diff --git a/lib/averages/dema/Dema.cs b/lib/averages/dema/Dema.cs
index 880c4984..d898720e 100644
--- a/lib/averages/dema/Dema.cs
+++ b/lib/averages/dema/Dema.cs
@@ -24,7 +24,7 @@ namespace QuanTAlib;
 [SkipLocalsInit]
 public sealed class Dema : ITValuePublisher
 {
-    private struct EmaState
+    private struct EmaState : IEquatable<EmaState>
     {
         public double Ema;
         public double E;
@@ -32,6 +32,20 @@ public sealed class Dema : ITValuePublisher
         public bool IsCompensated;
 
         public static EmaState New() => new() { Ema = 0, E = 1.0, IsHot = false, IsCompensated = false };
+
+        public override bool Equals(object? obj) => obj is EmaState other && Equals(other);
+
+        public bool Equals(EmaState other) =>
+            Ema == other.Ema &&
+            E == other.E &&
+            IsHot == other.IsHot &&
+            IsCompensated == other.IsCompensated;
+
+        public override int GetHashCode() => HashCode.Combine(Ema, E, IsHot, IsCompensated);
+
+        public static bool operator ==(EmaState left, EmaState right) => left.Equals(right);
+
+        public static bool operator !=(EmaState left, EmaState right) => !left.Equals(right);
     }
 
     private readonly double _alpha;
diff --git a/lib/averages/ema/Ema.cs b/lib/averages/ema/Ema.cs
index 13edbe7e..af98805f 100644
--- a/lib/averages/ema/Ema.cs
+++ b/lib/averages/ema/Ema.cs
@@ -27,7 +27,7 @@ namespace QuanTAlib;
 [SkipLocalsInit]
 public sealed class Ema : ITValuePublisher
 {
-    private struct State
+    private struct State : IEquatable<State>
     {
         public double Ema;
         public double E;
@@ -35,6 +35,20 @@ public sealed class Ema : ITValuePublisher
         public bool IsCompensated;
 
         public static State New() => new() { Ema = 0, E = 1.0, IsHot = false, IsCompensated = false };
+
+        public override bool Equals(object? obj) => obj is State other && Equals(other);
+
+        public bool Equals(State other) =>
+            Ema == other.Ema &&
+            E == other.E &&
+            IsHot == other.IsHot &&
+            IsCompensated == other.IsCompensated;
+
+        public override int GetHashCode() => HashCode.Combine(Ema, E, IsHot, IsCompensated);
+
+        public static bool operator ==(State left, State right) => left.Equals(right);
+
+        public static bool operator !=(State left, State right) => !left.Equals(right);
     }
 
     private readonly double _alpha;
diff --git a/lib/averages/hma/Hma.Tests.cs b/lib/averages/hma/Hma.Tests.cs
index 64d7ea40..f50bff4f 100644
--- a/lib/averages/hma/Hma.Tests.cs
+++ b/lib/averages/hma/Hma.Tests.cs
@@ -37,9 +37,9 @@ public class HmaTests
         // IsHot is defined as Full.IsHot && Sqrt.IsHot.
         // Full becomes hot after 9 updates.
         // Sqrt becomes hot after 3 updates.
-        // So HMA should be hot after 9 updates.
+        // So HMA should be hot after 9 + 3 - 1 = 11 updates.
 
-        for (int i = 0; i < 8; i++)
+        for (int i = 0; i < 10; i++)
         {
             hma.Update(new TValue(DateTime.UtcNow, 100));
             Assert.False(hma.IsHot);
diff --git a/lib/averages/hma/Hma.cs b/lib/averages/hma/Hma.cs
index d8552d02..93157a12 100644
--- a/lib/averages/hma/Hma.cs
+++ b/lib/averages/hma/Hma.cs
@@ -21,13 +21,15 @@ namespace QuanTAlib;
 public sealed class Hma : ITValuePublisher
 {
     private readonly int _period;
+    private readonly int _sqrtPeriod;
     private readonly Wma _wmaFull;
     private readonly Wma _wmaHalf;
     private readonly Wma _wmaSqrt;
+    private int _sampleCount;
 
     public string Name { get; }
     public TValue Last { get; private set; }
-    public bool IsHot => _wmaFull.IsHot && _wmaSqrt.IsHot;
+    public bool IsHot => _sampleCount >= _period + _sqrtPeriod - 1;
     public event Action<TValue>? Pub;
 
     public Hma(int period)
@@ -36,11 +38,11 @@ public sealed class Hma : ITValuePublisher
 
         _period = period;
         int halfPeriod = period / 2;
-        int sqrtPeriod = (int)Math.Sqrt(period);
+        _sqrtPeriod = (int)Math.Sqrt(period);
 
         _wmaFull = new Wma(period);
         _wmaHalf = new Wma(halfPeriod);
-        _wmaSqrt = new Wma(sqrtPeriod);
+        _wmaSqrt = new Wma(_sqrtPeriod);
 
         Name = $"Hma({period})";
     }
@@ -53,6 +55,8 @@ public sealed class Hma : ITValuePublisher
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
     public TValue Update(TValue input, bool isNew = true)
     {
+        if (isNew) _sampleCount++;
+
         // 1. Calculate WMA(n)
         TValue full = _wmaFull.Update(input, isNew);
 
@@ -188,6 +192,7 @@ public sealed class Hma : ITValuePublisher
         _wmaFull.Reset();
         _wmaHalf.Reset();
         _wmaSqrt.Reset();
+        _sampleCount = 0;
         Last = default;
     }
 }
diff --git a/lib/averages/t3/T3.cs b/lib/averages/t3/T3.cs
index cec59070..36e79027 100644
--- a/lib/averages/t3/T3.cs
+++ b/lib/averages/t3/T3.cs
@@ -26,15 +26,28 @@ namespace QuanTAlib;
 [SkipLocalsInit]
 public sealed class T3 : ITValuePublisher
 {
-    private struct State
+    private struct State : IEquatable<State>
     {
         public double E1, E2, E3, E4, E5, E6;
         public bool IsInitialized;
 
         public static State New() => new() { IsInitialized = false };
+
+        public override bool Equals(object? obj) => obj is State other && Equals(other);
+
+        public bool Equals(State other) =>
+            E1 == other.E1 && E2 == other.E2 && E3 == other.E3 &&
+            E4 == other.E4 && E5 == other.E5 && E6 == other.E6 &&
+            IsInitialized == other.IsInitialized;
+
+        public override int GetHashCode() => HashCode.Combine(E1, E2, E3, E4, E5, E6, IsInitialized);
+
+        public static bool operator ==(State left, State right) => left.Equals(right);
+
+        public static bool operator !=(State left, State right) => !left.Equals(right);
     }
 
-    private readonly struct Parameters
+    private readonly struct Parameters : IEquatable<Parameters>
     {
         public readonly double Alpha;
         public readonly double C1, C2, C3, C4;
@@ -47,6 +60,19 @@ public sealed class T3 : ITValuePublisher
             C3 = c3;
             C4 = c4;
         }
+
+        public override bool Equals(object? obj) => obj is Parameters other && Equals(other);
+
+        public bool Equals(Parameters other) =>
+            Alpha == other.Alpha &&
+            C1 == other.C1 && C2 == other.C2 &&
+            C3 == other.C3 && C4 == other.C4;
+
+        public override int GetHashCode() => HashCode.Combine(Alpha, C1, C2, C3, C4);
+
+        public static bool operator ==(Parameters left, Parameters right) => left.Equals(right);
+
+        public static bool operator !=(Parameters left, Parameters right) => !left.Equals(right);
     }
 
     private readonly Parameters _params;
diff --git a/lib/averages/tema/Tema.cs b/lib/averages/tema/Tema.cs
index d8ed2edf..6b7374f5 100644
--- a/lib/averages/tema/Tema.cs
+++ b/lib/averages/tema/Tema.cs
@@ -26,7 +26,7 @@ namespace QuanTAlib;
 [SkipLocalsInit]
 public sealed class Tema : ITValuePublisher
 {
-    private struct EmaState
+    private struct EmaState : IEquatable<EmaState>
     {
         public double Ema;
         public double E;
@@ -34,6 +34,20 @@ public sealed class Tema : ITValuePublisher
         public bool IsCompensated;
 
         public static EmaState New() => new() { Ema = 0, E = 1.0, IsHot = false, IsCompensated = false };
+
+        public override bool Equals(object? obj) => obj is EmaState other && Equals(other);
+
+        public bool Equals(EmaState other) =>
+            Ema == other.Ema &&
+            E == other.E &&
+            IsHot == other.IsHot &&
+            IsCompensated == other.IsCompensated;
+
+        public override int GetHashCode() => HashCode.Combine(Ema, E, IsHot, IsCompensated);
+
+        public static bool operator ==(EmaState left, EmaState right) => left.Equals(right);
+
+        public static bool operator !=(EmaState left, EmaState right) => !left.Equals(right);
     }
 
     private readonly double _alpha;