Application of Alternative Number Formats for Digital Signal Processing - An Evaluation on Sets Of Real Numbers

Abstract

The encoding and manipulation of binary numbers in digital systems is a major design challenge for modern high-performance computer arithmetic and digital signal processing. Besides unsigned and signed integer representation, fixed point and floating point are the two state-of-the-art choices for digital arithmetic. In recent years, however, machine learning and other applications increased the demands for alternative number representations, as well as inefficiencies and inaccuracies within the IEEE standard for floating point, which are tackled by the universal number (unum) format, proposed in 2015. This thesis deals with the Sets Of Real Numbers (SORN) format, which is a derivative of the unum approach. The SORN format represents the entire real numbers with a dedicated set of exact values and intervals, and implements arithmetic operations with pre-computed lookup tables, realized with simple Boolean logic circuits, which leads to low-complex and low-latency hardware designs. SORNs are well-suited for constraining high-dimensional optimization problems by means of preprocessing, as well as for implementing threshold-based algorithms. This thesis presents implementations of SORN arithmetic operations on register-transfer level and evaluates on different SORN datatype representations, as well as optimizations such as the introduction of fused SORN arithmetic. In order to facilitate a design space exploration with SORNs, an automated design flow is presented, which provides complete SORN datapaths for different algorithms and applications. By using this design flow, SORN arithmetic is applied within edge detection for image processing and as preprocessing for detection algorithms in wireless MIMO communication. The presented results show that the proposed SORN approach achieves an improvement of the hardware measures, while providing similar algorithmic performance as the state-of-the-art implementations with standard formats.