Compute Shaders - Parallel reduction for luminance measurement

So, how do we actually use the HDR render target mentioned in the previous post? What can we actually DO with color values that are greater than 1.0, since the screen will ultimately display them as 1.0? And how do we use a compute shader to make our life easier?

HDR Lighting - Intro to HDR, and HDR render target

HDR lighting is a very very big subject, but in a graphics or gaming context it basically means using some kind of average luminance measurements or other heuristic to tone-map our image differently to the "classic" effect. The reason to do that is that the "classic", LDR format actually proves too restrictive to provide us with a very realistic or artistically beautiful image on a scene that is designed to be real-time created.