I understood what was happening, I just didn't understand the purpose of it. But now I notice he's using boost, so I think I get the point.
And now I think that you don't: Using boost has nothing to do with anything. My point is that perhaps your renormalization procedure is broken, since the straight-forward code I wrote doesn't exhibit the undesired behavior you described. Perhaps you should post your renormalization code, because it might explain why you are seeing what you are seeing.
It's just a basic normalize method, scaling the quaternion by the inverse of its length [1 / sqrt( Dot(q,q) )] or [ 1 / sqrt(x*x + y*y + z*z + w*w) ]. But I'm pretty sure it's actually the way I compute the length that is causing the rounding error.
Looking at boost's abs() function, which I'm having difficulty tracing through all of their define usage, but I believe they are dividing all of the quaternion's components by the highest absolute component value, then squaring, then summing, then multiplying the result length with the highest absolute component value. I guess it may be worth the extra cycles to get rid of the small error.