e^x to n terms of accuracy http://swiftstub.com/71611885/

exponential.swift

// Computes an estimation of e^x using a Taylor series expansion with n terms.
// 1 + (x^1/1!) + (x^2/2!) + ... + (x^n/n!)
func exponential(x: Double, n: Double) -> Double {
    var exponential: Double = 1

    for var y: Double = 1; y <= n; y++ {
        var power: Double = 1
        var yFactorial: Double = 1
        for var i: Double = 1; i <= y; i++ {
            yFactorial *= i
        }
        exponential += (pow(x, y)/yFactorial)
    }

    return exponential
}

// 2.718281828459045235360287471352662497757247093699959574966967...
println(exponential(1, 17)) // right at the cut-off point for accuracy

// 20.08553692318766774092852965458171789698790783855415014437893...
println(exponential(3, 20))

println("\n")

// 148.4131591025766034211155800405522796234876675938789890467528...
for numterms in [1, 2, 3, 5, 10, 20] as [Double] {
    println(exponential(5, numterms))
}