Adaptive precision solvers for sparse linear systems

We formulate an implementation of a Jacobi iterative solver for sparse linear systems that iterates the distinct components of the solution with different precision in terms of mantissa length. Starting with very low accuracy, and using an inexpensive test, our technique extends the mantissa length for those component updates when and where this is required. Numerical experiments reveal that, for a solver that pursues IEEE double precision accuracy in the solution (i.e., mantissa of 52 binary digits), the precision required to reach convergence for the distinct components can differ significantly during the iteration so that, during most of this process, only a few components may require operating with the full length of the mantissa. Thus, with operations involving a longer mantissa yielding a higher power usage, energy savings can potentially be obtained by using a truncated format. Finally, we introduce a novel metric which quantifies the average mantissa length during the iteration, and exposes the resource savings of the Jacobi solver with adaptive mantissa.