This function, `sparse_cgemv8x4`, computes a sparse matrix-vector multiplication followed by...

August 28, 2025 at 05:47 AM

static inline void sparse_cgemv8x4(float *out, const opus_int8 *w, const int *idx, const float *scale, int rows, int cols, const float *_x)
{
   int i, j;
   opus_int8 x[MAX_INPUTS];
   for (i=0;i<rows;i++) out[i] = 0;
   for (i=0;i<cols;i++) x[i] = (int)floor(.5+127*_x[i]);
   for (i=0;i<rows;i+=8)
   {
      int colblocks;
      colblocks = *idx++;
      for (j=0;j<colblocks;j++)
      {
         int pos;
         float * restrict y;
         int 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+w[1]*xj1+w[2]*xj2+w[3]*xj3);
         y[1] += (w[4]*xj0+w[5]*xj1+w[6]*xj2+w[7]*xj3);
         y[2] += (w[8]*xj0+w[9]*xj1+w[10]*xj2+w[11]*xj3);
         y[3] += (w[12]*xj0+w[13]*xj1+w[14]*xj2+w[15]*xj3);
         y[4] += (w[16]*xj0+w[17]*xj1+w[18]*xj2+w[19]*xj3);
         y[5] += (w[20]*xj0+w[21]*xj1+w[22]*xj2+w[23]*xj3);
         y[6] += (w[24]*xj0+w[25]*xj1+w[26]*xj2+w[27]*xj3);
         y[7] += (w[28]*xj0+w[29]*xj1+w[30]*xj2+w[31]*xj3);
         w += 32;
      }
   }
   for (i=0;i<rows;i++) out[i] *= scale[i];
}

This function, sparse_cgemv8x4, computes a sparse matrix-vector multiplication followed by element-wise scaling for the output vector. Here are the steps describing what this code does:

Initialize Output Vector (out):
- The output vector out is initialized to zero for all rows.
Quantize Input Vector (_x) into Integers:
- The input vector _x (of floating-point values in the range [0, 1]) is scaled by 127, rounded using floor, and stored as integers (opus_int8) in the intermediate vector x. This effectively quantizes the floating-point input into integer values in [0, 127].
Perform Sparse Matrix-Vector Multiplication:
- The function iterates over blocks of 8 rows (i steps in increments of 8).
- For each block of rows:
  - The number of "column blocks" affecting the current row block is read (colblocks).
  - For each column block:
    - The position (pos) of the current column block in the input vector is read from idx.
    - Four input values from x (indices pos, pos+1, pos+2, pos+3) are extracted and stored in xj0, xj1, xj2, xj3.
    - A portion of the weight matrix (w) corresponding to the block is applied to these input values. Specifically, for each row i to i+7 in the row block, a weighted sum of the inputs is computed and added to the corresponding element in out. The weights are in a 32-element segment of w (8 rows × 4 columns).
Apply Scaling to out:
- After the matrix-vector multiplication, each entry in out is scaled by the corresponding element in the scale array.

Key Observations:

Sparse Representation: The input matrix is stored and accessed in a sparse format using idx to identify the non-zero column blocks. This avoids processing zeros in the matrix, improving efficiency.
8x4 Block Processing: The computation processes the rows in blocks of 8 and columns in blocks of 4, exploiting potential optimizations for vectorized hardware instructions (e.g., SIMD).
Quantization for Input Optimization: The floating-point input vector _x is quantized into integers (x) in the range [0, 127] to reduce computational cost and memory usage during matrix-vector multiplication. The precision loss is acceptable in contexts like signal processing.

Use Case:

The function is likely used in a scenario involving efficient computation of a sparse matrix-vector product, such as machine learning (e.g., neural network inference), signal processing, or other high-performance numerical applications.

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