The purpose of the book is to provide an understanding of the design methodologies and optimizations behind the hardware synthesis and software optimization of arithmetic functions. While we have provided a discussion on the fundamentals of software compilation, hardware synthesis and digital arithmetic, much of the material focuses on the implementation of linear systems and polynomial functions in hardware or software. It is therefore intended for students and researchers with a solid background in computing systems.

The three of us started looking into this topic in 2003, back when Anup was a graduate student of Ryan's at the University of California, Santa Barbara; Farzan was a researcher at Fujitsu at that time. Our initial research focused on the optimizations of polynomial functions, attempting to understand the optimal method for synthesizing these as a digital circuit. While developing the model for this synthesis process, we noticed that this same model could be used to describe linear systems. Therefore, the algorithms we developed to optimize polynomials were applicable to linear systems as well. Around this time we received additional funding from the UC Discovery grant and Fujitsu to further study these optimizations. The resulting research was published as numerous journal, conference and workshop papers, and was a basis for Anup's Ph. D. thesis. We noticed the significant lack of published material in this topic area and approached Cambridge University Press with the idea of writing a book on the topic; the obvious result of this lies in the following pages.