Analysis and Detection of Stagnation in Floating-Point Summation

Stagnation in the summation of floating-point numbers occurs when the running sum, or the accumulator, does not change its value despite addends being greater than zero. We define total stagnation in a summation, where operands are completely rounded off in addition operations, and provide examples of how stagnation may occur. We have developed StagnationDetection.jl for dynamic analysis of floating-point stagnation in Julia, and we apply the tool to basic vector summation and a fluid flow simulation model. Users are able to identify areas of their floating-point code where stagnation occurs, where they may prevent stagnation by applying higher precision, compensated summation or stochastic rounding. To the best of our knowledge we provide a first rigorous definition of stagnation in floating-point summation.