On Friday, 18 September 2015 at 03:19:26 UTC, Nick B wrote:
On Thursday, 17 September 2015 at 23:53:30 UTC, Anthony Di
Franco wrote:
I read the whole book and did not regret it at all, but I was
already looking for good interval arithmetic implementations.
I found that the techniques are not too different (though
improved in important ways) from what is mainstream in
verified computing.
Hi,
I haven't finished the book but have read over half of it and
browsed the rest. I wanted to add that an implementation of unums
would have advantages beyond verifiable computing. Some examples
that spring to mind are:
Using low precision (8-bit) unums to determine if an answer
exists before using a higher precision representation to do the
calculation (example briefly discussed in the book is ray
tracing).
More generally, unums can self-tune their precision which may be
generally useful in getting high precision answers efficiently.
It is possible for the programmer to specify the level of
accuracy so that unums don't waste time calculating bits that
have no meaning.
Parallelisation - floating point ops are not associative but unum
ops are.
Tighter bounds on results than interval arithmetic or
significance arithmetic.
These are just a few areas where a software implementation could
be useful. If you've ever had any issues with floating point, I'd
recommend reading the book, not just because of the approach it
proposes to solve these but also because it's very clearly
written and quite entertaining (given the subject matter).
Richard
