  As far as we know, usual computer algebra packages can not compute
denumerants for almost medium (about a hundred digits) or almost medium--large
(about a thousand digits) input data in a reasonably time cost on an ordinary
computer. Implemented algorithms can manage numerical $n$--semigroups for small
input data.
  Here we are interested in denumerants of numerical $3$--semigroups which have
almost medium input data. A new algorithm for computing denumerants is given
for this task. It can manage almost medium input data in the worst case and
medium--large or even large input data in some cases.
