1. A method for compiler pre-processing of an arithmetic expression for the execution by at least one computer processing unit comprising the steps of: scanning a character and determining a category of said character; when a character is a left parenthesis, placing said left parenthesis in a high order operand stack and in a low order operand stack; when a character is a variable, placing said variable in said low order operand stack; when a character is a right parenthesis, performing a preidentified stack processing procedure; when a character is an operators conducting first and second tests to identify redefined conditions of the character, wherein the first test determines the precedence of the scanned operator, and the second test determines the category of a preceding scanned character, and (i) if both the first and second tests are not satisfied, placing the character in an operator stack, and (ii) if either the first test or the second test is satisfied, performing a predefined stack processing procedure; and when a character is a semicolon, performing a preidentified stack processing procedure and stopping processing.