Open AccessBook
Modern Computer Arithmetic
Richard P. Brent,Paul Zimmermann +1 more
TLDR
Brent and Zimmermann as discussed by the authors present algorithms that are ready to implement in your favorite language, while keeping a high-level description and avoiding too low-level or machine-dependent details.Abstract:
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 favorite 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 are available from the authors.read more
Citations
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Journal ArticleDOI
High-Precision Computation: Mathematical Physics and Dynamics
TL;DR: It is concluded that high-precision arithmetic facilities are now an indispensable component of a modern large-scale scientific computing environment.
Journal ArticleDOI
Even faster integer multiplication
TL;DR: In this paper, the authors gave a new proof of Furer's bound for the cost of multiplying n-bit integers in the bit complexity model, and established the improved bound O(n log n K^(log √ n)) with K=8.
Journal ArticleDOI
Multipoint methods for solving nonlinear equations: A survey
TL;DR: This survey paper is intended as a review of the most efficient root-finding algorithms and developing techniques in a general sense and special attention is devoted to multipoint methods with memory that use already computed information to considerably increase convergence rate without additional computational costs.
Journal ArticleDOI
Constant-optimized quantum circuits for modular multiplication and exponentiation
Igor L. Markov,Mehdi Saeedi +1 more
TL;DR: In the context of modular exponentiation, this work offers several constant-factor improvements, as well as an improvement by a constant additive term that is significant for few-qubit circuits arising in ongoing laboratory experiments with Shor's algorithm.
Journal ArticleDOI
High-precision arithmetic in mathematical physics
TL;DR: The challenge of high-precision computation, in the context of mathematical physics, is discussed and what facilities are required to support future computations, in light of emerging developments in computer architecture are highlighted.
References
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