New Approach Could Sink Floating Point Computation

[Paul Dale]

I used to have a copy of his book, The End of Error. It's a decent read and he is persuasive. There has been some disagreement from inside the numerical analysis community (there is a video of a debate between William Kahan and John Gustafson somewhere).

The premise of the number system is to dynamically vary the length of numbers as required and to represent the gaps between exact values using intervals (hence the book title: round off isn't possible in this system because every number is either represented exactly or is part of an interval). It is a neat idea, but it doesn't mean the end of numerical analysis or error.

The variable length is where the claimed benefits come from. So long as the variations can be dealt with efficiently, less bits are required. This saves memory and power. Faster might be a misnomer. The reality is that modern processors implement IEEE floating point in hardware and this system is done in software -- it will be slower and use more power but it could still require less memory. A properly optimised hardware implementation would make things interesting.


Pauli