diff --git a/BizHawk.Client.Common/input/PolarRectConversion.cs b/BizHawk.Client.Common/input/PolarRectConversion.cs
index 7e61bbd59c..0cf906a903 100644
--- a/BizHawk.Client.Common/input/PolarRectConversion.cs
+++ b/BizHawk.Client.Common/input/PolarRectConversion.cs
@@ -1,20 +1,19 @@
-using System;
-
-using DoublePair = System.Tuple<double, double>;
+#nullable enable
 
 namespace BizHawk.Client.Common
 {
 	public static class PolarRectConversion
 	{
-		/// <param name="θ">angle in degrees</param>
-		/// <returns>rectangular (Cartesian) coordinates (x, y)</returns>
-		public static DoublePair PolarDegToRect(double r, double θ) => PolarRadToRect(r, θ * Math.PI / 180);
+		/// <param name="r">radial displacement in range <c>0..181</c> (this is not asserted)</param>
+		/// <param name="θ">angle (in degrees) in range <c>0..359</c> (this is not asserted)</param>
+		/// <returns>rectangular (Cartesian) coordinates <c>(x, y)</c>. <c>x</c> and/or <c>y</c> may be outside the range <c>-128..127</c>.</returns>
+		/// <seealso cref="RectToPolarLookup"/>
+		public static (short, short) PolarToRectLookup(ushort r, ushort θ) => (PolarRectConversionData._rθ2x[r, θ], PolarRectConversionData._rθ2y[r, θ]);
 
-		/// <param name="θ">angle in radians</param>
-		/// <returns>rectangular (Cartesian) coordinates (x, y)</returns>
-		public static DoublePair PolarRadToRect(double r, double θ) => new DoublePair(r * Math.Cos(θ), r * Math.Sin(θ));
-
-		/// <returns>polar coordinates (r, θ) where θ is in degrees</returns>
-		public static DoublePair RectToPolarDeg(double x, double y) => new DoublePair(Math.Sqrt(x * x + y * y), Math.Atan2(y, x) * 180 / Math.PI);
+		/// <param name="x">horizontal component of rectangular (Cartesian) coordinates <c>(x, y)</c>, in range <c>-128..127</c> (this is not asserted)</param>
+		/// <param name="y">vertical component, as <paramref name="x"/></param>
+		/// <returns>polar coordinates <c>(r, θ)</c> where <c>r</c> is radial displacement in range <c>0..181</c> and <c>θ</c> is angle (in degrees) in range <c>0..359</c> (from <c>+x</c> towards <c>+y</c>)</returns>
+		/// <seealso cref="PolarToRectLookup"/>
+		public static (ushort, ushort) RectToPolarLookup(sbyte x, sbyte y) => unchecked((PolarRectConversionData._xy2r[(byte) x, (byte) y], PolarRectConversionData._xy2θ[(byte) x, (byte) y]));
 	}
-}
\ No newline at end of file
+}
diff --git a/BizHawk.Client.Common/input/PolarRectConversionData.cs b/BizHawk.Client.Common/input/PolarRectConversionData.cs
new file mode 100644
index 0000000000..ee2643fce4
--- /dev/null
+++ b/BizHawk.Client.Common/input/PolarRectConversionData.cs
@@ -0,0 +1,902 @@
+#nullable enable
+
+using System;
+
+namespace BizHawk.Client.Common
+{
+	/// <remarks>This is separate from <see cref="PolarRectConversion"/> because its large size slows or prevents design-time code analysis.</remarks>
+	internal static class PolarRectConversionData
+	{
+		/// <remarks>generated with ruby: <c>def f(r, θ) (r * Math.cos(θ * Math::PI / 180)).round end; puts (0..181).map {|r| "{" + (0..359).map {|θ| f(r, θ)} * ", " + "}"} * ",\n"</c></remarks>
+		public static readonly short[,] _rθ2x = new short[,] {
+			{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
+			{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
+			{ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 },
+			{ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 },
+			{ 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 },
+			{ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5 },
+			{ 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6 },
+			{ 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -7, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -3, -3, -3, -3, -3, -3, -3, -3, -3, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7 },
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+			{ 176, 176, 176, 176, 176, 175, 175, 175, 174, 174, 173, 173, 172, 171, 171, 170, 169, 168, 167, 166, 165, 164, 163, 162, 161, 160, 158, 157, 155, 154, 152, 151, 149, 148, 146, 144, 142, 141, 139, 137, 135, 133, 131, 129, 127, 124, 122, 120, 118, 115, 113, 111, 108, 106, 103, 101, 98, 96, 93, 91, 88, 85, 83, 80, 77, 74, 72, 69, 66, 63, 60, 57, 54, 51, 49, 46, 43, 40, 37, 34, 31, 28, 24, 21, 18, 15, 12, 9, 6, 3, 0, -3, -6, -9, -12, -15, -18, -21, -24, -28, -31, -34, -37, -40, -43, -46, -49, -51, -54, -57, -60, -63, -66, -69, -72, -74, -77, -80, -83, -85, -88, -91, -93, -96, -98, -101, -103, -106, -108, -111, -113, -115, -118, -120, -122, -124, -127, -129, -131, -133, -135, -137, -139, -141, -142, -144, -146, -148, -149, -151, -152, -154, -155, -157, -158, -160, -161, -162, -163, -164, -165, -166, -167, -168, -169, -170, -171, -171, -172, -173, -173, -174, -174, -175, -175, -175, -176, -176, -176, -176, -176, -176, -176, -176, -176, -175, -175, -175, -174, -174, -173, -173, -172, -171, -171, -170, -169, -168, -167, -166, -165, -164, -163, -162, -161, -160, -158, -157, -155, -154, -152, -151, -149, -148, -146, -144, -142, -141, -139, -137, -135, -133, -131, -129, -127, -124, -122, -120, -118, -115, -113, -111, -108, -106, -103, -101, -98, -96, -93, -91, -88, -85, -83, -80, -77, -74, -72, -69, -66, -63, -60, -57, -54, -51, -49, -46, -43, -40, -37, -34, -31, -28, -24, -21, -18, -15, -12, -9, -6, -3, 0, 3, 6, 9, 12, 15, 18, 21, 24, 28, 31, 34, 37, 40, 43, 46, 49, 51, 54, 57, 60, 63, 66, 69, 72, 74, 77, 80, 83, 85, 88, 91, 93, 96, 98, 101, 103, 106, 108, 111, 113, 115, 118, 120, 122, 124, 127, 129, 131, 133, 135, 137, 139, 141, 142, 144, 146, 148, 149, 151, 152, 154, 155, 157, 158, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 171, 172, 173, 173, 174, 174, 175, 175, 175, 176, 176, 176, 176 },
+			{ 177, 177, 177, 177, 177, 176, 176, 176, 175, 175, 174, 174, 173, 172, 172, 171, 170, 169, 168, 167, 166, 165, 164, 163, 162, 160, 159, 158, 156, 155, 153, 152, 150, 148, 147, 145, 143, 141, 139, 138, 136, 134, 132, 129, 127, 125, 123, 121, 118, 116, 114, 111, 109, 107, 104, 102, 99, 96, 94, 91, 89, 86, 83, 80, 78, 75, 72, 69, 66, 63, 61, 58, 55, 52, 49, 46, 43, 40, 37, 34, 31, 28, 25, 22, 19, 15, 12, 9, 6, 3, 0, -3, -6, -9, -12, -15, -19, -22, -25, -28, -31, -34, -37, -40, -43, -46, -49, -52, -55, -58, -61, -63, -66, -69, -72, -75, -78, -80, -83, -86, -88, -91, -94, -96, -99, -102, -104, -107, -109, -111, -114, -116, -118, -121, -123, -125, -127, -129, -132, -134, -136, -138, -139, -141, -143, -145, -147, -148, -150, -152, -153, -155, -156, -158, -159, -160, -162, -163, -164, -165, -166, -167, -168, -169, -170, -171, -172, -172, -173, -174, -174, -175, -175, -176, -176, -176, -177, -177, -177, -177, -177, -177, -177, -177, -177, -176, -176, -176, -175, -175, -174, -174, -173, -172, -172, -171, -170, -169, -168, -167, -166, -165, -164, -163, -162, -160, -159, -158, -156, -155, -153, -152, -150, -148, -147, -145, -143, -141, -139, -138, -136, -134, -132, -129, -127, -125, -123, -121, -118, -116, -114, -111, -109, -107, -104, -102, -99, -96, -94, -91, -89, -86, -83, -80, -78, -75, -72, -69, -66, -63, -61, -58, -55, -52, -49, -46, -43, -40, -37, -34, -31, -28, -25, -22, -19, -15, -12, -9, -6, -3, 0, 3, 6, 9, 12, 15, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 63, 66, 69, 72, 75, 78, 80, 83, 86, 89, 91, 94, 96, 99, 102, 104, 107, 109, 111, 114, 116, 118, 121, 123, 125, 127, 129, 132, 134, 136, 138, 139, 141, 143, 145, 147, 148, 150, 152, 153, 155, 156, 158, 159, 160, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 172, 173, 174, 174, 175, 175, 176, 176, 176, 177, 177, 177, 177 },
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+			{ 179, 179, 179, 179, 179, 178, 178, 178, 177, 177, 176, 176, 175, 174, 174, 173, 172, 171, 170, 169, 168, 167, 166, 165, 164, 162, 161, 159, 158, 157, 155, 153, 152, 150, 148, 147, 145, 143, 141, 139, 137, 135, 133, 131, 129, 127, 124, 122, 120, 117, 115, 113, 110, 108, 105, 103, 100, 97, 95, 92, 90, 87, 84, 81, 78, 76, 73, 70, 67, 64, 61, 58, 55, 52, 49, 46, 43, 40, 37, 34, 31, 28, 25, 22, 19, 16, 12, 9, 6, 3, 0, -3, -6, -9, -12, -16, -19, -22, -25, -28, -31, -34, -37, -40, -43, -46, -49, -52, -55, -58, -61, -64, -67, -70, -73, -76, -78, -81, -84, -87, -89, -92, -95, -97, -100, -103, -105, -108, -110, -113, -115, -117, -120, -122, -124, -127, -129, -131, -133, -135, -137, -139, -141, -143, -145, -147, -148, -150, -152, -153, -155, -157, -158, -159, -161, -162, -164, -165, -166, -167, -168, -169, -170, -171, -172, -173, -174, -174, -175, -176, -176, -177, -177, -178, -178, -178, -179, -179, -179, -179, -179, -179, -179, -179, -179, -178, -178, -178, -177, -177, -176, -176, -175, -174, -174, -173, -172, -171, -170, -169, -168, -167, -166, -165, -164, -162, -161, -159, -158, -157, -155, -153, -152, -150, -148, -147, -145, -143, -141, -139, -137, -135, -133, -131, -129, -127, -124, -122, -120, -117, -115, -113, -110, -108, -105, -103, -100, -97, -95, -92, -90, -87, -84, -81, -78, -76, -73, -70, -67, -64, -61, -58, -55, -52, -49, -46, -43, -40, -37, -34, -31, -28, -25, -22, -19, -16, -12, -9, -6, -3, 0, 3, 6, 9, 12, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 78, 81, 84, 87, 90, 92, 95, 97, 100, 103, 105, 108, 110, 113, 115, 117, 120, 122, 124, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 148, 150, 152, 153, 155, 157, 158, 159, 161, 162, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 174, 175, 176, 176, 177, 177, 178, 178, 178, 179, 179, 179, 179 },
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+			{ 181, 181, 181, 181, 181, 180, 180, 180, 179, 179, 178, 178, 177, 176, 176, 175, 174, 173, 172, 171, 170, 169, 168, 167, 165, 164, 163, 161, 160, 158, 157, 155, 153, 152, 150, 148, 146, 145, 143, 141, 139, 137, 135, 132, 130, 128, 126, 123, 121, 119, 116, 114, 111, 109, 106, 104, 101, 99, 96, 93, 91, 88, 85, 82, 79, 76, 74, 71, 68, 65, 62, 59, 56, 53, 50, 47, 44, 41, 38, 35, 31, 28, 25, 22, 19, 16, 13, 9, 6, 3, 0, -3, -6, -9, -13, -16, -19, -22, -25, -28, -31, -35, -38, -41, -44, -47, -50, -53, -56, -59, -62, -65, -68, -71, -74, -76, -79, -82, -85, -88, -90, -93, -96, -99, -101, -104, -106, -109, -111, -114, -116, -119, -121, -123, -126, -128, -130, -132, -135, -137, -139, -141, -143, -145, -146, -148, -150, -152, -153, -155, -157, -158, -160, -161, -163, -164, -165, -167, -168, -169, -170, -171, -172, -173, -174, -175, -176, -176, -177, -178, -178, -179, -179, -180, -180, -180, -181, -181, -181, -181, -181, -181, -181, -181, -181, -180, -180, -180, -179, -179, -178, -178, -177, -176, -176, -175, -174, -173, -172, -171, -170, -169, -168, -167, -165, -164, -163, -161, -160, -158, -157, -155, -153, -152, -150, -148, -146, -145, -143, -141, -139, -137, -135, -132, -130, -128, -126, -123, -121, -119, -116, -114, -111, -109, -106, -104, -101, -99, -96, -93, -91, -88, -85, -82, -79, -76, -74, -71, -68, -65, -62, -59, -56, -53, -50, -47, -44, -41, -38, -35, -31, -28, -25, -22, -19, -16, -13, -9, -6, -3, 0, 3, 6, 9, 13, 16, 19, 22, 25, 28, 31, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 76, 79, 82, 85, 88, 91, 93, 96, 99, 101, 104, 106, 109, 111, 114, 116, 119, 121, 123, 126, 128, 130, 132, 135, 137, 139, 141, 143, 145, 146, 148, 150, 152, 153, 155, 157, 158, 160, 161, 163, 164, 165, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 176, 177, 178, 178, 179, 179, 180, 180, 180, 181, 181, 181, 181 }
+		};
+
+		/// <remarks>generated with ruby: <c>def f(r, θ) (r * Math.sin(θ * Math::PI / 180)).round end; puts (0..181).map {|r| "{" + (0..359).map {|θ| f(r, θ)} * ", " + "}"} * ",\n"</c></remarks>
+		public static readonly short[,] _rθ2y = new short[,] {
+			{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
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+		};
+
+		/// <remarks>generated with ruby: <c>def f(x, y) Math.hypot(x &lt; 128 ? x : x - 256, y &lt; 128 ? y : y - 256).round end; puts (0..255).map {|x| "{" + (0..255).map {|y| f(x, y)} * ", " + "}"} * ",\n"</c></remarks>
+		public static readonly ushort[,] _xy2r = new ushort[,] {
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+			{ 8, 8, 8, 9, 9, 9, 10, 11, 11, 12, 13, 14, 14, 15, 16, 17, 18, 19, 20, 21, 22, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 127, 126, 125, 124, 123, 122, 121, 120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 110, 109, 108, 107, 106, 105, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 22, 21, 20, 19, 18, 17, 16, 15, 14, 14, 13, 12, 11, 11, 10, 9, 9, 9, 8, 8 },
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+			{ 6, 6, 6, 7, 7, 8, 8, 9, 10, 11, 12, 13, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 127, 126, 125, 124, 123, 122, 121, 120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 110, 109, 108, 107, 106, 105, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 13, 12, 11, 10, 9, 8, 8, 7, 7, 6, 6 },
+			{ 5, 5, 5, 6, 6, 7, 8, 9, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 127, 126, 125, 124, 123, 122, 121, 120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 110, 109, 108, 107, 106, 105, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 9, 8, 7, 6, 6, 5, 5 },
+			{ 4, 4, 4, 5, 6, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 127, 126, 125, 124, 123, 122, 121, 120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 110, 109, 108, 107, 106, 105, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 6, 5, 4, 4 },
+			{ 3, 3, 4, 4, 5, 6, 7, 8, 9, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 127, 126, 125, 124, 123, 122, 121, 120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 110, 109, 108, 107, 106, 105, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 9, 8, 7, 6, 5, 4, 4, 3 },
+			{ 2, 2, 3, 4, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 127, 126, 125, 124, 123, 122, 121, 120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 110, 109, 108, 107, 106, 105, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 4, 3, 2 },
+			{ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 127, 126, 125, 124, 123, 122, 121, 120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 110, 109, 108, 107, 106, 105, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 }
+		};
+
+		/// <remarks>generated with ruby: <c>def f(x, y) x1 = x &lt; 128 ? x : x - 256; (180 * (y &lt; 128 ? Math.atan2(y, x1) / Math::PI : Math.atan2(y - 256, x1) / Math::PI + 2)).round end; puts (0..255).map {|x| "{ " + (0..255).map {|y| f(x, y)} * ", " + " }"} * ",\n"</c></remarks>
+		public static readonly ushort[,] _xy2θ = new ushort[,] {
+			{ 0, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270 },
+			{ 0, 45, 63, 72, 76, 79, 81, 82, 83, 84, 84, 85, 85, 86, 86, 86, 86, 87, 87, 87, 87, 87, 87, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 273, 273, 273, 273, 273, 273, 274, 274, 274, 274, 275, 275, 276, 276, 277, 278, 279, 281, 284, 288, 297, 315 },
+			{ 0, 27, 45, 56, 63, 68, 72, 74, 76, 77, 79, 80, 81, 81, 82, 82, 83, 83, 84, 84, 84, 85, 85, 85, 85, 85, 86, 86, 86, 86, 86, 86, 86, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 274, 274, 274, 274, 274, 274, 274, 275, 275, 275, 275, 275, 276, 276, 276, 277, 277, 278, 278, 279, 279, 280, 281, 283, 284, 286, 288, 292, 297, 304, 315, 333 },
+			{ 0, 18, 34, 45, 53, 59, 63, 67, 69, 72, 73, 75, 76, 77, 78, 79, 79, 80, 81, 81, 81, 82, 82, 83, 83, 83, 83, 84, 84, 84, 84, 84, 85, 85, 85, 85, 85, 85, 85, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 271, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 274, 274, 274, 274, 274, 274, 274, 274, 274, 274, 274, 275, 275, 275, 275, 275, 275, 275, 276, 276, 276, 276, 276, 277, 277, 277, 277, 278, 278, 279, 279, 279, 280, 281, 281, 282, 283, 284, 285, 287, 288, 291, 293, 297, 301, 307, 315, 326, 342 },
+			{ 0, 14, 27, 37, 45, 51, 56, 60, 63, 66, 68, 70, 72, 73, 74, 75, 76, 77, 77, 78, 79, 79, 80, 80, 81, 81, 81, 82, 82, 82, 82, 83, 83, 83, 83, 83, 84, 84, 84, 84, 84, 84, 85, 85, 85, 85, 85, 85, 85, 85, 85, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, 274, 274, 274, 274, 274, 274, 274, 274, 274, 274, 274, 274, 274, 274, 274, 275, 275, 275, 275, 275, 275, 275, 275, 275, 276, 276, 276, 276, 276, 276, 277, 277, 277, 277, 277, 278, 278, 278, 278, 279, 279, 279, 280, 280, 281, 281, 282, 283, 283, 284, 285, 286, 287, 288, 290, 292, 294, 297, 300, 304, 309, 315, 323, 333, 346 },
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+			{ 180, 166, 153, 143, 135, 129, 124, 120, 117, 114, 112, 110, 108, 107, 106, 105, 104, 103, 103, 102, 101, 101, 100, 100, 99, 99, 99, 98, 98, 98, 98, 97, 97, 97, 97, 97, 96, 96, 96, 96, 96, 96, 95, 95, 95, 95, 95, 95, 95, 95, 95, 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 266, 266, 266, 266, 266, 266, 266, 266, 266, 266, 266, 266, 266, 266, 266, 265, 265, 265, 265, 265, 265, 265, 265, 265, 264, 264, 264, 264, 264, 264, 263, 263, 263, 263, 263, 262, 262, 262, 262, 261, 261, 261, 260, 260, 259, 259, 258, 257, 257, 256, 255, 254, 253, 252, 250, 248, 246, 243, 240, 236, 231, 225, 217, 207, 194 },
+			{ 180, 162, 146, 135, 127, 121, 117, 113, 111, 108, 107, 105, 104, 103, 102, 101, 101, 100, 99, 99, 99, 98, 98, 97, 97, 97, 97, 96, 96, 96, 96, 96, 95, 95, 95, 95, 95, 95, 95, 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 266, 266, 266, 266, 266, 266, 266, 266, 266, 266, 266, 265, 265, 265, 265, 265, 265, 265, 264, 264, 264, 264, 264, 263, 263, 263, 263, 262, 262, 261, 261, 261, 260, 259, 259, 258, 257, 256, 255, 253, 252, 249, 247, 243, 239, 233, 225, 214, 198 },
+			{ 180, 153, 135, 124, 117, 112, 108, 106, 104, 103, 101, 100, 99, 99, 98, 98, 97, 97, 96, 96, 96, 95, 95, 95, 95, 95, 94, 94, 94, 94, 94, 94, 94, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 266, 266, 266, 266, 266, 266, 266, 265, 265, 265, 265, 265, 264, 264, 264, 263, 263, 262, 262, 261, 261, 260, 259, 257, 256, 254, 252, 248, 243, 236, 225, 207 },
+			{ 180, 135, 117, 108, 104, 101, 99, 98, 97, 96, 96, 95, 95, 94, 94, 94, 94, 93, 93, 93, 93, 93, 93, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 268, 267, 267, 267, 267, 267, 267, 266, 266, 266, 266, 265, 265, 264, 264, 263, 262, 261, 259, 256, 252, 243, 225 }
+		};
+	}
+}
diff --git a/BizHawk.Client.EmuHawk/tools/VirtualPads/controls/VirtualPadAnalogStick.Designer.cs b/BizHawk.Client.EmuHawk/tools/VirtualPads/controls/VirtualPadAnalogStick.Designer.cs
index 2d3abd745e..88006ea0fc 100644
--- a/BizHawk.Client.EmuHawk/tools/VirtualPads/controls/VirtualPadAnalogStick.Designer.cs
+++ b/BizHawk.Client.EmuHawk/tools/VirtualPads/controls/VirtualPadAnalogStick.Designer.cs
@@ -62,16 +62,6 @@
 			// 
 			this.ManualX.Anchor = ((System.Windows.Forms.AnchorStyles)((System.Windows.Forms.AnchorStyles.Top | System.Windows.Forms.AnchorStyles.Right)));
 			this.ManualX.Location = new System.Drawing.Point(205, 3);
-			this.ManualX.Maximum = new decimal(new int[] {
-            127,
-            0,
-            0,
-            0});
-			this.ManualX.Minimum = new decimal(new int[] {
-            127,
-            0,
-            0,
-            -2147483648});
 			this.ManualX.Name = "ManualX";
 			this.ManualX.Size = new System.Drawing.Size(44, 20);
 			this.ManualX.TabIndex = 24;
@@ -91,16 +81,6 @@
 			// 
 			this.ManualY.Anchor = ((System.Windows.Forms.AnchorStyles)((System.Windows.Forms.AnchorStyles.Top | System.Windows.Forms.AnchorStyles.Right)));
 			this.ManualY.Location = new System.Drawing.Point(205, 29);
-			this.ManualY.Maximum = new decimal(new int[] {
-            127,
-            0,
-            0,
-            0});
-			this.ManualY.Minimum = new decimal(new int[] {
-            127,
-            0,
-            0,
-            -2147483648});
 			this.ManualY.Name = "ManualY";
 			this.ManualY.RightToLeft = System.Windows.Forms.RightToLeft.No;
 			this.ManualY.Size = new System.Drawing.Size(44, 20);
@@ -121,16 +101,6 @@
 			// 
 			this.MaxXNumeric.Anchor = ((System.Windows.Forms.AnchorStyles)((System.Windows.Forms.AnchorStyles.Top | System.Windows.Forms.AnchorStyles.Right)));
 			this.MaxXNumeric.Location = new System.Drawing.Point(205, 124);
-			this.MaxXNumeric.Maximum = new decimal(new int[] {
-            127,
-            0,
-            0,
-            0});
-			this.MaxXNumeric.Minimum = new decimal(new int[] {
-            127,
-            0,
-            0,
-            -2147483648});
 			this.MaxXNumeric.Name = "MaxXNumeric";
 			this.MaxXNumeric.Size = new System.Drawing.Size(44, 20);
 			this.MaxXNumeric.TabIndex = 28;
@@ -141,16 +111,6 @@
 			// 
 			this.MaxYNumeric.Anchor = ((System.Windows.Forms.AnchorStyles)((System.Windows.Forms.AnchorStyles.Top | System.Windows.Forms.AnchorStyles.Right)));
 			this.MaxYNumeric.Location = new System.Drawing.Point(205, 147);
-			this.MaxYNumeric.Maximum = new decimal(new int[] {
-            127,
-            0,
-            0,
-            0});
-			this.MaxYNumeric.Minimum = new decimal(new int[] {
-            127,
-            0,
-            0,
-            -2147483648});
 			this.MaxYNumeric.Name = "MaxYNumeric";
 			this.MaxYNumeric.RightToLeft = System.Windows.Forms.RightToLeft.No;
 			this.MaxYNumeric.Size = new System.Drawing.Size(44, 20);
@@ -171,13 +131,8 @@
 			// manualR
 			// 
 			this.manualR.Anchor = ((System.Windows.Forms.AnchorStyles)((System.Windows.Forms.AnchorStyles.Top | System.Windows.Forms.AnchorStyles.Right)));
-			this.manualR.DecimalPlaces = 2;
 			this.manualR.Location = new System.Drawing.Point(193, 58);
-			this.manualR.Maximum = new decimal(new int[] {
-            182,
-            0,
-            0,
-            0});
+			this.manualR.Maximum = 181.0M;
 			this.manualR.Name = "manualR";
 			this.manualR.Size = new System.Drawing.Size(56, 20);
 			this.manualR.TabIndex = 31;
@@ -185,18 +140,8 @@
 			// manualTheta
 			// 
 			this.manualTheta.Anchor = ((System.Windows.Forms.AnchorStyles)((System.Windows.Forms.AnchorStyles.Top | System.Windows.Forms.AnchorStyles.Right)));
-			this.manualTheta.DecimalPlaces = 2;
 			this.manualTheta.Location = new System.Drawing.Point(193, 84);
-			this.manualTheta.Maximum = new decimal(new int[] {
-            360,
-            0,
-            0,
-            0});
-			this.manualTheta.Minimum = new decimal(new int[] {
-            360,
-            0,
-            0,
-            -2147483648});
+			this.manualTheta.Maximum = 359.0M;
 			this.manualTheta.Name = "manualTheta";
 			this.manualTheta.Size = new System.Drawing.Size(56, 20);
 			this.manualTheta.TabIndex = 33;
@@ -209,7 +154,7 @@
 			this.thetaLabel.Name = "thetaLabel";
 			this.thetaLabel.Size = new System.Drawing.Size(20, 13);
 			this.thetaLabel.TabIndex = 32;
-			this.thetaLabel.Text = "θ °";
+			this.thetaLabel.Text = "θ (°)";
 			// 
 			// AnalogStick
 			// 
diff --git a/BizHawk.Client.EmuHawk/tools/VirtualPads/controls/VirtualPadAnalogStick.cs b/BizHawk.Client.EmuHawk/tools/VirtualPads/controls/VirtualPadAnalogStick.cs
index 026489f496..c4a50acad4 100644
--- a/BizHawk.Client.EmuHawk/tools/VirtualPads/controls/VirtualPadAnalogStick.cs
+++ b/BizHawk.Client.EmuHawk/tools/VirtualPads/controls/VirtualPadAnalogStick.cs
@@ -1,22 +1,37 @@
-using System;
+#nullable enable
+
+using System;
 using System.Windows.Forms;
 
 using BizHawk.Emulation.Common;
 using BizHawk.Client.Common;
-using BizHawk.Common.NumberExtensions;
+using BizHawk.Common;
 
 namespace BizHawk.Client.EmuHawk
 {
 	public partial class VirtualPadAnalogStick : UserControl, IVirtualPadControl
 	{
-		#region Fields
+		/// <summary>for coordinate transformation when non orthogonal (like PSX for example)</summary>
+		private int rangeAverageX;
 
-		private bool _programmaticallyUpdatingNumerics;
-		private bool _readonly;
-		private int rangeAverageX; //for coordinate transformation when non orthogonal (like PSX for example)
+		/// <inheritdoc cref="rangeAverageX"/>
 		private int rangeAverageY;
 
-		#endregion
+		private Range<int> _rangeX = AnalogStickPanel.DefaultRange;
+
+		private Range<int> _rangeY = AnalogStickPanel.DefaultRange;
+
+		private bool _readonly;
+
+		private bool _reverseX;
+
+		private bool _reverseY;
+
+		private bool _updatingFromAnalog;
+
+		private bool _updatingFromPolar;
+
+		private bool _updatingFromXY;
 
 		public VirtualPadAnalogStick()
 		{
@@ -29,54 +44,58 @@ namespace BizHawk.Client.EmuHawk
 			manualTheta.ValueChanged += PolarNumeric_Changed;
 		}
 
-		public float[] RangeX = { -128f, 0.0f, 127f };
-		public float[] RangeY = { -128f, 0.0f, 127f };
-		private bool ReverseX;
-		private bool ReverseY;
+		public float[] RangeX
+		{
+			set
+			{
+				if (value.Length != 3) throw new ArgumentException("must be float[3]", nameof(value));
+#if false
+				_midX = (int) value[1];
+#endif
+				_reverseX = value[2] < value[0];
+				_rangeX = _reverseX ? ((int) value[2]).RangeTo((int) value[0]) : ((int) value[0]).RangeTo((int) value[2]);
+			}
+		}
+
+		public float[] RangeY
+		{
+			set
+			{
+				if (value.Length != 3) throw new ArgumentException("must be float[3]", nameof(value));
+#if false
+				_midY = (int) value[1];
+#endif
+				_reverseY = value[2] < value[0];
+				_rangeY = _reverseY ? ((int) value[2]).RangeTo((int) value[0]) : ((int) value[0]).RangeTo((int) value[2]);
+			}
+		}
 
 		public string SecondaryName { get; set; }
 
-
 		private void VirtualPadAnalogStick_Load(object sender, EventArgs e)
 		{
-			AnalogStick.Name = Name;
-			AnalogStick.XName = Name;
-			AnalogStick.YName = !string.IsNullOrEmpty(SecondaryName)
-				? SecondaryName
-				: Name.Replace("X", "Y"); // Fallback
-			if (RangeX[0] > RangeX[2])
-			{
-				RangeX = new[] { RangeX[2], RangeX[1], RangeX[0] };
-				ReverseX = true;
-			}
-			AnalogStick.SetRangeX(RangeX);
-			if (RangeY[0] > RangeY[2])
-			{
-				RangeY = new[] { RangeY[2], RangeY[1], RangeY[0] };
-				ReverseY = true;
-			}
-			AnalogStick.SetRangeY(RangeY);
-
-			ManualX.Minimum = (decimal)RangeX[0];
-			ManualX.Maximum = (decimal)RangeX[2];
-
-			ManualY.Minimum = (decimal)RangeX[0];
-			ManualY.Maximum = (decimal)RangeX[2];
+			AnalogStick.XName = AnalogStick.Name = Name;
+			AnalogStick.SetRangeX(_rangeX);
+			AnalogStick.YName = !string.IsNullOrEmpty(SecondaryName) ? SecondaryName : Name.Replace("X", "Y");
+			AnalogStick.SetRangeY(_rangeY);
 
+			ManualX.Minimum = _rangeX.Start;
+			ManualX.Maximum = _rangeX.EndInclusive;
+			ManualY.Minimum = _rangeY.Start;
+			ManualY.Maximum = _rangeY.EndInclusive;
 			MaxXNumeric.Minimum = 1;
 			MaxXNumeric.Maximum = 100;
-			MaxXNumeric.Value = 100;
-
 			MaxYNumeric.Minimum = 1;
 			MaxYNumeric.Maximum = 100;
-			MaxYNumeric.Value = 100; // Note: these trigger change events that change the analog stick too
 
-			rangeAverageX = (int)((RangeX[0] + RangeX[2]) / 2);
-			rangeAverageY = (int)((RangeY[0] + RangeY[2]) / 2);
+			// these trigger Change events that set the analog stick's values too
+			MaxXNumeric.Value = 100;
+			MaxYNumeric.Value = 100;
+
+			rangeAverageX = (_rangeX.Start + _rangeX.EndInclusive) / 2;
+			rangeAverageY = (_rangeY.Start + _rangeY.EndInclusive) / 2;
 		}
 
-		#region IVirtualPadControl Implementation
-
 		public void UpdateValues()
 		{
 			// Nothing to do
@@ -103,43 +122,33 @@ namespace BizHawk.Client.EmuHawk
 			AnalogStick.HasValue = false;
 		}
 
-		public void Clear()
-		{
-			AnalogStick.Clear();
-		}
+		public void Clear() => AnalogStick.Clear();
 
 		public bool ReadOnly
 		{
 			get => _readonly;
-
 			set
 			{
-				if (_readonly != value)
-				{
-					XLabel.Enabled =
-						ManualX.Enabled =
-						YLabel.Enabled =
-						ManualY.Enabled =
-						MaxLabel.Enabled =
-						MaxXNumeric.Enabled =
-						MaxYNumeric.Enabled =
-						manualR.Enabled =
-						rLabel.Enabled =
-						manualTheta.Enabled =
-						thetaLabel.Enabled =
+				if (_readonly == value) return;
+				XLabel.Enabled =
+					ManualX.Enabled =
+					YLabel.Enabled =
+					ManualY.Enabled =
+					MaxLabel.Enabled =
+					MaxXNumeric.Enabled =
+					MaxYNumeric.Enabled =
+					manualR.Enabled =
+					rLabel.Enabled =
+					manualTheta.Enabled =
+					thetaLabel.Enabled =
 						!value;
-
-					AnalogStick.ReadOnly =
-						_readonly =
+				AnalogStick.ReadOnly =
+					_readonly =
 						value;
-
-					Refresh();
-				}
+				Refresh();
 			}
 		}
 
-		#endregion
-
 		public void Bump(int? x, int? y)
 		{
 			if (x.HasValue)
@@ -157,118 +166,90 @@ namespace BizHawk.Client.EmuHawk
 			SetNumericsFromAnalog();
 		}
 
-		public void SetPrevious(IController previous)
-		{
-			AnalogStick.SetPrevious(previous);
-		}
+		public void SetPrevious(IController previous) => AnalogStick.SetPrevious(previous);
 
 		private void ManualXY_ValueChanged(object sender, EventArgs e)
 		{
-			SetAnalogControlFromNumerics();
+			if (_updatingFromAnalog || _updatingFromPolar) return;
+			_updatingFromXY = true;
+
+			var x = (sbyte) ManualX.Value;
+			var y = (sbyte) ManualY.Value;
+			var (r, θ) = PolarRectConversion.RectToPolarLookup(x, y);
+			SetAnalog(x, y);
+			SetPolar(r, θ);
+
+			_updatingFromXY = false;
 		}
+
 		private void MaxManualXY_ValueChanged(object sender, EventArgs e)
-		{
-			SetAnalogMaxFromNumerics();
-		}
+			=> AnalogStick.SetUserRange(_reverseX ? -MaxXNumeric.Value : MaxXNumeric.Value, _reverseY ? -MaxYNumeric.Value : MaxYNumeric.Value);
 
 		private void PolarNumeric_Changed(object sender, EventArgs e)
 		{
-			ManualX.ValueChanged -= ManualXY_ValueChanged; //TODO is setting and checking a bool faster than subscription?
-			ManualY.ValueChanged -= ManualXY_ValueChanged;
+			if (_updatingFromAnalog || _updatingFromXY) return;
+			_updatingFromPolar = true;
 
-			var rect = PolarRectConversion.PolarDegToRect((double) manualR.Value, (double) manualTheta.Value);
-			rect = new Tuple<double, double>(
-				rangeAverageX + Math.Ceiling(rect.Item1).Clamp(-127, 127),
-				rangeAverageY + Math.Ceiling(rect.Item2).Clamp(-127, 127));
-			ManualX.Value = (decimal) rect.Item1;
-			ManualY.Value = (decimal) rect.Item2;
-			AnalogStick.X = (int) rect.Item1;
-			AnalogStick.Y = (int) rect.Item2;
-			AnalogStick.HasValue = true;
-			AnalogStick.Refresh();
+			var (x, y) = PolarRectConversion.PolarToRectLookup((ushort) manualR.Value, (ushort) manualTheta.Value);
+			var x1 = (rangeAverageX + x).ConstrainWithin(_rangeX);
+			var y1 = (rangeAverageY + y).ConstrainWithin(_rangeY);
+			SetAnalog(x1, y1);
+			SetXY(x1, y1);
 
-			ManualX.ValueChanged += ManualXY_ValueChanged;
-			ManualY.ValueChanged += ManualXY_ValueChanged;
+			_updatingFromPolar = false;
 		}
 
-		private void SetAnalogControlFromNumerics()
+		private void SetAnalog(int x, int y)
 		{
-			if (!_programmaticallyUpdatingNumerics)
-			{
-				AnalogStick.X = (int)ManualX.Value;
-				AnalogStick.Y = (int)ManualY.Value;
-				AnalogStick.HasValue = true;
-				AnalogStick.Refresh();
-			}
+			AnalogStick.X = x;
+			AnalogStick.Y = y;
+			AnalogStick.HasValue = true;
+			AnalogStick.Refresh();
+		}
+
+		/// <remarks>setting <see cref="NumericUpDown.Value"/> causes a draw, so we avoid it unless necessary</remarks>
+		private void SetPolar(decimal r, decimal θ)
+		{
+			if (manualR.Value != r) manualR.Value = r;
+			if (manualTheta.Value != θ) manualTheta.Value = θ;
+		}
+
+		/// <inheritdoc cref="SetPolar"/>
+		private void SetXY(decimal x, decimal y)
+		{
+			if (ManualX.Value != x) ManualX.Value = x;
+			if (ManualY.Value != y) ManualY.Value = y;
 		}
 
 		private void SetNumericsFromAnalog()
 		{
-			_programmaticallyUpdatingNumerics = true;
+			_updatingFromAnalog = true;
 
 			if (AnalogStick.HasValue)
 			{
-				// Setting .Value of a numeric causes a draw, so avoid it unless necessary
-				if (ManualX.Value != AnalogStick.X)
-				{
-					ManualX.Value = AnalogStick.X;
-				}
-
-				if (ManualY.Value != AnalogStick.Y)
-				{
-					ManualY.Value = AnalogStick.Y;
-				}
+				var x = AnalogStick.X - rangeAverageX;
+				var y = AnalogStick.Y - rangeAverageY;
+				var (r, θ) = PolarRectConversion.RectToPolarLookup((sbyte) x, (sbyte) y);
+				SetPolar(r, θ);
+				SetXY(x, y);
 			}
 			else
 			{
-				if (ManualX.Value != 0)
-				{
-					ManualX.Value = 0;
-				}
-
-				if (ManualY.Value != 0)
-				{
-					ManualY.Value = 0;
-				}
+				SetPolar(0, 0);
+				SetXY(0, 0);
 			}
 
-			manualR.ValueChanged -= PolarNumeric_Changed;
-			manualTheta.ValueChanged -= PolarNumeric_Changed;
-
-			var polar = PolarRectConversion.RectToPolarDeg(AnalogStick.X - rangeAverageX, AnalogStick.Y - rangeAverageY);
-			manualR.Value = (decimal) polar.Item1;
-			manualTheta.Value = (decimal) polar.Item2;
-
-			manualR.ValueChanged += PolarNumeric_Changed;
-			manualTheta.ValueChanged += PolarNumeric_Changed;
-
-			_programmaticallyUpdatingNumerics = false;
+			_updatingFromAnalog = false;
 		}
 
 		private void AnalogStick_MouseDown(object sender, MouseEventArgs e)
 		{
-			if (!ReadOnly)
-			{
-				_programmaticallyUpdatingNumerics = true;
-				SetNumericsFromAnalog();
-				_programmaticallyUpdatingNumerics = false;
-			}
+			if (!ReadOnly) SetNumericsFromAnalog();
 		}
 
 		private void AnalogStick_MouseMove(object sender, MouseEventArgs e)
 		{
-			if (!ReadOnly)
-			{
-				_programmaticallyUpdatingNumerics = true;
-				SetNumericsFromAnalog();
-				_programmaticallyUpdatingNumerics = false;
-			}
-		}
-
-		private void SetAnalogMaxFromNumerics()
-		{
-			if (!_programmaticallyUpdatingNumerics)
-				AnalogStick.SetUserRange(ReverseX ? -MaxXNumeric.Value : MaxXNumeric.Value, ReverseY ? -MaxYNumeric.Value : MaxYNumeric.Value);
+			if (!ReadOnly) SetNumericsFromAnalog();
 		}
 	}
 }
diff --git a/BizHawk.Client.EmuHawk/tools/VirtualPads/controls/components/AnalogStickPanel.cs b/BizHawk.Client.EmuHawk/tools/VirtualPads/controls/components/AnalogStickPanel.cs
index 0f853701ae..f2985163ef 100644
--- a/BizHawk.Client.EmuHawk/tools/VirtualPads/controls/components/AnalogStickPanel.cs
+++ b/BizHawk.Client.EmuHawk/tools/VirtualPads/controls/components/AnalogStickPanel.cs
@@ -54,24 +54,22 @@ namespace BizHawk.Client.EmuHawk
 			Refresh();
 		}
 
-		public void SetRangeX(float[] range)
+		public void SetRangeX(Range<int> range)
 		{
-			_actualRangeX.Start = (int) range[0];
-			_actualRangeX.EndInclusive = (int) range[2];
+			_actualRangeX = range;
 			Rerange();
 		}
 
-		public void SetRangeY(float[] range)
+		public void SetRangeY(Range<int> range)
 		{
-			_actualRangeY.Start = (int) range[0];
-			_actualRangeY.EndInclusive = (int) range[2];
+			_actualRangeY = range;
 			Rerange();
 		}
 
-		private readonly MutableRange<int> _rangeX = new MutableRange<int>(-128, 127);
-		private readonly MutableRange<int> _rangeY = new MutableRange<int>(-128, 127);
-		private MutableRange<int> _actualRangeX = (-128).MutableRangeTo(127);
-		private MutableRange<int> _actualRangeY = (-128).MutableRangeTo(127);
+		private Range<int> _rangeX = DefaultRange;
+		private Range<int> _rangeY = DefaultRange;
+		private Range<int> _actualRangeX = DefaultRange;
+		private Range<int> _actualRangeY = DefaultRange;
 
 		private bool _reverseX;
 		private bool _reverseY;
@@ -83,11 +81,11 @@ namespace BizHawk.Client.EmuHawk
 
 			var midX = (_actualRangeX.Start + _actualRangeX.EndInclusive) / 2.0;
 			var halfRangeX = (_reverseX ? -1 : 1) * (_actualRangeX.EndInclusive - _actualRangeX.Start) * _userRangePercentageX / 200.0;
-			_rangeX.Overwrite((int) (midX - halfRangeX), (int) (midX + halfRangeX));
+			_rangeX = ((int) (midX - halfRangeX)).RangeTo((int) (midX + halfRangeX));
 
 			var midY = (_actualRangeY.Start + _actualRangeY.EndInclusive) / 2.0;
 			var halfRangeY = (_reverseY ? -1 : 1) * (_actualRangeY.EndInclusive - _actualRangeY.Start) * _userRangePercentageY / 200.0;
-			_rangeY.Overwrite((int) (midY - halfRangeY), (int) (midY + halfRangeY));
+			_rangeY = ((int) (midY - halfRangeY)).RangeTo((int) (midY + halfRangeY));
 			
 			// re-constrain after changing ranges
 			X = X;
@@ -287,5 +285,7 @@ namespace BizHawk.Client.EmuHawk
 			HasValue = true;
 			Refresh();
 		}
+
+		internal static readonly Range<int> DefaultRange = (-128).RangeTo(127);
 	}
 }