[Python-Dev] Expert floats

[Tim Peters]

[Andrew Koenig]
> ...
> For example, be it, binary or decimal, floating-point addition is
> still not associative, so even such a simple computation as a+b+c
> requires careful thought if you wish the maximum possible precision.

Not really for most everyday applications of decimal arithmetic.  People
work with decimal quantities in real life, and addition of fp decimals is
exact (hence also associative) provided the total precision isn't exceeded.
Since Decimal allows setting precision to whatever the user wants, it's very
easy to pick a precision obviously so large that even adding a billion
(e.g.) dollars-and-cents inputs yields the exact result, and regardless of
addition order.  For the truly paranoid, Decimal's "inexact flag" can be
inspected at the end to see whether the exactness assumption was violated,
and the absurdly paranoid can even ask that an exception get raised whenever
an inexact result would have been produced.

Binary fp loses in these common cases *just because* the true inputs can't
be represented, and the number printed at the end isn't even the true result
of approximately adding the approximated inputs.  Decimal easily avoids all
of that.

> Why are you not arguing against decimal floating-point if your goal
> is to expose users to the problems of floating-point as early as
> possible?

The overwhelmingly most common newbie binary fp traps today are failures to
realize that the numbers they type aren't the numbers they get, and that the
numbers they see aren't the results they got.  Adding 0.1 to itself 10 times
and not getting 1.0 exactly is universally considered to be "a bug" by
newbies (but it is exactly 1.0 in decimal).  OTOH, if they add 1./3. to
itself 3 times under decimal and don't get exactly 1.0, they won't be
surprised at all.  It's the same principle at work in both cases, but
they're already trained to expect 0.9...9 from the latter.

The primary newbie difficulty with binary fp is that the simplest use case
(just typing in an ordinary number) is already laced with surprises -- it
already violates WYSIWYG, and insults a lifetime of "intuition" gained from
by-hand and calculator math (of course it's not a coincidence that hand
calculators use decimal arithmetic internally -- they need to be
user-friendly).

You have to do things fancier than *just* typing in the prices of grocery
items to get in trouble with Decimal.