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Merge dev into main: v0.8.7 Kahan compensated summation

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Miha Kralj
2026-03-13 22:01:52 -07:00
parent 86a1db286c 67ad6f0cba
commit 9697facfb4
79 changed files with 2923 additions and 2495 deletions
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lib/statistics/jb/Jb.cs
+67 -87
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@@ -20,8 +20,8 @@ namespace QuanTAlib;
/// EK = excess kurtosis = (m₄ / m₂²) − 3
/// mₖ = k-th central moment = Σ(xᵢ − x̄)ᵏ / n
///
/// O(1) streaming via running sums of x, x², x³, x⁴ with periodic resync
/// to limit floating-point drift.
/// O(1) streaming via running sums of x, x², x³, x⁴ with Kahan compensated
/// summation for numerical stability over long streams.
///
/// Critical values (χ² with 2 df):
/// 10% → 4.605, 5% → 5.991, 1% → 9.210
@@ -46,11 +46,17 @@ public sealed class Jb : AbstractBase
private double _p_sumSq;
private double _p_sumCu;
private double _p_sumQu;
private double _sumComp;
private double _sumSqComp;
private double _sumCuComp;
private double _sumQuComp;
private double _p_sumComp;
private double _p_sumSqComp;
private double _p_sumCuComp;
private double _p_sumQuComp;
private double _lastValidValue;
private double _p_lastValidValue;
private int _updateCount;
private const int ResyncInterval = 1000;
private const double Epsilon = 1e-10;
public override bool IsHot => _buffer.IsFull;
@@ -103,9 +109,12 @@ public sealed class Jb : AbstractBase
_sumSq = 0;
_sumCu = 0;
_sumQu = 0;
_sumComp = 0;
_sumSqComp = 0;
_sumCuComp = 0;
_sumQuComp = 0;
_lastValidValue = 0;
_p_lastValidValue = 0;
_updateCount = 0;
int warmupLength = Math.Min(source.Length, WarmupPeriod);
int startIndex = source.Length - warmupLength;
@@ -142,29 +151,29 @@ public sealed class Jb : AbstractBase
_p_sumSq = _sumSq;
_p_sumCu = _sumCu;
_p_sumQu = _sumQu;
_p_sumComp = _sumComp;
_p_sumSqComp = _sumSqComp;
_p_sumCuComp = _sumCuComp;
_p_sumQuComp = _sumQuComp;
if (_buffer.IsFull)
{
double old = _buffer.Oldest;
double oldSq = old * old;
_sum -= old;
_sumSq -= oldSq;
_sumCu -= oldSq * old;
_sumQu -= oldSq * oldSq;
// Kahan subtract old values
{ double y = -old - _sumComp; double t = _sum + y; _sumComp = (t - _sum) - y; _sum = t; }
{ double y = -oldSq - _sumSqComp; double t = _sumSq + y; _sumSqComp = (t - _sumSq) - y; _sumSq = t; }
{ double y = -(oldSq * old) - _sumCuComp; double t = _sumCu + y; _sumCuComp = (t - _sumCu) - y; _sumCu = t; }
{ double y = -(oldSq * oldSq) - _sumQuComp; double t = _sumQu + y; _sumQuComp = (t - _sumQu) - y; _sumQu = t; }
}
_buffer.Add(value);
double vSq = value * value;
_sum += value;
_sumSq += vSq;
_sumCu += vSq * value;
_sumQu += vSq * vSq;
_updateCount++;
if (_updateCount % ResyncInterval == 0)
{
Resync();
}
// Kahan add new values
{ double y = value - _sumComp; double t = _sum + y; _sumComp = (t - _sum) - y; _sum = t; }
{ double y = vSq - _sumSqComp; double t = _sumSq + y; _sumSqComp = (t - _sumSq) - y; _sumSq = t; }
{ double y = (vSq * value) - _sumCuComp; double t = _sumCu + y; _sumCuComp = (t - _sumCu) - y; _sumCu = t; }
{ double y = (vSq * vSq) - _sumQuComp; double t = _sumQu + y; _sumQuComp = (t - _sumQu) - y; _sumQu = t; }
}
else
{
@@ -174,20 +183,25 @@ public sealed class Jb : AbstractBase
_sumSq = _p_sumSq;
_sumCu = _p_sumCu;
_sumQu = _p_sumQu;
_sumComp = _p_sumComp;
_sumSqComp = _p_sumSqComp;
_sumCuComp = _p_sumCuComp;
_sumQuComp = _p_sumQuComp;
if (_buffer.Count > 0)
{
_buffer.UpdateNewest(value);
Resync();
// Recalculate sums from buffer (O(N)) for perfect accuracy on correction
RecalculateSums();
}
else
{
_buffer.Add(value);
double vSq = value * value;
_sum += value;
_sumSq += vSq;
_sumCu += vSq * value;
_sumQu += vSq * vSq;
{ double y = value - _sumComp; double t = _sum + y; _sumComp = (t - _sum) - y; _sum = t; }
{ double y = vSq - _sumSqComp; double t = _sumSq + y; _sumSqComp = (t - _sumSq) - y; _sumSq = t; }
{ double y = (vSq * value) - _sumCuComp; double t = _sumCu + y; _sumCuComp = (t - _sumCu) - y; _sumCu = t; }
{ double y = (vSq * vSq) - _sumQuComp; double t = _sumQu + y; _sumQuComp = (t - _sumQu) - y; _sumQu = t; }
}
// Re-apply NaN guard for corrected value
@@ -229,9 +243,12 @@ public sealed class Jb : AbstractBase
_sumSq = 0;
_sumCu = 0;
_sumQu = 0;
_sumComp = 0;
_sumSqComp = 0;
_sumCuComp = 0;
_sumQuComp = 0;
_lastValidValue = 0;
_p_lastValidValue = 0;
_updateCount = 0;
// Prime the state
int primeStart = Math.Max(0, len - _period);
@@ -298,9 +315,16 @@ public sealed class Jb : AbstractBase
_p_sumSq = 0;
_p_sumCu = 0;
_p_sumQu = 0;
_sumComp = 0;
_sumSqComp = 0;
_sumCuComp = 0;
_sumQuComp = 0;
_p_sumComp = 0;
_p_sumSqComp = 0;
_p_sumCuComp = 0;
_p_sumQuComp = 0;
_lastValidValue = 0;
_p_lastValidValue = 0;
_updateCount = 0;
Last = default;
}
@@ -332,7 +356,7 @@ public sealed class Jb : AbstractBase
double mean = sum / n;
double meanSq = mean * mean;
// m₂ = (Σx̲ - Σx²/n) / n
// m₂ = (Σx² - Σx²/n) / n
double m2Numerator = sumSq - (sum * sum) / n;
if (m2Numerator < Epsilon)
{
@@ -365,7 +389,7 @@ public sealed class Jb : AbstractBase
return (n / 6.0) * Math.FusedMultiplyAdd(skewness, skewness, excessKurtosis * excessKurtosis / 4.0);
}
private void Resync()
private void RecalculateSums()
{
double sum = 0, sumSq = 0, sumCu = 0, sumQu = 0;
var span = _buffer.GetSpan();
@@ -382,6 +406,10 @@ public sealed class Jb : AbstractBase
_sumSq = sumSq;
_sumCu = sumCu;
_sumQu = sumQu;
_sumComp = 0;
_sumSqComp = 0;
_sumCuComp = 0;
_sumQuComp = 0;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
@@ -422,6 +450,7 @@ public sealed class Jb : AbstractBase
}
double sum = 0, sumSq = 0, sumCu = 0, sumQu = 0;
double sumComp = 0, sumSqComp = 0, sumCuComp = 0, sumQuComp = 0;
int i = 0;
// Warmup phase
@@ -430,16 +459,16 @@ public sealed class Jb : AbstractBase
{
double val = sanitized[i];
double vSq = val * val;
sum += val;
sumSq += vSq;
sumCu += vSq * val;
sumQu += vSq * vSq;
// Kahan add
{ double y = val - sumComp; double t = sum + y; sumComp = (t - sum) - y; sum = t; }
{ double y = vSq - sumSqComp; double t = sumSq + y; sumSqComp = (t - sumSq) - y; sumSq = t; }
{ double y = (vSq * val) - sumCuComp; double t = sumCu + y; sumCuComp = (t - sumCu) - y; sumCu = t; }
{ double y = (vSq * vSq) - sumQuComp; double t = sumQu + y; sumQuComp = (t - sumQu) - y; sumQu = t; }
output[i] = CalculateJbFromSums(sum, sumSq, sumCu, sumQu, i + 1);
}
// Sliding window phase
int tickCount = period;
for (; i < len; i++)
{
double val = sanitized[i];
@@ -447,19 +476,13 @@ public sealed class Jb : AbstractBase
double vSq = val * val;
double oSq = oldVal * oldVal;
sum = sum - oldVal + val;
sumSq = sumSq - oSq + vSq;
sumCu = sumCu - (oSq * oldVal) + (vSq * val);
sumQu = sumQu - (oSq * oSq) + (vSq * vSq);
// Kahan subtract old, add new
{ double y = (val - oldVal) - sumComp; double t = sum + y; sumComp = (t - sum) - y; sum = t; }
{ double y = (vSq - oSq) - sumSqComp; double t = sumSq + y; sumSqComp = (t - sumSq) - y; sumSq = t; }
{ double y = (vSq * val - oSq * oldVal) - sumCuComp; double t = sumCu + y; sumCuComp = (t - sumCu) - y; sumCu = t; }
{ double y = (vSq * vSq - oSq * oSq) - sumQuComp; double t = sumQu + y; sumQuComp = (t - sumQu) - y; sumQu = t; }
output[i] = CalculateJbFromSums(sum, sumSq, sumCu, sumQu, period);
tickCount++;
if (tickCount >= ResyncInterval)
{
tickCount = 0;
ResyncFromSanitized(sanitized, i, period, ref sum, ref sumSq, ref sumCu, ref sumQu);
}
}
}
finally
@@ -471,27 +494,6 @@ public sealed class Jb : AbstractBase
}
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static void ResyncFromSanitized(ReadOnlySpan<double> sanitized, int endIndex, int period,
ref double sum, ref double sumSq, ref double sumCu, ref double sumQu)
{
double s = 0, sSq = 0, sCu = 0, sQu = 0;
int startIdx = endIndex - period + 1;
for (int k = 0; k < period; k++)
{
double v = sanitized[startIdx + k];
double vSq = v * v;
s += v;
sSq += vSq;
sCu += vSq * v;
sQu += vSq * vSq;
}
sum = s;
sumSq = sSq;
sumCu = sCu;
sumQu = sQu;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static void WarmupJb(int period, ref double srcRef, ref double outRef,
out double sum, out double sumSq, out double sumCu, out double sumQu)
@@ -539,7 +541,6 @@ public sealed class Jb : AbstractBase
var vZero = Vector256<double>.Zero;
int simdEnd = period + ((len - period) / VectorWidth) * VectorWidth;
int tickCount = period;
for (int i = period; i < simdEnd; i += VectorWidth)
{
@@ -655,27 +656,6 @@ public sealed class Jb : AbstractBase
sumSq = vSumSqs.GetElement(3);
sumCu = vSumCus.GetElement(3);
sumQu = vSumQus.GetElement(3);
tickCount += VectorWidth;
if (tickCount >= ResyncInterval)
{
tickCount = 0;
double s = 0, sSq = 0, sCu = 0, sQu = 0;
int startIdx = i + VectorWidth - period;
for (int k = 0; k < period; k++)
{
double v = Unsafe.Add(ref srcRef, startIdx + k);
double v2 = v * v;
s += v;
sSq += v2;
sCu += v2 * v;
sQu += v2 * v2;
}
sum = s;
sumSq = sSq;
sumCu = sCu;
sumQu = sQu;
}
}
// Scalar tail