// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Rolling Sum", "SUM", overlay=false)

//@function Calculates Rolling Sum over a period using Kahan-Babuška algorithm
//@param   source Series to calculate sum from
//@param   length Number of bars to sum
//@returns Rolling sum of the last 'length' values
rolling_sum(series float source, simple int length) =>
    // Persistent state
    var float sum = 0.0
    var float c = 0.0    // First-order compensation
    var float cc = 0.0   // Second-order compensation

    float val = nz(source, 0.0)
    float oldVal = bar_index >= length ? nz(source[length], 0.0) : 0.0

    // Kahan-Babuška subtract old value
    if bar_index >= length
        float yS = -oldVal - c
        float tS = sum + yS
        c := tS - sum - yS
        sum := tS

        float zS = c - cc
        float ttS = sum + zS
        cc := ttS - sum - zS
        sum := ttS

    // Kahan-Babuška add new value
    float yA = val - c
    float tA = sum + yA
    c := tA - sum - yA
    sum := tA

    float zA = c - cc
    float ttA = sum + zA
    cc := ttA - sum - zA
    sum := ttA

    sum

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

// Inputs
i_length = input.int(14, "Length", minval=1)
i_source = input.source(close, "Source")

// Calculation
sum_value = rolling_sum(i_source, i_length)

// Equivalent built-in for comparison (disabled by default)
// sum_builtin = math.sum(i_source, i_length)

// Plot
plot(sum_value, "Sum", color=color.yellow, linewidth=2)