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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 .
Sign Function: Example and Test

# include <cppad/cppad.hpp>

bool sign(void)
{   bool ok = true;

    using CppAD::AD;
    using CppAD::NearEqual;

    // create f: x -> y where f(x) = sign(x)
    size_t n = 1;
    size_t m = 1;
    CPPAD_TESTVECTOR(AD<double>) ax(n), ay(m);
    ax[0]     = 0.;
    CppAD::Independent(ax);
    ay[0]     = sign(ax[0]);
    CppAD::ADFun<double> f(ax, ay);

    // check value during recording
    ok &= (ay[0] == 0.);

    // use f(x) to evaluate the sign function and its derivatives
    CPPAD_TESTVECTOR(double) x(n), y(m), dx(n), dy(m), w(m), dw(n);
    dx[0] = 1.;
    w[0] = 1.;
    //
    x[0]  = 2.;
    y     = f.Forward(0, x);
    ok   &= (y[0] == 1.);
    dy    = f.Forward(1, dx);
    ok   &= (dy[0] == 0.);
    dw   = f.Reverse(1, w);
    ok  &= (dw[0] == 0.);
    //
    x[0]  = 0.;
    y     = f.Forward(0, x);
    ok   &= (y[0] == 0.);
    dy    = f.Forward(1, dx);
    ok   &= (dy[0] == 0.);
    dw   = f.Reverse(1, w);
    ok  &= (dw[0] == 0.);
    //
    x[0]  = -2.;
    y     = f.Forward(0, x);
    ok   &= (y[0] == -1.);
    dy    = f.Forward(1, dx);
    ok   &= (dy[0] == 0.);
    dw   = f.Reverse(1, w);
    ok  &= (dw[0] == 0.);

    // use a VecAD<Base>::reference object with sign
    CppAD::VecAD<double> v(1);
    AD<double> zero(0);
    v[zero]           = 2.;
    AD<double> result = sign(v[zero]);
    ok   &= (result == 1.);

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