Competitiveness of a Non-Linear Block-Space GPU Thread Map for Simplex Domains

This work presents and studies the efficiency problem of mapping GPU threads onto simplex domains. A non-linear map
$\lambda (\omega)$
is formulated based on a block-space enumeration principle that reduces the number of thread-blocks by a factor of approximately
$2\times$
and
$6\times$
for 2-simplex and 3-simplex domains, respectively, when compared to the standard approach. Performance results show that
$\lambda (\omega)$
is competitive and even the fastest map when ran in recent GPU architectures such as the Tesla V100, where it reaches up to
$1.5\times$
of speedup in 2-simplex tests. In 3-simplex tests, it reaches up to
$2.3\times$
of speedup for small workloads and up to
$1.25\times$
for larger ones. The results obtained make
$\lambda (\omega)$
a useful GPU optimization technique with applications on parallel problems that define all-pairs, all-triplets or nearest neighbors interactions in a 2-simplex or 3-simplex domain.