Notes on Elias Gamma encoding in BitMagic 3.6.0

Version 3.6.0 implements a variant of Elias Gamma Encoding as part of bit-vector serialization.
Wikipedia has an article on this encoding here:
http://en.wikipedia.org/wiki/Elias_gamma_coding

The description is so good that one should be able to implement this encoding after reading a couple of pages.

Older versions of BM library used D-Gap compression which is a variant of run length encoding. Or used plain lists of integers to encode very sparse sets. All this compression methods used word aligned algorithms and rely on presence of long runs of identical bits. Word aligned compression is also very fast.

A lot of practical tests demonstrated that BM based search systems are bandwidth limited. It means that CPU is starved, waiting for memory operations or disk retrieval. Disk retrieval is particularly important because IO and network subsystems never followed terms of Moore Law. Non-Word-Aligned encoding seems to a good answer to this problem.

Elias Gamma encoding developed by Peter Elias postulates bit-encoding of positive (non-zero) integers . Positive non-zero integers are essentially the native format for BM library to store sparse bit-vectors or inverted lists (basic building blocks of efficient bitmap indexes).

Advantages:
1.Simple implementation, requires no compression dictionary. It is easy to compress just a few ints without constructing and storing a dictionary. BM library works with independent blocks of bits (potentially computed in parallel).
2.Implied probability favors small integers – good for BM library since it fragments bit-vector into blocks of 65K bits. Methods allows some blocks to be encoded, and some to remain in GAP or raw bit-block format (if statistical distribution of bits suddenly changes).
3.Compact implementation reduces code bloat, fits into a C++ template library paradigm.

Disadvantages:
1.True adaptive statistical methods (like arithmetic compression) can(should?) give better compression ratio.
2.Encoding and decoding method is sequential, it seems hard to implement a parallel encoder/decoder using SIMD, SSE or GP-GPU. (BM blocks can potentially be decoded in parallel so maybe there is a way to use parallel methods for this).

BitMagic Library v.3.6.0 released

improved bit-vector serialization with bitset compression.
New serialization adds Gamma encoding on top of D-Gap compression. This should
reduce IO for databases and search systems using serialized bit-vectors.

fixed functionality bug in deserialization with logical AND

new serialization API (old API kept for backward compatibility)

BitMagic version 3.5.4 released

The scope of this release is general code cleanup (only partially successful) and SSE2 for GCC compatibility fixes.

GCC supports SSE2 intrinsics, so this port was relatively easy. Practically the only change needed was correct syntax for 16-byte alignment declaration. SSE2 optimizations are now available for Intel C++, GCC and MSVC.

Download: https://sourceforge.net/projects/bmagic/files/

CUDA vs SSE

We all know that GPUs can be incredibly fast at some single precision floating point algorithms.
Developers of BitMagic Library Igor Tolstoy and Anatoliy Kuznetsov made an attempt to implement parallel bit-stream transposition and similarity algorithm (a lot of bit-shifting, population counting and general purpose integer logic) to better understand CUDA and GP-GPU computing in comparison with current (and future) Intel vectorization architectures (SSE2).

Benchmarking, CUDA and SSE source codes, some speculation about Larabee and implications for data-mining and large scale databases here:
http://bmagic.sourceforge.net/bmcudasse2.html

DoxyDocumentation

Doxygen documentation made available on the WEB:
http://bmagic.sourceforge.net/doxy/modules.html

Intel Atom: Best GCC settings

After several experiments with 32-bit GCC 4.3.3 on Intel Atom N270 here some recommendations for optimization parameters.
-march=core2 -O2 -fomit-frame-pointer -pipe
Another good alternative:
-mtune=native -O2 -fomit-frame-pointer -pipe

In some BM benchmarks -march=core2 is up to 20% better than -march=prescott
So it looks like, Intel Atom is more Core2 than Pentium4. For low power devices like Atom it looks very important to use right settings since platform balances on a very fine edge in terms of usability. Given the growing popularity of this CPU it would be nice to see binary builds of software products optimized for the target (or doing internal CPUID auto-detection) to load the right binaries.

SSE2 integer optimization seems to get a nice additional boost too. Current version of BitMagic Library (3.5.3) s not compatible with GCCs syntax for variable alignment (one of the key elements for getting best memory bandwidth with SSE). Next version is going to offer better compatibility.

BitMagic version 3.5.3 released

• improved performance of AND logical operations and derived DOT product algorithms (cound_and(), any_and())
• improved compression of serialized bvectors (serialization format remains backward compatible)
• fixed compatibility issues with MSVC8 and Intel C++ 11.1 (SSE2 optimization mode)
• improved automatic variables disambiguation using 'restrict'

Download: https://sourceforge.net/projects/bmagic/files/