Re: BLAS-3 in interval compuations
Jean-Luc Lamotte schrieb:
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 Vienna proposal has this conversion routines.
The controversial part is only whether the standard should require
an _arithmetic_ for _single_ midrad intervals.
So far, nobody has suggested to standardize the interval matrix
operations (where your arguments apply).
In any case, interval BLAS3 should not be standardized within 1788.
Arnold