interval-tree: Add a utility to iterate over spans in an interval tree

The span iterator travels over the indexes of the interval_tree, not the
nodes, and classifies spans of indexes as either 'used' or 'hole'.

'used' spans are fully covered by nodes in the tree and 'hole' spans have
no node intersecting the span.

This is done greedily such that spans are maximally sized and every
iteration step switches between used/hole.

As an example a trivial allocator can be written as:

	for (interval_tree_span_iter_first(&span, itree, 0, ULONG_MAX);
	     !interval_tree_span_iter_done(&span);
	     interval_tree_span_iter_next(&span))
		if (span.is_hole &&
		    span.last_hole - span.start_hole >= allocation_size - 1)
			return span.start_hole;

With all the tricky boundary conditions handled by the library code.

The following iommufd patches have several algorithms for its overlapping
node interval trees that are significantly simplified with this kind of
iteration primitive. As it seems generally useful, put it into lib/.

Link: https://lore.kernel.org/r/3-v6-a196d26f289e+11787-iommufd_jgg@nvidia.com
Reviewed-by: Kevin Tian <kevin.tian@intel.com>
Reviewed-by: Eric Auger <eric.auger@redhat.com>
Tested-by: Nicolin Chen <nicolinc@nvidia.com>
Tested-by: Yi Liu <yi.l.liu@intel.com>
Tested-by: Lixiao Yang <lixiao.yang@intel.com>
Tested-by: Matthew Rosato <mjrosato@linux.ibm.com>
Signed-off-by: Jason Gunthorpe <jgg@nvidia.com>

2 files changed, 136 insertions, 0 deletions

diff --git a/lib/Kconfig b/lib/Kconfig
index 9bbf8a4b2108..c6c323fd2517 100644
--- a/lib/Kconfig
+++ b/lib/Kconfig
@@ -479,6 +479,10 @@ config INTERVAL_TREE
 
 	  for more information.
 
+config INTERVAL_TREE_SPAN_ITER
+	bool
+	depends on INTERVAL_TREE
+
 config XARRAY_MULTI
 	bool
 	help
diff --git a/lib/interval_tree.c b/lib/interval_tree.c
index 593ce56ece50..3412737ff365 100644
--- a/lib/interval_tree.c
+++ b/lib/interval_tree.c
@@ -15,3 +15,135 @@ EXPORT_SYMBOL_GPL(interval_tree_insert);
 EXPORT_SYMBOL_GPL(interval_tree_remove);
 EXPORT_SYMBOL_GPL(interval_tree_iter_first);
 EXPORT_SYMBOL_GPL(interval_tree_iter_next);
+
+#ifdef CONFIG_INTERVAL_TREE_SPAN_ITER
+/*
+ * Roll nodes[1] into nodes[0] by advancing nodes[1] to the end of a contiguous
+ * span of nodes. This makes nodes[0]->last the end of that contiguous used span
+ * indexes that started at the original nodes[1]->start. nodes[1] is now the
+ * first node starting the next used span. A hole span is between nodes[0]->last
+ * and nodes[1]->start. nodes[1] must be !NULL.
+ */
+static void
+interval_tree_span_iter_next_gap(struct interval_tree_span_iter *state)
+{
+	struct interval_tree_node *cur = state->nodes[1];
+
+	state->nodes[0] = cur;
+	do {
+		if (cur->last > state->nodes[0]->last)
+			state->nodes[0] = cur;
+		cur = interval_tree_iter_next(cur, state->first_index,
+					      state->last_index);
+	} while (cur && (state->nodes[0]->last >= cur->start ||
+			 state->nodes[0]->last + 1 == cur->start));
+	state->nodes[1] = cur;
+}
+
+void interval_tree_span_iter_first(struct interval_tree_span_iter *iter,
+				   struct rb_root_cached *itree,
+				   unsigned long first_index,
+				   unsigned long last_index)
+{
+	iter->first_index = first_index;
+	iter->last_index = last_index;
+	iter->nodes[0] = NULL;
+	iter->nodes[1] =
+		interval_tree_iter_first(itree, first_index, last_index);
+	if (!iter->nodes[1]) {
+		/* No nodes intersect the span, whole span is hole */
+		iter->start_hole = first_index;
+		iter->last_hole = last_index;
+		iter->is_hole = 1;
+		return;
+	}
+	if (iter->nodes[1]->start > first_index) {
+		/* Leading hole on first iteration */
+		iter->start_hole = first_index;
+		iter->last_hole = iter->nodes[1]->start - 1;
+		iter->is_hole = 1;
+		interval_tree_span_iter_next_gap(iter);
+		return;
+	}
+
+	/* Starting inside a used */
+	iter->start_used = first_index;
+	iter->is_hole = 0;
+	interval_tree_span_iter_next_gap(iter);
+	iter->last_used = iter->nodes[0]->last;
+	if (iter->last_used >= last_index) {
+		iter->last_used = last_index;
+		iter->nodes[0] = NULL;
+		iter->nodes[1] = NULL;
+	}
+}
+EXPORT_SYMBOL_GPL(interval_tree_span_iter_first);
+
+void interval_tree_span_iter_next(struct interval_tree_span_iter *iter)
+{
+	if (!iter->nodes[0] && !iter->nodes[1]) {
+		iter->is_hole = -1;
+		return;
+	}
+
+	if (iter->is_hole) {
+		iter->start_used = iter->last_hole + 1;
+		iter->last_used = iter->nodes[0]->last;
+		if (iter->last_used >= iter->last_index) {
+			iter->last_used = iter->last_index;
+			iter->nodes[0] = NULL;
+			iter->nodes[1] = NULL;
+		}
+		iter->is_hole = 0;
+		return;
+	}
+
+	if (!iter->nodes[1]) {
+		/* Trailing hole */
+		iter->start_hole = iter->nodes[0]->last + 1;
+		iter->last_hole = iter->last_index;
+		iter->nodes[0] = NULL;
+		iter->is_hole = 1;
+		return;
+	}
+
+	/* must have both nodes[0] and [1], interior hole */
+	iter->start_hole = iter->nodes[0]->last + 1;
+	iter->last_hole = iter->nodes[1]->start - 1;
+	iter->is_hole = 1;
+	interval_tree_span_iter_next_gap(iter);
+}
+EXPORT_SYMBOL_GPL(interval_tree_span_iter_next);
+
+/*
+ * Advance the iterator index to a specific position. The returned used/hole is
+ * updated to start at new_index. This is faster than calling
+ * interval_tree_span_iter_first() as it can avoid full searches in several
+ * cases where the iterator is already set.
+ */
+void interval_tree_span_iter_advance(struct interval_tree_span_iter *iter,
+				     struct rb_root_cached *itree,
+				     unsigned long new_index)
+{
+	if (iter->is_hole == -1)
+		return;
+
+	iter->first_index = new_index;
+	if (new_index > iter->last_index) {
+		iter->is_hole = -1;
+		return;
+	}
+
+	/* Rely on the union aliasing hole/used */
+	if (iter->start_hole <= new_index && new_index <= iter->last_hole) {
+		iter->start_hole = new_index;
+		return;
+	}
+	if (new_index == iter->last_hole + 1)
+		interval_tree_span_iter_next(iter);
+	else
+		interval_tree_span_iter_first(iter, itree, new_index,
+					      iter->last_index);
+}
+EXPORT_SYMBOL_GPL(interval_tree_span_iter_advance);
+#endif