Redundant Floating-Point Decimal CORDIC Algorithm

Abstract

In this work, we propose a new decimal redundant CORDIC algorithm to manage transcendental functions, using floatingpoint representation. The algorithms determine the direction of the elementary rotation using sign estimations. Unlike binary redundant CORDIC, repetition of iterations are not required to ensure convergence since novel decimal codes have been carefully selected with sufficient redundancy to prevent any repetition. The algorithms are mapped to a low-cost unit based on a decimal 3-2 carry-save adder which can also be used as a floating-point decimal division unit. Compared to current decimal floating-point units, the implementation of our algorithm involves minor modifications of the native hardware, while providing a huge set of elementary functions.

A Practical Energy/Power Reduction Approach for Parallel Decimal Multiplier

“…Several processors have been announced, such as IBM eServer z900 [4], IBM POWER6 [5], and IBM z10 [6], which are equipped with a dedicated decimal arithmetic unit. On the other hand, a considerable number of research papers have been published on decimal arithmetic algorithms and hardware units such as decimal addition (two-operand (e.g., [7]) and multi-operand (e.g., [8])), decimal multiplication (sequential (e.g., [9]) and parallel (e.g., [10])), decimal division (subtractive (e.g., [11]) and multiplicative (e.g., [12])), and other arithmetic functions (e.g., [13]). Among various operations, decimal multiplication is known as one of the most complex operations, which is high frequency, time-consuming, and power-hungry.…”