[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

Re: better atan function?

bjackel@phys.ucalgary.ca wrote:
> 
> Hi Bob
> 
> Hmm.  A couple minutes playing with atan gives the following:
> 
> IDL> help,atan(1.0d-12,1.0d0)
> <Expression>    DOUBLE    =   1.0000000e-012
> 
> IDL> help,atan(1.0d-15,1.0d0)
> <Expression>    DOUBLE    =   1.0000000e-015
> 
> IDL> help,!dpi/2.0d0 - atan(1.0d0,1.0d-12)
> <Expression>    DOUBLE    =   9.9986686e-013
> 
> IDL> help,!dpi/2.0d0 - atan(1.0d0,1.0d-15)
> <Expression>    DOUBLE    =   8.8817842e-016
> 
> So the small angle stuff is essentially perfect.  The error
> at large angles is almost certainly due to subtracting two
> nearly equal quantities.  This of course doesn't rule out
> something funny for moderate angles, but it'd be surprising.

Some interesting observations on computing elementary functions are
available at
http://math.nist.gov/javanumerics/reports/jgfnwg-02.html#Appendix-3

Cheers,
Liam.
http://cimss.ssec.wisc.edu/~gumley