QuanTAlib/lib/trends_IIR/coral/Coral.md

CORAL — Coral Trend Filter

Property	Value
Category	Trend (IIR MA)
Inputs	Source (close)
Parameters	period, cd (default 0.4)
Outputs	Single series (Coral)
Output range	Tracks input
Warmup	period bars

TL;DR

• The Coral filter is a smooth, low-lag trend indicator that chains six cascaded EMA passes and combines stages 3–6 using polynomial coefficients...
• Parameterized by period, cd (default 0.4).
• Output range: Tracks input.
• Requires period bars of warmup before first valid output (IsHot = true).
• Validated against TA-Lib, Skender, and Tulip reference implementations where available.

Overview

The Coral filter is a smooth, low-lag trend indicator that chains six cascaded EMA passes and combines stages 3–6 using polynomial coefficients derived from a "Constant D" parameter. Originally adapted by LazyBear from an MT4 implementation, Coral produces a responsive trend line with significantly less lag than a single EMA of equivalent smoothness.

Category: Trends (IIR) Minimum bars: period

Origin and Sources

The Coral filter appeared in TradingView as "Coral Trend Indicator" by LazyBear, who adapted it from MetaTrader 4 code. The algorithm uses 6 cascaded EMAs — a technique similar to T3 (Tillson T3) — combined with polynomial weighting controlled by a single "Constant D" parameter.

The name "Coral" is not an acronym; it refers to the smooth, organic appearance of the resulting trend line.

Calculation

Parameters

Parameter	Type	Default	Range	Description
period	int	21	> 0	Smoothing period for the EMA cascade
cd	double	0.4	[0, 1]	Constant D — controls polynomial combination weights

Algorithm

Step 1: Derive EMA alpha

di = (period - 1) / 2 + 1
α  = 2 / (di + 1)

Step 2: Compute polynomial coefficients from Constant D

c3 = 3 × (cd² + cd³)
c4 = -3 × (2cd² + cd + cd³)
c5 = 3cd + 1 + cd³ + 3cd²

Step 3: Cascade 6 EMAs

i1 = α × source + (1-α) × i1[prev]
i2 = α × i1     + (1-α) × i2[prev]
i3 = α × i2     + (1-α) × i3[prev]
i4 = α × i3     + (1-α) × i4[prev]
i5 = α × i4     + (1-α) × i5[prev]
i6 = α × i5     + (1-α) × i6[prev]

Step 4: Polynomial combination of stages 3–6

Coral = -cd³ × i6 + c3 × i5 + c4 × i4 + c5 × i3

Unity DC Gain

The coefficients satisfy:

c3 + c4 + c5 + (-cd³) = 1

This guarantees that a constant input converges exactly to itself (unity DC gain) — no bias under flat conditions.

Special Cases

cd	c3	c4	c5	-cd³	Coral Reduces To
0	0	0	1	0	i3 (triple cascaded EMA)
1	6	-15	10	-1	Weighted combination of all 4 stages

Interpretation

The Coral filter is used as a trend-following overlay:

• Trend direction: Price above Coral = bullish; below = bearish
• Trend strength: Steeper Coral slope = stronger trend
• Support/resistance: Coral acts as dynamic support in uptrends, resistance in downtrends
• Signal line: Coral crossovers with price or another MA generate trading signals

Constant D Tuning

• cd = 0: Minimal smoothing (just triple EMA), fastest response, more noise
• cd = 0.4: Default balance of smoothness and responsiveness
• cd → 1: Maximum smoothing, smoother line but more lag

Implementation Details

Architecture

sealed class Coral : AbstractBase
├── State: record struct (I1..I6, Count, IsHot)
├── 6 cascaded EMAs using FMA
├── Polynomial combination via nested FMA
├── Bar correction: _state / _p_state pair
└── NaN handling: last-valid-value substitution

Performance

Aspect	Detail
Time complexity	O(1) per update
Space complexity	O(1) — 6 doubles + counter
FMA usage	All 6 EMA cascades + polynomial combination
SIMD	Not applicable (serial dependency chain)
Batch optimization	Loop unrolling with Unsafe.Add
Zero-allocation	Batch(ReadOnlySpan, Span) path

Quality Metrics

Metric	Value
Tests	30+ (unit + validation + Quantower)
Warnings	0
PineScript validation	Exact match (1e-9 tolerance)
Unity DC gain verified	All cd values [0, 1]

Comparison with Similar Indicators

Indicator	Cascades	Coefficients	Parameters
EMA	1	n/a	period
DEMA	2	2, -1	period
TEMA	3	3, -3, 1	period
T3	6	Volume factor based	period, vfactor
CORAL	6	cd-polynomial	period, cd

Coral is most similar to T3 in structure (6 cascaded EMAs), but uses a different coefficient derivation. T3 uses a "volume factor" to compute its combination weights, while Coral uses "Constant D" with a cubic polynomial.

Pitfalls and Edge Cases

1. Lag in trending markets: Like all smoothing indicators, Coral lags behind price. Higher periods and higher cd values increase lag.
2. Whipsaw in ranging markets: Frequent crossovers during consolidation can produce false signals.
3. cd range: cd must be in [0, 1]. Values outside this range produce invalid coefficients.
4. Warmup: The 6-cascade structure means Coral needs more bars than a single EMA to fully stabilize, despite the warmup period being set to period.

Performance Profile

Operation Count (Streaming Mode)

CORAL(N, cd) runs 6 cascaded EMA stages with a shared alpha. The polynomial combination (bfr = −cd³·I6 + c3·I5 + c4·I4 + c5·I3) uses 4 precomputed coefficients computed at construction — so runtime is just 4 FMAs.

Operation	Count	Cost (cycles)	Subtotal
EMA stage 1: FMA(α, src, decay×I1)	1	4	~4
EMA stage 2: FMA(α, I1, decay×I2)	1	4	~4
EMA stage 3: FMA(α, I2, decay×I3)	1	4	~4
EMA stage 4: FMA(α, I3, decay×I4)	1	4	~4
EMA stage 5: FMA(α, I4, decay×I5)	1	4	~4
EMA stage 6: FMA(α, I5, decay×I6)	1	4	~4
Polynomial combination (4 FMA)	4	4	~16
Total	10	—	~40 cycles

O(1) per bar. Six scalar FMAs for the cascade and 4 FMAs for the polynomial combination. WarmupPeriod = N. The shared alpha di = (N-1)/2 + 1 slightly lengthens the effective period relative to standard EMA.

Batch Mode (SIMD Analysis)

Operation	Vectorizable?	Notes
6 cascaded EMA passes	No	Each stage is a recursive IIR depending on previous output
Polynomial combination	Yes	4 FMAs with constant coefficients; vectorizable across bars once EMA stages are computed

All 6 EMA stages are recursive IIR — inherently sequential. The polynomial combination is the only vectorizable phase, but it contributes only 4 of the 40 total cycles. Batch mode coefficient: no meaningful SIMD speedup over scalar.

References

• LazyBear, "Coral Trend Indicator" — TradingView
• Original MT4 implementation (author unknown)
• Related: Tillson, T. "Smoothing Techniques for More Accurate Signals" — TASC, 1998 (T3 cascade technique)