// The MIT License (MIT)
// © mihakralj
//@version=6
indicator("Zero-Lag Double EMA (ZLDEMA)", "ZLDEMA", overlay=true)

//@function Calculates ZLDEMA using zero-lag price and double exponential smoothing with compensator
//@doc https://github.com/mihakralj/pinescript/blob/main/indicators/trends_IIR/zldema.md
//@param source Series to calculate ZLDEMA from
//@param period Smoothing period
//@param alpha Optional smoothing factor (overrides period if provided)
//@returns ZLDEMA value with zero-lag effect applied
//@optimized Uses lag compensation buffer and exponential warmup compensator on both EMA stages for O(1) complexity
zldema(series float source, simple int period=0, simple float alpha=0) =>
    if alpha <= 0 and period <= 0
        runtime.error("Alpha or period must be provided")
    float a = alpha > 0 ? alpha : 2.0 / (period + 1)
    float beta = 1.0 - a
    simple int lag = math.max(1, math.round((period - 1) / 2))
    var bool warmup = true
    var float e = 1.0
    var float ema1_raw = 0.0
    var float ema2_raw = 0.0
    var float ema1 = source
    var float ema2 = source
    var priceBuffer = array.new<float>(lag + 1, na)
    if not na(source)
        array.shift(priceBuffer)
        array.push(priceBuffer, source)
        float laggedPrice = nz(array.get(priceBuffer, 0), source)
        float signal = 2 * source - laggedPrice
        ema1_raw := a * (signal - ema1_raw) + ema1_raw
        if warmup
            e *= beta
            float c = 1.0 / (1.0 - e)
            ema1 := c * ema1_raw
            ema2_raw := a * (ema1 - ema2_raw) + ema2_raw
            ema2 := c * ema2_raw
            warmup := e > 1e-10
        else
            ema1 := ema1_raw
            ema2_raw := a * (ema1 - ema2_raw) + ema2_raw
            ema2 := ema2_raw
        2 * ema1 - ema2
    else
        na

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

// Inputs
i_period = input.int(10, "Period", minval=1)
i_source = input.source(close, "Source")

// Calculation
zldema_value = zldema(i_source, i_period)

// Plot
plot(zldema_value, "ZLDEMA", color=color.yellow, linewidth=2)