// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Second Derivative / Acceleration (ACCEL)", "ACCEL", overlay=false, precision=8)

//@function Calculates the second finite difference (acceleration): Accel = V[t] - 2*V[t-1] + V[t-2]
//@param src Source series
//@returns Second difference. Returns 0.0 until 3 bars are available.
//@optimized Uses direct history access and FMA-equivalent for zero-allocation streaming.
accel(series float src) =>
    float v0 = src
    float v1 = src[1]
    float v2 = src[2]
    if na(v1) or na(v2)
        0.0
    else
        v0 - 2.0 * v1 + v2

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

// Inputs
i_source = input.source(close, "Source")

// Calculation
a = accel(i_source)

// Plot
plot(a, "Accel", color=color.yellow, linewidth=2)