Abstract: An efficient implementation of a multidimensional data aggregation operator that generates all aggregates and super-aggregates for all available values in a results set by first generating a minimal number of aggregates at the lowest possible system level using a minimal number of function calls, and second categorizing the aggregate function being applied and applying the aggregate function with the fewest possible function calls. The aggregates are generated from a union of roll-ups of the n attributes to the GROUP BY clause of the SELECT statement. The number of roll-ups are minimized by including a barrel shift of the attributes being rolled up. A scoreboard array of 2.sup.n bits is updated during the roll-up and barrel shifting process to keep track of which roll-ups are complete and with are not yet complete. Generating super-aggregates is further optimized by identifying the type of aggregate function being applied and facilitating the most efficient application of the aggregate function. A lter.sub.