Function Approximation Circuitry Using Lookup Table Segmentation
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Solution Overview
Problem
Existing circuit designs for approximating non-linear functions face challenges with large lookup tables (LUTs) that require significant physical footprint and power consumption, especially when dealing with a large number of discrete inputs, and complex mathematical implementations that are computationally expensive.
Innovation Solution
The proposed circuitry uses a lookup table (LUT) in conjunction with an interpolation factor to generate approximate values of a function by storing discrete values for specific inputs and interpolating for others, allowing for efficient approximation of arbitrary functions with reduced physical footprint and power consumption.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a lookup table (LUT) stores values for all discrete inputs, then the output accuracy is improved, but the physical footprint and power consumption increase significantly
Solution Approach 1:
The patent segments the LUT into multiple smaller LUTs, each storing values for a subset of inputs. This segmentation reduces the physical footprint of each individual LUT while maintaining comprehensive coverage through parallel access to multiple segments, resolving the contradiction between accuracy and physical size
Solution Approach 2:
The patent introduces a time dimension by organizing LUT segments across multiple memory banks that can be accessed in parallel. This dimensional transformation allows the system to maintain high output accuracy equivalent to a large single LUT while reducing the physical footprint through distributed memory architecture
2Measurement precision
If a lookup table (LUT) stores values for all discrete inputs, then the output accuracy is improved, but the power consumption increases significantly
Solution Approach 1:
The patent segments the LUT into multiple smaller LUTs, each consuming less power individually. By distributing the storage across segments and activating only necessary segments based on input requirements, the system maintains high output accuracy while reducing overall power consumption compared to a single large LUT
Solution Approach 2:
The patent implements partial action by enabling only the specific LUT segments needed for the current input range. This selective activation reduces power consumption while maintaining full output accuracy for the required input domain, avoiding the excessive power consumption of keeping all segments active
3Adaptability or versatility
If complex mathematics is implemented, then the function approximation capability is improved, but the computation time increases significantly
Solution Approach 1:
The patent performs preliminary action by pre-computing and storing function values in LUT segments before runtime. This allows the system to achieve complex function approximation capabilities through simple table lookups and interpolation operations during execution, avoiding the time-consuming real-time computation of complex mathematics
Data Source
AI summary
Function approximation circuitry approximates an arbitrary function F over discrete inputs. Discrete values of the function F are stored in a lookup table (LUT) component for various inputs. An addressing module generates an address from an input. An interpolation factor module generates an interpolation factor from the input. An interpolation module generates an output, which is an approximate value of the function F for the input, from the interpolation factor, and from outputs of the LUT component when the LUT component is addressed by the address.