LEADER 05640nam 22007335 450 001 9910300110503321 005 20251202115642.0 010 $a3-319-76526-4 024 7 $a10.1007/978-3-319-76526-6 035 $a(CKB)4100000004243726 035 $a(DE-He213)978-3-319-76526-6 035 $a(MiAaPQ)EBC5379784 035 $a(PPN)227406230 035 $a(EXLCZ)994100000004243726 100 $a20180502d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHandbook of Floating-Point Arithmetic /$fby Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre, Guillaume Melquiond, Nathalie Revol, Serge Torres 205 $a2nd ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2018. 215 $a1 online resource (XXV, 627 p. 64 illus., 5 illus. in color.) 311 08$a3-319-76525-6 320 $aIncludes bibliographical references and index. 327 $aPart I: Introduction, Basic Definitions, and Standards -- Introduction -- Definitions and Basic Notations -- Floating-Point Formats and Environment -- Part II: Cleverly Using Floating-Point Arithmetic -- Basic Properties and Algorithms -- Enhanced FP Sums, Dot Products, and Polynomial Values -- Languages and Compilers -- Part III: Implementing Floating-Point Operators -- Algorithms for the Basic Operations -- Hardware Implementation of Floating-Point Arithmetic -- Software Implementation of Floating-Point Arithmetic -- Evaluating Floating-Point Elementary Functions -- Part IV: Extensions -- Complex Numbers -- Interval Arithmetic -- Verifying Floating-Point Arithmetic -- Extending the Precision -- Appendix A: Number Theory Tools -- Appendix B: Previous Standards -- References -- Index. 330 $aThis handbook is a definitive guide to the effective use of modern floating-point arithmetic, which has considerably evolved, from the frequently inconsistent floating-point number systems of early computing to the recent IEEE 754-2008 standard. Most of computational mathematics depends on floating-point numbers, and understanding their various implementations will allow readers to develop programs specifically tailored for the standard?s technical features. Algorithms for floating-point arithmetic are presented throughout the book and illustrated where possible by example programs which show how these techniques appear in actual coding and design. The volume itself breaks its core topic into four parts: the basic concepts and history of floating-point arithmetic; methods of analyzing floating-point algorithms and optimizing them; implementations of IEEE 754-2008 in hardware and software; and useful extensions to the standard floating-point system, such as interval arithmetic, double- and triple-word arithmetic, operations on complex numbers, and formal verification of floating-point algorithms. This new edition updates chapters to reflect recent changes to programming languages and compilers and the new prevalence of GPUs in recent years. The revisions also add material on fused multiply-add instruction, and methods of extending the floating-point precision. As supercomputing becomes more common, more numerical engineers will need to use number representation to account for trade-offs between various parameters, such as speed, accuracy, and energy consumption. The Handbook of Floating-Point Arithmetic is designed for students and researchers in numerical analysis, programmers of numerical algorithms, compiler designers, and designers of arithmetic operators. . 606 $aMathematics$xData processing 606 $aAlgorithms 606 $aComputer science$xMathematics 606 $aEngineering mathematics 606 $aEngineering$xData processing 606 $aCompilers (Computer programs) 606 $aComputational Mathematics and Numerical Analysis 606 $aAlgorithms 606 $aMathematical Applications in Computer Science 606 $aMathematical and Computational Engineering Applications 606 $aCompilers and Interpreters 615 0$aMathematics$xData processing. 615 0$aAlgorithms. 615 0$aComputer science$xMathematics. 615 0$aEngineering mathematics. 615 0$aEngineering$xData processing. 615 0$aCompilers (Computer programs). 615 14$aComputational Mathematics and Numerical Analysis. 615 24$aAlgorithms. 615 24$aMathematical Applications in Computer Science. 615 24$aMathematical and Computational Engineering Applications. 615 24$aCompilers and Interpreters. 676 $a518 700 $aMuller$b Jean-Michel$4aut$4http://id.loc.gov/vocabulary/relators/aut$0150061 702 $aBrunie$b Nicolas$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $ade Dinechin$b Florent$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aJeannerod$b Claude-Pierre$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aJoldes$b Mioara$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aLefèvre$b Vincent$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aMelquiond$b Guillaume$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aRevol$b Nathalie$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aTorres$b Serge$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910300110503321 996 $aHandbook of Floating-Point Arithmetic$92047137 997 $aUNINA