A mathematical procedure for machine division

Last month someone thought he had developed a new division method, at least until we dug an old paper out of our voluminous file of oldtirne miscellany. This was a memorandum from Dr. These rediscoveries are almost commonplace. Dr. Ervand Kogbetliantz turned up a logarithm method due to Briggs, around the middle 1600s, that seems to be just the thing for present day computers. Since it is a policy of this department to avoid waste by giving obscure methods a little wider circulation, the Gilman paper is included in this issue. With the establishment of the ACM Committee on the International Algebraic Language as a continuing body, it behooves workers in the field to present possible changes, modifications, and suggestions to the Committee for their approval and transmission to GAMe. The major responsibility will be the issuance of an updated and complete description of the language to replace the present specifications , which still contain many ambiguities and improper definitions. It has seemed to me that an expeditious way to help resolve these questions is to issue, for the sake of argument toward eventual agreement, a table of the permissible symbol pairs which may exist in IAL. Once this set of pairs has been agreed upon, the formation rules of program statement are fixed. Furthermore, the inspection of all possible pairs is an algorithmic method to determine validity and thus force attention to weak spots in statement of the rules. A first attempt at such a table is given here (Table 1). I shall be glad to accept correspondence on counter-examples , etc., and forward this material to the Committee for action. Certain obvious groupings have been made. It is the minor variances inhibiting further consolidation that i suggest how the language might be made more consistent. ! For example, the syntactical placement of declaratives has not been fully specified. Should they be bounded by semicolons? If so, the array and type declarators could i be made identical in action to procedure and switch. All i one must do is remove the requirement for redundant I parentheses so that an identifier directly follows the i declarator, rather than a left parenthesis. A typical i I declarative would be inserted in a program as: l Obviously array and the closing semicolon delimit the list. Another doubtful usage lies in the definition of arithmetic expressions (Paragraph 5b of the Preliminary Report). The …