[Python-ideas] Add nullifier argument to functools.reduce?

[Warren Weckesser]

On Sun, Aug 24, 2014 at 9:09 AM, Steven D'Aprano <steve at pearwood.info>
wrote:

> On Sun, Aug 24, 2014 at 02:35:57PM +0200, Peter Otten wrote:
> > David Mertz wrote:
> >
> > >   def reduce_with_attractor(func, it, start=None, end_if=None):
> > >       it = iter(it)
> > >       start = start if start!=None else it.__next__()
> > >       return list(takewhile(lambda x: x!=end_if,
> > >                             accumulate(chain([start],it), func)))[-1]
> >
> > Wouldn't it be better to break this into a function that limits a
> sequence
> > and to combine that with the original reduce()?
>
> In general, if x is an attractor, then we want to stop and return x if
> either of these two scenarios occur:
>
> - we come across x in the input;
>
> - or the sequence of intermediate values reaches x.
>
> You can do the first by filtering the input stream, but not the second.
>
> Here's a concrete example, sticking to product() where 0 is an
> attractor:
>
> # best viewed with a fixed-width font
> product([1, 2, 3, 9, 0, 8, 7, 4])
> .....................^ stop here
>
>
> But multiplication can underflow to zero too, and once it does,
> we likewise want to stop:
>
> product([1e-70, 2e-71, 6e-69, 4e-68, 1e-48, 2e-71, 1e-69, 3e-70])
> .....................................^ stop here
>
>
> Notice that 1e-48 is not only non-zero, but it's considerably bigger
> than the other numbers in the sequence. (About 100000000000000000000
> times bigger, give or take a factor of 10.) Yet it's enough to cause the
> product to underflow to zero, after which the product will never
> shift away from zero. (Ignoring NANs and INFs.)
>
>

An example I gave earlier  is the reduction of a collection of sets using
set intersection.  It is possible that (set1 & set2) gives the empty set,
so the nullifier can occur during the reduction without being in the given
iterable.  E.g.:

    reduce(lambda x, y: x & y, [{1,2}, {3}, {4, 5}, {6}], nullifier={})

That should stop iterating after the first operation.




> I'm still not convinced this belongs in the standard library, but it's a
> nice functional, er, function to add to your private library or as a
> third-party module.
>
>
>
> --
> Steven
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