Bollinger %B

// The MIT License (MIT)
// © mihakralj
//@version=6
indicator("Bollinger %B", "BBB", overlay=false)

//@function Calculates Bollinger Bands components for %B calculation
//@param source Series to calculate from
//@param period Lookback period for SMA and standard deviation
//@param multiplier Standard deviation multiplier for band width
//@returns Bollinger %B value (typically 0-1 range; can overshoot)
//@optimized Uses circular buffer with running sums, O(1) complexity per bar
bbb(series float source, simple int period, simple float multiplier) =>
    if period <= 0 or multiplier <= 0.0
        runtime.error("Period and multiplier must be greater than 0")

    var int p = 0
    var int head = 0
    var int count = 0
    var array<float> buffer = array.new_float(0)
    var float sum = 0.0
    var float sumSq = 0.0
    var string lastSymbol = ""
    var string lastTimeframe = ""

    string currentSymbol = syminfo.tickerid
    string currentTimeframe = timeframe.period
    bool needsReset = (p != period) or (currentSymbol != lastSymbol) or (currentTimeframe != lastTimeframe)

    if needsReset
        p := period
        head := 0
        count := 0
        buffer := array.new_float(p, na)
        sum := 0.0
        sumSq := 0.0
        lastSymbol := currentSymbol
        lastTimeframe := currentTimeframe

    float result = na

    if not na(source)
        float oldest = array.get(buffer, head)
        if not na(oldest)
            sum -= oldest
            sumSq -= oldest * oldest
        else
            count += 1

        sum += source
        sumSq += source * source
        array.set(buffer, head, source)
        head := (head + 1) % p

        int n = math.max(1, count)
        float basis = sum / n
        float variance = math.max(0.0, sumSq / n - basis * basis)
        float stddev = math.sqrt(variance)
        float dev = multiplier * stddev

        float upper = basis + dev
        float lower = basis - dev
        float bandWidth = upper - lower

        result := bandWidth > 0 ? (source - lower) / bandWidth : 0.5

    result

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

// Inputs
i_period = input.int(20, "Period", minval=1)
i_source = input.source(close, "Source")
i_multiplier = input.float(2.0, "StdDev Multiplier", minval=0.001, step=0.1)

// Calculation
result = bbb(i_source, i_period, i_multiplier)

// Plot
plot(result, "Bollinger %B", color=color.yellow, linewidth=2)
hline(1.0, "Upper Band Level", color=color.gray, linestyle=hline.style_dashed)
hline(0.8, "Overbought", color=color.red, linestyle=hline.style_dotted)
hline(0.5, "Midline", color=color.gray, linestyle=hline.style_solid)
hline(0.2, "Oversold", color=color.green, linestyle=hline.style_dotted)
hline(0.0, "Lower Band Level", color=color.gray, linestyle=hline.style_dashed)