[firedrake] Counting FLOPS for assembling residual and Jacobian

[Lawrence Mitchell]

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On 04/08/15 22:57, Justin Chang wrote:
> Hi all,
> 
> Is it possible to include manual/PETSc counts within the assembly
> of the FormResidual and FormJacobian routines? Because I think it
> would be nice to look at the performance of how firedrake is
> assembling these finite element discretization instead of always
> relying on hardware counters.

Hi Justin,

this is a good idea.  The question is how to provide the information
to PETSc.  We know how many times we execute an element-wise Kernel
(because we know how big the mesh is).  So calculating the number of
flops comes down to estimating the number of flops for a kernel.

I have added some code to do this in the log-flops branches of COFFEE
and PyOP2.  It seems to report reasonably sensible numbers (I haven't
compared with hardware counters).  Hopefully these will merge soon.

I use the same flop-counting approach as petsc, i.e. "effective double
precision flops", where each multiplication, division, addition or
subtraction counts as a single flop.  The approach is not perfect,
because I do not do this manually, so I'm currently assuming that any
function call I see in the code contributes zero flops.  This means
that I'm underestimating a little, since the (affine) Jacobian
computations are not counted.  However, it gives you a reasonable
estimate, and is better than laboriously counting by hand.

If you really want to count the flops by hand, we can have a look at
an example kernel.

Cheers,

Lawrence

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