When scanconverting polygon there must be computed gradients du/dx and dv/dx which represent steps taken in uv-texture space when moving along x-axel in screen space. For polygon segments which have constant z-value, these gradients are constant. When texture mapping polygons which are assumed to have constant z over whole polygon we call this affine mapping. When polygon has non-constant z over the polygon and it has been taken account when texture mapping it, we call this perspective correct texture mapping.
To explain this formula: (dux^2+dvx^2)^(1/2) is euclidean length of the step taken on a texture, log2(...) is used to compute how many times the step can be divided in half so that length of the step is greater or equal to 1, and À...- is just round down operation.
Anyway, we still have that log2 spooking around which isn't fast to compute either. Now because we have this nice IEEE floating point format which happens to store numbers in logarithmical form, we can use it for fast log-computation and rounding. We just need to compute dux^2+dvx^2 as float and handle the value like an integer. Because the integer value needs to get shifted right (get rid of the 23-bit mantissa in 32-bit float), you can include dividing by 2 there which like comes for free. Note that you need to subtract 127 from the exponent to get the real value.