Abstract

A different PEP suggests adding a builtin rational type to Python. This PEP suggests changing the ddd.ddd float literal to a rational in Python, and modifying non-integer division to return it.

BDFL Pronouncement

This PEP is rejected. The needs outlined in the rationale section have been addressed to some extent by the acceptance of PEP 327 for decimal arithmetic. Guido also noted, “Rational arithmetic was the default ‘exact’ arithmetic in ABC and it did not work out as expected”. See the python-dev discussion on 17 June 2005 [1].

Rationale

Rational numbers are useful for exact and unsurprising arithmetic. They give the correct results people have been taught in various math classes. Making the “obvious” non-integer type one with more predictable semantics will surprise new programmers less than using floating point numbers. As quite a few posts on c.l.py and on tutor@python.org have shown, people often get bit by strange semantics of floating point numbers: for example, round(0.98, 2) still gives 0.97999999999999998.

Proposal

Literals conforming to the regular expression '\d*.\d*' will be rational numbers.

Backwards Compatibility

The only backwards compatible issue is the type of literals mentioned above. The following migration is suggested:

1. The next Python after approval will allow from __future__ import rational_literals to cause all such literals to be treated as rational numbers.
2. Python 3.0 will have a warning, turned on by default, about such literals in the absence of a __future__ statement. The warning message will contain information about the __future__ statement, and indicate that to get floating point literals, they should be suffixed with “e0”.
3. Python 3.1 will have the warning turned off by default. This warning will stay in place for 24 months, at which time the literals will be rationals and the warning will be removed.

Common Objections

Rationals are slow and memory intensive! (Relax, I’m not taking floats away, I’m just adding two more characters. 1e0 will still be a float)

Rationals must present themselves as a decimal float or they will be horrible for users expecting decimals (i.e. str(.5) should return '.5' and not '1/2'). This means that many rationals must be truncated at some point, which gives us a new loss of precision.

References

Copyright

This document has been placed in the public domain.