Low-precision hardware, in particular half-precision (16-bit) floating-point arithmetic, is now commercially available, for example, in the NVIDIA V100 GPU and the AMD Radeon Instinct MI25 GPU. It is anticipated that exascale machines will include a range of hardware precisions including IEEE double precision, single precision, half precision, and even quarter precision. Using lower precision can offer significant savings in communication cost-- in particular, it reduces the amount of bits we need to move over the network or through the memory hierarchy, and we can fit more numbers into fast memory-- with proportional savings in energy cost. The potential performance improvements that come from the use of low precision therefore make it a critical direction of exploration in the exascale setting. This project involves studying the use of mixed precision computation within linear algebra computations and solvers.
Seznam odborné literatury
Higham, Nicholas J. Accuracy and stability of numerical algorithms. Vol. 80. Siam, 2002.
Carson, Erin, and Nicholas J. Higham. "Accelerating the solution of linear systems by iterative refinement in three precisions." SIAM Journal on Scientific Computing 40.2 (2018): A817-A847.
Haidar, Azzam, et al. "Harnessing GPU tensor cores for fast FP16 arithmetic to speed up mixed-precision iterative refinement solvers." Proceedings of the International Conference for High Performance Computing, Networking, Storage, and Analysis. IEEE Press, 2018.
Předběžná náplň práce v anglickém jazyce
The thesis will revolve around mixed precision computations in both sparse and dense linear algebra, and may involve aspects of high performance implementation and numerical stability analysis.
- zadáno a potvrzeno stud. odd.