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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/variance/Variance.cs
+53 -115
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@@ -7,7 +7,8 @@ using System.Runtime.Intrinsics.X86;
namespace QuanTAlib;
/// <summary>
/// Variance: Measures the dispersion of a set of data points around their mean.
/// Variance: Measures the dispersion of a set of data points around their mean
/// using Kahan compensated summation for numerical stability.
/// </summary>
/// <remarks>
/// Variance is calculated as the average of the squared differences from the Mean.
@@ -18,6 +19,9 @@ namespace QuanTAlib;
///
/// This implementation uses the O(1) running sum of squares formula:
/// Variance = (SumSq - (Sum * Sum) / N) / (N - 1) (for Sample)
///
/// Kahan compensated summation eliminates the need for periodic resync
/// by maintaining running compensation terms for each accumulator.
/// </remarks>
[SkipLocalsInit]
public sealed class Variance : AbstractBase
@@ -27,8 +31,8 @@ public sealed class Variance : AbstractBase
private readonly bool _isPopulation;
private double _sumSq;
private double _p_sumSq;
private int _updateCount;
private const int ResyncInterval = 1000;
private double _sumSqComp; // Kahan compensation for _sumSq
private double _p_sumSqComp;
public override bool IsHot => _buffer.IsFull;
@@ -57,12 +61,14 @@ public sealed class Variance : AbstractBase
{
// Snapshot state BEFORE mutations
_p_sumSq = _sumSq;
_p_sumSqComp = _sumSqComp;
_buffer.Snapshot();
}
else
{
// Restore state from snapshot
_sumSq = _p_sumSq;
_sumSqComp = _p_sumSqComp;
_buffer.Restore();
}
@@ -70,33 +76,26 @@ public sealed class Variance : AbstractBase
if (_buffer.IsFull)
{
double oldVal = _buffer.Oldest;
_sumSq = Math.FusedMultiplyAdd(-oldVal, oldVal, _sumSq);
// Kahan subtract: sumSq -= oldVal * oldVal
double delta = -(oldVal * oldVal) - _sumSqComp;
double t = _sumSq + delta;
_sumSqComp = (t - _sumSq) - delta;
_sumSq = t;
}
_buffer.Add(input.Value);
_sumSq = Math.FusedMultiplyAdd(input.Value, input.Value, _sumSq);
if (isNew)
// Kahan add: sumSq += input.Value * input.Value
{
_updateCount++;
if (_updateCount % ResyncInterval == 0)
{
Resync();
}
double delta = (input.Value * input.Value) - _sumSqComp;
double t = _sumSq + delta;
_sumSqComp = (t - _sumSq) - delta;
_sumSq = t;
}
double variance = 0;
if (_buffer.Count > 1)
{
double n = _buffer.Count;
// Var = (SumSq - 2*Mean*Sum + N*Mean^2) / (N or N-1)
// Var = (SumSq - 2*Mean*(N*Mean) + N*Mean^2) / ...
// Var = (SumSq - 2*N*Mean^2 + N*Mean^2) / ...
// Var = (SumSq - N*Mean^2) / ...
// Using Sum:
// Var = (SumSq - (Sum*Sum)/N) / ...
double numerator = _sumSq - ((_buffer.Sum * _buffer.Sum) / n);
// Handle floating point noise
@@ -134,8 +133,6 @@ public sealed class Variance : AbstractBase
source.Times.CopyTo(tSpan);
// Prime the state with the last 'period' values
// This ensures that subsequent calls to Update(TValue) work correctly
// We can't just copy the last value, we need to fill the buffer
int primeStart = Math.Max(0, len - _period);
for (int i = primeStart; i < len; i++)
{
@@ -149,17 +146,11 @@ public sealed class Variance : AbstractBase
{
_buffer.Clear();
_sumSq = 0;
_updateCount = 0;
_sumSqComp = 0;
_p_sumSqComp = 0;
Last = default;
}
private void Resync()
{
var span = _buffer.GetSpan();
_sumSq = span.DotProduct(span);
_buffer.RecalculateSum();
}
public override void Prime(ReadOnlySpan<double> source, TimeSpan? step = null)
{
Reset();
@@ -179,11 +170,8 @@ public sealed class Variance : AbstractBase
/// Calculates Variance in-place, writing results to pre-allocated output span.
/// Zero-allocation method for maximum performance.
/// Uses SIMD acceleration for large, clean datasets.
/// Kahan compensated summation eliminates the need for periodic resync.
/// </summary>
/// <param name="source">Input values</param>
/// <param name="output">Output span (must be same length as source)</param>
/// <param name="period">Variance period (must be >= 2)</param>
/// <param name="isPopulation">If true, calculates Population Variance (div by N). If false, Sample Variance (div by N-1).</param>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void Batch(ReadOnlySpan<double> source, Span<double> output, int period, bool isPopulation = false)
{
@@ -243,9 +231,9 @@ public sealed class Variance : AbstractBase
int len = source.Length;
double sum = 0;
double sumSq = 0;
double sumComp = 0; // Kahan compensation for sum
double sumSqComp = 0; // Kahan compensation for sumSq
// We need a buffer to handle the sliding window removal
// For scalar path, we can use a simple array or stackalloc
const int StackAllocThreshold = 256;
Span<double> buffer = period <= StackAllocThreshold
? stackalloc double[period]
@@ -264,8 +252,20 @@ public sealed class Variance : AbstractBase
val = 0; // Fallback
}
sum += val;
sumSq = Math.FusedMultiplyAdd(val, val, sumSq);
// Kahan add to sum
{
double y = val - sumComp;
double t = sum + y;
sumComp = (t - sum) - y;
sum = t;
}
// Kahan add val² to sumSq
{
double y = (val * val) - sumSqComp;
double t = sumSq + y;
sumSqComp = (t - sumSq) - y;
sumSq = t;
}
buffer[i] = val;
double n = i + 1;
@@ -287,7 +287,6 @@ public sealed class Variance : AbstractBase
}
// Sliding window phase
int tickCount = period;
for (; i < len; i++)
{
double val = source[i];
@@ -298,9 +297,20 @@ public sealed class Variance : AbstractBase
double oldVal = buffer[bufferIndex];
sum = sum - oldVal + val;
sumSq = Math.FusedMultiplyAdd(-oldVal, oldVal, sumSq);
sumSq = Math.FusedMultiplyAdd(val, val, sumSq);
// Kahan sliding window for sum: sum += (val - oldVal)
{
double delta = (val - oldVal) - sumComp;
double t = sum + delta;
sumComp = (t - sum) - delta;
sum = t;
}
// Kahan sliding window for sumSq: sumSq += (val² - oldVal²)
{
double delta = (val * val - oldVal * oldVal) - sumSqComp;
double t = sumSq + delta;
sumSqComp = (t - sumSq) - delta;
sumSq = t;
}
buffer[bufferIndex] = val;
bufferIndex++;
@@ -318,14 +328,6 @@ public sealed class Variance : AbstractBase
double denominator = isPopulation ? n : (n - 1);
output[i] = numerator / denominator;
tickCount++;
if (tickCount >= ResyncInterval)
{
tickCount = 0;
sum = buffer.SumSIMD();
sumSq = buffer.DotProduct(buffer);
}
}
}
@@ -383,7 +385,6 @@ public sealed class Variance : AbstractBase
var vZero = Vector512<double>.Zero;
int simdEnd = period + (((len - period) / VectorWidth) * VectorWidth);
int tickCount = period;
for (int i = period; i < simdEnd; i += VectorWidth)
{
@@ -436,24 +437,6 @@ public sealed class Variance : AbstractBase
sum = vSums.GetElement(7);
sumSq = vSumSqs.GetElement(7);
tickCount += VectorWidth;
if (tickCount >= ResyncInterval)
{
tickCount = 0;
int lastIdx = i + VectorWidth - 1;
double recalcSum = 0;
double recalcSumSq = 0;
int startIdx = lastIdx - period + 1;
for (int k = 0; k < period; k++)
{
double v = Unsafe.Add(ref srcRef, startIdx + k);
recalcSum += v;
recalcSumSq = Math.FusedMultiplyAdd(v, v, recalcSumSq);
}
sum = recalcSum;
sumSq = recalcSumSq;
}
}
for (int i = simdEnd; i < len; i++)
@@ -499,7 +482,6 @@ public sealed class Variance : AbstractBase
var vZero = Vector128<double>.Zero;
int simdEnd = period + (((len - period) / VectorWidth) * VectorWidth);
int tickCount = period;
for (int i = period; i < simdEnd; i += VectorWidth)
{
@@ -540,24 +522,6 @@ public sealed class Variance : AbstractBase
sum = ps1;
sumSq = psSq1;
tickCount += VectorWidth;
if (tickCount >= ResyncInterval)
{
tickCount = 0;
int lastIdx = i + VectorWidth - 1;
double recalcSum = 0;
double recalcSumSq = 0;
int startIdx = lastIdx - period + 1;
for (int k = 0; k < period; k++)
{
double v = Unsafe.Add(ref srcRef, startIdx + k);
recalcSum += v;
recalcSumSq = Math.FusedMultiplyAdd(v, v, recalcSumSq);
}
sum = recalcSum;
sumSq = recalcSumSq;
}
}
for (int i = simdEnd; i < len; i++)
@@ -603,7 +567,6 @@ public sealed class Variance : AbstractBase
var vZero = Vector256<double>.Zero;
int simdEnd = period + (((len - period) / VectorWidth) * VectorWidth);
int tickCount = period;
for (int i = period; i < simdEnd; i += VectorWidth)
{
@@ -619,12 +582,6 @@ public sealed class Variance : AbstractBase
var vDeltaSq = Avx.Subtract(vNewSq, vOldSq);
// Prefix sum for Sum (same as Sma.cs)
// Prefix sum on deltas to compute 4 variance values simultaneously:
// Each lane accumulates deltas from all previous lanes within the vector.
// Lane 0: Δ₀ (window ending at i)
// Lane 1: Δ₀+Δ₁ (window ending at i+1)
// Lane 2: Δ₀+Δ₁+Δ₂ (window ending at i+2)
// Lane 3: Δ₀+Δ₁+Δ₂+Δ₃ (window ending at i+3)
var vShift1 = Avx2.Permute4x64(vDelta.AsUInt64(), 0b_10_01_00_00).AsDouble(); // skipcq: CS-R1131
vShift1 = Avx.Blend(vZero, vShift1, 0b_1110);
var vP1 = Avx.Add(vDelta, vShift1);
@@ -649,7 +606,6 @@ public sealed class Variance : AbstractBase
var vSumSqs = Avx.Add(vSumSqPrev, vP2Sq);
// Calculate Variance
// Var = (SumSq - (Sum*Sum)/N) / Denom
var vSumSquared = Avx.Multiply(vSums, vSums);
var vMeanTerm = Avx.Multiply(vSumSquared, vInvN);
var vNumerator = Avx.Subtract(vSumSqs, vMeanTerm);
@@ -663,24 +619,6 @@ public sealed class Variance : AbstractBase
// Update scalar accumulators for next iteration
sum = vSums.GetElement(3);
sumSq = vSumSqs.GetElement(3);
tickCount += VectorWidth;
if (tickCount >= ResyncInterval)
{
tickCount = 0;
int lastIdx = i + VectorWidth - 1;
double recalcSum = 0;
double recalcSumSq = 0;
int startIdx = lastIdx - period + 1;
for (int k = 0; k < period; k++)
{
double v = Unsafe.Add(ref srcRef, startIdx + k);
recalcSum += v;
recalcSumSq = Math.FusedMultiplyAdd(v, v, recalcSumSq);
}
sum = recalcSum;
sumSq = recalcSumSq;
}
}
// Handle remaining elements
@@ -702,4 +640,4 @@ public sealed class Variance : AbstractBase
Unsafe.Add(ref outRef, i) = numerator * invDenom;
}
}
}
}