Gamma Midpoint/Offset ?

Hi guys,

I'm trying to implement a Levels algorithm like Photoshop. I think I have it all figured out except for one thing.

If the black and white points are 0.0 and 1.0 the midpoint is 0.5 and the gamma at that point in 1.0. The problem I'm having is if the midpoint is at (say) 0.375, how do I make it so that midpoint has a gamma of 1.0 ?

I'm doing it like this:

v=pixelValue // (0...1)
if(v < a)
 v=a;
else if(v > b)
 v=b;
else
 v=gamma(v); // the midpoint between a and b has a gamma of 1.0

Thank you.