Compressed Matrix Computations

Abstract: Frugal computing is becoming an important topic for environmental reasons. In this context, several techniques have been proposed to reduce the storage of scientific data by dedicated compression methods specially tailored for arrays of floating-point numbers. While these techniques are quite efficient to save memory, they introduce additional computations to compress and decompress the data before processing them. In this article, we introduce a new lossy, fixed-rate compression technique for 2D-arrays of floating-point numbers which allows one to compute directly on the compressed data, without decompressing them. We obtain important speedups since less operations are needed to compute among the compressed data and since no decompression and re-compression is needed. More precisely, our technique makes it possible to perform basic linear algebra operations such as addition, multiplication by a constant among compressed matrices and dot product and matrix multiplication among partly uncompressed matrices. This work has been implemented into a tool named blaz and a comparison with the well-known compressor zfp in terms of execution-time and accuracy is presented.