[Octave-bug-tracker] [bug #45339] sind, cosd don't do range reduction accurately

[Charles Karney]

URL:
  <http://savannah.gnu.org/bugs/?45339>

                 Summary: sind, cosd don't do range reduction accurately
                 Project: GNU Octave
            Submitted by: karney
            Submitted on: Wed 17 Jun 2015 10:13:08 AM GMT
                Category: Octave Function
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Inaccurate Result
                  Status: None
             Assigned to: None
         Originator Name: karney
        Originator Email: 
             Open/Closed: Open
         Discussion Lock: Any
                 Release: 3.8.2
        Operating System: GNU/Linux

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Details:

One of the reasons for working with degrees instead of radians
is that range reduction is exact.  However, the octave trig
functions in terms of degrees don't make use of this.  Thus
sind(1e9) + sind(80) returns 2e-10 instead of 0.

I attach replacements for these functions which remove this
deficiency and obey identities such as cosd(89) = sind(1).

Although the problems the atan2d are nearly as bad, I also
provide a replacement for this function which enforces the
quadrant symmetries.

The Matlab implementation of sind, cosd, atan2d behave
similarly to these attached versions.




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File Attachments:


-------------------------------------------------------
Date: Wed 17 Jun 2015 10:13:08 AM GMT  Name: sindx.m  Size: 319B   By: karney
Replacements for sind, cosd, and atan2d
<http://savannah.gnu.org/bugs/download.php?file_id=34242>
-------------------------------------------------------
Date: Wed 17 Jun 2015 10:13:08 AM GMT  Name: cosdx.m  Size: 323B   By: karney
Replacements for sind, cosd, and atan2d
<http://savannah.gnu.org/bugs/download.php?file_id=34243>
-------------------------------------------------------
Date: Wed 17 Jun 2015 10:13:08 AM GMT  Name: atan2dx.m  Size: 480B   By:
karney
Replacements for sind, cosd, and atan2d
<http://savannah.gnu.org/bugs/download.php?file_id=34244>

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