The exponential growth of floating point power in GPUs, combined with high
memory bandwidth, has given rise to an attractive platform upon which to
deploy HPC applications. We review the QUDA library which is a
domain-specific library designed to accelerate legacy lattice quantum
chromodynamics application through providing a rich library of the common
performance-critical algorithms, including highly optimized sparse linear
solvers. QUDA is a toolbox in which to research and develop algorithms for
the exascale future where flops are free and memory bandwidth determines
performance. We describe the techniques currently present in QUDA and also
consider future directions for development.