[issue2486] Consider using bytes type instead of str to store Decimal coefficients

[Mark Dickinson]

Mark Dickinson <dickinsm at gmail.com> added the comment:

I've made some progress here:  I have a version of decimal.py for
Python 3.0 that uses a Deccoeff instead of a string for the Decimal
coefficient.  It still needs a little work to make things efficient,
but it already passes all the tests in test_decimal.  There are no
API changes.

What's a Deccoeff?  Read on, and/or see attached file.

Deccoeff (for *Dec*imal *coeff*icient) is an extension type for Python
3.0 that combines some of the most useful aspects of both the integer
and string types.

First, you can do arithmetic directly with Deccoeff instances:

>>> from deccoeff import Deccoeff
>>> x = Deccoeff('7')
>>> y = Deccoeff('11')
>>> x + y
Deccoeff('18')
>>> x * y
Deccoeff('77')
>>> y - x
Deccoeff('4')
>>> x < y
True

Only nonnegative integers can be represented as Deccoeff instances,
since that's all that's needed for Decimal: a subtraction that would
produce a negative result instead raises OverflowError:

>>> x-y
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
    OverflowError: difference is negative and cannot be represented as a Deccoeff

Powering also works:

>>> x ** y
Deccoeff('1977326743')
>>> y ** x
Deccoeff('19487171')

So much for arithmetic:  a Deccoeff instance can also be treated as a sequence:
it can be sliced (though the 'step' argument is not supported):

>>> x = Deccoeff('123456789')
>>> x[2:]
Deccoeff('1234567')
>>> x[:5]
Deccoeff('56789')

and indexed:

>>> x[3]
Deccoeff('6')

The length gives the total number of digits:

>>> len(x)
9

Note that the indices work in the opposite direction to the one you
might expect by looking at the string representation of a Deccoeff:
indexing is set up so that index 0 refers to the units digit, 1 to the
tens digit, 2 to the hundreds digit, etc.

Negative indices also make sense (but not in the usual Python sense of
counting from the end of the object): you should imagine the Deccoeff
as a finite string of digits padded with zeros infinitely on both the
left and right.  Then it makes sense to do, for example:

>>> x[-2:]
Deccoeff('12345678900')
>>> x[-3:4]
Deccoeff('6789000')

This provides a convenient way to do a 'decimal shift left'.  There
are many places in Decimal where it's appropriate to use x[n:] without
knowing in advance whether n is positive or negative.

This is a work in progress...  Comments very welcome.

Added file: http://bugs.python.org/file10180/deccoeff.c

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