  We present and discuss the characteristics and performances, both in term of
computational speed and precision, of a numerical code which numerically
integrates the equation of motions of N 'particles' interacting via Newtonian
gravitation and move in an external galactic smooth field. The force evaluation
on every particle is done by mean of direct summation of the contribution of
all the other system's particle, avoiding truncation error. The time
integration is done with second-order and sixth-order symplectic schemes. The
code, NBSymple, has been parallelized twice, by mean of the Computer Unified
Device Architecture to make the all-pair force evaluation as fast as possible
on high-performance Graphic Processing Units NVIDIA TESLA C 1060, while the
O(N) computations are distributed on various CPUs by mean of OpenMP Application
Program. The code works both in single precision floating point arithmetics or
in double precision. The use of single precision allows the use at best of the
GPU performances but, of course, limits the precision of simulation in some
critical situations. We find a good compromise in using a software
reconstruction of double precision for those variables that are most critical
for the overall precision of the code. The code is available on the web site
astrowww.phys.uniroma1.it/dolcetta/nbsymple.html
