Exemple #1
0
void forward1sweep(
	std::ostream&         s_out,
	const bool            print,
	const size_t          p,
	const size_t          q,
	const size_t          n,
	const size_t          numvar,
	player<Base>*         play,
	const size_t          J,
	Base*                 taylor,
	bool*                 cskip_op,
	pod_vector<addr_t>&   var_by_load_op,
	size_t                compare_change_count,
	size_t&               compare_change_number,
	size_t&               compare_change_op_index
)
{
	// number of directions
	const size_t r = 1;

	CPPAD_ASSERT_UNKNOWN( p <= q );
	CPPAD_ASSERT_UNKNOWN( J >= q + 1 );
	CPPAD_ASSERT_UNKNOWN( play->num_var_rec() == numvar );

	/*
	<!-- replace forward0sweep_code_define -->
	*/
	// op code for current instruction
	OpCode op;

	// index for current instruction
	size_t i_op;

	// next variables
	size_t i_var;

	// operation argument indices
	const addr_t*   arg = CPPAD_NULL;

	// initialize the comparision operator counter
	if( p == 0 )
	{	compare_change_number   = 0;
		compare_change_op_index = 0;
	}

	// If this includes a zero calculation, initialize this information
	pod_vector<bool>   isvar_by_ind;
	pod_vector<size_t> index_by_ind;
	if( p == 0 )
	{	size_t i;

		// this includes order zero calculation, initialize vector indices
		size_t num = play->num_vec_ind_rec();
		if( num > 0 )
		{	isvar_by_ind.extend(num);
			index_by_ind.extend(num);
			for(i = 0; i < num; i++)
			{	index_by_ind[i] = play->GetVecInd(i);
				isvar_by_ind[i] = false;
			}
		}
		// includes zero order, so initialize conditional skip flags
		num = play->num_op_rec();
		for(i = 0; i < num; i++)
			cskip_op[i] = false;
	}

	// work space used by UserOp.
	vector<bool> user_vx;        // empty vecotor
	vector<bool> user_vy;        // empty vecotor
	vector<Base> user_tx;        // argument vector Taylor coefficients
	vector<Base> user_ty;        // result vector Taylor coefficients
	size_t user_index = 0;       // indentifier for this atomic operation
	size_t user_id    = 0;       // user identifier for this call to operator
	size_t user_i     = 0;       // index in result vector
	size_t user_j     = 0;       // index in argument vector
	size_t user_m     = 0;       // size of result vector
	size_t user_n     = 0;       // size of arugment vector
	//
	atomic_base<Base>* user_atom = CPPAD_NULL; // user's atomic op calculator
# ifndef NDEBUG
	bool               user_ok   = false;      // atomic op return value
# endif
	//
	// next expected operator in a UserOp sequence
	enum { user_start, user_arg, user_ret, user_end, user_trace }
	user_state = user_start;

	// length of the parameter vector (used by CppAD assert macros)
	const size_t num_par = play->num_par_rec();

	// pointer to the beginning of the parameter vector
	const Base* parameter = CPPAD_NULL;
	if( num_par > 0 )
		parameter = play->GetPar();

	// length of the text vector (used by CppAD assert macros)
	const size_t num_text = play->num_text_rec();

	// pointer to the beginning of the text vector
	const char* text = CPPAD_NULL;
	if( num_text > 0 )
		text = play->GetTxt(0);
	/*
	<!-- end forward0sweep_code_define -->
	*/
	// temporary indices
	size_t i, k;

	// number of orders for this user calculation
	// (not needed for order zero)
	const size_t user_q1 = q+1;

	// variable indices for results vector
	// (done differently for order zero).
	vector<size_t> user_iy;

	// skip the BeginOp at the beginning of the recording
	play->forward_start(op, arg, i_op, i_var);
	CPPAD_ASSERT_UNKNOWN( op == BeginOp );
# if CPPAD_FORWARD1SWEEP_TRACE
	std::cout << std::endl;
# endif
	bool more_operators = true;
	while(more_operators)
	{
		// this op
		play->forward_next(op, arg, i_op, i_var);
		CPPAD_ASSERT_UNKNOWN( (i_op > n)  | (op == InvOp) );
		CPPAD_ASSERT_UNKNOWN( (i_op <= n) | (op != InvOp) );
		CPPAD_ASSERT_UNKNOWN( i_op < play->num_op_rec() );
		CPPAD_ASSERT_ARG_BEFORE_RESULT(op, arg, i_var);

		// check if we are skipping this operation
		while( cskip_op[i_op] )
		{	if( op == CSumOp )
			{	// CSumOp has a variable number of arguments
				play->forward_csum(op, arg, i_op, i_var);
			}
			CPPAD_ASSERT_UNKNOWN( op != CSkipOp );
			// if( op == CSkipOp )
			// {	// CSkip has a variable number of arguments
			// 	play->forward_cskip(op, arg, i_op, i_var);
			// }
			play->forward_next(op, arg, i_op, i_var);
			CPPAD_ASSERT_UNKNOWN( i_op < play->num_op_rec() );
		}

		// action depends on the operator
		switch( op )
		{
			case AbsOp:
			forward_abs_op(p, q, i_var, arg[0], J, taylor);
			break;
			// -------------------------------------------------

			case AddvvOp:
			forward_addvv_op(p, q, i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case AddpvOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			forward_addpv_op(p, q, i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case AcosOp:
			// sqrt(1 - x * x), acos(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_acos_op(p, q, i_var, arg[0], J, taylor);
			break;
			// -------------------------------------------------

# if CPPAD_USE_CPLUSPLUS_2011
			case AcoshOp:
			// sqrt(x * x - 1), acosh(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_acosh_op(p, q, i_var, arg[0], J, taylor);
			break;
# endif
			// -------------------------------------------------

			case AsinOp:
			// sqrt(1 - x * x), asin(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_asin_op(p, q, i_var, arg[0], J, taylor);
			break;
			// -------------------------------------------------

# if CPPAD_USE_CPLUSPLUS_2011
			case AsinhOp:
			// sqrt(1 + x * x), asinh(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_asinh_op(p, q, i_var, arg[0], J, taylor);
			break;
# endif
			// -------------------------------------------------

			case AtanOp:
			// 1 + x * x, atan(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_atan_op(p, q, i_var, arg[0], J, taylor);
			break;
			// -------------------------------------------------

# if CPPAD_USE_CPLUSPLUS_2011
			case AtanhOp:
			// 1 - x * x, atanh(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_atanh_op(p, q, i_var, arg[0], J, taylor);
			break;
# endif
			// -------------------------------------------------

			case CExpOp:
			forward_cond_op(
				p, q, i_var, arg, num_par, parameter, J, taylor
			);
			break;
			// ---------------------------------------------------

			case CosOp:
			// sin(x), cos(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_cos_op(p, q, i_var, arg[0], J, taylor);
			break;
			// ---------------------------------------------------

			case CoshOp:
			// sinh(x), cosh(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_cosh_op(p, q, i_var, arg[0], J, taylor);
			break;
			// -------------------------------------------------

			case CSkipOp:
			// CSkipOp has a variable number of arguments and
			// forward_next thinks it has no arguments.
			// we must inform forward_next of this special case.
			if( p == 0 )
			{	forward_cskip_op_0(
					i_var, arg, num_par, parameter, J, taylor, cskip_op
				);
			}
			play->forward_cskip(op, arg, i_op, i_var);
			break;
			// -------------------------------------------------

			case CSumOp:
			// CSumOp has a variable number of arguments and
			// forward_next thinks it has no arguments.
			// we must inform forward_next of this special case.
			forward_csum_op(
				p, q, i_var, arg, num_par, parameter, J, taylor
			);
			play->forward_csum(op, arg, i_op, i_var);
			break;
			// -------------------------------------------------

			case DisOp:
			forward_dis_op(p, q, r, i_var, arg, J, taylor);
			break;
			// -------------------------------------------------

			case DivvvOp:
			forward_divvv_op(p, q, i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case DivpvOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			forward_divpv_op(p, q, i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case DivvpOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par );
			forward_divvp_op(p, q, i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case EndOp:
			CPPAD_ASSERT_NARG_NRES(op, 0, 0);
			more_operators = false;
			break;
			// -------------------------------------------------

			case EqpvOp:
			if( ( p == 0 ) & ( compare_change_count > 0 ) )
			{	forward_eqpv_op_0(
					compare_change_number, arg, parameter, J, taylor
				);
				if( compare_change_count == compare_change_number )
					compare_change_op_index = i_op;
			}
			break;
			// -------------------------------------------------

			case EqvvOp:
			if( ( p == 0 ) & ( compare_change_count > 0 ) )
			{	forward_eqvv_op_0(
					compare_change_number, arg, parameter, J, taylor
				);
				if( compare_change_count == compare_change_number )
					compare_change_op_index = i_op;
			}
			break;
			// -------------------------------------------------

# if CPPAD_USE_CPLUSPLUS_2011
			case ErfOp:
			CPPAD_ASSERT_UNKNOWN( CPPAD_USE_CPLUSPLUS_2011 );
			// 2DO: implement zero order version of this function
			forward_erf_op(p, q, i_var, arg, parameter, J, taylor);
			break;
# endif
			// -------------------------------------------------

			case ExpOp:
			forward_exp_op(p, q, i_var, arg[0], J, taylor);
			break;
			// ---------------------------------------------------

# if CPPAD_USE_CPLUSPLUS_2011
			case Expm1Op:
			forward_expm1_op(p, q, i_var, arg[0], J, taylor);
			break;
# endif
			// ---------------------------------------------------

			case InvOp:
			CPPAD_ASSERT_NARG_NRES(op, 0, 1);
			break;
			// -------------------------------------------------

			case LdpOp:
			if( p == 0 )
			{	forward_load_p_op_0(
					play,
					i_var,
					arg,
					parameter,
					J,
					taylor,
					isvar_by_ind.data(),
					index_by_ind.data(),
					var_by_load_op.data()
				);
				if( p < q ) forward_load_op(
					play,
					op,
					p+1,
					q,
					r,
					J,
					i_var,
					arg,
					var_by_load_op.data(),
					taylor
				);
			}
			else	forward_load_op(
				play,
				op,
				p,
				q,
				r,
				J,
				i_var,
				arg,
				var_by_load_op.data(),
				taylor
			);
			break;
			// -------------------------------------------------

			case LdvOp:
			if( p == 0 )
			{	forward_load_v_op_0(
					play,
					i_var,
					arg,
					parameter,
					J,
					taylor,
					isvar_by_ind.data(),
					index_by_ind.data(),
					var_by_load_op.data()
				);
				if( p < q ) forward_load_op(
					play,
					op,
					p+1,
					q,
					r,
					J,
					i_var,
					arg,
					var_by_load_op.data(),
					taylor
				);
			}
			else	forward_load_op(
				play,
				op,
				p,
				q,
				r,
				J,
				i_var,
				arg,
				var_by_load_op.data(),
				taylor
			);
			break;
			// -------------------------------------------------

			case LepvOp:
			if( ( p == 0 ) & ( compare_change_count > 0 ) )
			{	forward_lepv_op_0(
					compare_change_number, arg, parameter, J, taylor
				);
				if( compare_change_count == compare_change_number )
					compare_change_op_index = i_op;
			}
			break;

			case LevpOp:
			if( ( p == 0 ) & ( compare_change_count > 0 ) )
			{	forward_levp_op_0(
					compare_change_number, arg, parameter, J, taylor
				);
				if( compare_change_count == compare_change_number )
					compare_change_op_index = i_op;
			}
			break;
			// -------------------------------------------------

			case LevvOp:
			if( ( p == 0 ) & ( compare_change_count > 0 ) )
			{	forward_levv_op_0(
					compare_change_number, arg, parameter, J, taylor
				);
				if( compare_change_count == compare_change_number )
					compare_change_op_index = i_op;
			}
			break;
			// -------------------------------------------------

			case LogOp:
			forward_log_op(p, q, i_var, arg[0], J, taylor);
			break;
			// -------------------------------------------------

# if CPPAD_USE_CPLUSPLUS_2011
			case Log1pOp:
			forward_log1p_op(p, q, i_var, arg[0], J, taylor);
			break;
# endif
			// -------------------------------------------------

			case LtpvOp:
			if( ( p == 0 ) & ( compare_change_count > 0 ) )
			{	forward_ltpv_op_0(
					compare_change_number, arg, parameter, J, taylor
				);
				if( compare_change_count == compare_change_number )
					compare_change_op_index = i_op;
			}
			break;

			case LtvpOp:
			if( ( p == 0 ) & ( compare_change_count > 0 ) )
			{	forward_ltvp_op_0(
					compare_change_number, arg, parameter, J, taylor
				);
				if( compare_change_count == compare_change_number )
					compare_change_op_index = i_op;
			}
			break;
			// -------------------------------------------------

			case LtvvOp:
			if( ( p == 0 ) & ( compare_change_count > 0 ) )
			{	forward_ltvv_op_0(
					compare_change_number, arg, parameter, J, taylor
				);
				if( compare_change_count == compare_change_number )
					compare_change_op_index = i_op;
			}
			break;
			// -------------------------------------------------

			case MulvvOp:
			forward_mulvv_op(p, q, i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case MulpvOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			forward_mulpv_op(p, q, i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case NepvOp:
			if( ( p == 0 ) & ( compare_change_count > 0 ) )
			{	forward_nepv_op_0(
					compare_change_number, arg, parameter, J, taylor
				);
				if( compare_change_count == compare_change_number )
					compare_change_op_index = i_op;
			}
			break;
			// -------------------------------------------------

			case NevvOp:
			if( ( p == 0 ) & ( compare_change_count > 0 ) )
			{	forward_nevv_op_0(
					compare_change_number, arg, parameter, J, taylor
				);
				if( compare_change_count == compare_change_number )
					compare_change_op_index = i_op;
			}
			break;
			// -------------------------------------------------

			case ParOp:
			i = p;
			if( i == 0 )
			{	forward_par_op_0(
					i_var, arg, num_par, parameter, J, taylor
				);
				i++;
			}
			while(i <= q)
			{	taylor[ i_var * J + i] = Base(0);
				i++;
			}
			break;
			// -------------------------------------------------

			case PowvpOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par );
			forward_powvp_op(p, q, i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case PowpvOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			forward_powpv_op(p, q, i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case PowvvOp:
			forward_powvv_op(p, q, i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case PriOp:
			if( (p == 0) & print ) forward_pri_0(s_out,
				arg, num_text, text, num_par, parameter, J, taylor
			);
			break;
			// -------------------------------------------------

			case SignOp:
			// sign(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_sign_op(p, q, i_var, arg[0], J, taylor);
			break;
			// -------------------------------------------------

			case SinOp:
			// cos(x), sin(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_sin_op(p, q, i_var, arg[0], J, taylor);
			break;
			// -------------------------------------------------

			case SinhOp:
			// cosh(x), sinh(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_sinh_op(p, q, i_var, arg[0], J, taylor);
			break;
			// -------------------------------------------------

			case SqrtOp:
			forward_sqrt_op(p, q, i_var, arg[0], J, taylor);
			break;
			// -------------------------------------------------

			case StppOp:
			if( p == 0 )
			{	forward_store_pp_op_0(
					i_var,
					arg,
					num_par,
					J,
					taylor,
					isvar_by_ind.data(),
					index_by_ind.data()
				);
			}
			break;
			// -------------------------------------------------

			case StpvOp:
			if( p == 0 )
			{	forward_store_pv_op_0(
					i_var,
					arg,
					num_par,
					J,
					taylor,
					isvar_by_ind.data(),
					index_by_ind.data()
				);
			}
			break;
			// -------------------------------------------------

			case StvpOp:
			if( p == 0 )
			{	forward_store_vp_op_0(
					i_var,
					arg,
					num_par,
					J,
					taylor,
					isvar_by_ind.data(),
					index_by_ind.data()
				);
			}
			break;
			// -------------------------------------------------

			case StvvOp:
			if( p == 0 )
			{	forward_store_vv_op_0(
					i_var,
					arg,
					num_par,
					J,
					taylor,
					isvar_by_ind.data(),
					index_by_ind.data()
				);
			}
			break;
			// -------------------------------------------------

			case SubvvOp:
			forward_subvv_op(p, q, i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case SubpvOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			forward_subpv_op(p, q, i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case SubvpOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par );
			forward_subvp_op(p, q, i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case TanOp:
			// tan(x)^2, tan(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_tan_op(p, q, i_var, arg[0], J, taylor);
			break;
			// -------------------------------------------------

			case TanhOp:
			// tanh(x)^2, tanh(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_tanh_op(p, q, i_var, arg[0], J, taylor);
			break;
			// -------------------------------------------------

			case UserOp:
			// start or end an atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( NumRes( UserOp ) == 0 );
			CPPAD_ASSERT_UNKNOWN( NumArg( UserOp ) == 4 );
			if( user_state == user_start )
			{	user_index = arg[0];
				user_id    = arg[1];
				user_n     = arg[2];
				user_m     = arg[3];
				user_atom  = atomic_base<Base>::class_object(user_index);
# ifndef NDEBUG
				if( user_atom == CPPAD_NULL )
				{	std::string msg =
						atomic_base<Base>::class_name(user_index)
						+ ": atomic_base function has been deleted";
					CPPAD_ASSERT_KNOWN(false, msg.c_str() );
				}
# endif
				if(user_tx.size() != user_n * user_q1)
					user_tx.resize(user_n * user_q1);
				if(user_ty.size() != user_m * user_q1)
					user_ty.resize(user_m * user_q1);
				if(user_iy.size() != user_m)
					user_iy.resize(user_m);
				user_j     = 0;
				user_i     = 0;
				user_state = user_arg;
			}
			else
			{	CPPAD_ASSERT_UNKNOWN( user_state == user_end );
				CPPAD_ASSERT_UNKNOWN( user_index == size_t(arg[0]) );
				CPPAD_ASSERT_UNKNOWN( user_id    == size_t(arg[1]) );
				CPPAD_ASSERT_UNKNOWN( user_n     == size_t(arg[2]) );
				CPPAD_ASSERT_UNKNOWN( user_m     == size_t(arg[3]) );

				// call users function for this operation
				user_atom->set_id(user_id);
				CPPAD_ATOMIC_CALL(
					p, q, user_vx, user_vy, user_tx, user_ty
				);
# ifndef NDEBUG
				if( ! user_ok )
				{	std::string msg =
						atomic_base<Base>::class_name(user_index)
						+ ": atomic_base.forward: returned false";
					CPPAD_ASSERT_KNOWN(false, msg.c_str() );
				}
# endif
				for(i = 0; i < user_m; i++)
					if( user_iy[i] > 0 )
						for(k = p; k <= q; k++)
							taylor[ user_iy[i] * J + k ] =
								user_ty[ i * user_q1 + k ];
# if CPPAD_FORWARD1SWEEP_TRACE
				user_state = user_trace;
# else
				user_state = user_start;
# endif
			}
			break;

			case UsrapOp:
			// parameter argument in an atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( user_state == user_arg );
			CPPAD_ASSERT_UNKNOWN( user_j < user_n );
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			user_tx[user_j * user_q1 + 0] = parameter[ arg[0]];
			for(k = 1; k < user_q1; k++)
				user_tx[user_j * user_q1 + k] = Base(0);
			++user_j;
			if( user_j == user_n )
				user_state = user_ret;
			break;

			case UsravOp:
			// variable argument in an atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( user_state == user_arg );
			CPPAD_ASSERT_UNKNOWN( user_j < user_n );
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) <= i_var );
			for(k = 0; k < user_q1; k++)
				user_tx[user_j * user_q1 + k] = taylor[ arg[0] * J + k];
			++user_j;
			if( user_j == user_n )
				user_state = user_ret;
			break;

			case UsrrpOp:
			// parameter result in an atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( user_state == user_ret );
			CPPAD_ASSERT_UNKNOWN( user_i < user_m );
			user_iy[user_i] = 0;
			user_ty[user_i * user_q1 + 0] = parameter[ arg[0]];
			for(k = 1; k < p; k++)
				user_ty[user_i * user_q1 + k] = Base(0);
			user_i++;
			if( user_i == user_m )
				user_state = user_end;
			break;

			case UsrrvOp:
			// variable result in an atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( user_state == user_ret );
			CPPAD_ASSERT_UNKNOWN( user_i < user_m );
			user_iy[user_i] = i_var;
			for(k = 0; k < p; k++)
				user_ty[user_i * user_q1 + k] = taylor[ i_var * J + k];
			user_i++;
			if( user_i == user_m )
				user_state = user_end;
			break;
			// -------------------------------------------------

			default:
			CPPAD_ASSERT_UNKNOWN(0);
		}
# if CPPAD_FORWARD1SWEEP_TRACE
		if( user_state == user_trace )
		{	user_state = user_start;

			CPPAD_ASSERT_UNKNOWN( op == UserOp );
			CPPAD_ASSERT_UNKNOWN( NumArg(UsrrvOp) == 0 );
			for(i = 0; i < user_m; i++) if( user_iy[i] > 0 )
			{	size_t i_tmp   = (i_op + i) - user_m;
				printOp(
					std::cout,
					play,
					i_tmp,
					user_iy[i],
					UsrrvOp,
					CPPAD_NULL
				);
				Base* Z_tmp = taylor + user_iy[i] * J;
				printOpResult(
					std::cout,
					q + 1,
					Z_tmp,
					0,
					(Base *) CPPAD_NULL
				);
				std::cout << std::endl;
			}
		}
		Base*           Z_tmp   = taylor + J * i_var;
		const addr_t*   arg_tmp = arg;
		if( op == CSumOp )
			arg_tmp = arg - arg[-1] - 4;
		if( op == CSkipOp )
			arg_tmp = arg - arg[-1] - 7;
		if( op != UsrrvOp )
		{
			printOp(
				std::cout,
				play,
				i_op,
				i_var,
				op,
				arg_tmp
			);
			if( NumRes(op) > 0 ) printOpResult(
				std::cout,
				q + 1,
				Z_tmp,
				0,
				(Base *) CPPAD_NULL
			);
			std::cout << std::endl;
		}
	}
	std::cout << std::endl;
# else
	}
Exemple #2
0
void forward0sweep(
	std::ostream&         s_out,
	bool                  print,
	size_t                n,
	size_t                numvar,
	local::player<Base>*  play,
	size_t                J,
	Base*                 taylor,
	bool*                 cskip_op,
	pod_vector<addr_t>&   var_by_load_op,
	size_t                compare_change_count,
	size_t&               compare_change_number,
	size_t&               compare_change_op_index
)
{	CPPAD_ASSERT_UNKNOWN( J >= 1 );
	CPPAD_ASSERT_UNKNOWN( play->num_var_rec() == numvar );

	// use p, q, r so other forward sweeps can use code defined here
	size_t p = 0;
	size_t q = 0;
	size_t r = 1;
	/*
	<!-- define forward0sweep_code_define -->
	*/
	// op code for current instruction
	OpCode op;

	// index for current instruction
	size_t i_op;

	// next variables
	size_t i_var;

	// operation argument indices
	const addr_t*   arg = CPPAD_NULL;

	// initialize the comparision operator counter
	if( p == 0 )
	{	compare_change_number   = 0;
		compare_change_op_index = 0;
	}

	// If this includes a zero calculation, initialize this information
	pod_vector<bool>   isvar_by_ind;
	pod_vector<size_t> index_by_ind;
	if( p == 0 )
	{	size_t i;

		// this includes order zero calculation, initialize vector indices
		size_t num = play->num_vec_ind_rec();
		if( num > 0 )
		{	isvar_by_ind.extend(num);
			index_by_ind.extend(num);
			for(i = 0; i < num; i++)
			{	index_by_ind[i] = play->GetVecInd(i);
				isvar_by_ind[i] = false;
			}
		}
		// includes zero order, so initialize conditional skip flags
		num = play->num_op_rec();
		for(i = 0; i < num; i++)
			cskip_op[i] = false;
	}

	// work space used by UserOp.
	vector<bool> user_vx;        // empty vecotor
	vector<bool> user_vy;        // empty vecotor
	vector<Base> user_tx;        // argument vector Taylor coefficients
	vector<Base> user_ty;        // result vector Taylor coefficients
	//
	atomic_base<Base>* user_atom = CPPAD_NULL; // user's atomic op calculator
# ifndef NDEBUG
	bool               user_ok   = false;      // atomic op return value
# endif
	//
	// information defined by forward_user
	size_t user_old=0, user_m=0, user_n=0, user_i=0, user_j=0;
	enum_user_state user_state = start_user; // proper initialization

	// length of the parameter vector (used by CppAD assert macros)
	const size_t num_par = play->num_par_rec();

	// pointer to the beginning of the parameter vector
	const Base* parameter = CPPAD_NULL;
	if( num_par > 0 )
		parameter = play->GetPar();

	// length of the text vector (used by CppAD assert macros)
	const size_t num_text = play->num_text_rec();

	// pointer to the beginning of the text vector
	const char* text = CPPAD_NULL;
	if( num_text > 0 )
		text = play->GetTxt(0);
	/*
	<!-- end forward0sweep_code_define -->
	*/

# if CPPAD_FORWARD0SWEEP_TRACE
	// flag as to when to trace user function values
	bool user_trace            = false;

	// variable indices for results vector
	// (done differently for order zero).
	vector<size_t> user_iy;
# endif

	// skip the BeginOp at the beginning of the recording
	play->forward_start(op, arg, i_op, i_var);
	CPPAD_ASSERT_UNKNOWN( op == BeginOp );
# if CPPAD_FORWARD0SWEEP_TRACE
	std::cout << std::endl;
# endif
	bool flag; // a temporary flag to use in switch cases
	bool more_operators = true;
	while(more_operators)
	{
		// this op
		play->forward_next(op, arg, i_op, i_var);
		CPPAD_ASSERT_UNKNOWN( (i_op > n)  | (op == InvOp) );
		CPPAD_ASSERT_UNKNOWN( (i_op <= n) | (op != InvOp) );
		CPPAD_ASSERT_UNKNOWN( i_op < play->num_op_rec() );
		CPPAD_ASSERT_ARG_BEFORE_RESULT(op, arg, i_var);

		// check if we are skipping this operation
		while( cskip_op[i_op] )
		{	switch(op)
			{	case CSumOp:
				// CSumOp has a variable number of arguments
				play->forward_csum(op, arg, i_op, i_var);
				break;

				case CSkipOp:
				// CSkip has a variable number of arguments
				play->forward_cskip(op, arg, i_op, i_var);
				break;

				case UserOp:
				{	// skip all operations in this user atomic call
					CPPAD_ASSERT_UNKNOWN( user_state == start_user );
					play->forward_user(op, user_state,
						user_old, user_m, user_n, user_i, user_j
					);
					size_t n_skip = user_m + user_n + 1;
					for(size_t i = 0; i < n_skip; i++)
					{	play->forward_next(op, arg, i_op, i_var);
						play->forward_user(op, user_state,
							user_old, user_m, user_n, user_i, user_j
						);
					}
					CPPAD_ASSERT_UNKNOWN( user_state == start_user );
				}
				break;

				default:
				break;
			}
			play->forward_next(op, arg, i_op, i_var);
			CPPAD_ASSERT_UNKNOWN( i_op < play->num_op_rec() );
		}

		// action to take depends on the case
		switch( op )
		{
			case AbsOp:
			forward_abs_op_0(i_var, arg[0], J, taylor);
			break;
			// -------------------------------------------------

			case AddvvOp:
			forward_addvv_op_0(i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case AddpvOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			forward_addpv_op_0(i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case AcosOp:
			// sqrt(1 - x * x), acos(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_acos_op_0(i_var, arg[0], J, taylor);
			break;
			// -------------------------------------------------

# if CPPAD_USE_CPLUSPLUS_2011
			case AcoshOp:
			// sqrt(x * x - 1), acosh(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_acosh_op_0(i_var, arg[0], J, taylor);
			break;
# endif
			// -------------------------------------------------

			case AsinOp:
			// sqrt(1 - x * x), asin(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_asin_op_0(i_var, arg[0], J, taylor);
			break;
			// -------------------------------------------------

# if CPPAD_USE_CPLUSPLUS_2011
			case AsinhOp:
			// sqrt(1 + x * x), asinh(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_asinh_op_0(i_var, arg[0], J, taylor);
			break;
# endif
			// -------------------------------------------------

			case AtanOp:
			// 1 + x * x, atan(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_atan_op_0(i_var, arg[0], J, taylor);
			break;
			// -------------------------------------------------

# if CPPAD_USE_CPLUSPLUS_2011
			case AtanhOp:
			// 1 - x * x, atanh(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_atanh_op_0(i_var, arg[0], J, taylor);
			break;
# endif
			// -------------------------------------------------

			case CExpOp:
			// Use the general case with d == 0
			// (could create an optimzied verison for this case)
			forward_cond_op_0(
				i_var, arg, num_par, parameter, J, taylor
			);
			break;
			// ---------------------------------------------------

			case CosOp:
			// sin(x), cos(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_cos_op_0(i_var, arg[0], J, taylor);
			break;
			// ---------------------------------------------------

			case CoshOp:
			// sinh(x), cosh(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_cosh_op_0(i_var, arg[0], J, taylor);
			break;
			// -------------------------------------------------

			case CSkipOp:
			// CSkipOp has a variable number of arguments and
			// forward_next thinks it has no arguments.
			// we must inform forward_next of this special case.
			forward_cskip_op_0(
				i_var, arg, num_par, parameter, J, taylor, cskip_op
			);
			play->forward_cskip(op, arg, i_op, i_var);
			break;
			// -------------------------------------------------

			case CSumOp:
			// CSumOp has a variable number of arguments and
			// forward_next thinks it has no arguments.
			// we must inform forward_next of this special case.
			forward_csum_op(
				0, 0, i_var, arg, num_par, parameter, J, taylor
			);
			play->forward_csum(op, arg, i_op, i_var);
			break;
			// -------------------------------------------------

			case DisOp:
			forward_dis_op(p, q, r, i_var, arg, J, taylor);
			break;
			// -------------------------------------------------

			case DivvvOp:
			forward_divvv_op_0(i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case DivpvOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			forward_divpv_op_0(i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case DivvpOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par );
			forward_divvp_op_0(i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case EndOp:
			CPPAD_ASSERT_NARG_NRES(op, 0, 0);
			more_operators = false;
			break;
			// -------------------------------------------------

			case EqpvOp:
			if( compare_change_count )
			{	forward_eqpv_op_0(
					compare_change_number, arg, parameter, J, taylor
				);
				{	if( compare_change_count == compare_change_number )
						compare_change_op_index = i_op;
				}
			}
			break;
			// -------------------------------------------------

			case EqvvOp:
			if( compare_change_count )
			{	forward_eqvv_op_0(
					compare_change_number, arg, parameter, J, taylor
				);
				{	if( compare_change_count == compare_change_number )
						compare_change_op_index = i_op;
				}
			}
			break;
			// -------------------------------------------------

# if CPPAD_USE_CPLUSPLUS_2011
			case ErfOp:
			forward_erf_op_0(i_var, arg, parameter, J, taylor);
			break;
# endif
			// -------------------------------------------------

			case ExpOp:
			forward_exp_op_0(i_var, arg[0], J, taylor);
			break;
			// -------------------------------------------------

# if CPPAD_USE_CPLUSPLUS_2011
			case Expm1Op:
			forward_expm1_op_0(i_var, arg[0], J, taylor);
			break;
# endif
			// -------------------------------------------------

			case InvOp:
			CPPAD_ASSERT_NARG_NRES(op, 0, 1);
			break;
			// ---------------------------------------------------

			case LdpOp:
			forward_load_p_op_0(
				play,
				i_var,
				arg,
				parameter,
				J,
				taylor,
				isvar_by_ind.data(),
				index_by_ind.data(),
				var_by_load_op.data()
			);
			break;
			// -------------------------------------------------

			case LdvOp:
			forward_load_v_op_0(
				play,
				i_var,
				arg,
				parameter,
				J,
				taylor,
				isvar_by_ind.data(),
				index_by_ind.data(),
				var_by_load_op.data()
			);
			break;
			// -------------------------------------------------

			case LepvOp:
			if( compare_change_count )
			{	forward_lepv_op_0(
					compare_change_number, arg, parameter, J, taylor
				);
				{	if( compare_change_count == compare_change_number )
						compare_change_op_index = i_op;
				}
			}
			break;
			// -------------------------------------------------

			case LevpOp:
			if( compare_change_count )
			{	forward_levp_op_0(
					compare_change_number, arg, parameter, J, taylor
				);
				{	if( compare_change_count == compare_change_number )
						compare_change_op_index = i_op;
				}
			}
			break;
			// -------------------------------------------------

			case LevvOp:
			if( compare_change_count )
			{	forward_levv_op_0(
					compare_change_number, arg, parameter, J, taylor
				);
				{	if( compare_change_count == compare_change_number )
						compare_change_op_index = i_op;
				}
			}
			break;
			// -------------------------------------------------

			case LogOp:
			forward_log_op_0(i_var, arg[0], J, taylor);
			break;
			// -------------------------------------------------

# if CPPAD_USE_CPLUSPLUS_2011
			case Log1pOp:
			forward_log1p_op_0(i_var, arg[0], J, taylor);
			break;
# endif
			// -------------------------------------------------

			case LtpvOp:
			if( compare_change_count )
			{	forward_ltpv_op_0(
					compare_change_number, arg, parameter, J, taylor
				);
				{	if( compare_change_count == compare_change_number )
						compare_change_op_index = i_op;
				}
			}
			break;
			// -------------------------------------------------

			case LtvpOp:
			if( compare_change_count )
			{	forward_ltvp_op_0(
					compare_change_number, arg, parameter, J, taylor
				);
				{	if( compare_change_count == compare_change_number )
						compare_change_op_index = i_op;
				}
			}
			break;
			// -------------------------------------------------

			case LtvvOp:
			if( compare_change_count )
			{	forward_ltvv_op_0(
					compare_change_number, arg, parameter, J, taylor
				);
				{	if( compare_change_count == compare_change_number )
						compare_change_op_index = i_op;
				}
			}
			break;
			// -------------------------------------------------

			case MulpvOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			forward_mulpv_op_0(i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case MulvvOp:
			forward_mulvv_op_0(i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case NepvOp:
			if( compare_change_count )
			{	forward_nepv_op_0(
					compare_change_number, arg, parameter, J, taylor
				);
				{	if( compare_change_count == compare_change_number )
						compare_change_op_index = i_op;
				}
			}
			break;
			// -------------------------------------------------

			case NevvOp:
			if( compare_change_count )
			{	forward_nevv_op_0(
					compare_change_number, arg, parameter, J, taylor
				);
				{	if( compare_change_count == compare_change_number )
						compare_change_op_index = i_op;
				}
			}
			break;
			// -------------------------------------------------

			case ParOp:
			forward_par_op_0(
				i_var, arg, num_par, parameter, J, taylor
			);
			break;
			// -------------------------------------------------

			case PowvpOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par );
			forward_powvp_op_0(i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case PowpvOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			forward_powpv_op_0(i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case PowvvOp:
			forward_powvv_op_0(i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case PriOp:
			if( print ) forward_pri_0(s_out,
				arg, num_text, text, num_par, parameter, J, taylor
			);
			break;
			// -------------------------------------------------

			case SignOp:
			// cos(x), sin(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_sign_op_0(i_var, arg[0], J, taylor);
			break;
			// -------------------------------------------------

			case SinOp:
			// cos(x), sin(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_sin_op_0(i_var, arg[0], J, taylor);
			break;
			// -------------------------------------------------

			case SinhOp:
			// cosh(x), sinh(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_sinh_op_0(i_var, arg[0], J, taylor);
			break;
			// -------------------------------------------------

			case SqrtOp:
			forward_sqrt_op_0(i_var, arg[0], J, taylor);
			break;
			// -------------------------------------------------

			case StppOp:
			forward_store_pp_op_0(
				i_var,
				arg,
				num_par,
				J,
				taylor,
				isvar_by_ind.data(),
				index_by_ind.data()
			);
			break;
			// -------------------------------------------------

			case StpvOp:
			forward_store_pv_op_0(
				i_var,
				arg,
				num_par,
				J,
				taylor,
				isvar_by_ind.data(),
				index_by_ind.data()
			);
			break;
			// -------------------------------------------------

			case StvpOp:
			forward_store_vp_op_0(
				i_var,
				arg,
				num_par,
				J,
				taylor,
				isvar_by_ind.data(),
				index_by_ind.data()
			);
			break;
			// -------------------------------------------------

			case StvvOp:
			forward_store_vv_op_0(
				i_var,
				arg,
				num_par,
				J,
				taylor,
				isvar_by_ind.data(),
				index_by_ind.data()
			);
			break;
			// -------------------------------------------------

			case SubvvOp:
			forward_subvv_op_0(i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case SubpvOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			forward_subpv_op_0(i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case SubvpOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par );
			forward_subvp_op_0(i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case TanOp:
			// tan(x)^2, tan(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_tan_op_0(i_var, arg[0], J, taylor);
			break;
			// -------------------------------------------------

			case TanhOp:
			// tanh(x)^2, tanh(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_tanh_op_0(i_var, arg[0], J, taylor);
			break;
			// -------------------------------------------------

			case UserOp:
			// start or end an atomic operation sequence
			flag = user_state == start_user;
			user_atom = play->forward_user(op, user_state,
				user_old, user_m, user_n, user_i, user_j
			);
			if( flag )
			{	user_tx.resize(user_n);
				user_ty.resize(user_m);
# if CPPAD_FORWARD0SWEEP_TRACE
				user_iy.resize(user_m);
# endif
			}
			else
			{
# ifndef NDEBUG
				if( ! user_ok )
				{	std::string msg =
						user_atom->afun_name()
						+ ": atomic_base.forward: returned false";
					CPPAD_ASSERT_KNOWN(false, msg.c_str() );
				}
# endif
# if CPPAD_FORWARD0SWEEP_TRACE
				user_trace = true;
# endif
			}
			break;

			case UsrapOp:
			// parameter argument in an atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( size_t( arg[0] ) < num_par );
			user_tx[user_j] = parameter[ arg[0] ];
			play->forward_user(op, user_state,
				user_old, user_m, user_n, user_i, user_j
			);
			if( user_j == user_n )
			{	// call users function for this operation
				user_atom->set_old(user_old);
				CPPAD_ATOMIC_CALL(p, q,
					user_vx, user_vy, user_tx, user_ty
				);
			}
			break;

			case UsravOp:
			// variable argument in an atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) <= i_var );
			user_tx[user_j] = taylor[ arg[0] * J + 0 ];
			play->forward_user(op, user_state,
				user_old, user_m, user_n, user_i, user_j
			);
			if( user_j == user_n )
			{	// call users function for this operation
				user_atom->set_old(user_old);
				CPPAD_ATOMIC_CALL(p, q,
					user_vx, user_vy, user_tx, user_ty
				);
			}
			break;

			case UsrrpOp:
			// parameter result in an atomic operation sequence
# if CPPAD_FORWARD0SWEEP_TRACE
			user_iy[user_i] = 0;
# endif
			play->forward_user(op, user_state,
				user_old, user_m, user_n, user_i, user_j
			);
			break;

			case UsrrvOp:
			// variable result in an atomic operation sequence
# if CPPAD_FORWARD0SWEEP_TRACE
			user_iy[user_i] = i_var;
# endif
			taylor[ i_var * J + 0 ] = user_ty[user_i];
			play->forward_user(op, user_state,
				user_old, user_m, user_n, user_i, user_j
			);
			break;
			// -------------------------------------------------

			case ZmulpvOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			forward_zmulpv_op_0(i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case ZmulvpOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par );
			forward_zmulvp_op_0(i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			case ZmulvvOp:
			forward_zmulvv_op_0(i_var, arg, parameter, J, taylor);
			break;
			// -------------------------------------------------

			default:
			CPPAD_ASSERT_UNKNOWN(false);
		}
# if CPPAD_FORWARD0SWEEP_TRACE
		size_t  d  = 0;
		if( user_trace )
		{	user_trace = false;

			CPPAD_ASSERT_UNKNOWN( op == UserOp );
			CPPAD_ASSERT_UNKNOWN( NumArg(UsrrvOp) == 0 );
			for(size_t i = 0; i < user_m; i++) if( user_iy[i] > 0 )
			{	size_t i_tmp   = (i_op + i) - user_m;
				printOp(
					std::cout,
					play,
					i_tmp,
					user_iy[i],
					UsrrvOp,
					CPPAD_NULL
				);
				Base* Z_tmp = taylor + user_iy[i] * J;
				printOpResult(
					std::cout,
					d + 1,
					Z_tmp,
					0,
					(Base *) CPPAD_NULL
				);
				std::cout << std::endl;
			}
		}
		Base*           Z_tmp   = taylor + i_var * J;
		const addr_t*   arg_tmp = arg;
		if( op == CSumOp )
			arg_tmp = arg - arg[-1] - 4;
		if( op == CSkipOp )
			arg_tmp = arg - arg[-1] - 7;
		if( op != UsrrvOp )
		{
			printOp(
				std::cout,
				play,
				i_op,
				i_var,
				op,
				arg_tmp
			);
			if( NumRes(op) > 0 ) printOpResult(
				std::cout,
				d + 1,
				Z_tmp,
				0,
				(Base *) CPPAD_NULL
			);
			std::cout << std::endl;
		}
	}
	std::cout << std::endl;
# else
	}
size_t forward_sweep(
	bool                  print,
	size_t                d,
	size_t                n,
	size_t                numvar,
	player<Base>         *Rec,
	size_t                J,
	Base                 *Taylor
)
{	CPPAD_ASSERT_UNKNOWN( J >= d + 1 );

	// op code for current instruction
	OpCode           op;

	// index for current instruction
	size_t         i_op;

	// next variables 
	size_t        i_var;

# if CPPAD_USE_FORWARD0SWEEP
	CPPAD_ASSERT_UNKNOWN( d > 0 );
# else
	size_t*         non_const_arg;
# endif
	const size_t   *arg = 0;

	size_t            i;

	// initialize the comparision operator (ComOp) counter
	size_t compareCount = 0;

	// if this is an order zero calculation, initialize vector indices
	size_t *VectorInd = CPPAD_NULL;  // address for each element
	bool   *VectorVar = CPPAD_NULL;  // is element a variable
	i = Rec->num_rec_vecad_ind();
	if( i > 0 )
	{	VectorInd = CPPAD_TRACK_NEW_VEC(i, VectorInd);
		VectorVar = CPPAD_TRACK_NEW_VEC(i, VectorVar);
		while(i--)
		{	VectorInd[i] = Rec->GetVecInd(i);
			VectorVar[i] = false;
		}
	}

	// check numvar argument
	CPPAD_ASSERT_UNKNOWN( Rec->num_rec_var() == numvar );

	// length of the parameter vector (used by CppAD assert macros)
	const size_t num_par = Rec->num_rec_par();

	// length of the text vector (used by CppAD assert macros)
	const size_t num_text = Rec->num_rec_text();

	// pointer to the beginning of the parameter vector
	const Base* parameter = 0;
	if( num_par > 0 )
		parameter = Rec->GetPar();

	// pointer to the beginning of the text vector
	const char* text = 0;
	if( num_text > 0 )
		text = Rec->GetTxt(0);
	

	// skip the BeginOp at the beginning of the recording
	Rec->start_forward(op, arg, i_op, i_var);
	CPPAD_ASSERT_UNKNOWN( op == BeginOp );
# if CPPAD_FORWARD_SWEEP_TRACE
	std::cout << std::endl;
# endif
	while(op != EndOp)
	{
		// this op
		Rec->next_forward(op, arg, i_op, i_var);
		CPPAD_ASSERT_UNKNOWN( (i_op > n)  | (op == InvOp) );  
		CPPAD_ASSERT_UNKNOWN( (i_op <= n) | (op != InvOp) );  

		// action depends on the operator
		switch( op )
		{
			case AbsOp:
			forward_abs_op(d, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case AddvvOp:
			forward_addvv_op(d, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case AddpvOp:
			CPPAD_ASSERT_UNKNOWN( arg[0] < num_par );
			forward_addpv_op(d, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case AcosOp:
			// variables: sqrt(1 - x * x), acos(x) 
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_acos_op(d, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case AsinOp:
			// results: sqrt(1 - x * x), asin(x) 
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_asin_op(d, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case AtanOp:
			// results: 1 + x * x, atan(x) 
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_atan_op(d, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case CSumOp:
			// CSumOp has a variable number of arguments and
			// next_forward thinks it one has one argument.
			// we must inform next_forward of this special case.
			Rec->forward_csum(op, arg, i_op, i_var);
			forward_csum_op(
				d, i_var, arg, num_par, parameter, J, Taylor
			);
			break;
			// -------------------------------------------------

			case CExpOp:
			forward_cond_op(
				d, i_var, arg, num_par, parameter, J, Taylor
			);
			break;
			// ---------------------------------------------------

			case ComOp:
# if ! USE_FORWARD0SWEEP 
			if( d == 0 ) forward_comp_op_0(
			compareCount, arg, num_par, parameter, J, Taylor
			);
# endif
			break;
			// ---------------------------------------------------

			case CosOp:
			// variables: sin(x), cos(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_cos_op(d, i_var, arg[0], J, Taylor);
			break;
			// ---------------------------------------------------

			case CoshOp:
			// variables: sinh(x), cosh(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_cosh_op(d, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case DisOp:
# if ! CPPAD_USE_FORWARD0SWEEP
			if( d == 0 )
				forward_dis_op_0(i_var, arg, J, Taylor);
			else
# endif
			{	Taylor[ i_var * J + d] = Base(0);
			}
			break;
			// -------------------------------------------------

			case DivvvOp:
			forward_divvv_op(d, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case DivpvOp:
			CPPAD_ASSERT_UNKNOWN( arg[0] < num_par );
			forward_divpv_op(d, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case DivvpOp:
			CPPAD_ASSERT_UNKNOWN( arg[1] < num_par );
			forward_divvp_op(d, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case EndOp:
			CPPAD_ASSERT_NARG_NRES(op, 0, 0);
			break;
			// -------------------------------------------------

			case ExpOp:
			forward_exp_op(d, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case InvOp:
			CPPAD_ASSERT_UNKNOWN( NumArg(op) == 0 );
			break;
			// -------------------------------------------------

			case LdpOp:
# if ! CPPAD_USE_FORWARD0SWEEP
			if( d == 0 )
			{	non_const_arg = Rec->forward_non_const_arg();
				forward_load_p_op_0(
					i_var, 
					non_const_arg, 
					num_par, 
					parameter, 
					J, 
					Taylor,
					Rec->num_rec_vecad_ind(),
					VectorVar,
					VectorInd
				);
			}
			else
# endif
			{	forward_load_op( op, d, i_var, arg, J, Taylor);
			}
			break;
			// -------------------------------------------------

			case LdvOp:
# if ! CPPAD_USE_FORWARD0SWEEP
			if( d == 0 )
			{	non_const_arg = Rec->forward_non_const_arg();
				forward_load_v_op_0(
					i_var, 
					non_const_arg, 
					num_par, 
					parameter, 
					J, 
					Taylor,
					Rec->num_rec_vecad_ind(),
					VectorVar,
					VectorInd
				);
			}
			else
# endif
			{	forward_load_op( op, d, i_var, arg, J, Taylor);
			}
			break;
			// -------------------------------------------------

			case LogOp:
			forward_log_op(d, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case MulvvOp:
			forward_mulvv_op(d, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case MulpvOp:
			CPPAD_ASSERT_UNKNOWN( arg[0] < num_par );
			forward_mulpv_op(d, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case ParOp:
# if ! CPPAD_USE_FORWARD0SWEEP
			if( d == 0 ) forward_par_op_0(
				i_var, arg, num_par, parameter, J, Taylor
			);
			else
# endif
			{	Taylor[ i_var * J + d] = Base(0); 
			}
			break;
			// -------------------------------------------------

			case PowvpOp:
			CPPAD_ASSERT_UNKNOWN( arg[1] < num_par );
			forward_powvp_op(d, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case PowpvOp:
			CPPAD_ASSERT_UNKNOWN( arg[0] < num_par );
			forward_powpv_op(d, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case PowvvOp:
			forward_powvv_op(d, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case PripOp:
# if ! CPPAD_USE_FORWARD0SWEEP
			if( print && ( d == 0 ) ) forward_prip_0(
				arg, num_text, text, num_par, parameter
			);
# endif
			break;
			// -------------------------------------------------

			case PrivOp:
# if ! CPPAD_USE_FORWARD0SWEEP
			if( print && ( d == 0 ) ) forward_priv_0(
				i_var, arg, num_text, text, J, Taylor
			);
# endif
			break;
			// -------------------------------------------------

			case SinOp:
			// variables: cos(x), sin(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_sin_op(d, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case SinhOp:
			// variables: cosh(x), sinh(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_sinh_op(d, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case SqrtOp:
			forward_sqrt_op(d, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case StppOp:
# if ! CPPAD_USE_FORWARD0SWEEP
			if( d == 0 )
			{	forward_store_pp_op_0(
					i_var, 
					arg, 
					num_par, 
					J, 
					Taylor,
					Rec->num_rec_vecad_ind(),
					VectorVar,
					VectorInd
				);
			}
# endif
			break;
			// -------------------------------------------------

			case StpvOp:
# if ! CPPAD_USE_FORWARD0SWEEP
			if( d == 0 )
			{	forward_store_pv_op_0(
					i_var, 
					arg, 
					num_par, 
					J, 
					Taylor,
					Rec->num_rec_vecad_ind(),
					VectorVar,
					VectorInd
				);
			}
# endif
			break;
			// -------------------------------------------------

			case StvpOp:
# if ! CPPAD_USE_FORWARD0SWEEP
			if( d == 0 )
			{	forward_store_vp_op_0(
					i_var, 
					arg, 
					num_par, 
					J, 
					Taylor,
					Rec->num_rec_vecad_ind(),
					VectorVar,
					VectorInd
				);
			}
# endif
			break;
			// -------------------------------------------------

			case StvvOp:
# if ! CPPAD_USE_FORWARD0SWEEP
			if( d == 0 )
			{	forward_store_vv_op_0(
					i_var, 
					arg, 
					num_par, 
					J, 
					Taylor,
					Rec->num_rec_vecad_ind(),
					VectorVar,
					VectorInd
				);
			}
# endif
			break;
			// -------------------------------------------------

			case SubvvOp:
			forward_subvv_op(d, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case SubpvOp:
			CPPAD_ASSERT_UNKNOWN( arg[0] < num_par );
			forward_subpv_op(d, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case SubvpOp:
			CPPAD_ASSERT_UNKNOWN( arg[1] < num_par );
			forward_subvp_op(d, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			default:
			CPPAD_ASSERT_UNKNOWN(0);
		}
# if CPPAD_FORWARD_SWEEP_TRACE
		size_t       i_tmp  = i_var;
		Base*        Z_tmp  = Taylor + J * i_var;
		printOp(
			std::cout, 
			Rec,
			i_tmp,
			op, 
			arg,
			d + 1, 
			Z_tmp, 
			0, 
			(Base *) CPPAD_NULL
		);
	}
	std::cout << std::endl;
# else
	}
size_t forward_sweep(
	std::ostream&         s_out,
	const bool            print,
	const size_t          q,
	const size_t          p,
	const size_t          n,
	const size_t          numvar,
	player<Base>         *Rec,
	const size_t          J,
	Base                 *Taylor,
	CppAD::vector<bool>&  cskip_op
)
{	CPPAD_ASSERT_UNKNOWN( J >= p + 1 );
	CPPAD_ASSERT_UNKNOWN( q <= p );

	// op code for current instruction
	OpCode           op;

	// index for current instruction
	size_t         i_op;

	// next variables 
	size_t        i_var;

	// arg (not as a constant)
	addr_t*         non_const_arg = CPPAD_NULL;

	// arg (as a constant)
	const addr_t*   arg = CPPAD_NULL;

	// temporary indices
	size_t i, ell;

	// initialize the comparision operator (ComOp) counter
	size_t compareCount = 0;

	pod_vector<size_t> VectorInd;  // address for each element
	pod_vector<bool>   VectorVar;  // is element a variable
	if( q == 0 )
	{
		// this includes order zero calculation, initialize vector indices
		i = Rec->num_rec_vecad_ind();
		if( i > 0 )
		{	VectorInd.extend(i);
			VectorVar.extend(i);
			while(i--)
			{	VectorInd[i] = Rec->GetVecInd(i);
				VectorVar[i] = false;
			}
		}
		// includes zero order, so initialize conditional skip flags
		for(i = 0; i < Rec->num_rec_op(); i++)
			cskip_op[i] = false;
	}

	// Work space used by UserOp. Note User assumes q = p.
	const size_t user_p1 = p+1;  // number of orders for this user calculation
	vector<bool> user_vx;        // empty vector
	vector<bool> user_vy;        // empty vector
	vector<Base> user_tx;        // argument vector Taylor coefficients 
	vector<Base> user_ty;        // result vector Taylor coefficients 
	vector<size_t> user_iy;      // variable indices for results vector
	size_t user_index = 0;       // indentifier for this atomic operation
	size_t user_id    = 0;       // user identifier for this call to operator
	size_t user_i     = 0;       // index in result vector
	size_t user_j     = 0;       // index in argument vector
	size_t user_m     = 0;       // size of result vector
	size_t user_n     = 0;       // size of arugment vector
	//
	atomic_base<Base>* user_atom = CPPAD_NULL; // user's atomic op calculator
# ifndef NDEBUG
	bool               user_ok   = false;      // atomic op return value
# endif
	//
	// next expected operator in a UserOp sequence
	enum { user_start, user_arg, user_ret, user_end } user_state = user_start;

	// check numvar argument
	CPPAD_ASSERT_UNKNOWN( Rec->num_rec_var() == numvar );

	// length of the parameter vector (used by CppAD assert macros)
	const size_t num_par = Rec->num_rec_par();

	// pointer to the beginning of the parameter vector
	const Base* parameter = CPPAD_NULL;
	if( num_par > 0 )
		parameter = Rec->GetPar();

	// length of the text vector (used by CppAD assert macros)
	const size_t num_text = Rec->num_rec_text();

	// pointer to the beginning of the text vector
	const char* text = CPPAD_NULL;
	if( num_text > 0 )
		text = Rec->GetTxt(0);

	// skip the BeginOp at the beginning of the recording
	Rec->start_forward(op, arg, i_op, i_var);
	CPPAD_ASSERT_UNKNOWN( op == BeginOp );
# if CPPAD_FORWARD_SWEEP_TRACE
	std::cout << std::endl;
# endif
	bool more_operators = true;
	while(more_operators)
	{
		// this op
		Rec->next_forward(op, arg, i_op, i_var);
		CPPAD_ASSERT_UNKNOWN( (i_op > n)  | (op == InvOp) );  
		CPPAD_ASSERT_UNKNOWN( (i_op <= n) | (op != InvOp) );  

		// check if we are skipping this operation
		while( cskip_op[i_op] )
		{	if( op == CSumOp )
			{	// CSumOp has a variable number of arguments 
				Rec->forward_csum(op, arg, i_op, i_var);
			}
			Rec->next_forward(op, arg, i_op, i_var);
		}

		// action depends on the operator
		switch( op )
		{
			case AbsOp:
			forward_abs_op(q, p, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case AddvvOp:
			forward_addvv_op(q, p, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case AddpvOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			forward_addpv_op(q, p, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case AcosOp:
			// sqrt(1 - x * x), acos(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_acos_op(q, p, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case AsinOp:
			// sqrt(1 - x * x), asin(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_asin_op(q, p, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case AtanOp:
			// 1 + x * x, atan(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_atan_op(q, p, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case CExpOp:
			forward_cond_op(
				q, p, i_var, arg, num_par, parameter, J, Taylor
			);
			break;
			// ---------------------------------------------------

			case ComOp:
			if( q == 0 ) forward_comp_op_0(
			compareCount, arg, num_par, parameter, J, Taylor
			);
			break;
			// ---------------------------------------------------

			case CosOp:
			// sin(x), cos(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_cos_op(q, p, i_var, arg[0], J, Taylor);
			break;
			// ---------------------------------------------------

			case CoshOp:
			// sinh(x), cosh(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_cosh_op(q, p, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case CSkipOp:
			// CSkipOp has a variable number of arguments and
			// next_forward thinks it one has one argument.
			// we must inform next_forward of this special case.
			Rec->forward_cskip(op, arg, i_op, i_var);
			if( q == 0 )
			{	forward_cskip_op_0(
					i_var, arg, num_par, parameter, J, Taylor, cskip_op
				);
			}
			break;
			// -------------------------------------------------

			case CSumOp:
			// CSumOp has a variable number of arguments and
			// next_forward thinks it one has one argument.
			// we must inform next_forward of this special case.
			Rec->forward_csum(op, arg, i_op, i_var);
			forward_csum_op(
				q, p, i_var, arg, num_par, parameter, J, Taylor
			);
			break;
			// -------------------------------------------------

			case DisOp:
			i = q;
			if( i == 0 )
			{	forward_dis_op_0(i_var, arg, J, Taylor);
				i++;
			}
			while(i <= p)
			{	Taylor[ i_var * J + i] = Base(0);
				i++;
			}
			break;
			// -------------------------------------------------

			case DivvvOp:
			forward_divvv_op(q, p, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case DivpvOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			forward_divpv_op(q, p, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case DivvpOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par );
			forward_divvp_op(q, p, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case EndOp:
			CPPAD_ASSERT_NARG_NRES(op, 0, 0);
			more_operators = false;
			break;
			// -------------------------------------------------

			case ExpOp:
			forward_exp_op(q, p, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case InvOp:
			CPPAD_ASSERT_UNKNOWN( NumArg(op) == 0 );
			break;
			// -------------------------------------------------

			case LdpOp:
			if( q == 0 )
			{	non_const_arg = Rec->forward_non_const_arg();
				forward_load_p_op_0(
					i_var, 
					non_const_arg, 
					num_par, 
					parameter, 
					J, 
					Taylor,
					Rec->num_rec_vecad_ind(),
					VectorVar.data(),
					VectorInd.data()
				);
				if( q < p )
					forward_load_op( op, q+1, p, i_var, arg, J, Taylor);
			}
			else
			{	forward_load_op( op, q, p, i_var, arg, J, Taylor);
			}
			break;
			// -------------------------------------------------

			case LdvOp:
			if( q == 0 )
			{	non_const_arg = Rec->forward_non_const_arg();
				forward_load_v_op_0(
					i_var, 
					non_const_arg, 
					num_par, 
					parameter, 
					J, 
					Taylor,
					Rec->num_rec_vecad_ind(),
					VectorVar.data(),
					VectorInd.data()
				);
				if( q < p )
					forward_load_op( op, q+1, p, i_var, arg, J, Taylor);
			}
			else
			{	forward_load_op( op, q, p, i_var, arg, J, Taylor);
			}
			break;
			// -------------------------------------------------

			case LogOp:
			forward_log_op(q, p, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case MulvvOp:
			forward_mulvv_op(q, p, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case MulpvOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			forward_mulpv_op(q, p, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case ParOp:
			i = q;
			if( i == 0 )
			{	forward_par_op_0(
					i_var, arg, num_par, parameter, J, Taylor
				);
				i++;
			}
			while(i <= p)
			{	Taylor[ i_var * J + i] = Base(0); 
				i++;
			}
			break;
			// -------------------------------------------------

			case PowvpOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par );
			forward_powvp_op(q, p, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case PowpvOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			forward_powpv_op(q, p, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case PowvvOp:
			forward_powvv_op(q, p, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case PriOp:
			if( (q == 0) & print ) forward_pri_0(s_out,
				i_var, arg, num_text, text, num_par, parameter, J, Taylor
			);
			break;
			// -------------------------------------------------

			case SignOp:
			// sign(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_sign_op(q, p, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case SinOp:
			// cos(x), sin(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_sin_op(q, p, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case SinhOp:
			// cosh(x), sinh(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_sinh_op(q, p, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case SqrtOp:
			forward_sqrt_op(q, p, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case StppOp:
			if( q == 0 )
			{	forward_store_pp_op_0(
					i_var, 
					arg, 
					num_par, 
					J, 
					Taylor,
					Rec->num_rec_vecad_ind(),
					VectorVar.data(),
					VectorInd.data()
				);
			}
			break;
			// -------------------------------------------------

			case StpvOp:
			if( q == 0 )
			{	forward_store_pv_op_0(
					i_var, 
					arg, 
					num_par, 
					J, 
					Taylor,
					Rec->num_rec_vecad_ind(),
					VectorVar.data(),
					VectorInd.data()
				);
			}
			break;
			// -------------------------------------------------

			case StvpOp:
			if( q == 0 )
			{	forward_store_vp_op_0(
					i_var, 
					arg, 
					num_par, 
					J, 
					Taylor,
					Rec->num_rec_vecad_ind(),
					VectorVar.data(),
					VectorInd.data()
				);
			}
			break;
			// -------------------------------------------------

			case StvvOp:
			if( q == 0 )
			{	forward_store_vv_op_0(
					i_var, 
					arg, 
					num_par, 
					J, 
					Taylor,
					Rec->num_rec_vecad_ind(),
					VectorVar.data(),
					VectorInd.data()
				);
			}
			break;
			// -------------------------------------------------

			case SubvvOp:
			forward_subvv_op(q, p, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case SubpvOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			forward_subpv_op(q, p, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case SubvpOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par );
			forward_subvp_op(q, p, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case TanOp:
			// tan(x)^2, tan(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_tan_op(q, p, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case TanhOp:
			// tanh(x)^2, tanh(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_tanh_op(q, p, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case UserOp:
			// start or end an atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( NumRes( UserOp ) == 0 );
			CPPAD_ASSERT_UNKNOWN( NumArg( UserOp ) == 4 );
			if( user_state == user_start )
			{	user_index = arg[0];
				user_id    = arg[1];
				user_n     = arg[2];
				user_m     = arg[3];
				user_atom  = atomic_base<Base>::class_object(user_index);
# ifndef NDEBUG
				if( user_atom == CPPAD_NULL )
				{	std::string msg = 
						atomic_base<Base>::class_name(user_index)
						+ ": atomic_base function has been deleted";
					CPPAD_ASSERT_KNOWN(false, msg.c_str() );
				}
# endif
				if(user_tx.size() != user_n * user_p1)
					user_tx.resize(user_n * user_p1);
				if(user_ty.size() != user_m * user_p1)
					user_ty.resize(user_m * user_p1);
				if(user_iy.size() != user_m)
					user_iy.resize(user_m);
				user_j     = 0;
				user_i     = 0;
				user_state = user_arg;
			}
			else
			{	CPPAD_ASSERT_UNKNOWN( user_state == user_end );
				CPPAD_ASSERT_UNKNOWN( user_index == size_t(arg[0]) );
				CPPAD_ASSERT_UNKNOWN( user_id    == size_t(arg[1]) );
				CPPAD_ASSERT_UNKNOWN( user_n     == size_t(arg[2]) );
				CPPAD_ASSERT_UNKNOWN( user_m     == size_t(arg[3]) );

				// call users function for this operation
				user_atom->set_id(user_id);
				CPPAD_ATOMIC_CALL(
					q, p, user_vx, user_vy, user_tx, user_ty
				);
# ifndef NDEBUG
				if( ! user_ok )
				{	std::string msg = 
						atomic_base<Base>::class_name(user_index)
						+ ": atomic_base.forward: returned false";
					CPPAD_ASSERT_KNOWN(false, msg.c_str() );
				}
# endif
				for(i = 0; i < user_m; i++) 
					if( user_iy[i] > 0 )
						for(ell = q; ell <= p; ell++)
							Taylor[ user_iy[i] * J + ell ] = 
								user_ty[ i * user_p1 + ell ];

				user_state = user_start;
			}
			break;

			case UsrapOp:
			// parameter argument in an atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( user_state == user_arg );
			CPPAD_ASSERT_UNKNOWN( user_j < user_n );
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			user_tx[user_j * user_p1 + 0] = parameter[ arg[0]];
			for(ell = 1; ell < user_p1; ell++)
				user_tx[user_j * user_p1 + ell] = Base(0);
			++user_j;
			if( user_j == user_n )
				user_state = user_ret;
			break;

			case UsravOp:
			// variable argument in an atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( user_state == user_arg );
			CPPAD_ASSERT_UNKNOWN( user_j < user_n );
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) <= i_var );
			for(ell = 0; ell < user_p1; ell++)
				user_tx[user_j * user_p1 + ell] = Taylor[ arg[0] * J + ell];
			++user_j;
			if( user_j == user_n )
				user_state = user_ret;
			break;

			case UsrrpOp:
			// parameter result in an atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( user_state == user_ret );
			CPPAD_ASSERT_UNKNOWN( user_i < user_m );
			user_iy[user_i] = 0;
			user_ty[user_i * user_p1 + 0] = parameter[ arg[0]];
			for(ell = 1; ell < q; ell++)
				user_ty[user_i * user_p1 + ell] = Base(0);
			user_i++;
			if( user_i == user_m )
				user_state = user_end;
			break;

			case UsrrvOp:
			// variable result in an atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( user_state == user_ret );
			CPPAD_ASSERT_UNKNOWN( user_i < user_m );
			user_iy[user_i] = i_var;
			for(ell = 0; ell < q; ell++)
				user_ty[user_i * user_p1 + ell] = Taylor[ i_var * J + ell];
			user_i++;
			if( user_i == user_m )
				user_state = user_end;
			break;
			// -------------------------------------------------

			default:
			CPPAD_ASSERT_UNKNOWN(0);
		}
# if CPPAD_FORWARD_SWEEP_TRACE
		size_t       i_tmp  = i_var;
		Base*        Z_tmp  = Taylor + J * i_var;
		printOp(
			std::cout, 
			Rec,
			i_op,
			i_tmp,
			op, 
			arg,
			p + 1, 
			Z_tmp, 
			0, 
			(Base *) CPPAD_NULL
		);
	}
	std::cout << std::endl;
# else
	}
size_t forward_sweep(
	std::ostream&         s_out,
	bool                  print,
	size_t                d,
	size_t                n,
	size_t                numvar,
	player<Base>         *Rec,
	size_t                J,
	Base                 *Taylor
)
{	CPPAD_ASSERT_UNKNOWN( J >= d + 1 );

	// op code for current instruction
	OpCode           op;

	// index for current instruction
	size_t         i_op;

	// next variables 
	size_t        i_var;

	CPPAD_ASSERT_UNKNOWN( d == 0 || ! print );
# if CPPAD_USE_FORWARD0SWEEP
	CPPAD_ASSERT_UNKNOWN( d > 0 );
# else
	addr_t*         non_const_arg;
# endif
	const addr_t*   arg = 0;

	// temporary indices
	size_t i, ell;

	// initialize the comparision operator (ComOp) counter
	size_t compareCount = 0;

	// if this is an order zero calculation, initialize vector indices
	pod_vector<size_t> VectorInd;  // address for each element
	pod_vector<bool>   VectorVar;  // is element a variable
	i = Rec->num_rec_vecad_ind();
	if( i > 0 )
	{	VectorInd.extend(i);
		VectorVar.extend(i);
		while(i--)
		{	VectorInd[i] = Rec->GetVecInd(i);
			VectorVar[i] = false;
		}
	}

	// work space used by UserOp.
	const size_t user_k  = d;    // order of this forward mode calculation
	const size_t user_k1 = d+1;  // number of orders for this calculation
	vector<Base> user_tx;        // argument vector Taylor coefficients 
	vector<Base> user_ty;        // result vector Taylor coefficients 
	vector<size_t> user_iy;      // variable indices for results vector
	size_t user_index = 0;       // indentifier for this user_atomic operation
	size_t user_id    = 0;       // user identifier for this call to operator
	size_t user_i     = 0;       // index in result vector
	size_t user_j     = 0;       // index in argument vector
	size_t user_m     = 0;       // size of result vector
	size_t user_n     = 0;       // size of arugment vector
	// next expected operator in a UserOp sequence
	enum { user_start, user_arg, user_ret, user_end } user_state = user_start;

	// check numvar argument
	CPPAD_ASSERT_UNKNOWN( Rec->num_rec_var() == numvar );

	// length of the parameter vector (used by CppAD assert macros)
	const size_t num_par = Rec->num_rec_par();

	// pointer to the beginning of the parameter vector
	const Base* parameter = 0;
	if( num_par > 0 )
		parameter = Rec->GetPar();

# if ! CPPAD_USE_FORWARD0SWEEP
	// length of the text vector (used by CppAD assert macros)
	const size_t num_text = Rec->num_rec_text();

	// pointer to the beginning of the text vector
	const char* text = 0;
	if( num_text > 0 )
		text = Rec->GetTxt(0);
# endif

	// skip the BeginOp at the beginning of the recording
	Rec->start_forward(op, arg, i_op, i_var);
	CPPAD_ASSERT_UNKNOWN( op == BeginOp );
# if CPPAD_FORWARD_SWEEP_TRACE
	std::cout << std::endl;
# endif
	while(op != EndOp)
	{
		// this op
		Rec->next_forward(op, arg, i_op, i_var);
		CPPAD_ASSERT_UNKNOWN( (i_op > n)  | (op == InvOp) );  
		CPPAD_ASSERT_UNKNOWN( (i_op <= n) | (op != InvOp) );  

		// action depends on the operator
		switch( op )
		{
			case AbsOp:
			forward_abs_op(d, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case AddvvOp:
			forward_addvv_op(d, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case AddpvOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			forward_addpv_op(d, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case AcosOp:
			// sqrt(1 - x * x), acos(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_acos_op(d, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case AsinOp:
			// sqrt(1 - x * x), asin(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_asin_op(d, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case AtanOp:
			// 1 + x * x, atan(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_atan_op(d, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case CSumOp:
			// CSumOp has a variable number of arguments and
			// next_forward thinks it one has one argument.
			// we must inform next_forward of this special case.
			Rec->forward_csum(op, arg, i_op, i_var);
			forward_csum_op(
				d, i_var, arg, num_par, parameter, J, Taylor
			);
			break;
			// -------------------------------------------------

			case CExpOp:
			forward_cond_op(
				d, i_var, arg, num_par, parameter, J, Taylor
			);
			break;
			// ---------------------------------------------------

			case ComOp:
# if ! USE_FORWARD0SWEEP 
			if( d == 0 ) forward_comp_op_0(
			compareCount, arg, num_par, parameter, J, Taylor
			);
# endif
			break;
			// ---------------------------------------------------

			case CosOp:
			// sin(x), cos(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_cos_op(d, i_var, arg[0], J, Taylor);
			break;
			// ---------------------------------------------------

			case CoshOp:
			// sinh(x), cosh(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_cosh_op(d, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case DisOp:
# if ! CPPAD_USE_FORWARD0SWEEP
			if( d == 0 )
				forward_dis_op_0(i_var, arg, J, Taylor);
			else
# endif
			{	Taylor[ i_var * J + d] = Base(0);
			}
			break;
			// -------------------------------------------------

			case DivvvOp:
			forward_divvv_op(d, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case DivpvOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			forward_divpv_op(d, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case DivvpOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par );
			forward_divvp_op(d, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case EndOp:
			CPPAD_ASSERT_NARG_NRES(op, 0, 0);
			break;
			// -------------------------------------------------

			case ExpOp:
			forward_exp_op(d, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case InvOp:
			CPPAD_ASSERT_UNKNOWN( NumArg(op) == 0 );
			break;
			// -------------------------------------------------

			case LdpOp:
# if ! CPPAD_USE_FORWARD0SWEEP
			if( d == 0 )
			{	non_const_arg = Rec->forward_non_const_arg();
				forward_load_p_op_0(
					i_var, 
					non_const_arg, 
					num_par, 
					parameter, 
					J, 
					Taylor,
					Rec->num_rec_vecad_ind(),
					VectorVar.data(),
					VectorInd.data()
				);
			}
			else
# endif
			{	forward_load_op( op, d, i_var, arg, J, Taylor);
			}
			break;
			// -------------------------------------------------

			case LdvOp:
# if ! CPPAD_USE_FORWARD0SWEEP
			if( d == 0 )
			{	non_const_arg = Rec->forward_non_const_arg();
				forward_load_v_op_0(
					i_var, 
					non_const_arg, 
					num_par, 
					parameter, 
					J, 
					Taylor,
					Rec->num_rec_vecad_ind(),
					VectorVar.data(),
					VectorInd.data()
				);
			}
			else
# endif
			{	forward_load_op( op, d, i_var, arg, J, Taylor);
			}
			break;
			// -------------------------------------------------

			case LogOp:
			forward_log_op(d, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case MulvvOp:
			forward_mulvv_op(d, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case MulpvOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			forward_mulpv_op(d, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case ParOp:
# if ! CPPAD_USE_FORWARD0SWEEP
			if( d == 0 ) forward_par_op_0(
				i_var, arg, num_par, parameter, J, Taylor
			);
			else
# endif
			{	Taylor[ i_var * J + d] = Base(0); 
			}
			break;
			// -------------------------------------------------

			case PowvpOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par );
			forward_powvp_op(d, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case PowpvOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			forward_powpv_op(d, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case PowvvOp:
			forward_powvv_op(d, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case PriOp:
# if ! CPPAD_USE_FORWARD0SWEEP
			if( print ) forward_pri_0(s_out,
				i_var, arg, num_text, text, num_par, parameter, J, Taylor
			);
# endif
			break;
			// -------------------------------------------------

			case SignOp:
			// cos(x), sin(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_sign_op(d, i_var, arg[0], J, Taylor);
			break;

			case SinOp:
			// cos(x), sin(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_sin_op(d, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case SinhOp:
			// cosh(x), sinh(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_sinh_op(d, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case SqrtOp:
			forward_sqrt_op(d, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case StppOp:
# if ! CPPAD_USE_FORWARD0SWEEP
			if( d == 0 )
			{	forward_store_pp_op_0(
					i_var, 
					arg, 
					num_par, 
					J, 
					Taylor,
					Rec->num_rec_vecad_ind(),
					VectorVar.data(),
					VectorInd.data()
				);
			}
# endif
			break;
			// -------------------------------------------------

			case StpvOp:
# if ! CPPAD_USE_FORWARD0SWEEP
			if( d == 0 )
			{	forward_store_pv_op_0(
					i_var, 
					arg, 
					num_par, 
					J, 
					Taylor,
					Rec->num_rec_vecad_ind(),
					VectorVar.data(),
					VectorInd.data()
				);
			}
# endif
			break;
			// -------------------------------------------------

			case StvpOp:
# if ! CPPAD_USE_FORWARD0SWEEP
			if( d == 0 )
			{	forward_store_vp_op_0(
					i_var, 
					arg, 
					num_par, 
					J, 
					Taylor,
					Rec->num_rec_vecad_ind(),
					VectorVar.data(),
					VectorInd.data()
				);
			}
# endif
			break;
			// -------------------------------------------------

			case StvvOp:
# if ! CPPAD_USE_FORWARD0SWEEP
			if( d == 0 )
			{	forward_store_vv_op_0(
					i_var, 
					arg, 
					num_par, 
					J, 
					Taylor,
					Rec->num_rec_vecad_ind(),
					VectorVar.data(),
					VectorInd.data()
				);
			}
# endif
			break;
			// -------------------------------------------------

			case SubvvOp:
			forward_subvv_op(d, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case SubpvOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			forward_subpv_op(d, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case SubvpOp:
			CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par );
			forward_subvp_op(d, i_var, arg, parameter, J, Taylor);
			break;
			// -------------------------------------------------

			case TanOp:
			// tan(x)^2, tan(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_tan_op(d, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case TanhOp:
			// tanh(x)^2, tanh(x)
			CPPAD_ASSERT_UNKNOWN( i_var < numvar  );
			forward_tanh_op(d, i_var, arg[0], J, Taylor);
			break;
			// -------------------------------------------------

			case UserOp:
			// start or end an atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( NumRes( UserOp ) == 0 );
			CPPAD_ASSERT_UNKNOWN( NumArg( UserOp ) == 4 );
			if( user_state == user_start )
			{	user_index = arg[0];
				user_id    = arg[1];
				user_n     = arg[2];
				user_m     = arg[3];
				if(user_tx.size() < user_n * user_k1)
					user_tx.resize(user_n * user_k1);
				if(user_ty.size() < user_m * user_k1)
					user_ty.resize(user_m * user_k1);
				if(user_iy.size() < user_m)
					user_iy.resize(user_m);
				user_j     = 0;
				user_i     = 0;
				user_state = user_arg;
			}
			else
			{	CPPAD_ASSERT_UNKNOWN( user_state == user_end );
				CPPAD_ASSERT_UNKNOWN( user_index == size_t(arg[0]) );
				CPPAD_ASSERT_UNKNOWN( user_id    == size_t(arg[1]) );
				CPPAD_ASSERT_UNKNOWN( user_n     == size_t(arg[2]) );
				CPPAD_ASSERT_UNKNOWN( user_m     == size_t(arg[3]) );
				user_state = user_start;

				// call users function for this operation
				user_atomic<Base>::forward(user_index, user_id,
					user_k, user_n, user_m, user_tx, user_ty
				);
				for(i = 0; i < user_m; i++) if( user_iy[i] > 0 )
					Taylor[ user_iy[i] * J + user_k ] = 
						user_ty[ i * user_k1 + user_k ];
			}
			break;

			case UsrapOp:
			// parameter argument in an atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( user_state == user_arg );
			CPPAD_ASSERT_UNKNOWN( user_j < user_n );
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par );
			user_tx[user_j * user_k1 + 0] = parameter[ arg[0]];
			for(ell = 1; ell < user_k1; ell++)
				user_tx[user_j * user_k1 + ell] = Base(0);
			++user_j;
			if( user_j == user_n )
				user_state = user_ret;
			break;

			case UsravOp:
			// variable argument in an atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( user_state == user_arg );
			CPPAD_ASSERT_UNKNOWN( user_j < user_n );
			CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) <= i_var );
			for(ell = 0; ell < user_k1; ell++)
				user_tx[user_j * user_k1 + ell] = Taylor[ arg[0] * J + ell];
			++user_j;
			if( user_j == user_n )
				user_state = user_ret;
			break;

			case UsrrpOp:
			// parameter result in an atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( user_state == user_ret );
			CPPAD_ASSERT_UNKNOWN( user_i < user_m );
			user_iy[user_i] = 0;
			user_ty[user_i * user_k1 + 0] = parameter[ arg[0]];
			for(ell = 1; ell < user_k; ell++)
				user_ty[user_i * user_k1 + ell] = Base(0);
			user_i++;
			if( user_i == user_m )
				user_state = user_end;
			break;

			case UsrrvOp:
			// variable result in an atomic operation sequence
			CPPAD_ASSERT_UNKNOWN( user_state == user_ret );
			CPPAD_ASSERT_UNKNOWN( user_i < user_m );
			user_iy[user_i] = i_var;
			for(ell = 0; ell < user_k; ell++)
				user_ty[user_i * user_k1 + ell] = Taylor[ i_var * J + ell];
			user_i++;
			if( user_i == user_m )
				user_state = user_end;
			break;
			// -------------------------------------------------

			default:
			CPPAD_ASSERT_UNKNOWN(0);
		}
# if CPPAD_FORWARD_SWEEP_TRACE
		size_t       i_tmp  = i_var;
		Base*        Z_tmp  = Taylor + J * i_var;
		printOp(
			std::cout, 
			Rec,
			i_tmp,
			op, 
			arg,
			d + 1, 
			Z_tmp, 
			0, 
			(Base *) CPPAD_NULL
		);
	}
	std::cout << std::endl;
# else
	}