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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/stderr/Stderr.cs
+93 -32
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@@ -12,6 +12,8 @@ namespace QuanTAlib;
/// regression line fitted to the rolling window. Equivalent to the root mean
/// square of the residuals, scaled by N-2 degrees of freedom (one per
/// regression coefficient: slope and intercept).
/// Uses Kahan compensated summation for numerical stability of running regression sums,
/// eliminating the need for periodic resynchronization.
///
/// Formula:
/// SE = sqrt( SSR / (N - 2) )
@@ -41,17 +43,19 @@ public sealed class Stderr : AbstractBase
#pragma warning restore S2933
private bool _disposed;
// O(1) running regression sums
// O(1) running regression sums with Kahan compensation
private double _sumY;
private double _sumXY;
private double _p_sumY;
private double _p_sumXY;
private double _sumYComp; // Kahan compensation for _sumY
private double _sumXYComp; // Kahan compensation for _sumXY
private double _p_sumYComp;
private double _p_sumXYComp;
private double _lastVal;
private double _p_lastVal;
private double _lastValidValue;
private double _p_lastValidValue;
private int _tickCount;
private const int ResyncInterval = 1000;
// Precomputed constants (depend only on period)
private readonly double _sumX; // 0+1+…+(N-1) = N(N-1)/2
@@ -112,6 +116,8 @@ public sealed class Stderr : AbstractBase
UpdateStateNew(val);
_p_sumY = _sumY;
_p_sumXY = _sumXY;
_p_sumYComp = _sumYComp;
_p_sumXYComp = _sumXYComp;
_p_lastVal = _lastVal;
_p_lastValidValue = _lastValidValue;
_lastVal = val;
@@ -121,20 +127,26 @@ public sealed class Stderr : AbstractBase
_lastValidValue = _p_lastValidValue;
double val = GetValidValue(input.Value);
// Restore compensations
_sumYComp = _p_sumYComp;
_sumXYComp = _p_sumXYComp;
// Correct running sums for newest bar change
_sumY = _p_sumY - _p_lastVal + val;
_sumXY = _p_sumXY - (_period - 1) * (_p_lastVal - val);
// Re-derive sumXY correctly via resync to avoid drift on bar corrections
// Re-derive sumXY correctly via recalculation to avoid drift on bar corrections
if (_buffer.Count > 0)
{
_buffer.UpdateNewest(val);
ResyncSums();
RecalculateSums();
}
else
{
_buffer.Add(val);
_sumY = val;
_sumYComp = 0;
_sumXY = 0;
_sumXYComp = 0;
}
_lastVal = val;
@@ -172,10 +184,11 @@ public sealed class Stderr : AbstractBase
_buffer.Clear();
_sumY = 0;
_sumXY = 0;
_sumYComp = 0;
_sumXYComp = 0;
_lastVal = 0;
_lastValidValue = 0;
_p_lastValidValue = 0;
_tickCount = 0;
int primeStart = Math.Max(0, len - _period);
for (int i = primeStart; i < len; i++)
@@ -195,36 +208,50 @@ public sealed class Stderr : AbstractBase
double oldest = _buffer.Oldest;
double prevSumY = _sumY;
// O(1) update derivation (x_i = 0..N-1, oldest=0, newest=N-1):
// O(1) update for sumXY with Kahan compensation
// ΣXY_new = ΣXY_old - ΣY_old + oldest + (N-1)*val
_sumXY = _sumXY - prevSumY + oldest + (_period - 1) * val;
_sumY = prevSumY - oldest + val;
{
double delta = -prevSumY + oldest + (_period - 1) * val;
double y = delta - _sumXYComp;
double t = _sumXY + y;
_sumXYComp = (t - _sumXY) - y;
_sumXY = t;
}
// O(1) update for sumY with Kahan compensation
{
double delta = val - oldest;
double y = delta - _sumYComp;
double t = _sumY + y;
_sumYComp = (t - _sumY) - y;
_sumY = t;
}
}
else
{
_buffer.Add(val);
_sumY += val;
// Kahan add val to sumY
{
double y = val - _sumYComp;
double t = _sumY + y;
_sumYComp = (t - _sumY) - y;
_sumY = t;
}
// Recalculate sumXY from scratch during warmup (buffer not yet full)
_sumXY = 0;
_sumXYComp = 0;
var span = _buffer.GetSpan();
for (int i = 0; i < span.Length; i++)
{
// x=0 is oldest (index 0 in ordered span), x=count-1 is newest
_sumXY = Math.FusedMultiplyAdd(i, span[i], _sumXY);
}
_tickCount++;
return;
}
_buffer.Add(val);
_tickCount++;
if (_tickCount >= ResyncInterval)
{
_tickCount = 0;
ResyncSums();
}
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
@@ -263,18 +290,23 @@ public sealed class Stderr : AbstractBase
return Math.Sqrt(ssr / (n - 2.0));
}
private void ResyncSums()
private void RecalculateSums()
{
double sumY = 0;
double sumXY = 0;
_sumY = 0;
_sumYComp = 0;
_sumXY = 0;
_sumXYComp = 0;
var span = _buffer.GetSpan();
for (int i = 0; i < span.Length; i++)
{
sumY += span[i];
sumXY = Math.FusedMultiplyAdd(i, span[i], sumXY);
// Kahan add to sumY
double y = span[i] - _sumYComp;
double t = _sumY + y;
_sumYComp = (t - _sumY) - y;
_sumY = t;
_sumXY = Math.FusedMultiplyAdd(i, span[i], _sumXY);
}
_sumY = sumY;
_sumXY = sumXY;
}
/// <summary>Creates a Stderr from a TSeries source and returns result series.</summary>
@@ -323,10 +355,11 @@ public sealed class Stderr : AbstractBase
_buffer.Clear();
_sumY = 0;
_sumXY = 0;
_sumYComp = 0;
_sumXYComp = 0;
_lastVal = 0;
_lastValidValue = 0;
_p_lastValidValue = 0;
_tickCount = 0;
int warmupLength = Math.Min(source.Length, WarmupPeriod);
int startIndex = source.Length - warmupLength;
@@ -344,11 +377,14 @@ public sealed class Stderr : AbstractBase
_sumXY = 0;
_p_sumY = 0;
_p_sumXY = 0;
_sumYComp = 0;
_sumXYComp = 0;
_p_sumYComp = 0;
_p_sumXYComp = 0;
_lastVal = 0;
_p_lastVal = 0;
_lastValidValue = 0;
_p_lastValidValue = 0;
_tickCount = 0;
Last = default;
}
@@ -406,13 +442,22 @@ public sealed class Stderr : AbstractBase
double sumY = 0;
double sumXY = 0;
double sumYComp = 0; // Kahan compensation for sumY
double sumXYComp = 0; // Kahan compensation for sumXY
int i = 0;
// Warmup: growing window, recompute sums from scratch each bar
int warmupEnd = Math.Min(period, len);
for (; i < warmupEnd; i++)
{
sumY += sanitized[i];
// Kahan add to sumY
{
double y = sanitized[i] - sumYComp;
double t = sumY + y;
sumYComp = (t - sumY) - y;
sumY = t;
}
// Recalculate sumXY with new element appended (oldest=0, newest=i)
sumXY = 0;
for (int k = 0; k <= i; k++)
@@ -424,16 +469,32 @@ public sealed class Stderr : AbstractBase
output[i] = (n >= 3) ? CalcStderrFromSums(sanitized, 0, n, sumY, sumXY) : 0;
}
// Reset compensation at transition to sliding window
sumXYComp = 0;
// Sliding window: O(1) sum updates + O(N) residuals
for (; i < len; i++)
{
double oldest = sanitized[i - period];
double newest = sanitized[i];
// O(1) derivation (x_i = 0..N-1, drop oldest at x=0, add newest at x=N-1):
// ΣXY_new = ΣXY_old - ΣY_old + oldest + (period-1)*newest
sumXY = sumXY - sumY + oldest + (period - 1) * newest;
sumY = sumY - oldest + newest;
// O(1) Kahan compensated update for sumXY
{
double delta = -sumY + oldest + (period - 1) * newest;
double y = delta - sumXYComp;
double t = sumXY + y;
sumXYComp = (t - sumXY) - y;
sumXY = t;
}
// O(1) Kahan compensated update for sumY
{
double delta = newest - oldest;
double y = delta - sumYComp;
double t = sumY + y;
sumYComp = (t - sumY) - y;
sumY = t;
}
double slope = (period * sumXY - sumXFull * sumY) / denomFull;
double intercept = (sumY - slope * sumXFull) / period;