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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/beta/Beta.cs
+43 -43
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@@ -17,7 +17,8 @@ namespace QuanTAlib;
/// Ra = Return of Asset
/// Rm = Return of Market
///
/// This implementation uses the O(1) slope formula for linear regression of Ra vs Rm:
/// This implementation uses the O(1) slope formula for linear regression of Ra vs Rm
/// with Kahan compensated summation for numerical stability over long streams:
/// Beta = (N * Sum(Ra*Rm) - Sum(Ra) * Sum(Rm)) / (N * Sum(Rm^2) - Sum(Rm)^2)
/// </remarks>
[SkipLocalsInit]
@@ -37,9 +38,19 @@ public sealed class Beta : AbstractBase
private double _sumRaRm;
private double _sumRm2;
// Kahan compensation terms
private double _sumRaComp;
private double _sumRmComp;
private double _sumRaRmComp;
private double _sumRm2Comp;
// Previous compensation state for rollback
private double _p_sumRaComp;
private double _p_sumRmComp;
private double _p_sumRaRmComp;
private double _p_sumRm2Comp;
private const double Epsilon = 1e-10;
private int _updateCount;
private const int ResyncInterval = 1000;
public override bool IsHot => _returnsAsset.IsFull;
@@ -78,6 +89,10 @@ public sealed class Beta : AbstractBase
_p_prevAsset = _prevAsset;
_p_prevMarket = _prevMarket;
_p_sumRaComp = _sumRaComp;
_p_sumRmComp = _sumRmComp;
_p_sumRaRmComp = _sumRaRmComp;
_p_sumRm2Comp = _sumRm2Comp;
// Calculate returns with division-by-zero and NaN/Infinity guards
double ra, rm;
@@ -116,25 +131,21 @@ public sealed class Beta : AbstractBase
double oldRa = _returnsAsset.Oldest;
double oldRm = _returnsMarket.Oldest;
_sumRa -= oldRa;
_sumRm -= oldRm;
_sumRaRm = FusedMultiplyAdd(-oldRa, oldRm, _sumRaRm);
_sumRm2 = FusedMultiplyAdd(-oldRm, oldRm, _sumRm2);
// Kahan subtract old values
{ double y = -oldRa - _sumRaComp; double t = _sumRa + y; _sumRaComp = (t - _sumRa) - y; _sumRa = t; }
{ double y = -oldRm - _sumRmComp; double t = _sumRm + y; _sumRmComp = (t - _sumRm) - y; _sumRm = t; }
{ double y = -(oldRa * oldRm) - _sumRaRmComp; double t = _sumRaRm + y; _sumRaRmComp = (t - _sumRaRm) - y; _sumRaRm = t; }
{ double y = -(oldRm * oldRm) - _sumRm2Comp; double t = _sumRm2 + y; _sumRm2Comp = (t - _sumRm2) - y; _sumRm2 = t; }
}
_returnsAsset.Add(ra);
_returnsMarket.Add(rm);
_sumRa += ra;
_sumRm += rm;
_sumRaRm = FusedMultiplyAdd(ra, rm, _sumRaRm);
_sumRm2 = FusedMultiplyAdd(rm, rm, _sumRm2);
_updateCount++;
if (_updateCount % ResyncInterval == 0)
{
Resync();
}
// Kahan add new values
{ double y = ra - _sumRaComp; double t = _sumRa + y; _sumRaComp = (t - _sumRa) - y; _sumRa = t; }
{ double y = rm - _sumRmComp; double t = _sumRm + y; _sumRmComp = (t - _sumRm) - y; _sumRm = t; }
{ double y = (ra * rm) - _sumRaRmComp; double t = _sumRaRm + y; _sumRaRmComp = (t - _sumRaRm) - y; _sumRaRm = t; }
{ double y = (rm * rm) - _sumRm2Comp; double t = _sumRm2 + y; _sumRm2Comp = (t - _sumRm2) - y; _sumRm2 = t; }
}
else
{
@@ -155,6 +166,12 @@ public sealed class Beta : AbstractBase
return new TValue(asset.Time, 0);
}
// Restore compensation state
_sumRaComp = _p_sumRaComp;
_sumRmComp = _p_sumRmComp;
_sumRaRmComp = _p_sumRaRmComp;
_sumRm2Comp = _p_sumRm2Comp;
double oldRa = _returnsAsset.Newest;
double oldRm = _returnsMarket.Newest;
@@ -192,11 +209,11 @@ public sealed class Beta : AbstractBase
_returnsAsset.UpdateNewest(newRa);
_returnsMarket.UpdateNewest(newRm);
// Use FMA for better precision: _sumRa = _sumRa - oldRa + newRa
_sumRa = FusedMultiplyAdd(1.0, newRa, FusedMultiplyAdd(-1.0, oldRa, _sumRa));
_sumRm = FusedMultiplyAdd(1.0, newRm, FusedMultiplyAdd(-1.0, oldRm, _sumRm));
_sumRaRm = FusedMultiplyAdd(newRa, newRm, FusedMultiplyAdd(-oldRa, oldRm, _sumRaRm));
_sumRm2 = FusedMultiplyAdd(newRm, newRm, FusedMultiplyAdd(-oldRm, oldRm, _sumRm2));
// Kahan subtract old + add new
{ double y = (-oldRa + newRa) - _sumRaComp; double t = _sumRa + y; _sumRaComp = (t - _sumRa) - y; _sumRa = t; }
{ double y = (-oldRm + newRm) - _sumRmComp; double t = _sumRm + y; _sumRmComp = (t - _sumRm) - y; _sumRm = t; }
{ double y = (-(oldRa * oldRm) + (newRa * newRm)) - _sumRaRmComp; double t = _sumRaRm + y; _sumRaRmComp = (t - _sumRaRm) - y; _sumRaRm = t; }
{ double y = (-(oldRm * oldRm) + (newRm * newRm)) - _sumRm2Comp; double t = _sumRm2 + y; _sumRm2Comp = (t - _sumRm2) - y; _sumRm2 = t; }
}
double beta = 0;
@@ -247,31 +264,14 @@ public sealed class Beta : AbstractBase
_sumRm = 0;
_sumRaRm = 0;
_sumRm2 = 0;
_sumRaComp = 0;
_sumRmComp = 0;
_sumRaRmComp = 0;
_sumRm2Comp = 0;
_isInitialized = false;
_prevAsset = 0;
_prevMarket = 0;
_p_prevAsset = 0;
_p_prevMarket = 0;
_updateCount = 0;
}
private void Resync()
{
_sumRa = 0;
_sumRm = 0;
_sumRaRm = 0;
_sumRm2 = 0;
for (int i = 0; i < _returnsAsset.Count; i++)
{
double ra = _returnsAsset[i];
double rm = _returnsMarket[i];
_sumRa += ra;
_sumRm += rm;
// Use FMA for better precision in cross-term and squared-term
_sumRaRm = FusedMultiplyAdd(ra, rm, _sumRaRm);
_sumRm2 = FusedMultiplyAdd(rm, rm, _sumRm2);
}
}
}