On Sat, 10 Nov 2007 ajb@spamcop.net wrote:
Quoting jerzy.karczmarczuk@info.unicaen.fr:
Then, a *rational* approximation gives you the same precision with less coeffs. Nowadays the division is not sooo much more expensive than the multiplication, so the efficiency doesn't suffer much.
It might not cost much in the way of time, but it might complicate the implementation a lot. Using polynomials only probably uses a smaller number of transistors, disspiate less power and for all I know might be easier to parallelise than the alternatives.
I guess that the general answer to the question for the best algorithm is: "It depends ..." If your architecture (on hardware or machine code level) has no or slow multiplication, you will use an algorithm that avoids multiplications, same for division and so on.