#4807: bug in exponential integral
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Reporter: wdj | Owner: burcin
Type: defect | Status: new
Priority: major | Milestone: sage-3.3
Component: calculus | Keywords:
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This was reported by M. Yurko in an email to sage-support:
here are some examples of what I did:
#First, an 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 it 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
William Stein added this:
A quick remark: The Pari Ei only works with *real* input, whereas the
scipy one works with complex input.
The Sage function will have to fixed in the meantime or
at least as a bare minimum have a big comment at the top explaining that
there is a bug.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4807>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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