Faster Recursive Fibonacci Numbers

[geremy condra]

On Fri, May 20, 2011 at 10:07 AM, Steven D'Aprano
<steve+comp.lang.python at pearwood.info> wrote:
> On Fri, 20 May 2011 16:54:06 +1000, Chris Angelico wrote:
>
>> If someone has time to kill (as if!), it'd be awesome to get a new
>> numeric type that uses bc's code; any other numeric type (int, long,
>> float) could autopromote to it, removing the dilemma of which to promote
>> out of long and float. Hmm... Python 4.0, 'bc' is the new default
>> integer and everything else is a performance optimization? Heh.
>
> The problem is, it isn't *just* a performance optimization, there is a
> semantic difference too. Consider:
>
>>>> x = 1e-300
>>>> x*x == 0
> True
>
> But using something with more precision:
>
>>>> from fractions import Fraction
>>>> x = Fraction(10)**-300
>>>> x*x == 0
> False
>
>
> So you get different behaviour between floats and arbitrary precision
> numbers.

And this shows up in the above implementation; reimplementing it using
Fractions and a truncated continuing fraction approximation of phi and
the square root of 5 gets us up to about 500, at the cost of a very
long computation time.

Geremy Condra