Re: [Maxima-discuss] significant difference?

[Dr. S. <drs...@t-...>]

> Maxima uses Carlson's Rf function to compute the elliptic_k value.
thanks Ray, for clarifying that

IIRC, I determined the 2ULPs error bound on a system with intermediate
extended double precision on the x87 stack...
 
because only K is needed, one could give the old Gaussian algo 
involving the https://en.wikipedia.org/wiki/Arithmetic–geometric_mean 
a try

long time ago, I found that (1-x)*(1+x) is more accurate than 1-x^2 in
case abs(x)>1/sqrt(2), but is outperformed by 2*(1–x)–(1–x)^2 in case 
x>1/2, because then, 1-x does not produce any roundoff error (see 
Lemma of Sterbenz, which according to Sylvie Boldo in fact had been 
coined by Kahan).

I guess I need to repeat all the tests on SSE...

All the best
Schorsch