on floating-point numbers

[jak]

Il 03/09/2021 09:07, Julio Di Egidio ha scritto:
> On Friday, 3 September 2021 at 01:22:28 UTC+2, Chris Angelico wrote:
>> On Fri, Sep 3, 2021 at 8:15 AM Dennis Lee Bieber <wlf... at ix.netcom.com> wrote:
>>> On Fri, 3 Sep 2021 04:43:02 +1000, Chris Angelico <ros... 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.
> 
> The docs are quite misleading there, it is not accurate without further qualifications.
> 
> <https://docs.python.org/3.8/library/math.html#math.fsum>
> <https://code.activestate.com/recipes/393090/>
> 
> That said, fucking pathetic, when Dunning-Kruger is a compliment...
> 
> *Plonk*
> 
> Julio
> 

https://en.wikipedia.org/wiki/IEEE_754