Before revision:  With our algorithm, the Tracy-Widom distribution can be evaluated to full absolute precision everywhere rapidly , and, furthermore, its right tailcan be computed to full relative precision .
After revision:  With our algorithm, the Tracy-Widom distribution can be evaluated to full absolute precision . In addition, we characterize the eigenfunctions of the Airy integral operator, and describe their extremal properties in relation to an uncertainty principle involving the Airy transform. We observe that the Airy integral operator is fairly universal, and we describe a separate application to Airy beams in optics. Using the eigenfunctions, we compute a finite-energy Airy beam that is optimal, in the sense that the beam is both maximally concentrated, and maximally non-diffracting and self-accelerating .