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Volumn 57, Issue 4, 2008, Pages 462-471

Emulation of a FMA and correctly rounded sums: Proved algorithms using rounding to odd

Author keywords

Accurate summation; Coq; Floating point; FMA; Formal proof; Rounding to odd

Indexed keywords

ALGORITHMS; COMPUTATION THEORY; ITERATIVE METHODS; THEOREM PROVING;

EID: 40949118542     PISSN: 00189340     EISSN: None     Source Type: Journal    
DOI: 10.1109/TC.2007.70819     Document Type: Article
Times cited : (29)

References (23)
  • 1
    • 0019539209 scopus 로고
    • A Proposed Standard for Binary Floating Point Arithmetic
    • Mar
    • D. Stevenson et al., "A Proposed Standard for Binary Floating Point Arithmetic," Computer, vol. 14, no. 3, pp. 51-62, Mar. 1981.
    • (1981) Computer , vol.14 , Issue.3 , pp. 51-62
    • Stevenson, D.1
  • 2
    • 0002604680 scopus 로고
    • An American National Standard: IEEE Standard for Binary Floating-Point Arithmetic
    • D. Stevenson et al., "An American National Standard: IEEE Standard for Binary Floating-Point Arithmetic," ACM SIGPLAN Notices, vol. 22, no. 2, pp. 9-25, 1987.
    • (1987) ACM SIGPLAN Notices , vol.22 , Issue.2 , pp. 9-25
    • Stevenson, D.1
  • 3
    • 34848830926 scopus 로고    scopus 로고
    • Formally Certified Floating-Point Filters for Homogeneous Geometric Predicates
    • G. Melquiond and S. Pion, "Formally Certified Floating-Point Filters for Homogeneous Geometric Predicates," Theoretical Informatics and Applications, vol. 41, no. 1, pp. 57-70, 2007.
    • (2007) Theoretical Informatics and Applications , vol.41 , Issue.1 , pp. 57-70
    • Melquiond, G.1    Pion, S.2
  • 4
    • 40949122210 scopus 로고
    • When Is Double Rounding Innocuous
    • S.A. Figueroa, "When Is Double Rounding Innocuous," SIGNUM Newsletter, vol. 30, no. 3, pp. 21-26, 1995.
    • (1995) SIGNUM Newsletter , vol.30 , Issue.3 , pp. 21-26
    • Figueroa, S.A.1
  • 6
    • 0026122066 scopus 로고
    • What Every Computer Scientist Should Know about Floating-Point Arithmetic
    • D. Goldberg, "What Every Computer Scientist Should Know about Floating-Point Arithmetic," ACM Computing Surveys, vol. 23, no. 1, pp. 5-47, 1991.
    • (1991) ACM Computing Surveys , vol.23 , Issue.1 , pp. 5-47
    • Goldberg, D.1
  • 8
    • 34250860833 scopus 로고
    • Multistep Gradual Rounding
    • Apr
    • C. Lee, "Multistep Gradual Rounding," IEEE Trans. Computers, vol. 38, no. 4, pp. 595-600, Apr. 1989.
    • (1989) IEEE Trans. Computers , vol.38 , Issue.4 , pp. 595-600
    • Lee, C.1
  • 10
    • 24344470890 scopus 로고    scopus 로고
    • Interactive Theorem Proving and Program Development. Coq' Art: The Calculus of Inductive Constructions
    • Springer Verlag
    • Y. Bertot and P. Casteran, Interactive Theorem Proving and Program Development. Coq' Art: The Calculus of Inductive Constructions. Texts in Theoretical Computer Science, Springer Verlag, 2004.
    • (2004) Texts in Theoretical Computer Science
    • Bertot, Y.1    Casteran, P.2
  • 11
    • 33745964109 scopus 로고    scopus 로고
    • Preuves Formelles en Arithmétiques à Virgule Flottante,
    • PhD dissertation, École Normale Supérieure de Lyon, Nov
    • S. Boldo, "Preuves Formelles en Arithmétiques à Virgule Flottante," PhD dissertation, École Normale Supérieure de Lyon, Nov. 2004.
    • (2004)
    • Boldo, S.1
  • 13
    • 0000810983 scopus 로고
    • A Floating-Point Technique for Extending the Available Precision
    • T.J. Dekker, "A Floating-Point Technique for Extending the Available Precision," Numerische Mathematik, vol. 18, no. 3, pp. 224-242, 1971.
    • (1971) Numerische Mathematik , vol.18 , Issue.3 , pp. 224-242
    • Dekker, T.J.1
  • 15
    • 69149089213 scopus 로고    scopus 로고
    • Pitfalls of a Full Floating-Point Proof: Example on the Formal Proof of the Veltkamp/Dekker Algorithms
    • S. Boldo, "Pitfalls of a Full Floating-Point Proof: Example on the Formal Proof of the Veltkamp/Dekker Algorithms," Proc. Third Int'l Joint Conf. Automated Reasoning, 2006.
    • (2006) Proc. Third Int'l Joint Conf. Automated Reasoning
    • Boldo, S.1
  • 19
    • 0026169919 scopus 로고
    • Algorithms for Arbitrary Precision Floating-Point Arithmetic
    • D.M. Priest, "Algorithms for Arbitrary Precision Floating-Point Arithmetic," Proc. 10th IEEE Symp. Computer Arithmetic, pp. 132-144, 1991.
    • (1991) Proc. 10th IEEE Symp. Computer Arithmetic , pp. 132-144
    • Priest, D.M.1
  • 22
    • 33751029285 scopus 로고    scopus 로고
    • Basic Building Blocks for a Triple-Double Intermediate Format,
    • Technical Report RR2005-38, LIP, Sept
    • C.Q. Lauter, "Basic Building Blocks for a Triple-Double Intermediate Format," Technical Report RR2005-38, LIP, Sept. 2005.
    • (2005)
    • Lauter, C.Q.1
  • 23
    • 0034866245 scopus 로고    scopus 로고
    • Worst Cases for Correct Rounding of the Elementary Functions in Double Precision
    • V. Lefèvre and J.-M. Muller, "Worst Cases for Correct Rounding of the Elementary Functions in Double Precision," Proc. 15th IEEE Symp. Computer Arithmetic, pp. 111-118, 2001.
    • (2001) Proc. 15th IEEE Symp. Computer Arithmetic , pp. 111-118
    • Lefèvre, V.1    Muller, J.-M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.