Lexicographical Order

procedure ari thmetic (a, b, c, op); in t eger a, b, c, op; ¢ o n l m e n t This procedure will perform different order ar i thmetic operations with b and c, put t ing the result in a. The order of the operation is given by op. For op = 1 addit ion is performed. For op = 2 multiplicaLion, repeated addition, is done. Beyond these the operations are non-commutat ive. For op = 3 exponentiat ion, repeated multiplication, is done, raising b to the power c. Beyond these the question of grouping is important . The innermost implied parentheses are at the right. The hyper-exponent is always c. For op = 4 te t ra t ion, repeated exponentiat ion, is done. For op = 5, 6, 7, etc., the procedure performs pentat ion, hexation, heptat ion, etc., respectively. The routine was originally programmed in FORTRAN for the Control Data 160 desk-size computer. The original program was limited to te t ra t ion because subroutine recursiveness in Control Data 160 FORTRAN has been held down to four levels in the interests of economy. The input parameter , b, c, and op, must be positive integers, not zero; b e g i n own i n t e g e r d, e, f, drop; i f o p = 1 t h e n b e g i n a := h-4c; go t o l e n d i f o p = 2 t h e n d := 0; else d := 1; e := c; drop := op 1; for f := I s t e p 1 u n t i l e do b e g i n ari thmetic (a, b, d, drop);