gh-135487: fix reprlib.Repr.repr_int when given very large integers

[picnixz]

Getting the number of digits may be wrong due to some round-off errors but I don't want to overcomplicate the code.

• Issue: Using reprlib.repr fails for very large numbers #135487

[serhiy-storchaka]

I think that we can try to reproduce the result of old Python versions, before introducing the limitation on maximal digit count.

If the length exceeds maxlong, repr_int() returns the first i digits followed by fillvalue followed by the last j digits. I afraid that calculating the last j digits has the same complexity as calculating all digits. But for the first i digits it may be faster.

We could also use 10**math.floor(math.log(x)) to get first digits. There are several caveats. Firs, the precision of float is limited, and the larger x, the less significant digits we can get. But it still can be more than 10 digits in most practical cases. We can estimate the error and the number of reliable digits. Second, even with best effort, it can give wrong even the first digit -- it is difficult to differentiate 9999... from 10000.... In this case we should calculate the first i digits, multiply them by 100**(k-i), and then calculate the correction. This can be repeated iteratively, so we can get arbitrary number of first digits.

cc @tim-one

[serhiy-storchaka]

Why remove this? repr_TYPE is not a real method name.

[picnixz]

It was to make a link in the NEWS entry.

[serhiy-storchaka]

It can differ more than by 1 for large numbers with more than 2**53 digits. Yes, it will take long time (years?) to calculate the decimal digits, but let be more future proof.

[picnixz]

Ah yes, I actually didn't consider the possibility of having 2**53 digits...