In his Certification of Algorithm 245 , 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  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.
The full text of this article is premium content
No entries found
Log in to Read the Full Article
Purchase the Article
Create a Web Account
If you are an ACM member, Communications subscriber, Digital Library subscriber, or use your institution's subscription, please set up a web account to access premium content and site
features. If you are a SIG member or member of the general public, you may set up a web account to comment on free articles and sign up for email alerts.