Decimal CORDIC Rotation based on Selection by Rounding: Algorithm and Architecture

Hardware implementation of decimal floating-point arithmetic is a topic of great interest among the researchers in computer arithmetic and also the digital processor industry. Software packages for decimal arithmetic are actually being challenged by decimal hardware units. This spreading trend seems to include hardware implementation of elementary functions. The (Coordinate Rotation Digital Computer) CORDIC algorithm, due to its simplicity, is one of the most efficient methods for computing elementary functions. In this work, we develop a decimal CORDIC scheme with almost half number of equally long cycles with respect to the best previous design. This is achieved via retiming of the conventional CORDIC architecture and selection of the microrotation factors by rounding. However, the proposed design does not lead to a predetermined constant scaling factor. The solution that we use is to iteratively compute the logarithm of the scaling factor followed by a decimal exponentiation. The same CORDIC hardware is reused for performing the latter. The proposed CORDIC method requires 2n + 3 cycles for n-digit decimal operands vs. 4n cycles of the previous methods. Evaluations with 16-digit operands based on logical effort analysis conclude that the proposed architecture shows 82% speed advantage, at the cost of 60% more area and 2.5 KB more ROM.