mirror of
https://github.com/mihakralj/QuanTAlib.git
synced 2026-08-14 08:38:04 +00:00
Miha Kralj
b3a64f18fa
- Added Ztest class to compute the one-sample t-statistic using sample standard deviation with Bessel correction. - Implemented validation tests for Ztest to ensure accuracy against manual calculations and PineScript. - Updated documentation for Ztest, detailing its mathematical foundation, performance profile, and common pitfalls. - Adjusted NDepend badges to reflect changes in code metrics after implementation. - Updated missing indicators report to reflect the completion of statistical indicators, including ZTEST.
662 lines
23 KiB
C#
662 lines
23 KiB
C#
using System.Runtime.CompilerServices;
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using System.Runtime.InteropServices;
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using System.Runtime.Intrinsics;
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using System.Runtime.Intrinsics.X86;
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namespace QuanTAlib;
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/// <summary>
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/// Kurtosis: Measures the tailedness (heaviness of tails) of the probability distribution
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/// of a real-valued random variable.
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/// </summary>
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/// <remarks>
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/// This implementation calculates excess kurtosis (kurtosis - 3), so a normal distribution
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/// has excess kurtosis of 0.
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///
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/// Interpretation:
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/// - Positive (leptokurtic): Heavier tails than normal, more extreme events
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/// - Zero (mesokurtic): Normal distribution tail behavior
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/// - Negative (platykurtic): Lighter tails than normal, fewer extreme events
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///
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/// Formula (population excess kurtosis):
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/// g₂ = m₄ / m₂² - 3
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///
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/// where:
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/// m₂ = (1/n) Σ(xᵢ - μ)² (second central moment)
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/// m₄ = (1/n) Σ(xᵢ - μ)⁴ (fourth central moment)
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///
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/// Sample excess kurtosis applies Fisher's correction:
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/// G₂ = ((n-1)/((n-2)(n-3))) * ((n+1)*g₂ + 6)
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///
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/// Implementation uses O(1) running sums of powers (x, x², x³, x⁴) to avoid
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/// recomputing from the buffer each tick.
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/// </remarks>
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[SkipLocalsInit]
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public sealed class Kurtosis : AbstractBase
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{
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private readonly int _period;
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private readonly RingBuffer _buffer;
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private readonly bool _isPopulation;
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private double _sum;
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private double _sumSq;
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private double _sumCu;
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private double _sumQu;
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private int _updateCount;
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private const int ResyncInterval = 1000;
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private const double Epsilon = 1e-10;
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public override bool IsHot => _buffer.IsFull;
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/// <summary>
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/// Creates a new Kurtosis indicator.
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/// </summary>
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/// <param name="period">The lookback period (must be >= 4).</param>
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/// <param name="isPopulation">If true, calculates Population Kurtosis. If false, Sample Kurtosis (default).</param>
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public Kurtosis(int period, bool isPopulation = false)
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{
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if (period < 4)
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{
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throw new ArgumentOutOfRangeException(nameof(period), "Period must be greater than or equal to 4 for Kurtosis.");
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}
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_period = period;
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_isPopulation = isPopulation;
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_buffer = new RingBuffer(period);
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Name = $"Kurtosis({period})";
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WarmupPeriod = period;
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}
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/// <summary>
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/// Creates a chained Kurtosis indicator.
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/// </summary>
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/// <param name="source">The source indicator to chain from.</param>
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/// <param name="period">The lookback period.</param>
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/// <param name="isPopulation">If true, calculates Population Kurtosis.</param>
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public Kurtosis(ITValuePublisher source, int period, bool isPopulation = false) : this(period, isPopulation)
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{
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ArgumentNullException.ThrowIfNull(source);
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source.Pub += HandleInput;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private void HandleInput(object? sender, in TValueEventArgs e)
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{
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Update(e.Value);
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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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// Snapshot current state for rollback
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double p_sum = _sum;
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double p_sumSq = _sumSq;
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double p_sumCu = _sumCu;
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double p_sumQu = _sumQu;
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if (isNew)
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{
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if (_buffer.IsFull)
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{
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double oldVal = _buffer.Oldest;
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double oldSq = oldVal * oldVal;
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_sum -= oldVal;
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_sumSq -= oldSq;
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_sumCu -= oldSq * oldVal;
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_sumQu -= oldSq * oldSq;
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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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val = _buffer.Count > 0 ? _buffer.Newest : 0;
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}
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_buffer.Add(val);
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double valSq = val * val;
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_sum += val;
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_sumSq += valSq;
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_sumCu += valSq * val;
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_sumQu += valSq * valSq;
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_updateCount++;
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if (_updateCount % ResyncInterval == 0)
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{
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Resync();
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}
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}
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else
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{
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// Restore previous state before applying correction
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_sum = p_sum;
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_sumSq = p_sumSq;
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_sumCu = p_sumCu;
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_sumQu = p_sumQu;
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double oldNewest = _buffer.Newest;
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_buffer.UpdateNewest(input.Value);
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double val = input.Value;
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double valSq = val * val;
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double oldSq = oldNewest * oldNewest;
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_sum = _sum - oldNewest + val;
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_sumSq = _sumSq - oldSq + valSq;
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_sumCu = _sumCu - (oldSq * oldNewest) + (valSq * val);
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_sumQu = _sumQu - (oldSq * oldSq) + (valSq * valSq);
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}
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double kurtosis = 0;
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if (_buffer.Count >= 4)
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{
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double n = _buffer.Count;
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double mean = _sum / n;
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// Second central moment (variance): m₂ = Σ(x-μ)²/n
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// = (SumSq - Sum²/n) / n
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double m2Numerator = _sumSq - (_sum * _sum) / n;
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if (m2Numerator < Epsilon)
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{
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m2Numerator = 0;
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}
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double m2 = m2Numerator / n;
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if (m2 > Epsilon)
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{
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// Fourth central moment: m₄ = Σ(x-μ)⁴/n
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// Expanding (x-μ)⁴ = x⁴ - 4x³μ + 6x²μ² - 4xμ³ + μ⁴
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// m₄ = SumQu/n - 4·mean·SumCu/n + 6·mean²·SumSq/n - 3·mean⁴
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// Note: last term -4·mean³·Sum/n + mean⁴ = -4·mean⁴ + mean⁴ = -3·mean⁴
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double meanSq = mean * mean;
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double m4 = _sumQu / n
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- 4.0 * mean * _sumCu / n
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+ 6.0 * meanSq * _sumSq / n
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- 3.0 * meanSq * meanSq;
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// Population excess kurtosis: g₂ = m₄/m₂² - 3
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double g2 = (m4 / (m2 * m2)) - 3.0;
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if (_isPopulation)
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{
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kurtosis = g2;
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}
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else
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{
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// Sample excess kurtosis (Fisher's correction):
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// G₂ = ((n-1)/((n-2)(n-3))) · ((n+1)·g₂ + 6)
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double denom = (n - 2.0) * (n - 3.0);
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if (Math.Abs(denom) > Epsilon)
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{
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kurtosis = ((n - 1.0) / denom) * ((n + 1.0) * g2 + 6.0);
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}
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}
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}
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}
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Last = new TValue(input.Time, kurtosis);
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PubEvent(Last);
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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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var t = new List<long>(len);
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var v = new List<double>(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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Batch(source.Values, vSpan, _period, _isPopulation);
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source.Times.CopyTo(tSpan);
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// Reset running state before priming
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_buffer.Clear();
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_sum = 0;
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_sumSq = 0;
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_sumCu = 0;
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_sumQu = 0;
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_updateCount = 0;
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// Prime the state
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int primeStart = Math.Max(0, len - _period);
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for (int i = primeStart; i < len; i++)
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{
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Update(source[i]);
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}
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return new TSeries(t, v);
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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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_sum = 0;
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_sumSq = 0;
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_sumCu = 0;
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_sumQu = 0;
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_updateCount = 0;
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Last = default;
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}
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private void Resync()
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{
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double sum = 0;
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double sumSq = 0;
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double sumCu = 0;
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double sumQu = 0;
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var span = _buffer.GetSpan();
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for (int i = 0; i < span.Length; i++)
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{
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double val = span[i];
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double valSq = val * val;
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sum += val;
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sumSq += valSq;
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sumCu += valSq * val;
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sumQu += valSq * valSq;
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}
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_sum = sum;
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_sumSq = sumSq;
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_sumCu = sumCu;
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_sumQu = sumQu;
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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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DateTime ts = DateTime.MinValue;
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foreach (double value in source)
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{
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Update(new TValue(ts, value));
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if (step.HasValue)
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{
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ts = ts.Add(step.Value);
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}
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}
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}
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public static TSeries Batch(TSeries source, int period, bool isPopulation = false)
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{
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var kurtosis = new Kurtosis(period, isPopulation);
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return kurtosis.Update(source);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static void Batch(ReadOnlySpan<double> source, Span<double> output, int period, bool isPopulation = false)
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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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if (period < 4)
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{
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throw new ArgumentException("Period must be greater than or equal to 4", nameof(period));
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}
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int len = source.Length;
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if (len == 0)
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{
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return;
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}
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// SIMD path for large, clean datasets
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const int SimdThreshold = 256;
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if (len >= SimdThreshold && Avx2.IsSupported && !source.ContainsNonFinite())
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{
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CalculateAvx2Core(source, output, period, isPopulation);
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return;
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}
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// Scalar path
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CalculateScalarCore(source, output, period, isPopulation);
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}
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public static (TSeries Results, Kurtosis Indicator) Calculate(TSeries source, int period, bool isPopulation = false)
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{
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var indicator = new Kurtosis(period, isPopulation);
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TSeries results = indicator.Update(source);
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return (results, indicator);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static double CalculateKurtosisFromSums(double sum, double sumSq, double sumCu, double sumQu, double n, bool isPopulation)
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{
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double mean = sum / n;
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double m2Numerator = sumSq - (sum * sum) / n;
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if (m2Numerator < Epsilon)
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{
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return 0;
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}
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double m2 = m2Numerator / n;
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if (m2 <= Epsilon)
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{
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return 0;
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}
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// Fourth central moment via raw moments
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double meanSq = mean * mean;
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double m4 = sumQu / n
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- 4.0 * mean * sumCu / n
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+ 6.0 * meanSq * sumSq / n
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- 3.0 * meanSq * meanSq;
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double g2 = (m4 / (m2 * m2)) - 3.0;
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if (isPopulation)
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{
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return g2;
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}
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// Fisher's correction for sample excess kurtosis
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double denom = (n - 2.0) * (n - 3.0);
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if (Math.Abs(denom) < Epsilon)
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{
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return 0;
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}
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return ((n - 1.0) / denom) * ((n + 1.0) * g2 + 6.0);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static void CalculateScalarCore(ReadOnlySpan<double> source, Span<double> output, int period, bool isPopulation)
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{
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int len = source.Length;
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double sum = 0;
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double sumSq = 0;
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double sumCu = 0;
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double sumQu = 0;
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int i = 0;
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// Warmup phase
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int warmupEnd = Math.Min(period, len);
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for (; i < warmupEnd; 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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val = 0;
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}
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double valSq = val * val;
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sum += val;
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sumSq += valSq;
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sumCu += valSq * val;
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sumQu += valSq * valSq;
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double n = i + 1;
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output[i] = (n >= 4) ? CalculateKurtosisFromSums(sum, sumSq, sumCu, sumQu, n, isPopulation) : 0;
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}
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// Sliding window phase
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int tickCount = period;
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for (; 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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val = 0;
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}
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double oldVal = source[i - period];
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if (!double.IsFinite(oldVal))
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{
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oldVal = 0;
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}
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double valSq = val * val;
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double oldSq = oldVal * oldVal;
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sum = sum - oldVal + val;
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sumSq = sumSq - oldSq + valSq;
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sumCu = sumCu - (oldSq * oldVal) + (valSq * val);
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sumQu = sumQu - (oldSq * oldSq) + (valSq * valSq);
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output[i] = CalculateKurtosisFromSums(sum, sumSq, sumCu, sumQu, period, isPopulation);
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tickCount++;
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if (tickCount >= ResyncInterval)
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{
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tickCount = 0;
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double recalcSum = 0;
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double recalcSumSq = 0;
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double recalcSumCu = 0;
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double recalcSumQu = 0;
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int startIdx = i - period + 1;
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for (int k = 0; k < period; k++)
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{
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double v = source[startIdx + k];
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if (!double.IsFinite(v))
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{
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v = 0;
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}
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double vSq = v * v;
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recalcSum += v;
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recalcSumSq += vSq;
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recalcSumCu += vSq * v;
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recalcSumQu += vSq * vSq;
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}
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sum = recalcSum;
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sumSq = recalcSumSq;
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sumCu = recalcSumCu;
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sumQu = recalcSumQu;
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}
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}
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static void WarmupKurtosis(int period, bool isPopulation, ref double srcRef, ref double outRef, out double sum, out double sumSq, out double sumCu, out double sumQu)
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{
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sum = 0;
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sumSq = 0;
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sumCu = 0;
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sumQu = 0;
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for (int i = 0; i < period; i++)
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{
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double val = Unsafe.Add(ref srcRef, i);
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double valSq = val * val;
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sum += val;
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sumSq += valSq;
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sumCu += valSq * val;
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sumQu += valSq * valSq;
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double n = i + 1;
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Unsafe.Add(ref outRef, i) = (n >= 4) ? CalculateKurtosisFromSums(sum, sumSq, sumCu, sumQu, n, isPopulation) : 0;
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}
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}
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[MethodImpl(MethodImplOptions.AggressiveOptimization)]
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private static void CalculateAvx2Core(ReadOnlySpan<double> source, Span<double> output, int period, bool isPopulation)
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{
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int len = source.Length;
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const int VectorWidth = 4;
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ref double srcRef = ref MemoryMarshal.GetReference(source);
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ref double outRef = ref MemoryMarshal.GetReference(output);
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double invN = 1.0 / period;
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double n = period;
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WarmupKurtosis(period, isPopulation, ref srcRef, ref outRef, out double sum, out double sumSq, out double sumCu, out double sumQu);
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if (len <= period)
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{
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return;
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}
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var vInvN = Vector256.Create(invN);
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var vThree = Vector256.Create(3.0);
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var vFour = Vector256.Create(4.0);
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var vSix = Vector256.Create(6.0);
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var vEpsilon = Vector256.Create(Epsilon);
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var vZero = Vector256<double>.Zero;
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// Fisher's correction constants
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double fisherNum = isPopulation ? 1.0 : (n - 1.0);
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double fisherDenom = isPopulation ? 1.0 : ((n - 2.0) * (n - 3.0));
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double fisherNp1 = isPopulation ? 1.0 : (n + 1.0);
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double fisherAdd = isPopulation ? 0.0 : 6.0;
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var vFisherScale = Vector256.Create(isPopulation ? 1.0 : fisherNum / fisherDenom);
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var vFisherNp1 = Vector256.Create(isPopulation ? 1.0 : fisherNp1);
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var vFisherAdd = Vector256.Create(fisherAdd);
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int simdEnd = period + ((len - period) / VectorWidth) * VectorWidth;
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int tickCount = period;
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for (int i = period; i < simdEnd; i += VectorWidth)
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{
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var vNew = Vector256.LoadUnsafe(ref Unsafe.Add(ref srcRef, i));
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var vOld = Vector256.LoadUnsafe(ref Unsafe.Add(ref srcRef, i - period));
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// Deltas for Sum
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var vDelta = Avx.Subtract(vNew, vOld);
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// Deltas for SumSq
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var vNewSq = Avx.Multiply(vNew, vNew);
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var vOldSq = Avx.Multiply(vOld, vOld);
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var vDeltaSq = Avx.Subtract(vNewSq, vOldSq);
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// Deltas for SumCu
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var vNewCu = Avx.Multiply(vNewSq, vNew);
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var vOldCu = Avx.Multiply(vOldSq, vOld);
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var vDeltaCu = Avx.Subtract(vNewCu, vOldCu);
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// Deltas for SumQu
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var vNewQu = Avx.Multiply(vNewSq, vNewSq);
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var vOldQu = Avx.Multiply(vOldSq, vOldSq);
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var vDeltaQu = Avx.Subtract(vNewQu, vOldQu);
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// Prefix sum for Sum
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var vShift1 = Avx2.Permute4x64(vDelta.AsUInt64(), 0b_10_01_00_00).AsDouble(); // skipcq: CS-R1131 - SIMD prefix sum pattern requires specific permutation
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vShift1 = Avx.Blend(vZero, vShift1, 0b_1110);
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var vP1 = Avx.Add(vDelta, vShift1);
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var vShift2 = Avx2.Permute4x64(vP1.AsUInt64(), 0b_01_00_00_00).AsDouble(); // skipcq: CS-R1131 - SIMD prefix sum pattern requires specific permutation
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vShift2 = Avx.Blend(vZero, vShift2, 0b_1100);
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var vP2 = Avx.Add(vP1, vShift2);
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var vSums = Avx.Add(Vector256.Create(sum), vP2);
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// Prefix sum for SumSq
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var vShiftSq1 = Avx2.Permute4x64(vDeltaSq.AsUInt64(), 0b_10_01_00_00).AsDouble(); // skipcq: CS-R1131 - SIMD prefix sum pattern requires specific permutation
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vShiftSq1 = Avx.Blend(vZero, vShiftSq1, 0b_1110);
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var vP1Sq = Avx.Add(vDeltaSq, vShiftSq1);
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var vShiftSq2 = Avx2.Permute4x64(vP1Sq.AsUInt64(), 0b_01_00_00_00).AsDouble(); // skipcq: CS-R1131 - SIMD prefix sum pattern requires specific permutation
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vShiftSq2 = Avx.Blend(vZero, vShiftSq2, 0b_1100);
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var vP2Sq = Avx.Add(vP1Sq, vShiftSq2);
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var vSumSqs = Avx.Add(Vector256.Create(sumSq), vP2Sq);
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// Prefix sum for SumCu
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var vShiftCu1 = Avx2.Permute4x64(vDeltaCu.AsUInt64(), 0b_10_01_00_00).AsDouble(); // skipcq: CS-R1131 - SIMD prefix sum pattern requires specific permutation
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vShiftCu1 = Avx.Blend(vZero, vShiftCu1, 0b_1110);
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var vP1Cu = Avx.Add(vDeltaCu, vShiftCu1);
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var vShiftCu2 = Avx2.Permute4x64(vP1Cu.AsUInt64(), 0b_01_00_00_00).AsDouble(); // skipcq: CS-R1131 - SIMD prefix sum pattern requires specific permutation
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vShiftCu2 = Avx.Blend(vZero, vShiftCu2, 0b_1100);
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var vP2Cu = Avx.Add(vP1Cu, vShiftCu2);
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var vSumCus = Avx.Add(Vector256.Create(sumCu), vP2Cu);
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// Prefix sum for SumQu
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var vShiftQu1 = Avx2.Permute4x64(vDeltaQu.AsUInt64(), 0b_10_01_00_00).AsDouble(); // skipcq: CS-R1131 - SIMD prefix sum pattern requires specific permutation
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vShiftQu1 = Avx.Blend(vZero, vShiftQu1, 0b_1110);
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var vP1Qu = Avx.Add(vDeltaQu, vShiftQu1);
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var vShiftQu2 = Avx2.Permute4x64(vP1Qu.AsUInt64(), 0b_01_00_00_00).AsDouble(); // skipcq: CS-R1131 - SIMD prefix sum pattern requires specific permutation
|
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vShiftQu2 = Avx.Blend(vZero, vShiftQu2, 0b_1100);
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var vP2Qu = Avx.Add(vP1Qu, vShiftQu2);
|
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var vSumQus = Avx.Add(Vector256.Create(sumQu), vP2Qu);
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|
|
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// Calculate Kurtosis
|
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var vMean = Avx.Multiply(vSums, vInvN);
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var vMeanSq = Avx.Multiply(vMean, vMean);
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|
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// m2 = (SumSq - Sum²/n) / n
|
|
var vSumSquared = Avx.Multiply(vSums, vSums);
|
|
var vM2Num = Fma.IsSupported
|
|
? Fma.MultiplyAddNegated(vSumSquared, vInvN, vSumSqs)
|
|
: Avx.Subtract(vSumSqs, Avx.Multiply(vSumSquared, vInvN));
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vM2Num = Avx.Max(vZero, vM2Num);
|
|
var vM2 = Avx.Multiply(vM2Num, vInvN);
|
|
|
|
// m4 = SumQu/n - 4·mean·SumCu/n + 6·mean²·SumSq/n - 3·mean⁴
|
|
var vTerm1 = Avx.Multiply(vSumQus, vInvN);
|
|
var vTerm2 = Avx.Multiply(vFour, Avx.Multiply(vMean, Avx.Multiply(vSumCus, vInvN)));
|
|
var vTerm3 = Avx.Multiply(vSix, Avx.Multiply(vMeanSq, Avx.Multiply(vSumSqs, vInvN)));
|
|
var vTerm4 = Avx.Multiply(vThree, Avx.Multiply(vMeanSq, vMeanSq));
|
|
|
|
var vM4 = Avx.Subtract(Avx.Add(Avx.Subtract(vTerm1, vTerm2), vTerm3), vTerm4);
|
|
|
|
// g2 = m4 / m2² - 3
|
|
var vM2Sq = Avx.Multiply(vM2, vM2);
|
|
var vG2 = Avx.Subtract(Avx.Divide(vM4, vM2Sq), vThree);
|
|
|
|
// Apply Fisher's correction: scale * (np1 * g2 + 6)
|
|
Vector256<double> vResult;
|
|
if (isPopulation)
|
|
{
|
|
vResult = vG2;
|
|
}
|
|
else
|
|
{
|
|
var vCorrected = Fma.IsSupported
|
|
? Fma.MultiplyAdd(vFisherNp1, vG2, vFisherAdd)
|
|
: Avx.Add(Avx.Multiply(vFisherNp1, vG2), vFisherAdd);
|
|
vResult = Avx.Multiply(vFisherScale, vCorrected);
|
|
}
|
|
|
|
// Mask: zero out where m2 <= epsilon
|
|
var vMask = Avx.Compare(vM2, vEpsilon, FloatComparisonMode.OrderedGreaterThanNonSignaling);
|
|
vResult = Avx.BlendVariable(vZero, vResult, vMask);
|
|
|
|
vResult.StoreUnsafe(ref Unsafe.Add(ref outRef, i));
|
|
|
|
sum = vSums.GetElement(3);
|
|
sumSq = vSumSqs.GetElement(3);
|
|
sumCu = vSumCus.GetElement(3);
|
|
sumQu = vSumQus.GetElement(3);
|
|
|
|
tickCount += VectorWidth;
|
|
if (tickCount >= ResyncInterval)
|
|
{
|
|
tickCount = 0;
|
|
double recalcSum = 0;
|
|
double recalcSumSq = 0;
|
|
double recalcSumCu = 0;
|
|
double recalcSumQu = 0;
|
|
int startIdx = i + VectorWidth - period;
|
|
for (int k = 0; k < period; k++)
|
|
{
|
|
double v = Unsafe.Add(ref srcRef, startIdx + k);
|
|
double vSq = v * v;
|
|
recalcSum += v;
|
|
recalcSumSq += vSq;
|
|
recalcSumCu += vSq * v;
|
|
recalcSumQu += vSq * vSq;
|
|
}
|
|
sum = recalcSum;
|
|
sumSq = recalcSumSq;
|
|
sumCu = recalcSumCu;
|
|
sumQu = recalcSumQu;
|
|
}
|
|
}
|
|
|
|
for (int i = simdEnd; i < len; i++)
|
|
{
|
|
double val = Unsafe.Add(ref srcRef, i);
|
|
double oldVal = Unsafe.Add(ref srcRef, i - period);
|
|
|
|
double valSq = val * val;
|
|
double oldSq = oldVal * oldVal;
|
|
sum = sum - oldVal + val;
|
|
sumSq = sumSq - oldSq + valSq;
|
|
sumCu = sumCu - (oldSq * oldVal) + (valSq * val);
|
|
sumQu = sumQu - (oldSq * oldSq) + (valSq * valSq);
|
|
|
|
Unsafe.Add(ref outRef, i) = CalculateKurtosisFromSums(sum, sumSq, sumCu, sumQu, n, isPopulation);
|
|
}
|
|
}
|
|
}
|