Modern Computer Arithmetic (Cambridge Monographs on Applied and Computational Mathematics Book 18) 1st Edition by Richard P. Brent (PDF)

Description

Modern Computer Arithmetic focuses on arbitrary-precision algorithms for efficiently performing arithmetic operations such as addition, multiplication and division, and their connections to topics such as modular arithmetic, greatest common divisors, the Fast Fourier Transform (FFT), and the computation of elementary and special functions. Brent and Zimmermann present algorithms that are ready to implement in your favourite language, while keeping a high-level description and avoiding too low-level or machine-dependent details. The book is intended for anyone interested in the design and implementation of efficient high-precision algorithms for computer arithmetic, and more generally efficient multiple-precision numerical algorithms. It may also be used in a graduate course in mathematics or computer science, for which exercises are included. These vary considerably in difficulty, from easy to small research projects, and expand on topics discussed in the text. Solutions to selected exercises are available from the authors.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The authors try to bridge the razor’s edge of too much detail and machine implementation at one extreme, and too general a “current algorithm” approach at the other. If you’ve read Deschamps

⭐, you have a good feel for the circuits that implement those algorithms, and many large handbooks of arithmetic and algebra algorithms (or function libraries) are also available at the high/ summary level.So how did they do? An objective like this, especially in this few pages, runs the risk of making no one happy– too general for some, too detailed for others. Indeed, the fact that this is a very recent work DOES give students and design engineers a lot of very good places to look for the most recent updates of new (meaning since Euler!) hyphenated-name algorithms that are in more current use than, say, their 2001 versions. This alone makes the book worth it for researchers or students who don’t keep up with journal articles.On the other hand, if you hate pseudo code, you might not like this book. The “language independent” algorithms they show are quite strange to the uninitiated– they give traditional (read LaTex) math formulas and symbols as input (to please the mathematicians and piss off the software folks), followed by “algorithm like” (pseudo code) as output, to confuse the mathematicians and please the programmers. This runs the risk of pleasing nobody.If you’re looking for a reference volume to get you pointed in the right direction, this is it. As a teaching tool or complete survey of the field, not so much. However, the authors really do know their stuff, and are plentiful with proofs, whether using Newton or the Chudnovsky brothers, and are “up to date” in a 2013 sense– very few NEW CAS and Computer Arithmetic books are even being written today, unfortunately. The authors also have unexpectedly fun little quips that demonstrate “been there, done that”– like saying polynomials are actually easier than arithmetic because they don’t have n + 1 carrys or remainders!! If you’re new to all this, it will be too advanced; if you’re an old pro– it doesn’t go far enough in “completing” the coding in some ways– but gives a really good start, and is one of the few up to date books in this category anywhere. That begs the question of who this is really for– and brings us back to the beginning– 5 stars for the exactly right audience, and kudos to the authors for “daring” to write a RECENT book on a topic that’s rarely covered today — CA and CAS– at least in book rather than blog or journal form.

⭐If you like mathematics, but were always wondering how to make the magic box do it fast, this book is for you!

⭐

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