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@(@\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }@)@ This is cppad-20221105 documentation. Here is a link to its current documentation .
Taping Array Index Operation: Example and Test
# include <cppad/cppad.hpp>

namespace {
    double Array(const double &index)
    {   static double array[] = {
            5.,
            4.,
            3.,
            2.,
            1.
        };
        static size_t number = sizeof(array) / sizeof(array[0]);
        if( index < 0. )
            return array[0];

        size_t i = static_cast<size_t>(index);
        if( i >= number )
            return array[number-1];

        return array[i];
    }
    // in empty namespace and outside any other routine
    CPPAD_DISCRETE_FUNCTION(double, Array)
}

bool TapeIndex(void)
{   bool ok = true;
    using CppAD::AD;

    // domain space vector
    size_t n = 2;
    CPPAD_TESTVECTOR(AD<double>) X(n);
    X[0] = 2.;   // array index value
    X[1] = 3.;   // multiplier of array index value

    // declare independent variables and start tape recording
    CppAD::Independent(X);

    // range space vector
    size_t m = 1;
    CPPAD_TESTVECTOR(AD<double>) Y(m);
    Y[0] = X[1] * Array( X[0] );

    // create f: X -> Y and stop tape recording
    CppAD::ADFun<double> f(X, Y);

    // vectors for arguments to the function object f
    CPPAD_TESTVECTOR(double) x(n);   // argument values
    CPPAD_TESTVECTOR(double) y(m);   // function values
    CPPAD_TESTVECTOR(double) w(m);   // function weights
    CPPAD_TESTVECTOR(double) dw(n);  // derivative of weighted function

    // check function value
    x[0] = Value(X[0]);
    x[1] = Value(X[1]);
    y[0] = Value(Y[0]);
    ok  &= y[0] == x[1] * Array(x[0]);

    // evaluate f where x has different values
    x[0] = x[0] + 1.;  // new array index value
    x[1] = x[1] + 1.;  // new multiplier value
    y    = f.Forward(0, x);
    ok  &= y[0] == x[1] * Array(x[0]);

    // evaluate derivaitve of y[0]
    w[0] = 1.;
    dw   = f.Reverse(1, w);
    ok   &= dw[0] == 0.;              // partial w.r.t array index
    ok   &= dw[1] == Array(x[0]);     // partial w.r.t multiplier

    return ok;
}
Input File: example/general/tape_index.cpp