On Thu, Apr 24, 2014 at 12:46 AM, Gershom Bazerman <gershomb@gmail.com> wrote:

Let me try to be a bit concrete here.

Are there _any_ implementations of Floating outside of base that we know of, which we are _concretely_ worried will not implement log1p and thus cause algos to lose precision? If anybody knows of these implementations, let them speak!

 

I would like to avoid shoving this up to RealFloat for the simple pragmatic reason that it takes us right back where we started in many ways, the naive version of the algorithm would have weaker constraints, and so the thing that shouldn't need to exist would have an artificial lease on life as a result.

 

Furthermore, if we do know of them, then can't we submit patch requests for them? Unless there are too many of course, but I know of only one type of "typical" implementation of Floating outside of base. That implementation is constructive, arbitrary-precision, reals, and in that case, the default implementation should be fine.

 

The major implementations beyond base are in linear, vector-space, ad, numbers' CReal, and debug-simplereflect. 

There may be a dozen other automatic differentiation implementations out there, e.g. fad, my old rad, Conal's, old versions of monoids, etc.

That said, on this John's point is true, it is an open universe, there can be a lot of them out there.

That _also_ said, if we went with something like the MINIMAL pragma with default approach that we were just discussing those 'private application instances' would be the things people build locally that *would* blast them with warnings.

So that might suggest the concrete implementation strategy:

Add the methods to Floating with defaults, but include them in MINIMAL as in my previous modified proposal, but also commit to going through hackage looking for existing instances and reach out to authors to patch / with patches.

That pass over hackage might spackle over John's objection to default + MINIMAL in that it doesn't catch _everything_ for folks who install via a package manager, as the stuff that gets installed by such means after all starts out in the world of hackage.

... and with that we could all move on to other things. ;)

-Edward

 

(Outside of that, I know of two other perhaps implementations outside of base, one by edwardk, and he as well as the other author are fine adding log1p).

Also, in general, I don't care what happens to Floating, because it is a silly class with a hodgepodge of methods anyway (plenty of which potentially apply to things that aren't 'floating point' in any meaningful sense), although RealFloat is even sillier. (By the way did you know that RealFloat has a defaulted "atan2" method? Whatever we do, it won't be worse than that).

Anyway, +1 for the original proposal, and also +1 for adding this to RealFloat instead if that's acceptable, because I'm sure everyone could agree that class couldn't possibly get much worse, and there's precedent there anyway.

Also, I should add, as a rule, I think it is near-impossible to write numerical code where you genuinely care both about performance and accuracy in such a way as to be actually generic over the concrete representations involved.

Cheers,
Gershom

On 4/23/14, 7:57 PM, John Lato wrote:

There's one part of this alternative proposal I don't understand:

On Mon, Apr 21, 2014 at 5:04 AM, Edward Kmett <ekmett@gmail.com> wrote:

* If you can compile sans warnings you have nothing to fear. If you do get warnings, you can know precisely what types will have degraded back to the old precision at compile time, not runtime.

I don't understand the mechanism by which this happens (maybe I'm misunderstanding the MINIMAL pragma?).  If a module has e.g.

> import DodgyFloat (DodgyFloat) -- defined in a 3rd-party package, doesn't implement log1p etc.

>

> x = log1p 1e-10 :: DodgyFloat

I don't understand why this would generate a warning (i.e. I don't believe it will generate a warning).  So the user is in the same situation as with the original proposal.

John L.

On Mon, Apr 21, 2014 at 5:24 AM, Aleksey Khudyakov <alexey.skladnoy@gmail.com> wrote:

On 21 April 2014 09:38, John Lato <jwlato@gmail.com> wrote:
> I was just wondering, why not simply numerically robust algorithms as
> defaults for these functions?  No crashes, no errors, no loss of precision,
> everything would just work.  They aren't particularly complicated, so the
> performance should even be reasonable.
>

I think it's best option. log1p and exp1m come with guarantees
about precision. log(1+p) default makes it impossible to depend in such
guarantees. They will silenly give wrong answer

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