prediction mltidimensional / mltilayer prediction model Defalt setting in SZ-1.4 Using 1-layer prediction (n = 1) f(i 0, j 0 ) = V(i 0, j 0-1) + V(i 0-1, j 0 ) V(i 0-1, j 0-1) 17

18 Or Designs Mltidimensional / Mltilayer Prediction Model (3) Theorem The n(2n+1) points {(k 1,k 2 ) 0 k 1 +k 2 2n-1, k 1, k 2 0} can be sed for solving the n(2n+1) nknown coefficients in f(x, y) Fitting srface s vale on point (i 0, j 0 ), f(i 0, j 0 ), can be expressed explicitly by the n(2n+1) points vales f(i 0, j 0 ) serves as the prediction vale for point (i 0, j 0 ), i.e., Eqation (10) Note V(i, j) is the decompressed vale of point (i, j) Or model can tilize different nmber of layers (i.e., n) in prediction mltidimensional / mltilayer prediction model Defalt setting in SZ-1.4 Using 1-layer prediction (n = 1) f(i 0, j 0 ) = V(i 0, j 0-1) + V(i 0-1, j 0 ) V(i 0-1, j 0-1) 18

19 Or Designs Mltidimensional / Mltilayer Prediction Model (4) Prediction of each data point is same Coefficients are compted before whole compression Comptation complexity of prediction is O(1) for each point Relation with Lorenzo predictor Eqivalent to Lorenzo predictor when sing 1-layer prediction (n = 1) Or model is the generic expression 19

20 Otline Introdction Large amont of scientific data Limitations of lossless compression Existing lossy compressors and limitations Or Designs Mltidimensional / Mltilayer Prediction Model Adaptive Error-Controlled Qantization Metrics and Measrements Empirical Evalation Compression performance & Parallel evalation Conclsion 20

21 Or Designs Adaptive Error- Controlled Qantization (1) SZ-1.1 à SZ-1.4 (i) Expand qantization intervals from predicted vale (made by previos prediction model) by linear scaling of the error bond (ii) Encode the real vale sing the qantization interval nmber (qantization code) Error Bond Predicted Vale Real Vale New design 2*Error Bond 2*Error Bond First-phase Predicted Vale 2*Error Bond 2*Error Bond Second-phase Predicted Vale Real Vale +1 Second-phase Predicted Vale Error Bond Second-phase Predicted Vale Second-phase Predicted Vale Uniform Qan>za>on Code Qantization with one interval in SZ-1.1 Qantization with mltiple intervals (linear scaling) in SZ

22 Or Designs Adaptive Error- Controlled Qantization (2) Figre: distribtion of qantization codes prodced by errorcontrolled qantization encoder on climate simlation data (ATM) with two different error bonds and 255 qantization intervals (1 byte) Distribtion: FAIRLY UNEVEN We can frther redce the size of qantization codes by sing variable-length encoding (e.g., Hffman encoding, arithmetic encoding) 22

23 Or Designs Adaptive Error- Controlled Qantization (3) How many qantization intervals? Excess: wastefl bits for qantization code Insfficient: nable to cover irreglar/spiky data Unpredictable data: hard-tocompress, relatively larger than qantization code Adaptive # of qantization intervals to assre prediction-hitting rate > θ (θ is a threshold) 1. Sampling on initial data 2. Estimate qantization interval # for each sampling point 3. Cont how many sampling points for fixed interval # 4. Sm nmbers with increasing interval # ntil ratio of #covered_points / #total_points > θ 5. Take power of 2 for # of qantization intervals 23

24 Otline Introdction Large amont of scientific data Limitations of lossless compression Existing lossy compressors and limitations Or Designs Mltidimensional / Mltilayer Prediction Model Adaptive Error-Controlled Qantization Metrics and Measrements Empirical Evalation Compression performance & Parallel evalation Conclsion 24

25 Measrements and Metrics (1) Point-wise Compression Error Point-wise error e i = decompressed data initial data for data point i User-set error bond eb Error bonded: e i < eb for each point i Compression ratio (CR) CR = Initial data size / compressed data size Bit-rate (BR) Nmber of amortized bits per vale BR of initial floating-point data = 32 or 64 BR of compressed data = 32 (64) / CR Compression / decompression speed B, MB, GB / Seconds 25

26 Measrements and Metrics (2) Distortion Statistical error between initial and decompressed data Commonly sed metrics (based on L 2 norm) v Root mean sqared error (RMSE) v Normalized root mean sqared error (NRMSE) v Peak signal-to-noise ratio (PSNR) PSNR = - 20*log 10 (NRMSE) Rate-distortion For a fair comparison across fixed-rate (e.g., ZFP) and fixed-accracy compressors (e.g., SZ-1.1/SZ-1.4) Qality (distortion) per bit of compressed storage e.g., PSNR / BR (db/bit) Atocorrelation of Compression Errors 26

27 Otline Introdction Large amont of scientific data Limitations of lossless compression Existing lossy compressors and limitations Or Designs Mltidimensional / Mltilayer Prediction Model Adaptive Error-Controlled Qantization Metrics and Measrements Empirical Evalation Compression performance & Parallel evalation Conclsion 27

28 Empirical Evalation Experimental platforms Serial: imac with 2.3 GHz Intel Core i GB DDR3 Memory Parallel: Bles clster at ANL each node with 2 Intel Xeon E processors + 64 GB DDR3 Memory Experimental data (single-floating point) ATM: 2D data sets from climate/atmosphere simlations APS: 2D data sets from X-ray scientific research Hrricane: 3D data sets from hrricane Isabel simlation 28

29 Empirical Evalation Compression Ratio (1) ATM APS Hrricane Vale-range-based (VRB) relative error bond = absolte error bond / data vale range E.g., VRB relative error bond = 1E-4 1.9x ~ ZFP 2.2x ~ SZ

30 Empirical Evalation Compression Ratio (2) ATM VRB relative eb arond 1E-4 2.6x of ZFP on ATM 1.7x of ZFP on Hrricane Hrricane 30

31 Empirical Evalation Rate- Distortion ATM 25% ~ ZFP (NRMSE) APS Hrricane ZFP: Best mode fixed-accracy e.g., bit-rate = 8 bits/vale (CR = 4) 14 db higher than ZFP on ATM 9 db higher than ZFP on APS 11 db higher than ZFP on Hrricane NRMSE: 25% ~ ZFP on average 31

32 Empirical Evalation Comp/Decomp Speed 32

33 Empirical Evalation Atocorrelation of Errors FREQSH SNOWHLND 33

34 Empirical Evalation Parallel Compression (1) Parallel compression In-sit: embedded in a parallel application Off-line: MPI load data into mltiple processes, rn compression separately Experimental configrations 2.6 TB ATM data sets with files Bles clster at ANL Up to 1024 cores (64 nodes) 1 ~ 128 processes: parallel efficiency stay 100% - linear speedp > 128 processes (> 2 processes/node): parallel efficiency is decreased to 90% This performance degradation is de to node internal limitations 34

35 Empirical Evalation Parallel Compression (2) Nmber of Processes / Nodes > 32: Time (writing compressed data + compression) < Time (writing initial data) Time (reading compressed data + decompression) < Time (reading inital data) 35

36 Otline Introdction Large amont of scientific data Limitations of lossless compression Existing lossy compressors and limitations Or Designs Mltidimensional / Mltilayer Prediction Model Adaptive Error-Controlled Qantization Metrics and Measrements Empirical Evalation Compression performance & Parallel evalation Conclsion 36

37 Conclsions We derive a generic model for the mltidimensional prediction to frther se data s mltidimensional information We propose an adaptive error-controlled qantization to deal with irreglar and spiky data Or designs improve prediction-hitting rate significantly Compression ratio, rate-distortion better than second-best soltion Save large amont of I/O time in parallel Frtre work Optimize SZ code to accelerate speed, especailly on high dimensional datasets Develope SZ compressor for different architectres Frther redce atocorrelation of compression errors 37

38 Thank yo! Welcome to se or SZ lossy compressor! Any qestions are welcome! Contact: Dingwen Tao Sheng Di Acknowledgement: DOE EZ Project 38