.LEFT MARGIN 8
.RIGHT MARGIN 72
The following algorithm evaluates an algebraic expression
in two steps. The expression is first converted to a reverse Polish
notation expression and then the reverse Polish expression is
evaluated. 

Step one converts an algebraic expression (infix notation) to a
reverse Polish expression (postfix notation).  The algebraic
expression is first broken up into tokens which are passed to the
conversion algorithm which reassembles them into a reverse Polish
expression.  The tokens are of two types, operands (values) and
operators (+,-,*,/,etc).  The reverse polish expression is built in
a FIFO queue (called the "Intermediate Queue") which is used by step
two.  The conversion algorithm also uses a stack called the "Operator
Stack". 

Step two evaluates the reverse Polish expression and generate an
results.  This process requires a stack to hold operands called the
"Operand Stack".  Each token is read, one at a time, from the
"Intermediate Queue".  If the token is an operand it is pushed onto
the the "Operand Stack".  If the token is an operator the operation
is performed on the operands on the top of the stack and the results
pushed onto the stack.  When there are no more tokens in the queue
the results will be on the top of the stack. 
.LITERAL


Converting And Algebraic Expression To Reverse Polish Notation

1. Scan the algebraic expression form left to right breaking up
   into tokens.  Pass the tokens to the following steps. 

2. If the token is a operand (value), add it to the
   "Intermediate Queue". 

3. if the token is an operator (+,-,*,/,etc.) do one of the
   following: 

   (a) Look at the operator on the top of the "Operator Stack"
       (TOS).  If the TOS has an equal or greater precedence
       that the token, pop the TOS and add it to the
       "Intermediate Queue".  Got to step (a). 

   (b) If the TOS has a precedence less than the token, push the
       token onto the "Operator Stack". 

   (c) When the token is a left parenthesis push it onto the
       "Operator Stack". 

   (d) If the token is a right parenthesis discard it.  then pop
       operators one at a time from the "Operator Stack" and add
       them to the "Intermediate Queue".  Continue this until a
       left parenthesis is found, which is discarded. 

4. When the scan is complete, add any operators left on the
   "Operator Stack" to the "Intermediate Queue". 


Evaluating An Expression In Reverse Polish Notation

1. Scan the expression from left to right breaking it into      
   tokens which are passed to the following steps. 

2. Push any tokens that are operands onto the "Operand Stack".

3. If a token is a operator the appropriate number of operands
   are removed from the top of the stack and the operation
   preformed.  The results is pushed onto the operand stack. 

4. When the scan is complete the results of the expression is on
   the top of the stack. 
.END LITERAL