[swift-evolution] [Proposal] Add floor() and ceiling() functions to FloatingPoint

[Stephen Canon]

> On Jun 25, 2016, at 05:06, Karl via swift-evolution <swift-evolution at swift.org <mailto:swift-evolution at swift.org>> wrote:
> 
>> Proposal: https://gist.github.com/karwa/273db66cd8a5fe2c388ccc7de9c4cf31 <https://gist.github.com/karwa/273db66cd8a5fe2c388ccc7de9c4cf31>
Karl, thanks for writing this up.  It should be extended to include not only floor( ) and ceiling( ), but also:

	/// Returns the integral value closest to `self` whose magnitude is not greater than that of `self`.
	func truncate( ) -> Self

	/// Returns the integral value closest to `self`.  If two integrers are equally close, the even one
	/// is returned.
	//  NOTE: The name of this function requires bike-shedding.  I’ve chosen a deliberately poor
	//  name as a straw-man.
	func roundToNearestTiesToEven( ) -> Self

	/// Returns the integral value closest to `self`.  If two integrers are equally close, the one with
	/// greater magnitude is returned.
	//  NOTE: The name of this function requires bike-shedding.  I’ve chosen a deliberately poor
	//  name as a straw-man.
	func roundToNearestTiesAway( ) -> Self

and mutating versions of those.

Some collected responses to other comments on this thread:

> David Sweeris wrote:
> 
> The only thing I'm worried about is the situation where we have "x = N.M", and `x.ceiling` equals maybe "(N+2).0" instead of "(N+1).0" because we ran out of precision and can't represent (N+1).0. I'm not sure what the exact values are where floats (or doubles) stop having enough precision to represent inter-integer values... It might be a moot point.

This never happens.  Floor and ceiling are always exact operations.

> Austin Rathe wrote:
> 

> 	func roundedUp(withPrecision:Int) -> Self { … }

While I understand where you’re going with this, you can’t round non-decimal floating-point numbers to a non-zero number of decimal digits (the result won’t be representable, in general).  This should be available for decimal floating-point types if/when they are added, but should be handled as part of conversions to String for binary floating-point types.

– Steve
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