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Dear
colleagues,
I
completely agree with the remarks of Siegfried Rump. Due to the memory access,
it is not possible to develop efficient functions for BLAS 1 and BLAS 2. The
ratio between the data number and the operation number is too weak. So, the
peak performance of processors can not be reached with these functions.
Concerning
BLAS 3, the matrix product X*Y = sum_j X(:,j)*Y(j,:) algorithm is very bad with
an efficiency point of view. New algorithms are based on block operations which
reduce the memory accesses.
For 8-9
years, there has been a convergence between the multimedia and the scientific
computing. The new processors architecture will embed SIMD operators for the
vectorisation of computations. If you want to reach a high level of performance,
you need to avoid comparison. With this point of view, only the mid-rad form of
intervals allows to obtain a high level of performance. If we want to make more popular the
interval arithmetic, we have to propose an interval form allowing to reach a
level of performance in computing time.
If the
standard proposes only the infsup form, developers will have to perform 2
conversions to implement efficient functions on interval: infsup -> midrad ;
function midrad-> infsup. I think that a standard without a
mid-rad form would be a big error.
The
standard must take care to this point.
JL Le 13 févr. 09 à 01:22, Siegfried M. Rump a écrit :
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