11706 vs ([lno] Canonical iv creation)

[Richard Guenther]

Paolo Carlini wrote:
> Richard Guenther wrote:
> 
>> I'm curious to how the standard actually defines std::pow()s accuracy 
>> here though.  I know we're not optimizing ::pow(x, 4) to the above 
>> without -ffast-math because of accuracy concerns.  So how does 
>> std::pow() relate to ::pow in terms of accuracy guarrantees?
> 
> 
> Really interesting issue...
> 
> Anyway, from a practical point of view I'm not really worried, since:
> 
> 1- Glibc uses internally the very same algorithm, at least on x86 (just
>    checked).
> 
> 2- Which requires O(log n) multiplications and is discussed by Knuth in
>    Sec. 4.6.3 of the second volume. You can find it almost *everywhere*,
>    for instance also in SGI's power.

So there is no point in not optimizing ::pow(x, 4) without -ffast-math?

Richard.