3-arg pow() with negative exponent silently returns 0 instead of computing modular inverse

Port, board and/or hardware

Unix port, Linux

MicroPython version

MicroPython v1.27.0

Reproduction

print(pow(2, -1, 4))

[!NOTE]
The simplest demonstration would be pow(2, -1, None), where CPython produces the expected result 0.5. However, MicroPython issue #19137 causes pow(x, y, None) to raise TypeError before the negative-exponent code path is even reached, so that example cannot be used here. The reproduction below falls back to a 3-arg form where CPython raises ValueError for non-invertibility, which still exercises the same buggy code path in MicroPython.

Expected behaviour

CPython v3.11.15:

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: base is not invertible for the given modulus

Observed behaviour

MicroPython v1.27.0:

0

Additional Information

pow(base, exp, mod) with a negative exponent silently returns 0 instead of computing the modular inverse of base modulo mod (or raising ValueError when the inverse does not exist). This is a CPython compatibility issue.

Root Cause

mpz_pow3_inpl short-circuits any negative exponent by setting dest = 0 and returning, so mp_obj_int_pow3 silently yields 0 for every pow(x, neg_exp, mod) call regardless of whether the modular inverse exists.

// py/mpz.c:1358-1362
void mpz_pow3_inpl(mpz_t *dest, const mpz_t *lhs, const mpz_t *rhs, const mpz_t *mod) {
    if (lhs->len == 0 || rhs->neg != 0 || (mod->len == 1 && mod->dig[0] == 1)) {
        mpz_set_from_int(dest, 0);
        return;
    }
    ...

CPython's long_pow negates the exponent and calls long_invmod to compute the modular inverse, raising ValueError("base is not invertible for the given modulus") when gcd(base, |mod|) != 1.

CPython reference: Objects/longobject.c#L4455-L4474

// If exponent is negative, negate it and replace the base with
// its modular inverse; long_invmod raises ValueError when gcd != 1.
if (Py_SIZE(b) < 0) {
    temp = (PyLongObject *)_PyLong_Copy(b);
    if (temp == NULL)
        goto Error;
    Py_DECREF(b);
    b = temp;
    temp = NULL;
    _PyLong_Negate(&b);
    if (b == NULL)
        goto Error;

    temp = long_invmod(a, c);
    if (temp == NULL)
        goto Error;
    Py_DECREF(a);
    a = temp;
    temp = NULL;
}

Fix

Replace the rhs->neg != 0 short-circuit in mpz_pow3_inpl with a modular-inverse path (extended Euclidean), change the return type to bool, and raise ValueError("base is not invertible for the given modulus") from mp_obj_int_pow3 when the helper signals a non-invertible base.

Code of Conduct

Yes, I agree

Start by reproducing pow(2, -1, 4) and reading mpz_pow3_inpl in py/mpz.c together with mp_obj_int_pow3 in py/objint_mpz.c. Compare the negative-exponent behavior with the linked CPython long_pow reference. Done means modular inverses are computed when possible and the specified ValueError is raised for non-invertible bases.