  We present a numerically feasible semiclassical (SC) method to evaluate
quantum fidelity decay (Loschmidt echo, FD) in a classically chaotic system. It
was thought that such evaluation would be intractable, but instead we show that
a uniform SC expression not only is tractable but it gives remarkably accurate
numerical results for the standard map in both the Fermi-golden-rule and
Lyapunov regimes. Because it allows Monte Carlo evaluation, the uniform
expression is accurate at times when there are 10^70 semiclassical
contributions. Remarkably, it also explicitly contains the ``building blocks''
of analytical theories of recent literature, and thus permits a direct test of
the approximations made by other authors in these regimes, rather than an a
posteriori comparison with numerical results. We explain in more detail the
extended validity of the classical perturbation approximation (CPA) and show
that within this approximation, the so-called ``diagonal approximation'' is
automatic and does not require ensemble averaging.
