The Microsoft Excel File Format - OpenOffice.org

3.1 Common Formula Structure
3.1.3 Token Notation
Tokens are referred to by their name. All token names start with a small “t” (for “Token”). If a token contains additional
information, it is appended to the token name in parentheses.
Examples:
The addition operator + is represented by the token tAdd. It does not contain any additional data.
The integer constant 1 is represented by the token tInt(1).
An absolute reference to cell $A$1 is represented by the token tRef($A$1).
3.1.4 Operators
There are 3 types of operators:
• Unary operators like the minus sign that negates a value. These operators pop the topmost operand from the stack.
• Binary operators like addition or multiplication. These operators pop the two topmost operands from the stack.
• Function operators represent the sheet functions of Excel. They operate on different numbers of topmost operands on
the stack. Either the function expects a fixed number of operands (for instance SIN expects one operand), or a
variable number of operands given in the function token (for instance SUM is able to process 0 to 30 operands).
All operators push the (single) result of their operation back onto the stack.
3.1.5 Token Arrays
Definition: Token array
The token array represents an entire formula and contains all used tokens of the formula in a specific order.
The tokens of the formula are stored in the Reverse-Polish Notation (RPN). This means, first there occur all operands of
an operation, followed by the respective operator.
Example: the simple term 1+2 consists of the 3 tokens “1”, “+” and “2”. Written in RPN, the formula is
converted to the token list “1”, “2”, “+”.
During parsing such an expression, operands are pushed onto a stack. An operator pops the needed number of operands
from stack, performs the operation and pushes the result back onto the stack.
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