Overview

Arithmetic is one of the old topics in computing. It dates back to the many early civilizations that used the abacus to perform arithmetic operations. The seventeenth and eighteenth centuries brought many advances with the invention of mechanical counting machines like the slide rule, Schickard's Calculating Clock, Leibniz's Stepped Reckoner, the Pascaline, and Babbage's Difference and Analytical Engines. The vacuum tube computers of the early twentieth century were the first programmable, digital, electronic, computing devices. The introduction of the integrated circuit in the 1950s heralded the present era where the complexity of computing resources is growing exponentially. Today's computers perform extremely advanced operations such as wireless communication and audio, image, and video processing, and are capable of performing over 1015 operations per second.

Owing to the fact that computer arithmetic is a well-studied field, it should come as no surprise that there are many books on the various subtopics of computer arithmetic. This book provides a focused view on the optimization of polynomial functions and linear systems. The book discusses optimizations that are applicable to both software and hardware design flows; e.g., it describes the best way to implement arithmetic operations when your target computational device is a digital signal processor (DSP), a field programmable gate array (FPGA) or an application specific integrated circuit (ASIC).

Polynomials are among the most important functions in mathematics and are used in algebraic number theory, geometry, and applied analysis.