Fraction scientific formatting fails for near-unit values with large numerators and denominators

[augusto-rehfeldt]

Bug report

Bug description:

Documented behaviour: “Fraction instances support float-style formatting, with presentation types 'e', 'E', 'f', 'F', 'g', 'G' and '%'.” — Python standard library documentation, fractions module, Fraction formatting.

Expected: 1.00e+00

Actual: ValueError: Exceeds the limit (4300 digits) for integer string conversion; use sys.set_int_max_str_digits() to increase the limit

import fractions
import sys

if sys.version_info < (3, 12):
    print("REFUTATION REJECTED: float-style Fraction formatting requires Python 3.12+")
    sys.exit(0)

sys.set_int_max_str_digits(4300)
k = 4300
d = 10**k
n = d + 1
x = fractions.Fraction(n, d)
spec = ".2e"  # Valid Fraction and documented float-style presentation.

# Independent exact rounding to two decimal places; x has exponent zero.
q, r = divmod(100 * n, d)
q += 2 * r > d or (2 * r == d and q % 2)
expected = f"{q // 100}.{q % 100:02d}e+00"

try:
    actual = format(x, spec)
except Exception as e:
    actual = ("exception", type(e).__name__, str(e))

if actual != expected:
    print("REFUTATION CONFIRMED:",
          {"x": "Fraction(10**4300 + 1, 10**4300)",
           "int_max_str_digits": sys.get_int_max_str_digits(), "format": spec},
          "actual=", repr(actual), "expected=", repr(expected))
else:
    print("REFUTATION REJECTED: actual matches the exact rounding reference")

Output on Python 3.14.6 (Windows-11-10.0.26220-SP0), standard library fractions:

REFUTATION CONFIRMED: {'x': 'Fraction(10**4300 + 1, 10**4300)', 'int_max_str_digits': 4300, 'format': '.2e'} actual= ('exception', 'ValueError', 'Exceeds the limit (4300 digits) for integer string conversion; use sys.set_int_max_str_digits() to increase the limit') expected= '1.00e+00'

This report was found and written by an automated property-testing tool I run (bugforge). The reproducer above was executed and its output is pasted unedited; no person reviewed the report before it was filed. The search script is in https://github.com/augusto-rehfeldt/bugforge-results/tree/main/fractions-20261003-233134-c1

CPython versions tested on:

3.14

Operating systems tested on:

Windows

[ZeroIntensity]

See #158748 (comment).