@@ -99,6 +99,8 @@ typedef struct _gc_stats {
     uint64_t collections;
     uint64_t object_visits;
     uint64_t objects_collected;
+    uint64_t objects_transitively_reachable;
+    uint64_t objects_not_transitively_reachable;
 } GCStats;
 
 typedef struct _uop_stats {
 
@@ -75,6 +75,7 @@ typedef struct _PyInterpreterFrame {
     _PyStackRef *stackpointer;
     uint16_t return_offset;  /* Only relevant during a function call */
     char owner;
+    char visited;
     /* Locals and stack */
     _PyStackRef localsplus[1];
 } _PyInterpreterFrame;
@@ -207,6 +208,7 @@ _PyFrame_Initialize(
 #endif
     frame->return_offset = 0;
     frame->owner = FRAME_OWNED_BY_THREAD;
+    frame->visited = 0;
 
     for (int i = null_locals_from; i < code->co_nlocalsplus; i++) {
         frame->localsplus[i] = PyStackRef_NULL;
@@ -389,6 +391,7 @@ _PyFrame_PushTrampolineUnchecked(PyThreadState *tstate, PyCodeObject *code, int
     frame->instr_ptr = _PyCode_CODE(code);
 #endif
     frame->owner = FRAME_OWNED_BY_THREAD;
+    frame->visited = 0;
     frame->return_offset = 0;
 
 #ifdef Py_GIL_DISABLED
 
@@ -10,11 +10,11 @@ extern "C" {
 
 /* GC information is stored BEFORE the object structure. */
 typedef struct {
-    // Pointer to next object in the list.
+    // Tagged pointer to next object in the list.
     // 0 means the object is not tracked
     uintptr_t _gc_next;
 
-    // Pointer to previous object in the list.
+    // Tagged pointer to previous object in the list.
     // Lowest two bits are used for flags documented later.
     uintptr_t _gc_prev;
 } PyGC_Head;
@@ -284,6 +284,11 @@ struct gc_generation_stats {
     Py_ssize_t uncollectable;
 };
 
+enum _GCPhase {
+    GC_PHASE_MARK = 0,
+    GC_PHASE_COLLECT = 1
+};
+
 struct _gc_runtime_state {
     /* List of objects that still need to be cleaned up, singly linked
      * via their gc headers' gc_prev pointers.  */
@@ -311,6 +316,7 @@ struct _gc_runtime_state {
     Py_ssize_t work_to_do;
     /* Which of the old spaces is the visited space */
     int visited_space;
+    int phase;
 
 #ifdef Py_GIL_DISABLED
     /* This is the number of objects that survived the last full
 
@@ -471,8 +471,8 @@ static inline void _PyObject_GC_TRACK(
     PyGC_Head *last = (PyGC_Head*)(generation0->_gc_prev);
     _PyGCHead_SET_NEXT(last, gc);
     _PyGCHead_SET_PREV(gc, last);
-    /* Young objects will be moved into the visited space during GC, so set the bit here */
-    gc->_gc_next = ((uintptr_t)generation0) | (uintptr_t)interp->gc.visited_space;
+    uintptr_t not_visited = 1 ^ interp->gc.visited_space;
+    gc->_gc_next = ((uintptr_t)generation0) | not_visited;
     generation0->_gc_prev = (uintptr_t)gc;
 #endif
 }
 
@@ -137,6 +137,7 @@ extern PyTypeObject _PyExc_MemoryError;
                 { .threshold = 0, }, \
             }, \
             .work_to_do = -5000, \
+            .phase = GC_PHASE_MARK, \
         }, \
         .qsbr = { \
             .wr_seq = QSBR_INITIAL, \
 
@@ -477,6 +477,45 @@ specifically in a generation by calling `gc.collect(generation=NUM)`.
 ```
 
 
+Optimization: visiting reachable objects
+========================================
+
+An object cannot be garbage if it can be reached.
+
+To avoid having to identify reference cycles across the whole heap, we can
+reduce the amount of work done considerably by first moving most reachable objects
+to the `visited` space. Empirically, most reachable objects can be reached from a
+small set of global objects and local variables.
+This step does much less work per object, so reduces the time spent
+performing garbage collection by at least half.
+
+> [!NOTE]
+> Objects that are not determined to be reachable by this pass are not necessarily
+> unreachable. We still need to perform the main algorithm to determine which objects
+> are actually unreachable.
+We use the same technique of forming a transitive closure as the incremental
+collector does to find reachable objects, seeding the list with some global
+objects and the currently executing frames.
+
+This phase moves objects to the `visited` space, as follows:
+
+1. All objects directly referred to by any builtin class, the `sys` module, the `builtins`
+module and all objects directly referred to from stack frames are added to a working
+set of reachable objects.
+2. Until this working set is empty:
+   1. Pop an object from the set and move it to the `visited` space
+   2. For each object directly reachable from that object:
+      * If it is not already in `visited` space and it is a GC object,
+        add it to the working set
+
+
+Before each increment of collection is performed, the stacks are scanned
+to check for any new stack frames that have been created since the last
+increment. All objects directly referred to from those stack frames are
+added to the working set.
+Then the above algorithm is repeated, starting from step 2.
+
+
 Optimization: reusing fields to save memory
 ===========================================
 
 
@@ -123,9 +123,9 @@ def get_pooled_int(value):
     xml_filename = 'refleak-xml.tmp'
     result = None
     dash_R_cleanup(fs, ps, pic, zdc, abcs)
-    support.gc_collect()
 
     for i in rep_range:
+        support.gc_collect()
         current = refleak_helper._hunting_for_refleaks
         refleak_helper._hunting_for_refleaks = True
         try:
 
@@ -31,6 +31,11 @@ def __new__(cls, *args, **kwargs):
         return C
     ContainerNoGC = None
 
+try:
+    import _testinternalcapi
+except ImportError:
+    _testinternalcapi = None
+
 ### Support code
 ###############################################################################
 
@@ -1130,6 +1135,7 @@ def setUp(self):
     def tearDown(self):
         gc.disable()
 
+    @unittest.skipIf(_testinternalcapi is None, "requires _testinternalcapi")
     @requires_gil_enabled("Free threading does not support incremental GC")
     # Use small increments to emulate longer running process in a shorter time
     @gc_threshold(200, 10)
@@ -1167,20 +1173,15 @@ def make_ll(depth):
         enabled = gc.isenabled()
         gc.enable()
         olds = []
+        initial_heap_size = _testinternalcapi.get_tracked_heap_size()
         for i in range(20_000):
             newhead = make_ll(20)
             count += 20
             newhead.surprise = head
             olds.append(newhead)
             if len(olds) == 20:
-                stats = gc.get_stats()
-                young = stats[0]
-                incremental = stats[1]
-                old = stats[2]
-                collected = young['collected'] + incremental['collected'] + old['collected']
-                count += CORRECTION
-                live = count - collected
-                self.assertLess(live, 25000)
+                new_objects = _testinternalcapi.get_tracked_heap_size() - initial_heap_size
+                self.assertLess(new_objects, 27_000, f"Heap growing. Reached limit after {i} iterations")
                 del olds[:]
         if not enabled:
             gc.disable()
@@ -1322,7 +1323,8 @@ def test_refcount_errors(self):
             from test.support import gc_collect, SuppressCrashReport
 
             a = [1, 2, 3]
-            b = [a]
+            b = [a, a]
+            a.append(b)
 
             # Avoid coredump when Py_FatalError() calls abort()
             SuppressCrashReport().__enter__()
@@ -1332,6 +1334,8 @@ def test_refcount_errors(self):
             # (to avoid deallocating it):
             import ctypes
             ctypes.pythonapi.Py_DecRef(ctypes.py_object(a))
+            del a
+            del b
 
             # The garbage collector should now have a fatal error
             # when it reaches the broken object
@@ -1360,7 +1364,7 @@ def test_refcount_errors(self):
         self.assertRegex(stderr,
             br'object type name: list')
         self.assertRegex(stderr,
-            br'object repr     : \[1, 2, 3\]')
+            br'object repr     : \[1, 2, 3, \[\[...\], \[...\]\]\]')
 
 
 class GCTogglingTests(unittest.TestCase):
 
@@ -0,0 +1,4 @@
+Add a marking phase to the GC. All objects that can be transitively reached
+from builtin modules or the stacks are marked as reachable before cycle
+detection. This reduces the amount of work done by the GC by approximately
+half.
@@ -2076,6 +2076,11 @@ has_deferred_refcount(PyObject *self, PyObject *op)
     return PyBool_FromLong(_PyObject_HasDeferredRefcount(op));
 }
 
+static PyObject *
+get_tracked_heap_size(PyObject *self, PyObject *Py_UNUSED(ignored))
+{
+    return PyLong_FromInt64(PyInterpreterState_Get()->gc.heap_size);
+}
 
 static PyMethodDef module_functions[] = {
     {"get_configs", get_configs, METH_NOARGS},
@@ -2174,6 +2179,7 @@ static PyMethodDef module_functions[] = {
     {"get_static_builtin_types", get_static_builtin_types, METH_NOARGS},
     {"identify_type_slot_wrappers", identify_type_slot_wrappers, METH_NOARGS},
     {"has_deferred_refcount", has_deferred_refcount, METH_O},
+    {"get_tracked_heap_size", get_tracked_heap_size, METH_NOARGS},
     {NULL, NULL} /* sentinel */
 };