cmath.isclose incorrectly returns True for large finite opposite complex values

[augusto-rehfeldt]

Bug report

Bug description:

Documented behaviour: Python standard-library documentation, cmath.isclose: "If no errors occur, the result will be: abs(a-b) <= max(rel_tol * max(abs(a), abs(b)), abs_tol)."

Expected: False

Actual: True

import cmath
import math
from fractions import Fraction as F

p = dict(a=complex(1.7e308, 1.7e308), b=complex(-1.7e308, -1.7e308),
         rel_tol=1e-9, abs_tol=0.0)
a, b = p["a"], p["b"]
if not (all(map(math.isfinite, (a.real, a.imag, b.real, b.imag,
                                p["rel_tol"], p["abs_tol"])))
        and p["rel_tol"] >= 0 and p["abs_tol"] >= 0):
    print("REFUTATION REJECTED:", "invalid input", p)
else:
    x, y, u, v = map(F, (a.real, a.imag, b.real, b.imag))
    expected = (x-u)**2 + (y-v)**2 <= max(
        F(p["rel_tol"])**2 * max(x*x+y*y, u*u+v*v),
        F(p["abs_tol"])**2)
    actual = cmath.isclose(**p)
    if actual != expected:
        print("REFUTATION CONFIRMED:", p, "actual:", actual, "expected:", expected)
    else:
        print("REFUTATION REJECTED:", "actual agrees with exact expectation",
              p, "actual:", actual, "expected:", expected)

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

REFUTATION CONFIRMED: {'a': (1.7e+308+1.7e+308j), 'b': (-1.7e+308-1.7e+308j), 'rel_tol': 1e-09, 'abs_tol': 0.0} actual: True expected: False

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/cmath-20261003-033712-c2

CPython versions tested on:

3.14

Operating systems tested on:

Windows

[ZeroIntensity]

See #158748 (comment).