A Cross Stuck at 12 Percent

Where the interviewer goes next. Open a node to practise that follow-up.

What IfProve ItBreak ItCompare

1. A Cross Stuck at 12 Percent
2. What IfHow Long Random Stimulus Takes to Fill a CrossL2 Mid-Level

   What if every cell is legal and equally likely? Roughly how many random samples does a 512-cell cross need? Read the run.

   module tb;
     bit [2:0] a, b, c;
     covergroup cg;
       ca: coverpoint a { option.weight = 0; }
       cb: coverpoint b { option.weight = 0; }
       cc: coverpoint c { option.weight = 0; }
       x:  cross ca, cb, cc;              // 8 x 8 x 8 = 512 cells, all equally likely
     endgroup
     cg cov = new();
     int n = 0;
     initial begin
       while (cov.get_coverage() < 100.0) begin
         a = 3'($urandom); b = 3'($urandom); c = 3'($urandom);
         cov.sample();
         n++;
         if (n == 512)  $display("after 512 samples: %0.2f%%", cov.get_coverage());
         if (n == 1536) $display("after 1536 samples: %0.2f%%", cov.get_coverage());
       end
       $display("all 512 cells covered after %0d random samples", n);
     end
   endmodule
   

   Reveal the Model Answer

   Many more than 512. Random samples repeat cells, so the last few empty cells take the longest. After 512 samples this run has about 63% of the cells. It needs 3384 samples, more than six per cell, to fill them all. Uneven probabilities make it much worse, so rare cells need biased constraints or a directed test.

   Random samples	Cells covered (of 512)
   512	63.09%
   1536	94.73%
   3384	100%

   Measured by the run on this question. The last 5% of the cells took more samples than the first 63%.

   RUNVerilator (coverage build) · simulator service

   Edit the code, then run it

   OutputWaves

   RunReset codeExpected: after 512 samples: 63.09% after 1536 samples: 94.73% all 512 cells covered after 3384 random samples

   Self-Check

   Tick each key point you covered in your answer.

   Key point 1 Many more than 512. Key point 2 Random samples repeat cells, so the last few empty cells take the longest. Key point 3 After 512 samples this run has about 63% of the cells. Key point 4 It needs 3384 samples, more than six per cell, to fill them all. Key point 5 Uneven probabilities make it much worse, so rare cells need biased constraints or a directed test.

   Misconception

   "512 cells need about 512 random samples."

   Random samples land on cells already hit. The last empty cells are found slowly, which is why the run needs over six times as many.

   Source Spear & Tumbush, SystemVerilog for Verification (3rd ed.), §9.11 (PDF p395)

   • Lesson C7Closing Holes
3. CompareOne Big Cross vs Several PairsL2 Mid-LevelL3 Senior

   Compare one four-way cross with a set of two-way crosses over the same fields.

   Reveal the Model Answer

   The four-way cross demands every combination, 8192 cells here. The pairs, such as length with size and region with size, need every combination of two fields. That is a few hundred cells in all. Most spec rules involve two fields at a time, so pairs cover them at a small cost. Keep a three-way cross only where the spec states a rule that names three fields.

   Self-Check

   Tick each key point you covered in your answer.

   Key point 1 The four-way cross demands every combination, 8192 cells here. Key point 2 The pairs, such as length with size and region with size, need every combination of two fields. Key point 3 That is a few hundred cells in all. Key point 4 Most spec rules involve two fields at a time, so pairs cover them at a small cost. Key point 5 Keep a three-way cross only where the spec states a rule that names three fields.

   What Interviewers Listen For (Senior)

   A good senior answer points to the spec rule behind each cross it keeps. It drops every cross that has no such rule.

   Half-Truth

   "Pairs cover everything the big cross covers."

   Some bugs need three fields together, such as a burst that wraps at one size in one region. Pairs alone miss them.

   Source IEEE 1800-2017 §19.6

   • Lesson C5Cross Coverage
4. Break ItA Cross Hidden in the Covergroup TotalL2 Mid-Level

   How can the covergroup total make a weak cross look fine?

   Reveal the Model Answer

   By default the covergroup averages its coverpoints and crosses with equal weight. In the twin above, two closed coverpoints and a 12.5% cross average to 70.83%. With four closed coverpoints beside the cross, the total would pass 80% while the cross is nearly empty. Report each cross on its own.

   Self-Check

   Tick each key point you covered in your answer.

   Key point 1 By default the covergroup averages its coverpoints and crosses with equal weight. Key point 2 In the twin above, two closed coverpoints and a 12.5% cross average to 70.83%. Key point 3 With four closed coverpoints beside the cross, the total would pass 80% while the cross is nearly empty. Key point 4 Report each cross on its own.

   Misconception

   "The total weighs each bin equally, so a big cross dominates it."

   The total weighs each coverpoint and cross equally, whatever its size. A 128-cell cross counts the same as a 2-bin coverpoint.

   Source IEEE 1800-2017 §19.11

   • Lesson C5Cross Coverage
   • Lesson C7Closing Holes
5. Prove ItReading a Cross as Its Own NumberL2 Mid-Level

   Prove it: how do you get one number that is just the cross? What does this print?

   module tb;
     bit [1:0] a, b;
     covergroup cg;
       ca: coverpoint a { option.weight = 0; }   // still collected and reported
       cb: coverpoint b { option.weight = 0; }
       x:  cross ca, cb;                         // the only item that counts
     endgroup
     cg cov = new();
     initial begin
       for (int i = 0; i < 4; i++) begin a = 2'(i); b = 2'(i); cov.sample(); end
       $display("covergroup number = cross alone = %0.2f", cov.get_coverage());
     end
   endmodule
   

   Reveal the Model Answer

   It prints 25.00. The two coverpoints have weight 0, so they still collect data and show in the report, but they add nothing to the total. The cross is the only item left, and 4 of its 16 cells are hit. Put each key cross in a covergroup built this way, or read it from the report tool.

   RUNVerilator (coverage build) · simulator service

   Edit the code, then run it

   OutputWaves

   RunReset codeExpected: covergroup number = cross alone = 25.00

   Self-Check

   Tick each key point you covered in your answer.

   Key point 1 It prints 25.00. Key point 2 The two coverpoints have weight 0, so they still collect data and show in the report, but they add nothing to the total. Key point 3 The cross is the only item left, and 4 of its 16 cells are hit. Key point 4 Put each key cross in a covergroup built this way, or read it from the report tool.

   Tool as Truth

   "Call cg.x.get_coverage() to read the cross."

   The standard allows it, but some tools do not. This site's coverage build cannot read one item's coverage that way, so the weight trick is the portable route.

   Source IEEE 1800-2017 §19.8; ASIC Point engine notes (Verilator master b8e7f1e coverage build)

   • Lesson C5Cross Coverage
6. Prove ItSolve 7.5.9: The Cross That Can Never CloseSimulator-graded

   Show it, don't just say it: this Silicon Lab problem is graded by the simulator.

   Open Problem 7.5.9