Files
QuanTAlib/lib/averages/wma/Wma.cs
T
Miha Kralj 3ed35322a5 Add TRIMA implementation and benchmarks; optimize WMA with SIMD
- Introduced `TrimaVector` class for multi-period Triangular Moving Average (TRIMA) calculations, optimized for SIMD.
- Implemented last-value substitution for invalid inputs in TRIMA.
- Added methods for calculating TRIMA for entire series and individual updates.
- Enhanced `Wma` class with periodic resync to prevent floating-point drift and introduced SIMD optimizations for performance.
- Updated benchmark suite to include TRIMA calculations alongside existing SMA, EMA, and WMA benchmarks.
2025-12-04 13:05:56 -08:00

675 lines
25 KiB
C#

using System.Numerics;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
using System.Runtime.Intrinsics;
using System.Runtime.Intrinsics.X86;
namespace QuanTAlib;
/// <summary>
/// WMA: Weighted Moving Average
/// </summary>
/// <remarks>
/// WMA applies linear weighting to data points, giving more weight to recent values.
/// Uses dual running sums for O(1) complexity per update.
///
/// Key characteristics:
/// - Linear weighting: newest value has weight n, oldest has weight 1
/// - More responsive than SMA due to emphasis on recent data
/// - Less lag than SMA, but more than EMA
/// - O(1) time complexity for both update and bar correction
/// - O(1) space complexity for state save/restore (scalars only)
///
/// Calculation method:
/// WMA = (n*P_n + (n-1)*P_(n-1) + ... + 2*P_2 + 1*P_1) / (n*(n+1)/2)
///
/// O(1) update formula:
/// S_new = S - oldest + newest
/// W_new = W - S_old + n*newest
/// WMA = W_new / divisor
///
/// Bar correction (isNew=false):
/// - Restores to state after last isNew=true
/// - Then replaces the last value with new correction value
/// - All O(1) using scalar state
///
/// Sources:
/// - https://www.investopedia.com/terms/w/weightedaverage.asp
/// - https://school.stockcharts.com/doku.php?id=technical_indicators:weighted_moving_average
/// </remarks>
[SkipLocalsInit]
public sealed class Wma
{
private readonly int _period;
private readonly double _divisor;
private readonly RingBuffer _buffer;
// Dual running sums for O(1) WMA calculation
private double _sum; // Simple sum of values in window
private double _wsum; // Weighted sum of values in window
private double _p_sum; // Sum AFTER last isNew=true (for correction restore)
private double _p_wsum; // Weighted sum AFTER last isNew=true
private double _p_lastInput; // Input that was added on last isNew=true
private double _lastValidValue;
private double _p_lastValidValue;
private int _tickCount; // Counter for periodic sum resync
// Resync interval: recalculate sum from buffer every N ticks to prevent drift
private const int ResyncInterval = 1000;
/// <summary>
/// Display name for the indicator.
/// </summary>
public string Name { get; }
/// <summary>
/// Creates WMA with specified period.
/// </summary>
/// <param name="period">Number of values to average (must be > 0)</param>
public Wma(int period)
{
if (period <= 0)
throw new ArgumentException("Period must be greater than 0", nameof(period));
_period = period;
_divisor = period * (period + 1) * 0.5;
_buffer = new RingBuffer(period);
Name = $"Wma({period})";
}
/// <summary>
/// Current WMA value.
/// </summary>
public TValue Value { get; private set; }
/// <summary>
/// True if the WMA has enough data to produce valid results.
/// WMA is "hot" when the buffer is full (has received at least 'period' values).
/// </summary>
public bool IsHot => _buffer.IsFull;
/// <summary>
/// Gets a valid input value, using last-value substitution for non-finite inputs.
/// </summary>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private double GetValidValue(double input)
{
if (double.IsFinite(input))
{
_lastValidValue = input;
return input;
}
return _lastValidValue;
}
/// <summary>
/// Updates internal state with a new value.
/// Shared logic for both streaming and batch-reconstruction.
/// </summary>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private void UpdateState(double val)
{
if (_buffer.IsFull)
{
// Buffer is full: O(1) update using dual running sums
double oldSum = _sum; // Capture before update
double oldest = _buffer.Oldest;
_sum = _sum - oldest + val;
_wsum = _wsum - oldSum + (_period * val);
}
else
{
// Warmup phase: incrementally build sums
int count = _buffer.Count + 1;
_sum += val;
_wsum += count * val;
}
// Update buffer
_buffer.Add(val);
// Periodic resync: recalculate sums from scratch to eliminate floating-point drift
_tickCount++;
if (_buffer.IsFull && _tickCount >= ResyncInterval)
{
_tickCount = 0;
double recalcSum = 0;
double recalcWsum = 0;
int weight = 1;
foreach (double item in _buffer)
{
recalcSum += item;
recalcWsum += weight * item;
weight++;
}
_sum = recalcSum;
_wsum = recalcWsum;
}
}
/// <summary>
/// Updates WMA with the given value.
/// O(1) for both isNew=true and isNew=false.
/// </summary>
/// <param name="input">Input value</param>
/// <param name="isNew">True for new bar, false for update to current bar (default: true)</param>
/// <returns>Current WMA value</returns>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public TValue Update(TValue input, bool isNew = true)
{
if (isNew)
{
// Get valid value (this may update _lastValidValue)
double val = GetValidValue(input.Value);
UpdateState(val);
// Save state AFTER this update for potential future corrections
_p_sum = _sum;
_p_wsum = _wsum;
_p_lastInput = val;
_p_lastValidValue = _lastValidValue;
}
else
{
// Bar correction: restore to state AFTER last isNew=true, then swap last value
// Restore _lastValidValue BEFORE calling GetValidValue
_lastValidValue = _p_lastValidValue;
// Get valid value (this may update _lastValidValue)
double val = GetValidValue(input.Value);
// Restore sums to state after last isNew=true
_sum = _p_sum;
_wsum = _p_wsum;
// Correction: replace _p_lastInput with val
// S_corrected = S - lastInput + val
// W_corrected = W + weight*(val - lastInput), where weight = period (if full) or count (if warmup)
int weight = _buffer.IsFull ? _period : _buffer.Count;
_sum = _sum - _p_lastInput + val;
_wsum += weight * (val - _p_lastInput);
// Update buffer's newest value
_buffer.UpdateNewest(val);
}
// Calculate WMA using current divisor (handles warmup)
double currentDivisor = _buffer.IsFull ? _divisor : _buffer.Count * (_buffer.Count + 1) * 0.5;
double result = _wsum / currentDivisor;
Value = new TValue(input.Time, result);
return Value;
}
/// <summary>
/// Updates WMA with the entire series.
/// </summary>
/// <param name="source">Input series</param>
/// <returns>WMA series</returns>
public TSeries Update(TSeries source)
{
if (source.Count == 0) return new TSeries(new List<long>(), new List<double>());
int len = source.Count;
var t = new List<long>(len);
var v = new List<double>(len);
CollectionsMarshal.SetCount(t, len);
CollectionsMarshal.SetCount(v, len);
var tSpan = CollectionsMarshal.AsSpan(t);
var vSpan = CollectionsMarshal.AsSpan(v);
var sourceValues = source.Values;
var sourceTimes = source.Times;
// 1. Fast Batch Calculation (SIMD optimized)
Calculate(sourceValues, vSpan, _period);
// 2. Copy Times
sourceTimes.CopyTo(tSpan);
// 3. Reconstruct State for subsequent updates
// We need to restore _buffer, _sum, _wsum, and _lastValidValue
// Find the last valid value before the reconstruction window
int windowSize = Math.Min(len, _period);
int startIndex = len - windowSize;
// Restore _lastValidValue from before the window
if (startIndex > 0)
{
// Scan backwards to find last valid value
for (int i = startIndex - 1; i >= 0; i--)
{
if (double.IsFinite(sourceValues[i]))
{
_lastValidValue = sourceValues[i];
break;
}
}
}
else
{
_lastValidValue = 0; // Reset if starting from 0
}
// Rebuild buffer and sums from last 'period' values using shared logic
_buffer.Clear();
_sum = 0;
_wsum = 0;
_tickCount = 0;
for (int i = startIndex; i < len; i++)
{
double val = GetValidValue(sourceValues[i]);
UpdateState(val);
}
// Save state for potential future corrections
_p_sum = _sum;
_p_wsum = _wsum;
_p_lastInput = sourceValues[len - 1];
_p_lastValidValue = _lastValidValue;
Value = new TValue(tSpan[len - 1], vSpan[len - 1]);
return new TSeries(t, v);
}
/// <summary>
/// Calculates WMA for the entire series using a new instance.
/// </summary>
/// <param name="source">Input series</param>
/// <param name="period">WMA period</param>
/// <returns>WMA series</returns>
public static TSeries Calculate(TSeries source, int period)
{
var wma = new Wma(period);
return wma.Update(source);
}
/// <summary>
/// Calculates WMA in-place, writing results to pre-allocated output span.
/// Zero-allocation method for maximum performance.
/// Uses O(1) dual running sum algorithm.
/// Automatically uses SIMD acceleration for large, clean datasets.
/// </summary>
/// <param name="source">Input values</param>
/// <param name="output">Output span (must be same length as source)</param>
/// <param name="period">WMA period (must be > 0)</param>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void Calculate(ReadOnlySpan<double> source, Span<double> output, int period)
{
if (source.Length != output.Length)
throw new ArgumentException("Source and output must have the same length");
if (period <= 0)
throw new ArgumentException("Period must be greater than 0", nameof(period));
int len = source.Length;
if (len == 0) return;
// Try SIMD path for large, clean datasets
// Requirements: AVX2 support, large enough dataset, no NaN values
const int SimdThreshold = 256;
if (Avx2.IsSupported && len >= SimdThreshold && !HasNonFiniteValues(source))
{
CalculateSimdCore(source, output, period);
return;
}
CalculateScalarCore(source, output, period);
}
/// <summary>
/// Scalar implementation with NaN handling via last-value substitution.
/// Uses circular buffer for sliding window calculation.
/// Optimized with split loops and periodic resync.
/// </summary>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static void CalculateScalarCore(ReadOnlySpan<double> source, Span<double> output, int period)
{
int len = source.Length;
double divisor = period * (period + 1) * 0.5;
double sum = 0;
double wsum = 0;
double lastValid = 0;
// Ring buffer simulation
Span<double> buffer = period <= 512 ? stackalloc double[period] : new double[period];
int bufferIdx = 0;
int i = 0;
// Phase 1: Warmup (0 to period-1)
int warmupEnd = Math.Min(period, len);
for (; i < warmupEnd; i++)
{
double val = source[i];
if (double.IsFinite(val))
lastValid = val;
else
val = lastValid;
sum += val;
wsum += (i + 1) * val;
buffer[i] = val;
double currentDivisor = (i + 1) * (i + 2) * 0.5;
output[i] = wsum / currentDivisor;
}
// Phase 2: Hot loop (period to len)
int tickCount = 0;
for (; i < len; i++)
{
double val = source[i];
if (double.IsFinite(val))
lastValid = val;
else
val = lastValid;
// O(1) update using dual running sums
double oldSum = sum;
double oldest = buffer[bufferIdx];
sum = sum - oldest + val;
wsum = wsum - oldSum + (period * val);
buffer[bufferIdx] = val;
bufferIdx++;
if (bufferIdx >= period)
bufferIdx = 0;
output[i] = wsum / divisor;
// Periodic resync every 1000 ticks
tickCount++;
if (tickCount >= ResyncInterval)
{
tickCount = 0;
// Recalculate sums from buffer to prevent drift
double recalcSum = 0;
double recalcWsum = 0;
// Buffer contains values in order: [oldest ... newest] relative to current bufferIdx
// Actually buffer is circular.
// Oldest is at bufferIdx (which we just wrote to, so it's actually newest now? No, we incremented bufferIdx)
// bufferIdx points to the *next* overwrite location, which holds the *oldest* value.
// So buffer[bufferIdx] is oldest (weight 1).
// buffer[bufferIdx+1] is 2nd oldest (weight 2).
// ...
// buffer[bufferIdx-1] is newest (weight period).
for (int k = 0; k < period; k++)
{
int idx = (bufferIdx + k) % period; // Use modulo here for simplicity in resync (rare)
// Wait, modulo is slow.
if (idx >= period) idx -= period; // Manual modulo
double v = buffer[idx];
recalcSum += v;
recalcWsum += (k + 1) * v;
}
sum = recalcSum;
wsum = recalcWsum;
}
}
}
/// <summary>
/// SIMD-optimized implementation for WMA calculation.
/// Uses double prefix-sum approach to vectorize the coupled recurrence.
/// </summary>
[MethodImpl(MethodImplOptions.AggressiveOptimization)]
private static unsafe void CalculateSimdCore(ReadOnlySpan<double> source, Span<double> output, int period)
{
int len = source.Length;
const int VectorWidth = 4;
fixed (double* srcPtr = source)
fixed (double* outPtr = output)
{
double divisor = period * (period + 1) * 0.5;
double invDivisor = 1.0 / divisor;
// Phase 1: Warmup - scalar
int warmupEnd = Math.Min(period, len);
double sum = 0;
double wsum = 0;
for (int i = 0; i < warmupEnd; i++)
{
double val = srcPtr[i];
sum += val;
wsum += (i + 1) * val;
double currentDivisor = (i + 1) * (i + 2) * 0.5;
outPtr[i] = wsum / currentDivisor;
}
if (len <= period)
return;
// Phase 2: SIMD hot loop
var vInvDivisor = Vector256.Create(invDivisor);
var vPeriod = Vector256.Create((double)period);
var vZero = Vector256<double>.Zero;
int simdEnd = period + ((len - period) / VectorWidth) * VectorWidth;
// Initialize vector state
var vSumState = Vector256.Create(sum);
var vWsumState = Vector256.Create(wsum);
int idx = period;
while (idx < simdEnd)
{
int nextSync = Math.Min(simdEnd, idx + ResyncInterval);
// Inner hot loop without branches
// Unrolled 2x (process 8 doubles per iteration)
// Optimized Parallel Execution:
// - Parallel prefix sums for DeltaS
// - Fast S_shifted calculation using (S - DeltaS)
// - Parallel prefix sums for U
int unrolledSync = nextSync - (2 * VectorWidth);
for (; idx <= unrolledSync; idx += 2 * VectorWidth)
{
// Load data for both iterations
var vNew1 = Avx.LoadVector256(srcPtr + idx);
var vOld1 = Avx.LoadVector256(srcPtr + idx - period);
var vNew2 = Avx.LoadVector256(srcPtr + idx + VectorWidth);
var vOld2 = Avx.LoadVector256(srcPtr + idx + VectorWidth - period);
// 1. Update Sum (S) - Parallel Prefix Sums
var vDeltaS1 = Avx.Subtract(vNew1, vOld1);
var vDeltaS2 = Avx.Subtract(vNew2, vOld2);
// Prefix Sum DeltaS1
var vShiftS1_1 = Avx2.Permute4x64(vDeltaS1.AsUInt64(), 0b_10_01_00_00).AsDouble();
vShiftS1_1 = Avx.Blend(vZero, vShiftS1_1, 0b_1110);
var vPS_DeltaS1 = Avx.Add(vDeltaS1, vShiftS1_1);
var vShiftS2_1 = Avx2.Permute4x64(vPS_DeltaS1.AsUInt64(), 0b_01_00_00_00).AsDouble();
vShiftS2_1 = Avx.Blend(vZero, vShiftS2_1, 0b_1100);
vPS_DeltaS1 = Avx.Add(vPS_DeltaS1, vShiftS2_1);
// Prefix Sum DeltaS2
var vShiftS1_2 = Avx2.Permute4x64(vDeltaS2.AsUInt64(), 0b_10_01_00_00).AsDouble();
vShiftS1_2 = Avx.Blend(vZero, vShiftS1_2, 0b_1110);
var vPS_DeltaS2 = Avx.Add(vDeltaS2, vShiftS1_2);
var vShiftS2_2 = Avx2.Permute4x64(vPS_DeltaS2.AsUInt64(), 0b_01_00_00_00).AsDouble();
vShiftS2_2 = Avx.Blend(vZero, vShiftS2_2, 0b_1100);
vPS_DeltaS2 = Avx.Add(vPS_DeltaS2, vShiftS2_2);
// Combine Sums
var vSums1 = Avx.Add(vSumState, vPS_DeltaS1);
var vLastS1 = Avx2.Permute4x64(vSums1.AsUInt64(), 0b_11_11_11_11).AsDouble();
var vSums2 = Avx.Add(vLastS1, vPS_DeltaS2);
// 2. Update Weighted Sum (W)
// Optimization: S_shifted = S - DeltaS
// This avoids expensive Permute/Blend operations
var vSumsShifted1 = Avx.Subtract(vSums1, vDeltaS1);
var vSumsShifted2 = Avx.Subtract(vSums2, vDeltaS2);
Vector256<double> vU1, vU2;
if (Fma.IsSupported)
{
vU1 = Fma.MultiplySubtract(vPeriod, vNew1, vSumsShifted1);
vU2 = Fma.MultiplySubtract(vPeriod, vNew2, vSumsShifted2);
}
else
{
vU1 = Avx.Subtract(Avx.Multiply(vPeriod, vNew1), vSumsShifted1);
vU2 = Avx.Subtract(Avx.Multiply(vPeriod, vNew2), vSumsShifted2);
}
// Prefix Sum W1
var vShiftW1_1 = Avx2.Permute4x64(vU1.AsUInt64(), 0b_10_01_00_00).AsDouble();
vShiftW1_1 = Avx.Blend(vZero, vShiftW1_1, 0b_1110);
var vPW1_1 = Avx.Add(vU1, vShiftW1_1);
var vShiftW2_1 = Avx2.Permute4x64(vPW1_1.AsUInt64(), 0b_01_00_00_00).AsDouble();
vShiftW2_1 = Avx.Blend(vZero, vShiftW2_1, 0b_1100);
var vPW2_1 = Avx.Add(vPW1_1, vShiftW2_1);
// Prefix Sum W2
var vShiftW1_2 = Avx2.Permute4x64(vU2.AsUInt64(), 0b_10_01_00_00).AsDouble();
vShiftW1_2 = Avx.Blend(vZero, vShiftW1_2, 0b_1110);
var vPW1_2 = Avx.Add(vU2, vShiftW1_2);
var vShiftW2_2 = Avx2.Permute4x64(vPW1_2.AsUInt64(), 0b_01_00_00_00).AsDouble();
vShiftW2_2 = Avx.Blend(vZero, vShiftW2_2, 0b_1100);
var vPW2_2 = Avx.Add(vPW1_2, vShiftW2_2);
// Combine Weighted Sums
var vWsums1 = Avx.Add(vWsumState, vPW2_1);
var vLastW1 = Avx2.Permute4x64(vWsums1.AsUInt64(), 0b_11_11_11_11).AsDouble();
var vWsums2 = Avx.Add(vLastW1, vPW2_2);
// Store results
Avx.Store(outPtr + idx, Avx.Multiply(vWsums1, vInvDivisor));
Avx.Store(outPtr + idx + VectorWidth, Avx.Multiply(vWsums2, vInvDivisor));
// Update state for next iteration
vSumState = Avx2.Permute4x64(vSums2.AsUInt64(), 0b_11_11_11_11).AsDouble();
vWsumState = Avx2.Permute4x64(vWsums2.AsUInt64(), 0b_11_11_11_11).AsDouble();
}
// Handle remaining vectors (if any)
for (; idx < nextSync; idx += VectorWidth)
{
// Load 4 entering values and 4 leaving values
var vNew = Avx.LoadVector256(srcPtr + idx);
var vOld = Avx.LoadVector256(srcPtr + idx - period);
// 1. Update Sum (S)
// Delta S = New - Old
var vDeltaS = Avx.Subtract(vNew, vOld);
// Prefix sum of Delta S
var vShiftS1 = Avx2.Permute4x64(vDeltaS.AsUInt64(), 0b_10_01_00_00).AsDouble();
vShiftS1 = Avx.Blend(vZero, vShiftS1, 0b_1110);
var vPS1 = Avx.Add(vDeltaS, vShiftS1);
var vShiftS2 = Avx2.Permute4x64(vPS1.AsUInt64(), 0b_01_00_00_00).AsDouble();
vShiftS2 = Avx.Blend(vZero, vShiftS2, 0b_1100);
var vPS2 = Avx.Add(vPS1, vShiftS2);
// Add previous sum state
var vSums = Avx.Add(vSumState, vPS2);
// 2. Update Weighted Sum (W)
// Shift vSums right and insert sum (S_t) at pos 0
var vSumsShifted = Avx2.Permute4x64(vSums.AsUInt64(), 0b_10_01_00_00).AsDouble();
vSumsShifted = Avx.Blend(vSumState, vSumsShifted, 0b_1110);
// U = (n * New) - S_shifted
var vTerm1 = Avx.Multiply(vPeriod, vNew);
var vU = Avx.Subtract(vTerm1, vSumsShifted);
// Prefix sum of U
var vShiftW1 = Avx2.Permute4x64(vU.AsUInt64(), 0b_10_01_00_00).AsDouble();
vShiftW1 = Avx.Blend(vZero, vShiftW1, 0b_1110);
var vPW1 = Avx.Add(vU, vShiftW1);
var vShiftW2 = Avx2.Permute4x64(vPW1.AsUInt64(), 0b_01_00_00_00).AsDouble();
vShiftW2 = Avx.Blend(vZero, vShiftW2, 0b_1100);
var vPW2 = Avx.Add(vPW1, vShiftW2);
// Add previous wsum state
var vWsums = Avx.Add(vWsumState, vPW2);
// Store result
var vResult = Avx.Multiply(vWsums, vInvDivisor);
Avx.Store(outPtr + idx, vResult);
// Update state for next iteration
vSumState = Avx2.Permute4x64(vSums.AsUInt64(), 0b_11_11_11_11).AsDouble();
vWsumState = Avx2.Permute4x64(vWsums.AsUInt64(), 0b_11_11_11_11).AsDouble();
}
// Periodic resync
if (idx < len)
{
// Extract scalar state for resync logic
sum = vSumState.GetElement(0);
wsum = vWsumState.GetElement(0);
// Recalculate sums from scratch
int lastIdx = idx - 1;
double recalcSum = 0;
double recalcWsum = 0;
for (int k = 0; k < period; k++)
{
double val = srcPtr[lastIdx - k];
recalcSum += val;
recalcWsum += (period - k) * val;
}
sum = recalcSum;
wsum = recalcWsum;
// Update vector state after resync
vSumState = Vector256.Create(sum);
vWsumState = Vector256.Create(wsum);
}
}
// Extract final scalar state for tail
sum = vSumState.GetElement(0);
wsum = vWsumState.GetElement(0);
// Phase 3: Scalar tail
for (; idx < len; idx++)
{
double val = srcPtr[idx];
double oldSum = sum;
double oldest = srcPtr[idx - period];
sum = sum - oldest + val;
wsum = wsum - oldSum + (period * val);
outPtr[idx] = wsum * invDivisor;
}
}
}
/// <summary>
/// Checks if span contains any non-finite values (NaN or Infinity).
/// </summary>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static bool HasNonFiniteValues(ReadOnlySpan<double> span)
{
for (int idx = 0; idx < span.Length; idx++)
{
if (!double.IsFinite(span[idx]))
return true;
}
return false;
}
/// <summary>
/// Resets the WMA state.
/// </summary>
public void Reset()
{
_buffer.Clear();
_sum = 0;
_wsum = 0;
_p_sum = 0;
_p_wsum = 0;
_p_lastInput = 0;
_lastValidValue = 0;
_p_lastValidValue = 0;
Value = default;
}
}