Gregory wrote:
> I see the inner loop of construction and lookup are free of
> non-constant divmod. This will result in implementations being
> needlessly slow

Ahh, sipa brought this up other day, but I thought he was referring to the
coding loop (which uses a power of 2 divisor/modulus), not the
siphash-then-reduce loop.

> I believe this can be fixed by using this approach
>
http://lemire.me/blog/2016/06/27/a-fast-alternative-to-the-modulo-reduction/
> which has the same non-uniformity as mod but needs only a multiply and
> shift.

Very cool, I wasn't aware of the existence of such a mapping.

Correct me if I'm wrong, but from my interpretation we can't use that
method as described as we need to output 64-bit integers rather than
32-bit integers. A range of 32-bits would be constrain the number of items
we could encode to be ~4096 to ensure that we don't overflow with fp
values such as 20 (which we currently use in our code).

If filter commitment are to be considered for a soft-fork in the future,
then we should definitely optimize the construction of the filters as much
as possible! I'll look into that paper you referenced to get a feel for
just how complex the optimization would be.

> Shouldn't all cases in your spec where you have N=transactions be
> n=indexed-outputs? Otherwise, I think your golomb parameter and false
> positive rate are wrong.

Yep! Nice catch. Our code is correct, but mistake in the spec was an
oversight on my part. I've pushed a commit[1] to the bip repo referenced
in the OP to fix this error.

I've also pushed another commit to explicitly take advantage of the fact
that P is a power-of-two within the coding loop [2].

-- Laolu

[1]:
https://github.com/Roasbeef/bips/commit/bc5c6d6797f3df1c4a44213963ba12e72122163d
[2]:
https://github.com/Roasbeef/bips/commit/578a4e3aa8ec04524c83bfc5d14be1b2660e7f7a


On Wed, Jun 7, 2017 at 2:41 PM Gregory Maxwell <greg@xiph.org> wrote:

> On Thu, Jun 1, 2017 at 7:01 PM, Olaoluwa Osuntokun via bitcoin-dev
> <bitcoin-dev@lists.linuxfoundation.org> wrote:
> > Hi y'all,
> >
> > Alex Akselrod and I would like to propose a new light client BIP for
> > consideration:
> >    *
> https://github.com/Roasbeef/bips/blob/master/gcs_light_client.mediawiki
>
> I see the inner loop of construction and lookup are free of
> non-constant divmod. This will result in implementations being
> needlessly slow (especially on arm, but even on modern x86_64 a
> division is a 90 cycle-ish affair.)
>
> I believe this can be fixed by using this approach
>
> http://lemire.me/blog/2016/06/27/a-fast-alternative-to-the-modulo-reduction/
>    which has the same non-uniformity as mod but needs only a multiply
> and shift.
>
> Otherwise fast implementations will have to implement the code to
> compute bit twiddling hack exact division code, which is kind of
> complicated. (e.g. via the technique in "{N}-bit Unsigned Division via
> {N}-bit Multiply-Add" by Arch D. Robison).
>
> Shouldn't all cases in your spec where you have N=transactions be
> n=indexed-outputs? Otherwise, I think your golomb parameter and false
> positive rate are wrong.
>