Parabolic SAR Extended (SAREXT)

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

//@function Parabolic SAR Extended — asymmetric PSAR with separate long/short AF parameters,
//          auto-detect or forced initial direction, and an offset applied on reversal.
//          Output is sign-encoded: positive SAR = long mode, negative SAR = short mode.
//@param start_value Initial direction: >0 force long, <0 force short, 0 auto-detect from DM
//@param offset_on_reverse Gap added to SAR on reversal (default 0)
//@param af_init_long Initial AF for long positions (default 0.02)
//@param af_long AF increment per new EP in long (default 0.02)
//@param af_max_long Maximum AF for long (default 0.20)
//@param af_init_short Initial AF for short positions (default 0.02)
//@param af_short AF increment per new EP in short (default 0.02)
//@param af_max_short Maximum AF for short (default 0.20)
//@returns Sign-encoded SAR value (positive = long, negative = short)
//@reference J. Welles Wilder Jr., "New Concepts in Technical Trading Systems" (1978)
//@optimized O(1) per bar, state-machine with asymmetric acceleration factors
sarext(simple float start_value = 0.0, simple float offset_on_reverse = 0.0,
       simple float af_init_long = 0.02, simple float af_long = 0.02, simple float af_max_long = 0.20,
       simple float af_init_short = 0.02, simple float af_short = 0.02, simple float af_max_short = 0.20) =>
    if af_init_long <= 0 or af_long <= 0 or af_max_long <= af_init_long
        runtime.error("Long AF parameters invalid")
    if af_init_short <= 0 or af_short <= 0 or af_max_short <= af_init_short
        runtime.error("Short AF parameters invalid")
    if offset_on_reverse < 0
        runtime.error("Offset must be >= 0")

    var bool is_long = true
    var float sar = low
    var float ep = high
    var float af = af_init_long

    if bar_index == 0
        // Bar 0: collect first bar data
        is_long := true
        sar := high
        ep := low
        af := af_init_short
        float(na)
    else if bar_index == 1
        // Bar 1: determine initial direction
        if start_value > 0
            is_long := true
            sar := math.min(low[1], low)
            ep := math.max(high[1], high)
            af := af_init_long
        else if start_value < 0
            is_long := false
            sar := math.max(high[1], high)
            ep := math.min(low[1], low)
            af := af_init_short
        else
            // Auto-detect from DM
            float plus_dm = high - high[1]
            float minus_dm = low[1] - low
            if plus_dm > minus_dm and plus_dm > 0
                is_long := true
                sar := math.min(low[1], low)
                ep := math.max(high[1], high)
                af := af_init_long
            else
                is_long := false
                sar := math.max(high[1], high)
                ep := math.min(low[1], low)
                af := af_init_short
        is_long ? sar : -sar
    else
        // Bar 2+: standard SAR state machine with asymmetric AF
        float new_sar = sar + af * (ep - sar)
        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 to short
                is_long := false
                new_sar := ep + offset_on_reverse
                ep := low
                af := af_init_short
            else
                if high > ep
                    ep := high
                    af := math.min(af + af_long, af_max_long)
        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 to long
                is_long := true
                new_sar := ep - offset_on_reverse
                ep := high
                af := af_init_long
            else
                if low < ep
                    ep := low
                    af := math.min(af + af_short, af_max_short)
        sar := new_sar
        is_long ? sar : -sar

// ── Inputs ──
float i_start          = input.float(0.0,  "Start Value (0=auto)")
float i_offset         = input.float(0.0,  "Offset on Reverse", minval=0)
float i_af_init_long   = input.float(0.02, "AF Init Long",  minval=0.001, step=0.001)
float i_af_long        = input.float(0.02, "AF Long",       minval=0.001, step=0.001)
float i_af_max_long    = input.float(0.20, "AF Max Long",   minval=0.01,  step=0.01)
float i_af_init_short  = input.float(0.02, "AF Init Short", minval=0.001, step=0.001)
float i_af_short       = input.float(0.02, "AF Short",      minval=0.001, step=0.001)
float i_af_max_short   = input.float(0.20, "AF Max Short",  minval=0.01,  step=0.01)

// ── Calculation ──
float result = sarext(i_start, i_offset, i_af_init_long, i_af_long, i_af_max_long,
                      i_af_init_short, i_af_short, i_af_max_short)

float sar_val = math.abs(nz(result))
bool  is_long = nz(result) > 0
float sar_above = not is_long ? sar_val : na
float sar_below = is_long ? sar_val : na

// ── Plot ──
plot(sar_above, "SAREXT Above", color=color.red,   style=plot.style_linebr, linewidth=2)
plot(sar_below, "SAREXT Below", color=color.green, style=plot.style_linebr, linewidth=2)