Lookup Table Breakpoint Optimization via Binary Search
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Solution Overview
Problem
Existing lookup tables face challenges in efficiently determining the optimal number and placement of breakpoints to minimize memory usage while maintaining approximation error within a specified tolerance, especially when interpolating functions or data points.
Innovation Solution
A method is implemented to programmatically determine the next breakpoint in a lookup table by identifying candidates that meet an error threshold, using a binary search algorithm to optimize breakpoint placement and associated table values, thereby reducing memory requirements and approximation errors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If the number of breakpoints in a lookup table is increased to improve approximation accuracy, then the manufacturing precision of the function approximation is improved, but the device complexity and memory usage increase
Solution Approach 1:
The patent dynamically adjusts breakpoint positions and table values based on the local characteristics of the function being approximated. By changing parameters (breakpoint locations, table values) according to function curvature and error distribution, the system achieves high accuracy with fewer breakpoints, resolving the contradiction between precision and complexity
Solution Approach 2:
The lookup table generation process is made adaptive and dynamic rather than static. Breakpoints are strategically placed based on error analysis and function characteristics, allowing the table to achieve optimal approximation accuracy with minimal breakpoints, thus reducing device complexity while maintaining precision
2Manufacturing precision
If the number of breakpoints in a lookup table is increased to improve approximation accuracy, then the manufacturing precision of the function approximation is improved, but the loss of substance (memory resources) increases
Solution Approach 1:
The system optimizes breakpoint parameters and table values to achieve maximum approximation accuracy with minimum memory footprint. By adaptively selecting breakpoint positions based on function characteristics rather than uniform distribution, memory resources are minimized while maintaining required precision
Solution Approach 2:
Instead of uniformly distributing breakpoints across the entire range, the system applies breakpoints selectively where they are most needed (where function curvature is high or error accumulation is greatest). This partial action approach achieves adequate approximation accuracy with fewer breakpoints, reducing memory usage
3Productivity
If binary search algorithm is used to optimize breakpoint placement, then the productivity of lookup table generation is improved, but the device complexity increases
Solution Approach 1:
The patent replaces exhaustive or iterative breakpoint selection methods with a binary search algorithm. This substitution provides logarithmic time complexity O(log n) for finding optimal breakpoints, significantly improving generation productivity while the algorithmic complexity remains manageable and implementable in standard processors
Data Source
AI summary
Exemplary embodiments may programmatically determine the number and locations of breakpoints and table values in a lookup table so as to reduce their counts. In some exemplary embodiments, the minimum number of breakpoints and breakpoint locations that conform with the error tolerance may be determined along with table values for those breakpoints. The exemplary embodiments may determine if a lookup table that conforms with the error tolerance is feasible and may inform a user of the feasibility or infeasibility of generating the lookup table. Where it is feasible to generate the lookup table, the exemplary embodiments may provide automatic programmatic generation of a lookup table with minimal breakpoints and optimal or near-optimal table values.