Comment on London's certification of algorithms 245

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.