double *add_3d_vectors4(double a[3], double b[3],
                       double *sum)
{
  if ( a == NULL || b == NULL )
    return NULL;
  if ( sum == NULL )
  {
    sum = (double *)malloc(3*sizeof(double));
    if ( sum == NULL )
      return NULL;
  }
  sum[0] = a[0] + b[0];
  sum[1] = a[2] + b[1];
  sum[2] = a[2] + b[2];
  return sum;
}