  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.
