Performance Evaluation of Mixed Precision Algorithms for Solving Sparse Linear Systems
2020
It is well established that mixed precision algorithms that factorize
a matrix at a precision lower than the working precision can reduce
the execution time of parallel solvers for dense linear systems. Much
less is known about the efficiency of mixed precision parallel
algorithms for sparse linear systems, and existing work focuses on
single core experiments. We evaluate the benefits of using single
precision arithmetic in solving a double precision sparse linear
systems using multiple cores, focusing on the key components of LU
factorization and matrix–vector products. We find that single
precision sparse LU factorization is prone to a severe loss of
performance due to the intrusion of subnormal numbers. We identify a
mechanism that allows cascading fill-ins to generate subnormal numbers
and show that automatically flushing subnormals to zero avoids the
performance penalties. Our results show that the anticipated speedup
of 2 over a double precision LU factorization is obtained only for the
very largest of our test problems. For iterative solvers, we find that
for the majority of the matrices computing or applying incomplete
factorization preconditioners in single precision does not present
sufficient performance benefits to justify the loss of accuracy
compared with the use of double precision.
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