using System.Runtime.CompilerServices; using System.Runtime.InteropServices; using System.Runtime.Intrinsics; using System.Runtime.Intrinsics.Arm; using System.Runtime.Intrinsics.X86; namespace QuanTAlib; /// /// ACCEL: Second Derivative (Acceleration) /// Measures the rate of change of velocity - the acceleration of price movement. /// /// /// The second derivative approximates acceleration: how fast the velocity is changing. /// /// Formula: /// Accel_t = Slope_t - Slope_{t-1} /// = (Value_t - Value_{t-1}) - (Value_{t-1} - Value_{t-2}) /// = Value_t - 2*Value_{t-1} + Value_{t-2} /// /// Key properties: /// - O(1) streaming complexity /// - Zero allocations in hot path /// - SIMD-optimized batch calculation /// [SkipLocalsInit] public sealed class Accel : AbstractBase { [StructLayout(LayoutKind.Auto)] private record struct State(double Prev1, double Prev2, double LastValidValue, int Count); private State _state; private State _p_state; private readonly TValuePublishedHandler _handler; public override bool IsHot => _state.Count >= 3; /// /// Creates a new Accel (second derivative) indicator. /// public Accel() { Name = "Accel"; WarmupPeriod = 3; _handler = Handle; } /// /// Creates a new Accel indicator with event subscription. /// public Accel(ITValuePublisher source) : this() { source.Pub += _handler; } [MethodImpl(MethodImplOptions.AggressiveInlining)] private void Handle(object? sender, in TValueEventArgs args) => Update(args.Value, args.IsNew); [MethodImpl(MethodImplOptions.AggressiveInlining)] private double GetValidValue(double input) { if (double.IsFinite(input)) { _state.LastValidValue = input; return input; } return _state.LastValidValue; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public override TValue Update(TValue input, bool isNew = true) { double result; if (isNew) { _p_state = _state; double val = GetValidValue(input.Value); // accel = val - 2*prev1 + prev2 result = _state.Count >= 2 ? Math.FusedMultiplyAdd(-2.0, _state.Prev1, val + _state.Prev2) : 0.0; // Shift history _state.Prev2 = _state.Prev1; _state.Prev1 = val; _state.Count = Math.Min(_state.Count + 1, 3); } else { // Rollback for bar correction _state.LastValidValue = _p_state.LastValidValue; double val = GetValidValue(input.Value); // accel = val - 2*prev1 + prev2 result = _p_state.Count >= 2 ? Math.FusedMultiplyAdd(-2.0, _p_state.Prev1, val + _p_state.Prev2) : 0.0; // Update current state from previous (don't shift) _state.Prev2 = _p_state.Prev2; _state.Prev1 = val; _state.Count = Math.Max(_p_state.Count, 1); } Last = new TValue(input.Time, result); PubEvent(Last, isNew); return Last; } public override TSeries Update(TSeries source) { if (source.Count == 0) { return []; } int len = source.Count; // Cache source spans ONCE before any operations to avoid repeated property access ReadOnlySpan sourceValues = source.Values; ReadOnlySpan sourceTimes = source.Times; var t = new List(len); var v = new List(len); CollectionsMarshal.SetCount(t, len); CollectionsMarshal.SetCount(v, len); var tSpan = CollectionsMarshal.AsSpan(t); var vSpan = CollectionsMarshal.AsSpan(v); Batch(sourceValues, vSpan); sourceTimes.CopyTo(tSpan); // Prime state with last two values using cached span if (len >= 2) { double v1 = double.IsFinite(sourceValues[len - 1]) ? sourceValues[len - 1] : _state.LastValidValue; double v2 = double.IsFinite(sourceValues[len - 2]) ? sourceValues[len - 2] : v1; _state.Prev1 = v1; _state.Prev2 = v2; _state.LastValidValue = v1; _state.Count = Math.Min(len, 3); _p_state = _state; } else if (len == 1) { double v1 = double.IsFinite(sourceValues[0]) ? sourceValues[0] : _state.LastValidValue; _state.Prev1 = v1; _state.LastValidValue = v1; _state.Count = 1; _p_state = _state; } Last = new TValue(tSpan[len - 1], vSpan[len - 1]); return new TSeries(t, v); } public override void Reset() { _state = default; _p_state = default; Last = default; } public override void Prime(ReadOnlySpan source, TimeSpan? step = null) { // TValue is a readonly record struct - no heap allocation occurs TimeSpan interval = step ?? TimeSpan.FromSeconds(1); DateTime time = DateTime.UtcNow - (interval * source.Length); for (int i = 0; i < source.Length; i++) { Update(new TValue(time, source[i]), true); time += interval; } } public static TSeries Batch(TSeries source) { var accel = new Accel(); return accel.Update(source); } /// /// Calculates second derivative (acceleration) for a span. /// accel[i] = source[i] - 2*source[i-1] + source[i-2] /// [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void Batch(ReadOnlySpan source, Span output) { if (source.Length != output.Length) { throw new ArgumentException("Source and output must have the same length", nameof(output)); } int len = source.Length; if (len == 0) { return; } // First two elements have insufficient history output[0] = 0.0; if (len == 1) { return; } output[1] = 0.0; if (len == 2) { return; } int i = 2; // Check for non-finite values - if any exist, use scalar path only bool hasNonFinite = false; for (int k = 0; k < len && !hasNonFinite; k++) { hasNonFinite = !double.IsFinite(source[k]); } // AVX512: 8 doubles at once (only if all values are finite) if (!hasNonFinite && Avx512F.IsSupported && len >= 10) { var two = Vector512.Create(2.0); const int VectorWidth = 8; int simdEnd = len - ((len - 2) % VectorWidth); ref double srcRef = ref MemoryMarshal.GetReference(source); ref double outRef = ref MemoryMarshal.GetReference(output); for (; i < simdEnd; i += VectorWidth) { var current = Vector512.LoadUnsafe(ref Unsafe.Add(ref srcRef, i)); var prev1 = Vector512.LoadUnsafe(ref Unsafe.Add(ref srcRef, i - 1)); var prev2 = Vector512.LoadUnsafe(ref Unsafe.Add(ref srcRef, i - 2)); // accel = current - 2*prev1 + prev2 var twoTimesP1 = Avx512F.Multiply(two, prev1); var diff = Avx512F.Subtract(current, twoTimesP1); var result = Avx512F.Add(diff, prev2); result.StoreUnsafe(ref Unsafe.Add(ref outRef, i)); } } // AVX: 4 doubles at once (only if all values are finite) else if (!hasNonFinite && Avx.IsSupported && len >= 6) { var two = Vector256.Create(2.0); const int VectorWidth = 4; int simdEnd = len - ((len - 2) % VectorWidth); ref double srcRef = ref MemoryMarshal.GetReference(source); ref double outRef = ref MemoryMarshal.GetReference(output); for (; i < simdEnd; i += VectorWidth) { var current = Vector256.LoadUnsafe(ref Unsafe.Add(ref srcRef, i)); var prev1 = Vector256.LoadUnsafe(ref Unsafe.Add(ref srcRef, i - 1)); var prev2 = Vector256.LoadUnsafe(ref Unsafe.Add(ref srcRef, i - 2)); var twoTimesP1 = Avx.Multiply(two, prev1); var diff = Avx.Subtract(current, twoTimesP1); var result = Avx.Add(diff, prev2); result.StoreUnsafe(ref Unsafe.Add(ref outRef, i)); } } // ARM64 Neon: 2 doubles at once (only if all values are finite) else if (!hasNonFinite && AdvSimd.Arm64.IsSupported && len >= 4) { var two = Vector128.Create(2.0); const int VectorWidth = 2; int simdEnd = len - ((len - 2) % VectorWidth); ref double srcRef = ref MemoryMarshal.GetReference(source); ref double outRef = ref MemoryMarshal.GetReference(output); for (; i < simdEnd; i += VectorWidth) { var current = Vector128.LoadUnsafe(ref Unsafe.Add(ref srcRef, i)); var prev1 = Vector128.LoadUnsafe(ref Unsafe.Add(ref srcRef, i - 1)); var prev2 = Vector128.LoadUnsafe(ref Unsafe.Add(ref srcRef, i - 2)); var twoTimesP1 = AdvSimd.Arm64.Multiply(two, prev1); var diff = AdvSimd.Arm64.Subtract(current, twoTimesP1); var result = AdvSimd.Arm64.Add(diff, prev2); result.StoreUnsafe(ref Unsafe.Add(ref outRef, i)); } } // Scalar fallback for remaining elements // Initialize prev values from actual data at position i-1 and i-2 for (; i < len; i++) { double curr = source[i]; double p1 = source[i - 1]; double p2 = source[i - 2]; // Handle NaN/Infinity by substitution (find first finite value) double fallback = FindFinite(curr, p1, p2); if (!double.IsFinite(curr)) { curr = fallback; } if (!double.IsFinite(p1)) { p1 = fallback; } if (!double.IsFinite(p2)) { p2 = fallback; } // accel = curr - 2*prev1 + prev2 output[i] = Math.FusedMultiplyAdd(-2.0, p1, curr + p2); } } public static (TSeries Results, Accel Indicator) Calculate(TSeries source) { var indicator = new Accel(); TSeries results = indicator.Update(source); return (results, indicator); } [MethodImpl(MethodImplOptions.AggressiveInlining)] private static double FindFinite(double a, double b, double c) { if (double.IsFinite(a)) { return a; } if (double.IsFinite(b)) { return b; } if (double.IsFinite(c)) { return c; } return 0.0; } }