  We implement the numerical inverse scattering transform (NIST) for the
sine-Gordon equation in laboratory coordinates on the real line using the
method developed by Trogdon, Olver and Deconinck. The NIST allows one to
compute the solution at any x and t without having spatial discretization or
time-stepping. The numerical implementation is fully spectrally accurate. With
the help of the method of nonlinear steepest descent, the NIST is demonstrated
to be uniformly accurate.
