This C code performs a specialized operation for a sparse...

August 28, 2025 at 06:06 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;
      }
   }
}

This C code performs a specialized operation for a sparse matrix-vector multiplication, commonly used in machine learning and neural network computations, particularly in recurrent neural networks (RNNs). Let's break it down into steps:

Function Breakdown

Parameters:
- float *out: Output array to store the resulting vector (part of the result of a sparse matrix-vector multiplication).
- const float *w: Pointer to non-zero weights or elements of the sparse matrix.
- const int *idx: Array containing sparse matrix structure information (e.g., row-wise nonzero column indices or column-related metadata for operations).
- int rows: Number of rows in the output vector (out), which corresponds to the number of rows in the sparse matrix.
- const float *x: Input vector (the one that multiplies with the sparse matrix).
Helper Macros:
- RNN_CLEAR(out, rows): This macro clears or initializes the output vector out with zeros for all rows. This ensures the accumulation in the loop doesn't cause issues.
Overall Procedure:
- The function operates on blocks of 8 rows at a time (i progresses in increments of 8).
- The loop iterates over the sparse matrix to compute contributions to 8 rows of the output vector out at a time, leveraging the sparsity of the matrix.
Sparse Matrix Multiplication:
- For each block (i to i + 7) of 8 rows:
  - Retrieve the number of nonzero columns (cols) for the current block of rows via idx.
  - For each non-zero column (j up to cols):
    - Read the sparse column index or position (pos).
    - Fetch the corresponding values (xj0, xj1, xj2, xj3) from the input vector x (assuming data is grouped in blocks of 4 for efficiency).
    - Perform an unrolled dot-product computation between the sparse weights (w) and the corresponding values from x, adding the contribution directly to the relevant rows in the output vector out.
    - The computation does 4×8 (32) multiplications in one loop iteration, handling contributions for 4 components of input across 8 rows.
Weight Pointer Advancement:
- w advances by 32 elements after each nonzero column contribution because the code optimizes 4-element blocks across 8 rows.

Key Features:

Sparse Matrix Representation: The sparse matrix is represented using a compressed row/column structure indicated by idx. This avoids processing zero matrix entries, saving computational resources.
Efficient Block Processing: The code processes 8 rows at once and computes 4 values from the input vector (x[j:j+4]) for efficiency. This approach improves locality and benefits from SIMD (single instruction, multiple data) or vectorization-friendly inner-loops.
Accumulator Operations: Contributions from the sparse matrix (w) and input values (x) are accumulated into the output vector (out), following the logic of matrix-vector multiplication.

Summary:

This function computes the multiplication of a sparse matrix (represented via weights w and indices idx) and an input vector x, storing the result in the output vector out. The matrix multiplication is optimized for blocks of 8 rows and groups of 4 input values for performance benefits, making the function suitable for RNN or similar applications requiring sparse matrix operations.

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