// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Zero-Lag EMA (ZLEMA)", "ZLEMA", overlay=true)

//@function Calculates ZLEMA using zero-lag price and exponential smoothing with compensator
//@param source Series to calculate ZLEMA from
//@param period Smoothing period
//@param alpha Optional smoothing factor (overrides period if provided)
//@returns ZLEMA value with zero-lag effect applied
//@optimized Uses lag compensation buffer and exponential warmup compensator for O(1) complexity
zlema(series float source, simple int period=0, simple float alpha=0) =>
    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 zlema = 0.0
    var float result = source
    var priceBuffer = array.new<float>(lag + 1, 0.0)
    if not na(source)
        array.shift(priceBuffer)
        array.push(priceBuffer, source)
        float laggedPrice = array.get(priceBuffer, 0)
        float signal = 2 * source - laggedPrice
        zlema := a * (signal - zlema) + zlema
        if warmup
            e *= beta
            float c = 1.0 / (1.0 - e)
            result := c * zlema
            warmup := e > 1e-10
        else
            result := zlema
    result

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

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

// Calculation
zlema_value = zlema(i_source, i_period)

// Plot
plot(zlema_value, "ZLEMA", color=color.yellow, linewidth=2)