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Comment by slededit | Hacker News Reader

I've always thought that floats should be accompanied with a precision value specifying the number of significant digits. Ideally updated by hardware in the same operation.

All floating point code has subtle bugs if you don't track error accumulation.

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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.

Does it solve the equality issue? An epsilon tracker would allow you to say it's equal within the margin of error for the computation.

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.

I haven't really seen the issue of equality dealt with explicitly, but it appears that you can extract the bounds of the interval implied by a given unum. Essentially, it seems like an alternative to interval arithmetic with potentially tighter bounds and faster computation.

Yes, I think these are fair statements.

John Gustafson's presentation also includes a few important points about interval arithmetic:

http://www.johngustafson.net/presentations/Right-SizingPreci...

Wouldn't that be closer to interval arithmetic?

It's in a real scientific programming language, viz. Fortran, as SELECTED_REAL_KIND().

That is the precision of the type, but it does not track accumulated error which quickly gets into the representable range of the type. You need to know both the type, the precision of the data stored in the type and track the operations on it.

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