Tackling Gaps in Floating-Point Arithmetic: Unum Arithmetic Implementation on FPGA

Floating-point arithmetic is an important form in numerical computation, IEEE Standard for Floating-Point Arithmetic - IEEE 754 floats has been applied in overwhelming majority of microprocessors. However, as the increasing of data size and accuracy requirement of applications, bandwidth and precision are highly valued in floating-point computing, optimizing existing floating-point arithmetic is a way to improve current situation. Unum (universal number) arithmetic is a new floating-point arithmetic presented by John L. Gustafson in 2013, being compared with IEEE 754 floats, the outstanding features of unum are clearance of rounding errors, high information-per-bit and variable precision. However, unum was only implemented in software before due to technical complexity, we implement unum arithmetic on FPGA for the first time. We contrast the precision and bit width in computing with IEEE 754 floats, the comparison results show that unum need less bit width than IEEE 754 floats under same precision, it can decrease bandwidth requirement in computing.