A Permutation Built by Constraints

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What IfProve ItBreak ItCompare

1. A Permutation Built by Constraints
2. What IfA One-Hot Value Without the Onehot FunctionL0 FresherL1 Junior

   Constrain an 8-bit x to have exactly one bit set, without using $onehot.

   Reveal the Model Answer

   Write x != 0 && (x & (x - 1)) == 0;. Subtracting 1 clears the lowest set bit and sets the bits below it. So the AND is zero only when at most one bit was set. x != 0 removes the zero case. $countones(x) == 1 says the same thing more readably.

   Self-Check

   Tick each key point you covered in your answer.

   Key point 1 Write x != 0 && (x & (x - 1)) == 0;. Key point 2 Subtracting 1 clears the lowest set bit and sets the bits below it. Key point 3 So the AND is zero only when at most one bit was set. Key point 4 x != 0 removes the zero case. Key point 5 $countones(x) == 1 says the same thing more readably.

   Missed Corner

   "(x & (x - 1)) == 0 alone means exactly one bit set."

   It means at most one bit set; zero passes too. The twin generates zeros until x != 0 is added.

   Run It

   200 calls with only the power-of-two test.

   RUNVerilator · simulator service

   Edit the code, then run it

   OutputWaves

   RunReset codeExpected: FAIL: x = 0 also satisfies (x & (x - 1)) == 0, so zero was generated

   See the Fix

   class onehot_gen;
     rand bit [7:0] x;
     constraint c { x != 0 && (x & (x - 1)) == 0; }   // the fix: also exclude 0
   endclass
   module tb;
     onehot_gen g = new;
     int zeros = 0, bad = 0;
     initial begin
       repeat (200) begin
         void'(g.randomize());
         if (g.x == 0) zeros++;
         if ($countones(g.x) != 1) bad++;
       end
       if (bad == 0) $display("PASS: every value had exactly one bit set");
     end
   endmodule
   

   Prints: PASS: every value had exactly one bit set

   • Lesson 5.2Inside, Implication and Distributions
3. CompareUnique Versus Pairwise InequalityL1 Junior

   Compare unique {a}; with foreach (a[i]) foreach (a[j]) if (i < j) a[i] != a[j];.

   Reveal the Model Answer

   They allow exactly the same solutions. unique states the intent in one line and also accepts a mix of scalars and arrays, such as unique {a, b, c};. You write the nested loop on an older tool. Its i < j guard stops it from comparing an element with itself.

   Self-Check

   Tick each key point you covered in your answer.

   Key point 1 They allow exactly the same solutions. Key point 2 unique states the intent in one line and also accepts a mix of scalars and arrays, such as unique {a, b, c};. Key point 3 You write the nested loop on an older tool. Key point 4 Its i < j guard stops it from comparing an element with itself.

   Missed Corner

   Writes the nested loop without the i < j (or i != j) guard.

   Then a[i] != a[i] is required for every element, which is impossible, and every call fails.

   Source IEEE 1800-2017 §18.5.8.1

   • Lesson 5.2Inside, Implication and Distributions
4. What IfA Strictly Increasing Random ArrayL1 Junior

   Asked if they finish quickly

   Constrain a five-element array to be strictly increasing, with every element between 1 and 20.

   Reveal the Model Answer

   Use a range plus a guarded neighbour rule: foreach (a[i]) { a[i] inside {[1:20]}; if (i > 0) a[i] > a[i-1]; }. The guard keeps index 0 from referring to an element that does not exist. The solver then picks uniformly among all increasing sequences, rather than sorting random values afterwards.

   Self-Check

   Tick each key point you covered in your answer.

   Key point 1 Use a range plus a guarded neighbour rule: foreach (a[i]) { a[i] inside {[1:20]}; if (i > 0) a[i] > a[i-1]; }. Key point 2 The guard keeps index 0 from referring to an element that does not exist. Key point 3 The solver then picks uniformly among all increasing sequences, rather than sorting random values afterwards.

   • Lesson 5.2Inside, Implication and Distributions
5. Break ItA Sum Constraint That WrapsL1 JuniorL2 Mid-Level

   Now make the elements bit [4:0] and add a.sum() == 50. What can go wrong?

   Reveal the Model Answer

   The sum() method returns the element type, so the total is computed in 5 bits and wraps at 32. The solver may then satisfy the constraint with a sum that is 50 modulo 32, or fail to find one. Write a.sum() with (int'(item)) == 50 so the addition happens in 32 bits.

   Self-Check

   Tick each key point you covered in your answer.

   Key point 1 The sum() method returns the element type, so the total is computed in 5 bits and wraps at 32. Key point 2 The solver may then satisfy the constraint with a sum that is 50 modulo 32, or fail to find one. Key point 3 Write a.sum() with (int'(item)) == 50 so the addition happens in 32 bits.

   Tool as Truth

   "It worked on Verilator, so the narrow sum is fine."

   Verilator 5.052 widens the uncast form, so the bug cannot appear there; the standard result has the element width.

   Source Lesson 2.4 simulator note (Verilator 5.052 widens the uncast sum)

   • Lesson 2.4Array Methods and with Expressions
   • Problem 2.4.2Wide Population Reduction
6. Prove ItSolve 5.7.1: Aligned Burst RequestSimulator-graded

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

   Open Problem 5.7.1