X-propagation and methods to avoid X pitfalls

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  1. What is X-propagation?
  2. What are the sources of X-Values?
  3. What is the Impact of X-propagation?
  4. Why is X-propagation important for VLSI verification?
  5. What are the best practices to avoid and detect X-propagation?
  6. In Conclusion
  7. Additional Resources

What is X-propagation?

X-propagation is a term that refers to the phenomenon of unknown or uncertain values (represented by X in hardware description languages such as Verilog) spreading through a digital system and affecting its behavior. X values can arise from various sources, such as uninitialized signals, power gating, reset logic, timing violations, or simulation artifacts. X-propagation can cause problems in design verification, synthesis, and silicon testing, as it can mask or introduce bugs, reduce code coverage, or lead to non-deterministic results.

What are the sources of X values?

X values have existed in logic design forever, and are commonly used to represent the state of uninitialized signals, such as nets that are not driven, or storage elements that have no reset. For example, a flip-flop without a set/reset pin will have an X output until it receives a valid input and a clock edge. Similarly, a memory location that has not been initialized will have an X value until it is written.

Another source of X values is power gating, which is a technique to save energy by turning off parts of the circuit that are not in use. When a logic block is powered down, it no longer provides a reliable signal to downstream logic, which may not have been designed to cope properly. This can propagate errors through the chip when the blocks move between power states.

Reset logic is another potential cause of X values, especially if it is weak or incomplete. Reset logic is used to bring the system to a known state after power up or after an error. However, reset logic can be expensive in terms of area and routing overhead, so it may not be feasible to apply a reset to every memory element or logic block. Logic that has been designed with uninitialized memories and a weak reset strategy may be prone to more undiscovered bugs due to X propagation.

Timing violations can also generate X values in simulation or on silicon. A timing violation occurs when a signal does not meet the setup or hold requirement of a flip-flop or a latch, causing it to enter a metastable state. A metastable state is an unstable condition where the output can oscillate between 0 and 1 before settling to a final value. In simulation, some models can choose to output an X state when a timing violation occurs. On silicon, the final value may depend on factors such as noise, temperature, or process variation.

Simulation artifacts are another reason for X values in digital systems. Simulation artifacts are caused by the differences between how simulators and synthesizers interpret X values. For synthesis, X values are treated as don't cares, meaning that they can be replaced by 0 or 1, whichever reduces the number of gates required to implement the logic. For simulation, however, X values are treated as unknowns, meaning that they can affect the output of logic gates depending on their inputs. For example, if the input of a NOR gate is X and any of the other inputs is not 0 (the dominant value), then the output is X. This can lead to over-optimistic or over-pessimistic simulation results compared to synthesis or silicon.

What is the impacts of X-propagation?

X-propagation can have negative impacts on various aspects of design flow, such as verification, synthesis, and testing.

Verification: X-propagation can reduce the quality and coverage of verification by hiding or creating bugs in the design. For example, if an X value is converted inadvertently to a known value by overly optimistic simulation code (such as if-then-else or case statements), it may mask a bug that would otherwise be detected. Conversely, if an X value is propagated pessimistically by simulation code (such as when signals converge in a multiplexer), it may create false alarms or spurious errors that would not occur on silicon. Moreover, X-propagation can affect code coverage metrics by reducing the number of reachable states or transitions in the design.

Synthesis: X-propagation can affect synthesis results by introducing mismatches between simulation and synthesis outputs. For example, if an X value is used as a don't care condition for synthesis optimization (such as in case statements), it may result in different logic implementations than expected from simulation. Alternatively, if an X value is propagated through synthesis without being resolved (such as in power gating), it may cause glitches or incorrect functionality on silicon.

Testing: X-propagation can affect testing results by causing non-deterministic behavior on silicon. For example, if an X value is generated by timing violations or metastability on silicon (such as in reset logic), it may lead to different outcomes depending on factors such as noise, temperature, or process variation. This can make testing and debugging more difficult and unreliable.

Why is X-propagation important for VLSI verification?

X-propagation can cause problems for VLSI verification in two ways: X-optimism and X-pessimism.

X-optimism is when a simulator assigns a known value to an output that should be unknown, due to incomplete or incorrect coding. This can hide functional bugs in the RTL that may only show up in gate-level simulation or in hardware. For example, consider the following code snippet:

// if-else conditionals

reg out1;

always @ (*) begin

  if (condition)

    out_1 = 1'b1;


    out_1 = 1'b0;


If condition is X, then out_1 should also be X, but the simulator will assign it to 0, which may not match the actual hardware behavior.

X-pessimism is when a simulator assigns an unknown value to an output that should be known, due to conservative or inaccurate modeling. This can cause false alarms or unnecessary pessimism in verification. For example, consider the following code snippet:

// multiplexer

reg out2;

always @ (*) begin

  case (sel)

    2'b00: out_2 = in_0;

    2'b01: out_2 = in_1;

    2'b10: out_2 = in_2;

    2'b11: out_2 = in_3;



If sel is X, then out_2 should be the logical OR of all inputs, but the simulator will assign it to X, which may not reflect the actual hardware behavior.

What are the best practices to avoid and detect X-propagation?

There are several best practices that can help avoid or mitigate the effects of X-propagation in design flow, such as:

  1. Using formal verification tools to check for X sources and propagation paths, and to ensure that illegal states are unreachable.
  2. Using xprop simulation technology to replace every X with both 0 and 1 and calculate all possible values, and then merge them to decide which value should be driven to the output.
  3. Using randomization or assertion-based techniques to inject or check for X values in simulation.
  4. Using coding guidelines and best practices to avoid X-optimism or X-pessimism in RTL design.
  5. Using gate-level simulation with accurate timing and power models to verify the final netlist against RTL.
  6. Use resettable flops or initialize memory elements to avoid uninitialized signals.
  7. Use proper power gating techniques and ensure that downstream logic can handle power transitions correctly.
  8. Use robust reset logic and ensure that it covers all critical parts of the design.
  9. Avoid timing violations and ensure that signals meet setup and hold requirements.
  10. Use X-aware simulation tools and models that can detect and report X values and their sources.
  11. Use X-checking techniques that can compare simulation and synthesis outputs and identify mismatches due to X values.
  12. Use X-optimization techniques that can resolve or minimize X values in synthesis or post-synthesis stages.
  13. Use X-analysis techniques that can trace and debug X values on silicon or in simulation.

X-propagation is a common and challenging issue in digital system design, as it can affect verification, synthesis, and testing results. X values can arise from various sources, such as uninitialized signals, power gating, reset logic, timing violations, or simulation artifacts. To avoid or mitigate the impacts of X-propagation, designers should follow best practices such as using resettable flops, proper power gating, robust reset logic, X-aware simulation tools, X-checking techniques, X-optimization techniques, and X-analysis techniques.

Additional Resources




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