| better atan function? [message #20238] |
Tue, 30 May 2000 00:00  |
R
Messages: 4
Registered: May 2000
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Junior Member |
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Greetings all,
I have found that the phase I get from the FFT has
a precision of only ~10e-8, and that the precision depends
on what value phase has.
I think I've traced this to the atan function, or perhaps the
division that takes place in the atan function.
Does anyone have a better atan function (more precise)?
Or is this merely the way it is when one is bumping up against
precision errors?
By comparison, my "simulation" does get the amplitudes
of the spectral components to a precision of ~10e-14 or so.
(as expected for double precision variables, and no noise)
cheers,
bob
stockwell (at) co-ra (dot) com
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| Re: better atan function? [message #20319 is a reply to message #20238] |
Thu, 01 June 2000 00:00  |
Liam E. Gumley
Messages: 378
Registered: January 2000
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Senior Member |
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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#App endix-3
Cheers,
Liam.
http://cimss.ssec.wisc.edu/~gumley
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