Median

[benrimmington]

@beccadax

It seems like the N-parameter form might be better expressed as a method on something in the Collection hierarchy, much like how we have both the top-level function max() and the extension method max().

The global min and max functions have an overload with a variadic parameter, so it seemed natural to use a similar design in this proposal. Also, the median of two values (i.e. an empty variadic array) returns the arithmetic mean, which may be useful as a global function?

@beccadax

I also think we may want to perform this operation on integer types in addition to floating-point types. Is there something more general than FloatingPoint that we could require instead?

The most general requirements I tried were:

• T: Strideable where T.Stride: FloatingPoint
  but that wouldn't include any additional types, except maybe Foundation.Date — if a conformance was added (FB9452917).

• T: Strideable where T.Stride: ExpressibleByFloatLiteral
  but that would include Foundation.Decimal, which had a broken distance(to:) method for the last five years — only recently fixed by @xwu in SR-6785.

Also, the distance(to:) method would return infinity for some floating-point values.

@Nevin

I like the 3-element median, but I think the variadic version would feel more natural as a method on Collection, with both Comparable and custom-predicate versions.

I agree that median methods on sequences would be useful, but I didn't think they would be accepted for the standard library. There was a previous discussion on adding sum and product methods to Swift Numerics, so perhaps mean and median methods would also be considered for that package?

@Nevin

You’re right, what I meant was, for floating-point values, I sometimes want the median by \.magnitude or suchlike, rather than direct <.

Sorting by key paths was recently discussed in the apple/swift-algorithms#89 issue.

@young

I think the median for Integer type should be a Double.

The benchmark suite returns an Int median for an [Int] array, by rounding to the nearest index.