The provided function `sparse_sgemv8x4` appears to perform a **sparse matrix-vector...

August 28, 2025 at 05:35 AM


static inline void sparse_sgemv8x4(float *out, const float *w, const int *idx, int rows, const float *x)
{
   int i, j;
   RNN_CLEAR(out, rows);
   for (i=0;i<rows;i+=8)
   {
      int cols;
      cols = *idx++;
      for (j=0;j<cols;j++)
      {
         int pos;
         float * restrict y;
         float xj0, xj1, xj2, xj3;
         pos = (*idx++);
         xj0 = x[pos+0];
         xj1 = x[pos+1];
         xj2 = x[pos+2];
         xj3 = x[pos+3];
         y = &out[i];
         y[0] += w[0]*xj0;
         y[1] += w[1]*xj0;
         y[2] += w[2]*xj0;
         y[3] += w[3]*xj0;
         y[4] += w[4]*xj0;
         y[5] += w[5]*xj0;
         y[6] += w[6]*xj0;
         y[7] += w[7]*xj0;

         y[0] += w[8]*xj1;
         y[1] += w[9]*xj1;
         y[2] += w[10]*xj1;
         y[3] += w[11]*xj1;
         y[4] += w[12]*xj1;
         y[5] += w[13]*xj1;
         y[6] += w[14]*xj1;
         y[7] += w[15]*xj1;

         y[0] += w[16]*xj2;
         y[1] += w[17]*xj2;
         y[2] += w[18]*xj2;
         y[3] += w[19]*xj2;
         y[4] += w[20]*xj2;
         y[5] += w[21]*xj2;
         y[6] += w[22]*xj2;
         y[7] += w[23]*xj2;

         y[0] += w[24]*xj3;
         y[1] += w[25]*xj3;
         y[2] += w[26]*xj3;
         y[3] += w[27]*xj3;
         y[4] += w[28]*xj3;
         y[5] += w[29]*xj3;
         y[6] += w[30]*xj3;
         y[7] += w[31]*xj3;
         w += 32;
      }
   }
}

The provided function sparse_sgemv8x4 appears to perform a sparse matrix-vector multiplication operation in a highly specialized and optimized manner. Here's a breakdown of what the code does:

General Purpose

The function computes the result of out = Wx where:
- W is a sparse matrix (stored in a compact form using the w and idx inputs).
- x is a dense input vector.
- out is the dense output vector.
The operation is vectorized to process 8 rows of W at a time and 4 columns of W at a time for optimization purposes.

Breakdown of the Code

Input Parameters:
- float *out: The output vector where the results will be stored. Its size is equal to the number of rows in the sparse matrix.
- const float *w: The weights (nonzero values of the sparse matrix) stored in a compact, contiguous form.
- const int *idx: Indices array that indicates the structure of the sparse matrix:
  - The first value (cols) indicates the number of non-zero groups for the current row(s).
  - The subsequent values are indices of where the non-zero blocks occur in the input vector x.
- int rows: The number of rows in the sparse matrix W.
- const float *x: A dense vector used as an input for the multiplication.

Implementation Steps:
- Clear or Initialize Output Vector (RNN_CLEAR):
  - The result array out (of size rows) is cleared (e.g., set to zero) before accumulation begins. RNN_CLEAR(out, rows) is likely a macro or function that zeroes the array.
- Outer Loop over Rows (for (i = 0; i < rows; i += 8)):
  - The matrix is processed in chunks of 8 rows at a time for computational efficiency.
- Inner Loop over Non-Zero Column Groups (for (j = 0; j < cols; j++)):
  - cols (the first entry in idx) tells how many groups of non-zero columns exist in the current row block.
  - For each group, a block of 4 contiguous column values from x is loaded:
    - xj0, xj1, xj2, xj3 correspond to 4 consecutive values in the x vector.
  - Processing Non-Zero Elements:
    - For each group of columns:
      - pos = (*idx++) indicates the base position of non-zero column indices.
      - The values of x corresponding to these indices are loaded (xj0, xj1, xj2, xj3).
  - Perform Accumulation:
    - The contributions of the loaded columns (from x) are accumulated into the corresponding part of the out vector.
    - A total of 8 rows (from out[i:i+8]) are updated in this loop.
    - For each column value (xj0, xj1, xj2, xj3), the weights (w) are applied to all 8 rows, and the results are accumulated.
  - Advance Weights Pointer:
    - After processing 4 columns, the weights pointer w is advanced by 32 (since 4 columns × 8 rows = 32 weights).

Efficiency Aspects:
- The function is carefully written for performance:
  - Processing 8 rows at a time and 4 columns at a time makes good use of the memory hierarchy.
  - The use of restrict (e.g., float * restrict y) helps the compiler optimize memory operations by indicating that y does not alias other data.
  - Compact storage of the sparse matrix (w and idx) reduces memory usage and accesses only the non-zero elements.

Summary

This function performs a sparse general matrix-vector multiplication (SGEMV) optimized for specific use cases where the sparse matrix:

Has a block structure allowing it to be processed in batches of 8 rows and 4 columns.
Is stored in a compact form using the w (non-zero values) and idx (indexing) arrays.

This implementation might be part of a machine learning framework or a signal processing library where sparse matrices amplify performance benefits.

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