This sounds like unums, a proposed alternative to IEEE floats, where roughly speaking the significand can have variable size thus only boasting as much precision as the accuracy warrants.
If so that makes them much more interesting to me. Floating point bugs manifest themselves at non linear parts such as equality and comparison operators.
John Gustafson's presentation also includes a few important points about interval arithmetic:
http://www.johngustafson.net/presentations/Right-SizingPreci...