A ScientificComputing.com article by Rob Farber explores the topic of numerical precision in the context of future exascale computing, asking the question “how do we know that anything we compute is correct?”  The discussion centers around processors such as GPUs which provide both single- and double-precision computation but at different throughput levels. “Taking a multi-precision approach can enhance the accuracy of a calculation and justify the use of mainly single-precision arithmetic (for performance) along with the occasional use of double-precision (64-bit) arithmetic for precision-sensitive operations,” writes Farber. (Rob Farber. “Numerical Precision: How Much is Enough?” ScientificComputing.com.  Accessed July 1, 2008.)

This survey paper by D. Göddeke and R. Strzodka compares native double precision solvers for linear systems of equations as they typically arise in finite element discretizations with emulated- and mixed-precision schemes. Such schemes are particularly suitable for coupled hardware configurations such as GPUs and FPGAs, which serve as co-processors to the general purpose CPU. The results demonstrate that

1. accuracy is preserved even for very ill-conditioned systems,
2. significant speedups can be achieved (time aspect, GPUs) and
3. area requirements are reduced (space aspect, FPGA).

(link/preprint)