Quadruple (or higher) precision is needed in many scientific applications.

Do you know of any specific applications? "many" seems like an extraordinary claim. I'm under the impression that quad precision is fringe. Double precision support on GPUs is fairly recent.

Sure. Just for a start, some of David Bailey's papers (http://www.davidhbailey.com/dhbpapers/), e.g. "High-Precision Arithmetic: Progress and Challenges" and "High-Precision Floating-Point Arithmetic in Scientific Computation" show some concrete examples. You will find many others by searching for papers containing the words "quad double arithmetic", "high precision arithmetic", "multiple precision arithmetic" or similar terms. Most applications are probably in physics, and of course in pure mathematics.