QuanTAlib/lib/reversals/pivotfib/Pivotfib.md

PIVOTFIB: Fibonacci Pivot Points

Property	Value
Category	Reversal
Inputs	OHLCV bar (TBar)
Parameters	None
Outputs	Single series (PIVOTFIB)
Output range	Varies (see docs)
Warmup	2 bars

TL;DR

• Fibonacci Pivot Points apply Fibonacci retracement ratios (38.2%, 61.8%, 100%) to the standard pivot point formula.
• No configurable parameters; computation is stateless per bar.
• Output range: Varies (see docs).
• Requires 2 bars of warmup before first valid output (IsHot = true).
• Validated against TA-Lib, Skender, and Tulip reference implementations where available.

Overview

Fibonacci Pivot Points apply Fibonacci retracement ratios (38.2%, 61.8%, 100%) to the standard pivot point formula. The central pivot (PP) uses the classic HLC/3 calculation, while support and resistance levels are derived by adding or subtracting Fibonacci proportions of the previous bar's trading range.

Origin and Sources

• Concept: Adaptation of Leonardo Fibonacci's ratios (derived from the Fibonacci sequence) to traditional pivot point analysis
• Foundation: Standard pivot points combined with Fibonacci retracement levels (0.382, 0.618, 1.000)

Formula

Using previous bar's High (H), Low (L), Close (C):

PP    = (H + L + C) / 3
range = H - L

R1 = PP + 0.382 × range       S1 = PP - 0.382 × range
R2 = PP + 0.618 × range       S2 = PP - 0.618 × range
R3 = PP + 1.000 × range       S3 = PP - 1.000 × range

Known Values Example

For H = 110, L = 90, C = 100:

• PP = 100.0, range = 20
• R1 = 107.64, S1 = 92.36
• R2 = 112.36, S2 = 87.64
• R3 = 120.00, S3 = 80.00

Key Properties

• Symmetry: R_n - PP = PP - S_n for all levels
• Level ordering: S3 < S2 < S1 < PP < R1 < R2 < R3 (when range > 0)
• Fibonacci ratios: Distances from PP are proportional to 0.382, 0.618, and 1.000 of the range
• Golden ratio relationship: 0.618 ≈ φ - 1, where φ = (1 + √5) / 2; 0.382 = 1 - 0.618

Usage

// Streaming
var fib = new Pivotfib();
var result = fib.Update(bar);
double pp = fib.PP;
double r1 = fib.R1;  // 38.2% resistance
double r2 = fib.R2;  // 61.8% resistance
double r3 = fib.R3;  // 100% resistance
double s1 = fib.S1;  // 38.2% support
double s2 = fib.S2;  // 61.8% support
double s3 = fib.S3;  // 100% support

// Batch
var results = Pivotfib.Batch(bars);

// All 7 levels at once
Pivotfib.BatchAll(high, low, close, ppOut, r1Out, s1Out, r2Out, s2Out, r3Out, s3Out);

Comparison with Other Pivot Variants

Variant	R/S Formula	Levels	Ratios Used
PIVOT (Classic)	Arithmetic from PP	7	1×, 2× range
PIVOTFIB	Fibonacci × range	7	0.382, 0.618, 1.000
PIVOTCAM (Camarilla)	Close ± ratio × range	9	1.1/12 series
PIVOTEXT (Extended)	Arithmetic extended	11	1×–4× range
PIVOTDEM (DeMark)	Conditional X/4	3	Direction-based

Performance Profile

Operation Count (Streaming Mode)

PivotFib computes PP and 6 Fibonacci S/R levels from previous bar's HLC — O(1) pure arithmetic.

Operation	Count	Cost (cycles)	Subtotal
Store prev bar HLC	3	1 cy	~3 cy
PP = (H + L + C) / 3	1	2 cy	~2 cy
range = H - L	1	1 cy	~1 cy
R1/S1 via FMA (0.382 * range)	2	1 cy	~2 cy
R2/S2 via FMA (0.618 * range)	2	1 cy	~2 cy
R3/S3 = PP +/- range	2	1 cy	~2 cy
NaN guard + state update	1	2 cy	~2 cy
Total	O(1)	—	~14 cy

Pure O(1) arithmetic on previous-bar data. Fibonacci multipliers 0.382 and 0.618 are precomputed constants; FMA fuses multiply-add into a single instruction.

Batch Mode (SIMD Analysis)

Operation	Vectorizable?	Notes
PP computation	Yes	Vector (H+L+C)/3 across all bars
Range calculation	Yes	Vector subtract H-L
Fibonacci level projection	Yes	FMA with broadcast constants 0.382, 0.618
All 7 output spans	Yes	Full SIMD pass — no data dependencies

Excellent SIMD candidate — all 7 output levels are independent. BatchAll span overload processes 4 bars per AVX2 cycle. Expected 4× throughput vs scalar.

Implementation Details

• WarmupPeriod: 2 bars (need previous bar's HLC)
• Parameters: None
• Outputs: 7 (PP, R1, R2, R3, S1, S2, S3)
• Input: TBar (OHLCV)
• Complexity: O(1) per bar
• Uses FMA: Math.FusedMultiplyAdd for R1/S1/R2/S2 computations