Radix-4 PD Table for Division and Square Root Operations
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Solution Overview
Problem
Existing methods for performing division and square root operations require large partial remainder-divisor (PD) tables, which increase resource usage and complexity as the radix increases, leading to higher latency and increased storage needs.
Innovation Solution
Implementing radix-16 operations using a radix-4 PD table, which reduces latency without the complexity of a higher radix table, by adjusting partial remainder and divisor values to stay within a primary region of the PD table, allowing shared hardware for both operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If a higher radix PD table is used to perform division and square root operations, then the processing speed increases, but the table size and resource usage increase significantly
Solution Approach 1:
The radix-4 PD table is designed to perform both division and square root operations by interpreting the same table entries differently based on the operation type. The table stores values that can be used for quotient digit selection in division and for root digit selection in square root, eliminating the need for separate tables for each operation.
Solution Approach 2:
The patent changes the interpretation parameters of the PD table based on the operation being performed. For division, the table is accessed with specific row/column indexing schemes, while for square root, different indexing and interpretation methods are applied to the same table data, effectively adapting the table's function without changing its physical size.
2Loss of time
If a radix-16 PD table is implemented to reduce latency, then the number of iterations decreases, but the complexity and storage requirements increase
Solution Approach 1:
The patent segments the radix-16 operation into multiple radix-4 iterations. Instead of implementing a single large radix-16 table, the computation is divided into smaller steps using radix-4 operations, where each iteration processes a portion of the final result. This segmentation reduces the complexity of individual table lookups while achieving the same overall functionality through multiple smaller steps.
Data Source
AI summary
Apparatuses and methods of manufacturing same, systems, and methods for performing recursive operations using a partial remainder-divisor (PD) table are described. In one aspect, it is determined whether a current cell in the PD table indicated by a current partial remainder/radicand row value and a current divisor/root column value is outside a primary region of the PD table. If the current cell is outside the primary region of the PD table, at least one of the current partial remainder/radicand row value and the current divisor/root column value are adjusted so that the indicated current cell falls within the primary region of the PD table.