Tracking the Maslov index
The Maslov index helps track the sign of the contributions in a semiclassical IVR calculation, in order to ensure that they stay continuous. While I was a graduate student, I came up with an approach to do this, based on the IEEE standard for floating point numbers. While this isn’t necessarily a vital improvement in performance (other aspects of the calculation are more computationally expensive), it is a good example of how to optimize performance.