Square Root Circuit Single Cycle Iteration Lookup Table
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Solution Overview
Problem
Existing methods for binary division and square root determination, such as the SRT method, require two processor cycles per iteration, which increases computational speed and latency.
Innovation Solution
A method that determines a square root using a single processor cycle per iteration by obtaining a quotient digit and its square from a lookup table and using them to calculate a new solution, as described by the equation Pi+1=r·Pi−qi+1·2Qi−(qi+1)2·r(i+1), allowing for efficient computation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the SRT method is used for square root determination, then the computation follows a established iterative algorithm, but it requires two processor cycles per iteration which increases latency and reduces computational speed
Solution Approach 1:
The patent pre-computes and stores the values of q_i+1 and q_i+1² in a lookup table before the iterative process begins. During each iteration, these pre-computed values are directly retrieved rather than calculated, eliminating one processor cycle and reducing latency while maintaining the reliability of the SRT algorithm
Solution Approach 2:
The patent combines the retrieval of q_i+1 and the computation of q_i+1² into a single lookup table operation. By storing both values together and retrieving them simultaneously in one processor cycle, the patent merges two operations into one, thereby improving computational speed without sacrificing algorithm reliability
2Reliability
If the SRT method is used for square root determination, then the iterative computation follows a standard procedure, but the two processor cycles per iteration increase latency
Solution Approach 1:
The values q_i+1 and q_i+1² are pre-computed and stored in a lookup table before the iterative process. During computation, these values are directly retrieved in a single processor cycle, eliminating the time required for real-time calculation and reducing computational latency while preserving computation accuracy
Solution Approach 2:
The patent creates a copy of the necessary computational data (q_i+1 and q_i+1² values) in the form of a lookup table. This pre-generated copy allows for rapid retrieval during iteration without requiring recalculation, thereby reducing latency while maintaining the accuracy of the original computational procedure
3Reliability
If traditional SRT implementation is used, then the algorithm follows the recurrence equation Pi+1=r·Pi−qi+1·(2Qi+qi+1·r(i+1)), but it requires separate cycles for reading qi+1 and computing the multiplication term
Solution Approach 1:
The patent merges the retrieval of q_i+1 and the availability of q_i+1² into a single lookup table operation. Both values are obtained simultaneously in one processor cycle, allowing the iterative computation to proceed without waiting for separate calculation steps, thereby increasing productivity while maintaining algorithm correctness
Solution Approach 2:
The lookup table is pre-populated with both q_i+1 and q_i+1² values before the iterative process begins. This preliminary preparation allows both values to be retrieved together during each iteration in a single processor cycle, eliminating the need for sequential operations and increasing the number of iterations that can be performed per second
Data Source
AI summary
A method, performed by a processor, of determining a square root using a single processor cycle per iteration is described. The method includes, in a single cycle: obtaining, from a stored lookup table, a quotient digit and a square of the quotient digit; retrieving a current solution; and determining a new solution using the current solution and the quotient digit. Circuitry configured to perform the method is described.