LEADER 04218nam 2200721 a 450 001 9910811185003321 005 20200520144314.0 010 $a3-11-030179-2 024 7 $a10.1515/9783110301793 035 $a(CKB)2550000001096894 035 $a(EBL)1130308 035 $a(OCoLC)851970604 035 $a(SSID)ssj0000916704 035 $a(PQKBManifestationID)11466131 035 $a(PQKBTitleCode)TC0000916704 035 $a(PQKBWorkID)10877488 035 $a(PQKB)11593715 035 $a(DE-B1597)179444 035 $a(OCoLC)953308478 035 $a(OCoLC)990725657 035 $a(DE-B1597)9783110301793 035 $a(Au-PeEL)EBL1130308 035 $a(CaPaEBR)ebr10728884 035 $a(CaONFJC)MIL503428 035 $a(CaSebORM)9783110301731 035 $a(MiAaPQ)EBC1130308 035 $a(PPN)175495246 035 $a(EXLCZ)992550000001096894 100 $a20130419d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aComputer arithmetic and validity $etheory, implementation, and applications /$fUlrich Kulisch 205 $a2nd ed. 210 $aBerlin $cDe Gruyter$d2013 215 $a1 online resource (434 p.) 225 0 $aDe Gruyter Studies in Mathematics ;$v33 225 0$aDe Gruyter studies in mathematics,$x0179-0986 ;$v33 300 $aDescription based upon print version of record. 311 $a3-11-030173-3 311 $a1-299-72177-X 320 $aIncludes bibliographical references and index. 327 $t Frontmatter -- $tForeword to the second edition -- $tPreface -- $tContents -- $tIntroduction -- $tPart I. Theory of computer arithmetic -- $tChapter 1. First concepts -- $tChapter 2. Ringoids and vectoids -- $tChapter 3. Definition of computer arithmetic -- $tChapter 4. Interval arithmetic -- $tPart II. Implementation of arithmetic on computers -- $tChapter 5. Floating-point arithmetic -- $tChapter 6. Implementation of floating-point arithmetic on a computer -- $tChapter 7. Hardware support for interval arithmetic -- $tChapter 8. Scalar products and complete arithmetic -- $tPart III. Principles of verified computing -- $tChapter 9. Sample applications -- $tAppendix A. Frequently used symbols -- $tAppendix B. On homomorphism -- $tBibliography -- $tList of figures -- $tList of tables -- $tIndex 330 $aThis is the revised and extended second edition of the successful basic book on computer arithmetic. It is consistent with the newest recent standard developments in the field. The book shows how the arithmetic and mathematical capability of the digital computer can be enhanced in a quite natural way. The work is motivated by the desire and the need to improve the accuracy of numerical computing and to control the quality of the computed results (validity). The accuracy requirements for the elementary floating-point operations are extended to the customary product spaces of computations including interval spaces. The mathematical properties of these models are extracted into an axiomatic approach which leads to a general theory of computer arithmetic. Detailed methods and circuits for the implementation of this advanced computer arithmetic on digital computers are developed in part two of the book. Part three then illustrates by a number of sample applications how this extended computer arithmetic can be used to compute highly accurate and mathematically verified results. The book can be used as a high-level undergraduate textbook but also as reference work for research in computer arithmetic and applied mathematics. 410 3$aDe Gruyter Studies in Mathematics 606 $aComputer arithmetic 606 $aComputer arithmetic and logic units 606 $aFloating-point arithmetic 615 0$aComputer arithmetic. 615 0$aComputer arithmetic and logic units. 615 0$aFloating-point arithmetic. 676 $a005.101/5113 686 $aSK 900$2rvk 700 $aKulisch$b Ulrich$01631140 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910811185003321 996 $aComputer arithmetic and validity$93969809 997 $aUNINA