Added a new prime checking method.

Changelog.md

@@ -150,6 +150,7 @@
             + Lerp(Equation, Equation, float, bool)
             + Lerp(Equation, Equation, Equation, bool)
             + PrimeFactors(int)
+            + PowerMod(long, long, long)
             + SharedItems<T>(T[][])
             + SolveBisection(Equation, float, float, float, float, int)
             + SolveEquation(Equation, float, float, float, int)

Nerd_STF/Helpers/MathfHelper.cs

@@ -2,9 +2,90 @@
 
 internal static class MathfHelper
 {
-    public static bool IsPrimeClassic(int num)
+    public static (int[] group, long max)[] MillerRabinWitnessNumbers =
     {
-        for (int i = 2; i <= num / 2; i++) if (num % i == 0) return false;
+        (new int[] { 2, 3 }, 1_373_653),
+        (new int[] { 31, 73 }, 9_080_191),
+        (new int[] { 2, 3, 5 }, 25_326_001),
+        (new int[] { 2, 13, 23, 1_662_803 }, 1_122_004_669_633),
+        (new int[] { 2, 3, 5, 7, 11 }, 2_152_302_898_747),
+        (new int[] { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 }, long.MaxValue) // The real maximum is 318_665_857_834_031_151_167_461
+    };
+
+    public static bool IsPrimeClassic(long num)
+    {
+        for (long i = 2; i <= num / 2; i++) if (num % i == 0) return false;
         return true;
     }
+
+    // 0x49204655434B494E47204C4F5645204E554D42525048494C45
+    // For some reason (I think the witnesses are slightly off), 12 numbers under 100,000
+    // are misrepresented as prime. I guess one of the witnesses becomes a liar for them.
+    // Mostly works though.
+    //
+    // TODO: In 2.10, the Mathf.PowerMod(int, int, int) method needs to be reworked to
+    //       have a better O(n).
+    public static bool IsPrimeMillerRabin(long num)
+    {
+        // Negatives are composite, zero and one are composite, two and three are prime.
+        if (num <= 3) return num > 1;
+
+        long unchanged = num;
+
+        // Find the number's proper witness group.
+        int[]? witnessGroup = null;
+        for (int i = 0; i < MillerRabinWitnessNumbers.Length; i++)
+        {
+            if (num <= MillerRabinWitnessNumbers[i].max)
+            {
+                witnessGroup = MillerRabinWitnessNumbers[i].group;
+                break;
+            }
+        }
+        if (witnessGroup is null) throw new MathException($"The number {num} is out of range of the available witness " +
+            $"numbers. Use the {nameof(PrimeCheckMethod.Classic)} method instead."); // This should never happen.
+
+        // Prep the number for court.
+        num -= 1; // For clarity.
+
+        // Seperate out powers of two.
+        int m = 0;
+        while (num % 2 == 0)
+        {
+            m++;
+            num /= 2;
+        }
+
+        long d = num; // The rest.
+
+        // Our number is rewritten as 2^m * d + 1
+
+        foreach (int a in witnessGroup)
+        {
+            // Calculate a^d = 1 mod n
+            // If true, the number *may* be prime (test all star numbers to be sure)
+            // If false, the number is *definitely* composite.
+
+            bool thinks = false;
+            for (int m2 = 0; m2 < m; m2++)
+            {
+                // Add any amount of multiples of two as given, but not as many as the original breakdown.
+
+                int additional = 1;
+                for (int m3 = 0; m3 < m2; m3++) additional *= 2;
+
+                long result = Mathf.PowerMod(a, additional * d, unchanged);
+                if (Mathf.AbsoluteMod(result + 1, unchanged) == 0 || Mathf.AbsoluteMod(result - 1, unchanged) == 0)
+                {
+                    thinks = true;
+                    break;
+                }
+            }
+
+            if (!thinks) return false; // Definitely not prime.
+            else continue; // For clarity. A claim that the number is prime is not trustworthy until we've checked all witnesses.
+        }
+
+        return true; // Probably prime.
+    }
 }

Nerd_STF/Mathematics/Mathf.cs

@@ -141,6 +141,7 @@ public static class Mathf
         method switch
         {
             PrimeCheckMethod.Classic => MathfHelper.IsPrimeClassic(num),
+            PrimeCheckMethod.MillerRabin => MathfHelper.IsPrimeMillerRabin(num),
             _ => throw new ArgumentException("Unknown prime check method.", nameof(method))
         };
 
@@ -358,6 +359,14 @@ public static class Mathf
         for (int i = 0; i < pow; i++) val = val * num % mod;
         return val;
     }
+    public static long PowerMod(long num, long pow, long mod)
+    {
+        if (pow == 1) return num;
+        if (pow < 1) return 0;
+        long val = 1;
+        for (long i = 0; i < pow; i++) val = val * num % mod;
+        return val;
+    }
 
     public static float Root(float value, float index) => (float)Math.Exp(Math.Log(value) / index);
 

Nerd_STF/Mathematics/PrimeCheckMethod.cs

@@ -2,5 +2,6 @@
 
 public enum PrimeCheckMethod
 {
-    Classic
+    Classic,
+    MillerRabin
 }