%% NOTE: this file is shared directly between the Alegra Users Manual and
%%       the RTC writeup in alegra/toolkit/rtcompiler/writeup.tex

\subsection{The RTC language}

The RTC language can be thought of as a small subset of the
C language with a couple minor modifications. 

\subsubsection{Operators}

The RTC language has the following operators that work exactly as they do in C
and have the same precedence as they do in C:
\begin{itemize}
  \item $+$  Addition
  \item $-$  Subtration
  \item $-$  Negation
  \item $*$  Multiplication
  \item $/$  Division
  \item $==$ Equality
  \item $>$  Greater than
  \item $<$  Less than
  \item $>=$ Greater than or equal to
  \item $<=$ Less than or equal to
  \item $=$  Assignment
  \item $||$ Logical or
  \item $\&\&$ Logical and
  \item $!=$ Inequality
  \item $\%$ Modulo
  \item $!$  Logical not
\end{itemize}

\noindent The following operators do not occur in the C language, but
I added them into the RTC language for convenience:

\begin{itemize}
  \item \begin{verbatim}^ Exponentiation \end{verbatim}
\end{itemize}


\subsubsection{Control flow}

The RTC language has the following control flow statements:

\begin{itemize}
  \item for( expr ; expr ; expr ) \{ ... \}
  \item while( expr )  \{ ... \}
  \item if (expr) \{...\}
  \item else if (expr) \{...\}
  \item else \{...\}
\end{itemize}

\noindent These control flow statements work exactly as they do in C
except that the code blocks following a control flow statement 
\textbf{MUST} be enclosed within braces even if the block only consists of 
one line.

\subsubsection{Line Structure}

The line structure in the RTC language is the same as that of C. Expressions
end with a semicolon unless they are inside a control flow statement.

\subsubsection{Variables}

Declaring scalar variables in RTC is done exactly as it is done in C except 
that we are limited to the following types:

\begin{itemize}
  \item int
  \item float
  \item double
  \item char
\end{itemize}

\noindent For scalars, variables can be declared and assigned all at once. Both of the 
following approaches will work:

{\ttfamily \begin{verbatim}
int myVar = 9;

OR

int myVar;
myVar = 9;
\end{verbatim}
}

\noindent Arrays work a little differently in RTC than they do in C. There are
no \emph{new} or \emph{malloc} operators, so I have allowed the user to 
declare dynamically sized arrays in the same manner as statically sized 
arrays. Also, in C you can initialize all the values of an array at once by
putting the values within braces. In the RTC language, this is not supported.
Users will have to loop through the array and assign the values one by one.
For example:

{\ttfamily \begin{verbatim}
LEGAL:
   int ia[x*y];  //Note: in C this would not be legal for non-const x,y
   int ia2[3];

NOT LEGAL:
   int ia[3] = {1, 2, 3};
\end{verbatim}
}

\noindent Indexing arrays can be done using the index operator:
array[expr] = ...;

\noindent Bounds checking is done at run time. If you go past the end of an 
array, it will dump an error to stdout. 

\subsubsection{Math}

The following math.h functions are available in RTC:

\begin{itemize}
  \item asin(arg)  : returns the arc sine of arg
  \item acos(arg)  : returns the arc cosine of arg
  \item atan(arg)  : returns the arc tangent of arg
  \item atan2(y, x): returns the arc tangent of y/x
  \item sin(arg)   : returns the sine of arg
  \item cos(arg)   : returns the cosine of arg
  \item tan(arg)   : returns the tangent of arg
  \item sqrt(arg)  : returns the square root of arg
  \item exp(arg)   : returns the natural logarithm base e raised to the arg 
                     power
  \item sinh(arg)  : returns the hyperbolic sine of arg
  \item cosh(arg)  : returns the hyperbolic cosine of arg
  \item tanh(arg)  : returns the hyperbolic tangent of arg
  \item log(arg)   : returns the natural logarithm for arg
  \item log10(arg) : returns the base 10 logarithm for arg
  \item rand(arg)  : returns a system-generated random integer between 0 and RAND\_MAX using seed arg
  \item fabs(arg)  : returns the absolute value of arg
  \item pow(b, e)  : returns b to the e power 
                     (Note: you can use the Exponentiation operator instead)
  \item j0(arg)    : Bessel function of order zero
  \item j1(arg)    : Bessel function of order one
  \item i0(arg)    : Modified Bessel function of order zero
  \item i1(arg)    : Modified Bessel function of order one
  \item erf(arg)   : Error function 
  \item erfc(arg)  : Complementary error function  (1.0 - erf(x))
  \item gamma(arg)  : returns $\Gamma(arg)$
\end{itemize}

\subsubsection{Strings}

The user will now have the ability to pass quoted strings as arguments to 
functions. Note: you might have to escape-out the double quotes so that they
do not confuse the input-file parser. See printf section below for an example.

\subsubsection{Printf}

RTC now has much better output capability in its new printf method. The
new printf method is called just like its C counterpart. This first argument
is a quoted character string. This string will can contain the \% symbol 
which will tell RTC to output the corresponding argument. The only difference
between RTC's printf and C's printf is that in RTC's version, you do not have
to provide a type character after the \%. For example, inside your RTC method
you could do the following:

{\ttfamily \begin{verbatim}
printf(\"One:% Two:% Three:% \", 5-4, 2.0e0, 'c');\n\
\end{verbatim} }

\noindent
Which would generate this output: One:1 Two:2 Three:c

\subsubsection{Comments}

The traditional C-comment mechanism is now available for use inside RTC
functions. Use /* to begin a comment and */ to end the comment.

\subsubsection{Unsupported Features}

Implementing the entire C-language was well beyond the intend of RTC. We took
the liberty of cutting corners or leaving out features if we felt they were 
either too difficult or did not add enough value. The following is a list
of common C features that are unsupported in RTC:
\begin{itemize}
  \item There are no $++$ or $--$ operators. Use $i = i + 1$ instead of $++i$
  \item Structs
  \item Pointers
  \item Instant array initialization: int array[5] = {1,2,3,4,5};
  \item Case statements
  \item Casting
  \item Labels and gotos
  \item Function definition/declaration
  \item stdio
  \item Keywords: break, continue, const, enum, register, return, sizeof,
    typedef, union, volatile, static.
\end{itemize} 

\subsubsection{Examples}

I am going to use the following series of examples to try to illustrate the
use of the RTC language within the context of some simple user defined initial 
conditions.

\noindent For all user defined initial conditions, you can assume that you have
the following variables: 

\begin{itemize}
  \item coord - An array of coordinates. Use an index of zero to get the x 
                coordinate, an index of one to get the y coordinate, and an
                index of two to get the z coordinate (Available in 3D only).
  \item field - This is the means by which you can return the results of your
                function. The variable (ex: density, velocity) you specified 
                above the function is set according to the values of the field
                array. If you are setting a scalar variable, like density, you
                will only want to set field[0].
\end{itemize}

\subsubsection*{Example 1}

{\ttfamily \begin{verbatim}
  USER DEFINED INITIAL CONDITION, DENSITY
    "field[0] = 5000.0 + (1.0 / (coord[0] + atan2(2,3)));"
  END
\end{verbatim} }

\noindent In this example, we are setting the density of every element
equal to 5000 plus one over the x coordinate of the element plus the
arc tangent of 2 and 3.

\subsubsection*{Example 2}

{\ttfamily \begin{verbatim}
  USER DEFINED INITIAL CONDITION, DENSITY, BLOCK 5
  "
    double sum = coord[0] + coord[1] + coord[2];
    field[0] = sum / 0.0001;
  "
  END
\end{verbatim} }

\noindent In this example, we set the initial density of elements in
block 5 to the sum of the x, y, and z coordinates divided by 0.0001;

\subsubsection*{Example 3}

{\ttfamily \begin{verbatim}
  USER DEFINED INITIAL CONDITION, DENSITY, BLOCK 5
  "
    double newarray[10];
    field[0] = 0;
    for (int i = 0; i < 10; i = i + 1) {
      newarray[i] = -sin(-i*2) + 2;
    }
    for (int i = 0; i < 10; i = i + 1) {
      field[0] = field[0] + newarray[i % 10];
    }
  "
  END
\end{verbatim} }

\noindent This example shows how to use for-loops and arrays in the
RTC language. The density of the elements in block 5 is being set to
$\sum_{i=0}^9 (-sin(-i*2) + 2)$

\subsubsection*{Example 4}

{\ttfamily \begin{verbatim}
  USER DEFINED INITIAL CONDITION, VELOCITY, BLOCK 5 10
  "
     if ( fabs(coord[0]) < 1.10 ) {
       field[0] = 0.;
       field[1] = 0.;
       field[2] = 0.;
     }
     else {
       field[0] = 100.;
       field[1] = 200.;
       field[2] = 300.;
     }
  "
  END
\end{verbatim} }

\noindent In this example, we are taking the absolute value of the
x-coordinate of the element. If this value is less that 1.10, we set
velocity to zero in each direction, otherwise we set velocity to
100,200,300.

\noindent Notice in this example we are setting velocty, which is not
a scalar value, so we must assign to several indices of the field
array.

\subsection{Using RTC and APREPRO}

Frequently \textsc{alegra} users will place \texttt{aprepro} constructs into
their input decks and then preprocess the input deck with \texttt{aprepro} by
issuing the command:

\noindent
\texttt{Alegra -a runid.inp}

A problem may exist with curly braces, \{ and \}, in the runtime compiler coding
as in the above examples.  When the input deck is sent through \texttt{aprepro},
the preprocessor will evaluate expressions in curly braces, and the braces
will not appear in the processed input deck read by \textsc{alegra}.
This will cause an error when the runtime compiler processes the coding.

\noindent
There are two solutions:
\begin{enumerate}

\item Place the following lines before after the runtime compiler coding
      so that \texttt{aprepro} will copy the input lines to the output
      exactly as they are written:

{\ttfamily \begin{verbatim}
${VERBATIM(ON)}
    ... runtime compiler coding ...
${VERBATIM(OFF)}
\end{verbatim}
}

\item Omit the verbatim commands, but put the curly braces into string expressions
      that will be processed by \texttt{aprepro}.  Make the following substitutions:

{\ttfamily \begin{verbatim}
{   ->   {"{"}
}   ->   {"}"}
\end{verbatim}
}

The outer pair of opening and closing braces will be processed by \texttt{aprepro},
but the inner brace in quotes will be sent as a string to the output deck.

\item You can also place a backslash infront of your curly braces. This will
      tell APREPRO to ignore the curly brace. The RTC parser knows to ignore
      the backslash but not the curly brace. This method will work regardless
      of whether aprepro is run on the input deck or not.

\end{enumerate}

\noindent
For instance, we could write,
%
{\ttfamily \begin{verbatim}
${VERBATIM(ON)}
user defined initial condition, density, block 5
" 
  field[0] = 100.0;
  if(coord[0] > 0.0){
    double distance = sqrt ((coord[0]^2) + (coord[1]^2) + (coord[2]^2));
    field[0] = field[0] + distance;
  }
"
${VERBATIM(OFF)}
\end{verbatim}
}

\noindent
or it could be written as,
%
{\ttfamily \begin{verbatim}
user defined initial condition, density, block 5
" 
  field[0] = 100.0;
  if(coord[0] > 0.0) {"{"}
    double distance = sqrt ((coord[0]^2) + (coord[1]^2) + (coord[2]^2));
    field[0] = field[0] + distance;
   {"}"}
"
\end{verbatim}
}

\noindent
or it could be written as,
%
{\ttfamily \begin{verbatim}
user defined initial condition, density, block 5
" 
  field[0] = 100.0;
  if(coord[0] > 0.0) \{
    double distance = sqrt ((coord[0]^2) + (coord[1]^2) + (coord[2]^2));
    field[0] = field[0] + distance;
  \}
"
\end{verbatim}
}
