Harmonic Sum Calculation: Sneaking Finite Precision Principles into CS1

We describe using the calculation of harmonic sums to introduce and integrate the discussion and exploration of some elementary principles of finite precision floating point computation into a CS1 course. After students ’ exposure to this problem and its solutions, they should not only have a better understanding of when to exploit event-controlled vs. counter-controlled loops, but also be able to correctly answer the following two questions relating to operations on floating point data: 1. can (A + B) + C � = A + (B + C) for some floating point A, B, C? 2. can (A + B) = A, where |B |> 0 for some floating point A, B