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\section*{Comments on: Data Parallel Implementation of
Extensible Sparse Functional Arrays}

     The algorithms are quite clever, but it's unclear whether
this scheme is very practical.  It seems doubtful whether an
implementation on a general purpose massively parallel machine could
really achieve constant time access and updating---the broadcast
operations and reduction operations such as global bit-wise {\em or}
and {\em max} (which are de-emphasised but used in many of the
procedures) would dominate the parallel time on many architectures, and
introduce logarithmic terms in the time-complexity.  Probably
sequential algorithms based on trees can achieve logarithmic time (the
complexity of the best sequential algorithms isn't given, which is an
obvious omission).  It's claimed that special-purpose hardware might
overcome these problems, which is possible.  The analogy with RAM is
interesting.

     I couldn't see any comments on implementation of \verb$forward$
and \verb$backward$.

     It might be helpful to make clear early on what machine model
is envisaged---so we know from the start what primitives are allowed,
and what their cost is.

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