Comment on London's certification of algorithms 245

Authors:
K. A. Redish
Affiliations:
McMaster Univ., Hamilton, Ontarion, Canada
Venue:
Communications of the ACM
Year:
1971

Citing 7
Cited 0

The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms

The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
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Abstract

In his Certification of Algorithm 245 [1], Ralph L. London exhibits a common confusion between an algorithm, its representation, and its implementation on a processor—a code. In the present state of the art we can attempt, in general, to prove an algorithm and to test a code. For example, London states that “… the algorithm TREESORT 3 [2] is proved to perform properly its claimed task of sorting an array M[1:n] into ascending order.” While this is true of the algorithm, it is not true of the code unless we place restrictions on the array elements. The trouble arises in this example from the finite precision of processors; the Boolean expression A ≥ B (real A, B) will usually be implemented as A - B ≥ 0, which can fail due to floating point overflow or underflow.