hi simon, very interesting to know indeed! I'll keep that in mind. thanks!
On 17 July 2014 13:10, Simon Byrne <simonby...@gmail.com> wrote: > > On Wednesday, 16 July 2014 20:39:39 UTC+1, Florian Oswald wrote: >> >> myexp(parameter * mylog(x) ) >> >> and it does make a sizeable difference. I'll try your version right now. >> > > Keep in mind that this is going to be less accurate than using an x^y > function, as you can be approximately |y*log(x)| ulps out. I'm guessing if > you're this concerned with performance then you probably won't be too > concerned about losing a few significant digits, but it is worth keeping in > mind. > > If you look at the openlibm source, you can see that this is basically the > approach it uses, albeit using some strategic double-double arithmetic to > keep enough extra significant digits around. > > Interestingly, since |y*log(x)| can be at most 710 (otherwise the > resulting exp would overflow or underflow), if you could work in 80-bit > extended precision, the extra 11 bits in the significand should be > sufficient so that the final Float64 result should be accurate to within an > ulp. > > -Simon > > >
