Maybe I don't fully understand the issues at play here but I remember reading about so-called 'unums'[0], an alternative binary number representation that seems quite amazing. I don't understand why it doesn't get more attention, apart from the fact it would need to be supported in CPU hardware to be of any real use.

    [0]: http://sites.ieee.org/scv-cs/files/2013/03/Right-SizingPrecision1.pdf