A Formal Evaluation of the Design Space for SORN Arithmetic Datatypes
Moritz Bärthel, Yixuan Yao, Nils Hülsmeier, Steffen Paul · 2025
The Sets of Real Numbers (SORN) format is a low-complex and low-latency approach for computer arithmetic based on intervals. The application-specific nature of the format was shown to be beneficial for several use cases, particularly regarding their hardware performance. However, a potentially large design space has to be evaluated per application for determining the best-suited SORN datatype configuration. In order to generalize this approach and to allow for more flexible designs, this work describes a formal evaluation of the design space of SORN datatypes, analyzes how many configurations exist per bitwidth, and to what extend shared-logic SORN operations can be implemented. After deriving a general approach to determine all different SORN datatypes per bitwidth, a comprehensive evaluation of the hardware implementation of SORN datatypes for low bitwidths up to 11 bit is carried out for the arithmetic operations of addition and multiplication. The results show that the proposed shared-logic implementation of multi-datatype SORN operations significantly reduces the required hardware resources, compared to the instantiation of multiple single-datatype modules.