Add Exts.ISqrt to avoid fp sqrt calculations.

OpenRA.Game/Exts.cs

@@ -202,6 +202,91 @@ namespace OpenRA
 
 		public static Size NextPowerOf2(this Size s) { return new Size(NextPowerOf2(s.Width), NextPowerOf2(s.Height)); }
 
+		public enum ISqrtRoundMode { Floor, Nearest, Ceiling }
+		public static int ISqrt(int number, ISqrtRoundMode round = ISqrtRoundMode.Floor)
+		{
+			if (number < 0)
+				throw new InvalidOperationException("Attempted to calculate the square root of a negative integer: {0}".F(number));
+
+			return (int)ISqrt((uint)number, round);
+		}
+
+		public static uint ISqrt(uint number, ISqrtRoundMode round = ISqrtRoundMode.Floor)
+		{
+			var divisor = 1U << 30;
+
+			var root = 0U;
+			var remainder = number;
+
+			// Find the highest term in the divisor
+			while (divisor > number)
+				divisor >>= 2;
+
+			// Evaluate the root, two bits at a time
+			while (divisor != 0)
+			{
+				if (root + divisor <= remainder)
+				{
+					remainder -= root + divisor;
+					root += 2 * divisor;
+				}
+
+				root >>= 1;
+				divisor >>= 2;
+			}
+
+			// Adjust for other rounding modes
+			if (round == ISqrtRoundMode.Nearest && remainder > root)
+				root += 1;
+
+			else if (round == ISqrtRoundMode.Ceiling && root * root < number)
+				root += 1;
+
+			return root;
+		}
+
+		public static long ISqrt(long number, ISqrtRoundMode round = ISqrtRoundMode.Floor)
+		{
+			if (number < 0)
+				throw new InvalidOperationException("Attempted to calculate the square root of a negative integer: {0}".F(number));
+
+			return (long)ISqrt((ulong)number, round);
+		}
+
+		public static ulong ISqrt(ulong number, ISqrtRoundMode round = ISqrtRoundMode.Floor)
+		{
+			var divisor = 1UL << 62;
+
+			var root = 0UL;
+			var remainder = number;
+
+			// Find the highest term in the divisor
+			while (divisor > number)
+				divisor >>= 2;
+
+			// Evaluate the root, two bits at a time
+			while (divisor != 0)
+			{
+				if (root + divisor <= remainder)
+				{
+					remainder -= root + divisor;
+					root += 2 * divisor;
+				}
+
+				root >>= 1;
+				divisor >>= 2;
+			}
+
+			// Adjust for other rounding modes
+			if (round == ISqrtRoundMode.Nearest && remainder > root)
+				root += 1;
+
+			else if (round == ISqrtRoundMode.Ceiling && root * root < number)
+				root += 1;
+
+			return root;
+		}
+
 		public static string JoinWith<T>(this IEnumerable<T> ts, string j)
 		{
 			return string.Join(j, ts);