timing.swift

import Darwin

enum Timebase {
    private static let timebase: mach_timebase_info_data_t = {
        var data = mach_timebase_info_data_t()
        let ret = withUnsafeMutablePointer(&data, mach_timebase_info)
        assert(ret == KERN_SUCCESS)
        return data
    }()
    
    static func nsec(absoluteTime: UInt64) -> UInt {
        return UInt(absoluteTime * UInt64(timebase.numer) / UInt64(timebase.denom))
    }
}

/// Time the execution of the given `expr`.
func time<T>(@autoclosure expr: Void -> T) -> (nsec: UInt, value: T)
{
    let start = mach_absolute_time()
    let result = expr()
    let delta = Timebase.nsec(mach_absolute_time() - start)
    
    return (delta, result)
}

/// Evaluate `expr` `n` times and return the mean and sample standard deviation.
///
/// [Running mean/variance algorithm](https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Online_algorithm) due to Welford/Knuth.
func stats<T: IntegerType>(n: UInt, @autoclosure _ expr: Void -> T) -> (mean: Double, stdev: Double)
{
    var mean: Double = 0
    var variance: Double = 0
    
    for i in 1...n {
        let x = Double(expr().toIntMax())
        let delta = x - mean
        mean += delta / Double(i)
        variance += delta*(x - mean)
    }
    return (mean, sqrt(variance/Double(n - 1)))
}