NDLI: Correctness proofs outline for Newton-Raphson based floating-point divide and square root algorithms

Content Provider	IEEE Xplore Digital Library
Author	Cornea-Hasegan, M.A. Golliver, R.A. Markstein, P.
Copyright Year	1999
Description	Author affiliation: Intel Corp., Hillsboro, OR, USA (Cornea-Hasegan, M.A.)
Abstract	This paper describes a study of a class of algorithms for the floating-point divide and square root operations, based on the Newton-Raphson iterative method. The two main goals were. (1) Proving the IEEE correctness of these iterative floating-point algorithms, i.e. compliance with the IEEE-754 standard for binary floating-point operations. The focus was on software driven iterative algorithms, instead of the hardware based implementations that dominated until now. (2) Identifying the special cases of operands that require results. Assistance due to possible overflow, or loss of precision of intermediate This study was initiated in an attempt to prove the IEEE for a class of divide and square root based on the Newton-Rapshson iterative methods. As more insight into the inner workings of these algorithms was gained, it became obvious that a formal study and proof were necessary in order to achieve the desired objectives. The result is a complete and rigorous proof of IEEE correctness for floating-point divide and square root algorithms based on the Newton-Raphson iterative method. Even more, the method used in proving the IEEE correctness of the square root algorithm is applicable in principle to any iterative algorithm, not only based on the Newton-Raphson method. Conditions requiring Software Assistance (SWA) were also determined, and were used to identify cases when alternate algorithms are needed to generate correct results. Overall, this is one important step toward flawless implementation of these floating-point operations based on software implementations.
Starting Page	96
Ending Page	105
File Size	124690
Page Count	10
File Format	PDF
ISBN	0769501168
ISSN	10636889
DOI	10.1109/ARITH.1999.762834
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1999-04-14
Publisher Place	Australia
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Iterative methods Content addressable storage Throughput Emulation Libraries Cornea Identity-based encryption Iterative algorithms Software algorithms Availability
Content Type	Text
Resource Type	Article

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