systemverilog array reduction operator on 2-d array

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02-09-2025

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SystemVerilog's reduction operators provide a concise way to perform operations across all elements of an array. While straightforward for 1D arrays, applying them to 2D arrays requires a slightly different approach, often involving nested loops or clever use of array slicing. This guide will explore how to effectively use reduction operators on 2D arrays in SystemVerilog, addressing common questions and scenarios.

Understanding SystemVerilog Reduction Operators

Before delving into 2D arrays, let's review the basic reduction operators:

• &: Logical AND reduction. Returns 1'b1 only if all elements are 1'b1.
• |: Logical OR reduction. Returns 1'b0 only if all elements are 1'b0.
• ^: Logical XOR reduction.
• +: Addition reduction. Sums all elements.
• *: Multiplication reduction. Multiplies all elements.

These operators are applied using the syntax op reduction(expression), where op is the reduction operator and expression is the array or a slice of the array.

Applying Reduction Operators to 2D Arrays

The challenge with 2D arrays is that the reduction operator acts on a single dimension at a time. To achieve a reduction across the entire 2D array, you'll need to iterate. Here's how you can accomplish this using nested loops and array slicing techniques:

Method 1: Nested Loops

This method offers the most straightforward approach for beginners. We explicitly iterate through each row and then perform a reduction on each row. The result of the row reductions is then further reduced.

module reduction_example;

  int unsigned a [3][4];

  initial begin
    // Initialize the 2D array (example values)
    a = '{
      '{1, 2, 3, 4},
      '{5, 6, 7, 8},
      '{9, 10, 11, 12}
    };

    int sum_rows;
    int final_sum;

    // Summing the rows using nested loops
    for (int i = 0; i < 3; i++) begin
      sum_rows = 0;
      for (int j = 0; j < 4; j++) begin
        sum_rows += a[i][j];
      }
      final_sum += sum_rows;
    end

    $display("Sum of all elements: %0d", final_sum); // Output: 78
  end

endmodule

Method 2: Array Slicing and Reduction

This method leverages SystemVerilog's array slicing capabilities for a more concise (though potentially less readable for beginners) solution. We reduce each row individually and then reduce the resulting vector.

module reduction_example_slice;

  int unsigned a [3][4];

  initial begin
    a = '{
      '{1, 2, 3, 4},
      '{5, 6, 7, 8},
      '{9, 10, 11, 12}
    };

    int row_sums [3];

    // Reducing each row using array slicing
    for (int i = 0; i < 3; i++) begin
      row_sums[i] = +$reduce(+, a[i]); // Note the nested + reduction
    end

    int final_sum = +$reduce(+, row_sums);

    $display("Sum of all elements: %0d", final_sum); // Output: 78
  end

endmodule

Frequently Asked Questions (FAQs)

How do I perform a bitwise AND reduction on a 2D array of bits?

You can adapt either of the methods above, simply replacing the + reduction operator with &. The nested loop method would be:

bit b [3][4];
bit final_and;

for (int i = 0; i < 3; i++) begin
  bit row_and = 1'b1;
  for (int j = 0; j < 4; j++) begin
    row_and &= b[i][j];
  end
  final_and &= row_and;
end

The array slicing method would be similarly modified, using &$reduce(&, b[i]).

Can I use reduction operators directly on a multi-dimensional array without loops?

No, SystemVerilog's reduction operators do not inherently support direct application to multiple dimensions simultaneously. Iteration or slicing is required to achieve a complete reduction across all elements of a 2D array.

What are the performance implications of using nested loops versus array slicing?

In many cases, the performance difference will be negligible. The compiler might optimize both approaches similarly. However, for very large arrays, array slicing might offer a slight advantage due to potential vectorization opportunities. Profiling your specific code is essential to determine the optimal method in a performance-critical application.

This comprehensive guide demonstrates multiple approaches to using SystemVerilog's reduction operators with 2D arrays. Remember to choose the method that best suits your coding style and the complexity of your specific application. Always prioritize readability and maintainability while striving for efficient code.