The authors present a redundant representation for complex numbers called polygonal representation. This representation enables fast carry-free addition, in a way quite similar to the carry-free addition in signed-digit number systems and is convenient for multiplication. The technique is generalized in order to handle n-dimensional vectors.>

After a brief survey of the CORDIC algorithm, some new results that allow fast and easy signed-digit implementation of CORDIC, without modifying the basic iteration step are given. A slight modification would make it possible to use a carry-save representation of numbers, instead of a signed-digit one. The method, called the branching CORDIC method, consists of performing in parallel two classic CORDIC rotations. It gives a constant normalization factor. An online implementation of the algorithm is proposed with an online delay equal to 5 for the sine and cosine functions.>

A new redundant representation for complex numbers, called polygonal representation, is presented. This representation enables fast carry-free addition (in a way quite similar to the carry-free addition in signed-digits number systems), and is convenient for multiplication. In addition, the technique is extended to handle n-dimensional vectors.>

Fast evaluation of polynomials is a major goal of computer science, since any continuous function may be approximated as accurately as desired by a polynomial. For instance, most part of current computers evaluate elementary functions using polynomial or rational approximations. J. Duprat and J.M. Muller (1988) presented a new operator, a polynomier, suitable for VLSI implementation, and specifically designed for polynomials computations. This polynomier is composed of two pipe-lined subparts : a squarer (i.e. an operator able to compute the square of a number), and a binomier (i.e. an element which computes expressions of the form Ax+B). The authors present some possible applications of the polynomier. They recall briefly the main characteristics of the architecture. They describe a VLSI implementation of this architecture and present an extension of this architecture to the two's complement computation.>

Complexity results that allow the exact determination or bounding of the online delay of most common arithmetic and elementary functions are presented. These results show that many classical online operators presented in the literature are optimal in delay (but not necessarily in period). The authors propose a way to conserve, for large numbers of manipulations, the main advantage of online arithmetic (the capability of digit-level pipelining) by presenting sparse online arithmetic.>