This bit trick is no longer important to decode. I was trying to figure out how to convert a UInt64 of random bits into a normalised double in the range [0,1) in such a way that all 2^53 possible floating values could be produced. Some web sites suggested simply doing this:

I was suspicious that subtle rounding problems might produce a defective output range, but a quick experiment in LINQPad that fed limit values into the calculation demonstrated that a complete set of significand bit patterns was generated at the limits. This supplies good evidence that the above shift-and-multiply converts 53 of the 64 random bits into a complete possible double range.