Nathan Kurz

Daniel Lemire, Nathan Kurz, Christoph Rupp

Arrays of integers are often compressed in search engines. Though there are many ways to compress integers, we are interested in the popular byte-oriented integer compression techniques (e.g., VByte or Google's Varint-GB). They are appealing due to their simplicity and engineering convenience. Amazon's varint-G8IU is one of the fastest byte-oriented compression technique published so far. It makes judicious use of the powerful single-instruction-multiple-data (SIMD) instructions available in commodity processors. To surpass varint-G8IU, we present Stream VByte, a novel byte-oriented compression technique that separates the control stream from the encoded data. Like varint-G8IU, Stream VByte is well suited for SIMD instructions. We show that Stream VByte decoding can be up to twice as fast as varint-G8IU decoding over real data sets. In this sense, Stream VByte establishes new speed records for byte-oriented integer compression, at times exceeding the speed of the memcpy function. On a 3.4GHz Haswell processor, it decodes more than 4 billion differentially-coded integers per second from RAM to L1 cache.

Jeff Plaisance, Nathan Kurz, Daniel Lemire

We consider the ubiquitous technique of VByte compression, which represents each integer as a variable length sequence of bytes. The low 7 bits of each byte encode a portion of the integer, and the high bit of each byte is reserved as a continuation flag. This flag is set to 1 for all bytes except the last, and the decoding of each integer is complete when a byte with a high bit of 0 is encountered. VByte decoding can be a performance bottleneck especially when the unpredictable lengths of the encoded integers cause frequent branch mispredictions. Previous attempts to accelerate VByte decoding using SIMD vector instructions have been disappointing, prodding search engines such as Google to use more complicated but faster-to-decode formats for performance-critical code. Our decoder (Masked VByte) is 2 to 4 times faster than a conventional scalar VByte decoder, making the format once again competitive with regard to speed.

Daniel Lemire, Leonid Boytsov, Nathan Kurz

Sorted lists of integers are commonly used in inverted indexes and database systems. They are often compressed in memory. We can use the SIMD instructions available in common processors to boost the speed of integer compression schemes. Our S4-BP128-D4 scheme uses as little as 0.7 CPU cycles per decoded integer while still providing state-of-the-art compression. However, if the subsequent processing of the integers is slow, the effort spent on optimizing decoding speed can be wasted. To show that it does not have to be so, we (1) vectorize and optimize the intersection of posting lists; (2) introduce the SIMD Galloping algorithm. We exploit the fact that one SIMD instruction can compare 4 pairs of integers at once. We experiment with two TREC text collections, GOV2 and ClueWeb09 (Category B), using logs from the TREC million-query track. We show that using only the SIMD instructions ubiquitous in all modern CPUs, our techniques for conjunctive queries can double the speed of a state-of-the-art approach.