The other thing my algorithim does is dithering. Dithering adds noise to the floating point result before converting so that the resulting image averages more accurately to the actual brightness.

Here is a straight-forward result of converting a linear ramp to the nearest sRGB byte value. In these examples I have exaggerated the error by only using 32 levels instead of 256:

And here is the output of my algorithm (again if it is used to produce only 32 levels instead of 256). It is a lot smoother, and in the center you can see the dithering pattern:

Dithering is done by error diffusion: the error in luminosity of the output sRGB byte is added to the next pixel, so they all average out to the correct luminosity. The diffusion is done in the sRGB space, even though this is less accurate than in the linear space. The reason I do it in the sRGB space is partly that a much more efficient algorithim can be used and also that the linear one can introduce large enough changes that some byte values are skipped completely, resulting in less smooth patterns. Also at the scale of dithering (3 adjacent byte values) the sRGB plot is quite close to a straight line.