Re: Large errors for eint()

[Jeroen Demeyer <jdemeyer@cage.ugent.be>]

I did some tests and it still looks like the absolute error on
eint1(x, n)[15] is unbounded as x goes to 0 and n to infinity. 
Interestingly, it is always the 15th component which has the worst 
absolute error.

gp> \p38
   realprecision = 38 significant digits
gp> X=eint1(1.>>20, 10^5)[15];
gp> \p96
   realprecision = 96 significant digits
gp> Y=eint1(1.>>20, 10^5)[15];
gp> abs(X-Y)<<128
%7 = 208720.00000000000000

gp> \p134
   realprecision = 134 significant digits
gp> Z=eint1(1.>>20, 10^5)[15];
gp> abs(Y-Z)<<320
%18 = 208672.00000000000000

Note also that the absolute error divided by 2^bitprecision is almost 
independent of the precision, which seems to indicate some algorithmic 
error rather than a problem with floating-point cancellation.