000 05417nam a22006375i 4500
001 978-0-8176-4705-6
003 DE-He213
005 20140220084457.0
007 cr nn 008mamaa
008 100301s2010 xxu| s |||| 0|eng d
020 _a9780817647056
_9978-0-8176-4705-6
024 7 _a10.1007/978-0-8176-4705-6
_2doi
050 4 _aQA71-90
072 7 _aPBKS
_2bicssc
072 7 _aMAT006000
_2bisacsh
082 0 4 _a518
_223
082 0 4 _a518
_223
100 1 _aMuller, Jean-Michel.
_eauthor.
245 1 0 _aHandbook of Floating-Point Arithmetic
_h[electronic resource] /
_cby Jean-Michel Muller, Nicolas Brisebarre, Florent de Dinechin, Claude-Pierre Jeannerod, Vincent Lefèvre, Guillaume Melquiond, Nathalie Revol, Damien Stehlé, Serge Torres.
250 _a1.
264 1 _aBoston :
_bBirkhäuser Boston,
_c2010.
300 _aXXIV, 572 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aIntroduction, Basic Definitions, and Standards -- Definitions and Basic Notions -- Floating-Point Formats and Environment -- Cleverly Using Floating-Point Arithmetic -- Basic Properties and Algorithms -- The Fused Multiply-Add Instruction -- Enhanced Floating-Point Sums, Dot Products, and Polynomial Values -- Languages and Compilers -- Implementing Floating-Point Operators -- Algorithms for the Five Basic Operations -- Hardware Implementation of Floating-Point Arithmetic -- Software Implementation of Floating-Point Arithmetic -- Elementary Functions -- Evaluating Floating-Point Elementary Functions -- Solving the Table Maker’s Dilemma -- Extensions -- Formalisms for Certifying Floating-Point Algorithms -- Extending the Precision -- Perspectives and Appendix -- Conclusion and Perspectives -- Appendix: Number Theory Tools for Floating-Point Arithmetic.
520 _aFloating-point arithmetic is by far the most widely used way of implementing real-number arithmetic on modern computers. Although the basic principles of floating-point arithmetic can be explained in a short amount of time, making such an arithmetic reliable and portable, yet fast, is a very difficult task. From the 1960s to the early 1980s, many different arithmetics were developed, but their implementation varied widely from one machine to another, making it difficult for nonexperts to design, learn, and use the required algorithms. 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, including a detailed treatment of the newly revised (IEEE 754-2008) standard for floating-point arithmetic. Presented throughout are algorithms for implementing floating-point arithmetic as well as algorithms that use 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. Key topics and features include: * Presentation of the history and basic concepts of floating-point arithmetic and various aspects of the past and current standards * Development of smart and nontrivial algorithms, and algorithmic possibilities induced by the availability of a fused multiply-add (fma) instruction, e.g., correctly rounded software division and square roots * Implementation of floating-point arithmetic, either in software—on an integer processor—or hardware, and a discussion of issues related to compilers and languages * Coverage of several recent advances related to elementary functions: correct rounding of these functions and computation of very accurate approximations under constraints * Extensions of floating-point arithmetic such as certification, verification, and big precision Handbook of Floating-Point Arithmetic 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.
650 0 _aMathematics.
650 0 _aComputer science.
650 0 _aComputer software.
650 0 _aComputer science
_xMathematics.
650 0 _aAlgorithms.
650 0 _aEngineering mathematics.
650 1 4 _aMathematics.
650 2 4 _aComputational Mathematics and Numerical Analysis.
650 2 4 _aAlgorithm Analysis and Problem Complexity.
650 2 4 _aAlgorithms.
650 2 4 _aMath Applications in Computer Science.
650 2 4 _aAppl.Mathematics/Computational Methods of Engineering.
650 2 4 _aProgramming Languages, Compilers, Interpreters.
700 1 _aBrisebarre, Nicolas.
_eauthor.
700 1 _ade Dinechin, Florent.
_eauthor.
700 1 _aJeannerod, Claude-Pierre.
_eauthor.
700 1 _aLefèvre, Vincent.
_eauthor.
700 1 _aMelquiond, Guillaume.
_eauthor.
700 1 _aRevol, Nathalie.
_eauthor.
700 1 _aStehlé, Damien.
_eauthor.
700 1 _aTorres, Serge.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780817647049
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-8176-4705-6
912 _aZDB-2-SMA
999 _c109903
_d109903