math - How to calculate the 21! (21 factorial) in swift?

Question

I am making fuction that calculate factorial in swift. like this

func factorial(factorialNumber: UInt64) -> UInt64 {
    if factorialNumber == 0 {
        return 1
    } else {
        return factorialNumber * factorial(factorialNumber - 1)
    }
}

let x = factorial(20)

this fuction can calculate untill 20.

I think factorial(21) value bigger than UINT64_MAX.

then How to calculate the 21! (21 factorial) in swift?

Answer 1

func factorial(_ n: Int) -> Double {
  return (1...n).map(Double.init).reduce(1.0, *)
}

1. (1...n): We create an array of all the numbers that are involved in the operation (i.e: [1, 2, 3, ...]).

2. map(Double.init): We change from Int to Double because we can represent bigger numbers with Doubles than with Ints (https://en.wikipedia.org/wiki/Double-precision_floating-point_format). So, we now have the array of all the numbers that are involved in the operation as Doubles (i.e: [1.0, 2.0, 3.0, ...]).

3. reduce(1.0, *): We start multiplying 1.0 with the first element in the array (1.0*1.0 = 1.0), then the result of that with the next one (1.0*2.0 = 2.0), then the result of that with the next one (2.0*3.0 = 6.0), and so on.

Step 2 is to avoid the overflow issue.

Step 3 is to save us from explicitly defining a variable for keeping track of the partial results.