Project Euler #10 in Swift - Summation of primes

I just finished Project Euler #10 in Swift, and since there is not any version yet on Code Review, I would like to have some comments on what I did to try to improve it.

I hope I learned some from the previous code reviews :).

The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.

Find the sum of all the primes below two million.

import Foundation

func summationOfPrimesBelow(var n:Int) -> Int {

assert(n > 0, "argument must be positive")

var composite = [Bool](count: n, repeatedValue: false)

var x = 2
let maxPrime = Int(ceil(sqrt(Double(n))))

while x <= maxPrime {
if composite[x] == false {
for y in stride(from: x * x, through: n - 1, by: x) {
composite[y] = true
}
}
x++
}

var result = 0
for i in stride(from: 2, through: composite.count - 1, by: 1) {
if composite[i] == false {
result += i
}
}

return result
}

func euler10() {
let number = summationOfPrimesBelow(2_000_000)

println(number)
}

func printTimeElapsedWhenRunningCode(operation:() -> ()) {
let startTime = CFAbsoluteTimeGetCurrent()
operation()
let timeElapsed = CFAbsoluteTimeGetCurrent() - startTime
println("Time elapsed : \(timeElapsed) s")
}

printTimeElapsedWhenRunningCode(euler10)


The code executes in 0.012s in Release mode.

Since we know that primes can be represented by 6x+1 or 6x-1 except for 2,3, we could skip them as follows:

//Handle explicitly for n<5 i.e for n = 0,1,2,3,4 and proceed otherwise.
if n<3 { // n=0,1,2
return 0
}
if n<5 {// n = 3,4
return (n==3)?2:5
}

var x = 5
while x <= maxPrime {
if composite[x] == false {
for y in stride(from: x * x, through: n - 1, by: x) {
composite[y] = true
}
}
x+=2
if x<n && composite[x] == false {
for y in stride(from: x * x, through: n - 1, by: x) {
composite[y] = true
}
}
x+=4
}

var result = 5 // 2 + 3
for i in stride(from: 5, through: composite.count - 1, by: 4) {
if composite[i] == false {
result += i
}
i+=2
if i<n && composite[i] == false {
result += i
}
}


Results: With your code it took me 33ms with mine its down to 23ms.

• It is faster, thanks. The code does not work though for the values 1, 2, 3, and 6 : it returns 5 instead of 0, 1, 2 and 10. It crashes with 7. And you should replace for i in stride(from: 5, through: composite.count - 1, by: 4) { with for var i = 5; i < composite.count - 1; i += 4 { Otherwise you cannot use i += 2 in the loop Dec 28 '14 at 11:29
• For <4, we need to handle it explicitly. For 6, we would get 10. composite[5] = false. So result = 5 + 5 = 10. For 7 it wouldn't crash. Could you recheck ? For <2, it should be 0. Dec 29 '14 at 4:27
• I did test to write my comment. 6 gives back 5 as a result instead of 10. And 7 crashes. You should also edit your stride loop. Dec 29 '14 at 9:56
• My mistake. Sincere apologies. Will correct and generalise it as far as possible. Dec 29 '14 at 12:08