VPC3: A Fast and Effective Trace-Compression Algorithm

Martin Burtscher

Introduction Traces

PC values. Good compression algorithms e.g sequitur.

Extended traces PC values + Extended data (ED) ED = {load/store values, load/store addresses…} ED exihibit lower repeatability and span higher range

than PC values. No good compression algorithms.

Value predictors Compress extended traces. Preprocess extended traces for post compression.

Compression using value predictors Assume the following

A set of predictors each with 1 byte ID. 8 byte trace entries

Compression algorithm Compare trace entry with predicted values. If match, write ID of predictor. If no match,

Write special code followed by trace entry value. Update predictors with trace entry value.

Decompression is analogous.

vpc3 compression

Lossless compression Single pass algorithm Excellent compression rate Fixed memory requirement Fast decompression speed Fast compression speed

Evaluated compression algorithms Gzip

2.3MB memory usage. Fast (de)compression. Poor compression rate.

Bzip2 10MB memory usage. Slower (de)compression. Better compression rate.

Sequitur (modified) Source code optimizations. Split PC and ED into separate streams for compression. Bzip2 post compression. Impressive compression rate for traces. 951MB memory usage.

Value predictors (1)

Last-n-value predictor(LnV) Retain n most recent values. All n values are provided for prediction. Viewed as n independent predictors. Can predict sequence of repeating or

alternating values of length <= n. n <= 4 typically. Used for ED values but not PC values.

Value predictors (2) Finite-context-method predictor(FCM)

Hash of n most recent values used as index into hash table for predicting and for inserting new values.

FCMs are described by their n order, eg FCM3.

Most recent (a), and 2nd most recent (b) values retained and predicted for each hash index(line).

FCM3b = 3 order FCM predictor that predicts 2nd most recent value.

Can predict long arbitrary sequence of values. Used for both PC and ED values.

Value predictors (3) Differential-finite-context-method

predictor. Similar to FCM Predicts and stores strides instead of absolute

values. Final prediction is formed by adding predicted

stride to more recently seen value. Can predict never before seen values. Improved prediction of ED values over FCM. No improvement for PC values over FCM.

Extended trace Format

32 bit PC field 64 bit ED field

PC032,ED064,PC132,ED164,……

vpc0

Compressed only ED value. 27 predictors. Fixed bit predictor encoding i.e 5

bits. 2.6x compression rate limit

96 bit PC/ED compressed to 37 bit PC/ED.

vpc1 Compress PC using 10 predictors. Optimized predictor bit encoding using dynamic

huffman encoder. Use predictor with shortest huffman code. Compress unpredictable values.

Encode PC values with log2(Max(PC value)) bits. For ED values, store code of closest predictor and

difference. Many other optimizations to enhance

compression rate. 48x compression rate limit.

96 PC/ED compressed to 2 bit PC/ED.

vpc2 Vpc1 compressed traces are highly

compressible. Vpc2 = vpc1 + gzip post compression Improved compression rate over vpc1. 2x geometric mean compression rate

over sequitur. 3.5 times slower decompression speed.

vpc3 Expose and enhance patterns in

trace for bzip2 post compression. Simpler than vpc2

14 predictors, down from 37 in vpc2. Fixed byte encoding for predictors. Unpredictable values not compressed. Eliminated vpc1 optimizations that

hurt post compression rate.

vpc3 Value predictors tuned using gcc load value

trace L4V for ED values. FCM{1a,1b,3a,3b} for PC values. FCM{1a,1b} for ED values. DFCM{1a,1b,3a,3b} for ED values.

Trace converted into 4 streams PC predictor codes stream Unpredicted PC values stream ED predictor codes stream Unpredicted ED values stream

Evaluation 64-bit CS20 system with dual 833MHz

21264B Alpha CPUs. Only one CPU used. Spec2k int and float programs. Generated traces (<= 12 GB)

PC + effective address of store instructions. PC + effective address of misses on

simulated L1 cache. PC + load value.

Compressors compiled with same compiler and compile flags.

Evaluation

vpc3 predictor configuration Lots of state sharing amongst

predictors. 5MB for PC predictors 21MB for ED predictors 27MB total memory used by vpc3.

Compression Rate

Decompression Speed

Compression speed

Predictor Usage

Conclusion

Questions Insights Discussions