Integrated Circuit for Constant Multiplication Using Lookup Table Seeds
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Solution Overview
Problem
Existing technologies face challenges in efficiently processing large-sized digital signals for multiplication operations, particularly in machine learning models, due to increased computational costs and complexity.
Innovation Solution
An integrated circuit is designed with a lookup table memory and processing circuitry to generate products of inputs and constants by extracting parts from the input, generating addresses, obtaining seeds from the lookup table, and summing partial products, with the number of seeds being less than the number of possible partial products.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the input size for multiplication is increased to improve accuracy, then measurement precision is improved, but device complexity and computational cost increase
Solution Approach 1:
The input number is divided into multiple parts (e.g., high-order bits and low-order bits), and each part is multiplied separately using pre-stored seeds. The partial products are then combined to produce the final result. This segmentation allows accurate multiplication of large numbers while reducing the complexity of individual multiplication operations.
Solution Approach 2:
Seeds corresponding to multiples of the constant are pre-stored in the lookup table memory before the multiplication operation. This preliminary preparation eliminates the need for complex real-time calculations, reducing computational complexity while maintaining accuracy for large input sizes.
2Reliability
If the number of seeds stored in lookup table memory is increased to cover all possible partial products, then reliability is improved, but device complexity increases
Solution Approach 1:
Instead of storing all possible partial products in the lookup table, the patent stores only a subset of seeds (partial action). The processing circuitry then generates additional partial products by combining these stored seeds with the input parts, achieving sufficient coverage without the complexity of storing every possible value.
Solution Approach 2:
The patent uses an intermediate representation where seeds are stored for specific input parts, and the processing circuitry acts as a mediator to combine these seeds with the actual input parts to generate the required partial products. This intermediary approach reduces the lookup table size while maintaining functional equivalence.
3Measurement precision
If conventional multiplication methods are used to process large inputs, then measurement precision is maintained, but productivity decreases due to higher computational cost
Solution Approach 1:
The multiplication operation is segmented into smaller sub-operations where pre-stored seeds are combined with input parts. This segmentation reduces the computational burden per operation while maintaining overall accuracy, thereby improving productivity for large input sizes.
Solution Approach 2:
By pre-computing and storing seeds for multiplication operations, the patent eliminates the need for complex real-time calculations. This preliminary action significantly reduces computational cost and improves processing speed while maintaining accuracy for large inputs.
Data Source
AI summary
An integrated circuit for generating a product of an input and a constant includes a lookup table memory configured to store seeds corresponding to multiples of the constant, processing circuitry configured to generate a plurality of addresses respectively corresponding to a plurality of parts extracted from the input, configured to receive a plurality of seeds from the lookup table memory based on the plurality of addresses, and configured to generate a plurality of partial products based on the plurality of seeds. The processing circuitry is configured to sum the plurality of partial products. A number of the plurality of seeds stored in the lookup table memory is less than a number of possible values of the plurality of partial products.