Kernel_23: Exploit Uncertain in collinear_3()

[afabri]

Summary of Changes

Make collinear_3() exploit uncertainty to make it faster. See discussion in PR #5207

Release Management

• Affected package(s): Kernel_23
• License and copyright ownership: unchanged

[sloriot]

I think the new code and the old code are doing exactly the same thing when it comes to filter failure. Indeed the only way you would save something is if the first determinant is -1 or +1, which is not possible as 0 would also be a positive value in that case.

[mglisse]

the only way you would save something is if the first determinant is -1 or +1

Why? If the first sign of determinant is an uncertain containing 0 and at least one of ±1, the old code will throw trying to convert to bool in if, while the new code will continue (and if the second determinant is clearly non-zero, it will be able to conclude without going to exact computation).

[sloriot]

Indeed I missed the fact that is_zero is uncertain. Looking again at CGAL_AND, I agree that exact computation will be triggered only if the interval/static det signs are all indeterminate.

[sloriot]

Successfully tested in CGAL-6.0-Ic-96