fix(input): map POSIX stick endpoints exactly (#244)

src/SharpEmu.Libs/Pad/HostWindowInput.cs

@@ -253,9 +253,9 @@ public static class HostWindowInput
         };
     }
 
-    private static byte ToStickByte(float value)
+    internal static byte ToStickByte(float value)
     {
-        return (byte)Math.Clamp((int)(128.0f + value * 127.0f), 0, 255);
+        return (byte)Math.Clamp((int)MathF.Round((value + 1.0f) * 127.5f), 0, 255);
     }
 
     private static HostGamepadButtons MapButton(ButtonName name) => name switch

tests/SharpEmu.Libs.Tests/Pad/HostWindowInputTests.cs

@@ -0,0 +1,19 @@
+// Copyright (C) 2026 SharpEmu Emulator Project
+// SPDX-License-Identifier: GPL-2.0-or-later
+
+using SharpEmu.Libs.Pad;
+using Xunit;
+
+namespace SharpEmu.Libs.Tests.Pad;
+
+public sealed class HostWindowInputTests
+{
+    [Theory]
+    [InlineData(-1.0f, 0)]
+    [InlineData(0.0f, 128)]
+    [InlineData(1.0f, 255)]
+    public void ToStickByteMapsFullSilkRange(float value, int expected)
+    {
+        Assert.Equal((byte)expected, HostWindowInput.ToStickByte(value));
+    }
+}