Semantics of floating point arithmetic and elementary functions
This paper begins with a discussion of properties that one might like to have satisfied by calculations involving floating point arithmetic and elementary function approximations. It concludes with a summary of the main characteristics that it is believed any detailed specification of these operations should provide. The point of view is based on starting with a description of what is needed by someone who either uses or analyzes numerical software, and then proposing specifications that are both sufficient to meet these needs and relatively simple. One principal motivation is that proofs concerning programs should be portable, so in studying software portability it is as important to concern ourselves with semantic as well as syntactic details.
KeywordsArithmetic Operation Double Precision Decimal Digit Point Arithmetic Floating Point Number
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- 1.Cody, W. J., Desirable Hardware Characteristics for Scientific Computation, ACM SIGNUM Newsletter, 6, 1 (January, 1971) 16–31.Google Scholar
- 2.Hull, T. E. and Hofbauer, J. J., Language Facilities for Multiple Precision Floating Point Computation, With Examples, and the Description of a Preprocessor, Technical Report No. 63, Department of Computer Science, University of Toronto (1974).Google Scholar
- 3.Hull, T. E. and Hofbauer, J. J., Language Facilities for Numerical Computation, Proceedings of the ACM-SIAM Conference on Mathematical Software II, Purdue University (1974) 1–18.Google Scholar
- 4.Kahan, W., A Survey of Error Analysis, Proceedings IFIP Congress 1971, vol. 2, Ed. C. V. Freeman, North-Holland Publishing Co. (1972) 1214–1239.Google Scholar
- 5.Kahan, W., Implementation of Algorithms, Part I, Technical Report 20, Department of Computer Science, University of California, Berkeley (1973); available through NTIS, AD-769 124.Google Scholar
- 6.Neely, Peter M., On Conventions for Systems of Numerical Representations, Proceedings ACM Annual Conference (1972) 644–651.Google Scholar