What does the constant 0.0039215689 represent?

Solution 1:

0.0039215689 is approximately equal to 1/255.

Seeing that this is OpenGL, performance is probably important. So it's probably safe to guess that this was done for performance reasons.

Multiplying by the reciprocal is faster than repeatedly dividing by 255.

Side Note:

If you're wondering why such a micro-optimization isn't left to the compiler, it's because it is an unsafe floating-point optimization. In other words:

x / 255  !=  x * (1. / 255)

due to floating-point round-off errors.

So while modern compilers may be smart enough to do this optimization, they are not allowed to do it unless you explicitly tell them to via a compiler flag.

Related: Why doesn't GCC optimize a*a*a*a*a*a to (a*a*a)*(a*a*a)?

Solution 2:

This multiplication by 0.0039215689f converts an integer valued color intensity in the range 0 to 255 to a real valued color intensity in the range 0 to 1.

As Ilmari Karonen points out, even if this is an optimisation it's a rather badly expressed one. It would be so much clearer to multiply by (1.0f/255).