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adding missing validations
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Miha Kralj
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// FFT: Fast Fourier Transform — Dominant Cycle Detector
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// Estimates the dominant cycle period in bars using a DFT on a windowed price buffer.
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// Algorithm: Ehlers, J.F. "Cycle Analytics for Traders." Wiley, 2013.
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// Hanning-windowed DFT across bins [minBin..maxBin], with parabolic interpolation
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// for sub-bin period estimation. Output: dominant cycle period in bars (clamped).
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using System.Buffers;
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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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/// FFT: Fast Fourier Transform Dominant Cycle Detector
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/// Computes the dominant cycle period using a Hanning-windowed DFT
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/// over a rolling price buffer, with parabolic interpolation refinement.
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/// </summary>
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/// <remarks>
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/// Key properties:
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/// - Output: dominant cycle period in bars, clamped to [minPeriod, maxPeriod]
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/// - windowSize must be 32, 64, or 128
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/// - WarmupPeriod = windowSize bars
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/// - No allocation in Update (RingBuffer + precomputed Hanning weights)
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/// - Parabolic interpolation on peak bin for sub-bin accuracy
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/// </remarks>
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[SkipLocalsInit]
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public sealed class Fft : AbstractBase
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{
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private readonly int _windowSize;
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private readonly int _minPeriod;
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private readonly int _maxPeriod;
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private readonly int _minBin;
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private readonly int _maxBin;
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private readonly double _twoPiOverN;
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private readonly double[] _hanning;
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private readonly RingBuffer _buffer;
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[StructLayout(LayoutKind.Auto)]
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private record struct State(double LastValid);
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private State _state, _p_state;
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public override bool IsHot => _buffer.Count >= _windowSize;
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/// <summary>
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/// Initializes a new Fft indicator.
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/// </summary>
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/// <param name="windowSize">DFT window size in bars. Must be 32, 64, or 128. Default 64.</param>
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/// <param name="minPeriod">Minimum detectable cycle period. Must be >= 2. Default 4.</param>
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/// <param name="maxPeriod">Maximum detectable cycle period. Must be <= windowSize/2. Default 32.</param>
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public Fft(int windowSize = 64, int minPeriod = 4, int maxPeriod = 32)
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{
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if (windowSize != 32 && windowSize != 64 && windowSize != 128)
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{
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throw new ArgumentException("windowSize must be 32, 64, or 128", nameof(windowSize));
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}
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if (minPeriod < 2)
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{
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throw new ArgumentException("minPeriod must be >= 2", nameof(minPeriod));
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}
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if (maxPeriod > windowSize / 2)
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{
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throw new ArgumentException($"maxPeriod must be <= windowSize/2 ({windowSize / 2})", nameof(maxPeriod));
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}
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_windowSize = windowSize;
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_minPeriod = minPeriod;
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_maxPeriod = maxPeriod;
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_twoPiOverN = 2.0 * Math.PI / windowSize;
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// bin k corresponds to period N/k; k=minBin → period=N/minBin=maxPeriod, k=maxBin → period=N/maxBin=minPeriod
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_minBin = Math.Max(1, windowSize / maxPeriod);
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_maxBin = Math.Min(windowSize / 2, windowSize / minPeriod);
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// Precompute Hanning window: w[n] = 0.5 - 0.5*cos(2π*n/N), n=0..N-1
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_hanning = new double[windowSize];
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for (int n = 0; n < windowSize; n++)
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{
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_hanning[n] = 0.5 - 0.5 * Math.Cos(_twoPiOverN * n);
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}
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_buffer = new RingBuffer(windowSize);
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Name = $"Fft({windowSize},{minPeriod},{maxPeriod})";
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WarmupPeriod = windowSize;
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_state = new State((minPeriod + maxPeriod) * 0.5);
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_p_state = _state;
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}
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/// <summary>
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/// Initializes a new Fft indicator with source for event-based chaining.
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/// </summary>
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/// <param name="source">Source indicator for chaining</param>
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/// <param name="windowSize">DFT window size. Must be 32, 64, or 128. Default 64.</param>
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/// <param name="minPeriod">Minimum detectable period. Must be >= 2. Default 4.</param>
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/// <param name="maxPeriod">Maximum detectable period. Must be <= windowSize/2. Default 32.</param>
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public Fft(ITValuePublisher source, int windowSize = 64, int minPeriod = 4, int maxPeriod = 32)
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: this(windowSize, minPeriod, maxPeriod)
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{
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source.Pub += HandleUpdate;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private void HandleUpdate(object? sender, in TValueEventArgs e) => Update(e.Value, e.IsNew);
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private double ComputeDominantPeriod()
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{
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var span = _buffer.GetSpan();
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int n = _windowSize;
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double maxMag = 0.0;
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int peakBin = _minBin;
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double magBefore = 0.0;
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double magAtPeak = 0.0;
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double magAfter = 0.0;
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for (int k = _minBin; k <= _maxBin; k++)
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{
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double omegaK = _twoPiOverN * k;
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double re = 0.0;
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double im = 0.0;
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for (int idx = 0; idx < n; idx++)
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{
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// span[0]=oldest, span[n-1]=newest
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// n=0 in DFT = current (newest): map DFT-n to span index (n-1-dftN)
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// span[n-1-dftN]: dftN=0 → span[n-1] (newest), dftN=n-1 → span[0] (oldest)
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double val = span[n - 1 - idx];
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double xw = val * _hanning[idx];
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double angle = omegaK * idx;
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double cosA = Math.Cos(angle);
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double sinA = Math.Sin(angle);
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re = Math.FusedMultiplyAdd(xw, cosA, re);
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im = Math.FusedMultiplyAdd(xw, -sinA, im);
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}
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double mag = Math.FusedMultiplyAdd(re, re, im * im);
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if (mag > maxMag)
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{
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magBefore = magAtPeak;
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magAfter = 0.0;
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maxMag = mag;
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magAtPeak = mag;
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peakBin = k;
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}
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else if (peakBin > 0 && magAfter == 0.0)
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{
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magAfter = mag;
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}
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}
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// Parabolic interpolation for sub-bin refinement
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double denom = magBefore + 2.0 * maxMag + magAfter;
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double shift = (denom > 0.0) ? (magBefore - magAfter) / denom : 0.0;
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double dominantPeriod = (double)_windowSize / (peakBin + shift);
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// Clamp to [minPeriod, maxPeriod]
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return Math.Clamp(dominantPeriod, _minPeriod, _maxPeriod);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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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_state = _state;
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}
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else
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{
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_state = _p_state;
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}
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double value = input.Value;
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double result;
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if (double.IsFinite(value))
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{
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_buffer.Add(value, isNew);
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if (IsHot)
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{
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result = ComputeDominantPeriod();
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_state = new State(result);
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}
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else
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{
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result = _state.LastValid;
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}
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}
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else
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{
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result = _state.LastValid;
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}
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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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var result = new TSeries(source.Count);
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ReadOnlySpan<double> values = source.Values;
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ReadOnlySpan<long> times = source.Times;
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for (int i = 0; i < source.Count; i++)
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{
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var tv = Update(new TValue(new DateTime(times[i], DateTimeKind.Utc), values[i]), true);
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result.Add(tv, true);
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}
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return result;
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}
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public override void Prime(ReadOnlySpan<double> source, TimeSpan? step = null)
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{
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TimeSpan interval = step ?? TimeSpan.FromSeconds(1);
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DateTime time = DateTime.UtcNow - (interval * source.Length);
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for (int i = 0; i < source.Length; i++)
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{
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Update(new TValue(time, source[i]), true);
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time += interval;
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}
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}
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public static TSeries Batch(TSeries source, int windowSize = 64, int minPeriod = 4, int maxPeriod = 32)
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{
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var indicator = new Fft(windowSize, minPeriod, maxPeriod);
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return indicator.Update(source);
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}
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/// <summary>
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/// Computes dominant cycle period over a span of values using a sliding Hanning-windowed DFT.
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/// Uses stackalloc for Hanning weights when windowSize <= 64, otherwise ArrayPool.
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/// </summary>
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public static void Batch(
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ReadOnlySpan<double> src, Span<double> output,
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int windowSize = 64, int minPeriod = 4, int maxPeriod = 32)
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{
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if (src.Length == 0)
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{
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throw new ArgumentException("Source cannot be empty", nameof(src));
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}
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if (output.Length < src.Length)
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{
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throw new ArgumentException("Output length must be >= source length", nameof(output));
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}
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if (windowSize != 32 && windowSize != 64 && windowSize != 128)
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{
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throw new ArgumentException("windowSize must be 32, 64, or 128", nameof(windowSize));
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}
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if (minPeriod < 2)
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{
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throw new ArgumentException("minPeriod must be >= 2", nameof(minPeriod));
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}
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if (maxPeriod > windowSize / 2)
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{
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throw new ArgumentException($"maxPeriod must be <= windowSize/2", nameof(maxPeriod));
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}
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double twoPiOverN = 2.0 * Math.PI / windowSize;
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int minBin = Math.Max(1, windowSize / maxPeriod);
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int maxBin = Math.Min(windowSize / 2, windowSize / minPeriod);
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double defaultPeriod = (minPeriod + maxPeriod) * 0.5;
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double lastValid = defaultPeriod;
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const int StackallocThreshold = 64;
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double[]? rentedW = null;
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scoped Span<double> hanning;
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if (windowSize <= StackallocThreshold)
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{
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hanning = stackalloc double[windowSize];
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}
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else
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{
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rentedW = ArrayPool<double>.Shared.Rent(windowSize);
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hanning = rentedW.AsSpan(0, windowSize);
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}
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try
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{
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for (int n = 0; n < windowSize; n++)
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{
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hanning[n] = 0.5 - 0.5 * Math.Cos(twoPiOverN * n);
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}
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for (int i = 0; i < src.Length; i++)
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{
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double val = src[i];
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if (!double.IsFinite(val))
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{
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output[i] = lastValid;
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continue;
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}
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if (i < windowSize - 1)
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{
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output[i] = lastValid;
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continue;
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}
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double maxMag = 0.0;
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int peakBin = minBin;
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double magBefore = 0.0;
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double magAtPeak = 0.0;
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double magAfter = 0.0;
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for (int k = minBin; k <= maxBin; k++)
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{
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double omegaK = twoPiOverN * k;
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double re = 0.0;
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double im = 0.0;
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for (int dftN = 0; dftN < windowSize; dftN++)
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{
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// dftN=0 → newest (src[i]), dftN=windowSize-1 → oldest (src[start])
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double v = src[i - dftN];
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if (!double.IsFinite(v))
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{
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v = lastValid;
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}
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double xw = v * hanning[dftN];
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double angle = omegaK * dftN;
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re = Math.FusedMultiplyAdd(xw, Math.Cos(angle), re);
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im = Math.FusedMultiplyAdd(xw, -Math.Sin(angle), im);
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}
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double mag = Math.FusedMultiplyAdd(re, re, im * im);
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if (mag > maxMag)
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{
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magBefore = magAtPeak;
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magAfter = 0.0;
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maxMag = mag;
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magAtPeak = mag;
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peakBin = k;
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}
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else if (peakBin > 0 && magAfter == 0.0)
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{
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magAfter = mag;
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}
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}
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double denom = magBefore + 2.0 * maxMag + magAfter;
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double shift = (denom > 0.0) ? (magBefore - magAfter) / denom : 0.0;
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double dominant = (double)windowSize / (peakBin + shift);
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double clamped = Math.Clamp(dominant, minPeriod, maxPeriod);
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lastValid = clamped;
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output[i] = clamped;
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}
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}
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finally
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{
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if (rentedW != null)
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{
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ArrayPool<double>.Shared.Return(rentedW);
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}
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}
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}
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public static (TSeries Results, Fft Indicator) Calculate(
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TSeries source, int windowSize = 64, int minPeriod = 4, int maxPeriod = 32)
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{
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var indicator = new Fft(windowSize, minPeriod, maxPeriod);
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TSeries results = indicator.Update(source);
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return (results, indicator);
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}
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public override void Reset()
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{
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_buffer.Clear();
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_state = new State((_minPeriod + _maxPeriod) * 0.5);
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_p_state = _state;
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Last = default;
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}
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}
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