Sparse Look-Up Table for High Radix Division

The patent segments the division operation into multiple iterations, where each iteration processes a portion of the quotient digits. Instead of determining all quotient digits simultaneously through a large look-up table, the algorithm divides the problem into smaller steps, determining one or a few quotient digits per iteration. This segmentation allows the use of smaller, more manageable look-up tables while maintaining division speed through iterative processing.

The patent implements partial action by determining only a portion of the quotient digits in each iteration rather than all digits at once. The algorithm performs partial division operations iteratively, where each iteration computes a subset of the final quotient. This approach reduces the complexity of individual look-up table operations while achieving the complete division result through multiple passes.

The patent segments both the radix processing and the look-up table structure. Instead of using a single large look-up table for high radix operations, the algorithm segments the radix processing into multiple iterations with smaller look-up tables. Each iteration handles a portion of the radix processing, effectively dividing the large table requirement into multiple smaller tables that are processed sequentially.

The patent introduces a time dimension to the division process by using iterative computation. Instead of resolving the radix-size tradeoff in a single spatial dimension (look-up table size), the algorithm distributes the computation across multiple time steps (iterations). This dimensional transformation allows the system to use smaller look-up tables at each step while achieving high radix division efficiency through the accumulation of results across iterations.