William Kahan, who's the person mainly responsible for IEEE 754, has a critique of Gustafson's proposal: http://people.eecs.berkeley.edu/~wkahan/UnumSORN.pdf h

William Kahan, who's the person mainly responsible for IEEE 754, has a critique of Gustafson's proposal: http://people.eecs.berkeley.edu/~wkahan/UnumSORN.pdf http://people.eecs.berkeley.edu/~wkahan/UnumSORN.pdf IEEE 754 is not a trivial standard (it earned Kahan a Turing award). Error modes for IEEE 754 are precisely defined, even though it requires a lot of effort to understand what they mean. (For example, overflow triggers an exception, but gradual underflow is allowed.) Going beyond it requires some serious effort, and unums seem not to be the solution. A good book to understand the IEEE 754 standard is the book by Michael Overton. The quoted article is unfortunately an example of floating-point "scaremongering". Floating point arithmetic is not approximate, it is accurately defined with precise error modes. Base-10 arithmetic is not however, the model to understand it, but rather "units in last place".