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Floating point verification in HOL Light: the exponential function
 UNIVERSITY OF CAMBRIDGE COMPUTER LABORATORY
, 1997
"... Since they often embody compact but mathematically sophisticated algorithms, operations for computing the common transcendental functions in floating point arithmetic seem good targets for formal verification using a mechanical theorem prover. We discuss some of the general issues that arise in veri ..."
Abstract

Cited by 31 (6 self)
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Since they often embody compact but mathematically sophisticated algorithms, operations for computing the common transcendental functions in floating point arithmetic seem good targets for formal verification using a mechanical theorem prover. We discuss some of the general issues that arise in verifications of this class, and then present a machinechecked verification of an algorithm for computing the exponential function in IEEE754 standard binary floating point arithmetic. We confirm (indeed strengthen) the main result of a previously published error analysis, though we uncover a minor error in the hand proof and are forced to confront several subtle issues that might easily be overlooked informally. The development described here includes, apart from the proof itself, a formalization of IEEE arithmetic, a mathematical semantics for the programming language in which the algorithm is expressed, and the body of pure mathematics needed. All this is developed logically from first prin...