  The recently proposed Fast Fourier Transform (FFT)-based accountant for
evaluating $(\varepsilon,\delta)$-differential privacy guarantees using the
privacy loss distribution formalism has been shown to give tighter bounds than
commonly used methods such as R\'enyi accountants when applied to homogeneous
compositions, i.e., to compositions of identical mechanisms. In this paper, we
extend this approach to heterogeneous compositions. We carry out a full error
analysis that allows choosing the parameters of the algorithm such that a
desired accuracy is obtained. The analysis also extends previous results by
taking into account all the parameters of the algorithm. Using the error
analysis, we also give a bound for the computational complexity in terms of the
error which is analogous to and slightly tightens the one given by Murtagh and
Vadhan (2018). We also show how to speed up the evaluation of tight privacy
guarantees using the Plancherel theorem at the cost of increased
pre-computation and memory usage.
