feat(engine)!: add audio latency reporting and tail compensation

src/Beutl.Engine/Animation/Easings/BackEaseIn.cs

@@ -2,6 +2,15 @@
 
 public sealed class BackEaseIn : Easing
 {
+    public override bool TryGetOutputRange(out float minimum, out float maximum)
+    {
+        // p^3 - p*sin(pi*p), with p in [0,1]. Since p^3 - p is minimized at
+        // -2/(3*sqrt(3)) ~= -0.3849 and sin(pi*p) <= 1, [-0.39, 1] is conservative.
+        minimum = -0.39f;
+        maximum = 1;
+        return true;
+    }
+
     public override float Ease(float progress)
     {
         return Funcs.BackEaseIn(progress);

src/Beutl.Engine/Animation/Easings/BackEaseInOut.cs

@@ -2,6 +2,13 @@
 
 public sealed class BackEaseInOut : Easing
 {
+    public override bool TryGetOutputRange(out float minimum, out float maximum)
+    {
+        minimum = -0.195f;
+        maximum = 1.195f;
+        return true;
+    }
+
     public override float Ease(float progress)
     {
         return Funcs.BackEaseInOut(progress);

src/Beutl.Engine/Animation/Easings/BackEaseOut.cs

@@ -2,6 +2,13 @@
 
 public sealed class BackEaseOut : Easing
 {
+    public override bool TryGetOutputRange(out float minimum, out float maximum)
+    {
+        minimum = 0;
+        maximum = 1.39f;
+        return true;
+    }
+
     public override float Ease(float progress)
     {
         return Funcs.BackEaseOut(progress);

src/Beutl.Engine/Animation/Easings/BounceEaseIn.cs

@@ -1,6 +1,6 @@
 namespace Beutl.Animation.Easings;
 
-public sealed class BounceEaseIn : Easing
+public sealed class BounceEaseIn : UnitRangeEasing
 {
     public override float Ease(float progress)
     {

src/Beutl.Engine/Animation/Easings/BounceEaseInOut.cs

@@ -1,6 +1,6 @@
 namespace Beutl.Animation.Easings;
 
-public sealed class BounceEaseInOut : Easing
+public sealed class BounceEaseInOut : UnitRangeEasing
 {
     public override float Ease(float progress)
     {

src/Beutl.Engine/Animation/Easings/BounceEaseOut.cs

@@ -1,6 +1,6 @@
 namespace Beutl.Animation.Easings;
 
-public sealed class BounceEaseOut : Easing
+public sealed class BounceEaseOut : UnitRangeEasing
 {
     public override float Ease(float progress)
     {

src/Beutl.Engine/Animation/Easings/CircularEaseIn.cs

@@ -1,6 +1,6 @@
 namespace Beutl.Animation.Easings;
 
-public sealed class CircularEaseIn : Easing
+public sealed class CircularEaseIn : UnitRangeEasing
 {
     public override float Ease(float progress)
     {

src/Beutl.Engine/Animation/Easings/CircularEaseInOut.cs

@@ -1,6 +1,6 @@
 namespace Beutl.Animation.Easings;
 
-public sealed class CircularEaseInOut : Easing
+public sealed class CircularEaseInOut : UnitRangeEasing
 {
     public override float Ease(float progress)
     {

src/Beutl.Engine/Animation/Easings/CircularEaseOut.cs

@@ -1,6 +1,6 @@
 namespace Beutl.Animation.Easings;
 
-public sealed class CircularEaseOut : Easing
+public sealed class CircularEaseOut : UnitRangeEasing
 {
     public override float Ease(float progress)
     {

src/Beutl.Engine/Animation/Easings/CubicEaseIn.cs

@@ -1,6 +1,6 @@
 namespace Beutl.Animation.Easings;
 
-public sealed class CubicEaseIn : Easing
+public sealed class CubicEaseIn : UnitRangeEasing
 {
     public override float Ease(float progress)
     {

src/Beutl.Engine/Animation/Easings/CubicEaseInOut.cs

@@ -1,6 +1,6 @@
 namespace Beutl.Animation.Easings;
 
-public sealed class CubicEaseInOut : Easing
+public sealed class CubicEaseInOut : UnitRangeEasing
 {
     public override float Ease(float progress)
     {

src/Beutl.Engine/Animation/Easings/CubicEaseOut.cs

@@ -1,6 +1,6 @@
 namespace Beutl.Animation.Easings;
 
-public sealed class CubicEaseOut : Easing
+public sealed class CubicEaseOut : UnitRangeEasing
 {
     public override float Ease(float progress)
     {

src/Beutl.Engine/Animation/Easings/Easing.cs

@@ -3,4 +3,19 @@
 public abstract class Easing
 {
     public abstract float Ease(float progress);
+
+    /// <summary>
+    /// Tries to provide conservative bounds for every value <see cref="Ease"/> can return when
+    /// <c>progress</c> is in the inclusive range [0, 1].
+    /// </summary>
+    /// <remarks>
+    /// Custom easings should override this when they can prove finite bounds. Consumers must treat
+    /// <see langword="false"/> as unbounded rather than estimating the range by sampling.
+    /// </remarks>
+    public virtual bool TryGetOutputRange(out float minimum, out float maximum)
+    {
+        minimum = default;
+        maximum = default;
+        return false;
+    }
 }

src/Beutl.Engine/Animation/Easings/ElasticEaseIn.cs

@@ -2,6 +2,13 @@
 
 public sealed class ElasticEaseIn : Easing
 {
+    public override bool TryGetOutputRange(out float minimum, out float maximum)
+    {
+        minimum = -1;
+        maximum = 1;
+        return true;
+    }
+
     public override float Ease(float progress)
     {
         return Funcs.ElasticEaseIn(progress);

src/Beutl.Engine/Animation/Easings/ElasticEaseInOut.cs

@@ -2,6 +2,13 @@
 
 public sealed class ElasticEaseInOut : Easing
 {
+    public override bool TryGetOutputRange(out float minimum, out float maximum)
+    {
+        minimum = -0.5f;
+        maximum = 1.5f;
+        return true;
+    }
+
     public override float Ease(float progress)
     {
         return Funcs.ElasticEaseInOut(progress);

src/Beutl.Engine/Animation/Easings/ElasticEaseOut.cs

@@ -2,6 +2,13 @@
 
 public sealed class ElasticEaseOut : Easing
 {
+    public override bool TryGetOutputRange(out float minimum, out float maximum)
+    {
+        minimum = 0;
+        maximum = 2;
+        return true;
+    }
+
     public override float Ease(float progress)
     {
         return Funcs.ElasticEaseOut(progress);

src/Beutl.Engine/Animation/Easings/ExponentialEaseIn.cs

@@ -1,6 +1,6 @@
 namespace Beutl.Animation.Easings;
 
-public sealed class ExponentialEaseIn : Easing
+public sealed class ExponentialEaseIn : UnitRangeEasing
 {
     public override float Ease(float progress)
     {

src/Beutl.Engine/Animation/Easings/ExponentialEaseInOut.cs

@@ -1,6 +1,6 @@
 namespace Beutl.Animation.Easings;
 
-public sealed class ExponentialEaseInOut : Easing
+public sealed class ExponentialEaseInOut : UnitRangeEasing
 {
     public override float Ease(float progress)
     {

src/Beutl.Engine/Animation/Easings/ExponentialEaseOut.cs

@@ -1,6 +1,6 @@
 namespace Beutl.Animation.Easings;
 
-public sealed class ExponentialEaseOut : Easing
+public sealed class ExponentialEaseOut : UnitRangeEasing
 {
     public override float Ease(float progress)
     {

src/Beutl.Engine/Animation/Easings/HoldEasing.cs

@@ -1,6 +1,6 @@
 namespace Beutl.Animation.Easings;
 
-public sealed class HoldEasing : Easing
+public sealed class HoldEasing : UnitRangeEasing
 {
     public override float Ease(float progress)
     {

src/Beutl.Engine/Animation/Easings/LinearEasing.cs

@@ -1,6 +1,6 @@
 namespace Beutl.Animation.Easings;
 
-public sealed class LinearEasing : Easing
+public sealed class LinearEasing : UnitRangeEasing
 {
     public override float Ease(float progress)
     {

src/Beutl.Engine/Animation/Easings/QuadraticEaseIn.cs

@@ -1,6 +1,6 @@
 namespace Beutl.Animation.Easings;
 
-public sealed class QuadraticEaseIn : Easing
+public sealed class QuadraticEaseIn : UnitRangeEasing
 {
     public override float Ease(float progress)
     {

src/Beutl.Engine/Animation/Easings/QuadraticEaseInOut.cs

@@ -1,6 +1,6 @@
 namespace Beutl.Animation.Easings;
 
-public sealed class QuadraticEaseInOut : Easing
+public sealed class QuadraticEaseInOut : UnitRangeEasing
 {
     public override float Ease(float progress)
     {

src/Beutl.Engine/Animation/Easings/QuadraticEaseOut.cs

@@ -1,6 +1,6 @@
 namespace Beutl.Animation.Easings;
 
-public sealed class QuadraticEaseOut : Easing
+public sealed class QuadraticEaseOut : UnitRangeEasing
 {
     public override float Ease(float progress)
     {

src/Beutl.Engine/Animation/Easings/QuarticEaseIn.cs

@@ -1,6 +1,6 @@
 namespace Beutl.Animation.Easings;
 
-public sealed class QuarticEaseIn : Easing
+public sealed class QuarticEaseIn : UnitRangeEasing
 {
     public override float Ease(float progress)
     {

src/Beutl.Engine/Animation/Easings/QuarticEaseInOut.cs

@@ -1,6 +1,6 @@
 namespace Beutl.Animation.Easings;
 
-public sealed class QuarticEaseInOut : Easing
+public sealed class QuarticEaseInOut : UnitRangeEasing
 {
     public override float Ease(float progress)
     {

src/Beutl.Engine/Animation/Easings/QuarticEaseOut.cs

@@ -1,6 +1,6 @@
 namespace Beutl.Animation.Easings;
 
-public sealed class QuarticEaseOut : Easing
+public sealed class QuarticEaseOut : UnitRangeEasing
 {
     public override float Ease(float progress)
     {

src/Beutl.Engine/Animation/Easings/QuinticEaseIn.cs

@@ -1,6 +1,6 @@
 namespace Beutl.Animation.Easings;
 
-public sealed class QuinticEaseIn : Easing
+public sealed class QuinticEaseIn : UnitRangeEasing
 {
     public override float Ease(float progress)
     {

src/Beutl.Engine/Animation/Easings/QuinticEaseInOut.cs

@@ -1,6 +1,6 @@
 namespace Beutl.Animation.Easings;
 
-public sealed class QuinticEaseInOut : Easing
+public sealed class QuinticEaseInOut : UnitRangeEasing
 {
     public override float Ease(float progress)
     {

src/Beutl.Engine/Animation/Easings/QuinticEaseOut.cs

@@ -1,6 +1,6 @@
 namespace Beutl.Animation.Easings;
 
-public sealed class QuinticEaseOut : Easing
+public sealed class QuinticEaseOut : UnitRangeEasing
 {
     public override float Ease(float progress)
     {

src/Beutl.Engine/Animation/Easings/SineEaseIn.cs

@@ -1,6 +1,6 @@
 namespace Beutl.Animation.Easings;
 
-public sealed class SineEaseIn : Easing
+public sealed class SineEaseIn : UnitRangeEasing
 {
     public override float Ease(float progress)
     {

src/Beutl.Engine/Animation/Easings/SineEaseInOut.cs

@@ -1,6 +1,6 @@
 namespace Beutl.Animation.Easings;
 
-public sealed class SineEaseInOut : Easing
+public sealed class SineEaseInOut : UnitRangeEasing
 {
     public override float Ease(float progress)
     {

src/Beutl.Engine/Animation/Easings/SineEaseOut.cs

@@ -1,6 +1,6 @@
 namespace Beutl.Animation.Easings;
 
-public sealed class SineEaseOut : Easing
+public sealed class SineEaseOut : UnitRangeEasing
 {
     public override float Ease(float progress)
     {

src/Beutl.Engine/Animation/Easings/SplineEasing.cs

@@ -66,6 +66,14 @@ public float Y2
 
     private readonly KeySpline _internalKeySpline;
 
+    public override bool TryGetOutputRange(out float minimum, out float maximum)
+    {
+        // A cubic Bézier curve stays inside the convex hull of its control points.
+        minimum = Math.Min(0, Math.Min(Y1, Math.Min(Y2, 1)));
+        maximum = Math.Max(0, Math.Max(Y1, Math.Max(Y2, 1)));
+        return float.IsFinite(minimum) && float.IsFinite(maximum);
+    }
+
     public override float Ease(float progress)
     {
         return _internalKeySpline.GetSplineProgress(progress);

src/Beutl.Engine/Animation/Easings/UnitRangeEasing.cs

@@ -0,0 +1,12 @@
+namespace Beutl.Animation.Easings;
+
+/// <summary>An easing whose output is guaranteed to stay in [0, 1] for progress in [0, 1].</summary>
+public abstract class UnitRangeEasing : Easing
+{
+    public sealed override bool TryGetOutputRange(out float minimum, out float maximum)
+    {
+        minimum = 0;
+        maximum = 1;
+        return true;
+    }
+}