  In this paper we describe an algorithm and a Fortran 90 module ({\bf
Conical}) for the computation of the conical function
$P^m_{-\tfrac12+i\tau}(x)$ for $x>-1$, $m \ge 0$, $\tau >0$. These functions
appear in the solution of Dirichlet problems for domains bounded by cones;
because of this, they are involved in a large number of applications in
Engineering and Physics.
  In the Fortran 90 module, the admissible parameter ranges for computing the
conical functions in standard IEEE double precision arithmetic are restricted
to $(x,m,\tau) \in (-1,1) \times [0,\,40] \times [0,\,100]$ and $(x,m,\tau) \in
(1,100) \times [0,\,100] \times [0,\,100]$. Based on tests of the three-term
recurrence relation satisfied by these functions and direct comparison with
Maple, we claim a relative accuracy close to $10^{-12}$ in the full parameter
range, although a mild loss of accuracy can be found at some points of the
oscillatory region of the conical functions. The relative accuracy increases to
$10^{-13}\,-\,10^{-14}$ in the region of the monotonic regime of the functions
where integral representations are computed ($-1<x<0$).
