[Python-ideas] Python Numbers as Human Concept Decimal System

[Steven D'Aprano]

On Fri, Mar 07, 2014 at 09:33:38PM -0800, Andrew Barnert wrote:

> Today, given any real, Decimal(float('real')) always gives you the 
> value of the closest binary float to that real. With this change, it 
> will sometimes give you the value of the second-closest 
> repr-of-a-binary-float to that real.

Please don't talk about "reals". "Real" has a technical meaning in 
mathematics, and no computer number system is able to represent the 
reals. In Python, we have floats, which are C doubles, and Decimals.

Putting that aside, I'm afraid I don't understand how Guido's suggestion 
to use repr() in the Decimal constructor will sometimes give the 
second-closest value. Can you explain in more detail? If you can show an 
example, that would be great too.


> This means the error across any 
> range of reals increases. It's still below the rule-of-thumb cutoff 
> that everyone uses for converting through floats, but it is higher by 
> a nonzero amount that doesn't cancel out.
>
> Similarly, today, the distribution of float values across the real 
> number line is... not uniform (because of exponents), and I don't know 
> the right technical term, you know what it looks like. The 
> distribution of repr-of-float variables is not.

Nope, sorry, I don't get you.

I think that what you are trying to say is that for each binary 
exponent, the floats with that same exponent are distributed uniformly:

|...|...|...|...|...|...|...|...|

but their reprs are not:

|...|..|..|....|...|....|..|....|

Is this what you mean?



-- 
Steven