Hardware Modulo Generator Iterative Range Reduction
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Solution Overview
Problem
Existing methods for generating hardware designs to implement modulo operations are often constrained to using a single range reduction method per stage and rely on static numerical metrics, which limits efficiency and speed in producing hardware designs for modulo operations, especially when dealing with large input ranges.
Innovation Solution
The approach involves an iterative process using multiple range reduction methods to generate hardware design components that map successively increasing input ranges to a target output range, synthesizing these components, and selecting the optimum based on synthesis metrics such as delay time and area, allowing for the use of different methods at each stage to achieve the target output range efficiently.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If a single range reduction method is used per stage, then the hardware design process is simpler, but the time and resources required to produce hardware designs are significantly increased
Solution Approach 1:
The system dynamically selects and switches between multiple range reduction methods (subtraction, multiplication, division) based on the specific input parameters and synthesis metrics. This dynamic approach allows the hardware design process to adapt to different scenarios, optimizing both complexity management and production speed by using the most efficient method for each case rather than being constrained to a single static method
Solution Approach 2:
The system changes parameters by evaluating multiple range reduction methods with different characteristics (subtraction for small ranges, multiplication for medium ranges, division for large ranges) and selecting the optimum based on synthesis metrics such as delay time and area. This parameter-based selection resolves the contradiction by allowing simple decision criteria while achieving high productivity through method optimization
2Productivity
If static numerical metrics are used for component selection, then the selection process is faster, but the quality and efficiency of the generated hardware design is limited
Solution Approach 1:
The system implements feedback by synthesizing each candidate hardware design component and evaluating it against multiple synthesis metrics (delay time, area, power consumption). This feedback loop allows the system to iteratively refine component selection, choosing the optimum component that balances speed and quality requirements. The synthesis metrics provide quantitative feedback that guides the selection process, resolving the contradiction between fast selection and high-quality design
Solution Approach 2:
The component selection process is made dynamic by evaluating multiple candidates using synthesis metrics and selecting the optimum based on performance criteria. Rather than using fixed static rules, the system adapts its selection based on the specific characteristics of each candidate design, achieving both speed and quality through dynamic optimization guided by synthesis feedback
3Manufacturing precision
If multiple range reduction methods are evaluated and synthesized, then the optimum hardware design component can be selected for better efficiency, but the time required for synthesis increases
Solution Approach 1:
The system applies partial action by evaluating multiple range reduction methods but not necessarily synthesizing all of them to completion. Instead, it uses synthesis metrics to evaluate candidates and selects the optimum component, performing only the necessary synthesis work required to make an informed selection. This resolves the contradiction by doing enough synthesis to ensure optimization while avoiding unnecessary time expenditure on exhaustive evaluation of all possible variants
Data Source
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AI summary
A method of generating a hardware design to calculate a modulo value for any input value in a target input range with respect to a constant value d using one or more range reduction stages. The hardware design is generated through an iterative process that selects the optimum component for mapping successively increasing input ranges to the target output range until a component is selected that maps the target input range to the target output range. Each iteration includes generating hardware design components for mapping the input range to the target output range using each of a plurality of modulo preserving range reduction methods, synthesizing the generated hardware design components, and selecting one of the generated hardware design components based on the results of the synthesis.