Fast Multiplication Of Multiple Precision Integers

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Fast Multiplication Of Multiple Precision Integers

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Author : Sonja Benz
language : en
Publisher:
Release Date : 1991

Fast Multiplication Of Multiple Precision Integers written by Sonja Benz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Algorithms categories.

"Multiple-precision multiplication algorithms are of fundamental interest for both theoretical and practical reasons. The conventional method requires 0(n2) bit operations whereas the fastest known multiplication algorithm is of order 0(n log n log log n). The price that has to be paid for the increase in speed is a much more sophisticated theory and programming code. This work presents an extensive study of the best known multiple-precision multiplication algorithms. Different algorithms are implemented in C, their performance is analyzed in detail and compared to each other. The break even points, which are essential for the selection of the fastest algorithm for a particular task, are determined for a given hardware software combination."--Abstract.

Fast Multiple Precision Arithmetic On Distributed Memory Parallel Computers And Its Applications

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Author : Daisuke Takahashi
language : en
Publisher:
Release Date : 1998

Fast Multiple Precision Arithmetic On Distributed Memory Parallel Computers And Its Applications written by Daisuke Takahashi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Electronic data processing categories.

Fast Multiplication Of Arbitrary Precision Integers With Application To Cryptography

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Author : Andrew Shawn Dyer
language : en
Publisher:
Release Date : 1994

Fast Multiplication Of Arbitrary Precision Integers With Application To Cryptography written by Andrew Shawn Dyer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.

Multiple Precision Integer Arithmetic And Public Key Encryption

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Author : Mathias Engan
language : en
Publisher: Lulu.com
Release Date :

Multiple Precision Integer Arithmetic And Public Key Encryption written by Mathias Engan and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Modern Computer Arithmetic

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Author : Richard P. Brent
language : en
Publisher: Cambridge University Press
Release Date : 2010-11-25

Modern Computer Arithmetic written by Richard P. Brent and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-25 with Computers categories.

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.

Adaptive Precision Floating Point Arithmetic And Fast Robust Geometric Predicates

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Author : Carnegie Mellon University. Computer Science Department
language : en
Publisher:
Release Date : 1996

Adaptive Precision Floating Point Arithmetic And Fast Robust Geometric Predicates written by Carnegie Mellon University. Computer Science Department and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Computer algorithms categories.

Abstract: "Exact computer arithmetic has a variety of uses including, but not limited to, the robust implementation of geometric algorithms. This report has three purposes. The first is to offer fast software-level algorithms for exact addition and multiplication of arbitrary precision floating-point values. The second is to propose a technique for adaptive-precision arithmetic that can often speed these algorithms when one wishes to perform multiprecision calculations that do not always require exact arithmetic, but must satisfy some error bound. The third is to provide a practical demonstration of these techniques, in the form of implementations of several common geometric calculations whose required degree of accuracy depends on their inputs. These robust geometric predicates are adaptive; their running time depends on the degree of uncertainty of the result, and is usually small. These algorithms work on computers whose floating-point arithmetic uses radix two and exact rounding, including machines complying with the IEEE 754 standard. The inputs to the predicates may be arbitrary single or double precision floating-point numbers. C code is publicly available for the 2D and 3D orientation and incircle tests, and robust Delaunay triangulation using these tests. Timings of the implementations demonstrate their effectiveness."

Handbook Of Floating Point Arithmetic

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Author : Jean-Michel Muller
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-11-11

Handbook Of Floating Point Arithmetic written by Jean-Michel Muller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-11 with Mathematics categories.

Floating-point arithmetic is the most widely used way of implementing real-number arithmetic on modern computers. However, making such an arithmetic reliable and portable, yet fast, is a very difficult task. As a result, floating-point arithmetic is far from being exploited to its full potential. This handbook aims to provide a complete overview of modern floating-point arithmetic. So that the techniques presented can be put directly into practice in actual coding or design, they are illustrated, whenever possible, by a corresponding program. The handbook is designed for programmers of numerical applications, compiler designers, programmers of floating-point algorithms, designers of arithmetic operators, and more generally, students and researchers in numerical analysis who wish to better understand a tool used in their daily work and research.

Improving The Karatsuba Ofman Multiplication Algorithm For Special Applications

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Author : Serdar S. Erdem
language : en
Publisher:
Release Date : 2001

Improving The Karatsuba Ofman Multiplication Algorithm For Special Applications written by Serdar S. Erdem and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Multiplication categories.

In this thesis, we study the Karatsuba-Ofman Algorithm (KOA), which is a recursive multi-precision multiplication method, and improve it for certain special applications. This thesis is in two parts. In the first part, we derive an efficient algorithm from the KOA to multiply the operands having a precision of 2[superscript m] computer words for some integer m. This new algorithm is less complex and three times less recursive than the KOA. However, the order of the complexity is the same as the KOA. In the second part of the thesis, we introduce a novel method to perform fast multiplication in GF(2[superscript m]), using the KOA. This method is intended for software implementations and has two phases. In the first phase, we treat the field elements in GF(2[superscript m]) as polynomials over GF(2) and multiply them by a technique based on the KOA, which we call the LKOA (lean KOA). In the second phase, we reduce the product with an irreducible trinomial or pentanomial. The LKOA is similar to the KOA. However, it stops the recursions early and switches to some nonrecursive algorithms which can efficiently multiply small polynomials over GF(2). We derive these nonrecursive algorithms from the KOA, by removing its recursions. Additionally, we optimize them, exploiting the arithmetic of the polynomials over GF(2). As a result, we obtain a decrease in complexity, as well as a reduction in the recursion overhead.

Multiple Precision Multiplication Using The Number Theoretic Transform

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Author : Jason R. Bock
language : en
Publisher:
Release Date : 1995

Multiple Precision Multiplication Using The Number Theoretic Transform written by Jason R. Bock and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Algebra categories.

Adaptive Precision Floating Point Arithmetic And Fast Robust Geometric Predicates

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Author : Carnegie-Mellon University. Computer Science Dept
language : en
Publisher:
Release Date : 1996

Adaptive Precision Floating Point Arithmetic And Fast Robust Geometric Predicates written by Carnegie-Mellon University. Computer Science Dept and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Computer algorithms categories.

Abstract: "Exact computer arithmetic has a variety of uses including, but not limited to, the robust implementation of geometric algorithms. This report has three purposes. The first is to offer fast software-level algorithms for exact addition and multiplication of arbitrary precision floating-point values. The second is to propose a technique for adaptive-precision arithmetic that can often speed these algorithms when one wishes to perform multiprecision calculations that do not always require exact arithmetic, but must satisfy some error bound. The third is to provide a practical demonstration of these techniques, in the form of implementations of several common geometric calculations whose required degree of accuracy depends on their inputs. These robust geometric predicates are adaptive; their running time depends on the degree of uncertainty of the result, and is usually small. These algorithms work on computers whose floating-point arithmetic uses radix two and exact rounding, including machines complying with the IEEE 754 standard. The inputs to the predicates may be arbitrary single or double precision floating-point numbers. C code is publicly available for the 2D and 3D orientation and incircle tests, and robust Delaunay triangulation using these tests. Timings of the implementations demonstrate their effectiveness."