\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)

sub.cpp

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AD Binary Subtraction: Example and Test

# include <cppad/cppad.hpp>

bool Sub(void)
{   bool ok = true;
    using CppAD::AD;
    using CppAD::NearEqual;
    double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

    // domain space vector
    size_t  n =  1;
    double x0 = .5;
    CPPAD_TESTVECTOR(AD<double>) x(1);
    x[0]      = x0;

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

    AD<double> a = 2. * x[0] - 1.; // AD<double> - double
    AD<double> b = a  - 2;         // AD<double> - int
    AD<double> c = 3. - b;         // double     - AD<double>
    AD<double> d = 4  - c;         // int        - AD<double>

    // range space vector
    size_t m = 1;
    CPPAD_TESTVECTOR(AD<double>) y(m);
    y[0] = x[0] - d;              // AD<double> - AD<double>

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

    // check value
    ok &= NearEqual(y[0], x0-4.+3.+2.-2.*x0+1., eps99, eps99);

    // forward computation of partials w.r.t. x[0]
    CPPAD_TESTVECTOR(double) dx(n);
    CPPAD_TESTVECTOR(double) dy(m);
    dx[0] = 1.;
    dy    = f.Forward(1, dx);
    ok   &= NearEqual(dy[0], -1., eps99, eps99);

    // reverse computation of derivative of y[0]
    CPPAD_TESTVECTOR(double)  w(m);
    CPPAD_TESTVECTOR(double) dw(n);
    w[0]  = 1.;
    dw    = f.Reverse(1, w);
    ok   &= NearEqual(dw[0], -1., eps99, eps99);

    // use a VecAD<Base>::reference object with subtraction
    CppAD::VecAD<double> v(1);
    AD<double> zero(0);
    v[zero] = b;
    AD<double> result = 3. - v[zero];
    ok     &= (result == c);

    return ok;
}