Reciprocal Unit Using Lookup Tables and Newton-Raphson
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Solution Overview
Problem
Existing reciprocal computation techniques require large hardware units with high latency, complexity, and power consumption, making them unsuitable for applications needing high precision and low latency, such as communication signal processing and scientific computing.
Innovation Solution
A reciprocal unit comprising a register, two lookup tables, a multiplier circuit, and an adder-subtractor circuit that uses a subset of bits to compute an estimated reciprocal in a single iteration, reducing hardware overhead and latency by employing a smaller memory footprint and simplified architecture.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If large lookup tables are used to compute reciprocals with high precision, then measurement precision is improved, but device complexity and memory usage increase
Solution Approach 1:
The patent divides the reciprocal computation into two stages: first using a small lookup table to obtain an initial estimate, then applying one iteration of the Newton-Raphson algorithm to refine the result. This segmentation allows achieving high precision without requiring a large lookup table, thus reducing device complexity while maintaining measurement precision.
Solution Approach 2:
The small lookup table performs preliminary action by providing an initial estimate of the reciprocal. This preliminary result is then refined through one iteration of Newton-Raphson computation, eliminating the need for the lookup table to directly provide the final high-precision result, thereby reducing memory requirements while maintaining precision.
2Measurement precision
If iterative techniques like Newton-Raphson are used to achieve high precision, then measurement precision is improved, but latency and computation time increase
Solution Approach 1:
The small lookup table provides a preliminary estimate that is already close to the final result, requiring only one iteration of the Newton-Raphson algorithm to achieve the desired precision. This preliminary action significantly reduces the number of iterations needed compared to starting from scratch, thereby reducing computation latency while maintaining high precision.
3Measurement precision
If multiple iterations of Newton-Raphson algorithm are performed, then measurement precision is improved, but productivity and processing speed decrease
Solution Approach 1:
The computation is segmented into a lookup table stage and a single Newton-Raphson iteration stage. This segmentation achieves high precision with minimal iterations, optimizing the balance between measurement precision and productivity by avoiding multiple iterations while still achieving the desired accuracy level.
4Measurement precision
If large hardware units are used to ensure high precision reciprocal computation, then measurement precision is improved, but use of energy increases
Solution Approach 1:
The patent segments the computation into a small lookup table and one Newton-Raphson iteration, avoiding the need for large hardware units with multiple iterations. This segmentation reduces the overall hardware complexity and associated power consumption while maintaining high precision reciprocal computation capability.
Data Source
AI summary
A reciprocal unit for computing an estimated reciprocal of a number represented by a bit string. The unit comprises a first lookup table configured to receive one or more of the bits in the bit string and to output an initial estimate of the reciprocal of the number. The unit further comprises a second lookup table configured to receive one or more of the bits in the bit string and to output the square of the initial estimate of the reciprocal of the number. The unit still further comprises a multiplier circuit configured to multiply the square of the initial estimate by the number, and an adder-subtractor circuit for subtracting the product of the multiplication from a scaled value of the initial estimate to determine a final estimate of the reciprocal of the number.