String representations of numbers and approximate equality

[Dan Stromberg]

On Wed, Sep 24, 2014 at 9:54 AM, Chris Angelico <rosuav at gmail.com> wrote:
> Yes, it's another "how can I see if two numbers are approximately
> equal" thread, but this time I have a concrete definition of
> "approximately equal"... and they're Decimals, not floats.
>
> I have a number of files (this is an ongoing thing) in which there are
> two columns of numbers. One of them should be equal to the other times
> some factor which the program knows from elsewhere. All the numbers
> are represented as strings of ASCII decimal digits, possibly including
> a U+002E decimal point. Something like this:
>
> # (these are calculated on factor 30)
> ["0.75", "22.5"]
> ["0.80", "24"]
> ["4.73", "142"]
>
> The definition of valid is that, within the rounding they've been
> given, the values are correct. The first two are strictly correct; the
> third would be 141.9 with full accuracy but 142 is deemed good enough.
> But this should fail:
>
> ["0.1", "10"]
>
> 0.1 * 30 should be 3, not 10; and 10 / 30 should be 0.333, not 0.1;
> therefore this is wrong.

tolerance = decimal.Decimal('0.1') # I hesitate to call it epsilon

if abs(decimal1 - decimal2) <= tolerance:
   print('They are close')
else:
   print('They are different')