Merge pull request aalhour#73 from adamfisher/Implement_Sieve_Of_Atkins

Added Sieve of Atkin algorithm for finding prime numbers.

Author: aalhour

Algorithms/Numeric/SieveOfAtkin.cs

@@ -0,0 +1,73 @@
+using System.Collections.Generic;
+using System.Reflection.Metadata.Ecma335;
+using System.Threading.Tasks;
+
+/***
+* Generates all prime numbers up to a given number
+* Wikipedia: https://en.wikipedia.org/wiki/Sieve_of_Atkin
+*/
+
+
+namespace Algorithms.Numeric
+{
+    public static class SieveOfAtkin
+    {
+        /// <summary>
+        /// Calculate primes up to a given number
+        /// </summary>
+        public static List<int> GeneratePrimesUpTo(int max)
+        {
+            if (max == 2)
+            {
+                return new List<int>() { 2 };
+            }
+
+            if (max < 2)
+            {
+                return new List<int>();
+            }
+
+            var isPrime = new bool[max + 1];
+            var sqrt = (int)System.Math.Sqrt(max);
+
+            Parallel.For(1, sqrt, x =>
+            {
+                var xx = x * x;
+                for (var y = 1; y <= sqrt; y++)
+                {
+                    var yy = y * y;
+                    var n = 4 * xx + yy;
+                    if (n <= max && (n % 12 == 1 || n % 12 == 5))
+                        isPrime[n] ^= true;
+
+                    n = 3 * xx + yy;
+                    if (n <= max && n % 12 == 7)
+                        isPrime[n] ^= true;
+
+                    n = 3 * xx - yy;
+                    if (x > y && n <= max && n % 12 == 11)
+                        isPrime[n] ^= true;
+                }
+            });
+
+            var primes = new List<int>() { 2, 3 };
+            for (var n = 5; n <= sqrt; n++)
+            {
+                if (isPrime[n])
+                {
+                    primes.Add(n);
+                    var nn = n * n;
+                    for (var k = nn; k <= max; k += nn)
+                        isPrime[k] = false;
+                }
+            }
+
+            for (var n = sqrt + 1; n <= max; n++)
+                if (isPrime[n])
+                    primes.Add(n);
+
+            return primes;
+        }
+
+    }
+}

UnitTest/AlgorithmsTests/SieveOfAtkinTest.cs

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+using System.Linq;
+using Algorithms.Numeric;
+using Xunit;
+
+namespace UnitTest.AlgorithmsTests
+{
+    public class SieveOfAtkinTest
+    {
+        [Theory]
+        [InlineData("Primes up to -100", -100)]
+        [InlineData("Primes up to 2", 2, 2)]
+        [InlineData("Primes up to 3", 3, 2, 3)]
+        [InlineData("Primes up to 100", 100, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97)]
+        public static void GeneratePrimesUpTo(string test, int max, params int[] expectedResult)
+        {
+            var result = SieveOfAtkin.GeneratePrimesUpTo(max);
+            Assert.True(result.SequenceEqual(expectedResult), test);
+        }
+    }
+}