Python Cookbook 2Nd Edition Jun 1002005 [Electronic resources] نسخه متنی

Recipe 3.12. Doing Decimal Arithmetic

Credit: Anna Martelli Ravenscroft

Problem

You
want to perform some simple arithmetic computations in Python 2.4,
but you want decimal results, not the Python
default of float.

Solution

To get the normal, expected results from plain, simple computations,
use the decimal module introduced in Python
2.4:

>>> import decimal
>>> d1 = decimal.Decimal('0.3')   # assign a decimal-number object
>>> d1/3                          # try some division
Decimal("0.1")
>>> (d1/3)*3                      # can we get back where we started?
Decimal("0.3")

Discussion

Newcomers to Python (particularly ones without experience with binary
float calculations in other programming languages) are often
surprised by the results of seemingly simple calculations. For
example:

>>> f1 = .3                     # assign a float
>>> f1/3                        # try some division
0.099999999999999992
>>> (f1/3)*3                    # can we get back where we started?
0.29999999999999999

Binary floating-point arithmetic is the default in Python for very
good reasons. You can read all about them in the Python FAQ
(Frequently Asked Questions) document at http://www.python.org/doc/faq/generall#why-are-floating-point-calculations-so-inaccurate,
and even in the appendix to the Python
Tutorial at http://docs.python.org/tut/node15l.

Many people, however, were unsatisfied with binary floats being the
only optionthey wanted to be able to
specify the precision, or wanted to use decimal arithmetic for
monetary calculations with predictable results. Some of us just
wanted the predictable results. (A True Numerical Analyst
does, of course, find all results of binary
floating-point computations to be perfectly predictable; if any of
you three are reading this chapter, you can skip to the next recipe,
thanks.)

The new decimal type affords a great deal of
control over the context for your
calculations, allowing you, for example, to set the precision and
rounding method to use for the results. However, when all you want is
to run simple arithmetical operations that return predictable
results, decimal's default
context works just fine.

Just keep in mind a few points: you may pass a string, integer,
tuple, or other decimal object to create a new
decimal object, but if you have a float
n that you want to make into a
decimal, pass str(n),
not bare n. Also,
decimal objects can interact (i.e., be subject to
arithmetical operations) with integers, longs, and other
decimal objects, but not with
floats. These restrictions are anything but
arbitrary. Decimal numbers have been added to Python exactly to
provide the precision and predictability that
float lacks: if it was allowed to build a decimal
number from a float, or by operating with one, the
whole purpose would be defeated. decimal objects,
on the other hand, can be coerced into other numeric types such as
float, long, and
int, just as you would expect.

Keep in mind that decimal is still floating point,
not fixed point. If you want fixed point, take a
look at Tim Peter's FixedPoint at
http://fixedpoint.sourceforge.net/. Also, no
money data type is yet available in Python,
although you can look at Recipe 3.13 to learn how to
roll-your-own money formatting on top of decimal.
Last but not least, it is not obvious (at least not to me), when an
intermediate computation produces more digits than the inputs,
whether you should keep the extra digits for further intermediate
computations, and round only when you're done
computing a formula (and are about to display or store a result), or
whether you should instead round at each step. Different textbooks
suggest different answers. I tend to do the former, simply because
it's more convenient.

If you're stuck with Python 2.3, you may still take
advantage of the decimal module, by downloading
and installing it as a third-party extensionsee http://www.taniquetil.com.ar/facundo/bdv/image/library/english/10241_get_decimall.

See Also

The explanation of floating-point arithmetic in Appendix B of the
Python Tutorial at http://docs.python.org/tut/node15l; the
Python FAQ at http://www.python.org/doc/faq/generall#why-are-floating-point-calculations-so-inaccurate;
Tim Peter's FixedPoint at http://fixedpoint.sourceforge.net/; using
decimal as currency, see Recipe 3.13; decimal
is documented in the Python 2.4 Library
Reference and is available for download to use with 2.3
at http://cvs.sourceforge.net/viewcvs.py/python/python/dist/src/Lib/decimal.py;
the decimal PEP (Python Enhancement Proposal), PEP 327, is at
http://www.python.org/peps/pep-0327l.