  We have developed a highly-tuned software library that accelerates the
calculation of quadrupole terms in the Barnes-Hut tree code by use of a SIMD
instruction set on the x86 architecture, Advanced Vector eXtensions 2 (AVX2).
Our code is implemented as an extension of Phantom-GRAPE software library
(Tanikawa et al. 2012, 2013) that significantly accelerates the calculation of
monopole terms. If the same accuracy is required, the calculation of quadrupole
terms can accelerate the evaluation of forces than that of only monopole terms
because we can approximate gravitational forces from closer particles by
quadrupole moments than by only monopole moments. Our implementation can
calculate gravitational forces about 1.1 times faster in any system than the
combination of the pseudoparticle multipole method and Phantom-GRAPE. Our
implementation allows simulating homogeneous systems up to 2.2 times faster
than that with only monopole terms, however, speed up for clustered systems is
not enough because the increase of approximated interactions is insufficient to
negate the increased calculation cost by computing quadrupole terms. We have
estimated that improvement in performance can be achieved by the use of a new
SIMD instruction set, AVX-512. Our code is expected to be able to accelerate
simulations of clustered systems up to 1.08 times faster on AVX-512 environment
than that with only monopole terms.
