Gamma Transform Unit Lookup Table Difference Values
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Solution Overview
Problem
Existing Gamma transform methods require significant storage space due to the long bit length of Gamma function output values, leading to increased hardware costs, even when only partial values are stored with interpolation used to obtain the rest.
Innovation Solution
A Gamma transform unit utilizing a lookup table to store difference values between ideal and Gamma function output values, reducing storage requirements by using shorter bit lengths for difference values.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If all 256 Gamma function output values are stored in the lookup table, then the Gamma function output can be obtained directly without complex calculations, but the storage space occupied and hardware cost increase significantly
Solution Approach 1:
The patent extracts only the essential correction information (difference values) from the complete Gamma function output values. Instead of storing all 256 Gamma function output values, it stores only the differences between ideal and actual Gamma values, which are much smaller in magnitude and require fewer bits to represent.
Solution Approach 2:
The patent changes the parameter representation from storing complete 10-bit Gamma function output values to storing much smaller difference values that require only 4 bits. This parameter transformation reduces the storage requirement from 2560 bits to 1024 bits while maintaining the ability to reconstruct accurate Gamma function outputs.
2Quantity of substance
If only part of the Gamma function output values are stored in the lookup table, then the storage space is reduced, but more operations must be performed to obtain the required output values through interpolation
Solution Approach 1:
The patent extracts only the correction component (difference value) rather than storing complete Gamma function values. This extraction allows the system to use a compact lookup table with minimal entries while maintaining high output accuracy through simple addition operations instead of complex interpolation.
Solution Approach 2:
The patent introduces difference values as an intermediary between the compact lookup table and the final Gamma function output. These difference values act as correction terms that are added to the lookup results, enabling accurate Gamma transformation with minimal storage and simple operations.
3Quantity of substance
If the bit length of Gamma function output values is reduced to save storage space, then the storage space and hardware cost are reduced, but the precision of the output values may be compromised
Solution Approach 1:
The patent transforms the parameter representation from storing complete high-precision Gamma function values to storing small difference values. By changing what is stored (from absolute values to relative corrections), the system achieves both compact representation and high precision in the final output.
Solution Approach 2:
The patent creates a composite approach by combining a compact lookup table storing difference values with an ideal Gamma function model. The final high-precision output is constructed by combining these two components, achieving both space efficiency and accuracy.
Data Source
AI summary
The invention discloses a Gamma transform unit. The Gamma transform unit has a lookup table. The lookup table stores a plurality of difference values corresponding to a plurality of predetermined input values. Each of the difference values substantially equals a difference between an ideal output value and a Gamma function output value, both of which correspond to one of the predetermined input values. After the Gamma transform unit has received an input value, it generates a required Gamma function output value corresponding to the received input value through referring to the lookup table.