  This note shows how to compute, to high relative accuracy under mild
assumptions, complex Jacobi rotations for diagonalization of Hermitian matrices
of order two, using the correctly rounded functions $\mathtt{cr\_hypot}$ and
$\mathtt{cr\_rsqrt}$, proposed for standardization in the C programming
language as recommended by the IEEE-754 floating-point standard. The rounding
to nearest (ties to even) and the non-stop arithmetic are assumed. The
numerical examples compare the observed with theoretical bounds on the relative
errors in the rotations' elements, and show that the maximal observed departure
of the rotations' determinants from unity is smaller than that of the
transformations computed by LAPACK.
