It's not a continuous piecewise linear approximation of the logarithm, it's a discrete piecewise linear approximation of the logarithm. You are correct that the

It's not a continuous piecewise linear approximation of the logarithm, it's a discrete piecewise linear approximation of the logarithm. You are correct that the blue lines aren't continuous, but incorrect about their interpretation - there are 256 individual points evenly spaced along the that x axis that make up the blue graph, not just a handful at the intersections. (A full graph would have 2^32 options in a piecewise linear pattern, but that isn't what the OP has graphed.) Given that the article is talking about operations on 32 bit integers and IEEE-754 32-bit floats, I personally think it's fine to leave out "discrete" in the description.