This is a rough implementation of a new scheme for frequency-dependent
broadening. The instrumental broadening function for TOSCA has an
energy-dependent width; while there are several ways of sequencing and
implementating the process, it generally requires a fresh Gaussian to
be evaluated at every frequency bin and those Gaussians to be combined
in a weighted sum.

We note that a Gaussian function may be approximated by a linear
combination of Gaussians with width parameters (sigma) that bracket
the target and are not too far away. An error of ~1% may be reached by
limiting the sigma span to a factor of sqrt(2), while a factor of two
gives error of ~5%. Given the relevant range of widths for
instrumental broadening, a suitable collection of broadening functions
may be obtained with just a few logarithmically-spaced function
evaluations.

In this proof-of-concept, the spectrum is convolved with five
Gaussian kernels, logarithmically spaced by factors of two. At each bin, the
broadened value is drawn from a corresponding broad spectrum, obtained
by interpolation from those at neighbouring sigma values. This
interpolation involves some "magic numbers" in the form of a cubic
function fitted to reproduce a Gaussian as closely as possible from
wider and narrower functions.

The main assumption made in this approach is that the broadening
function is short-ranged relative to the rate of change in width.
Compared to a sum of functions centered at each bin, this method
introduces a slight asymmetry to the peaks. The benefit is a
drastically reduced cost of evaluation; the implementation here is far
from optimal (as it convolutes larger spectral regions than necessary)
and reduces the runtime of Abins by almost half compared to the
fastest implementation of a full sum.