메뉴 건너뛰기




Volumn 3965 LNCS, Issue , 2006, Pages 211-242

Floating-point verification using theorem proving

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SOFTWARE; NUMERICAL METHODS;

EID: 33745934660     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11757283_8     Document Type: Conference Paper
Times cited : (41)

References (60)
  • 1
    • 33745935331 scopus 로고    scopus 로고
    • M. Aagaard and J. Harrison, editors. Theorem Proving in Higher Order Logics: 13th International Conference, TPHOLs 2000, Springer-Verlag
    • M. Aagaard and J. Harrison, editors. Theorem Proving in Higher Order Logics: 13th International Conference, TPHOLs 2000, volume 1869 of Lecture Notes in Computer Science. Springer-Verlag, 2000.
    • (2000) Lecture Notes in Computer Science , vol.1869
  • 6
    • 0019663774 scopus 로고
    • A simple but realistic model of floating-point computation
    • W. S. Brown. A simple but realistic model of floating-point computation. ACM Transactions on Mathematical Software, 7:445-480, 1981.
    • (1981) ACM Transactions on Mathematical Software , vol.7 , pp. 445-480
    • Brown, W.S.1
  • 7
    • 0022769976 scopus 로고
    • Graph-based algorithms for Boolean function manipulation
    • R. E. Bryant. Graph-based algorithms for Boolean function manipulation. IEEE Transactions on Computers, C-35:677-691, 1986.
    • (1986) IEEE Transactions on Computers , vol.C-35 , pp. 677-691
    • Bryant, R.E.1
  • 9
    • 0003180840 scopus 로고
    • A formulation of the simple theory of types
    • A. Church. A formulation of the Simple Theory of Types. Journal of Symbolic Logic, 5:56-68, 1940.
    • (1940) Journal of Symbolic Logic , vol.5 , pp. 56-68
    • Church, A.1
  • 10
    • 85037030721 scopus 로고
    • Design and synthesis of synchronization skeletons using branching-time temporal logic
    • D. Kozen, editor, Logics of Programs, Yorktown Heights, Springer-Verlag
    • E. M. Clarke and E. A. Emerson. Design and synthesis of synchronization skeletons using branching-time temporal logic. In D. Kozen, editor, Logics of Programs, volume 131 of Lecture Notes in Computer Science, pages 52-71, Yorktown Heights, 1981. Springer-Verlag.
    • (1981) Lecture Notes in Computer Science , vol.131 , pp. 52-71
    • Clarke, E.M.1    Emerson, E.A.2
  • 13
    • 0011644151 scopus 로고    scopus 로고
    • Proving the IEEE correctness of iterative floating-point square root, divide and remainder algorithms
    • M. Cornea-Hasegan. Proving the IEEE correctness of iterative floating-point square root, divide and remainder algorithms. Intel Technology Journal, 1998-Q2:1-11, 1998. Available on the Web as http://developer.intel.com/ technology/itj/q21998/articles/art_3.htm.
    • (1998) Intel Technology Journal , vol.1998 , Issue.Q2 , pp. 1-11
    • Cornea-Hasegan, M.1
  • 16
    • 0000810983 scopus 로고
    • A floating-point technique for extending the available precision
    • T. J. Dekker. A floating-point technique for extending the available precision. Numerical Mathematics, 18:224-242, 1971.
    • (1971) Numerical Mathematics , vol.18 , pp. 224-242
    • Dekker, T.J.1
  • 17
    • 0032123777 scopus 로고    scopus 로고
    • The IA-64 architecture at work
    • July
    • C. Dulong. The IA-64 architecture at work. IEEE Computer, 64(7):24-32, July 1998.
    • (1998) IEEE Computer , vol.64 , Issue.7 , pp. 24-32
    • Dulong, C.1
  • 19
    • 84893808653 scopus 로고    scopus 로고
    • BerkMin: A fast and robust Sat-solver
    • C. D. Kloos and J. D. Franca, editors, Paris, France, IEEE Computer Society Press
    • E. Goldberg and Y. Novikov. BerkMin: a fast and robust Sat-solver. In C. D. Kloos and J. D. Franca, editors, Design, Automation and Test in Europe Conference and Exhibition (DATE 2002), pages 142-149, Paris, France, 2002. IEEE Computer Society Press.
    • (2002) Design, Automation and Test in Europe Conference and Exhibition (DATE 2002) , pp. 142-149
    • Goldberg, E.1    Novikov, Y.2
  • 20
    • 2342664583 scopus 로고
    • Representing a logic in the LCF metalanguage
    • D. Néel, editor, Cambridge University Press
    • M. J. C. Gordon. Representing a logic in the LCF metalanguage. In D. Néel, editor, Tools and notions for program construction: an advanced course, pages 163-185. Cambridge University Press, 1982.
    • (1982) Tools and Notions for Program Construction: An Advanced Course , pp. 163-185
    • Gordon, M.J.C.1
  • 23
    • 84957700828 scopus 로고    scopus 로고
    • HOL Light: A tutorial introduction
    • M. Srivas and A. Camilleri, editors, Proceedings of the First International Conference on Formal Methods in Computer-Aided Design (FMCAD'96), Springer-Verlag
    • J. Harrison. HOL Light: A tutorial introduction. In M. Srivas and A. Camilleri, editors, Proceedings of the First International Conference on Formal Methods in Computer-Aided Design (FMCAD'96), volume 1166 of Lecture Notes in Computer Science, pages 265-269. Springer-Verlag, 1996.
    • (1996) Lecture Notes in Computer Science , vol.1166 , pp. 265-269
    • Harrison, J.1
  • 24
    • 84958964101 scopus 로고    scopus 로고
    • Proof style
    • E. Giménez and C. Paulin-Mohring, editors, Types for Proofs and Programs: International Workshop TYPES'96, Aussois, France, Springer-Verlag
    • J. Harrison. Proof style. In E. Giménez and C. Paulin-Mohring, editors, Types for Proofs and Programs: International Workshop TYPES'96, volume 1512 of Lecture Notes in Computer Science, pages 154-172, Aussois, France, 1996, Springer-Verlag.
    • (1996) Lecture Notes in Computer Science , vol.1512 , pp. 154-172
    • Harrison, J.1
  • 26
    • 84957799469 scopus 로고    scopus 로고
    • A machine-checked theory of floating point arithmetic
    • Y. Bertot, G. Dowek, A. Hirschowitz, C. Paulin, and L. Théry, editors, Theorem Proving in Higher Order Logics: 12th International Conference, TPHOLs'99, Nice, France, Springer-Verlag
    • J. Harrison. A machine-checked theory of floating point arithmetic, In Y. Bertot, G. Dowek, A. Hirschowitz, C. Paulin, and L. Théry, editors, Theorem Proving in Higher Order Logics: 12th International Conference, TPHOLs'99, volume 1690 of Lecture Notes in Computer Science, pages 113-130, Nice, France, 1999. Springer-Verlag.
    • (1999) Lecture Notes in Computer Science , vol.1690 , pp. 113-130
    • Harrison, J.1
  • 27
    • 84947223461 scopus 로고    scopus 로고
    • Formal verification of floating point trigonometric functions
    • W. A. Hunt and S. D. Johnson, editors, Formal Methods in Computer-Aided Design: Third International Conference FMCAD 2000, Springer-Verlag
    • J. Harrison. Formal verification of floating point trigonometric functions. In W. A. Hunt and S. D. Johnson, editors, Formal Methods in Computer-Aided Design: Third International Conference FMCAD 2000, volume 1954 of Lecture Notes in Computer Science, pages 217-233. Springer-Verlag, 2000.
    • (2000) Lecture Notes in Computer Science , vol.1954 , pp. 217-233
    • Harrison, J.1
  • 29
    • 0038343516 scopus 로고    scopus 로고
    • Formal verification of square root algorithms
    • J. Harrison. Formal verification of square root algorithms. Formal Methods in System Design., 22:143-153, 2003.
    • (2003) Formal Methods in System Design. , vol.22 , pp. 143-153
    • Harrison, J.1
  • 30
    • 0043136377 scopus 로고    scopus 로고
    • Isolating critical cases for reciprocals using integer factorization
    • J.-C. Bajard and M. Schulte, editors, Santiago de Compostela, Spain, IEEE Computer Society
    • J. Harrison. Isolating critical cases for reciprocals using integer factorization. In J.-C. Bajard and M. Schulte, editors, Proceedings, 16th IEEE Symposium on Computer Arithmetic, pages 148-157, Santiago de Compostela, Spain, 2003. IEEE Computer Society. Currently available from symposium Web site at http://www.dec.usc.es/arith16/papers/paper-150.pdf.
    • (2003) Proceedings, 16th IEEE Symposium on Computer Arithmetic , pp. 148-157
    • Harrison, J.1
  • 32
    • 0003589321 scopus 로고
    • ANSI/IEEE Standard 754-1985, The Institute of Electrical and Electronic Engineers, Inc., 345 East 47th Street, New York, NY 10017, USA
    • IEEE. Standard for binary floating point arithmetic. ANSI/IEEE Standard 754-1985, The Institute of Electrical and Electronic Engineers, Inc., 345 East 47th Street, New York, NY 10017, USA, 1985.
    • (1985) Standard for Binary Floating Point Arithmetic
  • 35
    • 0012061797 scopus 로고
    • Analysis of some known methods of improving the accuracy of floating-point sums
    • S. Linnainmaa. Analysis of some known methods of improving the accuracy of floating-point sums. BIT, 14:167-202, 1974.
    • (1974) BIT , vol.14 , pp. 167-202
    • Linnainmaa, S.1
  • 36
    • 84945709685 scopus 로고
    • Mechanical theorem-proving by model elimination
    • D. W. Loveland. Mechanical theorem-proving by model elimination. Journal of the ACM, 15:236-251, 1968.
    • (1968) Journal of the ACM , vol.15 , pp. 236-251
    • Loveland, D.W.1
  • 38
    • 0025228329 scopus 로고
    • Computation of elementary functions on the IBM RISC system/6000 processor
    • P. W. Markstein. Computation of elementary functions on the IBM RISC System/6000 processor. IBM Journal of Research and Development, 34:111-119, 1990.
    • (1990) IBM Journal of Research and Development , vol.34 , pp. 111-119
    • Markstein, P.W.1
  • 39
    • 0002811620 scopus 로고
    • Quasi double-precision in floating-point addition
    • O. Møller. Quasi double-precision in floating-point addition. BIT, 5:37-50, 1965.
    • (1965) BIT , vol.5 , pp. 37-50
    • Møller, O.1
  • 43
    • 33749583441 scopus 로고    scopus 로고
    • On the definition of ulp(x)
    • ENS Lyon
    • J.-M. Muller. On the definition of ulp(x). Research Report 2005-09, ENS Lyon, 2005.
    • (2005) Research Report , vol.2005 , Issue.9
    • Muller, J.-M.1
  • 44
    • 0000291586 scopus 로고    scopus 로고
    • Formally verifying IEEE compliance of floating-point hardware
    • J. O'Leary, X, Zhao, R. Gerth, and C.-J. H. Seger. Formally verifying IEEE compliance of floating-point hardware. Intel Technology Journal, 1999-Q1:1-14, 1999. Available on the Web as http://developer.intel.com/ technology/itj/q11999/articles/art_5.htm.
    • (1999) Intel Technology Journal , vol.1999 , Issue.Q1 , pp. 1-14
    • O'Leary, J.1    Zhao, X.2    Gerth, R.3    Seger, C.-J.H.4
  • 45
    • 84957646690 scopus 로고
    • Anatomy of the Pentium bug
    • P. D. Mosses, M. Nielsen, and M. I. Schwartzbach, editors, Proceedings of the 5th International Joint Conference on the theory and practice of software development (TAPSOFT'95), Aarhus, Denmark, Springer-Verlag
    • V. R. Pratt. Anatomy of the Pentium bug. In P. D. Mosses, M. Nielsen, and M. I. Schwartzbach, editors, Proceedings of the 5th International Joint Conference on the theory and practice of software development (TAPSOFT'95), volume 915 of Lecture Notes in Computer Science, pages 97-107, Aarhus, Denmark, 1995. Springer-Verlag.
    • (1995) Lecture Notes in Computer Science , vol.915 , pp. 97-107
    • Pratt, V.R.1
  • 47
    • 0001439560 scopus 로고
    • Specification and verification of concurrent programs in CESAR
    • Proceedings of the 5th International Symposium on Programming, Springer-Verlag
    • J. P. Queille and J. Sifakis. Specification and verification of concurrent programs in CESAR. In Proceedings of the 5th International Symposium on Programming, volume 137 of Lecture Notes in Computer Science, pages 195-220. Springer-Verlag, 1982.
    • (1982) Lecture Notes in Computer Science , vol.137 , pp. 195-220
    • Queille, J.P.1    Sifakis, J.2
  • 48
    • 84937534389 scopus 로고
    • Ever had problems rounding off figures? The stock exchange has
    • November 8
    • K. Quinn. Ever had problems rounding off figures? The stock exchange has. Wall Street Journal, November 8, 1983.
    • (1983) Wall Street Journal
    • Quinn, K.1
  • 50
    • 0001582662 scopus 로고    scopus 로고
    • A mechanically checked proof of IEEE compliance of a register-transfer- level specification of the AMD-K7 floating-point multiplication, division, and square root instructions
    • D. Rusinoff. A mechanically checked proof of IEEE compliance of a register-transfer-level specification of the AMD-K7 floating-point multiplication, division, and square root instructions. LMS Journal of Computation and Mathematics, 1:148-200, 1998. Available on the Web via http://www.onr.com/user/russ/david/k7-div-sqrt.html.
    • (1998) LMS Journal of Computation and Mathematics , vol.1 , pp. 148-200
    • Rusinoff, D.1
  • 51
    • 27944473005 scopus 로고    scopus 로고
    • Formal verification of divide and square root algorithms using series calculation
    • D. Borrione, M. Kaufmann, and J. Moore, editors, University of Grenoble
    • J. Sawada. Formal verification of divide and square root algorithms using series calculation. In D. Borrione, M. Kaufmann, and J. Moore, editors, 3rd International Workshop on the ACL2 Theorem Prover and its Applications, pages 31-49. University of Grenoble, 2002.
    • (2002) 3rd International Workshop on the ACL2 Theorem Prover and Its Applications , pp. 31-49
    • Sawada, J.1
  • 52
    • 0001510331 scopus 로고
    • Formal verification by symbolic evaluation of partially-ordered trajectories
    • C.-J. H. Seger and R. E. Bryant. Formal verification by symbolic evaluation of partially-ordered trajectories. Formal Methods in System Design, 6:147-189, 1995.
    • (1995) Formal Methods in System Design , vol.6 , pp. 147-189
    • Seger, C.-J.H.1    Bryant, R.E.2
  • 53
    • 0001381792 scopus 로고
    • Modeling and verifying systems and software in prepositional logic
    • B. K. Daniels, editor, Gatwick, UK, Pergamon Press
    • G. Stålmarck and M. Säflund. Modeling and verifying systems and software in prepositional logic. In B. K. Daniels, editor, Safety of Computer Control Systems, 1990 (SAFECOMP '90), pages 31-36, Gatwick, UK, 1990. Pergamon Press.
    • (1990) Safety of Computer Control Systems, 1990 (SAFECOMP '90) , pp. 31-36
    • Stålmarck, G.1    Säflund, M.2
  • 55
    • 0032678601 scopus 로고    scopus 로고
    • New algorithms for improved transcendental functions on IA-64
    • I. Koren and P. Kornerup, editors, Adelaide, Australia, IEEE Computer Society
    • S. Story and P. T. P. Tang. New algorithms for improved transcendental functions on IA-64. In I. Koren and P. Kornerup, editors, Proceedings, 14th IEEE symposium on on computer arithmetic, pages 4-11, Adelaide, Australia, 1999. IEEE Computer Society.
    • (1999) Proceedings, 14th IEEE Symposium on on Computer Arithmetic , pp. 4-11
    • Story, S.1    Tang, P.T.P.2
  • 56
    • 0026171455 scopus 로고
    • Table-lookup algorithms for elementary functions and their error analysis
    • P. Kornerup and D. W. Matula, editors
    • th Symposium on Computer Arithemtic, pages 232-236, 1991.
    • (1991) th Symposium on Computer Arithemtic , pp. 232-236
    • Tang, P.T.P.1
  • 58
    • 0002900871 scopus 로고
    • Numerical analysis as an independent science
    • A. v. Wijngaarden. Numerical analysis as an independent science. BIT, 6:68-81, 1966.
    • (1966) BIT , vol.6 , pp. 68-81
    • Wijngaarden, A.V.1
  • 59
    • 33745948489 scopus 로고
    • Rounding Errors in Algebraic Processes, Her Majesty's Stationery Office (HMSO), London
    • J. H. Wilkinson. Rounding Errors in Algebraic Processes, volume 32 of National Physical Laboratory Notes on Applied Science. Her Majesty's Stationery Office (HMSO), London, 1963.
    • (1963) National Physical Laboratory Notes on Applied Science , vol.32
    • Wilkinson, J.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.