# Computer Arithmetic and Formal Proofs

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## Computer Arithmetic and Formal Proofs

Author | : Sylvie Boldo,Guillaume Melquiond |

Publsiher | : Elsevier |

Total Pages | : 326 |

Release | : 2017-11-17 |

ISBN 10 | : 0081011709 |

ISBN 13 | : 9780081011706 |

Language | : EN, FR, DE, ES & NL |

**Computer Arithmetic and Formal Proofs Book Review:**

Floating-point arithmetic is ubiquitous in modern computing, as it is the tool of choice to approximate real numbers. Due to its limited range and precision, its use can become quite involved and potentially lead to numerous failures. One way to greatly increase confidence in floating-point software is by computer-assisted verification of its correctness proofs. This book provides a comprehensive view of how to formally specify and verify tricky floating-point algorithms with the Coq proof assistant. It describes the Flocq formalization of floating-point arithmetic and some methods to automate theorem proofs. It then presents the specification and verification of various algorithms, from error-free transformations to a numerical scheme for a partial differential equation. The examples cover not only mathematical algorithms but also C programs as well as issues related to compilation. Describes the notions of specification and weakest precondition computation and their practical use Shows how to tackle algorithms that extend beyond the realm of simple floating-point arithmetic Includes real analysis and a case study about numerical analysis

## Computer Arithmetic and Enclosure Methods

Author | : Lidiya Atanassova,Jurgen Herzberger,Jürgen Herzberger |

Publsiher | : North Holland |

Total Pages | : 504 |

Release | : 1992 |

ISBN 10 | : |

ISBN 13 | : UCAL:B4202574 |

Language | : EN, FR, DE, ES & NL |

**Computer Arithmetic and Enclosure Methods Book Review:**

Scientists concerned with the interaction between computer arithmetic, programming languages and scientific computing will be particularly interested in this book. It focuses on papers presented at the conference and highlights the increasing impact of SCAN-91 in this area. The volume contains original research and expository articles on the field of interaction between computer arithmetic and its realization in programming languages and the construction and investigation of numerical algorithms for computing guaranteed error-bounds for the solution of various problems in applied mathematics and engineering. Main subjects are: software tools for enclosure algorithms and inclusion methods with the help of interval arithmetic, in particular for the numerical solution of differential equations.

## Modern Computer Arithmetic

Author | : Richard P. Brent,Paul Zimmermann |

Publsiher | : Cambridge University Press |

Total Pages | : 329 |

Release | : 2010-11-25 |

ISBN 10 | : 1139492284 |

ISBN 13 | : 9781139492287 |

Language | : EN, FR, DE, ES & NL |

**Modern Computer Arithmetic Book Review:**

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.

## Handbook of Floating Point Arithmetic

Author | : Jean-Michel Muller,Nicolas Brunie,Florent de Dinechin,Claude-Pierre Jeannerod,Mioara Joldes,Vincent Lefèvre,Guillaume Melquiond,Nathalie Revol,Serge Torres |

Publsiher | : Birkhäuser |

Total Pages | : 627 |

Release | : 2018-05-02 |

ISBN 10 | : 3319765264 |

ISBN 13 | : 9783319765266 |

Language | : EN, FR, DE, ES & NL |

**Handbook of Floating Point Arithmetic Book Review:**

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.

## Computer Arithmetic

Author | : Earl E Swartzlander,Carl E Lemonds |

Publsiher | : World Scientific |

Total Pages | : 472 |

Release | : 2015-02-12 |

ISBN 10 | : 981465115X |

ISBN 13 | : 9789814651158 |

Language | : EN, FR, DE, ES & NL |

**Computer Arithmetic Book Review:**

Computer Arithmetic Volume III is a compilation of key papers in computer arithmetic on floating-point arithmetic and design. The intent is to show progress, evolution, and novelty in the area of floating-point arithmetic. This field has made extraordinary progress since the initial software routines on mainframe computers have evolved into hardware implementations in processors spanning a wide range of performance. Nevertheless, these papers pave the way to the understanding of modern day processors design where computer arithmetic are supported by floating-point units. The goal of Volume III is to collect the defining document for floating-point arithmetic and many of the key papers on the implementation of both binary and decimal floating-point arithmetic into a single volume. Although fewer than forty papers are included, their reference lists will direct the interested reader to other excellent work that could not be included here. Volume III is specifically oriented to the needs of designers and users of both general-purpose computers and special-purpose digital processors. The book should also be useful to systems engineers, computer architects, and logic designers. It is also intended to serve as a primary text for a course on floating-point arithmetic, as well as a supplementary text for courses in digital arithmetic and high-speed signal processing. This volume is part of a 3 volume set: Computer Arithmetic Volume I Computer Arithmetic Volume II Computer Arithmetic Volume III The full set is available for sale in a print-only version. Contents:OverviewFloating-Point AdditionFloating-Point MultiplicationRoundingFused Multiply AddFloating-Point DivisionElementary FunctionsDecimal Floating-Point Arithmetic Readership: Graduate students and research professionals interested in computer arithmetic. Key Features:The papers that are included cover the key concepts needed to develop efficient (fast, small and low-power) floating-point processing unitsThe papers include presentations by the initial developers in their own words to better explain the basic techniquesIncludes five papers on decimal floating-point arithmetic, which has been added to the IEEE standardKeywords:Floating-Point Addition;Floating-Point Multiplication;Floating-Point Division;Decimal Floating-Point Arithmetic

## Proof and Computation

Author | : Helmut Schwichtenberg |

Publsiher | : Springer Science & Business Media |

Total Pages | : 470 |

Release | : 2012-12-06 |

ISBN 10 | : 3642793614 |

ISBN 13 | : 9783642793615 |

Language | : EN, FR, DE, ES & NL |

**Proof and Computation Book Review:**

Logical concepts and methods are of growing importance in many areas of computer science. The proofs-as-programs paradigm and the wide acceptance of Prolog show this clearly. The logical notion of a formal proof in various constructive systems can be viewed as a very explicit way to describe a computation procedure. Also conversely, the development of logical systems has been influenced by accumulating knowledge on rewriting and unification techniques. This volume contains a series of lectures by leading researchers giving a presentation of new ideas on the impact of the concept of a formal proof on computation theory. The subjects covered are: specification and abstract data types, proving techniques, constructive methods, linear logic, and concurrency and logic.

## Formal Verification of Floating Point Hardware Design

Author | : David M. Russinoff |

Publsiher | : Springer |

Total Pages | : 382 |

Release | : 2018-10-13 |

ISBN 10 | : 3319955136 |

ISBN 13 | : 9783319955131 |

Language | : EN, FR, DE, ES & NL |

**Formal Verification of Floating Point Hardware Design Book Review:**

This is the first book to focus on the problem of ensuring the correctness of floating-point hardware designs through mathematical methods. Formal Verification of Floating-Point Hardware Design advances a verification methodology based on a unified theory of register-transfer logic and floating-point arithmetic that has been developed and applied to the formal verification of commercial floating-point units over the course of more than two decades, during which the author was employed by several major microprocessor design companies. The book consists of five parts, the first two of which present a rigorous exposition of the general theory based on the first principles of arithmetic. Part I covers bit vectors and the bit manipulation primitives, integer and fixed-point encodings, and bit-wise logical operations. Part II addresses the properties of floating-point numbers, the formats in which they are encoded as bit vectors, and the various modes of floating-point rounding. In Part III, the theory is extended to the analysis of several algorithms and optimization techniques that are commonly used in commercial implementations of elementary arithmetic operations. As a basis for the formal verification of such implementations, Part IV contains high-level specifications of correctness of the basic arithmetic instructions of several major industry-standard floating-point architectures, including all details pertaining to the handling of exceptional conditions. Part V illustrates the methodology, applying the preceding theory to the comprehensive verification of a state-of-the-art commercial floating-point unit. All of these results have been formalized in the logic of the ACL2 theorem prover and mechanically checked to ensure their correctness. They are presented here, however, in simple conventional mathematical notation. The book presupposes no familiarity with ACL2, logic design, or any mathematics beyond basic high school algebra. It will be of interest to verification engineers as well as arithmetic circuit designers who appreciate the value of a rigorous approach to their art, and is suitable as a graduate text in computer arithmetic.

## Mathematics for Computer Science

Author | : Eric Lehman,F. Thomson Leighton,Albert R. Meyer |

Publsiher | : Unknown |

Total Pages | : 988 |

Release | : 2017-03-08 |

ISBN 10 | : 9789888407064 |

ISBN 13 | : 9888407066 |

Language | : EN, FR, DE, ES & NL |

**Mathematics for Computer Science Book Review:**

This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.

## Knowing Machines

Author | : Donald A. MacKenzie |

Publsiher | : MIT Press |

Total Pages | : 338 |

Release | : 1998 |

ISBN 10 | : 9780262631884 |

ISBN 13 | : 0262631881 |

Language | : EN, FR, DE, ES & NL |

**Knowing Machines Book Review:**

The essays are tied together by their explorations of connections (primarily among technology, society, and knowledge) and by their general focus on modern "high" technology. They also share an emphasis on the complexity of technological formation and fixation and on the role of belief (especially self-validating belief) in technological change.

## Intelligent Computer Mathematics

Author | : James H. Davenport,William M. Farmer,Florian Rabe,Josef Urban |

Publsiher | : Springer |

Total Pages | : 312 |

Release | : 2011-07-18 |

ISBN 10 | : 3642226736 |

ISBN 13 | : 9783642226731 |

Language | : EN, FR, DE, ES & NL |

**Intelligent Computer Mathematics Book Review:**

This book constitutes the joint refereed proceedings of three international events, namely the 18th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2011, the 10th International Conference on Mathematical Knowledge Management, MKM 2011, and a new track on Systems and Projects descriptions that span both the Calculemus and MKM topics, all held in Bertinoro, Italy, in July 2011. All 51 submissions passed through a rigorous review process. A total of 15 papers were submitted to Calculemus, of which 9 were accepted. Systems and Projects track 2011 there have been 12 papers selected out of 14 submissions while MKM 2011 received 22 submissions, of which 9 were accepted for presentation and publication. The events focused on the use of AI techniques within symbolic computation and the application of symbolic computation to AI problem solving; the combination of computer algebra systems and automated deduction systems; and mathematical knowledge management, respectively.

## Handbook of Floating Point Arithmetic

Author | : Jean-Michel Muller,Nicolas Brisebarre,Florent de Dinechin,Claude-Pierre Jeannerod,Vincent Lefèvre,Guillaume Melquiond,Nathalie Revol,Damien Stehlé,Serge Torres |

Publsiher | : Springer Science & Business Media |

Total Pages | : 572 |

Release | : 2009-11-11 |

ISBN 10 | : 9780817647056 |

ISBN 13 | : 0817647058 |

Language | : EN, FR, DE, ES & NL |

**Handbook of Floating Point Arithmetic Book Review:**

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.

## Conference Proceedings

Author | : European Microwave Conference |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 1991 |

ISBN 10 | : 9780946821426 |

ISBN 13 | : 0946821429 |

Language | : EN, FR, DE, ES & NL |

**Conference Proceedings Book Review:**

## Principia Mathematica to 56

Author | : Alfred North Whitehead,Bertrand Russell |

Publsiher | : Cambridge University Press |

Total Pages | : 410 |

Release | : 1997-09-11 |

ISBN 10 | : 0521626064 |

ISBN 13 | : 9780521626064 |

Language | : EN, FR, DE, ES & NL |

**Principia Mathematica to 56 Book Review:**

This abridged text of the most famous work ever written on the foundations of mathematics contains material that is most relevant to an introductory study of logic and the philosophy of mathematics.

## Computer Arithmetic Scientific Computation and Mathematical Modelling

Author | : Edgar W. Kaucher |

Publsiher | : Unknown |

Total Pages | : 498 |

Release | : 1991 |

ISBN 10 | : |

ISBN 13 | : UOM:39015032425863 |

Language | : EN, FR, DE, ES & NL |

**Computer Arithmetic Scientific Computation and Mathematical Modelling Book Review:**

## Logical Foundations of Proof Complexity

Author | : Stephen Cook,Phuong Nguyen |

Publsiher | : Cambridge University Press |

Total Pages | : 329 |

Release | : 2010-01-25 |

ISBN 10 | : 1139486306 |

ISBN 13 | : 9781139486309 |

Language | : EN, FR, DE, ES & NL |

**Logical Foundations of Proof Complexity Book Review:**

This book treats bounded arithmetic and propositional proof complexity from the point of view of computational complexity. The first seven chapters include the necessary logical background for the material and are suitable for a graduate course. Associated with each of many complexity classes are both a two-sorted predicate calculus theory, with induction restricted to concepts in the class, and a propositional proof system. The complexity classes range from AC0 for the weakest theory up to the polynomial hierarchy. Each bounded theorem in a theory translates into a family of (quantified) propositional tautologies with polynomial size proofs in the corresponding proof system. The theory proves the soundness of the associated proof system. The result is a uniform treatment of many systems in the literature, including Buss's theories for the polynomial hierarchy and many disparate systems for complexity classes such as AC0, AC0(m), TC0, NC1, L, NL, NC, and P.

## A Computer System for Checking Proofs

Author | : Scott D. Johnson |

Publsiher | : Unknown |

Total Pages | : 262 |

Release | : 1982 |

ISBN 10 | : |

ISBN 13 | : UCAL:B3678290 |

Language | : EN, FR, DE, ES & NL |

**A Computer System for Checking Proofs Book Review:**

## Interactive Theorem Proving and Program Development

Author | : Yves Bertot,Pierre Castéran |

Publsiher | : Springer Science & Business Media |

Total Pages | : 472 |

Release | : 2013-03-14 |

ISBN 10 | : 366207964X |

ISBN 13 | : 9783662079645 |

Language | : EN, FR, DE, ES & NL |

**Interactive Theorem Proving and Program Development Book Review:**

A practical introduction to the development of proofs and certified programs using Coq. An invaluable tool for researchers, students, and engineers interested in formal methods and the development of zero-fault software.

## Formal Methods in Computer aided Design

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 2002 |

ISBN 10 | : |

ISBN 13 | : UOM:39015047929420 |

Language | : EN, FR, DE, ES & NL |

**Formal Methods in Computer aided Design Book Review:**

## University level Computer assisted Instruction at Stanford 1968 1980

Author | : Stanford University. Institute for Mathematical Studies in the Social Sciences |

Publsiher | : Unknown |

Total Pages | : 930 |

Release | : 1981 |

ISBN 10 | : |

ISBN 13 | : UOM:39015001071235 |

Language | : EN, FR, DE, ES & NL |

**University level Computer assisted Instruction at Stanford 1968 1980 Book Review:**

## Tutorial Programming Language Design

Author | : Anthony I. Wasserman |

Publsiher | : Unknown |

Total Pages | : 527 |

Release | : 1980 |

ISBN 10 | : |

ISBN 13 | : UOM:39015009806129 |

Language | : EN, FR, DE, ES & NL |

**Tutorial Programming Language Design Book Review:**