  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 compositions
of homogeneous mechanisms. This approach is also applicable to certain discrete
mechanisms that cannot be analysed with R\'enyi accountants. In this paper, we
extend this approach to compositions of heterogeneous mechanisms. We carry out
a full error analysis that allows choosing the parameters of the algorithm such
that a desired accuracy is obtained. Using our 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.
