Synthesis of Arithmetic Circuits: FPGA, ASIC and Embedded Systems

7

OTHER ARITHMETIC OPERATIONS

This chapter is devoted to arithmetic functions and operations other than the four basic ones. Number representation systems conversion procedures are first analyzed; they play a prominent role in arithmetic processes since a variety of algorithms are designed for a wide-ranging number of systems and/or bases (radices). Further on, this chapter reviews classical methods for approximating logarithmic, exponential, and trigonometric functions. Polynomial approximation, Taylor-MacLaurin series, and convergence methods are described with a special attention to CORDIC algorithms and their applications to trigonometric functions. Square rooting algorithms founded on digit recurrence and convergence methods are finally surveyed.

A common feature of a number of modern algorithm implementations is the increased use of look-up tables (LUTs), a practice fully compatible with the evolution of the ROM technology toward larger size and lower cost. The main consequence of LUT-based techniques is then a low-cost speed-up of the overall procedures.