Fixed division bug in max_inscribed_ball causing test_max_ball failure

[Shorya777]

Fixes - #453

This PR resolves the numerical instability reported in #453 by introducing a safeguarded division helper to prevent divisions by extremely small values during the interior-point iterations of max_inscribed_ball.

Implementation
Added a helper function:

template <typename NT>
inline NT safe_div(NT num, NT denom) {
    constexpr NT eps = NT(1e-12);
    if (std::abs(denom) < eps)
        denom = (denom >= 0 ? eps : -eps);
    return num / denom;
}

The unstable division was replaced with guarded divisions using safe_div, ensuring that denominators do not approach zero.

Testing
test_max_ball now passes.

[Dev-sh21]

Hey @Shorya777 , in calcstep line 45, it seems the grouping of the division has changed during refactoring.
The original code was ((v4/v2) - v5) / v3, but the new line is (v4/v2) - (v5/v3),
earlier v3 was dividing the entire numerator, but now its just dividing v5
This would change the mathematical result of the iteration

just verify pls

[Dev-sh21]

also
@Shorya777 ,

using std::max(denom, eps) is risky if denom is negative. In optimization edge cases, if the denominator is a small negative number, safe_div will flip its sign to positive eps, leading to incorrect directional updates, a better approach would be to using the ternary operation something like

(denom >= 0 ? std::max(denom, eps) : std::min(denom, -eps)) to preserve the sign

just verify pls

[Shorya777]

Hey @Shorya777 , in calcstep line 45, it seems the grouping of the division has changed during refactoring. The original code was ((v4/v2) - v5) / v3, but the new line is (v4/v2) - (v5/v3), earlier v3 was dividing the entire numerator, but now its just dividing v5 This would change the mathematical result of the iteration

just verify pls

yeah I fixed it now! I just saw that because of it test_max_ball_sparse was failing but now it's okay.
every test is passing now.

[Shorya777]

also @Shorya777 ,

using std::max(denom, eps) is risky if denom is negative. In optimization edge cases, if the denominator is a small negative number, safe_div will flip its sign to positive eps, leading to incorrect directional updates, a better approach would be to using the ternary operation something like

(denom >= 0 ? std::max(denom, eps) : std::min(denom, -eps)) to preserve the sign

just verify pls

yeah I think that would be a problem. Working on it.

[Shorya777]

Hi @vissarion and @TolisChal, I would appreciate your feedback on this PR when you have time. Please let me know if any adjustments are needed.

[Akash504-ai]

Thanks for addressing this and correcting the formula, with the fixes in place and tests passing...this looks good.

[vissarion]

Thanks for this PR.

Could you please explain why did you decide to use NT(1e-12)? Is it part of some experimentation?