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Re: a question about formatOf operations
Nick Maclaren a écrit :
But even that doesn't extrapolate to all problems, such as global
optimisation and chaotic PDEs. I sincerely hope that nobody here
thinks that defining a bitwise predictable solution to a chaotic
system actually makes any mathematical sense.
No mathematical sense for sure, but it is very useful nevertheless. Here
is an example.
People at CERN wanted to simulate the Large Hadron Collider in a
Seti@Home way, on a large number of untrusted, heterogeneous systems.
As you don't trust the computers, you need to distribute the same
computation to several unrelated computers, and if all the results agree
you conclude that the computers were all faithful. How do you do this,
when the system is cahotic (as are particle trajectories) and the
computation not bit-exact? The best you can do is partition your set of
computers into subsets with identical OS and processor, and it adds a
lot of complexity to the management.
Another possibility is to do the equivalent of what your did: the
trajectory of each particle is cahotic, but their average (the beam)
should be similar, so one may try to compare results based on this
average. This means that you have to set an error treshold under which
simulations agree. This was not applicable for the LHC, because the goal
of the computation was, more or less, to compute the information that
allows to set such a treshold.
It was simpler to design LHC@home for bit-exact computations, actually
all they needed was a Fortran compiler that can be coerced to do the
same optimisations on Linux and Windows (they used Lahey), and a
correctly rounded libm (they used our CRLibm).
Florent