Comparing posit and IEEE-754 hardware cost

The posit number system is an elegant encoding of floating-point values proposed as a drop-in replacement for the IEEE-754 standard. On the one side, posits sacrifice some of IEEE-754 complexity (directed rounding modes, infinities, NaNs). On the other side, their variable-size exponent and significand fields require extra encoding and decoding steps, and their higher best-case accuracy requires wider data-paths. The posit encoding/decoding overhead can be reduced by keeping posits decoded in processor registers, with the operators suitably modified to avoid double-rounding issues. An unbiased quantitative comparison of the hardware costs of these two encodings is based on an analytical study and an open-source C++ library suitable for High-Level Synthesis. This library offers posit and IEEE-754 parametrized operators for addition/subtraction, multiplication, and exact accumulation, all developed with the same high design effort and fully compliant to their respective standards. This library improves the state of the art of posit hardware arithmetic, and still, IEEE-754 operators remain between 30% and 60% faster and smaller than their posit counterparts.