This code defines a function `sparse_sgemv4x4` that performs a sparse...

This code defines a function sparse_sgemv4x4 that performs a sparse matrix-vector multiplication involving 4 rows of the output at a time. Here's a line-by-line breakdown of what it does:

• Function Inputs:
  1. float *out: A pointer to the output vector where the result will be written.
  2. const float *w: A pointer to the array of weights (non-zero elements of the sparse matrix w stored in a row-major format).
  3. const int *idx: A pointer to the array of indices that provide metadata for the sparse rows (e.g., number of non-zero elements per row, and their positions).
  4. int rows: The number of rows in the output vector out.
  5. const float *x: A pointer to the input vector.

Key steps in the function:

1. Clear the output vector out:

   RNN_CLEAR(out, rows);
   

   Here, RNN_CLEAR is presumably a macro or function that initializes the out array to zero. This ensures that out is ready to store the final result.

2. Outer Loop for the Output Rows:

   for (i=0; i<rows; i+=4) {
   

   This loop processes 4 rows of the output vector at a time. The step size of 4 indicates this is optimized for blocks of 4 rows.

3. Retrieve the Number of Non-Zero Columns:

   cols = *idx++;
   

   For the current block of 4 rows (i to i+3), this tells how many non-zero columns contribute to those rows.

4. Inner Loop for Non-Zero Columns:

   for (j=0; j<cols; j++) {
   

   This loop iterates over the non-zero contributions for the current block.

5. Extract Sparse Metadata:

   pos = (*idx++);
   

   pos specifies the column index in the x vector where the non-zero contribution is located.

6. Load 4 Elements of the x Vector:

   xj0 = x[pos+0];
   xj1 = x[pos+1];
   xj2 = x[pos+2];
   xj3 = x[pos+3];
   

   This retrieves 4 consecutive elements from the x input vector, starting at pos.

7. Compute Contributions to the Output Vector:

   y[0] += w[0]*xj0; y[1] += w[1]*xj0; y[2] += w[2]*xj0; y[3] += w[3]*xj0;
   ...
   y[0] += w[8]*xj1; y[1] += w[9]*xj1; ...
   

   For each block of 4 output rows and non-zero column values, it accumulates the weighted contribution of x into the out array. It does this by applying the weights stored in w to the elements of x.

   The weight array w is divided into sub-blocks of size 16 (4 rows x 4 columns). The loop accumulates contributions from these sub-blocks into the respective rows of the output.

8. Move to the Next Chunk of Weights:

   w += 16;
   

   After processing a block of weights (4 rows x 4 columns), the pointer w is advanced to the next block of weights.

Summary:

This function implements a sparse matrix-vector multiplication, optimized for 4 rows at a time (4x4 block-based processing). The sparse matrix is represented by:

• w: A weight array storing only the non-zero elements.
• idx: An index array that specifies the number of non-zero columns for each row block and their positions in the input vector x.

The output vector out is computed by iterating through the sparse blocks and performing the multiplication and accumulation of contributions from non-zero elements. This method is efficient and minimizes unnecessary operations on zero elements in the matrix.