Decimal and Exponentiation

[Tim Peters]

[elventear]
> I am the in the need to do some numerical calculations that involve
> real numbers that are larger than what the native float can handle.
>
> I've tried to use Decimal, but I've found one main obstacle that I
> don't know how to sort. I need to do exponentiation with real
> exponents, but it seems that Decimal does not support non integer
> exponents.
>
> I would appreciate if anyone could recommend a solution for this
> problem.

Wait <0.3 wink>.  Python's Decimal module intends to be a faithful
implementation of IBM's proposed standard for decimal arithmetic:

    http://www2.hursley.ibm.com/decimal/

Last December, ln, log10, exp, and exponentiation to non-integral
powers were added to the proposed standard, but nobody yet has written
implementation code for Python's  module.  [Python-Dev:  somebody
wants to volunteer for this :-)]

If you're not a numeric expert, I wouldn't recommend that you try this
yourself (in particular, trying to implement x**y as exp(ln(x)*y)
using the same precision is mathematically correct but is numerically
badly naive).

The GNU GMP library (for which Python bindings are available) also
supports "big floats", but their power operation is also restricted to
integer powers and/or exact roots.  This can be painful even to try;
e.g.,

    >>> from gmpy import mpf
    >>> mpf("1e10000") ** mpf("3.01")

consumed well over a minute of CPU time (on a 3.4 GHz box) before dying with

    ValueError: mpq.pow fractional exponent, inexact-root

If you're working with floats outside the range of IEEE double, you
_probably_ want to be working with logarithms instead anyway; but that
depends on you app, and I don't want to know about it ;-)