Multiphase SBS Generation for Accurate Low-Overhead Multiplication
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Solution Overview
Problem
Current stochastic binary string (SBS) representations for numeric values require large string lengths to achieve accurate multiplication, leading to inefficient storage and hardware requirements, especially for large values, and existing generation methods like the ρ-sequence method suffer from inaccuracies and the need for pseudo-random number generators.
Innovation Solution
The δ-sequence generator and multiphase δ-sequence generator methods distribute ones evenly throughout the string, eliminating the need for random number generators and improving accuracy by generating SBS sequences without binomial error distributions, enabling more efficient and accurate multiplication operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If stochastic binary string (SBS) representations are used for numeric values, then multiplication operations can be performed more efficiently, but large string lengths are required to achieve accurate multiplication, leading to inefficient storage and hardware requirements
Solution Approach 1:
The patent divides the SBS generation process into multiple phases (first phase, second phase, third phase) where each phase generates a portion of the final SBS sequence. This segmentation allows the system to achieve accurate multiplication results without requiring excessively long single-phase strings, thereby reducing storage and hardware requirements while maintaining computational efficiency.
Solution Approach 2:
The patent employs a preliminary action by generating a first SBS sequence in a first phase before completing the full multiplication operation. This preliminary sequence is then refined in subsequent phases to achieve the final accurate result, allowing the system to start with shorter strings and progressively improve accuracy without requiring the full final string length from the beginning.
2Ease of manufacture
If traditional ρ-sequence method is used to generate SBS sequences, then generation can be accomplished, but inaccuracies occur due to binomial error distributions and pseudo-random number generators are required
Solution Approach 1:
The patent extracts and eliminates the problematic binomial error distribution component from the SBS generation process. By removing the reliance on pseudo-random number generators and their inherent error distributions, the system achieves more accurate SBS sequences without sacrificing generation capability. The invention replaces the random-based approach with a deterministic multi-phase generation method.
Solution Approach 2:
The patent uses a copying approach by generating multiple phases of SBS sequences (first phase, second phase, third phase) where each phase produces a version of the sequence that is then combined and refined. This multi-copy process allows errors to be distributed and corrected across phases, achieving higher accuracy than single-phase generation while maintaining ease of manufacture through systematic repetition.
3Measurement precision
If large string lengths are used to achieve accurate multiplication, then multiplication accuracy improves, but hardware requirements and storage efficiency worsen
Solution Approach 1:
The patent implements a dynamic multi-phase generation process where the SBS sequences are built and refined progressively through multiple phases rather than being generated statically in a single step. This dynamic approach allows the system to achieve high multiplication accuracy with more efficient hardware by adapting the generation process to the specific requirements of each phase, rather than over-provisioning for worst-case scenarios from the start.
Data Source
AI summary
Some of the disclosed methods and apparatuses use several types of stochastic binary string (SBS) generators to generate SBS sequences based on the particular values to be multiplied. Some embodiments use a multiphase SBS generator to more efficiently generate multiple SBS sequences that are offset from one another in “phase”.