understanding of the log map and distance function

[nag92]

Is the distance function implemented in the library use the logarithmic map function as defined in this paper? I am implemented a QGMM algorithm and I need this use this function to get the distance between two quaternion.

https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.104.2293&rep=rep1&type=pdf