Function Approximation Using Quantized Range Sections
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Solution Overview
Problem
In computer graphics processing, approximating functions to improve computational efficiency while minimizing errors is challenging, especially when division operations are involved, as existing methods can introduce significant errors when approximations and their inverses are repeatedly applied.
Innovation Solution
A method that quantizes input and output values into predetermined range sections with associated gradients, allowing for efficient conversion of input data values to output data values using section end values and gradients, thereby optimizing computational efficiency and error reduction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If division operations are used to implement functions in graphics processing, then computational accuracy is improved, but computational efficiency deteriorates
Solution Approach 1:
The patent divides the input range into multiple sections and uses different approximation methods for different sections. This segmentation allows the use of simpler, faster approximation methods in regions where high precision is less critical, while reserving more accurate but computationally expensive division operations for regions where precision is most important, thus resolving the contradiction between accuracy and efficiency.
Solution Approach 2:
The patent changes the parameter representation by using gradient values and section end values instead of performing direct division operations. By pre-calculating and storing these parameters, the system transforms expensive runtime division operations into cheaper lookup and multiplication operations, maintaining accuracy while improving computational efficiency.
2Productivity
If approximations of functions are used to improve computational efficiency, then computational cost is reduced, but measurement precision deteriorates due to introduced errors
Solution Approach 1:
The patent applies different approximation qualities to different local regions (sections) of the input range. By identifying which sections require higher precision and applying more accurate approximation methods specifically to those regions, the system minimizes overall error while maintaining computational efficiency in less critical regions.
Solution Approach 2:
The patent incorporates error compensation mechanisms where the approximation errors are identified and corrected through feedback loops. By monitoring the deviation from true values and adjusting the approximation accordingly, the system maintains high accuracy while benefiting from the computational efficiency of approximation methods.
3Productivity
If approximations and their inverses are repeatedly applied to data, then computational efficiency is improved, but measurement precision deteriorates due to compounded errors
Solution Approach 1:
The patent prepares compensation values and correction parameters in advance, before the repeated approximation operations are performed. By pre-calculating these cushioning values that account for expected error accumulation, the system can apply corrections at each stage to prevent error compounding, thus maintaining precision through multiple repeated operations while preserving computational efficiency.
Data Source
AI summary
A data processor of a processing system, such as a graphics processing system, converts an input data value into an output data value by approximating a function which maps input values to output values. The data processor approximates the function using first and second predetermined ranges of values which are quantized into plural corresponding pairs of range sections, a predetermined gradient for each pair of range sections, and predetermined section end values for each pair of range sections. By using these predetermined parameters, the approximation of the function can be implemented efficiently by the data processor of the processing system.