Improving Supercomputing Accuracy by Sacrificing Precision(top500.org)
top500.org
Improving Supercomputing Accuracy by Sacrificing Precision
https://www.top500.org/news/improving-supercomputing-accuracy-by-sacrificing-precision/
4 comments
Sorry--forgot to specify the values for the polynomial: 77617 and 33096. In Maxima, the effects of precision can be simulated thus:
google will find you more info about Rump's polynomial..
for fpprec:10 step 5 thru 50 do print (rp(77617.0b0, 33096.0b0));google will find you more info about Rump's polynomial..
Numbers of that magnitude combined with sixth and eighth powers should get you thinking 'hey, something's fishy here'.
Also, here's a good reference: http://epubs.siam.org/doi/book/10.1137/1.9780898718027
And I'm too headachey to bother trying, but I wonder what happens if you ignore that x/2y part and put the rest of the thing into Horner's form.
Also, here's a good reference: http://epubs.siam.org/doi/book/10.1137/1.9780898718027
And I'm too headachey to bother trying, but I wonder what happens if you ignore that x/2y part and put the rest of the thing into Horner's form.
[deleted]
Accuracy estimation is a fundamental part of numerical analysis and has been since day one.
TLDR: When using an iterative solver, do the first few calculations in reduced precision, and only then switch to double -- It is more energy efficient.
I always thought it would be cool to have a top500 list that does not restrict the algorithm, just accuracy and precision of fft. It would be interesting to see how algorithms would get us from 10 petaflops to "1 exaflop equivalent" -- the flops equivalent would be time speedup to get the same answer in less time. As it is they have very strict algorithm requirements (which makes sense if you are regularizing on flops). Just curious, but of course execution time on the top supercomputers isn't cheap.
What about doing something like the inverse? Top500 for algorithms on a fixed hardware configuration. You have an input dataset and an answer (perhaps something with an analytic solution, for sake of comparison). That would let you compare the algorithm more directly.
The idea of changing the method as you advance in the problem is not a new one, here's a recent article in SIAM Review http://epubs.siam.org/doi/abs/10.1137/130936725
Googling yields a not pay walled one
Paper title is
Composing Scalable Nonlinear Algebraic Solvers
I have a simple example of that: a polynomial rp(x,y):=1335/4y^6+x^2(11x^2y^2-y^6+(-121)y^4-2)+11/2y^8+x/(2*y) that evaluates to about 1.1726 in both single and double precision, but whose real value is -0.827....
So, the bottom line is that I'd gladly trade off precision for better accuracy guarantees---but it turns out that's surprisingly hard in general case.