Williams Alligator

// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Williams Alligator", "ALLIGATOR", overlay=true)

//@function Calculates Williams Alligator indicator using SMMA (RMA)
//@param source Series to calculate Alligator from
//@param jawPeriod Period for Jaw line (typically 13)
//@param jawOffset Forward offset for Jaw line (typically 8)
//@param teethPeriod Period for Teeth line (typically 8)
//@param teethOffset Forward offset for Teeth line (typically 5)
//@param lipsPeriod Period for Lips line (typically 5)
//@param lipsOffset Forward offset for Lips line (typically 3)
//@returns Tuple [jaw, teeth, lips] values
//@optimized Uses Wilder's RMA (SMMA) with exponential warmup compensator for O(1) complexity
alligator(series float source, simple int jawPeriod, simple int jawOffset, simple int teethPeriod, simple int teethOffset, simple int lipsPeriod, simple int lipsOffset) =>
    if jawPeriod <= 0 or teethPeriod <= 0 or lipsPeriod <= 0
        runtime.error("All periods must be greater than 0")
    if jawOffset < 0 or teethOffset < 0 or lipsOffset < 0
        runtime.error("All offsets must be non-negative")
    float alphaJaw = 1.0 / float(jawPeriod)
    float alphaTeeth = 1.0 / float(teethPeriod)
    float alphaLips = 1.0 / float(lipsPeriod)
    var bool warmupJaw = true
    var bool warmupTeeth = true
    var bool warmupLips = true
    var float eJaw = 1.0
    var float eTeeth = 1.0
    var float eLips = 1.0
    var float emaJaw = 0.0
    var float emaTeeth = 0.0
    var float emaLips = 0.0
    var float jaw = source
    var float teeth = source
    var float lips = source
    emaJaw := alphaJaw * (source - emaJaw) + emaJaw
    emaTeeth := alphaTeeth * (source - emaTeeth) + emaTeeth
    emaLips := alphaLips * (source - emaLips) + emaLips
    if warmupJaw
        eJaw *= (1.0 - alphaJaw)
        float cJaw = 1.0 / (1.0 - eJaw)
        jaw := cJaw * emaJaw
        warmupJaw := eJaw > 1e-10
    else
        jaw := emaJaw
    if warmupTeeth
        eTeeth *= (1.0 - alphaTeeth)
        float cTeeth = 1.0 / (1.0 - eTeeth)
        teeth := cTeeth * emaTeeth
        warmupTeeth := eTeeth > 1e-10
    else
        teeth := emaTeeth
    if warmupLips
        eLips *= (1.0 - alphaLips)
        float cLips = 1.0 / (1.0 - eLips)
        lips := cLips * emaLips
        warmupLips := eLips > 1e-10
    else
        lips := emaLips
    [jaw, teeth, lips]

// ---------- Main loop ----------

// Inputs
i_source = input.source(hlc3, "Source")
i_jawPeriod = input.int(13, "Jaw Period", minval=1)
i_jawOffset = input.int(8, "Jaw Offset", minval=0)
i_teethPeriod = input.int(8, "Teeth Period", minval=1)
i_teethOffset = input.int(5, "Teeth Offset", minval=0)
i_lipsPeriod = input.int(5, "Lips Period", minval=1)
i_lipsOffset = input.int(3, "Lips Offset", minval=0)

// Calculation
[jaw, teeth, lips] = alligator(i_source, i_jawPeriod, i_jawOffset, i_teethPeriod, i_teethOffset, i_lipsPeriod, i_lipsOffset)

// Plot with offsets
plot(jaw[i_jawOffset], "Jaw", color=color.blue, linewidth=2)
plot(teeth[i_teethOffset], "Teeth", color=color.red, linewidth=2)
plot(lips[i_lipsOffset], "Lips", color=color.green, linewidth=2)