ASIC Backend Design Flow in VLSI (Part-2) : Logic Equivalence Check

A logic equivalence check is a crucial step in the VLSI physical design flow that ensures the gate-level netlist produced during the RTL synthesis is functionally equivalent to the original RTL description. This verification step is essential to confirm that the optimization and synthesis processes did not introduce any errors or unintended changes in the design's functionality.

Logic Equivalence Check (LEC) is a formal verification technique used in VLSI design to verify that two different representations of a digital circuit, often an RTL description and a gate-level netlist, exhibit functional equivalence. It ensures that the logical behavior of the two representations is identical for all possible input combinations.

Purpose of Logic Equivalence Check

The primary purpose pf LEC is to verify that two different representations of a digital circuit are functionally equivalent. Specifically, it compares the behavior of the original RTL description of the circuit with the gate-level netlist generated after RTL synthesis.

1. Functional Verification: The primary and most fundamental purpose of the logic equivalence check is to ensure that the functionality of the circuit remains consistent throughout the design process. It verifies that the gate-level netlist produced during RTL synthesis performs the same logical operations and produces the same output as the original RTL description.
2. Detecting Synthesis Errors: RTL synthesis is a complex process involving various optimizations and transformations. Errors or unintended changes can occur during synthesis, potentially altering the functionality of the circuit. The logic equivalence check acts as a quality control mechanism to detect and highlight any discrepancies between the RTL description and the synthesized netlist.
3. Optimization Validation: During RTL synthesis, the design often undergoes optimization steps, such as logic minimization, retiming, and technology mapping. While these optimizations aim to improve factors like area, power, and timing, they should not alter the intended functionality of the circuit. The logic equivalence check ensures that the optimizations are applied correctly and do not compromise functional correctness.
4. Compliance with Design Specifications: Integrated circuits are designed to meet specific functional requirements and adhere to design specifications. The logic equivalence check helps verify that the final gate-level design complies with these requirements, ensuring that the chip behaves as expected in its target application.
5. Error Prevention Downstream: Identifying and rectifying discrepancies at the logic equivalence check stage is critical for preventing errors from propagating further downstream in the design flow. Errors that go undetected at this stage could lead to costly and time-consuming design rework in later phases, such as physical design and manufacturing.
6. Formal Verification: In some cases, the logic equivalence check employs formal verification techniques to rigorously prove that the RTL description and the synthesized netlist are indeed functionally equivalent. Formal methods use mathematical algorithms to exhaustively analyze all possible input combinations, providing a high level of confidence in correctness.
7. Reducing Risk and Liability: In safety-critical applications like automotive, aerospace, and medical devices, any functional errors in the final chip can have severe consequences. The logic equivalence check helps mitigate the risk of these errors, reducing liability for the chip manufacturer.
8. Design Iteration and Debugging: If discrepancies are found during the logic equivalence check, designers can use the results to debug and correct the issues promptly. This iterative process ensures that the design is thoroughly tested and refined, leading to a more reliable and robust end product.

Steps involved in LEC flow

1. Generate Reference Outputs:

• Begin by simulating the original RTL description using a simulation tool (e.g., ModelSim, VCS) and a comprehensive set of test vectors or stimuli.
• Execute the simulation for each test vector and record the outputs produced by the RTL description. These outputs serve as the reference outputs against which the synthesized design will be compared.

2. Generate Synthesized Outputs:

• Next, simulate the gate-level netlist obtained after RTL synthesis using the same set of test vectors.
• Execute the simulation for each test vector and record the outputs produced by the synthesized design. These outputs will be compared with the reference outputs to check for equivalence.

3. Output Comparison:

• Compare the outputs generated by the RTL description (reference outputs) with the outputs produced by the gate-level netlist (synthesized outputs).
• Check that the outputs match exactly for every test vector. Any discrepancies between the two indicate a potential functional mismatch.

4. Error Detection and Debugging:

• If discrepancies or mismatches are detected, identify the specific test vectors and conditions under which they occur.
• Debug the design to pinpoint the location and nature of the mismatches. This may involve analyzing simulation waveforms, log files, and debugging tools.

5. Correction and Iteration:

• Once mismatches are identified, correct the issues that led to the discrepancies.
• These corrections may involve adjusting synthesis settings, modifying constraints, or revisiting the RTL description.
• After making corrections, repeat the logic equivalence check by going back to the "Generate Synthesized Outputs" step.

6. Formal Verification (Optional):

• In some cases, formal verification tools may be employed to perform a more rigorous equivalence check.
• Formal methods use mathematical techniques to prove or disprove the functional equivalence of the two designs without the need for simulation.
• While not always required, formal verification can be highly effective for complex designs.

7. Regression Testing:

• After multiple iterations and successful equivalence checks, conduct comprehensive regression testing.
• This involves running a battery of test vectors and cases to verify that the design remains functionally equivalent after any changes or optimizations.

8. Documentation and Reporting:

• Maintain detailed documentation of the equivalence checking process, including test vectors, simulation results, and debugging steps.
• Generate reports summarizing the results of the logic equivalence check. Document any issues found and their resolutions.

9. Sign-Off:

• Once the logic equivalence check confirms that the synthesized design is functionally equivalent to the RTL description and all issues are resolved, it is considered ready for further stages in the VLSI design flow, such as placement, routing, and manufacturing.

Importance of LEC flow in VLSI

1. Functional Correctness Assurance:Primary Objective: The most fundamental role of a logic equivalence check is to verify that the gate-level netlist produced during RTL (Register-Transfer Level) synthesis is functionally equivalent to the original RTL description. In other words, it ensures that the design's behavior hasn't changed during the transformation from RTL to gates.Complex Designs: VLSI designs often contain millions to billions of transistors and complex interconnections. Ensuring that this complexity doesn't introduce unintended functional errors is paramount.
2. Optimization Validation:Optimization Steps: RTL synthesis involves various optimization techniques, including logic minimization, retiming, and technology mapping. These optimizations aim to improve the design in terms of area, power, and performance.Verification of Optimizations: The logic equivalence check validates that these optimizations have been applied correctly and haven't compromised the functionality of the design. This is especially crucial since optimizations can introduce subtle errors if not handled carefully.
3. Quality Control:Quality Assurance: The logic equivalence check serves as a quality assurance step in the design process. It verifies that the design meets its functional requirements and behaves as expected.Preventing Costly Errors: Identifying functional mismatches early in the design flow is essential. Correcting errors in the RTL stage is far less costly and time-consuming than discovering and fixing them later in the physical design or post-fabrication stages.
4. Debugging and Iteration:Debugging Tool: If discrepancies between the RTL description and the gate-level netlist are found during the logic equivalence check, it serves as a debugging tool. Engineers can use the results to pinpoint and correct issues in the design.Iterative Process: The check can be run iteratively. Corrections are made, and the check is repeated until functional equivalence is established. This iterative process ensures a robust and accurate design.
5. Formal Verification:Rigorous Analysis: In some cases, formal methods are used for the logic equivalence check. Formal verification provides a mathematically rigorous analysis of design equivalence and can prove that two designs are indeed equivalent under all possible input conditions.
6. Preventing Design Flaws:Design Validation: By confirming that the RTL-to-gate-level transformation has preserved the intended functionality, the logic equivalence check minimizes the risk of design flaws that could have serious consequences in real-world applications.
7. Compliance with Specifications:Meeting Functional Requirements: Ensuring functional equivalence is essential for meeting the design's specifications and requirements. For example, in safety-critical applications (e.g., automotive or medical devices), incorrect functionality can have severe consequences.
8. Confidence in Physical Design Steps:Subsequent Stages: The gate-level netlist generated after synthesis is used in subsequent physical design steps, such as placement and routing.Foundation for Subsequent Steps: A successful logic equivalence check provides confidence that the design is a reliable foundation for further physical design stages. If discrepancies exist, they could lead to further complications in the design flow.

the logic equivalence check is an essential step in the VLSI physical design flow that verifies the functional equivalence between the original RTL description and the gate-level netlist generated during synthesis. This verification process helps ensure the integrity and correctness of the design before moving on to subsequent physical design and manufacturing stages.