|Jeroen Demeyer on Wed, 13 Nov 2013 01:06:51 +0100|
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|Re: Large errors for eint()|
I did some tests and it still looks like the absolute error oneint1(x, n) 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); gp> \p96 realprecision = 96 significant digits gp> Y=eint1(1.>>20, 10^5); gp> abs(X-Y)<<128 %7 = 208720.00000000000000 gp> \p134 realprecision = 134 significant digits gp> Z=eint1(1.>>20, 10^5); gp> abs(Y-Z)<<320 %18 = 208672.00000000000000Note 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.