[racket] Nice article on scientific computing in Racket

Thanks!

The main challenge in a static analysis as you describe is that the 
badlands aren't compositional. The `fllog` function reduces error on 
most of its domain, for example. Other places this crops up is 
approximating special functions using polynomials: if you use Horner's 
rule, it *tends to* result in something with much less error than you 
might expect. I also ran into noncompositionality the other day, when I 
told someone that exponentiated log probabilities can't be trusted when 
they're close to zero... and then ran some simulations that suggested 
the central limit theorem is nicely at play and averages out worst-case 
error most of the time.

Oh, yeah, that was you that I accidentally lied to. :D

That being said, I've played around a bit with making languages that 
reduce floating-point error automatically, and the most successful so 
far just avoids the badlands at every intermediate computation. It does 
a runtime search for formulations that don't increase error too much, by 
backtracking when it wanders into the badlands with inexact arguments. 
The produced code is in continuation-passing style, and when it's fully 
inlined, it looks a lot like math library functions I've written:

   (cond [input-in-subdomain-1?  formulation-1]
         [input-in-subdomain-2?  formulation-2]
         ...)

It probably wouldn't scale well past library functions, but I could 
imagine using it as part of a larger system that uses differentiation 
(automatic, empirical, or user-supplied) to prune the search and deal 
better with noncompositionality.

Neil

On 10/28/2014 01:21 PM, Laurent wrote:
> This is a very nice article indeed. A lot of useful information.
>
> Just a not-at-all-thought-through idea: Since we can know the badlands
> of the primitives, couldn't we do something similar to an annotation
> system that would tell you where the badlands of a function that
> composes such primitives are?
>
> For example, to each primitive is associated a set of critical points or
> intervals possibly with typical error bounds, so as to know interesting
> intervals where to do random testing, and possibly compute error bounds
> (sometimes inf.0).
>
> Probably not that simple I guess.
>
> Laurent
>
> On Mon, Oct 27, 2014 at 1:14 PM, Neil Toronto <neil.toronto at gmail.com
> <mailto:neil.toronto at gmail.com>> wrote:
>
>     This is the article I mentioned in my RacketCon talk this year,
>     which is an expansion of my RacketCon talk from last year.
>     Self-serving Hacker News link:
>
>     https://news.ycombinator.com/__item?id=8514965
>     <https://news.ycombinator.com/item?id=8514965>
>
>     (Every week on Hacker News discussions, I see some of the same
>     misinformed arguments about floating point. This article addresses
>     most of them, so please go upvote it for the sake of informed
>     discussion. We do not want people being wrong on the Internet!)
>
>     A big thanks to Konrad, his co-editor Matthew Turk, and the CiSE
>     editing staff, who worked very hard with us on the article. Also,
>     thanks to Vincent Lefèvre (http://www.vinc17.org), Matthias
>     Felleisen, and Robby Findler, who reviewed it.
>
>     Neil
>
>
>     On 10/27/2014 06:05 AM, Konrad Hinsen wrote:
>
>         The current issue of "Computing in Science and Engineering" has
>         a nice
>         article by Neil Toronto and Jay McCarthy on "Practically Accurate
>         Floating-Point Math" in Racket. It is currently freely available
>         via IEEE's Computing Now platform:
>
>         http://www.computer.org/__portal/web/computingnow/__content?g=53319&type=article&__urlTitle=practically-accurate-__floating-point-math
>         <http://www.computer.org/portal/web/computingnow/content?g=53319&type=article&urlTitle=practically-accurate-floating-point-math>
>
>         Free access is typically limited in time, so grab your copy now!
>
>         Konrad
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