What complexity have a log(sum) shape?

[Timon Gehr via Digitalmars-d]

On 12/08/2015 04:25 PM, Andrei Alexandrescu wrote:
> I'm working on the complexity algebra and of course trying to simplify
> my life :o). One good simplification would be to get rid of
> log(polynomial_sum) terms such as:
>
> log(n + m)
> log(n^^3 + n1^^2 + n2)
>
> etc.
>
> Do any of these occur in some important algorithms? I couldn't think of
> any nor find any on the various complexity cheat sheets around.
>
>
> Thanks,
>
> Andrei

You don't need to support those terms in the internal representation, 
because they don't add anything to the expressiveness of the notation:

O(log(n+m)) = O(log(n)+log(m)).

O(log(n^^3+n1^^2+n2)) = O(log(n)+log(n1)+log(n2)).

(I have already noted this in the other thread, in case you have missed it.)