[Proposal] Expose additional MidpointRounding modes

[tannergooding]

Rationale

The IEEE 754:2008 spec calls out five different supported "rounding directions", 4 of which are required for binary-floating point values.

CoreFX currently exposes only 1 of the required rounding directions and the 1 optional rounding mode. We should expose the remaining three rounding directions in order to be more compliant and give users the greatest flexibility when writing their applications.

Proposed API

public partial enum MidpointRounding
{
    ToPositiveInfinity, // `roundTowardPositive` - the result closest to and no less than the infinitely precise result
    ToNegativeInfinity, // `roundTowardNegative` - the result closest to and no greater than the infinitely precise result
    ToZero              // `roundTowardZero` - the result closest to and no greater in magnitude than the infinitely precise result
}

[tannergooding]

Part of https://github.com/dotnet/corefx/issues/31901

[tannergooding]

This will require additional work in Math.Round, MathF.Round, and Decimal.Round.

[tannergooding]

CC. @eerhardt, @danmosemsft

[hamish-rose]

Hello

I would like to contribute to corefx - May I take this one ?

[danmoseley]

For sure you can @hamish-rose. I sent you a collaborator link. If you accept, I can sign this to you. Note when you join it defaults to subscribing you to all repo activity, you will profligate want to switch that off as this repo is busy.

[danmoseley]

Please ask here if you have questions. In the documentation folder in this repo is everything you should need to get started.

[hamish-rose]

Thanks, I've accepted.

[pentp]

These are not midpoint rounding modes but directed rounding modes.
Naming them as Truncate/Floor/Ceiling would be more consistent with the existing Math class API names.

[tannergooding]

This was discussed in the API review and it was determined that we should still expose them on MidpointRoundingMode rather than introducing a new type (such as DirectedRoundingMode).

CC. @terrajobst who may have the notes from that meeting?

[tannergooding]

I'm not opposed to having separate overloads that take a DirectedRoundingMode enum, but we would need to take this back through API review and update the corresponding PRs.

[pentp]

I'm still concerned about naming - it's really confusing to see MidpointRounding.AwayFromZero and MidpointRounding.ToPositiveInfinity next to each other when they actually mean completely different things (at first look, one would assume that for positive numbers they would behave identically).

I propose renaming them to Truncate/Floor/Ceiling to avoid such confusion.

[tannergooding]

I propose renaming them to Truncate/Floor/Ceiling to avoid such confusion.

I don't think Truncate/Floor/Ceiling will help avoid any of the confusion here. The names mean effectively the same thing either way, the "confusion" comes from it being on MidpointRounding when they are in-fact DirectedRounding modes.