Confusing math problem

[Dave Angel]

On 02/21/2013 05:44 PM, Schizoid Man wrote:
>   <snip>
>
>
> No, I was aware to be honest. I thought ** was just short hand for
> math.pow(). Since ** is the integer operation

It's an integer operation because you started with two ints.  Unlike 
math.pow, which converts to floats, whatever you feed it.

>
> I compared the difference and got a large blob of numbers. To make a
> proper comparison I'll need to compare the base and exponent for which
> the numbers are different rather than the numbers themselves. I'm
> following Dave's suggestion of determining the symmetric difference of
> the sets.

But once you have a few that are just plain way off, it doesn't really 
matter whether some others differ in the 17th place.  All the other 
discussion is interesting, but don't forget the main point, that trying 
to represent large integers (over 17 or so digits) as floats is going to 
lose precision.  That can happen a number of ways, and math.pow is just 
one of them.

Floats use a finite precision to store their value, and the radix is 
binary, not decimal.  So figuring where they start to lose precision is 
tricky.  If you're doing a calculation where all intermediate values are 
integers, you're usually better off sticking with int/long.

There are many other kinds of constraints that come up in programming, 
and Python usually has an answer for each.  But in a machine of finite 
size, and when we care at least a little about performance, we 
frequently have to pick our algorithm, our set of functions, and our 
data format carefully.

Someone else has mentioned the decimal package and the fractions.  Each 
of those has a lot to offer in specific situations.  But none is a panacea.


-- 
DaveA