Open AccessBook
Modern Computer Arithmetic
Richard P. Brent,Paul Zimmermann +1 more
- 27 Dec 2010
TL;DR: 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.
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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.
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Citations
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.
159
Black-Box Quantum State Preparation without Arithmetic
TL;DR: A new algorithm is presented that avoids arithmetic and reduces the number of gates by a factor of 286-374 over the best prior work for realistic precision; the improvement factor increases with the precision.
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.
121
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.
High-precision arithmetic in mathematical physics
David H. Bailey,Jonathan M. Borwein +1 more
- 12 May 2015
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.
85
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Handbook of Applied Cryptography
Alfred Menezes,Scott A. Vanstone,Paul C. van Oorschot +2 more
- 01 Jan 1996
TL;DR: A valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography, this book provides easy and rapid access of information and includes more than 200 algorithms and protocols.
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Computer Architecture: A Quantitative Approach
John L. Hennessy,David A. Patterson +1 more
- 01 Dec 1989
TL;DR: This best-selling title, considered for over a decade to be essential reading for every serious student and practitioner of computer design, has been updated throughout to address the most important trends facing computer designers today.
12.6K
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The Design and Analysis of Computer Algorithms
Alfred V. Aho,John E. Hopcroft +1 more
- 01 Jan 1974
TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
10.6K
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A treatise on the theory of Bessel functions
G. N. Watson
- 01 Jan 1944
TL;DR: The tabulation of Bessel functions can be found in this paper, where the authors present a comprehensive survey of the Bessel coefficients before and after 1826, as well as their extensions.
10.3K