uLog: a software-based approximate logarithmic number system for computations on SIMD processors

Abstract

AbstractThis paper presents a new number representation based on logarithmic number system (LNS) called unsigned logarithmic number system (ulog), as an alternative to the conventional floating-point (FP) number format, to use in approximate computing applications. ulog is tailored for software implementation on commercial general-purpose processors, and uses the same dynamic range as conventional IEEE Standard FP formats to prevent overflow and underflow. ulog converts FP numbers to fixed-point numbers and uses integer operations for all computations. Moreover, vectorization and approximate logarithmic addition have been used to increase the performance of the software implementation of ulog. Then, we used different BLAS benchmarks to evaluate the performance of the proposed format than IEEE standard formats. 16- and 32-bit ulog improve the runtime than double-precision at most 70.26% and 46.36%, respectively. Besides, accuracy analysis of the ulog based on different logarithm bases showed that base 4 has the lowest error in most cases.