/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-20 Bradley M. Bell

CppAD is distributed under the terms of the
             Eclipse Public License Version 2.0.

This Source Code may also be made available under the following
Secondary License when the conditions for such availability set forth
in the Eclipse Public License, Version 2.0 are satisfied:
      GNU General Public License, Version 2.0 or later.
---------------------------------------------------------------------------- */

/*
$begin expm1.cpp$$
$spell
    exp
$$

$section The AD exp Function: Example and Test$$

$srcthisfile%0%// BEGIN C++%// END C++%1%$$

$end
*/
// BEGIN C++

# include <cppad/cppad.hpp>
# include <cmath>

bool expm1(void)
{   bool ok = true;

    using CppAD::AD;
    using CppAD::NearEqual;
    double eps = 10. * std::numeric_limits<double>::epsilon();

    // domain space vector
    size_t n  = 1;
    double x0 = 0.5;
    CPPAD_TESTVECTOR(AD<double>) ax(n);
    ax[0]     = x0;

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

    // range space vector
    size_t m = 1;
    CPPAD_TESTVECTOR(AD<double>) ay(m);
    ay[0] = CppAD::expm1(ax[0]);

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

    // expx0 value
    double expx0 = std::exp(x0);
    ok &= NearEqual(ay[0], expx0-1.0,  eps, eps);

    // forward computation of first partial 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], expx0, eps, eps);

    // 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], expx0, eps, eps);

    // use a VecAD<Base>::reference object with exp
    CppAD::VecAD<double> v(1);
    AD<double> zero(0);
    v[zero]           = x0;
    AD<double> result = CppAD::expm1(v[zero]);
    ok   &= NearEqual(result, expx0-1.0, eps, eps);

    return ok;
}

// END C++
