Parabolic SAR

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

//@function Calculates Parabolic Stop And Reverse (SAR)
//@param af_start Initial acceleration factor (Wilder's original: 0.02)
//@param af_increment Acceleration factor increment per new extreme (Wilder's original: 0.02)
//@param af_max Maximum acceleration factor (Wilder's original: 0.20)
//@returns SAR value (stop level for current trend)
//@optimized Minimal state variables, O(1) per bar
sar(simple float af_start=0.02, simple float af_increment=0.02, simple float af_max=0.20) =>
    if af_start <= 0 or af_start > af_max
        runtime.error("Start AF must be > 0 and <= Max AF")
    if af_increment <= 0
        runtime.error("AF increment must be > 0")
    if af_max <= af_start
        runtime.error("Max AF must be > Start AF")
    var bool is_long = true
    var float sar = low
    var float ep = high
    var float af = af_start
    if bar_index == 0
        is_long := close > open
        sar := is_long ? low : high
        ep := is_long ? high : low
        af := af_start
    else
        float new_sar = sar + af * (ep - sar)
        bool reverse = false
        if is_long
            new_sar := math.min(new_sar, low[1])
            if bar_index > 1
                new_sar := math.min(new_sar, low[2])
            if low < new_sar
                reverse := true
                is_long := false
                new_sar := ep
                ep := low
                af := af_start
            else
                if high > ep
                    ep := high
                    af := math.min(af + af_increment, af_max)
        else
            new_sar := math.max(new_sar, high[1])
            if bar_index > 1
                new_sar := math.max(new_sar, high[2])
            if high > new_sar
                reverse := true
                is_long := true
                new_sar := ep
                ep := high
                af := af_start
            else
                if low < ep
                    ep := low
                    af := math.min(af + af_increment, af_max)
        sar := new_sar
    sar

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

// Inputs
i_af_start = input.float(0.02, "Start AF", minval=0.001, maxval=1.0, step=0.001)
i_af_increment = input.float(0.02, "AF Increment", minval=0.001, maxval=1.0, step=0.001)
i_af_max = input.float(0.20, "Max AF", minval=0.001, maxval=1.0, step=0.01)

// Calculation
sar = sar(i_af_start, i_af_increment, i_af_max)
psar_above = sar > close ? sar : na
psar_below = sar < close ? sar : na

// Plot
plot(psar_above, "SAR Above", color=color.red,   style=plot.style_linebr, linewidth=2)
plot(psar_below, "SAR Below", color=color.green, style=plot.style_linebr, linewidth=2)