diff --git a/Makefile b/Makefile
index bb8bd672016ddb..d69f9d415d294e 100644
--- a/Makefile
+++ b/Makefile
@@ -716,6 +716,7 @@ TEST_BUILTINS_OBJS += test-mktemp.o
 TEST_BUILTINS_OBJS += test-online-cpus.o
 TEST_BUILTINS_OBJS += test-path-utils.o
 TEST_BUILTINS_OBJS += test-prio-queue.o
+TEST_BUILTINS_OBJS += test-reach.o
 TEST_BUILTINS_OBJS += test-read-cache.o
 TEST_BUILTINS_OBJS += test-ref-store.o
 TEST_BUILTINS_OBJS += test-regex.o
@@ -829,6 +830,7 @@ LIB_OBJS += column.o
 LIB_OBJS += combine-diff.o
 LIB_OBJS += commit.o
 LIB_OBJS += commit-graph.o
+LIB_OBJS += commit-reach.o
 LIB_OBJS += compat/obstack.o
 LIB_OBJS += compat/terminal.o
 LIB_OBJS += config.o
diff --git a/bisect.c b/bisect.c
index e1275ba79e8e73..d023543c911d04 100644
--- a/bisect.c
+++ b/bisect.c
@@ -13,6 +13,7 @@
 #include "sha1-array.h"
 #include "argv-array.h"
 #include "commit-slab.h"
+#include "commit-reach.h"
 
 static struct oid_array good_revs;
 static struct oid_array skipped_revs;
diff --git a/builtin/branch.c b/builtin/branch.c
index a50632fb23f52e..9a787447f47bac 100644
--- a/builtin/branch.c
+++ b/builtin/branch.c
@@ -23,6 +23,7 @@
 #include "ref-filter.h"
 #include "worktree.h"
 #include "help.h"
+#include "commit-reach.h"
 
 static const char * const builtin_branch_usage[] = {
 	N_("git branch [<options>] [-r | -a] [--merged | --no-merged]"),
diff --git a/builtin/commit.c b/builtin/commit.c
index 158e3f843afbf8..b5c608458e8a20 100644
--- a/builtin/commit.c
+++ b/builtin/commit.c
@@ -33,6 +33,7 @@
 #include "sequencer.h"
 #include "mailmap.h"
 #include "help.h"
+#include "commit-reach.h"
 
 static const char * const builtin_commit_usage[] = {
 	N_("git commit [<options>] [--] <pathspec>..."),
diff --git a/builtin/fetch.c b/builtin/fetch.c
index f5d960baecf6c9..7de234774be038 100644
--- a/builtin/fetch.c
+++ b/builtin/fetch.c
@@ -22,6 +22,7 @@
 #include "utf8.h"
 #include "packfile.h"
 #include "list-objects-filter-options.h"
+#include "commit-reach.h"
 
 static const char * const builtin_fetch_usage[] = {
 	N_("git fetch [<options>] [<repository> [<refspec>...]]"),
diff --git a/builtin/fmt-merge-msg.c b/builtin/fmt-merge-msg.c
index ff165c0fcd209f..7277d557b2d197 100644
--- a/builtin/fmt-merge-msg.c
+++ b/builtin/fmt-merge-msg.c
@@ -12,6 +12,7 @@
 #include "fmt-merge-msg.h"
 #include "gpg-interface.h"
 #include "repository.h"
+#include "commit-reach.h"
 
 static const char * const fmt_merge_msg_usage[] = {
 	N_("git fmt-merge-msg [-m <message>] [--log[=<n>] | --no-log] [--file <file>]"),
diff --git a/builtin/log.c b/builtin/log.c
index 55a6286d7f4a95..333d97c69288ac 100644
--- a/builtin/log.c
+++ b/builtin/log.c
@@ -31,6 +31,7 @@
 #include "progress.h"
 #include "commit-slab.h"
 #include "repository.h"
+#include "commit-reach.h"
 
 #define MAIL_DEFAULT_WRAP 72
 
diff --git a/builtin/merge-base.c b/builtin/merge-base.c
index 08d91b1f0c0172..1c920990701381 100644
--- a/builtin/merge-base.c
+++ b/builtin/merge-base.c
@@ -7,6 +7,7 @@
 #include "revision.h"
 #include "parse-options.h"
 #include "repository.h"
+#include "commit-reach.h"
 
 static int show_merge_base(struct commit **rev, int rev_nr, int show_all)
 {
diff --git a/builtin/merge.c b/builtin/merge.c
index d1b547d97376d7..4c601c40a2efbb 100644
--- a/builtin/merge.c
+++ b/builtin/merge.c
@@ -36,6 +36,7 @@
 #include "packfile.h"
 #include "tag.h"
 #include "alias.h"
+#include "commit-reach.h"
 
 #define DEFAULT_TWOHEAD (1<<0)
 #define DEFAULT_OCTOPUS (1<<1)
diff --git a/builtin/pull.c b/builtin/pull.c
index 4e789353922340..15ad01096817c9 100644
--- a/builtin/pull.c
+++ b/builtin/pull.c
@@ -22,6 +22,7 @@
 #include "tempfile.h"
 #include "lockfile.h"
 #include "wt-status.h"
+#include "commit-reach.h"
 
 enum rebase_type {
 	REBASE_INVALID = -1,
diff --git a/builtin/receive-pack.c b/builtin/receive-pack.c
index 400d31c18ccd97..d8467f97343438 100644
--- a/builtin/receive-pack.c
+++ b/builtin/receive-pack.c
@@ -27,6 +27,7 @@
 #include "packfile.h"
 #include "object-store.h"
 #include "protocol.h"
+#include "commit-reach.h"
 
 static const char * const receive_pack_usage[] = {
 	N_("git receive-pack <git-dir>"),
diff --git a/builtin/remote.c b/builtin/remote.c
index c74ee886900176..79b03264463795 100644
--- a/builtin/remote.c
+++ b/builtin/remote.c
@@ -10,6 +10,7 @@
 #include "refspec.h"
 #include "object-store.h"
 #include "argv-array.h"
+#include "commit-reach.h"
 
 static const char * const builtin_remote_usage[] = {
 	N_("git remote [-v | --verbose]"),
diff --git a/builtin/rev-parse.c b/builtin/rev-parse.c
index 0f09bbbf65a4bc..455f62246d69ad 100644
--- a/builtin/rev-parse.c
+++ b/builtin/rev-parse.c
@@ -14,6 +14,7 @@
 #include "revision.h"
 #include "split-index.h"
 #include "submodule.h"
+#include "commit-reach.h"
 
 #define DO_REVS		1
 #define DO_NOREV	2
diff --git a/commit-graph.c b/commit-graph.c
index b0a55ad128fbca..e9786fa8640ec4 100644
--- a/commit-graph.c
+++ b/commit-graph.c
@@ -233,6 +233,24 @@ static int prepare_commit_graph(struct repository *r)
 	return !!r->objects->commit_graph;
 }
 
+int generation_numbers_enabled(struct repository *r)
+{
+	uint32_t first_generation;
+	struct commit_graph *g;
+	if (!prepare_commit_graph(r))
+	       return 0;
+
+	g = r->objects->commit_graph;
+
+	if (!g->num_commits)
+		return 0;
+
+	first_generation = get_be32(g->chunk_commit_data +
+				    g->hash_len + 8) >> 2;
+
+	return !!first_generation;
+}
+
 static void close_commit_graph(void)
 {
 	free_commit_graph(the_repository->objects->commit_graph);
diff --git a/commit-graph.h b/commit-graph.h
index 76e098934a7f67..0de8f88316fd46 100644
--- a/commit-graph.h
+++ b/commit-graph.h
@@ -51,6 +51,12 @@ struct commit_graph {
 
 struct commit_graph *load_commit_graph_one(const char *graph_file);
 
+/*
+ * Return 1 if and only if the repository has a commit-graph
+ * file and generation numbers are computed in that file.
+ */
+int generation_numbers_enabled(struct repository *r);
+
 void write_commit_graph_reachable(const char *obj_dir, int append);
 void write_commit_graph(const char *obj_dir,
 			struct string_list *pack_indexes,
diff --git a/commit-reach.c b/commit-reach.c
new file mode 100644
index 00000000000000..c9965240323633
--- /dev/null
+++ b/commit-reach.c
@@ -0,0 +1,662 @@
+#include "cache.h"
+#include "commit.h"
+#include "commit-graph.h"
+#include "decorate.h"
+#include "prio-queue.h"
+#include "tree.h"
+#include "ref-filter.c"
+#include "revision.h"
+#include "tag.h"
+#include "commit-reach.h"
+
+/* Remember to update object flag allocation in object.h */
+#define REACHABLE       (1u<<15)
+#define PARENT1		(1u<<16)
+#define PARENT2		(1u<<17)
+#define STALE		(1u<<18)
+#define RESULT		(1u<<19)
+
+static const unsigned all_flags = (PARENT1 | PARENT2 | STALE | RESULT);
+
+static int queue_has_nonstale(struct prio_queue *queue)
+{
+	int i;
+	for (i = 0; i < queue->nr; i++) {
+		struct commit *commit = queue->array[i].data;
+		if (!(commit->object.flags & STALE))
+			return 1;
+	}
+	return 0;
+}
+
+/* all input commits in one and twos[] must have been parsed! */
+static struct commit_list *paint_down_to_common(struct commit *one, int n,
+						struct commit **twos,
+						int min_generation)
+{
+	struct prio_queue queue = { compare_commits_by_gen_then_commit_date };
+	struct commit_list *result = NULL;
+	int i;
+	uint32_t last_gen = GENERATION_NUMBER_INFINITY;
+
+	one->object.flags |= PARENT1;
+	if (!n) {
+		commit_list_append(one, &result);
+		return result;
+	}
+	prio_queue_put(&queue, one);
+
+	for (i = 0; i < n; i++) {
+		twos[i]->object.flags |= PARENT2;
+		prio_queue_put(&queue, twos[i]);
+	}
+
+	while (queue_has_nonstale(&queue)) {
+		struct commit *commit = prio_queue_get(&queue);
+		struct commit_list *parents;
+		int flags;
+
+		if (commit->generation > last_gen)
+			BUG("bad generation skip %8x > %8x at %s",
+			    commit->generation, last_gen,
+			    oid_to_hex(&commit->object.oid));
+		last_gen = commit->generation;
+
+		if (commit->generation < min_generation)
+			break;
+
+		flags = commit->object.flags & (PARENT1 | PARENT2 | STALE);
+		if (flags == (PARENT1 | PARENT2)) {
+			if (!(commit->object.flags & RESULT)) {
+				commit->object.flags |= RESULT;
+				commit_list_insert_by_date(commit, &result);
+			}
+			/* Mark parents of a found merge stale */
+			flags |= STALE;
+		}
+		parents = commit->parents;
+		while (parents) {
+			struct commit *p = parents->item;
+			parents = parents->next;
+			if ((p->object.flags & flags) == flags)
+				continue;
+			if (parse_commit(p))
+				return NULL;
+			p->object.flags |= flags;
+			prio_queue_put(&queue, p);
+		}
+	}
+
+	clear_prio_queue(&queue);
+	return result;
+}
+
+static struct commit_list *merge_bases_many(struct commit *one, int n, struct commit **twos)
+{
+	struct commit_list *list = NULL;
+	struct commit_list *result = NULL;
+	int i;
+
+	for (i = 0; i < n; i++) {
+		if (one == twos[i])
+			/*
+			 * We do not mark this even with RESULT so we do not
+			 * have to clean it up.
+			 */
+			return commit_list_insert(one, &result);
+	}
+
+	if (parse_commit(one))
+		return NULL;
+	for (i = 0; i < n; i++) {
+		if (parse_commit(twos[i]))
+			return NULL;
+	}
+
+	list = paint_down_to_common(one, n, twos, 0);
+
+	while (list) {
+		struct commit *commit = pop_commit(&list);
+		if (!(commit->object.flags & STALE))
+			commit_list_insert_by_date(commit, &result);
+	}
+	return result;
+}
+
+struct commit_list *get_octopus_merge_bases(struct commit_list *in)
+{
+	struct commit_list *i, *j, *k, *ret = NULL;
+
+	if (!in)
+		return ret;
+
+	commit_list_insert(in->item, &ret);
+
+	for (i = in->next; i; i = i->next) {
+		struct commit_list *new_commits = NULL, *end = NULL;
+
+		for (j = ret; j; j = j->next) {
+			struct commit_list *bases;
+			bases = get_merge_bases(i->item, j->item);
+			if (!new_commits)
+				new_commits = bases;
+			else
+				end->next = bases;
+			for (k = bases; k; k = k->next)
+				end = k;
+		}
+		ret = new_commits;
+	}
+	return ret;
+}
+
+static int remove_redundant(struct commit **array, int cnt)
+{
+	/*
+	 * Some commit in the array may be an ancestor of
+	 * another commit.  Move such commit to the end of
+	 * the array, and return the number of commits that
+	 * are independent from each other.
+	 */
+	struct commit **work;
+	unsigned char *redundant;
+	int *filled_index;
+	int i, j, filled;
+
+	work = xcalloc(cnt, sizeof(*work));
+	redundant = xcalloc(cnt, 1);
+	ALLOC_ARRAY(filled_index, cnt - 1);
+
+	for (i = 0; i < cnt; i++)
+		parse_commit(array[i]);
+	for (i = 0; i < cnt; i++) {
+		struct commit_list *common;
+		uint32_t min_generation = array[i]->generation;
+
+		if (redundant[i])
+			continue;
+		for (j = filled = 0; j < cnt; j++) {
+			if (i == j || redundant[j])
+				continue;
+			filled_index[filled] = j;
+			work[filled++] = array[j];
+
+			if (array[j]->generation < min_generation)
+				min_generation = array[j]->generation;
+		}
+		common = paint_down_to_common(array[i], filled, work,
+					      min_generation);
+		if (array[i]->object.flags & PARENT2)
+			redundant[i] = 1;
+		for (j = 0; j < filled; j++)
+			if (work[j]->object.flags & PARENT1)
+				redundant[filled_index[j]] = 1;
+		clear_commit_marks(array[i], all_flags);
+		clear_commit_marks_many(filled, work, all_flags);
+		free_commit_list(common);
+	}
+
+	/* Now collect the result */
+	COPY_ARRAY(work, array, cnt);
+	for (i = filled = 0; i < cnt; i++)
+		if (!redundant[i])
+			array[filled++] = work[i];
+	for (j = filled, i = 0; i < cnt; i++)
+		if (redundant[i])
+			array[j++] = work[i];
+	free(work);
+	free(redundant);
+	free(filled_index);
+	return filled;
+}
+
+static struct commit_list *get_merge_bases_many_0(struct commit *one,
+						  int n,
+						  struct commit **twos,
+						  int cleanup)
+{
+	struct commit_list *list;
+	struct commit **rslt;
+	struct commit_list *result;
+	int cnt, i;
+
+	result = merge_bases_many(one, n, twos);
+	for (i = 0; i < n; i++) {
+		if (one == twos[i])
+			return result;
+	}
+	if (!result || !result->next) {
+		if (cleanup) {
+			clear_commit_marks(one, all_flags);
+			clear_commit_marks_many(n, twos, all_flags);
+		}
+		return result;
+	}
+
+	/* There are more than one */
+	cnt = commit_list_count(result);
+	rslt = xcalloc(cnt, sizeof(*rslt));
+	for (list = result, i = 0; list; list = list->next)
+		rslt[i++] = list->item;
+	free_commit_list(result);
+
+	clear_commit_marks(one, all_flags);
+	clear_commit_marks_many(n, twos, all_flags);
+
+	cnt = remove_redundant(rslt, cnt);
+	result = NULL;
+	for (i = 0; i < cnt; i++)
+		commit_list_insert_by_date(rslt[i], &result);
+	free(rslt);
+	return result;
+}
+
+struct commit_list *get_merge_bases_many(struct commit *one,
+					 int n,
+					 struct commit **twos)
+{
+	return get_merge_bases_many_0(one, n, twos, 1);
+}
+
+struct commit_list *get_merge_bases_many_dirty(struct commit *one,
+					       int n,
+					       struct commit **twos)
+{
+	return get_merge_bases_many_0(one, n, twos, 0);
+}
+
+struct commit_list *get_merge_bases(struct commit *one, struct commit *two)
+{
+	return get_merge_bases_many_0(one, 1, &two, 1);
+}
+
+/*
+ * Is "commit" a descendant of one of the elements on the "with_commit" list?
+ */
+int is_descendant_of(struct commit *commit, struct commit_list *with_commit)
+{
+	if (!with_commit)
+		return 1;
+
+	if (generation_numbers_enabled(the_repository)) {
+		struct commit_list *from_list = NULL;
+		int result;
+		commit_list_insert(commit, &from_list);
+		result = can_all_from_reach(from_list, with_commit, 0);
+		free_commit_list(from_list);
+		return result;
+	} else {
+		while (with_commit) {
+			struct commit *other;
+
+			other = with_commit->item;
+			with_commit = with_commit->next;
+			if (in_merge_bases(other, commit))
+				return 1;
+		}
+		return 0;
+	}
+}
+
+/*
+ * Is "commit" an ancestor of one of the "references"?
+ */
+int in_merge_bases_many(struct commit *commit, int nr_reference, struct commit **reference)
+{
+	struct commit_list *bases;
+	int ret = 0, i;
+	uint32_t min_generation = GENERATION_NUMBER_INFINITY;
+
+	if (parse_commit(commit))
+		return ret;
+	for (i = 0; i < nr_reference; i++) {
+		if (parse_commit(reference[i]))
+			return ret;
+		if (reference[i]->generation < min_generation)
+			min_generation = reference[i]->generation;
+	}
+
+	if (commit->generation > min_generation)
+		return ret;
+
+	bases = paint_down_to_common(commit, nr_reference, reference, commit->generation);
+	if (commit->object.flags & PARENT2)
+		ret = 1;
+	clear_commit_marks(commit, all_flags);
+	clear_commit_marks_many(nr_reference, reference, all_flags);
+	free_commit_list(bases);
+	return ret;
+}
+
+/*
+ * Is "commit" an ancestor of (i.e. reachable from) the "reference"?
+ */
+int in_merge_bases(struct commit *commit, struct commit *reference)
+{
+	return in_merge_bases_many(commit, 1, &reference);
+}
+
+struct commit_list *reduce_heads(struct commit_list *heads)
+{
+	struct commit_list *p;
+	struct commit_list *result = NULL, **tail = &result;
+	struct commit **array;
+	int num_head, i;
+
+	if (!heads)
+		return NULL;
+
+	/* Uniquify */
+	for (p = heads; p; p = p->next)
+		p->item->object.flags &= ~STALE;
+	for (p = heads, num_head = 0; p; p = p->next) {
+		if (p->item->object.flags & STALE)
+			continue;
+		p->item->object.flags |= STALE;
+		num_head++;
+	}
+	array = xcalloc(num_head, sizeof(*array));
+	for (p = heads, i = 0; p; p = p->next) {
+		if (p->item->object.flags & STALE) {
+			array[i++] = p->item;
+			p->item->object.flags &= ~STALE;
+		}
+	}
+	num_head = remove_redundant(array, num_head);
+	for (i = 0; i < num_head; i++)
+		tail = &commit_list_insert(array[i], tail)->next;
+	free(array);
+	return result;
+}
+
+void reduce_heads_replace(struct commit_list **heads)
+{
+	struct commit_list *result = reduce_heads(*heads);
+	free_commit_list(*heads);
+	*heads = result;
+}
+
+int ref_newer(const struct object_id *new_oid, const struct object_id *old_oid)
+{
+	struct object *o;
+	struct commit *old_commit, *new_commit;
+	struct commit_list *old_commit_list = NULL;
+
+	/*
+	 * Both new_commit and old_commit must be commit-ish and new_commit is descendant of
+	 * old_commit.  Otherwise we require --force.
+	 */
+	o = deref_tag(the_repository, parse_object(the_repository, old_oid),
+		      NULL, 0);
+	if (!o || o->type != OBJ_COMMIT)
+		return 0;
+	old_commit = (struct commit *) o;
+
+	o = deref_tag(the_repository, parse_object(the_repository, new_oid),
+		      NULL, 0);
+	if (!o || o->type != OBJ_COMMIT)
+		return 0;
+	new_commit = (struct commit *) o;
+
+	if (parse_commit(new_commit) < 0)
+		return 0;
+
+	commit_list_insert(old_commit, &old_commit_list);
+	return is_descendant_of(new_commit, old_commit_list);
+}
+
+/*
+ * Mimicking the real stack, this stack lives on the heap, avoiding stack
+ * overflows.
+ *
+ * At each recursion step, the stack items points to the commits whose
+ * ancestors are to be inspected.
+ */
+struct contains_stack {
+	int nr, alloc;
+	struct contains_stack_entry {
+		struct commit *commit;
+		struct commit_list *parents;
+	} *contains_stack;
+};
+
+static int in_commit_list(const struct commit_list *want, struct commit *c)
+{
+	for (; want; want = want->next)
+		if (!oidcmp(&want->item->object.oid, &c->object.oid))
+			return 1;
+	return 0;
+}
+
+/*
+ * Test whether the candidate is contained in the list.
+ * Do not recurse to find out, though, but return -1 if inconclusive.
+ */
+static enum contains_result contains_test(struct commit *candidate,
+					  const struct commit_list *want,
+					  struct contains_cache *cache,
+					  uint32_t cutoff)
+{
+	enum contains_result *cached = contains_cache_at(cache, candidate);
+
+	/* If we already have the answer cached, return that. */
+	if (*cached)
+		return *cached;
+
+	/* or are we it? */
+	if (in_commit_list(want, candidate)) {
+		*cached = CONTAINS_YES;
+		return CONTAINS_YES;
+	}
+
+	/* Otherwise, we don't know; prepare to recurse */
+	parse_commit_or_die(candidate);
+
+	if (candidate->generation < cutoff)
+		return CONTAINS_NO;
+
+	return CONTAINS_UNKNOWN;
+}
+
+static void push_to_contains_stack(struct commit *candidate, struct contains_stack *contains_stack)
+{
+	ALLOC_GROW(contains_stack->contains_stack, contains_stack->nr + 1, contains_stack->alloc);
+	contains_stack->contains_stack[contains_stack->nr].commit = candidate;
+	contains_stack->contains_stack[contains_stack->nr++].parents = candidate->parents;
+}
+
+static enum contains_result contains_tag_algo(struct commit *candidate,
+					      const struct commit_list *want,
+					      struct contains_cache *cache)
+{
+	struct contains_stack contains_stack = { 0, 0, NULL };
+	enum contains_result result;
+	uint32_t cutoff = GENERATION_NUMBER_INFINITY;
+	const struct commit_list *p;
+
+	for (p = want; p; p = p->next) {
+		struct commit *c = p->item;
+		load_commit_graph_info(the_repository, c);
+		if (c->generation < cutoff)
+			cutoff = c->generation;
+	}
+
+	result = contains_test(candidate, want, cache, cutoff);
+	if (result != CONTAINS_UNKNOWN)
+		return result;
+
+	push_to_contains_stack(candidate, &contains_stack);
+	while (contains_stack.nr) {
+		struct contains_stack_entry *entry = &contains_stack.contains_stack[contains_stack.nr - 1];
+		struct commit *commit = entry->commit;
+		struct commit_list *parents = entry->parents;
+
+		if (!parents) {
+			*contains_cache_at(cache, commit) = CONTAINS_NO;
+			contains_stack.nr--;
+		}
+		/*
+		 * If we just popped the stack, parents->item has been marked,
+		 * therefore contains_test will return a meaningful yes/no.
+		 */
+		else switch (contains_test(parents->item, want, cache, cutoff)) {
+		case CONTAINS_YES:
+			*contains_cache_at(cache, commit) = CONTAINS_YES;
+			contains_stack.nr--;
+			break;
+		case CONTAINS_NO:
+			entry->parents = parents->next;
+			break;
+		case CONTAINS_UNKNOWN:
+			push_to_contains_stack(parents->item, &contains_stack);
+			break;
+		}
+	}
+	free(contains_stack.contains_stack);
+	return contains_test(candidate, want, cache, cutoff);
+}
+
+int commit_contains(struct ref_filter *filter, struct commit *commit,
+		    struct commit_list *list, struct contains_cache *cache)
+{
+	if (filter->with_commit_tag_algo)
+		return contains_tag_algo(commit, list, cache) == CONTAINS_YES;
+	return is_descendant_of(commit, list);
+}
+
+static int compare_commits_by_gen(const void *_a, const void *_b)
+{
+	const struct commit *a = (const struct commit *)_a;
+	const struct commit *b = (const struct commit *)_b;
+
+	if (a->generation < b->generation)
+		return -1;
+	if (a->generation > b->generation)
+		return 1;
+	return 0;
+}
+
+int can_all_from_reach_with_flag(struct object_array *from,
+				 unsigned int with_flag,
+				 unsigned int assign_flag,
+				 time_t min_commit_date,
+				 uint32_t min_generation)
+{
+	struct commit **list = NULL;
+	int i;
+	int result = 1;
+
+	ALLOC_ARRAY(list, from->nr);
+	for (i = 0; i < from->nr; i++) {
+		list[i] = (struct commit *)from->objects[i].item;
+
+		if (parse_commit(list[i]) ||
+		    list[i]->generation < min_generation)
+			return 0;
+	}
+
+	QSORT(list, from->nr, compare_commits_by_gen);
+
+	for (i = 0; i < from->nr; i++) {
+		/* DFS from list[i] */
+		struct commit_list *stack = NULL;
+
+		list[i]->object.flags |= assign_flag;
+		commit_list_insert(list[i], &stack);
+
+		while (stack) {
+			struct commit_list *parent;
+
+			if (stack->item->object.flags & with_flag) {
+				pop_commit(&stack);
+				continue;
+			}
+
+			for (parent = stack->item->parents; parent; parent = parent->next) {
+				if (parent->item->object.flags & (with_flag | RESULT))
+					stack->item->object.flags |= RESULT;
+
+				if (!(parent->item->object.flags & assign_flag)) {
+					parent->item->object.flags |= assign_flag;
+
+					if (parse_commit(parent->item) ||
+					    parent->item->date < min_commit_date ||
+					    parent->item->generation < min_generation)
+						continue;
+
+					commit_list_insert(parent->item, &stack);
+					break;
+				}
+			}
+
+			if (!parent)
+				pop_commit(&stack);
+		}
+
+		if (!(list[i]->object.flags & (with_flag | RESULT))) {
+			result = 0;
+			goto cleanup;
+		}
+	}
+
+cleanup:
+	for (i = 0; i < from->nr; i++) {
+		clear_commit_marks(list[i], RESULT);
+		clear_commit_marks(list[i], assign_flag);
+	}
+	return result;
+}
+
+int can_all_from_reach(struct commit_list *from, struct commit_list *to,
+		       int cutoff_by_min_date)
+{
+	struct object_array from_objs = OBJECT_ARRAY_INIT;
+	time_t min_commit_date = cutoff_by_min_date ? from->item->date : 0;
+	struct commit_list *from_iter = from, *to_iter = to;
+	int result;
+	uint32_t min_generation = GENERATION_NUMBER_INFINITY;
+
+	while (from_iter) {
+		add_object_array(&from_iter->item->object, NULL, &from_objs);
+
+		if (!parse_commit(from_iter->item)) {
+			if (from_iter->item->date < min_commit_date)
+				min_commit_date = from_iter->item->date;
+
+			if (from_iter->item->generation < min_generation)
+				min_generation = from_iter->item->generation;
+		}
+
+		from_iter = from_iter->next;
+	}
+
+	while (to_iter) {
+		if (!parse_commit(to_iter->item)) {
+			if (to_iter->item->date < min_commit_date)
+				min_commit_date = to_iter->item->date;
+
+			if (to_iter->item->generation < min_generation)
+				min_generation = to_iter->item->generation;
+		}
+
+		to_iter->item->object.flags |= PARENT2;
+
+		to_iter = to_iter->next;
+	}
+
+	result = can_all_from_reach_with_flag(&from_objs, PARENT2, PARENT1,
+					      min_commit_date, min_generation);
+
+	while (from) {
+		clear_commit_marks(from->item, PARENT1);
+		from = from->next;
+	}
+
+	while (to) {
+		clear_commit_marks(to->item, PARENT2);
+		to = to->next;
+	}
+
+	object_array_clear(&from_objs);
+	return result;
+}
diff --git a/commit-reach.h b/commit-reach.h
new file mode 100644
index 00000000000000..7d313e2975a28e
--- /dev/null
+++ b/commit-reach.h
@@ -0,0 +1,77 @@
+#ifndef __COMMIT_REACH_H__
+#define __COMMIT_REACH_H__
+
+#include "commit-slab.h"
+
+struct commit;
+struct commit_list;
+struct contains_cache;
+struct ref_filter;
+
+struct commit_list *get_merge_bases_many(struct commit *one,
+					 int n,
+					 struct commit **twos);
+struct commit_list *get_merge_bases_many_dirty(struct commit *one,
+					       int n,
+					       struct commit **twos);
+struct commit_list *get_merge_bases(struct commit *one, struct commit *two);
+struct commit_list *get_octopus_merge_bases(struct commit_list *in);
+
+/* To be used only when object flags after this call no longer matter */
+struct commit_list *get_merge_bases_many_dirty(struct commit *one, int n, struct commit **twos);
+
+int is_descendant_of(struct commit *commit, struct commit_list *with_commit);
+int in_merge_bases_many(struct commit *commit, int nr_reference, struct commit **reference);
+int in_merge_bases(struct commit *commit, struct commit *reference);
+
+/*
+ * Takes a list of commits and returns a new list where those
+ * have been removed that can be reached from other commits in
+ * the list. It is useful for, e.g., reducing the commits
+ * randomly thrown at the git-merge command and removing
+ * redundant commits that the user shouldn't have given to it.
+ *
+ * This function destroys the STALE bit of the commit objects'
+ * flags.
+ */
+struct commit_list *reduce_heads(struct commit_list *heads);
+
+/*
+ * Like `reduce_heads()`, except it replaces the list. Use this
+ * instead of `foo = reduce_heads(foo);` to avoid memory leaks.
+ */
+void reduce_heads_replace(struct commit_list **heads);
+
+int ref_newer(const struct object_id *new_oid, const struct object_id *old_oid);
+
+/*
+ * Unknown has to be "0" here, because that's the default value for
+ * contains_cache slab entries that have not yet been assigned.
+ */
+enum contains_result {
+	CONTAINS_UNKNOWN = 0,
+	CONTAINS_NO,
+	CONTAINS_YES
+};
+
+define_commit_slab(contains_cache, enum contains_result);
+
+int commit_contains(struct ref_filter *filter, struct commit *commit,
+		    struct commit_list *list, struct contains_cache *cache);
+
+/*
+ * Determine if every commit in 'from' can reach at least one commit
+ * that is marked with 'with_flag'. As we traverse, use 'assign_flag'
+ * as a marker for commits that are already visited. Do not walk
+ * commits with date below 'min_commit_date' or generation below
+ * 'min_generation'.
+ */
+int can_all_from_reach_with_flag(struct object_array *from,
+				 unsigned int with_flag,
+				 unsigned int assign_flag,
+				 time_t min_commit_date,
+				 uint32_t min_generation);
+int can_all_from_reach(struct commit_list *from, struct commit_list *to,
+		       int commit_date_cutoff);
+
+#endif
diff --git a/commit.c b/commit.c
index 39b80bd21d59ca..32d1234bd745fa 100644
--- a/commit.c
+++ b/commit.c
@@ -843,364 +843,6 @@ void sort_in_topological_order(struct commit_list **list, enum rev_sort_order so
 		clear_author_date_slab(&author_date);
 }
 
-/* merge-base stuff */
-
-/* Remember to update object flag allocation in object.h */
-#define PARENT1		(1u<<16)
-#define PARENT2		(1u<<17)
-#define STALE		(1u<<18)
-#define RESULT		(1u<<19)
-
-static const unsigned all_flags = (PARENT1 | PARENT2 | STALE | RESULT);
-
-static int queue_has_nonstale(struct prio_queue *queue)
-{
-	int i;
-	for (i = 0; i < queue->nr; i++) {
-		struct commit *commit = queue->array[i].data;
-		if (!(commit->object.flags & STALE))
-			return 1;
-	}
-	return 0;
-}
-
-/* all input commits in one and twos[] must have been parsed! */
-static struct commit_list *paint_down_to_common(struct commit *one, int n,
-						struct commit **twos,
-						int min_generation)
-{
-	struct prio_queue queue = { compare_commits_by_gen_then_commit_date };
-	struct commit_list *result = NULL;
-	int i;
-	uint32_t last_gen = GENERATION_NUMBER_INFINITY;
-
-	one->object.flags |= PARENT1;
-	if (!n) {
-		commit_list_append(one, &result);
-		return result;
-	}
-	prio_queue_put(&queue, one);
-
-	for (i = 0; i < n; i++) {
-		twos[i]->object.flags |= PARENT2;
-		prio_queue_put(&queue, twos[i]);
-	}
-
-	while (queue_has_nonstale(&queue)) {
-		struct commit *commit = prio_queue_get(&queue);
-		struct commit_list *parents;
-		int flags;
-
-		if (commit->generation > last_gen)
-			BUG("bad generation skip %8x > %8x at %s",
-			    commit->generation, last_gen,
-			    oid_to_hex(&commit->object.oid));
-		last_gen = commit->generation;
-
-		if (commit->generation < min_generation)
-			break;
-
-		flags = commit->object.flags & (PARENT1 | PARENT2 | STALE);
-		if (flags == (PARENT1 | PARENT2)) {
-			if (!(commit->object.flags & RESULT)) {
-				commit->object.flags |= RESULT;
-				commit_list_insert_by_date(commit, &result);
-			}
-			/* Mark parents of a found merge stale */
-			flags |= STALE;
-		}
-		parents = commit->parents;
-		while (parents) {
-			struct commit *p = parents->item;
-			parents = parents->next;
-			if ((p->object.flags & flags) == flags)
-				continue;
-			if (parse_commit(p))
-				return NULL;
-			p->object.flags |= flags;
-			prio_queue_put(&queue, p);
-		}
-	}
-
-	clear_prio_queue(&queue);
-	return result;
-}
-
-static struct commit_list *merge_bases_many(struct commit *one, int n, struct commit **twos)
-{
-	struct commit_list *list = NULL;
-	struct commit_list *result = NULL;
-	int i;
-
-	for (i = 0; i < n; i++) {
-		if (one == twos[i])
-			/*
-			 * We do not mark this even with RESULT so we do not
-			 * have to clean it up.
-			 */
-			return commit_list_insert(one, &result);
-	}
-
-	if (parse_commit(one))
-		return NULL;
-	for (i = 0; i < n; i++) {
-		if (parse_commit(twos[i]))
-			return NULL;
-	}
-
-	list = paint_down_to_common(one, n, twos, 0);
-
-	while (list) {
-		struct commit *commit = pop_commit(&list);
-		if (!(commit->object.flags & STALE))
-			commit_list_insert_by_date(commit, &result);
-	}
-	return result;
-}
-
-struct commit_list *get_octopus_merge_bases(struct commit_list *in)
-{
-	struct commit_list *i, *j, *k, *ret = NULL;
-
-	if (!in)
-		return ret;
-
-	commit_list_insert(in->item, &ret);
-
-	for (i = in->next; i; i = i->next) {
-		struct commit_list *new_commits = NULL, *end = NULL;
-
-		for (j = ret; j; j = j->next) {
-			struct commit_list *bases;
-			bases = get_merge_bases(i->item, j->item);
-			if (!new_commits)
-				new_commits = bases;
-			else
-				end->next = bases;
-			for (k = bases; k; k = k->next)
-				end = k;
-		}
-		ret = new_commits;
-	}
-	return ret;
-}
-
-static int remove_redundant(struct commit **array, int cnt)
-{
-	/*
-	 * Some commit in the array may be an ancestor of
-	 * another commit.  Move such commit to the end of
-	 * the array, and return the number of commits that
-	 * are independent from each other.
-	 */
-	struct commit **work;
-	unsigned char *redundant;
-	int *filled_index;
-	int i, j, filled;
-
-	work = xcalloc(cnt, sizeof(*work));
-	redundant = xcalloc(cnt, 1);
-	ALLOC_ARRAY(filled_index, cnt - 1);
-
-	for (i = 0; i < cnt; i++)
-		parse_commit(array[i]);
-	for (i = 0; i < cnt; i++) {
-		struct commit_list *common;
-		uint32_t min_generation = array[i]->generation;
-
-		if (redundant[i])
-			continue;
-		for (j = filled = 0; j < cnt; j++) {
-			if (i == j || redundant[j])
-				continue;
-			filled_index[filled] = j;
-			work[filled++] = array[j];
-
-			if (array[j]->generation < min_generation)
-				min_generation = array[j]->generation;
-		}
-		common = paint_down_to_common(array[i], filled, work,
-					      min_generation);
-		if (array[i]->object.flags & PARENT2)
-			redundant[i] = 1;
-		for (j = 0; j < filled; j++)
-			if (work[j]->object.flags & PARENT1)
-				redundant[filled_index[j]] = 1;
-		clear_commit_marks(array[i], all_flags);
-		clear_commit_marks_many(filled, work, all_flags);
-		free_commit_list(common);
-	}
-
-	/* Now collect the result */
-	COPY_ARRAY(work, array, cnt);
-	for (i = filled = 0; i < cnt; i++)
-		if (!redundant[i])
-			array[filled++] = work[i];
-	for (j = filled, i = 0; i < cnt; i++)
-		if (redundant[i])
-			array[j++] = work[i];
-	free(work);
-	free(redundant);
-	free(filled_index);
-	return filled;
-}
-
-static struct commit_list *get_merge_bases_many_0(struct commit *one,
-						  int n,
-						  struct commit **twos,
-						  int cleanup)
-{
-	struct commit_list *list;
-	struct commit **rslt;
-	struct commit_list *result;
-	int cnt, i;
-
-	result = merge_bases_many(one, n, twos);
-	for (i = 0; i < n; i++) {
-		if (one == twos[i])
-			return result;
-	}
-	if (!result || !result->next) {
-		if (cleanup) {
-			clear_commit_marks(one, all_flags);
-			clear_commit_marks_many(n, twos, all_flags);
-		}
-		return result;
-	}
-
-	/* There are more than one */
-	cnt = commit_list_count(result);
-	rslt = xcalloc(cnt, sizeof(*rslt));
-	for (list = result, i = 0; list; list = list->next)
-		rslt[i++] = list->item;
-	free_commit_list(result);
-
-	clear_commit_marks(one, all_flags);
-	clear_commit_marks_many(n, twos, all_flags);
-
-	cnt = remove_redundant(rslt, cnt);
-	result = NULL;
-	for (i = 0; i < cnt; i++)
-		commit_list_insert_by_date(rslt[i], &result);
-	free(rslt);
-	return result;
-}
-
-struct commit_list *get_merge_bases_many(struct commit *one,
-					 int n,
-					 struct commit **twos)
-{
-	return get_merge_bases_many_0(one, n, twos, 1);
-}
-
-struct commit_list *get_merge_bases_many_dirty(struct commit *one,
-					       int n,
-					       struct commit **twos)
-{
-	return get_merge_bases_many_0(one, n, twos, 0);
-}
-
-struct commit_list *get_merge_bases(struct commit *one, struct commit *two)
-{
-	return get_merge_bases_many_0(one, 1, &two, 1);
-}
-
-/*
- * Is "commit" a descendant of one of the elements on the "with_commit" list?
- */
-int is_descendant_of(struct commit *commit, struct commit_list *with_commit)
-{
-	if (!with_commit)
-		return 1;
-	while (with_commit) {
-		struct commit *other;
-
-		other = with_commit->item;
-		with_commit = with_commit->next;
-		if (in_merge_bases(other, commit))
-			return 1;
-	}
-	return 0;
-}
-
-/*
- * Is "commit" an ancestor of one of the "references"?
- */
-int in_merge_bases_many(struct commit *commit, int nr_reference, struct commit **reference)
-{
-	struct commit_list *bases;
-	int ret = 0, i;
-	uint32_t min_generation = GENERATION_NUMBER_INFINITY;
-
-	if (parse_commit(commit))
-		return ret;
-	for (i = 0; i < nr_reference; i++) {
-		if (parse_commit(reference[i]))
-			return ret;
-		if (reference[i]->generation < min_generation)
-			min_generation = reference[i]->generation;
-	}
-
-	if (commit->generation > min_generation)
-		return ret;
-
-	bases = paint_down_to_common(commit, nr_reference, reference, commit->generation);
-	if (commit->object.flags & PARENT2)
-		ret = 1;
-	clear_commit_marks(commit, all_flags);
-	clear_commit_marks_many(nr_reference, reference, all_flags);
-	free_commit_list(bases);
-	return ret;
-}
-
-/*
- * Is "commit" an ancestor of (i.e. reachable from) the "reference"?
- */
-int in_merge_bases(struct commit *commit, struct commit *reference)
-{
-	return in_merge_bases_many(commit, 1, &reference);
-}
-
-struct commit_list *reduce_heads(struct commit_list *heads)
-{
-	struct commit_list *p;
-	struct commit_list *result = NULL, **tail = &result;
-	struct commit **array;
-	int num_head, i;
-
-	if (!heads)
-		return NULL;
-
-	/* Uniquify */
-	for (p = heads; p; p = p->next)
-		p->item->object.flags &= ~STALE;
-	for (p = heads, num_head = 0; p; p = p->next) {
-		if (p->item->object.flags & STALE)
-			continue;
-		p->item->object.flags |= STALE;
-		num_head++;
-	}
-	array = xcalloc(num_head, sizeof(*array));
-	for (p = heads, i = 0; p; p = p->next) {
-		if (p->item->object.flags & STALE) {
-			array[i++] = p->item;
-			p->item->object.flags &= ~STALE;
-		}
-	}
-	num_head = remove_redundant(array, num_head);
-	for (i = 0; i < num_head; i++)
-		tail = &commit_list_insert(array[i], tail)->next;
-	free(array);
-	return result;
-}
-
-void reduce_heads_replace(struct commit_list **heads)
-{
-	struct commit_list *result = reduce_heads(*heads);
-	free_commit_list(*heads);
-	*heads = result;
-}
-
 static const char gpg_sig_header[] = "gpgsig";
 static const int gpg_sig_header_len = sizeof(gpg_sig_header) - 1;
 
diff --git a/commit.h b/commit.h
index da0db36eba2bf1..e2c99d9b04f6b2 100644
--- a/commit.h
+++ b/commit.h
@@ -204,13 +204,6 @@ struct commit_graft *read_graft_line(struct strbuf *line);
 int register_commit_graft(struct repository *r, struct commit_graft *, int);
 struct commit_graft *lookup_commit_graft(struct repository *r, const struct object_id *oid);
 
-extern struct commit_list *get_merge_bases(struct commit *rev1, struct commit *rev2);
-extern struct commit_list *get_merge_bases_many(struct commit *one, int n, struct commit **twos);
-extern struct commit_list *get_octopus_merge_bases(struct commit_list *in);
-
-/* To be used only when object flags after this call no longer matter */
-extern struct commit_list *get_merge_bases_many_dirty(struct commit *one, int n, struct commit **twos);
-
 /* largest positive number a signed 32-bit integer can contain */
 #define INFINITE_DEPTH 0x7fffffff
 
@@ -258,32 +251,10 @@ extern int delayed_reachability_test(struct shallow_info *si, int c);
 extern void prune_shallow(int show_only);
 extern struct trace_key trace_shallow;
 
-int is_descendant_of(struct commit *, struct commit_list *);
-int in_merge_bases(struct commit *, struct commit *);
-int in_merge_bases_many(struct commit *, int, struct commit **);
-
 extern int interactive_add(int argc, const char **argv, const char *prefix, int patch);
 extern int run_add_interactive(const char *revision, const char *patch_mode,
 			       const struct pathspec *pathspec);
 
-/*
- * Takes a list of commits and returns a new list where those
- * have been removed that can be reached from other commits in
- * the list. It is useful for, e.g., reducing the commits
- * randomly thrown at the git-merge command and removing
- * redundant commits that the user shouldn't have given to it.
- *
- * This function destroys the STALE bit of the commit objects'
- * flags.
- */
-extern struct commit_list *reduce_heads(struct commit_list *heads);
-
-/*
- * Like `reduce_heads()`, except it replaces the list. Use this
- * instead of `foo = reduce_heads(foo);` to avoid memory leaks.
- */
-extern void reduce_heads_replace(struct commit_list **heads);
-
 struct commit_extra_header {
 	struct commit_extra_header *next;
 	char *key;
diff --git a/fast-import.c b/fast-import.c
index 3ea5781029de66..4a93df3839dcb4 100644
--- a/fast-import.c
+++ b/fast-import.c
@@ -171,6 +171,7 @@ Format of STDIN stream:
 #include "packfile.h"
 #include "object-store.h"
 #include "mem-pool.h"
+#include "commit-reach.h"
 
 #define PACK_ID_BITS 16
 #define MAX_PACK_ID ((1<<PACK_ID_BITS)-1)
diff --git a/http-push.c b/http-push.c
index 5eaf551b51e7aa..91fdc7e1d5d987 100644
--- a/http-push.c
+++ b/http-push.c
@@ -14,7 +14,7 @@
 #include "argv-array.h"
 #include "packfile.h"
 #include "object-store.h"
-
+#include "commit-reach.h"
 
 #ifdef EXPAT_NEEDS_XMLPARSE_H
 #include <xmlparse.h>
diff --git a/merge-recursive.c b/merge-recursive.c
index 1dd6ec384de132..8155dee9a98cbe 100644
--- a/merge-recursive.c
+++ b/merge-recursive.c
@@ -27,6 +27,7 @@
 #include "dir.h"
 #include "submodule.h"
 #include "revision.h"
+#include "commit-reach.h"
 
 struct path_hashmap_entry {
 	struct hashmap_entry e;
diff --git a/notes-merge.c b/notes-merge.c
index 76ab19e702423a..12dfdf6c170154 100644
--- a/notes-merge.c
+++ b/notes-merge.c
@@ -12,6 +12,7 @@
 #include "notes-merge.h"
 #include "strbuf.h"
 #include "notes-utils.h"
+#include "commit-reach.h"
 
 struct notes_merge_pair {
 	struct object_id obj, base, local, remote;
diff --git a/object.h b/object.h
index fa5ca975678630..b132944c51d968 100644
--- a/object.h
+++ b/object.h
@@ -60,12 +60,12 @@ struct object_array {
  * revision.h:               0---------10                                26
  * fetch-pack.c:             0----5
  * walker.c:                 0-2
- * upload-pack.c:                4       11----------------19
+ * upload-pack.c:                4       11-----14  16-----19
  * builtin/blame.c:                        12-13
  * bisect.c:                                        16
  * bundle.c:                                        16
  * http-push.c:                                     16-----19
- * commit.c:                                        16-----19
+ * commit-reach.c:                                15-------19
  * sha1-name.c:                                              20
  * list-objects-filter.c:                                      21
  * builtin/fsck.c:           0--3
diff --git a/pack-bitmap-write.c b/pack-bitmap-write.c
index 953c5dd84dff2d..55bcab907c0ecf 100644
--- a/pack-bitmap-write.c
+++ b/pack-bitmap-write.c
@@ -11,6 +11,7 @@
 #include "pack-bitmap.h"
 #include "sha1-lookup.h"
 #include "pack-objects.h"
+#include "commit-reach.h"
 
 struct bitmapped_commit {
 	struct commit *commit;
diff --git a/ref-filter.c b/ref-filter.c
index 9b2da883926dce..495e830fa58d26 100644
--- a/ref-filter.c
+++ b/ref-filter.c
@@ -19,6 +19,7 @@
 #include "wt-status.h"
 #include "commit-slab.h"
 #include "commit-graph.h"
+#include "commit-reach.h"
 
 static struct ref_msg {
 	const char *gone;
@@ -1623,144 +1624,6 @@ static int get_ref_atom_value(struct ref_array_item *ref, int atom,
 	return 0;
 }
 
-/*
- * Unknown has to be "0" here, because that's the default value for
- * contains_cache slab entries that have not yet been assigned.
- */
-enum contains_result {
-	CONTAINS_UNKNOWN = 0,
-	CONTAINS_NO,
-	CONTAINS_YES
-};
-
-define_commit_slab(contains_cache, enum contains_result);
-
-struct ref_filter_cbdata {
-	struct ref_array *array;
-	struct ref_filter *filter;
-	struct contains_cache contains_cache;
-	struct contains_cache no_contains_cache;
-};
-
-/*
- * Mimicking the real stack, this stack lives on the heap, avoiding stack
- * overflows.
- *
- * At each recursion step, the stack items points to the commits whose
- * ancestors are to be inspected.
- */
-struct contains_stack {
-	int nr, alloc;
-	struct contains_stack_entry {
-		struct commit *commit;
-		struct commit_list *parents;
-	} *contains_stack;
-};
-
-static int in_commit_list(const struct commit_list *want, struct commit *c)
-{
-	for (; want; want = want->next)
-		if (!oidcmp(&want->item->object.oid, &c->object.oid))
-			return 1;
-	return 0;
-}
-
-/*
- * Test whether the candidate is contained in the list.
- * Do not recurse to find out, though, but return -1 if inconclusive.
- */
-static enum contains_result contains_test(struct commit *candidate,
-					  const struct commit_list *want,
-					  struct contains_cache *cache,
-					  uint32_t cutoff)
-{
-	enum contains_result *cached = contains_cache_at(cache, candidate);
-
-	/* If we already have the answer cached, return that. */
-	if (*cached)
-		return *cached;
-
-	/* or are we it? */
-	if (in_commit_list(want, candidate)) {
-		*cached = CONTAINS_YES;
-		return CONTAINS_YES;
-	}
-
-	/* Otherwise, we don't know; prepare to recurse */
-	parse_commit_or_die(candidate);
-
-	if (candidate->generation < cutoff)
-		return CONTAINS_NO;
-
-	return CONTAINS_UNKNOWN;
-}
-
-static void push_to_contains_stack(struct commit *candidate, struct contains_stack *contains_stack)
-{
-	ALLOC_GROW(contains_stack->contains_stack, contains_stack->nr + 1, contains_stack->alloc);
-	contains_stack->contains_stack[contains_stack->nr].commit = candidate;
-	contains_stack->contains_stack[contains_stack->nr++].parents = candidate->parents;
-}
-
-static enum contains_result contains_tag_algo(struct commit *candidate,
-					      const struct commit_list *want,
-					      struct contains_cache *cache)
-{
-	struct contains_stack contains_stack = { 0, 0, NULL };
-	enum contains_result result;
-	uint32_t cutoff = GENERATION_NUMBER_INFINITY;
-	const struct commit_list *p;
-
-	for (p = want; p; p = p->next) {
-		struct commit *c = p->item;
-		load_commit_graph_info(the_repository, c);
-		if (c->generation < cutoff)
-			cutoff = c->generation;
-	}
-
-	result = contains_test(candidate, want, cache, cutoff);
-	if (result != CONTAINS_UNKNOWN)
-		return result;
-
-	push_to_contains_stack(candidate, &contains_stack);
-	while (contains_stack.nr) {
-		struct contains_stack_entry *entry = &contains_stack.contains_stack[contains_stack.nr - 1];
-		struct commit *commit = entry->commit;
-		struct commit_list *parents = entry->parents;
-
-		if (!parents) {
-			*contains_cache_at(cache, commit) = CONTAINS_NO;
-			contains_stack.nr--;
-		}
-		/*
-		 * If we just popped the stack, parents->item has been marked,
-		 * therefore contains_test will return a meaningful yes/no.
-		 */
-		else switch (contains_test(parents->item, want, cache, cutoff)) {
-		case CONTAINS_YES:
-			*contains_cache_at(cache, commit) = CONTAINS_YES;
-			contains_stack.nr--;
-			break;
-		case CONTAINS_NO:
-			entry->parents = parents->next;
-			break;
-		case CONTAINS_UNKNOWN:
-			push_to_contains_stack(parents->item, &contains_stack);
-			break;
-		}
-	}
-	free(contains_stack.contains_stack);
-	return contains_test(candidate, want, cache, cutoff);
-}
-
-static int commit_contains(struct ref_filter *filter, struct commit *commit,
-			   struct commit_list *list, struct contains_cache *cache)
-{
-	if (filter->with_commit_tag_algo)
-		return contains_tag_algo(commit, list, cache) == CONTAINS_YES;
-	return is_descendant_of(commit, list);
-}
-
 /*
  * Return 1 if the refname matches one of the patterns, otherwise 0.
  * A pattern can be a literal prefix (e.g. a refname "refs/heads/master"
@@ -1987,6 +1850,13 @@ static int filter_ref_kind(struct ref_filter *filter, const char *refname)
 	return ref_kind_from_refname(refname);
 }
 
+struct ref_filter_cbdata {
+	struct ref_array *array;
+	struct ref_filter *filter;
+	struct contains_cache contains_cache;
+	struct contains_cache no_contains_cache;
+};
+
 /*
  * A call-back given to for_each_ref().  Filter refs and keep them for
  * later object processing.
diff --git a/remote.c b/remote.c
index 26b1fbd9a881d2..f0c23bae487954 100644
--- a/remote.c
+++ b/remote.c
@@ -12,6 +12,7 @@
 #include "string-list.h"
 #include "mergesort.h"
 #include "argv-array.h"
+#include "commit-reach.h"
 
 enum map_direction { FROM_SRC, FROM_DST };
 
@@ -1783,55 +1784,6 @@ int resolve_remote_symref(struct ref *ref, struct ref *list)
 	return 1;
 }
 
-static void unmark_and_free(struct commit_list *list, unsigned int mark)
-{
-	while (list) {
-		struct commit *commit = pop_commit(&list);
-		commit->object.flags &= ~mark;
-	}
-}
-
-int ref_newer(const struct object_id *new_oid, const struct object_id *old_oid)
-{
-	struct object *o;
-	struct commit *old_commit, *new_commit;
-	struct commit_list *list, *used;
-	int found = 0;
-
-	/*
-	 * Both new_commit and old_commit must be commit-ish and new_commit is descendant of
-	 * old_commit.  Otherwise we require --force.
-	 */
-	o = deref_tag(the_repository, parse_object(the_repository, old_oid),
-		      NULL, 0);
-	if (!o || o->type != OBJ_COMMIT)
-		return 0;
-	old_commit = (struct commit *) o;
-
-	o = deref_tag(the_repository, parse_object(the_repository, new_oid),
-		      NULL, 0);
-	if (!o || o->type != OBJ_COMMIT)
-		return 0;
-	new_commit = (struct commit *) o;
-
-	if (parse_commit(new_commit) < 0)
-		return 0;
-
-	used = list = NULL;
-	commit_list_insert(new_commit, &list);
-	while (list) {
-		new_commit = pop_most_recent_commit(&list, TMP_MARK);
-		commit_list_insert(new_commit, &used);
-		if (new_commit == old_commit) {
-			found = 1;
-			break;
-		}
-	}
-	unmark_and_free(list, TMP_MARK);
-	unmark_and_free(used, TMP_MARK);
-	return found;
-}
-
 /*
  * Lookup the upstream branch for the given branch and if present, optionally
  * compute the commit ahead/behind values for the pair.
diff --git a/remote.h b/remote.h
index 45ecc6cefafdea..56fb9cbb27258b 100644
--- a/remote.h
+++ b/remote.h
@@ -149,7 +149,6 @@ extern struct ref **get_remote_refs(int fd_out, struct packet_reader *reader,
 				    const struct string_list *server_options);
 
 int resolve_remote_symref(struct ref *ref, struct ref *list);
-int ref_newer(const struct object_id *new_oid, const struct object_id *old_oid);
 
 /*
  * Remove and free all but the first of any entries in the input list
diff --git a/revision.c b/revision.c
index 4dbe406bed2aa1..3205a3947ad122 100644
--- a/revision.c
+++ b/revision.c
@@ -24,6 +24,7 @@
 #include "packfile.h"
 #include "worktree.h"
 #include "argv-array.h"
+#include "commit-reach.h"
 
 volatile show_early_output_fn_t show_early_output;
 
diff --git a/sequencer.c b/sequencer.c
index d1d07bed5bb051..97bdfd48b42c14 100644
--- a/sequencer.c
+++ b/sequencer.c
@@ -30,6 +30,7 @@
 #include "oidset.h"
 #include "commit-slab.h"
 #include "alias.h"
+#include "commit-reach.h"
 
 #define GIT_REFLOG_ACTION "GIT_REFLOG_ACTION"
 
diff --git a/sha1-name.c b/sha1-name.c
index 009faab4aefc34..7215b30b8861aa 100644
--- a/sha1-name.c
+++ b/sha1-name.c
@@ -12,6 +12,7 @@
 #include "packfile.h"
 #include "object-store.h"
 #include "repository.h"
+#include "commit-reach.h"
 
 static int get_oid_oneline(const char *, struct object_id *, struct commit_list *);
 
diff --git a/shallow.c b/shallow.c
index dbe8a2a2906abf..99fd2d1ba0f70a 100644
--- a/shallow.c
+++ b/shallow.c
@@ -16,6 +16,7 @@
 #include "list-objects.h"
 #include "commit-slab.h"
 #include "repository.h"
+#include "commit-reach.h"
 
 void set_alternate_shallow_file(struct repository *r, const char *path, int override)
 {
diff --git a/submodule.c b/submodule.c
index 6688dd5d459495..6650ed7aa02b2b 100644
--- a/submodule.c
+++ b/submodule.c
@@ -22,6 +22,7 @@
 #include "worktree.h"
 #include "parse-options.h"
 #include "object-store.h"
+#include "commit-reach.h"
 
 static int config_update_recurse_submodules = RECURSE_SUBMODULES_OFF;
 static struct string_list changed_submodule_names = STRING_LIST_INIT_DUP;
diff --git a/t/helper/test-reach.c b/t/helper/test-reach.c
new file mode 100644
index 00000000000000..eb2110399829d3
--- /dev/null
+++ b/t/helper/test-reach.c
@@ -0,0 +1,130 @@
+#include "test-tool.h"
+#include "cache.h"
+#include "commit.h"
+#include "commit-reach.h"
+#include "config.h"
+#include "parse-options.h"
+#include "ref-filter.h"
+#include "string-list.h"
+#include "tag.h"
+
+static void print_sorted_commit_ids(struct commit_list *list)
+{
+	int i;
+	struct string_list s = STRING_LIST_INIT_DUP;
+
+	while (list) {
+		string_list_append(&s, oid_to_hex(&list->item->object.oid));
+		list = list->next;
+	}
+
+	string_list_sort(&s);
+
+	for (i = 0; i < s.nr; i++)
+		printf("%s\n", s.items[i].string);
+
+	string_list_clear(&s, 0);
+}
+
+int cmd__reach(int ac, const char **av)
+{
+	struct object_id oid_A, oid_B;
+	struct commit *A, *B;
+	struct commit_list *X, *Y;
+	struct commit **X_array;
+	int X_nr, X_alloc;
+	struct strbuf buf = STRBUF_INIT;
+	struct repository *r = the_repository;
+
+	setup_git_directory();
+
+	if (ac < 2)
+		exit(1);
+
+	A = B = NULL;
+	X = Y = NULL;
+	X_nr = 0;
+	X_alloc = 16;
+	ALLOC_ARRAY(X_array, X_alloc);
+
+	while (strbuf_getline(&buf, stdin) != EOF) {
+		struct object_id oid;
+		struct object *o;
+		struct commit *c;
+		if (buf.len < 3)
+			continue;
+
+		if (get_oid_committish(buf.buf + 2, &oid))
+			die("failed to resolve %s", buf.buf + 2);
+
+		o = parse_object(r, &oid);
+		o = deref_tag_noverify(o);
+
+		if (!o)
+			die("failed to load commit for input %s resulting in oid %s\n",
+			    buf.buf, oid_to_hex(&oid));
+
+		c = object_as_type(r, o, OBJ_COMMIT, 0);
+
+		if (!c)
+			die("failed to load commit for input %s resulting in oid %s\n",
+			    buf.buf, oid_to_hex(&oid));
+
+		switch (buf.buf[0]) {
+			case 'A':
+				oidcpy(&oid_A, &oid);
+				A = c;
+				break;
+
+			case 'B':
+				oidcpy(&oid_B, &oid);
+				B = c;
+				break;
+
+			case 'X':
+				commit_list_insert(c, &X);
+				ALLOC_GROW(X_array, X_nr + 1, X_alloc);
+				X_array[X_nr++] = c;
+				break;
+
+			case 'Y':
+				commit_list_insert(c, &Y);
+				break;
+
+			default:
+				die("unexpected start of line: %c", buf.buf[0]);
+		}
+	}
+	strbuf_release(&buf);
+
+	if (!strcmp(av[1], "ref_newer"))
+		printf("%s(A,B):%d\n", av[1], ref_newer(&oid_A, &oid_B));
+	else if (!strcmp(av[1], "in_merge_bases"))
+		printf("%s(A,B):%d\n", av[1], in_merge_bases(A, B));
+	else if (!strcmp(av[1], "is_descendant_of"))
+		printf("%s(A,X):%d\n", av[1], is_descendant_of(A, X));
+	else if (!strcmp(av[1], "get_merge_bases_many")) {
+		struct commit_list *list = get_merge_bases_many(A, X_nr, X_array);
+		printf("%s(A,X):\n", av[1]);
+		print_sorted_commit_ids(list);
+	} else if (!strcmp(av[1], "reduce_heads")) {
+		struct commit_list *list = reduce_heads(X);
+		printf("%s(X):\n", av[1]);
+		print_sorted_commit_ids(list);
+	} else if (!strcmp(av[1], "can_all_from_reach")) {
+		printf("%s(X,Y):%d\n", av[1], can_all_from_reach(X, Y, 1));
+	} else if (!strcmp(av[1], "commit_contains")) {
+		struct ref_filter filter;
+		struct contains_cache cache;
+		init_contains_cache(&cache);
+
+		if (ac > 2 && !strcmp(av[2], "--tag"))
+			filter.with_commit_tag_algo = 1;
+		else
+			filter.with_commit_tag_algo = 0;
+
+		printf("%s(_,A,X,_):%d\n", av[1], commit_contains(&filter, A, X, &cache));
+	}
+
+	exit(0);
+}
diff --git a/t/helper/test-tool.c b/t/helper/test-tool.c
index dafc91c240a440..582d02adfd93ef 100644
--- a/t/helper/test-tool.c
+++ b/t/helper/test-tool.c
@@ -26,6 +26,7 @@ static struct test_cmd cmds[] = {
 	{ "online-cpus", cmd__online_cpus },
 	{ "path-utils", cmd__path_utils },
 	{ "prio-queue", cmd__prio_queue },
+	{ "reach", cmd__reach },
 	{ "read-cache", cmd__read_cache },
 	{ "ref-store", cmd__ref_store },
 	{ "regex", cmd__regex },
diff --git a/t/helper/test-tool.h b/t/helper/test-tool.h
index 80cbcf08575d5e..a7e53c420e1f44 100644
--- a/t/helper/test-tool.h
+++ b/t/helper/test-tool.h
@@ -20,6 +20,7 @@ int cmd__mktemp(int argc, const char **argv);
 int cmd__online_cpus(int argc, const char **argv);
 int cmd__path_utils(int argc, const char **argv);
 int cmd__prio_queue(int argc, const char **argv);
+int cmd__reach(int argc, const char **argv);
 int cmd__read_cache(int argc, const char **argv);
 int cmd__ref_store(int argc, const char **argv);
 int cmd__regex(int argc, const char **argv);
diff --git a/t/t6600-test-reach.sh b/t/t6600-test-reach.sh
new file mode 100755
index 00000000000000..d139a00d1dd2bb
--- /dev/null
+++ b/t/t6600-test-reach.sh
@@ -0,0 +1,242 @@
+#!/bin/sh
+
+test_description='basic commit reachability tests'
+
+. ./test-lib.sh
+
+# Construct a grid-like commit graph with points (x,y)
+# with 1 <= x <= 10, 1 <= y <= 10, where (x,y) has
+# parents (x-1, y) and (x, y-1), keeping in mind that
+# we drop a parent if a coordinate is nonpositive.
+#
+#             (10,10)
+#            /       \
+#         (10,9)    (9,10)
+#        /     \   /      \
+#    (10,8)    (9,9)      (8,10)
+#   /     \    /   \      /    \
+#         ( continued...)
+#   \     /    \   /      \    /
+#    (3,1)     (2,2)      (1,3)
+#        \     /    \     /
+#         (2,1)      (2,1)
+#              \    /
+#              (1,1)
+#
+# We use branch 'commit-x-y' to refer to (x,y).
+# This grid allows interesting reachability and
+# non-reachability queries: (x,y) can reach (x',y')
+# if and only if x' <= x and y' <= y.
+test_expect_success 'setup' '
+	for i in $(test_seq 1 10)
+	do
+		test_commit "1-$i" &&
+		git branch -f commit-1-$i
+	done &&
+	for j in $(test_seq 1 9)
+	do
+		git reset --hard commit-$j-1 &&
+		x=$(($j + 1)) &&
+		test_commit "$x-1" &&
+		git branch -f commit-$x-1 &&
+
+		for i in $(test_seq 2 10)
+		do
+			git merge commit-$j-$i -m "$x-$i" &&
+			git branch -f commit-$x-$i
+		done
+	done &&
+	git commit-graph write --reachable &&
+	mv .git/objects/info/commit-graph commit-graph-full &&
+	git show-ref -s commit-5-5 | git commit-graph write --stdin-commits &&
+	mv .git/objects/info/commit-graph commit-graph-half &&
+	git config core.commitGraph true
+'
+
+test_three_modes () {
+	test_when_finished rm -rf .git/objects/info/commit-graph &&
+	test-tool reach $1 <input >actual &&
+	test_cmp expect actual &&
+	cp commit-graph-full .git/objects/info/commit-graph &&
+	test-tool reach $1 <input >actual &&
+	test_cmp expect actual &&
+	cp commit-graph-half .git/objects/info/commit-graph &&
+	test-tool reach $1 <input >actual &&
+	test_cmp expect actual
+}
+
+test_expect_success 'ref_newer:miss' '
+	cat >input <<-\EOF &&
+	A:commit-5-7
+	B:commit-4-9
+	EOF
+	echo "ref_newer(A,B):0" >expect &&
+	test_three_modes ref_newer
+'
+
+test_expect_success 'ref_newer:hit' '
+	cat >input <<-\EOF &&
+	A:commit-5-7
+	B:commit-2-3
+	EOF
+	echo "ref_newer(A,B):1" >expect &&
+	test_three_modes ref_newer
+'
+
+test_expect_success 'in_merge_bases:hit' '
+	cat >input <<-\EOF &&
+	A:commit-5-7
+	B:commit-8-8
+	EOF
+	echo "in_merge_bases(A,B):1" >expect &&
+	test_three_modes in_merge_bases
+'
+
+test_expect_success 'in_merge_bases:miss' '
+	cat >input <<-\EOF &&
+	A:commit-6-8
+	B:commit-5-9
+	EOF
+	echo "in_merge_bases(A,B):0" >expect &&
+	test_three_modes in_merge_bases
+'
+
+test_expect_success 'is_descendant_of:hit' '
+	cat >input <<-\EOF &&
+	A:commit-5-7
+	X:commit-4-8
+	X:commit-6-6
+	X:commit-1-1
+	EOF
+	echo "is_descendant_of(A,X):1" >expect &&
+	test_three_modes is_descendant_of
+'
+
+test_expect_success 'is_descendant_of:miss' '
+	cat >input <<-\EOF &&
+	A:commit-6-8
+	X:commit-5-9
+	X:commit-4-10
+	X:commit-7-6
+	EOF
+	echo "is_descendant_of(A,X):0" >expect &&
+	test_three_modes is_descendant_of
+'
+
+test_expect_success 'get_merge_bases_many' '
+	cat >input <<-\EOF &&
+	A:commit-5-7
+	X:commit-4-8
+	X:commit-6-6
+	X:commit-8-3
+	EOF
+	{
+		echo "get_merge_bases_many(A,X):" &&
+		git rev-parse commit-5-6 \
+			      commit-4-7 | sort
+	} >expect &&
+	test_three_modes get_merge_bases_many
+'
+
+test_expect_success 'reduce_heads' '
+	cat >input <<-\EOF &&
+	X:commit-1-10
+	X:commit-2-8
+	X:commit-3-6
+	X:commit-4-4
+	X:commit-1-7
+	X:commit-2-5
+	X:commit-3-3
+	X:commit-5-1
+	EOF
+	{
+		echo "reduce_heads(X):" &&
+		git rev-parse commit-5-1 \
+			      commit-4-4 \
+			      commit-3-6 \
+			      commit-2-8 \
+			      commit-1-10 | sort
+	} >expect &&
+	test_three_modes reduce_heads
+'
+
+test_expect_success 'can_all_from_reach:hit' '
+	cat >input <<-\EOF &&
+	X:commit-2-10
+	X:commit-3-9
+	X:commit-4-8
+	X:commit-5-7
+	X:commit-6-6
+	X:commit-7-5
+	X:commit-8-4
+	X:commit-9-3
+	Y:commit-1-9
+	Y:commit-2-8
+	Y:commit-3-7
+	Y:commit-4-6
+	Y:commit-5-5
+	Y:commit-6-4
+	Y:commit-7-3
+	Y:commit-8-1
+	EOF
+	echo "can_all_from_reach(X,Y):1" >expect &&
+	test_three_modes can_all_from_reach
+'
+
+test_expect_success 'can_all_from_reach:miss' '
+	cat >input <<-\EOF &&
+	X:commit-2-10
+	X:commit-3-9
+	X:commit-4-8
+	X:commit-5-7
+	X:commit-6-6
+	X:commit-7-5
+	X:commit-8-4
+	X:commit-9-3
+	Y:commit-1-9
+	Y:commit-2-8
+	Y:commit-3-7
+	Y:commit-4-6
+	Y:commit-5-5
+	Y:commit-6-4
+	Y:commit-8-5
+	EOF
+	echo "can_all_from_reach(X,Y):0" >expect &&
+	test_three_modes can_all_from_reach
+'
+
+test_expect_success 'commit_contains:hit' '
+	cat >input <<-\EOF &&
+	A:commit-7-7
+	X:commit-2-10
+	X:commit-3-9
+	X:commit-4-8
+	X:commit-5-7
+	X:commit-6-6
+	X:commit-7-5
+	X:commit-8-4
+	X:commit-9-3
+	EOF
+	echo "commit_contains(_,A,X,_):1" >expect &&
+	test_three_modes commit_contains &&
+	test_three_modes commit_contains --tag
+'
+
+test_expect_success 'commit_contains:miss' '
+	cat >input <<-\EOF &&
+	A:commit-6-5
+	X:commit-2-10
+	X:commit-3-9
+	X:commit-4-8
+	X:commit-5-7
+	X:commit-6-6
+	X:commit-7-5
+	X:commit-8-4
+	X:commit-9-3
+	EOF
+	echo "commit_contains(_,A,X,_):0" >expect &&
+	test_three_modes commit_contains &&
+	test_three_modes commit_contains --tag
+'
+
+test_done
diff --git a/upload-pack.c b/upload-pack.c
index 4ca052d0b64184..1e498f1188c90e 100644
--- a/upload-pack.c
+++ b/upload-pack.c
@@ -24,13 +24,13 @@
 #include "quote.h"
 #include "upload-pack.h"
 #include "serve.h"
+#include "commit-reach.h"
 
 /* Remember to update object flag allocation in object.h */
 #define THEY_HAVE	(1u << 11)
 #define OUR_REF		(1u << 12)
 #define WANTED		(1u << 13)
 #define COMMON_KNOWN	(1u << 14)
-#define REACHABLE	(1u << 15)
 
 #define SHALLOW		(1u << 16)
 #define NOT_SHALLOW	(1u << 17)
@@ -336,64 +336,16 @@ static int got_oid(const char *hex, struct object_id *oid)
 	return 0;
 }
 
-static int reachable(struct commit *want)
-{
-	struct prio_queue work = { compare_commits_by_commit_date };
-
-	prio_queue_put(&work, want);
-	while (work.nr) {
-		struct commit_list *list;
-		struct commit *commit = prio_queue_get(&work);
-
-		if (commit->object.flags & THEY_HAVE) {
-			want->object.flags |= COMMON_KNOWN;
-			break;
-		}
-		if (!commit->object.parsed)
-			parse_object(the_repository, &commit->object.oid);
-		if (commit->object.flags & REACHABLE)
-			continue;
-		commit->object.flags |= REACHABLE;
-		if (commit->date < oldest_have)
-			continue;
-		for (list = commit->parents; list; list = list->next) {
-			struct commit *parent = list->item;
-			if (!(parent->object.flags & REACHABLE))
-				prio_queue_put(&work, parent);
-		}
-	}
-	want->object.flags |= REACHABLE;
-	clear_commit_marks(want, REACHABLE);
-	clear_prio_queue(&work);
-	return (want->object.flags & COMMON_KNOWN);
-}
-
 static int ok_to_give_up(void)
 {
-	int i;
+	uint32_t min_generation = GENERATION_NUMBER_ZERO;
 
 	if (!have_obj.nr)
 		return 0;
 
-	for (i = 0; i < want_obj.nr; i++) {
-		struct object *want = want_obj.objects[i].item;
-
-		if (want->flags & COMMON_KNOWN)
-			continue;
-		want = deref_tag(the_repository, want, "a want line", 0);
-		if (!want || want->type != OBJ_COMMIT) {
-			/* no way to tell if this is reachable by
-			 * looking at the ancestry chain alone, so
-			 * leave a note to ourselves not to worry about
-			 * this object anymore.
-			 */
-			want_obj.objects[i].item->flags |= COMMON_KNOWN;
-			continue;
-		}
-		if (!reachable((struct commit *)want))
-			return 0;
-	}
-	return 1;
+	return can_all_from_reach_with_flag(&want_obj, THEY_HAVE,
+					    COMMON_KNOWN, oldest_have,
+					    min_generation);
 }
 
 static int get_common_commits(void)