`INT::div_euclid` and `INT::rem_euclid` return incorrect values for negative numerators

[toothbrush7777777]

The results of SIGNED_INT::div_euclid and SIGNED_INT::rem_euclid are always incorrect when a % b != 0 && a.is_negative() (where a is the dividend and b is the divisor).

I tried something similar to this code:

fn main() {
    assert_eq!(div(-32768, -32767), (1, 1));
}
fn div(num: i16, div: i16) -> (i16, i16) {
    (num.div_euclid(div), num.rem_euclid(div))
}

I expected to see this happen:
The assert should not fire.

Instead, this happened:
The assert fired. The return value is (2, 32766) instead of (1, 1).

More general test case on playground

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This bug exists in the latest stable, beta and nightly.
The bug appears to have been present since 1.38, when div_euclid and rem_euclid where introduced.
The profile (release or debug) makes no difference.