Combination.swift

import Foundation

extension Array {
    /// Returns unique pairs from array
    /// Following is result of `[1, 2, 3, 4].pairs()`
    /// [(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]
    func pairs() -> [(Element, Element)] {
        return enumerated()
            .flatMap { index, element in
                dropFirst(index.advanced(by: 1))
                    .map { (element, $0) }
        }
    }
}

private extension Double {
    /// Calculate the average angle
    /// If average does not exists, this will return Double.nan (like [0°, 180°])
    static func averageAngle(_ angles: [Double]) -> Double {
        let (x, y) = angles.map { (cos($0), sin($0)) }
            .reduce((0, 0)) { result, item in (result.0 + item.0, result.1 + item.1) }
        return atan(y / x)
    }

    /// Calculate the distance of periodic value
    /// result x meets `0 <= x < period / 2`
    static func periodicDistance(_ lhs: Double, _ rhs: Double, period: Double) -> Double {
        let diff = lhs - rhs
        let normalized = diff - period * floor(diff / period)
        return normalized < (period / 2) ? normalized : period - normalized
    }
}