Pub Date : 2018-06-01DOI: 10.1109/ARITH.2018.8464690
Nir Drucker, S. Gueron, V. Krasnov
Distributed storage systems utilize erasure codes to reduce their storage costs while efficiently handling failures. Many of these codes (e. g., Reed-Solomon (RS) codes) rely on Galois Field (GF) arithmetic, which is considered to be fast when the field characteristic is 2. Nevertheless, some developments in the field of erasure codes offer new efficient techniques that require mostly XOR operations, and are thus faster than GF operations. Recently, Intel announced [1] that its future architecture (codename “Ice Lake”) will introduce new set of instructions called Galois Field New Instruction (GF-NI). These instructions allow software flows to perform vector and matrix multiplications over GF (28) on the wide registers that are available on the AVX512 architectures. In this paper, we explain the functionality of these instructions, and demonstrate their usage for some fast computations in GF(28). We also use the Intel® Intelligent Storage Acceleration Library (ISA-L) in order to estimate potential future improvement for erasure codes that are based on RS codes. Our results predict $approx 1.4mathrm{x}$ speedup for vectorized multiplication, and 1.83x speedup for the actual encoding.
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Pub Date : 2018-06-01DOI: 10.1109/ARITH.2018.8464784
D. Defour
When dealing with floating-point numbers, there are several sources of error which can drastically reduce the numerical quality of computed results. One of those error sources is the loss of significance or cancellation, which occurs during for example, the subtraction of two nearly equal numbers. In this article, we propose a representation format named Floating-Point Adaptive Noise Reduction (FP-ANR). This format embeds cancellation information directly into the floating-point representation format thanks to a dedicated pattern. With this format, insignificant trailing bits lost during cancellation are removed from every manipulated floating-point number. The immediate consequence is that it increases the numerical confidence of computed values. The proposed representation format corresponds to a simple and efficient implementation of significance arithmetic based and compatible with the IEEE Standard 754 standard.
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