siz_t bli_thread_get_range_weighted_b2t
(
thrinfo_t* thr,
obj_t* a,
blksz_t* bmult,
dim_t* start,
dim_t* end
)
{
siz_t area;
// This function assigns area-weighted ranges in the m dimension
// where the total range spans 0 to m-1 with 0 at the bottom end and
// m-1 at the top end.
if ( bli_obj_intersects_diag( *a ) &&
bli_obj_is_upper_or_lower( *a ) )
{
doff_t diagoff = bli_obj_diag_offset( *a );
uplo_t uplo = bli_obj_uplo( *a );
dim_t m = bli_obj_length( *a );
dim_t n = bli_obj_width( *a );
dim_t bf = bli_blksz_get_def_for_obj( a, bmult );
// Support implicit transposition.
if ( bli_obj_has_trans( *a ) )
{
bli_reflect_about_diag( diagoff, uplo, m, n );
}
bli_reflect_about_diag( diagoff, uplo, m, n );
bli_rotate180_trapezoid( diagoff, uplo );
area = bli_thread_get_range_weighted_sub
(
thr, diagoff, uplo, m, n, bf,
TRUE, start, end
);
}
else // if dense or zeros
{
area = bli_thread_get_range_b2t
(
thr, a, bmult,
start, end
);
}
return area;
}
siz_t bli_thread_get_range_weighted
(
thrinfo_t* thread,
doff_t diagoff,
uplo_t uplo,
dim_t m,
dim_t n,
dim_t bf,
bool_t handle_edge_low,
dim_t* j_start_thr,
dim_t* j_end_thr
)
{
dim_t n_way = thread->n_way;
dim_t my_id = thread->work_id;
dim_t bf_left = n % bf;
dim_t j;
dim_t off_j;
doff_t diagoff_j;
dim_t n_left;
dim_t width_j;
dim_t offm_inc, offn_inc;
double tri_dim, tri_area;
double area_total, area_per_thr;
siz_t area = 0;
// In this function, we assume that the caller has already determined
// that (a) the diagonal intersects the submatrix, and (b) the submatrix
// is either lower- or upper-stored.
if ( bli_is_lower( uplo ) )
{
// Prune away the unstored region above the diagonal, if it exists,
// and then to the right of where the diagonal intersects the bottom,
// if it exists. (Also, we discard the offset deltas since we don't
// need to actually index into the subpartition.)
bli_prune_unstored_region_top_l( diagoff, m, n, offm_inc );
bli_prune_unstored_region_right_l( diagoff, m, n, offn_inc );
// We don't need offm_inc, offn_inc here. These statements should
// prevent compiler warnings.
( void )offm_inc;
( void )offn_inc;
// Now that pruning has taken place, we know that diagoff >= 0.
// Compute the total area of the submatrix, accounting for the
// location of the diagonal, and divide it by the number of ways
// of parallelism.
tri_dim = ( double )( n - diagoff - 1 );
tri_area = tri_dim * ( tri_dim + 1.0 ) / 2.0;
area_total = ( double )m * ( double )n - tri_area;
area_per_thr = area_total / ( double )n_way;
// Initialize some variables prior to the loop: the offset to the
// current subpartition, the remainder of the n dimension, and
// the diagonal offset of the current subpartition.
off_j = 0;
diagoff_j = diagoff;
n_left = n;
// Iterate over the subpartition indices corresponding to each
// thread/caucus participating in the n_way parallelism.
for ( j = 0; j < n_way; ++j )
{
// Compute the width of the jth subpartition, taking the
// current diagonal offset into account, if needed.
width_j = bli_thread_get_range_width_l( diagoff_j, m, n_left,
j, n_way,
bf, bf_left,
area_per_thr,
handle_edge_low );
// If the current thread belongs to caucus j, this is his
// subpartition. So we compute the implied index range and
// end our search.
if ( j == my_id )
{
*j_start_thr = off_j;
*j_end_thr = off_j + width_j;
area = bli_find_area_trap_l( m, width_j, diagoff_j );
break;
}
// Shift the current subpartition's starting and diagonal offsets,
// as well as the remainder of the n dimension, according to the
// computed width, and then iterate to the next subpartition.
off_j += width_j;
diagoff_j -= width_j;
n_left -= width_j;
}
}
else // if ( bli_is_upper( uplo ) )
{
// Express the upper-stored case in terms of the lower-stored case.
// First, we convert the upper-stored trapezoid to an equivalent
// lower-stored trapezoid by rotating it 180 degrees.
bli_rotate180_trapezoid( diagoff, uplo );
// Now that the trapezoid is "flipped" in the n dimension, negate
// the bool that encodes whether to handle the edge case at the
// low (or high) end of the index range.
bli_toggle_bool( handle_edge_low );
// Compute the appropriate range for the rotated trapezoid.
area = bli_thread_get_range_weighted( thread, diagoff, uplo, m, n, bf,
handle_edge_low,
j_start_thr, j_end_thr );
// Reverse the indexing basis for the subpartition ranges so that
// the indices, relative to left-to-right iteration through the
// unrotated upper-stored trapezoid, map to the correct columns
// (relative to the diagonal). This amounts to subtracting the
// range from n.
bli_reverse_index_direction( *j_start_thr, *j_end_thr, n );
}
return area;
}