ESOP Refactoring for XOR-Heavy Logic Optimization
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Solution Overview
Problem
Conventional logic optimization techniques for integrated circuits (ICs) based on sum-of-products (SOP) representations fail to achieve optimal compactness and efficiency, particularly in XOR-heavy logic, missing out on potential optimizations due to their limitations in handling XOR operators.
Innovation Solution
The implementation of robust exclusive sum-of-products (ESOP) refactoring techniques, which generate and minimize ESOP expressions to refactor logic networks, decompose them into and-inverter graphs, and optimize using balanced XOR trees, enabling more compact and efficient logic representations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If conventional sum-of-products (SOP) representations are used for logic optimization, then the implementation is simple and widely used, but the logic network size and complexity are larger compared to ESOP representations
Solution Approach 1:
The patent changes the logical parameter from OR-based SOP representation to XOR-based ESOP representation. This parameter change in the logical operation type enables exponential compactness for XOR-heavy functions while maintaining a systematic optimization approach through ESOP minimization algorithms and structured refactoring processes.
2Device complexity
If SOP representations are used, then the method is straightforward and widely applicable, but it fails to achieve optimal compactness for XOR-heavy logic
Solution Approach 1:
The patent introduces a dynamic refactoring process that adapts the logic representation based on the function type. The method dynamically selects between SOP and ESOP representations, applying ESOP minimization specifically for XOR-heavy logic while maintaining SOP for other cases, thus achieving optimal compactness for each logic type.
Solution Approach 2:
The optimization process is segmented into distinct phases: ESOP expression generation, ESOP minimization, intermediate logic network extraction, and refactoring. This segmentation allows the method to handle different aspects of logic optimization separately, achieving both compactness for XOR functions and broad applicability through modular processing.
3Productivity
If ESOP expressions are used to refactor logic networks, then logic levels and network size are significantly reduced, but the optimization process becomes more complex
Solution Approach 1:
The patent performs preliminary ESOP expression generation and minimization before constructing the final logic network. By pre-minimizing the ESOP expressions and preparing the intermediate logic network in advance, the method reduces the complexity of the final refactoring step while achieving significant productivity gains in terms of logic levels and network size reduction.
Data Source
AI summary
Robust logic optimization on an IC design based on exclusive sum-of-products (ESOP) refactoring is described. ESOP expressions are two-level logic representation forms, similar to sum-of-product SOP representations. However, since ESOPs use exclusive-OR (XOR) instead of OR operators they can be exponentially more compact than sum-of-product (SOP) expressions for important classes of functions. In XOR heavy logic, ESOP expressions allow us to find optimizations that SOPs simply do not have access to.