Sure, here are some examples of what I did:
#First, and example of the bug
Ei(20)
Output: 25615646.4145 + 6.28318530718*I #it should instead be just
25615646.4145
Ei(19)
Output: 9950907.25105 #the error doesn't occur here
-exponential_integral_1(-20).n(digits=50)
Output: 25615652.664056588 #here the bug doesn't occur, although the
code for exponential_integral_1 loses a lot of accuracy by converting
the number returned from PARI into a float, so i has much less
accuracy
-pari(-20).eint1().n(digits = 50)
Output: 2.5615652664056588773746625520288944244384765625000e7 #here
the full accuracy from PARI is preserved
#the following shows the difference in the speed of the two methods
#the current implementation
%time
for i in srange (1,10^6):
num = Ei(10)
Output: CPU time: 51.64 s, Wall time: 51.81 s
#the time of PARI's implementation
%time
for i in srange (1,10^6):
num = pari(-i).eint1()
Output: CPU time: 20.12 s, Wall time: 20.32 s
#PARI's implementation seems to be more than twice as fast
On Dec 15, 8:00 pm, "David Joyner" <wdjoy...@gmail.com> wrote:
> Thank you for this bug report. I wonder if you would be kind enough to
> include some commented code in an email, so someone can fill out a trac
> report for the issue?
>
> On Mon, Dec 15, 2008 at 7:13 PM, M. Yurko <myu...@gmail.com> wrote:
>
> > I have noticed recently that when evaluating the EI function at any
> > number over 20, it adds 2pi i, which shouldn't be there. After looking
> > at the code it appears that it uses scipy, so the error is probably
> > there. However, when looking for alternatives, I found the
> > exponential_integral_1 from PARI function which doesn't seem to suffer
> > from the same issue as scipy. When I did a test using the identity Ei
> > (x) = -exponential_integral_1(-x), PARI's implementation was about
> > twice as fast as scipy and had a much greater precision.
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