// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("HEMA (Exponential Hull Analog)", "HEMAx", overlay=true)

//@function Calculates Hull Exponential Moving Average (EMA-domain HMA analog)
//@param src Series to calculate HEMA from
//@param N Period (matches HMA lag at same period)
//@returns HEMA value with reduced lag
//@optimized Uses cascaded EMA de-lag structure with O(1) complexity per bar

// WMA-lag-matched alpha: EMA lag = (P-1)/3, same as WMA(P)
alphaFromWmaLag(int p) =>
    float fp = math.max(float(p), 1.0)
    3.0 / (fp + 2.0)

// Exponential Hull Analog (EMA-domain HMA)
hema(series float src, simple int N) =>
    // --- guardrails ---
    int n = math.max(N, 2)  // HMA-like structure needs N>=2

    // --- sub-periods matching HMA's integer floor divisions ---
    int halfN = int(n / 2)                        // floor(N/2), same as HMA
    int sqrtN = math.max(int(math.sqrt(n)), 1)    // floor(sqrt(N)), same as HMA

    // --- alphas (lag-matched to WMA) ---
    float aS = alphaFromWmaLag(n)
    float aF = alphaFromWmaLag(math.max(halfN, 1))
    float aM = alphaFromWmaLag(math.max(sqrtN, 1))

    float bS = 1.0 - aS
    float bF = 1.0 - aF
    float bM = 1.0 - aM

    // --- lag-derived ratio for the de-lag combiner ---
    float lagS = bS / aS
    float lagF = bF / aF
    float r = lagF / lagS
    r := math.min(math.max(r, 0.0), 0.999999)  // keep denom sane

    // --- state (unbiased EMA warmup) ---
    var bool warmup = true
    var float dS = 1.0
    var float dF = 1.0
    var float dM = 1.0
    var float eSraw = 0.0
    var float eFraw = 0.0
    var float eMraw = 0.0

    float eS = na
    float eF = na
    float out = na

    // raw EMAs
    eSraw := aS * (src - eSraw) + eSraw
    eFraw := aF * (src - eFraw) + eFraw

    if warmup
        // update decays for unbiased correction
        dS *= bS
        dF *= bF
        dM *= bM

        float invS = 1.0 / math.max(1.0 - dS, 1e-12)
        float invF = 1.0 / math.max(1.0 - dF, 1e-12)
        float invM = 1.0 / math.max(1.0 - dM, 1e-12)

        eS := eSraw * invS
        eF := eFraw * invF

        float deLag = (eF - r * eS) / (1.0 - r)

        eMraw := aM * (deLag - eMraw) + eMraw
        out := eMraw * invM

        // end warmup only when ALL stages are effectively unbiased
        warmup := math.max(dS, math.max(dF, dM)) > 1e-10
    else
        eS := eSraw
        eF := eFraw
        float deLag = (eF - r * eS) / (1.0 - r)
        eMraw := aM * (deLag - eMraw) + eMraw
        out := eMraw

    out

// Inputs
i_period = input.int(10, "Period", minval=2)
i_source = input.source(close, "Source")

hema_value = hema(i_source, i_period)
plot(hema_value, "HEMA", color=color.yellow, linewidth=2)