continued_fraction uses float division, producing invalid terms for large integers and raising OverflowError #15655

Repository commit

6e03a48579ca212a08b36be00378f887dc41a003

Python version (python --version)

Python 3.11.0, macOS

Dependencies version (pip freeze)

The reproduction uses only Python's standard library; no third-party dependencies are involved.

Expected behavior

continued_fraction(Fraction(2**53 + 3)) should return [9007199254740995], the continued fraction of that integer. Large exact fractions should not fail merely because they exceed floating-point range.

Actual behavior

Run from the repository root:

from fractions import Fraction
from maths.continued_fraction import continued_fraction

print(continued_fraction(Fraction(2**53 + 3)))
try:
    print(continued_fraction(Fraction(10**400, 3)))
except OverflowError as exc:
    print(type(exc).__name__ + ':', exc)

Output:

[9007199254740996, -1]
OverflowError: integer division result too large for a float

The first result represents the same integer numerically, but is not the regular continued fraction: the trailing term is negative because the first quotient was rounded upward.

In maths/continued_fraction.py, floor(numerator / denominator) first converts the integer ratio to a float. This loses precision for sufficiently large values and can overflow. Computing the quotient directly with integer floor division (numerator // denominator) preserves exact arithmetic and also handles negative fractions.

I searched existing issues and PRs for continued fraction and continued_fraction; I did not find an existing report of this problem.