Hybrid Lookup Table for Function Approximation
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Solution Overview
Problem
Existing computing systems are inefficient in approximating functions due to the lack of optimized methods for handling polynomial calculations, leading to longer processing times and increased processor cycles.
Innovation Solution
A system utilizing a hybrid lookup table for storing coefficients of polynomials in factored form and a function approximation device with multiple processors to efficiently approximate functions by selecting appropriate polynomials and evaluating them concurrently.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional single-processor methods are used to approximate functions, then the calculation can be performed, but the processing time is longer and processor cycles are increased
Solution Approach 1:
The function approximation process is segmented into distinct phases: argument classification to identify the appropriate polynomial, coefficient retrieval from lookup tables, and parallel evaluation of polynomial terms. This segmentation allows each phase to be optimized independently and enables parallel processing of multiple polynomial evaluations simultaneously
Solution Approach 2:
Coefficients for multiple polynomials are pre-calculated and stored in lookup tables during system initialization. When a function approximation is requested, the system only needs to retrieve pre-computed coefficients rather than calculating them in real-time, significantly reducing processing time
Solution Approach 3:
The patent replaces traditional sequential mechanical computation with a parallel processing architecture where multiple processors evaluate different polynomial terms simultaneously. This substitution of parallel computational mechanics for sequential processing achieves the stated 4x speedup in function approximation
2Measurement precision
If more processor cycles are allocated to function approximation, then calculation precision can be improved, but resource usage increases
Solution Approach 1:
The system uses polynomial approximations that provide sufficient accuracy for practical applications without computing the full precise function value. By selecting appropriate polynomial degrees and using factored forms with pre-computed coefficients, the system achieves acceptable precision while consuming fewer processor cycles than exact calculation methods
Solution Approach 2:
The patent changes the parameter representation by using factored polynomial forms with pre-computed coefficients stored in lookup tables. This parameter transformation allows the system to achieve high precision function approximation by retrieving and evaluating compact coefficient representations rather than performing complex real-time calculations
Data Source
AI summary
A method and system for approximating functions, including a function approximation repository, which includes a hybrid lookup table configured to store coefficients associated with polynomials in factored form (PFFs), and a results store configured to store results. The system also includes a function approximation device that includes two processors, memory, an IO module and a function approximation module, which includes functionality to receive a request to approximate the function for an argument; verify that the argument falls within a function interval; perform a determination to find a subinterval in which the argument falls; select a PFF associated with the subinterval; obtain PFF coefficients associated with the PFF from the hybrid lookup table; evaluate the PFF using the PFF coefficients and the argument to obtain a result; store the result in the results store; and return the result as an answer to the requesting entity via the IO module.