/* $Id$ */
/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell

CppAD is distributed under multiple licenses. This distribution is under
the terms of the
                    GNU General Public License Version 3.

A copy of this license is included in the COPYING file of this distribution.
Please visit http://www.coin-or.org/CppAD/ for information on other licenses.
-------------------------------------------------------------------------- */

/*
$begin azmul.cpp$$
$spell
$$

$section AD Absolute Zero Multiplication: Example and Test$$

$code
$verbatim%example/azmul.cpp%0%// BEGIN C++%// END C++%1%$$
$$

$end
*/
// BEGIN C++

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

bool azmul(void)
{	bool ok = true;

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

	// domain space vector
	size_t n  = 2;
	double x = 0.5;
	double y = 2.0;
	CPPAD_TESTVECTOR(AD<double>) axy(n);
	axy[0]      = x;
	axy[1]      = y;

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

	// range space vector
	size_t m = 5;
	CPPAD_TESTVECTOR(AD<double>) az(m);
	az[0] = CppAD::azmul(axy[0], axy[1]); // azmul(variable, variable)
	az[1] = CppAD::azmul(axy[0], inf);    // azmul(variable, parameter=inf)
	az[2] = CppAD::azmul(axy[0], 3.0);    // azmul(variable, parameter=3.0)
	az[3] = CppAD::azmul(0.0, axy[1]);    // azmul(parameter=0.0, variable)
	az[4] = CppAD::azmul(4.0, axy[1]);    // azmul(parameter=4.0, variable)

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

	// check value when x is not zero
	ok &= NearEqual(az[0] , x * y,  eps, eps);
	ok &= az[1] == inf;
	ok &= NearEqual(az[2] , x * 3.0,  eps, eps);
	ok &= az[3] == 0.0;
	ok &= NearEqual(az[4] , 4.0 * y,  eps, eps);


	// check value x is zero and y is infinity
	CPPAD_TESTVECTOR(double) xy(n), z(m);
	xy[0] = 0.0;
	xy[1] = inf;
	z     = f.Forward(0, xy);
	ok &= z[0] == 0.0;
	ok &= z[1] == 0.0;
	ok &= z[2] == 0.0;
	ok &= z[3] == 0.0;
	ok &= z[4] == inf;

	return ok;
}

// END C++
