Shachar Shemesh <shachar@shemesh.biz> writes:
> Before you explode at me (again :), I'm not arguing that you can do
> binary based calculations of decimal numbers without having rounding
> errors that come to bite you. I know you can't. What I'm saying is that
> we have two cases to consider. In one of them the above is irrelevant,
> and in the other I'm not so sure it's true.
You're setting up a straw-man argument, though. The real-world problem
cases here are not decimal, they are non-IEEE binary floating
arithmetic. The typical difference from IEEE is slightly different
tradeoffs in number of mantissa bits vs number of exponent bits within a
32- or 64-bit value. I seem to recall also that there are machines that
treat the exponent as power-of-16 not power-of-2. So depending on which
way the tradeoffs went, the other format will have either more precision
or more range than IEEE.
regards, tom lane