atan2(0,0) is not undefined (NaN)

I'm using MATLAB R2020a Home Edition on a Windows® machine. I have a need to calculate atan2(0,0) which, if I am correct should result in NaN (undefined). The answer I get is zero. Is this not bug in the underline algorithm for computation of atan2()?

Thank you in advance.

Answer 1

[Star Strider]

That is defined in the IEEE Compliance section of the atan2 documentation.

The result also isd not completely standardised. See the section in the Wikipedia article on Atan2 on Realizations of the function in common computer languages.

[Daven Gooden]

Star Strider thank you for replying! I did not realize the C language implementation of atan2(0,0) == 0 is what MATLAB is using. This is not what I want, but is good to know. I can compensate for that.

[Star Strider]

As always, my pleasure!

MATLAB began as a FORTRAN implementation, later switching to C.

Answer 2

[James Tursa]

This is a documented convention.

https://ch.mathworks.com/help/matlab/ref/atan2.html

[Daven Gooden]

James thanks for your reply. I now see the "IEEE Compliance" section within the help documentation. That is good information to keep in mind!

Answer 3

[hosein Javan]

it is not a bug. although in analytic math it is undefined, the trigonometric functions are usually calculated by their taylor series expansion on numerical softwares. no doubt it results zero. however when you try very small values, it is still correct:

atan2(1e-301,1e-301)*180/pi

ans =

45

[Daven Gooden]

Thanks Hosein! I appreciate your willingness to help. Your input is very helpful.

[hosein Javan]

don't mention it.