High-Precision Low-Latency Method and Architecture for Computing Binary and Decimal Logarithms

Binary and decimal logarithms (BDLs) are commonly used in science and engineering. This brief presents a theory of the radix-4 generalized hyperbolic coordinate rotation digital computer (GH-CORDIC) to compute them directly. Compared with traditional hyperbolic CORDIC (TH-CORDIC), the two logarithms can be calculated without extra dividers or multipliers. Compared with the GH-CORDIC, this theory has low iterations under the same high precision. Through theoretical derivation and software simulation, we can find that the calculation accuracy can reach the magnitude of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10^{-7}$</tex-math> </inline-formula>, and the number of iterations can be reduced by more than 50%. Through hardware implementation, the synthesis report shows that the proposed architecture can save 53.44% area and 46.36% power consumption compared with the latest radix-2 GH-CORDIC method.