On Jun 24, 2009, at 1:49 AM, Christian Plesner Hansen wrote:
I don't know, the user doesn't say why this inaccuracy is a problem.
It sounds like he's just generally unhappy that arithmetic is
approximate. Decimal is approximate too.
That's true at very extreme margins only! Decimal does not fail to
round
power-of-five products so badly, and I think you know this.
I know, and just after what you quoted I said "unless we know we'll
stay in base 10". It's a fact that if you venture outside of base 10
you'll get more accurate results using k-bit binary than k-bit
decimal.
If a computation favors base 3 or base 7, you're right -- no one radix
fits all cases when precision is finite. But people have 10 fingers,
and they expect sums and differences to work the way they learned on
paper.
Your mode of argument makes it sound like each radix is equally likely
to be best, that base 10 is not privileged in everyday practice -- or
from your "k-bit binary" remark, that Shannon's ghost is whispering
"base e is best, approximate with base 2 or 3!" :-P
Most users do not know and do not care about information theory
optimality, they just want sums and differences to "work".
/be
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