[Octave-bug-tracker] [bug #47738] expint is inaccurate for imaginary inputs

[Colin Macdonald]

URL:
  <http://savannah.gnu.org/bugs/?47738>

                 Summary: expint is inaccurate for imaginary inputs
                 Project: GNU Octave
            Submitted by: cbm
            Submitted on: Tue 19 Apr 2016 09:18:35 PM GMT
                Category: Octave Function
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Inaccurate Result
                  Status: None
             Assigned to: None
         Originator Name: 
        Originator Email: 
             Open/Closed: Open
         Discussion Lock: Any
                 Release: dev
        Operating System: Any

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Details:

For some imaginary inputs, the error can be as large as 10^-6.


>> A = expint(10i)
A =   0.0454579311577793 +   0.0875455463635251i
>> S = double(expint(sym(10i)))
S =   0.0454564330044554 +   0.0875512674239774i
>> err = A - S
err = 1.49815332391168e-06 - 5.72106045235166e-06i


Matlab:

>> M = expint(10i)                                 
M =
         0.0454564330044556 +     0.087551267423977i
>> M - S
ans =
       1.80411241501588e-16 -  3.46944695195361e-16i


I'll attach a figure of the error along line in the complex plane.

Looking at the code shows it switches between two implementations at abs(x) ==
10.  There is a FIXME there, but I think the inaccuracy is more serious than
it suggests.





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