/* $Id: std_math.cpp 2506 2012-10-24 19:36:49Z bradbell $ */
/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-07 Bradley M. Bell

CppAD is distributed under multiple licenses. This distribution is under
the terms of the 
                    Eclipse Public License Version 1.0.

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.
-------------------------------------------------------------------------- */

/*
Test the using standard math functions with AD< AD<double> >
*/

# include <cppad/cppad.hpp>

typedef CppAD::AD<double>      ADdouble;
typedef CppAD::AD< ADdouble > ADDdouble;

bool std_math(void)
{	using CppAD::NearEqual;	
	bool ok = true;
	ADDdouble half   = .5;
	ADDdouble one    = 1.;
	ADDdouble two    = 2.;
	ADDdouble ten    = 10.;
	ADDdouble small  = 1e-6;
	ADDdouble pi_4   = 3.141592653 / 4.;
	ADDdouble root_2 =  sqrt(two);

	ADDdouble y = acos(one / root_2);
	ok &= NearEqual( pi_4, y, small, small );

	y = cos(pi_4);
	ok &= NearEqual( one / root_2, y, small, small );

	y = asin(one / root_2);
	ok &= NearEqual( pi_4, y, small, small );

	y = sin(pi_4);
	ok &= NearEqual( one / root_2, y, small, small );

	y = atan(one);
	ok &= NearEqual( pi_4, y, small, small );

	y = tan(pi_4);
	ok &= NearEqual( one, y, small, small );

	y = two * cosh(one);
	ok &= NearEqual( exp(one) + exp(-one), y, small, small );

	y = two * sinh(one);
	ok &= NearEqual( exp(one) - exp(-one), y, small, small );

	y = log( exp(one) );
	ok &= NearEqual( one, y, small, small );

	y = log10( exp( log(ten) ) );
	ok &= NearEqual( one, y, small, small );

	return ok;
}
