[Python-Dev] Return type of round, floor, and ceil in 2.6

[Tim Peters]

[skip at pobox.com]
> Thanks for the pointer.  Given that it's [round-to-even[ been an ASTM
> standard since 1940 and apparently in fairly common use since the
> early 1900s, I wonder why it's not been more widely used in the past
> in programming languages.

Because "add a half and chop" was also in wide use for even longer, is
also (Wikipedia notwithstanding) part of many standards (for example,
the US IRS requires it if you do your taxes under the "round to whole
dollars" option), and-- probably the real driver --is a little cheaper
to implement for "normal sized" floats.  Curiously, round-to-nearest
can be unboundedly more expensive to implement in some obscure
contexts when floats can have very large exponents (as they can in
Python's "decimal" module -- this is why the proposed decimal standard
allows operations like "remainder-near" to fail if applied to inputs
that are "too far apart":

    http://www2.hursley.ibm.com/decimal/daops.html#footnote.8

The "secret reason" is that it can be unboundedly more expensive to
determine the last bit of the quotient (to see whether it's even or
odd) than to determine an exact remainder).