mirror of
https://github.com/mihakralj/QuanTAlib.git
synced 2026-08-13 08:08:05 +00:00
588 lines
18 KiB
C#
588 lines
18 KiB
C#
using System.Runtime.CompilerServices;
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using System.Runtime.InteropServices;
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namespace QuanTAlib;
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/// <summary>
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/// QEMA: Quad Exponential Moving Average
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/// </summary>
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/// <remarks>
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/// Four cascaded EMAs with progressive alphas combined using zero-lag optimized weights.
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/// Minimizes energy while achieving zero DC lag through Lagrange optimization.
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///
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/// Key features: progressive alpha ramp (α^(1/4) spacing), bias-corrected EMAs, O(1) streaming.
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/// </remarks>
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/// <seealso href="Qema.md">Detailed documentation</seealso>
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[SkipLocalsInit]
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public sealed class Qema : AbstractBase
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{
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[StructLayout(LayoutKind.Auto)]
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private record struct EmaState(double Ema, double E, bool IsHot, bool IsCompensated)
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{
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public static EmaState New() => new() { Ema = 0, E = 1.0, IsHot = false, IsCompensated = false };
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}
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private readonly double _alpha1, _alpha2, _alpha3, _alpha4;
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private readonly double _decay1, _decay2, _decay3, _decay4;
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private EmaState _state1 = EmaState.New();
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private EmaState _state2 = EmaState.New();
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private EmaState _state3 = EmaState.New();
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private EmaState _state4 = EmaState.New();
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private EmaState _p_state1 = EmaState.New();
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private EmaState _p_state2 = EmaState.New();
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private EmaState _p_state3 = EmaState.New();
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private EmaState _p_state4 = EmaState.New();
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private readonly TValuePublishedHandler _handler;
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private double _lastValidValue;
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private double _p_lastValidValue;
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private const double COVERAGE_THRESHOLD = 0.05;
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private const double COMPENSATOR_THRESHOLD = 1e-10;
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private const double DEGENERATE_THRESHOLD = 1e-12;
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/// <summary>
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/// True when the slowest EMA (stage 1) has warmed up and is providing valid results.
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/// </summary>
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public override bool IsHot => _state1.E <= COVERAGE_THRESHOLD;
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/// <summary>
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/// Creates QEMA with specified period.
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/// Alpha1 = 2 / (period + 1), with progressive alphas ramped geometrically.
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/// </summary>
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/// <param name="period">Period for base EMA calculation (must be > 0)</param>
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public Qema(int period)
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{
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ArgumentOutOfRangeException.ThrowIfNegativeOrZero(period);
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_alpha1 = Clamp01(2.0 / (period + 1));
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// Progressive alpha ramp: r = (1/α₁)^(1/4) → α₂=α₁^(3/4), α₃=α₁^(1/2), α₄=α₁^(1/4)
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double r = Math.Pow(1.0 / _alpha1, 0.25);
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_alpha2 = Clamp01(_alpha1 * r);
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_alpha3 = Clamp01(_alpha2 * r);
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_alpha4 = Clamp01(_alpha3 * r);
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_decay1 = 1.0 - _alpha1;
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_decay2 = 1.0 - _alpha2;
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_decay3 = 1.0 - _alpha3;
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_decay4 = 1.0 - _alpha4;
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Name = $"Qema({period})";
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WarmupPeriod = period;
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_handler = Handle;
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}
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/// <summary>
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/// Creates QEMA with specified source and period.
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/// Subscribes to source.Pub event.
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/// </summary>
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/// <param name="source">Source to subscribe to</param>
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/// <param name="period">Period for base EMA calculation</param>
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public Qema(ITValuePublisher source, int period) : this(period)
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{
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source.Pub += _handler;
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}
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/// <summary>
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/// Creates QEMA with specified source TSeries and period.
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/// Primes with historical data and subscribes to updates.
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/// </summary>
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/// <param name="source">Source TSeries</param>
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/// <param name="period">Period for base EMA calculation</param>
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public Qema(TSeries source, int period) : this(period)
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{
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Prime(source.Values);
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if (source.Count > 0)
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{
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Last = new TValue(source.LastTime, Last.Value);
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}
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source.Pub += _handler;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static double Clamp01(double x) => Math.Min(1.0, Math.Max(x, DEGENERATE_THRESHOLD));
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static double Lag(double alpha) => (1.0 - alpha) / alpha;
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private void Handle(object? sender, in TValueEventArgs e) => Update(e.Value, e.IsNew);
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/// <summary>
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/// Initializes the indicator state using the provided history.
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/// </summary>
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/// <param name="source">Historical data</param>
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/// <param name="step">Optional time step (not used)</param>
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public override void Prime(ReadOnlySpan<double> source, TimeSpan? step = null)
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{
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if (source.Length == 0)
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{
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return;
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}
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// Reset state
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_state1 = EmaState.New();
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_state2 = EmaState.New();
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_state3 = EmaState.New();
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_state4 = EmaState.New();
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_p_state1 = EmaState.New();
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_p_state2 = EmaState.New();
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_p_state3 = EmaState.New();
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_p_state4 = EmaState.New();
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_lastValidValue = 0;
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_p_lastValidValue = 0;
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int len = source.Length;
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double lastValid = 0;
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// Find first finite value
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for (int i = 0; i < len; i++)
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{
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if (double.IsFinite(source[i]))
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{
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lastValid = source[i];
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break;
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}
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}
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EmaState s1 = _state1;
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EmaState s2 = _state2;
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EmaState s3 = _state3;
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EmaState s4 = _state4;
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for (int i = 0; i < len; i++)
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{
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double val = source[i];
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if (double.IsFinite(val))
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{
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lastValid = val;
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}
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else
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{
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val = lastValid;
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}
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double e1 = ComputeEma(val, _alpha1, _decay1, ref s1);
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double e2 = ComputeEma(e1, _alpha2, _decay2, ref s2);
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double e3 = ComputeEma(e2, _alpha3, _decay3, ref s3);
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ComputeEma(e3, _alpha4, _decay4, ref s4);
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}
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_state1 = s1;
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_state2 = s2;
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_state3 = s3;
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_state4 = s4;
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_lastValidValue = lastValid;
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// Calculate final output
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double e1_final = GetCompensated(_state1);
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double e2_final = GetCompensated(_state2);
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double e3_final = GetCompensated(_state3);
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double e4_final = GetCompensated(_state4);
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var (w1, w2, w3, w4) = ComputeWeights(_alpha1, _alpha2, _alpha3, _alpha4);
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double result = Math.FusedMultiplyAdd(w1, e1_final, Math.FusedMultiplyAdd(w2, e2_final, Math.FusedMultiplyAdd(w3, e3_final, w4 * e4_final)));
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Last = new TValue(DateTime.MinValue, result);
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_p_state1 = _state1;
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_p_state2 = _state2;
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_p_state3 = _state3;
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_p_state4 = _state4;
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_p_lastValidValue = _lastValidValue;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static double GetCompensated(EmaState s)
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{
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if (s.IsCompensated)
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{
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return s.Ema;
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}
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return s.Ema / (1.0 - s.E);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
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public override TValue Update(TValue input, bool isNew = true)
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{
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if (isNew)
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{
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_p_state1 = _state1;
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_p_state2 = _state2;
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_p_state3 = _state3;
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_p_state4 = _state4;
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_p_lastValidValue = _lastValidValue;
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}
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else
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{
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_state1 = _p_state1;
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_state2 = _p_state2;
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_state3 = _p_state3;
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_state4 = _p_state4;
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_lastValidValue = _p_lastValidValue;
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}
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double val = input.Value;
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if (double.IsFinite(val))
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{
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_lastValidValue = val;
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}
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else
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{
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val = _lastValidValue;
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}
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// Cascaded EMAs
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double e1 = ComputeEma(val, _alpha1, _decay1, ref _state1);
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double e2 = ComputeEma(e1, _alpha2, _decay2, ref _state2);
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double e3 = ComputeEma(e2, _alpha3, _decay3, ref _state3);
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double e4 = ComputeEma(e3, _alpha4, _decay4, ref _state4);
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// Compute weights and combine
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var (w1, w2, w3, w4) = ComputeWeights(_alpha1, _alpha2, _alpha3, _alpha4);
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double result = Math.FusedMultiplyAdd(w1, e1, Math.FusedMultiplyAdd(w2, e2, Math.FusedMultiplyAdd(w3, e3, w4 * e4)));
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Last = new TValue(input.Time, result);
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PubEvent(Last, isNew);
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return Last;
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}
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public override TSeries Update(TSeries source)
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{
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if (source.Count == 0)
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{
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return [];
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}
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int len = source.Count;
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List<long> t = new(len);
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List<double> v = new(len);
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CollectionsMarshal.SetCount(t, len);
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CollectionsMarshal.SetCount(v, len);
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var tSpan = CollectionsMarshal.AsSpan(t);
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var vSpan = CollectionsMarshal.AsSpan(v);
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source.Times.CopyTo(tSpan);
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var sourceValues = source.Values;
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EmaState s1 = _state1;
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EmaState s2 = _state2;
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EmaState s3 = _state3;
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EmaState s4 = _state4;
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double lastValid = _lastValidValue;
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var (w1, w2, w3, w4) = ComputeWeights(_alpha1, _alpha2, _alpha3, _alpha4);
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for (int i = 0; i < len; i++)
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{
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double val = sourceValues[i];
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if (double.IsFinite(val))
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{
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lastValid = val;
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}
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else
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{
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val = lastValid;
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}
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double e1 = ComputeEma(val, _alpha1, _decay1, ref s1);
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double e2 = ComputeEma(e1, _alpha2, _decay2, ref s2);
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double e3 = ComputeEma(e2, _alpha3, _decay3, ref s3);
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double e4 = ComputeEma(e3, _alpha4, _decay4, ref s4);
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vSpan[i] = Math.FusedMultiplyAdd(w1, e1, Math.FusedMultiplyAdd(w2, e2, Math.FusedMultiplyAdd(w3, e3, w4 * e4)));
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}
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_state1 = s1;
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_state2 = s2;
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_state3 = s3;
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_state4 = s4;
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_p_state1 = s1;
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_p_state2 = s2;
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_p_state3 = s3;
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_p_state4 = s4;
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_lastValidValue = lastValid;
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_p_lastValidValue = lastValid;
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Last = new TValue(tSpan[len - 1], vSpan[len - 1]);
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return new TSeries(t, v);
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}
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/// <summary>
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/// Computes the bias-corrected EMA value and updates state.
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/// </summary>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static double ComputeEma(double input, double alpha, double decay, ref EmaState state)
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{
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state.Ema = Math.FusedMultiplyAdd(state.Ema, decay, alpha * input);
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double result;
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if (!state.IsCompensated)
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{
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state.E *= decay;
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if (!state.IsHot && state.E <= COVERAGE_THRESHOLD)
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{
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state.IsHot = true;
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}
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if (state.E <= COMPENSATOR_THRESHOLD)
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{
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state.IsCompensated = true;
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result = state.Ema;
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}
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else
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{
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result = state.Ema / (1.0 - state.E);
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}
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}
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else
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{
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result = state.Ema;
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}
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return result;
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}
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/// <summary>
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/// Computes Option A weights for minimum energy with zero DC lag constraint.
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/// Solves: Σw = 1, Σw·L = 0 (δ=0 for zero lag)
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/// </summary>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static (double w1, double w2, double w3, double w4) ComputeWeights(double a1, double a2, double a3, double a4)
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{
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double t1 = Lag(a1);
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double t2 = Lag(a2);
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double t3 = Lag(a3);
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double t4 = Lag(a4);
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// Cumulative lags
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double L1 = t1;
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double L2 = t1 + t2;
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double L3 = L2 + t3;
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double L4 = L3 + t4;
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// Option A: min-energy with constraints Σw=1, Σw·L=δ (δ=0)
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double B = L1 + L2 + L3 + L4;
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double C = Math.FusedMultiplyAdd(L1, L1, Math.FusedMultiplyAdd(L2, L2, Math.FusedMultiplyAdd(L3, L3, L4 * L4)));
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double D = Math.FusedMultiplyAdd(4.0, C, -B * B);
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double w1, w2, w3, w4;
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if (Math.Abs(D) < DEGENERATE_THRESHOLD)
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{
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// Degenerate case (e.g., alpha=1 → all L=0): output is EMA1≈input
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w1 = 1.0;
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w2 = 0.0;
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w3 = 0.0;
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w4 = 0.0;
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}
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else
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{
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double lambda = C / D;
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double mu = -B / D;
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w1 = Math.FusedMultiplyAdd(mu, L1, lambda);
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w2 = Math.FusedMultiplyAdd(mu, L2, lambda);
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w3 = Math.FusedMultiplyAdd(mu, L3, lambda);
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w4 = Math.FusedMultiplyAdd(mu, L4, lambda);
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}
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return (w1, w2, w3, w4);
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}
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/// <summary>
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/// Calculates QEMA for the entire series using a new instance.
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/// </summary>
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/// <param name="source">Input series</param>
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/// <param name="period">QEMA period</param>
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/// <returns>QEMA series</returns>
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public static TSeries Batch(TSeries source, int period)
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{
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var qema = new Qema(period);
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return qema.Update(source);
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}
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/// <summary>
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/// Calculates QEMA in-place using period, writing results to pre-allocated output span.
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/// Zero-allocation method for maximum performance.
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/// </summary>
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/// <param name="source">Input values</param>
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/// <param name="output">Output span (must be same length as source)</param>
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/// <param name="period">QEMA period (must be > 0)</param>
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[MethodImpl(MethodImplOptions.AggressiveOptimization)]
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public static void Batch(ReadOnlySpan<double> source, Span<double> output, int period)
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{
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if (source.Length != output.Length)
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{
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throw new ArgumentException("Source and output must have the same length", nameof(output));
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}
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ArgumentOutOfRangeException.ThrowIfNegativeOrZero(period);
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if (source.Length == 0)
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{
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return;
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}
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double alpha1 = Clamp01(2.0 / (period + 1));
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double r = Math.Pow(1.0 / alpha1, 0.25);
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double alpha2 = Clamp01(alpha1 * r);
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double alpha3 = Clamp01(alpha2 * r);
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double alpha4 = Clamp01(alpha3 * r);
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double decay1 = 1.0 - alpha1;
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double decay2 = 1.0 - alpha2;
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double decay3 = 1.0 - alpha3;
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double decay4 = 1.0 - alpha4;
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double lastValid = 0;
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// Find first finite value
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for (int i = 0; i < source.Length; i++)
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{
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if (double.IsFinite(source[i]))
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{
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lastValid = source[i];
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break;
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}
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}
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// EMA states
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double ema1_val = 0, ema1_e = 1.0;
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bool ema1_compensated = false;
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double ema2_val = 0, ema2_e = 1.0;
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bool ema2_compensated = false;
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double ema3_val = 0, ema3_e = 1.0;
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bool ema3_compensated = false;
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double ema4_val = 0, ema4_e = 1.0;
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bool ema4_compensated = false;
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var (w1, w2, w3, w4) = ComputeWeights(alpha1, alpha2, alpha3, alpha4);
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for (int i = 0; i < source.Length; i++)
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{
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double val = source[i];
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if (double.IsFinite(val))
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{
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lastValid = val;
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}
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else
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{
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val = lastValid;
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}
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// EMA1
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ema1_val = Math.FusedMultiplyAdd(ema1_val, decay1, alpha1 * val);
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double e1;
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if (!ema1_compensated)
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{
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ema1_e *= decay1;
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if (ema1_e <= COMPENSATOR_THRESHOLD)
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{
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ema1_compensated = true;
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e1 = ema1_val;
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}
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else
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{
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e1 = ema1_val / (1.0 - ema1_e);
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}
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}
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else
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{
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e1 = ema1_val;
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}
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// EMA2
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ema2_val = Math.FusedMultiplyAdd(ema2_val, decay2, alpha2 * e1);
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double e2;
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if (!ema2_compensated)
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{
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ema2_e *= decay2;
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if (ema2_e <= COMPENSATOR_THRESHOLD)
|
||
{
|
||
ema2_compensated = true;
|
||
e2 = ema2_val;
|
||
}
|
||
else
|
||
{
|
||
e2 = ema2_val / (1.0 - ema2_e);
|
||
}
|
||
}
|
||
else
|
||
{
|
||
e2 = ema2_val;
|
||
}
|
||
|
||
// EMA3
|
||
ema3_val = Math.FusedMultiplyAdd(ema3_val, decay3, alpha3 * e2);
|
||
double e3;
|
||
if (!ema3_compensated)
|
||
{
|
||
ema3_e *= decay3;
|
||
if (ema3_e <= COMPENSATOR_THRESHOLD)
|
||
{
|
||
ema3_compensated = true;
|
||
e3 = ema3_val;
|
||
}
|
||
else
|
||
{
|
||
e3 = ema3_val / (1.0 - ema3_e);
|
||
}
|
||
}
|
||
else
|
||
{
|
||
e3 = ema3_val;
|
||
}
|
||
|
||
// EMA4
|
||
ema4_val = Math.FusedMultiplyAdd(ema4_val, decay4, alpha4 * e3);
|
||
double e4;
|
||
if (!ema4_compensated)
|
||
{
|
||
ema4_e *= decay4;
|
||
if (ema4_e <= COMPENSATOR_THRESHOLD)
|
||
{
|
||
ema4_compensated = true;
|
||
e4 = ema4_val;
|
||
}
|
||
else
|
||
{
|
||
e4 = ema4_val / (1.0 - ema4_e);
|
||
}
|
||
}
|
||
else
|
||
{
|
||
e4 = ema4_val;
|
||
}
|
||
|
||
output[i] = Math.FusedMultiplyAdd(w1, e1, Math.FusedMultiplyAdd(w2, e2, Math.FusedMultiplyAdd(w3, e3, w4 * e4)));
|
||
}
|
||
}
|
||
|
||
public static (TSeries Results, Qema Indicator) Calculate(TSeries source, int period)
|
||
{
|
||
var indicator = new Qema(period);
|
||
TSeries results = indicator.Update(source);
|
||
return (results, indicator);
|
||
}
|
||
|
||
/// <summary>
|
||
/// Resets the QEMA state.
|
||
/// </summary>
|
||
public override void Reset()
|
||
{
|
||
_state1 = EmaState.New();
|
||
_state2 = EmaState.New();
|
||
_state3 = EmaState.New();
|
||
_state4 = EmaState.New();
|
||
_p_state1 = EmaState.New();
|
||
_p_state2 = EmaState.New();
|
||
_p_state3 = EmaState.New();
|
||
_p_state4 = EmaState.New();
|
||
_lastValidValue = 0;
|
||
_p_lastValidValue = 0;
|
||
Last = default;
|
||
}
|
||
} |