  Fast Multipole Methods (FMMs) based on the oscillatory Helmholtz kernel can
reduce the cost of solving N-body problems arising from Boundary Integral
Equations (BIEs) in acoustic or electromagnetics. However, their cost strongly
increases in the high-frequency regime. This paper introduces a new directional
FMM for oscillatory kernels (defmm - directional equispaced interpolation-based
fmm), whose precomputation and application are FFT-accelerated due to
polynomial interpolations on equispaced grids. We demonstrate the consistency
of our FFT approach, and show how symmetries can be exploited in the Fourier
domain. We also describe the algorithmic design of defmm, well-suited for the
BIE non-uniform particle distributions, and present performance optimizations
on one CPU core. Finally, we exhibit important performance gains on all test
cases for defmm over a state-of-the-art FMM library for oscillatory kernels.
