How to check a color is out of cmyk gamut (range)?

Question

There is a color in RGB model, such as rgb(255,0,0) or #FF0000, I know that the RGB gamut is bigger than cmyk gamut, I also know that cmyk is related to printing devices and ICC files. Is there any way or algorithm figure out is out of the CMYK gamut(space/range) ,just like the "Gamut warning" of Adobe Photoshop ?

I've got a sample(not efficient) way: convert rgb to cmyk, then convert cmyk back to rgb, calculate the distance between 2 rgb colors. I think that there must be some better way, like： if (R > 250 && G>250 && B>250) then (out of cmyk color space)=true.

Any help? Thanks a lot