on floating-point numbers

[Chris Angelico]

On Fri, Sep 3, 2021 at 8:15 AM Dennis Lee Bieber <wlfraed at ix.netcom.com> wrote:
>
> On Fri, 3 Sep 2021 04:43:02 +1000, Chris Angelico <rosuav at gmail.com>
> declaimed the following:
>
> >
> >The naive summation algorithm used by sum() is compatible with a
> >variety of different data types - even lists, although it's documented
> >as being intended for numbers - but if you know for sure that you're
> >working with floats, there's a more accurate algorithm available to
> >you.
> >
> >>>> math.fsum([7.23, 8.41, 6.15, 2.31, 7.73, 7.77])
> >39.6
> >>>> math.fsum([8.41, 6.15, 2.31, 7.73, 7.77, 7.23])
> >39.6
> >
> >It seeks to minimize loss to repeated rounding and is, I believe,
> >independent of data order.
> >
>
>         Most likely it sorts the data so the smallest values get summed first,
> and works its way up to the larger values. That way it minimizes the losses
> that occur when denormalizing a value (to set the exponent equal to that of
> the next larger value).
>

I'm not sure, but that sounds familiar. It doesn't really matter
though - the docs just say that it is an "accurate floating point
sum", so the precise algorithm is an implementation detail.

ChrisA