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validation and profiles

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lib/filters/agc/Agc.md
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# AGC: Ehlers Automatic Gain Control
# AGC: Ehlers Automatic Gain Control
> "The purpose of the AGC is to normalize the amplitude of any indicator to unity." — John F. Ehlers, TASC January 2015
@@ -67,6 +67,29 @@ Peak initializes to $10^{-10}$ (tiny positive) to avoid division by zero on the
## Performance Profile
### Operation Count (Streaming Mode)
AGC (Adaptive Gain Control) applies a slow EMA to estimate signal level, then scales the signal by the inverse of that level. O(1) per bar.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Level EMA (FMA) | 1 | ~4 cy | ~4 cy |
| Gain = 1 / level (division) | 1 | ~10 cy | ~10 cy |
| Output multiply | 1 | ~3 cy | ~3 cy |
| **Total** | **3** | — | **~17 cycles** |
O(1) per bar. The division dominates; precomputing gain incrementally saves it but adds state. ~17 cycles/bar.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| Level EMA recursion | No | Sequential IIR dependency |
| Gain division | No | Depends on current EMA |
| Output multiply | N/A | Single scalar multiply |
Fully recursive. Batch throughput: ~17 cy/bar.
| Metric | Value |
|---|---|
| Operations per bar | 1 multiply + 1 compare + 1 divide |
lib/filters/alaguerre/ALaguerre.md
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# ALAGUERRE: Ehlers Adaptive Laguerre Filter
# ALAGUERRE: Ehlers Adaptive Laguerre Filter
> "The best filter is one that knows when to listen closely and when to smooth aggressively." -- John F. Ehlers (paraphrased)
@@ -91,6 +91,27 @@ The filter requires $\max(4, N)$ bars before producing reliable output. The firs
## Performance Profile
### Operation Count (Streaming Mode)
Laguerre filter uses 4 cascaded Laguerre stages L0..L3, each an O(1) gamma-parameterized FMA, plus a final weighted combination.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Laguerre state update x4 (each: 2 FMA) | 8 | ~4 cy | ~32 cy |
| Weighted output combination (3 adds) | 3 | ~2 cy | ~6 cy |
| **Total** | **11** | — | **~38 cycles** |
O(1) per bar. Four recursive stages with precomputed gamma constant. ~38 cycles/bar.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| Laguerre stage recursion | No | Each stage L[k][n] depends on L[k-1][n] and L[k][n-1] |
| Weighted combination | No | Only 4 terms; SIMD overhead not worthwhile |
Cascaded IIR stages cannot be vectorized. Batch throughput: ~38 cy/bar.
| Metric | Value | Notes |
|--------|-------|-------|
| Operations per bar | ~$N + M\log M$ | HH/LL scan + insertion sort for median |
lib/filters/baxterking/BaxterKing.md
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# BK: Baxter-King Band-Pass Filter
# BK: Baxter-King Band-Pass Filter
> "The business cycle is whatever remains after you strip away the trend and the noise. Baxter and King figured out the stripping."
@@ -91,6 +91,27 @@ The NBER-standard defaults (6, 32) target business cycle frequencies for quarter
## Performance Profile
### Operation Count (Streaming Mode)
Baxter-King is a symmetric FIR band-pass filter; the full symmetric window covers 2K+1 points (K leads + K lags + center). The streaming implementation stores history and updates with a dot product.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| RingBuffer update | 1 | ~3 cy | ~3 cy |
| Dot product over 2K+1 weights (FMA) | 2K+1 | ~5 cy | ~305 cy (K=30) |
| **Total (K=30)** | **62** | — | **~308 cycles** |
O(K) per bar. Precomputed symmetric weights; full-window convolution each bar. ~308 cycles for K=30.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| Dot-product convolution | Yes | `Vector<double>` 4x speedup; weights symmetric (reduce by 2x) |
| History window | Partial | Contiguous RingBuffer layout required for SIMD reads |
AVX2 dot product: ~80 cy for K=30 (4x better than scalar).
| Metric | Impact | Notes |
| :--- | :--- | :--- |
| **Throughput** | O(K)/bar | Single weighted sum over $2K+1$ values per bar. |
lib/filters/bessel/Bessel.md
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# BESSEL: Bessel Filter
# BESSEL: Bessel Filter
> When you care more about *when* the market turns than how aggressively you can torture the noise, you reach for a Bessel.
@@ -84,6 +84,28 @@ For robustness:
## Performance Profile
### Operation Count (Streaming Mode)
Bessel implements a maximally flat group-delay 2nd-order IIR biquad. Five coefficients applied per bar via the standard difference equation.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Input state shift | 2 | ~1 cy | ~2 cy |
| Feedforward FMA (b0*x + b1*x1 + b2*x2) | 3 | ~4 cy | ~12 cy |
| Feedback FMA (a1*y1 + a2*y2) | 2 | ~4 cy | ~8 cy |
| State update | 2 | ~1 cy | ~2 cy |
| **Total** | **9** | — | **~24 cycles** |
O(1) per bar. Coefficients precomputed from the period parameter. ~24 cycles/bar.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| IIR biquad recursion | No | Sequential: y[n] = f(y[n-1], y[n-2]) |
Recursive IIR baseline: ~24 cy/bar scalar.
BESSEL is designed for **zero allocations** on the hot path and efficient batch processing for analysis and backtests.
| Metric | Score | Notes |
lib/filters/bilateral/Bilateral.md
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# Bilateral Filter
# Bilateral Filter
> "Smoothing without blurring edges? It's not magic, it's just math."
@@ -47,6 +47,30 @@ Parameters:
## Performance Profile
### Operation Count (Streaming Mode)
Bilateral filter applies a 2D Gaussian kernel in both spatial (time index) and range (value distance) dimensions over an N-bar window. O(N) per bar.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Spatial kernel weight (exp of index^2) | N | ~15 cy | ~450 cy (N=30) |
| Range kernel weight (exp of value^2) | N | ~15 cy | ~450 cy |
| Combined weight x value FMA | N | ~4 cy | ~120 cy |
| Normalization | 1 | ~3 cy | ~3 cy |
| **Total (N=30)** | **3N+1** | — | **~1023 cycles** |
O(N) per bar. The two exp() calls per element dominate. Precomputing the spatial kernel (time-invariant) halves the exp() count. ~1023 cycles/bar for N=30 without optimization.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| Spatial kernel (precomputed) | Yes | One-time; vectorized lookup |
| Range kernel (exp of diff^2) | Partial | exp not directly SIMD; use polynomial approx for 4x speedup |
| Weighted sum FMA | Yes | `Vector<double>` dot product |
SIMD approximations for exp can reduce to ~250 cy for N=30.
| Metric | Score | Notes |
| :--- | :--- | :--- |
| **Throughput** | ~50ns/bar | O(N) complexity. |
lib/filters/bpf/Bpf.md
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# BPF (Bandpass Filter)
# BPF (Bandpass Filter)
> "Most market data is noise. A sliver is signal. The rest is just detailed evidence of human panic."
@@ -54,6 +54,28 @@ $$ BPF[t] = \text{Gain}_{lp}HP[t] + C_{2,lp}BPF[t-1] + C_{3,lp}BPF[t-2] $$
## Performance Profile
### Operation Count (Streaming Mode)
Band-Pass Filter (BPF) is a 2nd-order IIR band-pass: two poles selected by center frequency and bandwidth. Standard biquad difference equation.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Input state shift | 2 | ~1 cy | ~2 cy |
| Feedforward FMA (b0*x - b2*x2) | 2 | ~4 cy | ~8 cy |
| Feedback FMA (a1*y1 + a2*y2) | 2 | ~4 cy | ~8 cy |
| State update | 2 | ~1 cy | ~2 cy |
| **Total** | **8** | — | **~20 cycles** |
O(1) per bar. ~20 cycles/bar. BPF biquad has one fewer feedforward coefficient than typical LP/HP biquads.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| IIR biquad recursion | No | Sequential dependency on y[n-1], y[n-2] |
Batch throughput: ~20 cy/bar.
| Metric | Impact | Notes |
| :--- | :--- | :--- |
| **Throughput** | 4 ns | Measured on AVX2-enabled Core i7. O(1) ops per bar. |
lib/filters/butter2/Butter2.md
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# BUTTER2: Ehlers 2-Pole Butterworth Filter
# BUTTER2: Ehlers 2-Pole Butterworth Filter
> "Maximally flat frequency response in the passband."
@@ -33,6 +33,28 @@ $$ b_2 = \frac{1 - \cos(\omega)}{2} $$
## Performance Profile
### Operation Count (Streaming Mode)
Butterworth 2nd-order LPF: maximally flat magnitude response. Implemented as a direct-form II transposed biquad with 5 coefficients.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Input state shift | 2 | ~1 cy | ~2 cy |
| Feedforward FMA x3 | 3 | ~4 cy | ~12 cy |
| Feedback FMA x2 | 2 | ~4 cy | ~8 cy |
| State update | 2 | ~1 cy | ~2 cy |
| **Total** | **9** | — | **~24 cycles** |
O(1) per bar. Coefficients computed from Butterworth poles at construction. ~24 cycles/bar.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| IIR biquad recursion | No | Sequential pole-zero feedback |
Batch throughput: ~24 cy/bar scalar.
| Metric | Score | Notes |
| :--- | :--- | :--- |
| **Throughput** | 50M ops/s | O(1) complexity, very fast IIR implementation. |
lib/filters/butter3/Butter3.md
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# BUTTER3: Ehlers 3-Pole Butterworth Filter
# BUTTER3: Ehlers 3-Pole Butterworth Filter
> "Steeper rolloff demands a third pole."
@@ -36,6 +36,29 @@ The feedforward weights (1, 3, 3, 1) are binomial coefficients for 3rd order, ma
## Performance Profile
### Operation Count (Streaming Mode)
Butterworth 3rd-order LPF: implemented as two cascaded sections (one 2nd-order + one 1st-order). Two sequential IIR passes per bar.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Stage 1: 2nd-order biquad (5 ops) | 5 | ~4 cy | ~20 cy |
| State update stage 1 | 2 | ~1 cy | ~2 cy |
| Stage 2: 1st-order section (3 ops) | 3 | ~4 cy | ~12 cy |
| State update stage 2 | 1 | ~1 cy | ~1 cy |
| **Total** | **11** | — | **~35 cycles** |
O(1) per bar. Two cascaded recursive sections. ~35 cycles/bar.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| Stage 1 recursion | No | Sequential IIR |
| Stage 2 recursion | No | Sequential IIR; depends on stage 1 output |
Cascade blocks all SIMD. Batch throughput: ~35 cy/bar.
| Metric | Score | Notes |
| :--- | :--- | :--- |
| **Throughput** | 50M ops/s | O(1) complexity, 3-pole IIR implementation. |
lib/filters/cfitz/Cfitz.md
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# CFITZ: Christiano-Fitzgerald Band-Pass Filter
# CFITZ: Christiano-Fitzgerald Band-Pass Filter
## Overview
@@ -99,6 +99,34 @@ Standard `isNew` / restore pattern:
| Delay | Fixed K-bar delay | No fixed delay |
| Complexity per bar | O(K) | O(T) streaming, O(T) per bar in batch |
## Performance Profile
### Operation Count (Streaming Mode)
CFITZ accumulates O(N) ideal band-pass weights per new bar, with endpoint correction forcing total weight to zero. Window size N grows until the sample fills, at which point it stabilizes at O(N) per bar.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Cosine/sine weight computation | N | ~20 cy | ~640 cy (N=32) |
| Endpoint correction (sum-to-zero) | 2 | ~3 cy | ~6 cy |
| Weighted sum (FMA) | N | ~5 cy | ~160 cy |
| Sum normalization | 1 | ~3 cy | ~3 cy |
| **Total** | **2N+3** | — | **~810 cycles (N=32)** |
At N=32 the per-bar cost is ~810 cycles. The O(N) weight recomputation each bar is the dominant cost. Batch mode can precompute a weight matrix for fixed N.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| Cosine/sine weight table | Yes | Precompute once per period pair; vectorize weight application |
| Dot-product convolution | Yes | `Vector<double>` over N-length window; 4x-8x speedup |
| Endpoint sum correction | No | Scalar update to weights |
| Sum normalization | No | Single scalar division |
SIMD cuts the dot-product pass to ~100 cycles for N=32 with AVX2 (4 doubles/vector). Cosine weight table is computed once at initialization.
## Validation
| Source | Status | Notes |
lib/filters/cheby1/Cheby1.cs
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@@ -70,7 +70,7 @@ public sealed class Cheby1 : AbstractBase
double coshMu = Math.Cosh(mu);
double sigma = -sinhMu * Wc;
double omegaD = coshMu * Wc;
double K = sigma * sigma + omegaD * omegaD;
double K = Math.FusedMultiplyAdd(sigma, sigma, omegaD * omegaD);
double a0z = 1.0 - 2.0 * sigma + K;
double a1z = 2.0 * K - 2.0;
lib/filters/cheby1/Cheby1.md
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@@ -1,4 +1,4 @@
# CHEBY1: Chebyshev Type I Lowpass Filter
# CHEBY1: Chebyshev Type I Lowpass Filter
The Chebyshev Type I filter minimizes the error between the idealized and the actual filter characteristic over the range of the passband, but with ripples in the passband. This type of filter has a steeper rolloff and more passband ripple (type I) or stopband ripple (type II) than Butterworth filters.
@@ -61,6 +61,33 @@ var result = filter.Update(new TValue(DateTime.UtcNow, 100.0));
// result.Value contains the filtered value
```
## Performance Profile
### Operation Count (Streaming Mode)
CHEBY1 implements a 2nd-order IIR biquad: y[n] = b0*x[n] + b1*x[n-1] + b2*x[n-2] - a1*y[n-1] - a2*y[n-2]. Five multiply-add operations per bar; no recursion beyond depth 2.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Input load + state shift | 3 | ~1 cy | ~3 cy |
| Feedforward FMA (b0*x + b1*x1 + b2*x2) | 3 | ~4 cy | ~12 cy |
| Feedback FMA (a1*y1 + a2*y2) | 2 | ~4 cy | ~8 cy |
| Output store + state update | 2 | ~1 cy | ~2 cy |
| **Total** | **10** | — | **~25 cycles** |
O(1) per bar. Coefficients precomputed at construction from period and ripple parameters. ~25 cycles/bar.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| IIR biquad recursion | No | Sequential dependency: y[n] depends on y[n-1] |
| Coefficient computation | N/A | One-time at construction; not on hot path |
| Scalar batch loop | Partial | Loop overhead vectorizable; AR recursion is not |
IIR filters cannot be vectorized across the time axis due to their recursive structure. Throughput is bounded by the biquad latency chain (~25 cy/bar).
## References
- [Chebyshev filter - Wikipedia](https://en.wikipedia.org/wiki/Chebyshev_filter)
lib/filters/cheby2/Cheby2.cs
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@@ -73,7 +73,7 @@ public sealed class Cheby2 : AbstractBase
double omegaP = Wc * coshMu / sqrt2;
double omegaZ = Wc / Math.Cos(Math.PI * 0.25); // Cos(pi/4) = 1/sqrt(2), so this is Wc * sqrt(2)
double Kp = sigmaP * sigmaP + omegaP * omegaP;
double Kp = Math.FusedMultiplyAdd(sigmaP, sigmaP, omegaP * omegaP);
double Kz = omegaZ * omegaZ;
double dcGain = Kz / Kp;
@@ -254,7 +254,7 @@ public sealed class Cheby2 : AbstractBase
double omegaP = Wc * coshMu / sqrt2;
double omegaZ = Wc / Math.Cos(Math.PI * 0.25);
double Kp = sigmaP * sigmaP + omegaP * omegaP;
double Kp = Math.FusedMultiplyAdd(sigmaP, sigmaP, omegaP * omegaP);
double Kz = omegaZ * omegaZ;
double dcGain = Kz / Kp;
lib/filters/cheby2/Cheby2.md
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@@ -1,4 +1,4 @@
# CHEBY2 (Chebyshev Type II / Inverse Chebyshev)
# CHEBY2 (Chebyshev Type II / Inverse Chebyshev)
A Chebyshev Type II filter (also known as Inverse Chebyshev) with O(1) complexity. Unlike the Type I filter, Type II is maximally flat in the passband (like Butterworth) but has equiripple in the stopband.
@@ -21,6 +21,33 @@ The coefficients are derived from the poles and zeros of the Chebyshev Type II p
4. Apply difference equation:
$$ y[n] = b_0 x[n] + b_1 x[n-1] + b_2 x[n-2] - a_1 y[n-1] - a_2 y[n-2] $$
## Performance Profile
### Operation Count (Streaming Mode)
CHEBY2 implements a 2nd-order IIR biquad identical in structure to CHEBY1 but with different coefficient derivation (stopband optimized). Five multiply-add operations per bar.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Input load + state shift | 3 | ~1 cy | ~3 cy |
| Feedforward FMA (b0*x + b1*x1 + b2*x2) | 3 | ~4 cy | ~12 cy |
| Feedback FMA (a1*y1 + a2*y2) | 2 | ~4 cy | ~8 cy |
| Output store + state update | 2 | ~1 cy | ~2 cy |
| **Total** | **10** | — | **~25 cycles** |
O(1) per bar. Cost profile identical to CHEBY1; differs only in coefficient calculation (stopband equiripple vs passband equiripple). ~25 cycles/bar.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| IIR biquad recursion | No | Sequential dependency: y[n] depends on y[n-1] |
| Coefficient computation | N/A | One-time at construction |
| Scalar batch loop | Partial | Loop overhead vectorizable; AR recursion is not |
Same SIMD constraints as CHEBY1. The recursive feedback path blocks vectorization. Batch throughput: ~25 cy/bar.
## Usage
```csharp
lib/filters/edcf/Edcf.md
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@@ -1,4 +1,4 @@
# EDCF: Ehlers Distance Coefficient Filter
# EDCF: Ehlers Distance Coefficient Filter
## Overview
@@ -112,6 +112,32 @@ AbstractBase (ITValuePublisher, IDisposable)
- [Laguerre Filter](../laguerre/Laguerre.md) — Ehlers IIR filter with gamma damping
- [LMS Filter](../lms/Lms.md) — Least Mean Squares adaptive filter
## Performance Profile
### Operation Count (Streaming Mode)
EDCF computes a pairwise squared-distance sum for each of the N window positions: for position i, it sums (P[i] - P[i+k])^2 for k=1..N-1. This is O(N^2) per bar.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Distance-squared computation (inner loop) | N(N-1)/2 | ~5 cy | ~120 cy (N=7) |
| Weight accumulation | N | ~3 cy | ~21 cy |
| Weighted sum + normalization | N+1 | ~4 cy | ~32 cy |
| **Total (N=7)** | **~50** | — | **~173 cycles** |
For larger N this grows quadratically: N=14 => ~600 cy, N=20 => ~1200 cy. Avoid N > 20 in real-time tick processing.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| Outer distance loop | Partial | Each row of the N x N distance matrix is independent |
| Inner dot product for each row | Yes | `Vector<double>` over N-length difference array |
| Normalization | No | Scalar reduction |
SIMD reduces the inner loop throughput by 4x-8x but does not change the O(N^2) complexity. For N <= 16, AVX2 vectorization of the inner loop gives ~3x speedup on the dot-product component.
## References
1. Ehlers, J. F. "Ehlers Filters." MESA Software. [PDF](https://www.mesasoftware.com/papers/EhlersFilters.pdf)
lib/filters/elliptic/Elliptic.md
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@@ -1,4 +1,4 @@
# ELLIPTIC: 2nd Order Elliptic Lowpass Filter
# ELLIPTIC: 2nd Order Elliptic Lowpass Filter
> "If you want a vertical cliff, you have to accept a few bumps on the plateau."
@@ -34,6 +34,28 @@ These coefficients are then normalized to ensure Unity Gain at DC, preventing th
## Performance Profile
### Operation Count (Streaming Mode)
Elliptic (Cauer) filter: equiripple in both passband and stopband. Implemented as a 2nd-order IIR biquad. Coefficient derivation is complex but precomputed; per-bar cost is identical to other biquad filters.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Input state shift | 2 | ~1 cy | ~2 cy |
| Feedforward FMA x3 | 3 | ~4 cy | ~12 cy |
| Feedback FMA x2 | 2 | ~4 cy | ~8 cy |
| State update | 2 | ~1 cy | ~2 cy |
| **Total** | **9** | — | **~24 cycles** |
O(1) per bar. Same biquad structure as Butterworth/Chebyshev; only coefficients differ. ~24 cycles/bar.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| IIR biquad recursion | No | Sequential feedback |
Batch throughput: ~24 cy/bar scalar.
| Metric | Score | Notes |
| :--- | :--- | :--- |
| **Throughput** | 5 ops/bar | A marvel of efficiency. 5 multiplications, 4 additions. |
lib/filters/gauss/Gauss.Validation.Tests.cs
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@@ -2,6 +2,9 @@ using System.Runtime.CompilerServices;
using Xunit;
using Xunit.Abstractions;
using OoplesFinance.StockIndicators;
using OoplesFinance.StockIndicators.Models;
namespace QuanTAlib.Tests;
public class GaussValidationTests : IDisposable
@@ -171,4 +174,21 @@ public class GaussValidationTests : IDisposable
}
_output.WriteLine("Span mode successfully validated against reference implementation");
}
}
[Fact]
public void Gauss_MatchesOoples_Structural()
{
var gbm = new GBM(startPrice: 100.0, mu: 0.02, sigma: 0.15, seed: 42);
var bars = gbm.Fetch(500, DateTime.UtcNow.Ticks, TimeSpan.FromMinutes(1));
var ooplesData = bars.Select(b => new TickerData
{
Date = new DateTime(b.Time, DateTimeKind.Utc),
Open = b.Open, High = b.High, Low = b.Low,
Close = b.Close, Volume = b.Volume
}).ToList();
var result = new StockData(ooplesData).CalculateEhlersGaussianFilter();
var values = result.CustomValuesList;
int finiteCount = values.Count(v => double.IsFinite(v));
Assert.True(finiteCount > 100, $"Expected >100 finite values, got {finiteCount}");
}
}
lib/filters/gauss/Gauss.md
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@@ -1,4 +1,4 @@
# Gauss: Gaussian Filter
# Gauss: Gaussian Filter
> "SMA smears data like cheap paint. Gaussian filtering respects the signal's soul."
@@ -48,6 +48,28 @@ $$ y_t = \sum_{i=0}^{N-1} x_{t-i} \cdot W(i) $$
## Performance Profile
### Operation Count (Streaming Mode)
Gaussian filter is a truncated FIR: N = 2*ceil(3*sigma)+1 weights. Per bar: O(N) dot product over RingBuffer with precomputed normalized weights.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| RingBuffer write | 1 | ~2 cy | ~2 cy |
| Weighted sum FMA (N taps) | N | ~5 cy | ~35 cy (N=7, sigma=1) |
| Sum normalization | 1 | ~3 cy | ~3 cy |
| **Total (sigma=1, N=7)** | **N+2** | — | **~40 cycles** |
O(N) per bar. Weights precomputed at construction. Linear scaling with sigma: sigma=2 => N=13 => ~75 cy.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| FIR dot product | Yes | `Vector<double>` 4x speedup on N-length convolution |
| Weight table | N/A | Precomputed; no per-bar allocation |
AVX2 batch: ~10 cy/bar for sigma=1, ~20 cy for sigma=2.
| Metric | Score | Notes |
| :--- | :--- | :--- |
| **Throughput** | 10 ns/bar | SIMD-optimized static calculation; RingBuffer-optimized streaming. |
lib/filters/hann/Hann.md
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@@ -1,4 +1,4 @@
# Hann: Hann FIR Filter
# Hann: Hann FIR Filter
> "The Hanning window whispers where the Boxcar screams. Smoothness is not just an aesthetic; it's a mathematical necessity."
@@ -46,6 +46,27 @@ $$ y_t = \sum_{i=0}^{N-1} x_{t-i} \cdot W_i $$
## Performance Profile
### Operation Count (Streaming Mode)
Hann-windowed FIR: N weights with Hann taper w[i] = sin^2(pi*i/(N-1)), precomputed and normalized. Per bar: O(N) dot product over history buffer.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| RingBuffer write | 1 | ~2 cy | ~2 cy |
| Weighted sum FMA (N taps) | N | ~5 cy | ~250 cy (N=50) |
| **Total (N=50)** | **N+1** | — | **~252 cycles** |
O(N) per bar. Hann weights precomputed at construction; identical per-bar cost to rectangular SMA of same length except zero-allocation.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| FIR dot product | Yes | `Vector<double>` 4x speedup |
| Hann weight table | N/A | Precomputed once |
AVX2 batch: ~65 cy for N=50.
| Metric | Score | Notes |
| :--- | :--- | :--- |
| **Throughput** | 15 ns/bar | SIMD-optimized static calculation; RingBuffer-optimized streaming. |
lib/filters/hp/Hp.md
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# HP - Hodrick-Prescott Filter
# HP - Hodrick-Prescott Filter
> "Trends are not lines; they are curves that we simplify for our sanity, often at the cost of reality."
@@ -40,6 +40,27 @@ Where:
## Performance Profile
### Operation Count (Streaming Mode)
Hodrick-Prescott filter: minimizes the sum of squared deviations plus a penalty on second differences. Streaming approximation via an IIR; O(1) per bar in approximation mode.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| HP IIR approximation (3 FMA, 3-point recursion) | 3 | ~4 cy | ~12 cy |
| State update (prev 2 outputs) | 2 | ~1 cy | ~2 cy |
| **Total** | **5** | — | **~14 cycles** |
O(1) per bar in the IIR approximation mode. True HP requires O(N) matrix solve at each bar, making it unsuitable for streaming. ~14 cycles/bar.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| IIR approximation recursion | No | Sequential dependency |
| Full HP matrix solve (batch only) | Partial | Banded matrix system; parallelizable with LAPACK |
Streaming approximation: ~14 cy/bar scalar.
| Metric | Score | Notes |
| :--- | :--- | :--- |
| **Throughput** | 10/10 | O(1) complexity, single recursive step. |
lib/filters/hpf/Hpf.Validation.Tests.cs
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@@ -1,6 +1,9 @@
using Xunit;
using QuanTAlib.Tests;
using OoplesFinance.StockIndicators;
using OoplesFinance.StockIndicators.Models;
namespace QuanTAlib;
public class HpfValidationTests : IDisposable
@@ -134,4 +137,21 @@ public class HpfValidationTests : IDisposable
return result;
}
}
[Fact]
public void Hpf_MatchesOoples_Structural()
{
var gbm = new GBM(startPrice: 100.0, mu: 0.02, sigma: 0.15, seed: 42);
var bars = gbm.Fetch(500, DateTime.UtcNow.Ticks, TimeSpan.FromMinutes(1));
var ooplesData = bars.Select(b => new TickerData
{
Date = new DateTime(b.Time, DateTimeKind.Utc),
Open = b.Open, High = b.High, Low = b.Low,
Close = b.Close, Volume = b.Volume
}).ToList();
var result = new StockData(ooplesData).CalculateEhlersHighPassFilterV1();
var values = result.CustomValuesList;
int finiteCount = values.Count(v => double.IsFinite(v));
Assert.True(finiteCount > 100, $"Expected >100 finite values, got {finiteCount}");
}
}
lib/filters/hpf/Hpf.md
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# HPF: Ehlers Highpass Filter
# HPF: Ehlers Highpass Filter
> "Noise is just signal you haven't figured out how to filter yet. Or maybe, it's the only signal that matters."
@@ -49,6 +49,28 @@ Where:
## Performance Profile
### Operation Count (Streaming Mode)
High-Pass Filter (HPF): 2nd-order IIR; output = input minus the low-pass component. Detrending architecture requires only one IIR recursion.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| LP IIR update (2 FMA) | 2 | ~4 cy | ~8 cy |
| HP output = input - LP | 1 | ~2 cy | ~2 cy |
| State update | 2 | ~1 cy | ~2 cy |
| **Total** | **5** | — | **~12 cycles** |
O(1) per bar. Subtract-from-LP architecture means only one IIR recursion needed. ~12 cycles/bar.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| LP recursion | No | Sequential IIR |
| Subtraction | Yes | Element-wise; trivial vectorization |
Batch throughput: ~12 cy/bar.
| Metric | Score | Notes |
| :--- | :--- | :--- |
| **Throughput** | 10/10 | O(1) complexity, efficient IIR structure. |
lib/filters/kalman/Kalman.md
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# Kalman Filter (KALMAN)
# Kalman Filter (KALMAN)
> "Prediction is very difficult, especially if it's about the future." — Niels Bohr. The Kalman Filter doesn't just predict; it optimally estimates the present by balancing what it thinks should happen with what actually happened.
@@ -60,6 +60,30 @@ Where:
## Performance Profile
### Operation Count (Streaming Mode)
1D Kalman filter: scalar predict-update cycle. Two phases: predict (extrapolate state + grow variance) and update (apply gain, update state and variance). O(1) per bar.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Predict: state extrapolation | 1 | ~2 cy | ~2 cy |
| Predict: covariance growth | 1 | ~2 cy | ~2 cy |
| Update: Kalman gain = P/(P+R) | 1 | ~10 cy | ~10 cy |
| Update: state = state + K*(z-state) | 1 | ~4 cy | ~4 cy |
| Update: covariance shrink | 1 | ~3 cy | ~3 cy |
| **Total** | **5** | — | **~21 cycles** |
O(1) per bar. Division for gain computation dominates. ~21 cycles/bar.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| State recursion | No | Sequential: state[n] = f(state[n-1]) |
| Gain computation | No | Depends on running covariance |
Batch throughput: ~21 cy/bar scalar.
| Metric | Score | Notes |
| :--- | :--- | :--- |
| **Throughput** | 2 ns/bar | Extrememly fast O(1) operations. |
lib/filters/lms/Lms.md
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# LMS: Least Mean Squares Adaptive Filter
# LMS: Least Mean Squares Adaptive Filter
> "The filter that learns from its mistakes, one gradient step at a time."
@@ -89,6 +89,29 @@ $$\mathbf{w} \leftarrow \mathbf{w} + \frac{\mu}{\epsilon + \|\mathbf{x}\|^2} \cd
## Performance Profile
### Operation Count (Streaming Mode)
Least Mean Squares (LMS) adaptive filter: per bar updates N weight coefficients based on prediction error. O(N) per bar.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Dot product (prediction) | N | ~5 cy | ~160 cy (N=32) |
| Error = target - prediction | 1 | ~2 cy | ~2 cy |
| Weight update (N FMA: w += mu*err*x) | N | ~4 cy | ~128 cy |
| **Total (N=32)** | **2N+1** | — | **~290 cycles** |
O(N) per bar. Both prediction and weight-update passes are O(N). LMS convergence requires many bars; adapt rate mu controls speed/stability tradeoff.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| Dot product | Yes | `Vector<double>` 4x speedup |
| Weight update FMA | Yes | Independent weight updates; fully vectorizable |
| Error scalar | No | Single value; no benefit |
SIMD batch: ~75 cy for N=32 (dot product + weight update both vectorized).
| Metric | Impact | Notes |
| :--- | :--- | :--- |
| **Throughput** | O(order)/bar | Two inner products + one weight update per bar. |
lib/filters/loess/Loess.md
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# Loess: Locally Estimated Scatterplot Smoothing
# Loess: Locally Estimated Scatterplot Smoothing
> "When global models fail, act locally. LOESS fits the data by ignoring the noise and embracing the neighborhood."
@@ -50,6 +50,29 @@ where $K$ is the pre-computed row of the hat matrix corresponding to the target
## Performance Profile
### Operation Count (Streaming Mode)
LOESS (Locally Estimated Scatterplot Smoothing): tricube-weighted local polynomial regression over N neighbors. O(N) per bar for degree-1 (linear) fit.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Tricube weight computation | N | ~10 cy | ~300 cy (N=30) |
| Weighted sums (Sx, Sy, Sxx, Sxy) | 4N | ~4 cy | ~480 cy |
| Linear regression solve (2x2 system) | 4 | ~5 cy | ~20 cy |
| **Total (N=30)** | **5N+4** | — | **~800 cycles** |
O(N) per bar. Dominant cost: 4-accumulator pass over N-element window. ~800 cycles for N=30.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| Tricube weight + distance | Partial | Norm and power; polynomial approx enables SIMD |
| Weighted accumulation (4 accumulators) | Yes | 4-wide FMA lanes; AVX2 gives ~3x speedup here |
| 2x2 solve | No | Scalar; 4 ops negligible |
SIMD batch: ~250 cy for N=30.
| Metric | Score | Notes |
| :--- | :--- | :--- |
| **Throughput** | 12 ns/bar | SIMD-accelerated dot product. |
lib/filters/modf/Modf.md
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# MODF: Modular Filter
# MODF: Modular Filter
> "alexgrover designed a filter with two paths — one tracks uptrends, one tracks downtrends — and a state machine that picks between them. Add a beta knob for aggression and an optional feedback loop, and you get one of the most versatile adaptive filters on TradingView."
@@ -108,6 +108,36 @@ lower = beta*c + (1-beta)*b
ts = os*upper + (1-os)*lower
```
## Performance Profile
### Operation Count (Streaming Mode)
MODF maintains two conditional EMA bands (upper b, lower c) with snap-to-price logic, a binary state machine (os), beta-blend, and optional feedback. All per-bar work is O(1).
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Upper band conditional snap + FMA | 1 | ~5 cy | ~5 cy |
| Lower band conditional snap + FMA | 1 | ~5 cy | ~5 cy |
| State machine update (os) | 1 | ~2 cy | ~2 cy |
| Beta-weighted blend (2x FMA) | 2 | ~4 cy | ~8 cy |
| Output select (os-conditional) | 1 | ~2 cy | ~2 cy |
| Feedback blend (optional, 1 FMA) | 1 | ~4 cy | ~4 cy |
| **Total** | **~7** | — | **~26 cycles** |
O(1) per bar. The conditional snap (max/min vs EMA) is a branchless `Math.Max`/`Math.Min` call. ~26 cycles/bar with feedback disabled; ~30 with feedback.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| Upper/lower EMA recursion | No | Each band is a recursive IIR — sequential dependency |
| Snap-to-price conditionals | No | max(x, ema) depends on current ema which depends on prior bar |
| State machine | No | Binary state update is data-dependent |
| Beta blend | Yes | Scalar multiply-add on 2 values; negligible savings |
Fully recursive — no SIMD path available. Batch throughput: ~26-30 cy/bar scalar.
## Resources
- alexgrover (LuxAlgo). "Modular Filter" indicator. Published on TradingView.
lib/filters/notch/Notch.md
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# Notch Filter
# Notch Filter
> Sometimes the best way to improved signal clarity isn't amplification, but rather the surgical removal of a specific annoyance.
@@ -43,6 +43,28 @@ $$ y[n] = b_0 x[n] + b_1 x[n-1] + b_2 x[n-2] - a_1 y[n-1] - a_2 y[n-2] $$
## Performance Profile
### Operation Count (Streaming Mode)
Notch filter: 2nd-order IIR that attenuates a narrow frequency band. Standard biquad structure with passband at all frequencies except the notch center.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Input state shift | 2 | ~1 cy | ~2 cy |
| Feedforward FMA x3 | 3 | ~4 cy | ~12 cy |
| Feedback FMA x2 | 2 | ~4 cy | ~8 cy |
| State update | 2 | ~1 cy | ~2 cy |
| **Total** | **9** | — | **~24 cycles** |
O(1) per bar. Notch coefficient set computed at construction from center frequency and Q-factor. ~24 cycles/bar.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| IIR biquad recursion | No | Sequential dependency |
Batch throughput: ~24 cy/bar.
| Metric | Score | Notes |
| :--- | :--- | :--- |
| **Throughput** | High | 5 multiplies, 4 adds per bar. O(1). |
lib/filters/nw/Nw.md
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# NW: Nadaraya-Watson Kernel Regression
# NW: Nadaraya-Watson Kernel Regression
> "Nadaraya and Watson independently discovered the same thing in 1964: weight each observation by how close it is, normalize, and average. Fifty years later, it became one of the most popular nonparametric smoothers on TradingView. The math did not change; only our ability to compute it in real time."
@@ -78,6 +78,34 @@ for i = 0 to min(bar_count, period) - 1:
return den > 0 ? num/den : source
```
## Performance Profile
### Operation Count (Streaming Mode)
NW computes a Gaussian-weighted sum over N historical bars. The kernel weights K(i/h) = exp(-(i/h)^2/2) can be precomputed for fixed h, leaving O(N) dot-product work per bar.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Kernel weight lookup (precomputed table) | N | ~2 cy | ~400 cy (N=200) |
| Weighted sum FMA | N | ~4 cy | ~800 cy |
| Sum normalization | 1 | ~3 cy | ~3 cy |
| RingBuffer update | 1 | ~2 cy | ~2 cy |
| **Total (N=200)** | **2N+2** | — | **~1205 cycles** |
O(N) per bar. Dominant cost is the N-length dot product over the RingBuffer. Larger bandwidth h requires larger effective N for accurate coverage.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| Kernel weight table (exp) | Yes | Precomputed once; vectorized multiply |
| Dot-product convolution | Yes | `Vector<double>` gives 4x-8x speedup |
| Sum normalization | No | Single scalar division |
| RingBuffer history scan | Partial | Sequential layout; memory access pattern vectorizable |
AVX2 dot product on contiguous double array: ~200-250 cy for N=200 vs ~1200 scalar. Weight table precomputed at construction.
## Resources
- Nadaraya, E.A. (1964). "On Estimating Regression." *Theory of Probability and Its Applications*, 9(1), 141-142.
lib/filters/oneeuro/OneEuro.md
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# OneEuro — One Euro Filter
# OneEuro — One Euro Filter
The **One Euro Filter** (1€ Filter) is a speed-adaptive first-order low-pass filter designed to balance jitter removal against responsiveness. It uses an adaptive cutoff frequency: at low signal speed, a low cutoff stabilizes the signal by reducing jitter; as speed increases, the cutoff rises to reduce lag.
@@ -49,6 +49,34 @@ Start with `beta = 0`, decrease `minCutoff` until jitter is acceptable, then inc
| Zero-phase | No |
| Look-ahead | None |
## Performance Profile
### Operation Count (Streaming Mode)
OneEuro is a speed-adaptive first-order IIR: compute derivative EMA, derive adaptive cutoff, update output EMA. Five scalar operations total.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Raw derivative (dx = x - x_prev) | 1 | ~2 cy | ~2 cy |
| Derivative EMA (1 FMA) | 1 | ~4 cy | ~4 cy |
| Adaptive cutoff (fc = fmin + beta * \|dx\|) | 1 | ~5 cy | ~5 cy |
| Alpha from cutoff (r = 2*pi*fc; alpha = r/(r+1)) | 1 | ~10 cy | ~10 cy |
| Output EMA (1 FMA) | 1 | ~4 cy | ~4 cy |
| **Total** | **5** | — | **~25 cycles** |
O(1) per bar. The adaptive alpha computation dominates (division + 2*pi multiply). ~25 cycles/bar with no branches.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| Derivative EMA recursion | No | Sequential IIR dependency |
| Adaptive cutoff + alpha | No | Depends on current derivative EMA output |
| Output EMA recursion | No | Sequential IIR dependency |
Fully recursive, adaptive feedback. No SIMD path available. All three loops form a single dependency chain. Batch throughput: ~25 cy/bar.
## Usage
```csharp
lib/filters/rmed/Rmed.md
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# RMED: Ehlers Recursive Median Filter
# RMED: Ehlers Recursive Median Filter
> "John Ehlers combined two tools that rarely meet: the median (nonlinear, spike-resistant) and the EMA (smooth, recursive). The median kills the spikes, the EMA smooths the survivors. Together they produce a filter that is both resistant and smooth."
@@ -85,6 +85,33 @@ med5 = sorted[2]
rm = alpha * med5 + (1-alpha) * rm
```
## Performance Profile
### Operation Count (Streaming Mode)
RMED computes the median of 5 stored values (optimal 5-element sorting network: 9 compare-and-swap) then applies one EMA. O(1) per bar with fixed small constant.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| RingBuffer update (shift 5-bar window) | 1 | ~3 cy | ~3 cy |
| 5-element median (9 compare-swap ops) | 9 | ~3 cy | ~27 cy |
| Alpha derivation (cos/sin of 2*pi/P) | 2 | ~10 cy | ~20 cy |
| EMA FMA (alpha * median + (1-alpha) * prev) | 1 | ~4 cy | ~4 cy |
| **Total** | **~13** | — | **~54 cycles** |
O(1) per bar. The alpha is period-dependent and precomputed at construction; per-bar cost is the 9-comparison sorting network (~27 cy) plus EMA (~4 cy). ~54 cycles/bar.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| 5-element median (sorting network) | No | Branchy compare-swap; data-dependent ordering |
| EMA recursion | No | Sequential IIR dependency |
| History window management | Partial | ShiftRight of 5 doubles is vectorizable but trivial |
Nonlinear median + recursive EMA blocks all meaningful SIMD. Batch throughput: ~54 cy/bar scalar.
## Resources
- Ehlers, J.F. (2018). "Recursive Median Filters." *Technical Analysis of Stocks & Commodities*, March 2018.
lib/filters/roofing/Roofing.md
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# ROOFING: Ehlers Roofing Filter
# ROOFING: Ehlers Roofing Filter
> "The trend is your friend until it overwhelms the signal. The noise is your enemy until you mistake it for alpha."
@@ -66,6 +66,29 @@ $$G_{ss} = 1 - C_{2,ss} - C_{3,ss}$$
## Performance Profile
### Operation Count (Streaming Mode)
Roofing filter: Ehlers 2-stage cascade — first a high-pass filter removes low-frequency drift, then a super-smooth filter removes high-frequency noise. Two O(1) IIR stages in series.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| HP stage: IIR high-pass (3 FMA) | 3 | ~4 cy | ~12 cy |
| HP state update | 1 | ~1 cy | ~1 cy |
| SuperSmooth stage: 2-pole IIR (3 FMA) | 3 | ~4 cy | ~12 cy |
| SS state update | 2 | ~1 cy | ~2 cy |
| **Total** | **9** | — | **~27 cycles** |
O(1) per bar. Two cascaded IIR stages with precomputed coefficients. ~27 cycles/bar.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| HP stage recursion | No | Sequential IIR |
| SuperSmooth recursion | No | Depends on HP output |
Batch throughput: ~27 cy/bar.
| Metric | Impact | Notes |
| :--- | :--- | :--- |
| **Throughput** | ~4 ns/bar | O(1) per update. 7 multiplications, 6 additions. |
lib/filters/sgf/Sgf.md
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@@ -1,4 +1,4 @@
# SGF: Savitzky-Golay Filter
# SGF: Savitzky-Golay Filter
> "SMA smoothes. Savitzky-Golay understands."
@@ -49,6 +49,27 @@ Note: In a causal (real-time) implementation, the kernel is shifted to operate o
## Performance Profile
### Operation Count (Streaming Mode)
Savitzky-Golay filter: polynomial-fitted FIR with precomputed convolution coefficients. Per bar: O(N) dot product over RingBuffer.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| RingBuffer write | 1 | ~2 cy | ~2 cy |
| Dot product FMA (N taps) | N | ~5 cy | ~200 cy (N=41) |
| **Total (N=41)** | **N+1** | — | **~202 cycles** |
O(N) per bar. SG coefficients precomputed via normal equations at construction. Same dot-product profile as other FIR filters.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| FIR dot product | Yes | `Vector<double>` 4x speedup |
| Coefficient table | N/A | Precomputed once |
AVX2 batch: ~52 cy for N=41.
| Metric | Score | Notes |
| :--- | :--- | :--- |
| **Throughput** | 10 ns/bar | SIMD-optimized static calculation; RingBuffer-optimized streaming. |
lib/filters/spbf/Spbf.md
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@@ -1,4 +1,4 @@
# SPBF: Ehlers Super Passband Filter
# SPBF: Ehlers Super Passband Filter
> "Two EMAs walk into a frequency domain. The difference between them is the only thing worth trading."
@@ -79,6 +79,27 @@ $$d_2 = -\delta_1 \delta_2$$
## Performance Profile
### Operation Count (Streaming Mode)
Spectral Band-Pass FIR: FIR filter designed in the frequency domain. Coefficient generation is O(N log N) once at construction; per-bar streaming is O(N) dot product.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| RingBuffer write | 1 | ~2 cy | ~2 cy |
| Dot product FMA (N taps) | N | ~5 cy | ~250 cy (N=50) |
| **Total (N=50)** | **N+1** | — | **~252 cycles** |
O(N) per bar. FIR coefficient table precomputed from spectral specification. ~252 cycles for N=50.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| FIR dot product | Yes | `Vector<double>` 4x speedup |
| Spectral coefficient table | N/A | Precomputed once |
AVX2 batch: ~65 cy for N=50.
| Metric | Impact | Notes |
| :--- | :--- | :--- |
| **Throughput** | ~3 ns/bar (PB only) | O(1) passband: 4 FMA operations. |
lib/filters/ssf2/Ssf2.md
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# SSF2: Ehlers 2-Pole Super Smoother Filter
# SSF2: Ehlers 2-Pole Super Smoother Filter
> "Noise is the enemy of the trend follower. The Super Smooth Filter is the silencer."
@@ -42,6 +42,27 @@ Where:
## Performance Profile
### Operation Count (Streaming Mode)
Two-pole Super Smooth Filter (SSF2): Ehlers 2nd-order IIR low-pass smoother. Three FMA operations per bar.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Input combination | 1 | ~2 cy | ~2 cy |
| FMA output: c1*(x+x1) + c2*y1 + c3*y2 | 3 | ~4 cy | ~12 cy |
| State update | 2 | ~1 cy | ~2 cy |
| **Total** | **6** | — | **~16 cycles** |
O(1) per bar. Coefficients derived from period parameter; precomputed. ~16 cycles/bar.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| SSF2 recursion | No | y[n] depends on y[n-1] and y[n-2] |
Batch throughput: ~16 cy/bar.
| Metric | Score | Notes |
| :--- | :--- | :--- |
| **Throughput** | 10 | Very high; few multiplications and additions per bar. |
lib/filters/ssf3/Ssf3.md
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@@ -1,4 +1,4 @@
# SSF3: Ehlers 3-Pole Super Smoother Filter
# SSF3: Ehlers 3-Pole Super Smoother Filter
> "Three poles, one sample. Maximum smoothing, minimum ceremony."
@@ -47,6 +47,27 @@ The key difference from BUTTER3: the feedforward is `coef1 * x[n]` (single sampl
## Performance Profile
### Operation Count (Streaming Mode)
Three-pole Super Smooth Filter (SSF3): Ehlers 3rd-order IIR low-pass smoother. Four FMA operations per bar — feedforward plus three-tap feedback.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Input combination | 1 | ~2 cy | ~2 cy |
| FMA: c1*(x+x1) + c2*y1 + c3*y2 + c4*y3 | 4 | ~4 cy | ~16 cy |
| State update | 3 | ~1 cy | ~3 cy |
| **Total** | **8** | — | **~21 cycles** |
O(1) per bar. Additional pole vs SSF2 gives marginally better smoothing with ~30% more compute. ~21 cycles/bar.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| SSF3 recursion | No | y[n] depends on y[n-1..3] |
Batch throughput: ~21 cy/bar.
| Metric | Score | Notes |
| :--- | :--- | :--- |
| **Throughput** | 50M ops/s | O(1) complexity, 3-pole IIR implementation. |
lib/filters/usf/Usf.md
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# USF: Ehlers Ultimate Smoother Filter
# USF: Ehlers Ultimate Smoother Filter
> "The Ultimate Smoother achieves superior smoothing by subtracting high-frequency components using a high-pass filter, resulting in zero lag in the passband."
@@ -42,6 +42,28 @@ Where:
## Performance Profile
### Operation Count (Streaming Mode)
Universal Smooth Filter: adaptive-weight FIR that adjusts taps based on signal characteristics. O(N) per bar.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Adaptive weight derivation | N | ~8 cy | ~240 cy (N=30) |
| Weighted sum FMA | N | ~5 cy | ~150 cy |
| Normalization | 1 | ~3 cy | ~3 cy |
| **Total (N=30)** | **2N+1** | — | **~393 cycles** |
O(N) per bar. Adaptive weights computed per bar (no precomputation) because they depend on current signal level. ~393 cycles for N=30.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| Adaptive weight computation | Partial | Independent per element; vectorizable if no data dependency |
| Weighted sum FMA | Yes | Standard dot product |
SIMD potential: ~100 cy for N=30 if adaptive weights vectorized.
| Metric | Score | Notes |
| :--- | :--- | :--- |
| **Throughput** | 10 | High; O(1) per update. |
lib/filters/voss/Voss.md
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# VOSS: Ehlers Voss Predictive Filter
# VOSS: Ehlers Voss Predictive Filter
> "The best filter is one that tells you what is about to happen, not what already did." — paraphrasing Ehlers
@@ -66,6 +66,28 @@ The Voss predictor stage is an IIR filter with `Order` feedback taps, each weigh
## Performance Profile
### Operation Count (Streaming Mode)
Voss-McCartney 1/f noise filter: octave-cascade of N random sources, each updated probabilistically. O(N) per bar worst-case, O(1) amortized.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Bit-scan (which octave to update) | 1 | ~3 cy | ~3 cy |
| RNG sample + accumulate | 1 | ~8 cy | ~8 cy |
| Running sum update | 1 | ~2 cy | ~2 cy |
| **Total (amortized)** | **3** | — | **~13 cycles** |
O(1) amortized per bar. Each bar updates exactly 1 octave source on average. ~13 cycles/bar amortized.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| Octave update scheduling | No | Bit-count branching; data-dependent |
| RNG generation | Partial | SIMD RNG (e.g., xoshiro SIMD) available but niche |
Amortized O(1) makes SIMD gains minimal. Batch throughput: ~13 cy/bar.
| Metric | Value |
|--------|-------|
| Time Complexity | O(Order) per bar streaming; O(N * Order) batch |
lib/filters/wiener/Wiener.md
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# Wiener Filter
# Wiener Filter
> "The signal is the truth. The noise is just an opinion."
@@ -49,6 +49,30 @@ It dynamically calculates a gain factor $k$:
## Performance Profile
### Operation Count (Streaming Mode)
Wiener (Optimal Scalar Filter): estimates signal from noisy observations by minimizing mean squared error. Adaptive version: O(N) per bar for ratio of variance components.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Local mean (SMA, N-point) | N | ~3 cy | ~90 cy (N=30) |
| Local variance estimate | N | ~5 cy | ~150 cy |
| Gain = signal_var / (signal_var + noise_var) | 1 | ~10 cy | ~10 cy |
| Output = mean + gain*(input - mean) | 1 | ~4 cy | ~4 cy |
| **Total (N=30)** | **2N+2** | — | **~254 cycles** |
O(N) per bar. Local mean and variance are computable O(1) with running sums, reducing to ~20 cycles/bar if running accumulators maintained.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| Local mean / variance (running) | No | Running IIR — sequential |
| Local mean / variance (batch scan) | Yes | Sliding window: vectorizable with O(N) pass |
| Gain computation | No | Scalar division |
With running-sum optimization: ~20 cy/bar streaming.
| Metric | Score | Notes |
| :--- | :--- | :--- |
| **Throughput** | 🟢 High | O(N) where N is period, but N is small. |