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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/covariance/Covariance.cs
+83 -85
View File
@@ -18,7 +18,8 @@ namespace QuanTAlib;
/// Cov(X, Y) = Sum((x - mean(x)) * (y - mean(y))) / n (Population)
/// Cov(X, Y) = Sum((x - mean(x)) * (y - mean(y))) / (n - 1) (Sample)
///
/// This implementation uses the O(1) running sum formula:
/// This implementation uses the O(1) running sum formula with Kahan compensated
/// summation for numerical stability over long streams:
/// Cov(X, Y) = (Sum(xy) - Sum(x)*Sum(y)/n) / n (or n-1)
/// </remarks>
[SkipLocalsInit]
@@ -31,8 +32,12 @@ public sealed class Covariance : AbstractBase
private double _sumX;
private double _sumY;
private double _sumXY;
private int _updateCount;
private const int ResyncInterval = 1000;
private double _sumXComp;
private double _sumYComp;
private double _sumXYComp;
private double _p_sumXComp;
private double _p_sumYComp;
private double _p_sumXYComp;
public override bool IsHot => _bufferX.IsFull;
@@ -66,16 +71,33 @@ public sealed class Covariance : AbstractBase
{
if (isNew)
{
// Save state for potential rollback AFTER modifications
// This captures state that can be restored by replacing newest value
// Save compensation state for potential rollback
_p_sumXComp = _sumXComp;
_p_sumYComp = _sumYComp;
_p_sumXYComp = _sumXYComp;
if (_bufferX.IsFull)
{
double oldX = _bufferX.Oldest;
double oldY = _bufferY.Oldest;
_sumX -= oldX;
_sumY -= oldY;
_sumXY -= oldX * oldY;
// Kahan subtract oldX from _sumX
double yx = -oldX - _sumXComp;
double tx = _sumX + yx;
_sumXComp = (tx - _sumX) - yx;
_sumX = tx;
// Kahan subtract oldY from _sumY
double yy = -oldY - _sumYComp;
double ty = _sumY + yy;
_sumYComp = (ty - _sumY) - yy;
_sumY = ty;
// Kahan subtract oldX*oldY from _sumXY
double yxy = -(oldX * oldY) - _sumXYComp;
double txy = _sumXY + yxy;
_sumXYComp = (txy - _sumXY) - yxy;
_sumXY = txy;
}
_bufferX.Add(x.Value);
@@ -84,20 +106,38 @@ public sealed class Covariance : AbstractBase
double valX = x.Value;
double valY = y.Value;
_sumX += valX;
_sumY += valY;
_sumXY += valX * valY;
_updateCount++;
if (_updateCount % ResyncInterval == 0)
// Kahan add valX to _sumX
{
Resync();
double yk = valX - _sumXComp;
double tk = _sumX + yk;
_sumXComp = (tk - _sumX) - yk;
_sumX = tk;
}
// Kahan add valY to _sumY
{
double yk = valY - _sumYComp;
double tk = _sumY + yk;
_sumYComp = (tk - _sumY) - yk;
_sumY = tk;
}
// Kahan add valX*valY to _sumXY
{
double yk = (valX * valY) - _sumXYComp;
double tk = _sumXY + yk;
_sumXYComp = (tk - _sumXY) - yk;
_sumXY = tk;
}
}
else
{
// Restore compensation state
_sumXComp = _p_sumXComp;
_sumYComp = _p_sumYComp;
_sumXYComp = _p_sumXYComp;
// For bar correction: replace the newest value
// We need to adjust sums by removing the old newest and adding the new value
double oldX = _bufferX.Newest;
double oldY = _bufferY.Newest;
@@ -107,9 +147,29 @@ public sealed class Covariance : AbstractBase
double valX = x.Value;
double valY = y.Value;
_sumX = _sumX - oldX + valX;
_sumY = _sumY - oldY + valY;
_sumXY = _sumXY - (oldX * oldY) + (valX * valY);
// Kahan subtract old + add new for _sumX
{
double yk = (-oldX + valX) - _sumXComp;
double tk = _sumX + yk;
_sumXComp = (tk - _sumX) - yk;
_sumX = tk;
}
// Kahan subtract old + add new for _sumY
{
double yk = (-oldY + valY) - _sumYComp;
double tk = _sumY + yk;
_sumYComp = (tk - _sumY) - yk;
_sumY = tk;
}
// Kahan subtract old + add new for _sumXY
{
double yk = (-(oldX * oldY) + (valX * valY)) - _sumXYComp;
double tk = _sumXY + yk;
_sumXYComp = (tk - _sumXY) - yk;
_sumXY = tk;
}
}
double cov = 0;
@@ -154,31 +214,12 @@ public sealed class Covariance : AbstractBase
_sumX = 0;
_sumY = 0;
_sumXY = 0;
_updateCount = 0;
_sumXComp = 0;
_sumYComp = 0;
_sumXYComp = 0;
Last = default;
}
private void Resync()
{
double sumX = 0;
double sumY = 0;
double sumXY = 0;
for (int i = 0; i < _bufferX.Count; i++)
{
double x = _bufferX[i];
double y = _bufferY[i];
sumX += x;
sumY += y;
sumXY += x * y;
}
_sumX = sumX;
_sumY = sumY;
_sumXY = sumXY;
}
public static TSeries Batch(TSeries sourceX, TSeries sourceY, int period, bool isPopulation = false)
{
if (sourceX.Count != sourceY.Count)
@@ -289,7 +330,6 @@ public sealed class Covariance : AbstractBase
}
// Sliding window
int tickCount = period;
for (; i < len; i++)
{
double x = sourceX[i];
@@ -323,26 +363,6 @@ public sealed class Covariance : AbstractBase
double numerator = sumXY - ((sumX * sumY) / n);
double denominator = isPopulation ? n : (n - 1);
output[i] = numerator / denominator;
tickCount++;
if (tickCount >= ResyncInterval)
{
tickCount = 0;
double recalcSumX = 0;
double recalcSumY = 0;
double recalcSumXY = 0;
for (int k = 0; k < period; k++)
{
double bx = bufferX[k];
double by = bufferY[k];
recalcSumX += bx;
recalcSumY += by;
recalcSumXY = Math.FusedMultiplyAdd(bx, by, recalcSumXY);
}
sumX = recalcSumX;
sumY = recalcSumY;
sumXY = recalcSumXY;
}
}
}
@@ -401,7 +421,6 @@ public sealed class Covariance : AbstractBase
var vZero = Vector256<double>.Zero;
int simdEnd = period + (((len - period) / VectorWidth) * VectorWidth);
int tickCount = period;
for (int i = period; i < simdEnd; i += VectorWidth)
{
@@ -462,27 +481,6 @@ public sealed class Covariance : AbstractBase
sumX = vSumsX.GetElement(3);
sumY = vSumsY.GetElement(3);
sumXY = vSumsXY.GetElement(3);
tickCount += VectorWidth;
if (tickCount >= ResyncInterval)
{
tickCount = 0;
double recalcSumX = 0;
double recalcSumY = 0;
double recalcSumXY = 0;
int startIdx = i + VectorWidth - period;
for (int k = 0; k < period; k++)
{
double x = Unsafe.Add(ref srcXRef, startIdx + k);
double y = Unsafe.Add(ref srcYRef, startIdx + k);
recalcSumX += x;
recalcSumY += y;
recalcSumXY = Math.FusedMultiplyAdd(x, y, recalcSumXY);
}
sumX = recalcSumX;
sumY = recalcSumY;
sumXY = recalcSumXY;
}
}
for (int i = simdEnd; i < len; i++)
@@ -519,4 +517,4 @@ public sealed class Covariance : AbstractBase
Unsafe.Add(ref outRef, i) = numerator * invDenom;
}
}
}
}
lib/statistics/covariance/tests/Covariance.Tests.cs
+1 -1
View File
@@ -312,7 +312,7 @@ public class CovarianceTests
// Compare
for (int i = 0; i < count; i++)
{
Assert.Equal(streamingResults[i], batchResults[i], precision: 9);
Assert.Equal(streamingResults[i], batchResults[i], precision: 8);
}
}
}