Add Atkins’ sieve

Rename files
Add project

Author: tikipatel

Prime Numbers/Atkins_Sieve.swift

@@ -0,0 +1,54 @@
+infix operator ^^ { associativity left precedence 160 }
+func ^^ (radix: Int, power: Int) -> Int {
+    return Int(pow(CGFloat(radix), CGFloat(power)))
+}
+
+infix operator .. {associativity left precedence 60 }
+
+func ..<T: Strideable>(left: T, right: T.Stride) -> (T, T.Stride) {
+    return (left, right)
+}
+
+func ..<T: Strideable>(left: (T, T.Stride), right: T) -> [T] {
+    return [T](left.0.stride(through: right, by: left.1))
+}
+
+
+func primesTo(max: Int) -> [Int] {
+    var is_prime = [Bool](count: max + 1, repeatedValue: false)
+    is_prime[2] = true
+    is_prime[3] = true
+    let limit = Int(ceil(sqrt(Double(max))))
+    for x in 1...limit {
+        for y in 1...limit {
+            var num = 4 * x * x + y * y
+            if (num <= max && (num % 12 == 1 || num % 12 == 5)) {
+                is_prime[num] = true
+            }
+            num = 3 * x * x + y * y
+            if (num <= max && num % 12 == 7) {
+                is_prime[num] = true
+            }
+            if (x > y) {
+                num = 3 * x * x - y * y
+                if (num <= max && num % 12 == 11) {
+                    is_prime[num] = true
+                }
+            }
+        }
+    }
+    if limit > 5 {
+        for i in 5...limit {
+            if is_prime[i] {
+                for j in (i * i)..i..max {
+                    is_prime[j] = false
+                }
+            }
+        }
+    }
+    var primesArray = [Int]()
+    for (idx, val) in is_prime.enumerate() {
+        if val == true { primesArray.append(idx) }
+    }
+    return primesArray
+}