On Saturday, 8 October 2016 at 00:35:31 UTC, Nick B wrote:
On Sunday, 25 September 2016 at 02:22:01 UTC, Nick B wrote:
I suggest that now, programmers would/may have a choice: be
slow and correct, or fast and incorrect, and that would depend
if real accuracy is important or not, the types of problems
being work on, and cost of failure. (see examples in John
Powerpoint presentation).
But I will ask John G, on the types of users showing interest
in UNUMS.
Hi.
Below is a copy of John's reply, which is interesting and
insightful!
[starts]
There are some kinds of problems that can only be solved by
unums and not by floats. Initially, those are the main focus.
Examples include:
* Global optimization where proof is needed that all optima
have been found
* Root-finding methods for fully general functions, including
non-differentiable functions and other poorly-behaved functions
* N-body dynamics with rigorous bounds on the orbital
trajectories that grow only linearly in the number of time steps
* Methods that need ultra-fast but ultra-low-precision initial
solution with guaranteed mathematical correctness
* Solutions of systems of nonlinear equations that also reveal
whether the problem is stiff or unstable.
It is a misconception, more common than I would like, that the
purpose of unums is to substitute for floats in existing floats
and then show some kind of superiority. That can happen in
terms of getting better answers with fewer bits, and I gave
some examples in my book, but they won't be "faster," whatever
that means. Floats are a guess about the answer, so they
contain no rigorous mathematical bound on the answer; how do I
compare their speed at guessing, with the speed of a method
that is rigorous? Most people don't even think about the
information in an answer as the goal of a benchmark, and just
measure the time to finish an algorithm and print a result.
Put another way, if you don't care whether an answer is
mathematically correct, then I can compute very fast indeed.
Instantly, in fact.
[ends]
Insightful indeed. Of course, these types of problems may be
too specialised for the general D community. I really don't
know for sure.
I decided to pop this [John G's reply] up again, in case anyone
was interested in * rigorous mathematical bound [solutions] on
[an] answer * even if this is for a small D audience.
Nick
