bugGNU Octave - Bugs: bug #44280, atan, atand have different phase...


bug #44280: atan, atand have different phase from other SW when outside principal branch.

Submitted by:  None
Submitted on:  Tue 17 Feb 2015 01:31:28 AM UTC  
Category:  Octave Function Severity:  3 - Normal
Priority:  5 - Normal Item Group:  Incorrect Result
Status:  Fixed Assigned to:  None
Originator Name:  jeff pantazes Originator Email:  -email is unavailable-
Open/Closed:  Closed Release:  3.8.1
Operating System:  Mac OS

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Tue 17 Feb 2015 04:35:03 PM UTC, comment #5: 

@Michael: You're right.  Even if other SW packages have chosen a particular phase for the return value, we need to follow Matlab's lead in this regard for compatibility.  Closing report.

Rik <rik5>
Project Administrator
Tue 17 Feb 2015 04:30:43 PM UTC, comment #4: 

in Matlab 2014a:

>> atand(5i)

ans =

 -90.0000 +11.6157i

>> atan(5i)

ans =

  -1.5708 + 0.2027i

>> version

ans = (R2014a)

Should we accept this and leave things as they are?

Michael Godfrey <godfrey>
Project Member
Tue 17 Feb 2015 04:12:42 PM UTC, comment #3: 

Thanks.  This has already been partially addressed in the development branch that will be released as Octave 4.0 within the next month or so.  The NEWS file reads

 ** The trigonometric functions asin and acos return different phase values
    from previous versions of Octave when the input is outside the principal
    branch ([-1, 1]).  If the real portion of the input is greater than 1 then
    the limit from below is taken.  If the real portion is less than 1 then the
    limit from above is taken.  This criteria is consistent with several other
    numerical analysis software packages.

However, I do note that atan (and by extension atand), do not produce the same phase.  Re-titling the bug report to reflect this remaining issue.

Rik <rik5>
Project Administrator
Tue 17 Feb 2015 04:14:51 AM UTC, comment #2: 

Oh, I notice you have version 3.8.1.  The complex conjugation for asin() may be this bug


that was fixed in October 2014.  So maybe this isn't as severe a problem as I thought.  So, that is atan() that has a problem (atand is derivative of atan).

Dan Sebald <sebald>
Tue 17 Feb 2015 03:31:14 AM UTC, comment #1: 

Thanks for reporting this.  I've confirmed one bug for sure.

Here's what I'm seeing on a linux system:

>> asind(3)

ans =   90.000 - 100.998i

>> atand(5i)

ans = -90.000 + 11.616i

>> atan(5i)

ans = -1.57080 + 0.20273i

>> asin(3)

ans =  1.5708 - 1.7627i

This looks to be an incorrect formula for arc tangent in liboctave/numberic/lo-mappers.c:

atan (const Complex& x)
  static Complex i (0, 1);

  return i * log ((i + x) / (i - x)) / 2.0;

I think it should be (i - x) / (i + x) in the argument of the complex logarithm.  Or i/2 * (ln(i-x) - ln(i+x)).  In the case of x=5i, something for which the argument of the logarithm is solely imaginary (i.e., -4i and 6i), the imaginary portion of the logarithm in both cases is -pi/2*i - -pi/2*i = -pi*i, multiplying by i/2 gives us pi/2, or 90 degrees.

So, yes, atand() seems like a bug.  But more than that we should have some good test cases to find these bugs, and that's a bit of a project.

But I don't know why your build of Octave is having problems with asin() as well.  Different library for the Apple products?  I don't know.  I will look into this more and try making some guesses.

Dan Sebald <sebald>
Tue 17 Feb 2015 01:31:28 AM UTC, original submission:  

GNU Octave, version 3.8.1
Octave was configured for "x86_64-apple-darwin14.1.0".

octave --eval "asind(3)" yields 90.000 + 100.998i
however wolfram alpha yields
89.999999999999...-100.9979734210524220... i
Please note the negative sign next to the imaginary number.
My personal calculations give 90 + -100.997973421052i
Again I am noting the negative sign not the rounding.

Found same for:
octave --eval "atand(5i)"
result: -90.000 + 11.616i
wolfram alpha:
89.99999999... + 11.61571971720673661409100... i
note the -90 instead of 90

octave: -1.57080 + 0.20273i
wolfram alpha: 1.5707963267... + 0.20273255... i
personal: 1.570796326+0.202732554i

octave: 1.5708 + 1.7627i
wolfram alpha: 1.570796326... -1.7627471740... i
personal: 1.570796326+-1.76274717i

Most likely I am in error, if so I apologize ahead of time.  Thanks for looking at this.



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    Follow 3 latest changes.

    Date Changed by Updated Field Previous Value => Replaced by
    2015-02-17 rik5 StatusNone => Fixed
        Open/ClosedOpen => Closed
    2015-02-17 rik5 Summaryasin, asind, atan, and atand may have incorrect values => atan, atand have different phase from other SW when outside principal branch.

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