Nonlinear Function Computing Device Using Piecewise Linear Approximation
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Solution Overview
Problem
Existing methods for calculating nonlinear functions are slow, require a large operation device area, and consume high power due to the need for complex operations that are typically broken down into several cycles.
Innovation Solution
A nonlinear function operation device and method that uses a table looking-up section to store slope and intercept values of piecewise-linear functions, allowing for the calculation of a function value based on a floating-point input through simple linear fitting operations, reducing the need for complex calculations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If complex operations are used to calculate nonlinear functions, then calculation accuracy is maintained, but operation speed decreases and device area increases
Solution Approach 1:
The patent divides the domain of the nonlinear function into multiple intervals and creates separate lookup tables for each interval. This segmentation allows the system to use simple linear approximation within each interval rather than complex global calculations, achieving both speed and accuracy.
Solution Approach 2:
The patent pre-calculates and stores slope and intercept values for linear functions in lookup tables before runtime. This preliminary action eliminates the need for complex real-time calculations, allowing the system to quickly retrieve pre-computed values and perform simple arithmetic operations.
2Measurement precision
If complex operations are used to calculate nonlinear functions, then calculation accuracy is maintained, but device area increases
Solution Approach 1:
By segmenting the function domain into intervals with separate lookup tables, the patent replaces large complex calculation units with multiple smaller tables and simple arithmetic logic, reducing overall device area while maintaining accuracy through interval-specific optimization.
Solution Approach 2:
The patent uses lookup tables that store pre-computed slope and intercept values as copies of calculation results. Instead of implementing complex calculation circuits, the system copies pre-stored values from tables and combines them through simple arithmetic, significantly reducing hardware area.
3Measurement precision
If complex operations are used to calculate nonlinear functions, then calculation accuracy is maintained, but power consumption increases
Solution Approach 1:
The patent segments the calculation into simple lookup and arithmetic operations across multiple intervals, replacing power-intensive complex operations with low-power table access and basic math, thereby maintaining accuracy while reducing power consumption.
Solution Approach 2:
By copying pre-computed values from lookup tables rather than performing complex real-time calculations, the patent eliminates power-intensive computational operations, achieving the same accuracy with significantly lower power consumption.
4Speed
If piecewise-linear fitting is used, then operation speed improves and device area reduces, but hardware design complexity increases
Solution Approach 1:
The patent manages hardware complexity by segmenting the problem into standardized intervals with uniform lookup table structures and consistent arithmetic operations, making the overall complex task manageable through repeated simple patterns.
Data Source
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AI summary
A nonlinear function operation device and method are provided. The device includes a table looking-up section and a linear fitting section. The table looking-up section is configured to store slope values and intercept values of a plurality of linear functions, and to acquire a slope value k and an intercept value b based on a floating-point number. The linear fitting section is configured to obtain a linear function expressed as y=k×x+b based on the slope value k and the intercept value b acquired by the table looking-up section, and to substitute the floating-point number into the linear function to calculate a function value of the linear function, where the calculated function value is determined as a function value of the nonlinear function corresponding to the floating-point number. According to the disclosure, the nonlinear function is fitted as the plurality of linear functions, and, for different arguments, a linear function corresponding to each argument only needs to be selected, so that only simple addition and multiplication operations are required during the operation, thereby simplifying the hardware design, improving the operation speed, and reducing the power consumption and area of the chip.