Williams Gator Oscillator

// The MIT License (MIT)
// © mihakralj
//@version=6
indicator("Williams Gator Oscillator", "GATOR", overlay=false)

//@function Calculates Williams Gator Oscillator from Alligator lines
//@param source Series to calculate from
//@param jawPeriod Period for Jaw SMMA (typically 13)
//@param jawOffset Forward offset for Jaw line (typically 8)
//@param teethPeriod Period for Teeth SMMA (typically 8)
//@param teethOffset Forward offset for Teeth line (typically 5)
//@param lipsPeriod Period for Lips SMMA (typically 5)
//@param lipsOffset Forward offset for Lips line (typically 3)
//@returns Tuple [upper, lower] histogram values
//@optimized Uses Wilder's RMA (SMMA) with exponential warmup compensator for O(1) complexity
gator(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")

    // Step 1: Compute SMMA (Wilder's RMA) for each Alligator line
    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

    // Step 2: Apply offsets and compute histogram differences
    float jawShifted = jaw[jawOffset]
    float teethShifted = teeth[teethOffset]
    float lipsShifted = lips[lipsOffset]

    // Upper histogram: abs(Jaw - Teeth), always positive
    float upper = math.abs(jawShifted - teethShifted)
    // Lower histogram: -abs(Teeth - Lips), always negative
    float lower = -math.abs(teethShifted - lipsShifted)

    [upper, lower]

// ---------- 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
[upper, lower] = gator(i_source, i_jawPeriod, i_jawOffset, i_teethPeriod, i_teethOffset, i_lipsPeriod, i_lipsOffset)
float prevUpper = upper[1]
float prevLower = lower[1]

// Colors: green when expanding (upper rising or lower falling), red when contracting
color upperColor = upper >= prevUpper ? color.green : color.red
color lowerColor = lower <= prevLower ? color.green : color.red

// Plot
plot(upper, "Upper", color=upperColor, style=plot.style_histogram, linewidth=2)
plot(lower, "Lower", color=lowerColor, style=plot.style_histogram, linewidth=2)
plot(0, "Zero", color=color.gray, linewidth=1)