  Gyrokinetic modeling is appropriate for describing Tokamak plasma turbulence,
and the gyroaverage operator is a cornerstone of this approach. In a
gyrokinetic code, the gyroaveraging scheme needs to be accurate enough to avoid
spoiling the data but also requires a low computation cost because it is
applied often on the main unknown, the 5D guiding-center distribution function,
and on the 3D electric potentials. In the present paper, we improve a
gyroaverage scheme based on Hermite interpolation used in the Gysela code. This
initial implementation represents a too large fraction of the total execution
time. The gyroaverage operator has been reformulated and is now expressed as a
matrix-vector product and a cache-friendly algorithm has been setup. Different
techniques have been investigated to quicken the computations by more than a
factor two. Description of the algorithms is given, together with an analysis
of the achieved performance.
