[petsc-users] Lapack with Quadruple Precision in PETSc and SLEPc

[Tobias Jawecki]

Dear all,

I am interested in computations with higher precision. The application 
is mainly error analysis of high order Magnus integrators. In some cases 
the asymptotic behavior of the error can only be observed when the error 
is already on double precision and round-off errors of the subroutines 
can matter. Computation with higher precision then helps to compute a 
reference solution.

Using PETSc/SLEPc with the float128 setting works for me, but I do have 
some questions on how it works with Lapack/Blas.
Does PETSc use the standard Lapack package with double precision changed 
to quadruple precision?
I did not find a lot about using the standard Lapack with quadruple 
precision online, I just saw that all the routines in Lapack expect 
double precision input (according to netlib.org).

For example the Lapack routine dstevr for the eigenvalue computation of 
small problems which appears in the Lanczos code of SLEPc.

I assume some Lapack methods use parameters which are adjusted on double 
precision?

To give an example what kind of parameters would need to be considered:
Using the Matrix Function structure of SLEPc to compute the Matrix 
Exponential Function with Krylov methods seems to use a Padé 
approximation for the small problem. The used Padé approximation is of 
order 6 with scaling and squaring s.t. |H 2^(-s)|<0.5. This choice of 
parameter leads to an error smaller than 1e-16 (N. Higham book on Matrix 
Functions) for approximating the Matrix Exponential of the small 
problem. The solution is then correct only up to double precision even 
if higher precision is used for the computations.

My question is how PETSc and SLEPc handle the Lapack methods which are 
needed on quadruple precision. My main concern is that some Lapack 
methods use parameters which are chosen so that the results are correct 
up to double precision.

Thanks for your efforts and greetings,
Tobias Jawecki