// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Bollinger Band Width (BBW)", "BBW", overlay=false)

//@function Calculates Bollinger Band Width as the difference between upper and lower bands
//@param source Series to calculate Bollinger Bands from
//@param period Lookback period for calculations
//@param multiplier Standard deviation multiplier for band width
//@returns BBW value representing the width between Bollinger Bands
//@optimized for performance and dirty data
bbw(series float source, simple int period, simple float multiplier) =>
    var int p = math.max(1, period), var int head = 0, var int count = 0
    var array<float> buffer = array.new_float(p, na)
    var float sum = 0.0, var float sumSq = 0.0
    float oldest = array.get(buffer, head)
    if not na(oldest)
        sum -= oldest
        sumSq -= oldest * oldest
        count -= 1
    float current_val = nz(source)
    sum += current_val
    sumSq += current_val * current_val
    count += 1
    array.set(buffer, head, current_val)
    head := (head + 1) % p
    float basis = nz(sum / count, source)
    float dev = count > 1 ? multiplier * math.sqrt(math.max(0.0, sumSq / count - basis * basis)) : 0.0
    basis != 0.0 ? 2 * dev / basis : 0.0

// ---------- 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)

// Calculation
bbw_value = bbw(i_source, i_period, i_multiplier)

// Plot
plot(bbw_value, "BBW", color=color.yellow, linewidth=2)