Analytics & ML

Statistical Primitives

Foundation accumulators used by every higher-level kernel. SMA-seeded EMAs, numerically stable Welford variance, nearest-rank percentile rings, z-scores, crossover detection, and hysteresis gates.

`ewmaAccumulator_c`

SMA-seeded EMA. First period samples average into the seed; subsequent samples apply ema += 2/(period+1) × (value - ema). Returns false while seeding.

Method	Purpose
`configure(period)`	Set EMA period
`reset()`	Clear state
`update(value, outResult)`	Feed sample; false while seeding
`seeded()`	Seed complete flag
`value()`	Current EMA

`welfordAccumulator_c`

One-pass running mean/variance/stddev. Numerically stable against catastrophic cancellation. Variance is sample estimator M2/(n-1); single-sample reads 0.

Method	Purpose
`reset()`	Clear state
`update(value)`	Feed one sample
`count()`	Sample count
`mean()`	Running mean
`variance()`	Sample variance
`stdDev()`	Sample standard deviation

`percentileRing_c`

Ring of newest capacity samples with nearest-rank percentile queries. Scratch buffer sorted in-place per query. Also provides fractionBelowOrEqual for rank queries.

Method	Purpose
`configure(capacity)`	Allocate ring + scratch via st_malloc
`reset()`	Clear samples
`push(value)`	Add sample
`percentile(p, outResult)`	Nearest-rank percentile [0,1]
`fractionBelowOrEqual(value)`	Fraction of samples ≤ value

`algoZScore`

Free function: (value - mean) / sigma. Returns 0 when sigma ≤ 0 to prevent division-by-zero signals.

`algoCrossOver`

Detects UP/DOWN/NONE transitions between two series. Free function comparing previous and current values of A vs B.

`algoHysteresisGate_c`

N-consecutive-in / M-consecutive-out dwell logic. Prevents rapid state toggling at threshold boundaries. Configure enter/exit thresholds plus dwell counts.

Online Learning

In-process models that learn from live data without external services. Logistic regression with drift freeze, hidden Markov forward filter, conformal abstention, Bayesian change-point detection, recursive least squares, and extreme-value tail estimation.

`algoOnlineLogistic_c`

Decimal online logistic regression: Welford standardization, bounded SGD, L2 regularization, weight clipping. Up to 32 features. Optional drift-freeze monitor (fast/slow loss-EMA latch) and win-rate EMA tracker. JSON-serializable for restart persistence.

Config Field	Default	Purpose
`ui32FeatureCount`	0	[1, 32]
`decLearnRate`	0.03	SGD step size
`decL2`	0.0001	L2 regularization
`decWeightClip`	20	Weight bounds
`fDriftMonitor`	false	Enable drift freeze
`fWinRateTracker`	false	Enable win-rate EMA

Method	Purpose
`predict(features, count)`	Probability [1e-6, 1-1e-6]
`train(features, count, label)`	One labelled sample {0,1}
`onTradeOutcome(isWin)`	Feed closed-trade result
`frozen()`	Drift freeze active
`toJson() / fromJson()`	State persistence

`algoHmm_c`

Online hidden Markov forward filter. Up to 4 states, 8 observation dimensions. Diagonal Gaussian emissions learned online from posterior responsibilities. EWMA transition matrix updates converge from uniform prior — no training corpus needed.

Method	Purpose
`init(stateCount, stayProb, ewmaAlpha)`	Scalar or array overload
`reset()`	Clear state
`update(observations, count)`	Feed vector; returns log-likelihood
`posterior(state)`	Current posterior probability
`argmaxState()`	Most likely state index

`conformalGate_c`

Split/Mondrian conformal abstention gate. Per-bucket residual rings calibrate a quantile. Entry admitted only when finite-sample lower bound on edge clears round-trip cost. Fixed double[6][400] rings.

Method	Purpose
`init(alpha, minResiduals)`	Configure miscoverage
`pushResidual(bucket, absResidual)`	Feed residual
`admits(bucket, yHat, sigma, horizon, cost, theta)`	Admission decision struct

`changePoint_c`

Bayesian online change-point detection (BOCPD). Run-length posterior over Normal predictive model with constant hazard. Truncated at 600 run lengths. Fixed double[600] arrays.

Method	Purpose
`init(hazardLambda, knownSigma, shortRunThreshold)`	Configure
`update(observation)`	Returns break probability struct

`valueHead_c`

Recursive least squares with ridge regularization and exponential forgetting. Up to 32 features. Fixed double[32] + double[32×32].

Method	Purpose
`init(dim, delta, gamma, ridge)`	Configure
`predict(features)`	Linear prediction
`update(features, target)`	One RLS step

`tailIndex_c`

Extreme-value fragility via peaks-over-threshold. Hill tail index, GPD scale, expected shortfall ES_99, z-scored fragility score against slow EWMA baseline. Fixed double[1800] ring.

Method	Purpose
`push(absReturn)`	Ingest one absolute log-return
`compute()`	Hill, ES99, fragility struct

Regime Detectors

All regime detectors implement algoRegimeDetector_c and produce algoRegimeResult_s with regime classification, signal quality, trend/volatility state, strength, confidence, and validity flag.

Shared Types (`algoRegimeTypes.h`)

Type	Kind	Values
`algoMarketRegime_e`	enum	UNKNOWN, TRENDING_UP, TRENDING_DOWN, RANGE_BOUND, HIGH_VOLATILITY, LOW_VOLATILITY, BREAKOUT, MEAN_REVERTING
`algoSignalQuality_e`	enum	NONE, WEAK, MODERATE, STRONG, VERY_STRONG
`algoTrendState_e`	enum	FLAT, UPTREND, DOWNTREND, TRANSITIONING
`algoVolatilityState_e`	enum	NORMAL, COMPRESSED, EXPANDING, ELEVATED
`algoRegimeResult_s`	struct	eRegime, eQuality, eTrend, eVolatility, decStrength, decConfidence, fValid

`algoRegimeHmm_c`

Wraps algoHmm_c and maps dominant state posterior to market regime. Configurable thresholds for trending vs range-bound classification. Ready after 30 steps minimum. Input: observation vectors up to 8 dimensions.

Config	Default	Purpose
`i32StateCount`	3	HMM states [2,4]
`decStayProbability`	0.95	Transition diagonal
`decEwmaAlpha`	0.02	Online learning rate
`decTrendThreshold`	0.6	Posterior ≥ this → trending
`decRangeThreshold`	0.4	Posterior < this → transitioning

`algoRegimeAdx_c`

Classic Wilder ADX/+DI/-DI over configurable period. Smoothed true range and directional movement. Classifies trending vs range-bound based on ADX thresholds. Input: OHLC bars.

Config	Default
`ui32Period`	14 (max 256)
`decTrendingThreshold`	25
`decStrongTrendThreshold`	40
`decRangeThreshold`	20

`algoRegimeBollinger_c`

Bollinger bandwidth and %B. Detects squeeze (low bandwidth → breakout imminent) and expansion (high bandwidth → elevated vol). Input: close prices.

Config	Default
`ui32Period`	20 (max 512)
`decBandWidth`	2
`decSqueezeThreshold`	0.005
`decExpansionThreshold`	0.03

`algoRegimeVolCluster_c`

Short-window vs long-window realized vol ratio. Expansion above threshold → HIGH_VOLATILITY; compression below → LOW_VOLATILITY. Newton's method integer sqrt. Input: per-bar returns.

Config	Default
`ui32ShortWindow`	10
`ui32LongWindow`	100 (max 512)
`decExpansionRatio`	1.5
`decCompressionRatio`	0.7

`algoRegimeCvd_c`

Rolling correlation between CVD delta and price changes. Positive correlation → trending (accumulation/distribution confirms price). Negative or diverging → mean-reverting signal. Tracks cumulative CVD. Input: paired CVD delta + price change per bar.

Config	Default	Purpose
`ui32Window`	50 (max 512)	Rolling correlation window
`decAccumulationThreshold`	0.3	Corr > this → TRENDING_UP
`decDistributionThreshold`	-0.3	Corr < this → TRENDING_DOWN
`decDivergenceThreshold`	0.5	\|corr\| < this with large CVD → MEAN_REVERTING

Strength Calculators

All strength calculators implement algoRegimeStrength_c and produce a normalized decimal_t strength [0,1] plus an algoSignalQuality_e mapping.

`algoCompositeStrength_c`

Combines up to 8 weighted source strengths into a single composite. Clamped to [0,1]. Quality mapped through configurable thresholds.

Config	Default	Purpose
`ui32SourceCount`	0 (max 8)	Number of sources
`arrWeights`	{}	Per-source weight
`decStrongThreshold`	0.7	→ STRONG
`decModerateThreshold`	0.4	→ MODERATE
`decWeakThreshold`	0.2	→ WEAK

Method	Purpose
`setSource(index, value)`	Set one source strength
`compute()`	Calculate weighted composite
`strength()`	Last computed composite
`quality()`	Threshold-mapped quality

`algoTrendConviction_c`

Fast/slow EMA spread in bps plus consecutive-bar persistence tracking. Strength blends normalized absolute spread and consecutive-bar count. Spread below minimum yields zero.

Config	Default
`ui32EmaFastPeriod`	5
`ui32EmaSlowPeriod`	20
`ui32ConsecutiveBars`	3
`decMinSpreadBps`	5

Outputs: strength() [0,1], quality(), trendState() (FLAT/UPTREND/DOWNTREND/TRANSITIONING), emaSpread() raw bps.

`algoVolNormalization_c`

Current vol as ratio of Welford running mean. Drives both strength output and discrete volatility state classification (NORMAL/COMPRESSED/EXPANDING/ELEVATED).

Config	Default
`ui32Lookback`	100
`decLowVolThreshold`	0.5 (≤ → COMPRESSED)
`decHighVolThreshold`	1.5 (≥ → EXPANDING)
`decExtremeVolThreshold`	2.5 (≥ → ELEVATED)

`algoFlowImbalance_c`

Buy/sell imbalance as signed-flow / total-flow over a trailing window via algoSignedFlowBuckets_c. Feed from onMarketdataTick, read in onMarketdataOhlcClose.

Config	Default
`ui32BucketCount`	60
`ui64BucketDurationMs`	1000
`ui64WindowMs`	30000
`decStrongThreshold`	0.6
`decModerateThreshold`	0.3

Market Data Analytics

On-demand candle analytics and signed-flow accumulation. Not indicator plugins — stateless pure functions and bucket rings with zero per-bar cost when unused.

Candle Analytics (free functions)

On-demand pure functions over the candle ring. Zero per-bar cost when unused. Header-only.

Function	Purpose
`candleCvdDelta(candle)`	Single-bar signed flow from taker aggressor split
`candleCvdWindow(ohlc, sequence, bars)`	Dense-window CVD delta + volume over N bars
`candleCvdAnchored(ohlc, sequence)`	Ring-lifetime cumulative CVD from oldest retained bar
`candleHeikinAshiWindow(ohlc, sequence, out, bars)`	HA transform in offset order, seeded at window's oldest bar

`algoSignedFlowBuckets_c`

Ring of fixed-duration time buckets accumulating signed and total flow. Stale buckets zero out of window queries automatically. Covers per-bar, 1s notional, and accumulator patterns.

Method	Purpose
`configure(bucketCount, bucketDurationMs)`	Allocate ring via st_malloc
`onTrade(signed, total, nowMs)`	Stamp trade into bucket
`windowSigned(windowMs)`	Sum signed over window
`windowTotal(windowMs)`	Sum total over window
`windowSums(windowMs, outSigned, outTotal)`	Combined single-walk

Cross-Asset Engines

Multi-asset covariance, lead/lag transmission, Mahalanobis turbulence, and synchronous BBO resampling for cross-venue strategies.

`algoCrossAssetEngine_c`

EWMA covariance + dominant eigenfactor extraction for up to 8 assets. Reports per-asset loading, sigma, and lagging score relative to common factor. Fixed decimal_t[8][8] arrays.

Method	Purpose
`init(assetCount, ewmaAlpha)`	Configure
`update(returns, count)`	Ingest return vector
`compute()`	Recompute eigenfactor
`laggingScore(asset)`	(factor × loading − return) / sigma
`dominantShare()`	λ[0] / Σλ

`algoXCorrLeadLag_c`

Rolling cross-correlation at configurable lags between two return series. Transmission score is max_tau rho(tau) signed by lead return at winning lag. Fixed decimal_t[256] rings.

Method	Purpose
`init(window, maxLag)`	Configure
`update(leadReturn, lagReturn)`	Push paired observation
`bestLag()`	Winning lag index
`score()`	max(rho) × sign(lead at best lag)

`algoTurbulence_c`

Mahalanobis turbulence index via EWMA mean/covariance + eigendecomposition. Static variance-ratio helper. Fixed decimal_t[8][8] arrays.

Method	Purpose
`init(dim, ewmaAlpha)`	Configure
`update(values, count)`	Ingest observation vector
`turbulence()`	Mahalanobis distance
`volRatio(shortVar, longVar)`	Static; ≥ 1 means expansion

`algoVenueGrid_c`

Synchronous BBO resampling grid for cross-venue strategies. Each venue pushes latest BBO; per grid step strategy reads one snapshot where every venue is represented by its most recent pre-grid quote. Fixed algoGridQuote_s[8].

Method	Purpose
`init(venueCount, gridMs)`	Configure
`update(venue, quote)`	Ingest BBO sample
`snapshot(now, maxStaleMs, out)`	Write quotes; returns fresh count

Numerical Primitives

Low-level mathematical building blocks: eigensolver, rough-path signatures, and optimal transport displacement profiles.

`algoEig_c`

Fixed-capacity symmetric Jacobi eigensolver (up to 8×8). Solver internals in double; API boundary in decimal_t. Caller-provided output arrays.

Method	Purpose
`solve(matrix, dim, outEigenvalues, outEigenvectors)`	A = V·diag(λ)·Vᵀ
`dominantShare(eigenvalues, dim)`	λ[0] / Σλ
`reconstruct(eigenvalues, eigenvectors, dim, out)`	Rebuild A
`reconstructionError(...)`	Accuracy metric

`pathSignature_c`

Truncated path log-signature (rough-path theory). Chen recursion levels 1–3 on up to 3 channels, projected onto 14 Lyndon words. Accumulation in double.

Method	Purpose
`pushSegment(increment, channelCount)`	Append piecewise-linear segment
`logSignature(out[14])`	14-word log-signature
`levyArea(i, j)`	Antisymmetric area component
`combine(left, right)`	Chen concatenation

`ladderTransport_c`

Quantile-displacement profile comparing book snapshots. Evaluates D0 (centroid), D1 (slope), D2 (curvature), W1 (Wasserstein cost), Λ (mass log-ratio) at 7 quantile levels over up to 20 price levels per side.

Method	Purpose
`compute(prevBook, curBook, tick)`	Full displacement profile struct

 Architecture: Signal Layer Composition

					Kernels compose hierarchically. A typical production algo chains: signed flow buckets feed
					into flow imbalance strength; Welford accumulators feed into
					vol normalization; HMM feeds into regime HMM detector;
					all strengths merge through composite strength which gates entry alongside
					cost model admission and risk kernel approval before reaching the
					sizing stack. Every link is a separate, tested class — swap any component without
					touching the rest.
				

Statistical Primitives

ewmaAccumulator_c

welfordAccumulator_c

percentileRing_c

algoZScore

algoCrossOver

algoHysteresisGate_c

Online Learning

algoOnlineLogistic_c

algoHmm_c

conformalGate_c

changePoint_c

valueHead_c

tailIndex_c

Regime Detectors

Shared Types (algoRegimeTypes.h)

algoRegimeHmm_c

algoRegimeAdx_c

algoRegimeBollinger_c

algoRegimeVolCluster_c

algoRegimeCvd_c