Partial Product Generation for Polynomial Operations
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Solution Overview
Problem
Existing image processing devices require significant processing time for transcendental functions due to the lengthy processing time of multiplication operations, which hinders the efficiency of polynomial expansions and overall device performance.
Innovation Solution
An apparatus and method utilizing first and second encoders to generate and select partial products based on Propagation, Generation, and Termination values, along with Radix-4 Booth encoding, to reduce processing time by generating candidate partial products and carry estimation values, thereby optimizing polynomial operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If multiplication operations are performed using conventional methods, then the polynomial expansion can be completed, but the processing time becomes excessively long
Solution Approach 1:
The patent segments the multiplication operation into multiple parallel partial product generation paths. Each path processes different bit combinations simultaneously using first and second encoders, breaking down the sequential multiplication process into concurrent operations that reduce overall processing time.
Solution Approach 2:
The patent performs preliminary encoding of input bits into Propagation, Generation, and Termination values before the actual multiplication. This preliminary action prepares the data in a format that enables faster parallel processing and reduces the computational burden during the multiplication phase.
2Productivity
If dedicated processing units are used for transcendental functions, then processing speed improves, but device complexity increases
Solution Approach 1:
The patent implements a universal polynomial operation apparatus that can handle multiple transcendental functions (trigonometric, logarithm, exponential) through a single integrated structure. The same encoder and multiplexer components serve different function types, reducing the need for separate dedicated units for each function.
Solution Approach 2:
The patent changes the operational parameters of the processing unit by dynamically selecting between different polynomial expansions based on the required function. The multiplexer switches between different sets of partial products corresponding to different transcendental functions, allowing one unit to perform multiple functions with varying parameters.
Data Source
AI summary
An apparatus and a method for generating a partial product for a polynomial operation are provided. The apparatus includes first encoders, each of the first encoders configured to selectively generate and output one of mutually exclusive values based on two inputs. The apparatus further includes a second encoder configured to generate and output two candidate partial products based on an output from a first one of the first encoders that is provided at a reference bit position of the inputs, an output from a second one of the first encoders that is provided at an upper bit position of the inputs, and a multiplicand. The apparatus further includes a multiplexer configured to select one of the candidate partial products output from the second encoder.