boehm-gc/backgraph.c - native_client/nacl-gcc - Git at Google

 /*
  * Copyright (c) 2001 by Hewlett-Packard Company. All rights reserved.
  *
  * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY EXPRESSED
  * OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.
  *
  * Permission is hereby granted to use or copy this program
  * for any purpose,  provided the above notices are retained on all copies.
  * Permission to modify the code and to distribute modified code is granted,
  * provided the above notices are retained, and a notice that the code was
  * modified is included with the above copyright notice.
  *
  */

 /*
  * This implements a full, though not well-tuned, representation of the
  * backwards points-to graph.  This is used to test for non-GC-robust
  * data structures; the code is not used during normal garbage collection.
  *
  * One restriction is that we drop all back-edges from nodes with very
  * high in-degree, and simply add them add them to a list of such
  * nodes.  They are then treated as permanent roots.  Id this by itself
  * doesn't introduce a space leak, then such nodes can't contribute to
  * a growing space leak.
  */

 #include "gc.h"	/* For configuration information. */

 #ifdef MAKE_BACK_GRAPH

 #define MAX_IN	10	/* Maximum in-degree we handle directly */

 #include "private/dbg_mlc.h"
 #include <unistd.h>

 #if !defined(DBG_HDRS_ALL) || (ALIGNMENT != CPP_WORDSZ/8) || !defined(UNIX_LIKE)
 # error Configuration doesnt support MAKE_BACK_GRAPH
 #endif

 /* We store single back pointers directly in the object's oh_bg_ptr field.   */
 /* If there is more than one ptr to an object, we store q | FLAG_MANY, 	     */
 /* where q is a pointer to a back_edges object.				     */
 /* Every once in a while we use a back_edges object even for a single	     */
 /* pointer, since we need the other fields in the back_edges structure to    */
 /* be present in some fraction of the objects.  Otherwise we get serious     */
 /* performance issues.							     */
 #define FLAG_MANY 2

 typedef struct back_edges_struct {
   word n_edges;	/* Number of edges, including those in continuation	*/
   		/* structures.						*/
   unsigned short flags;
 #	define RETAIN 1	/* Directly points to a reachable object;	*/
   			/* retain for next GC.				*/
   unsigned short height_gc_no;
   		/* If height > 0, then the GC_gc_no value when it	*/
   		/* was computed.  If it was computed this cycle, then	*/
   		/* it is current.  If it was computed during the	*/
   		/* last cycle, then it represents the old height,	*/
   		/* which is only saved for live objects referenced by	*/
   		/* dead ones.  This may grow due to refs from newly	*/
 		/* dead objects.				        */
   signed_word height;
   		/* Longest path through unreachable nodes to this node	*/
   		/* that we found using depth first search.		*/

 #   define HEIGHT_UNKNOWN ((signed_word)(-2))
 #   define HEIGHT_IN_PROGRESS ((signed_word)(-1))
   ptr_t edges[MAX_IN];
   struct back_edges_struct *cont;
   		/* Pointer to continuation structure; we use only the	*/
   		/* edges field in the continuation.			*/
   		/* also used as free list link.				*/
 } back_edges;

 /* Allocate a new back edge structure.  Should be more sophisticated	*/
 /* if this were production code.					*/
 #define MAX_BACK_EDGE_STRUCTS 100000
 static back_edges *back_edge_space = 0;
 int GC_n_back_edge_structs = 0;	/* Serves as pointer to never used	*/
 				/* back_edges space.			*/
 static back_edges *avail_back_edges = 0;
 				/* Pointer to free list of deallocated	*/
 				/* back_edges structures.		*/

 static back_edges * new_back_edges(void)
 {
   if (0 == back_edge_space) {
     back_edge_space = (back_edges *)
 	    		GET_MEM(MAX_BACK_EDGE_STRUCTS*sizeof(back_edges));
   }
   if (0 != avail_back_edges) {
     back_edges * result = avail_back_edges;
     avail_back_edges = result -> cont;
     result -> cont = 0;
     return result;
   }
   if (GC_n_back_edge_structs >= MAX_BACK_EDGE_STRUCTS - 1) {
     ABORT("needed too much space for back edges: adjust "
 	  "MAX_BACK_EDGE_STRUCTS");
   }
   return back_edge_space + (GC_n_back_edge_structs++);
 }

 /* Deallocate p and its associated continuation structures.	*/
 static void deallocate_back_edges(back_edges *p)
 {
    back_edges *last = p;

    while (0 != last -> cont) last = last -> cont;
    last -> cont = avail_back_edges;
    avail_back_edges = p;
 }

 /* Table of objects that are currently on the depth-first search	*/
 /* stack.  Only objects with in-degree one are in this table.		*/
 /* Other objects are identified using HEIGHT_IN_PROGRESS.		*/
 /* FIXME: This data structure NEEDS IMPROVEMENT.			*/
 #define INITIAL_IN_PROGRESS 10000
 static ptr_t * in_progress_space = 0;
 static size_t in_progress_size = 0;
 static size_t n_in_progress = 0;

 static void push_in_progress(ptr_t p)
 {
   if (n_in_progress >= in_progress_size)
     if (in_progress_size == 0) {
       in_progress_size = INITIAL_IN_PROGRESS;
       in_progress_space = (ptr_t *)GET_MEM(in_progress_size * sizeof(ptr_t));
     } else {
       ptr_t * new_in_progress_space;
       in_progress_size *= 2;
       new_in_progress_space = (ptr_t *)
 	      			GET_MEM(in_progress_size * sizeof(ptr_t));
       BCOPY(in_progress_space, new_in_progress_space,
 	    n_in_progress * sizeof(ptr_t));
       in_progress_space = new_in_progress_space;
       /* FIXME: This just drops the old space.	*/
     }
   if (in_progress_space == 0)
       ABORT("MAKE_BACK_GRAPH: Out of in-progress space: "
 	    "Huge linear data structure?");
   in_progress_space[n_in_progress++] = p;
 }

 static GC_bool is_in_progress(ptr_t p)
 {
   int i;
   for (i = 0; i < n_in_progress; ++i) {
     if (in_progress_space[i] == p) return TRUE;
   }
   return FALSE;
 }

 static void pop_in_progress(ptr_t p)
 {
   --n_in_progress;
   GC_ASSERT(in_progress_space[n_in_progress] == p);
 }

 #define GET_OH_BG_PTR(p) \
 		(ptr_t)REVEAL_POINTER(((oh *)(p)) -> oh_bg_ptr)
 #define SET_OH_BG_PTR(p,q) (((oh *)(p)) -> oh_bg_ptr) = HIDE_POINTER(q)

 /* Execute s once for each predecessor q of p in the points-to graph. 	*/
 /* s should be a bracketed statement.  We declare q.			*/
 #define FOR_EACH_PRED(q, p, s) \
   { \
     ptr_t q = GET_OH_BG_PTR(p); \
     if (!((word)q & FLAG_MANY)) { \
       if (q && !((word)q & 1)) s \
 	      /* !((word)q & 1) checks for a misnterpreted freelist link */ \
     } else { \
       back_edges *orig_be_ = (back_edges *)((word)q & ~FLAG_MANY); \
       back_edges *be_ = orig_be_; \
       int total_, local_; \
       int n_edges_ = be_ -> n_edges; \
       for (total_ = 0, local_ = 0; total_ < n_edges_; ++local_, ++total_) { \
 	  if (local_ == MAX_IN) { \
 	      be_ = be_ -> cont; \
 	      local_ = 0; \
 	  } \
 	  q = be_ -> edges[local_]; s \
       } \
     } \
   }

 /* Ensure that p has a back_edges structure associated with it.	*/
 static void ensure_struct(ptr_t p)
 {
   ptr_t old_back_ptr = GET_OH_BG_PTR(p);

   if (!((word)old_back_ptr & FLAG_MANY)) {
     back_edges *be = new_back_edges();
     be -> flags = 0;
     if (0 == old_back_ptr) {
       be -> n_edges = 0;
     } else {
       be -> n_edges = 1;
       be -> edges[0] = old_back_ptr;
     }
     be -> height = HEIGHT_UNKNOWN;
     be -> height_gc_no = GC_gc_no - 1;
     GC_ASSERT(be >= back_edge_space);
     SET_OH_BG_PTR(p, (word)be | FLAG_MANY);
   }
 }

 /* Add the (forward) edge from p to q to the backward graph.  Both p	*/
 /* q are pointers to the object base, i.e. pointers to an oh.		*/
 static void add_edge(ptr_t p,  ptr_t q)
 {
     ptr_t old_back_ptr = GET_OH_BG_PTR(q);
     back_edges * be, *be_cont;
     word i;
     static unsigned random_number = 13;
 #   define GOT_LUCKY_NUMBER (((++random_number) & 0x7f) == 0)
       /* A not very random number we use to occasionally allocate a	*/
       /* back_edges structure even for a single backward edge.  This	*/
       /* prevents us from repeatedly tracing back through very long	*/
       /* chains, since we will have some place to store height and	*/
       /* in_progress flags along the way.				*/

     GC_ASSERT(p == GC_base(p) && q == GC_base(q));
     if (!GC_HAS_DEBUG_INFO(q) || !GC_HAS_DEBUG_INFO(p)) {
       /* This is really a misinterpreted free list link, since we saw */
       /* a pointer to a free list.  Dont overwrite it!		      */
       return;
     }
     if (0 == old_back_ptr) {
 	SET_OH_BG_PTR(q, p);
 	if (GOT_LUCKY_NUMBER) ensure_struct(q);
 	return;
     }
     /* Check whether it was already in the list of predecessors. */
       FOR_EACH_PRED(pred, q, { if (p == pred) return; });
     ensure_struct(q);
     old_back_ptr = GET_OH_BG_PTR(q);
     be = (back_edges *)((word)old_back_ptr & ~FLAG_MANY);
     for (i = be -> n_edges, be_cont = be; i > MAX_IN;
 	be_cont = be_cont -> cont, i -= MAX_IN) {}
     if (i == MAX_IN) {
 	be_cont -> cont = new_back_edges();
 	be_cont = be_cont -> cont;
 	i = 0;
     }
     be_cont -> edges[i] = p;
     be -> n_edges++;
     if (be -> n_edges == 100) {
 #       if 0
 	  if (GC_print_stats) {
 	    GC_err_printf0("The following object has in-degree >= 100:\n");
 	    GC_print_heap_obj(q);
 	  }
 #	endif
     }
 }

 typedef void (*per_object_func)(ptr_t p, word n_words, word gc_descr);

 static void per_object_helper(struct hblk *h, word fn)
 {
   hdr * hhdr = HDR(h);
   word sz = hhdr -> hb_sz;
   word descr = hhdr -> hb_descr;
   per_object_func f = (per_object_func)fn;
   int i = 0;

   do {
     f((ptr_t)(h -> hb_body + i), sz, descr);
     i += sz;
   } while (i + sz <= BYTES_TO_WORDS(HBLKSIZE));
 }

 void GC_apply_to_each_object(per_object_func f)
 {
   GC_apply_to_all_blocks(per_object_helper, (word)f);
 }

 static void reset_back_edge(ptr_t p, word n_words, word gc_descr)
 {
   /* Skip any free list links, or dropped blocks */
   if (GC_HAS_DEBUG_INFO(p)) {
     ptr_t old_back_ptr = GET_OH_BG_PTR(p);
     if ((word)old_back_ptr & FLAG_MANY) {
       back_edges *be = (back_edges *)((word)old_back_ptr & ~FLAG_MANY);
       if (!(be -> flags & RETAIN)) {
 	deallocate_back_edges(be);
         SET_OH_BG_PTR(p, 0);
       } else {
         word *currentp;

 	GC_ASSERT(GC_is_marked(p));

 	/* Back edges may point to objects that will not be retained. 	*/
 	/* Delete them for now, but remember the height.		*/
 	/* Some will be added back at next GC.				*/
 	  be -> n_edges = 0;
 	  if (0 != be -> cont) {
 	    deallocate_back_edges(be -> cont);
 	    be -> cont = 0;
 	  }

 	GC_ASSERT(GC_is_marked(p));

 	/* We only retain things for one GC cycle at a time.		*/
 	  be -> flags &= ~RETAIN;
       }
     } else /* Simple back pointer */ {
       /* Clear to avoid dangling pointer. */
       SET_OH_BG_PTR(p, 0);
     }
   }
 }

 static void add_back_edges(ptr_t p, word n_words, word gc_descr)
 {
   word *currentp = (word *)(p + sizeof(oh));

   /* For now, fix up non-length descriptors conservatively.	*/
     if((gc_descr & GC_DS_TAGS) != GC_DS_LENGTH) {
       gc_descr = WORDS_TO_BYTES(n_words);
     }
   while (currentp < (word *)(p + gc_descr)) {
     word current = *currentp++;
     FIXUP_POINTER(current);
     if (current >= (word)GC_least_plausible_heap_addr &&
 	current <= (word)GC_greatest_plausible_heap_addr) {
        ptr_t target = GC_base((GC_PTR)current);
        if (0 != target) {
 	 add_edge(p, target);
        }
     }
   }
 }

 /* Rebuild the representation of the backward reachability graph.	*/
 /* Does not examine mark bits.  Can be called before GC.		*/
 void GC_build_back_graph(void)
 {
   GC_apply_to_each_object(add_back_edges);
 }

 /* Return an approximation to the length of the longest simple path	*/
 /* through unreachable objects to p.  We refer to this as the height	*/
 /* of p.								*/
 static word backwards_height(ptr_t p)
 {
   word result;
   ptr_t back_ptr = GET_OH_BG_PTR(p);
   back_edges *be;

   if (0 == back_ptr) return 1;
   if (!((word)back_ptr & FLAG_MANY)) {
     if (is_in_progress(p)) return 0;  /* DFS back edge, i.e. we followed  */
     				      /* an edge to an object already	  */
     				      /* on our stack: ignore		  */
     push_in_progress(p);
     result = backwards_height(back_ptr)+1;
     pop_in_progress(p);
     return result;
   }
   be = (back_edges *)((word)back_ptr & ~FLAG_MANY);
   if (be -> height >= 0 && be -> height_gc_no == GC_gc_no)
       return be -> height;
   /* Ignore back edges in DFS */
     if (be -> height == HEIGHT_IN_PROGRESS) return 0;
   result = (be -> height > 0? be -> height : 1);
   be -> height = HEIGHT_IN_PROGRESS;
   FOR_EACH_PRED(q, p, {
     word this_height;
     if (GC_is_marked(q) && !(FLAG_MANY & (word)GET_OH_BG_PTR(p))) {
       if (GC_print_stats)
 	  GC_printf2("Found bogus pointer from 0x%lx to 0x%lx\n", q, p);
 	/* Reachable object "points to" unreachable one.		*/
 	/* Could be caused by our lax treatment of GC descriptors.	*/
       this_height = 1;
     } else {
         this_height = backwards_height(q);
     }
     if (this_height >= result) result = this_height + 1;
   });
   be -> height = result;
   be -> height_gc_no = GC_gc_no;
   return result;
 }

 word GC_max_height;
 ptr_t GC_deepest_obj;

 /* Compute the maximum height of every unreachable predecessor p of  a 	*/
 /* reachable object.  Arrange to save the heights of all such objects p	*/
 /* so that they can be used in calculating the height of objects in the	*/
 /* next GC.								*/
 /* Set GC_max_height to be the maximum height we encounter, and 	*/
 /* GC_deepest_obj to be the corresponding object.			*/
 static void update_max_height(ptr_t p, word n_words, word gc_descr)
 {
   if (GC_is_marked(p) && GC_HAS_DEBUG_INFO(p)) {
     int i;
     word p_height = 0;
     ptr_t p_deepest_obj = 0;
     ptr_t back_ptr;
     back_edges *be = 0;

     /* If we remembered a height last time, use it as a minimum.	*/
     /* It may have increased due to newly unreachable chains pointing	*/
     /* to p, but it can't have decreased.				*/
     back_ptr = GET_OH_BG_PTR(p);
     if (0 != back_ptr && ((word)back_ptr & FLAG_MANY)) {
       be = (back_edges *)((word)back_ptr & ~FLAG_MANY);
       if (be -> height != HEIGHT_UNKNOWN) p_height = be -> height;
     }
     FOR_EACH_PRED(q, p, {
       if (!GC_is_marked(q) && GC_HAS_DEBUG_INFO(q)) {
         word q_height;

         q_height = backwards_height(q);
 	if (q_height > p_height) {
 	  p_height = q_height;
 	  p_deepest_obj = q;
 	}
       }
     });
     if (p_height > 0) {
       /* Remember the height for next time. */
 	if (be == 0) {
     	  ensure_struct(p);
     	  back_ptr = GET_OH_BG_PTR(p);
   	  be = (back_edges *)((word)back_ptr & ~FLAG_MANY);
 	}
 	be -> flags |= RETAIN;
 	be -> height = p_height;
 	be -> height_gc_no = GC_gc_no;
     }
     if (p_height > GC_max_height) {
 	GC_max_height = p_height;
 	GC_deepest_obj = p_deepest_obj;
     }
   }
 }

 word GC_max_max_height = 0;

 void GC_traverse_back_graph(void)
 {
   GC_max_height = 0;
   GC_apply_to_each_object(update_max_height);
 }

 void GC_print_back_graph_stats(void)
 {
   GC_printf2("Maximum backwards height of reachable objects at GC %lu is %ld\n",
 	     (unsigned long) GC_gc_no, GC_max_height);
   if (GC_max_height > GC_max_max_height) {
     GC_max_max_height = GC_max_height;
     GC_printf0("The following unreachable object is last in a longest chain "
 	       "of unreachable objects:\n");
     GC_print_heap_obj(GC_deepest_obj);
   }
   if (GC_print_stats) {
     GC_printf1("Needed max total of %ld back-edge structs\n",
 	       GC_n_back_edge_structs);
   }
   GC_apply_to_each_object(reset_back_edge);
   GC_deepest_obj = 0;
 }

 #endif /* MAKE_BACK_GRAPH */
	/*
	* Copyright (c) 2001 by Hewlett-Packard Company. All rights reserved.
	*
	* THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY EXPRESSED
	* OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
	*
	* Permission is hereby granted to use or copy this program
	* for any purpose, provided the above notices are retained on all copies.
	* Permission to modify the code and to distribute modified code is granted,
	* provided the above notices are retained, and a notice that the code was
	* modified is included with the above copyright notice.
	*
	*/

	/*
	* This implements a full, though not well-tuned, representation of the
	* backwards points-to graph. This is used to test for non-GC-robust
	* data structures; the code is not used during normal garbage collection.
	*
	* One restriction is that we drop all back-edges from nodes with very
	* high in-degree, and simply add them add them to a list of such
	* nodes. They are then treated as permanent roots. Id this by itself
	* doesn't introduce a space leak, then such nodes can't contribute to
	* a growing space leak.
	*/

	#include "gc.h" /* For configuration information. */

	#ifdef MAKE_BACK_GRAPH

	#define MAX_IN 10 /* Maximum in-degree we handle directly */

	#include "private/dbg_mlc.h"
	#include <unistd.h>

	#if !defined(DBG_HDRS_ALL) \|\| (ALIGNMENT != CPP_WORDSZ/8) \|\| !defined(UNIX_LIKE)
	# error Configuration doesnt support MAKE_BACK_GRAPH
	#endif

	/* We store single back pointers directly in the object's oh_bg_ptr field. */
	/* If there is more than one ptr to an object, we store q \| FLAG_MANY, */
	/* where q is a pointer to a back_edges object. */
	/* Every once in a while we use a back_edges object even for a single */
	/* pointer, since we need the other fields in the back_edges structure to */
	/* be present in some fraction of the objects. Otherwise we get serious */
	/* performance issues. */
	#define FLAG_MANY 2

	typedef struct back_edges_struct {
	word n_edges; /* Number of edges, including those in continuation */
	/* structures. */
	unsigned short flags;
	# define RETAIN 1 /* Directly points to a reachable object; */
	/* retain for next GC. */
	unsigned short height_gc_no;
	/* If height > 0, then the GC_gc_no value when it */
	/* was computed. If it was computed this cycle, then */
	/* it is current. If it was computed during the */
	/* last cycle, then it represents the old height, */
	/* which is only saved for live objects referenced by */
	/* dead ones. This may grow due to refs from newly */
	/* dead objects. */
	signed_word height;
	/* Longest path through unreachable nodes to this node */
	/* that we found using depth first search. */

	# define HEIGHT_UNKNOWN ((signed_word)(-2))
	# define HEIGHT_IN_PROGRESS ((signed_word)(-1))
	ptr_t edges[MAX_IN];
	struct back_edges_struct *cont;
	/* Pointer to continuation structure; we use only the */
	/* edges field in the continuation. */
	/* also used as free list link. */
	} back_edges;

	/* Allocate a new back edge structure. Should be more sophisticated */
	/* if this were production code. */
	#define MAX_BACK_EDGE_STRUCTS 100000
	static back_edges *back_edge_space = 0;
	int GC_n_back_edge_structs = 0; /* Serves as pointer to never used */
	/* back_edges space. */
	static back_edges *avail_back_edges = 0;
	/* Pointer to free list of deallocated */
	/* back_edges structures. */

	static back_edges * new_back_edges(void)
	{
	if (0 == back_edge_space) {
	back_edge_space = (back_edges *)
	GET_MEM(MAX_BACK_EDGE_STRUCTS*sizeof(back_edges));
	}
	if (0 != avail_back_edges) {
	back_edges * result = avail_back_edges;
	avail_back_edges = result -> cont;
	result -> cont = 0;
	return result;
	}
	if (GC_n_back_edge_structs >= MAX_BACK_EDGE_STRUCTS - 1) {
	ABORT("needed too much space for back edges: adjust "
	"MAX_BACK_EDGE_STRUCTS");
	}
	return back_edge_space + (GC_n_back_edge_structs++);
	}

	/* Deallocate p and its associated continuation structures. */
	static void deallocate_back_edges(back_edges *p)
	{
	back_edges *last = p;

	while (0 != last -> cont) last = last -> cont;
	last -> cont = avail_back_edges;
	avail_back_edges = p;
	}

	/* Table of objects that are currently on the depth-first search */
	/* stack. Only objects with in-degree one are in this table. */
	/* Other objects are identified using HEIGHT_IN_PROGRESS. */
	/* FIXME: This data structure NEEDS IMPROVEMENT. */
	#define INITIAL_IN_PROGRESS 10000
	static ptr_t * in_progress_space = 0;
	static size_t in_progress_size = 0;
	static size_t n_in_progress = 0;

	static void push_in_progress(ptr_t p)
	{
	if (n_in_progress >= in_progress_size)
	if (in_progress_size == 0) {
	in_progress_size = INITIAL_IN_PROGRESS;
	in_progress_space = (ptr_t )GET_MEM(in_progress_size sizeof(ptr_t));
	} else {
	ptr_t * new_in_progress_space;
	in_progress_size *= 2;
	new_in_progress_space = (ptr_t *)
	GET_MEM(in_progress_size * sizeof(ptr_t));
	BCOPY(in_progress_space, new_in_progress_space,
	n_in_progress * sizeof(ptr_t));
	in_progress_space = new_in_progress_space;
	/* FIXME: This just drops the old space. */
	}
	if (in_progress_space == 0)
	ABORT("MAKE_BACK_GRAPH: Out of in-progress space: "
	"Huge linear data structure?");
	in_progress_space[n_in_progress++] = p;
	}

	static GC_bool is_in_progress(ptr_t p)
	{
	int i;
	for (i = 0; i < n_in_progress; ++i) {
	if (in_progress_space[i] == p) return TRUE;
	}
	return FALSE;
	}

	static void pop_in_progress(ptr_t p)
	{
	--n_in_progress;
	GC_ASSERT(in_progress_space[n_in_progress] == p);
	}

	#define GET_OH_BG_PTR(p) \
	(ptr_t)REVEAL_POINTER(((oh *)(p)) -> oh_bg_ptr)
	#define SET_OH_BG_PTR(p,q) (((oh *)(p)) -> oh_bg_ptr) = HIDE_POINTER(q)

	/* Execute s once for each predecessor q of p in the points-to graph. */
	/* s should be a bracketed statement. We declare q. */
	#define FOR_EACH_PRED(q, p, s) \
	{ \
	ptr_t q = GET_OH_BG_PTR(p); \
	if (!((word)q & FLAG_MANY)) { \
	if (q && !((word)q & 1)) s \
	/* !((word)q & 1) checks for a misnterpreted freelist link */ \
	} else { \
	back_edges orig_be_ = (back_edges )((word)q & ~FLAG_MANY); \
	back_edges *be_ = orig_be_; \
	int total_, local_; \
	int n_edges_ = be_ -> n_edges; \
	for (total_ = 0, local_ = 0; total_ < n_edges_; ++local_, ++total_) { \
	if (local_ == MAX_IN) { \
	be_ = be_ -> cont; \
	local_ = 0; \
	} \
	q = be_ -> edges[local_]; s \
	} \
	} \
	}

	/* Ensure that p has a back_edges structure associated with it. */
	static void ensure_struct(ptr_t p)
	{
	ptr_t old_back_ptr = GET_OH_BG_PTR(p);

	if (!((word)old_back_ptr & FLAG_MANY)) {
	back_edges *be = new_back_edges();
	be -> flags = 0;
	if (0 == old_back_ptr) {
	be -> n_edges = 0;
	} else {
	be -> n_edges = 1;
	be -> edges[0] = old_back_ptr;
	}
	be -> height = HEIGHT_UNKNOWN;
	be -> height_gc_no = GC_gc_no - 1;
	GC_ASSERT(be >= back_edge_space);
	SET_OH_BG_PTR(p, (word)be \| FLAG_MANY);
	}
	}

	/* Add the (forward) edge from p to q to the backward graph. Both p */
	/* q are pointers to the object base, i.e. pointers to an oh. */
	static void add_edge(ptr_t p, ptr_t q)
	{
	ptr_t old_back_ptr = GET_OH_BG_PTR(q);
	back_edges * be, *be_cont;
	word i;
	static unsigned random_number = 13;
	# define GOT_LUCKY_NUMBER (((++random_number) & 0x7f) == 0)
	/* A not very random number we use to occasionally allocate a */
	/* back_edges structure even for a single backward edge. This */
	/* prevents us from repeatedly tracing back through very long */
	/* chains, since we will have some place to store height and */
	/* in_progress flags along the way. */

	GC_ASSERT(p == GC_base(p) && q == GC_base(q));
	if (!GC_HAS_DEBUG_INFO(q) \|\| !GC_HAS_DEBUG_INFO(p)) {
	/* This is really a misinterpreted free list link, since we saw */
	/* a pointer to a free list. Dont overwrite it! */
	return;
	}
	if (0 == old_back_ptr) {
	SET_OH_BG_PTR(q, p);
	if (GOT_LUCKY_NUMBER) ensure_struct(q);
	return;
	}
	/* Check whether it was already in the list of predecessors. */
	FOR_EACH_PRED(pred, q, { if (p == pred) return; });
	ensure_struct(q);
	old_back_ptr = GET_OH_BG_PTR(q);
	be = (back_edges *)((word)old_back_ptr & ~FLAG_MANY);
	for (i = be -> n_edges, be_cont = be; i > MAX_IN;
	be_cont = be_cont -> cont, i -= MAX_IN) {}
	if (i == MAX_IN) {
	be_cont -> cont = new_back_edges();
	be_cont = be_cont -> cont;
	i = 0;
	}
	be_cont -> edges[i] = p;
	be -> n_edges++;
	if (be -> n_edges == 100) {
	# if 0
	if (GC_print_stats) {
	GC_err_printf0("The following object has in-degree >= 100:\n");
	GC_print_heap_obj(q);
	}
	# endif
	}
	}

	typedef void (*per_object_func)(ptr_t p, word n_words, word gc_descr);

	static void per_object_helper(struct hblk *h, word fn)
	{
	hdr * hhdr = HDR(h);
	word sz = hhdr -> hb_sz;
	word descr = hhdr -> hb_descr;
	per_object_func f = (per_object_func)fn;
	int i = 0;

	do {
	f((ptr_t)(h -> hb_body + i), sz, descr);
	i += sz;
	} while (i + sz <= BYTES_TO_WORDS(HBLKSIZE));
	}

	void GC_apply_to_each_object(per_object_func f)
	{
	GC_apply_to_all_blocks(per_object_helper, (word)f);
	}

	static void reset_back_edge(ptr_t p, word n_words, word gc_descr)
	{
	/* Skip any free list links, or dropped blocks */
	if (GC_HAS_DEBUG_INFO(p)) {
	ptr_t old_back_ptr = GET_OH_BG_PTR(p);
	if ((word)old_back_ptr & FLAG_MANY) {
	back_edges be = (back_edges )((word)old_back_ptr & ~FLAG_MANY);
	if (!(be -> flags & RETAIN)) {
	deallocate_back_edges(be);
	SET_OH_BG_PTR(p, 0);
	} else {
	word *currentp;

	GC_ASSERT(GC_is_marked(p));

	/* Back edges may point to objects that will not be retained. */
	/* Delete them for now, but remember the height. */
	/* Some will be added back at next GC. */
	be -> n_edges = 0;
	if (0 != be -> cont) {
	deallocate_back_edges(be -> cont);
	be -> cont = 0;
	}

	GC_ASSERT(GC_is_marked(p));

	/* We only retain things for one GC cycle at a time. */
	be -> flags &= ~RETAIN;
	}
	} else /* Simple back pointer */ {
	/* Clear to avoid dangling pointer. */
	SET_OH_BG_PTR(p, 0);
	}
	}
	}

	static void add_back_edges(ptr_t p, word n_words, word gc_descr)
	{
	word currentp = (word )(p + sizeof(oh));

	/* For now, fix up non-length descriptors conservatively. */
	if((gc_descr & GC_DS_TAGS) != GC_DS_LENGTH) {
	gc_descr = WORDS_TO_BYTES(n_words);
	}
	while (currentp < (word *)(p + gc_descr)) {
	word current = *currentp++;
	FIXUP_POINTER(current);
	if (current >= (word)GC_least_plausible_heap_addr &&
	current <= (word)GC_greatest_plausible_heap_addr) {
	ptr_t target = GC_base((GC_PTR)current);
	if (0 != target) {
	add_edge(p, target);
	}
	}
	}
	}

	/* Rebuild the representation of the backward reachability graph. */
	/* Does not examine mark bits. Can be called before GC. */
	void GC_build_back_graph(void)
	{
	GC_apply_to_each_object(add_back_edges);
	}

	/* Return an approximation to the length of the longest simple path */
	/* through unreachable objects to p. We refer to this as the height */
	/* of p. */
	static word backwards_height(ptr_t p)
	{
	word result;
	ptr_t back_ptr = GET_OH_BG_PTR(p);
	back_edges *be;

	if (0 == back_ptr) return 1;
	if (!((word)back_ptr & FLAG_MANY)) {
	if (is_in_progress(p)) return 0; /* DFS back edge, i.e. we followed */
	/* an edge to an object already */
	/* on our stack: ignore */
	push_in_progress(p);
	result = backwards_height(back_ptr)+1;
	pop_in_progress(p);
	return result;
	}
	be = (back_edges *)((word)back_ptr & ~FLAG_MANY);
	if (be -> height >= 0 && be -> height_gc_no == GC_gc_no)
	return be -> height;
	/* Ignore back edges in DFS */
	if (be -> height == HEIGHT_IN_PROGRESS) return 0;
	result = (be -> height > 0? be -> height : 1);
	be -> height = HEIGHT_IN_PROGRESS;
	FOR_EACH_PRED(q, p, {
	word this_height;
	if (GC_is_marked(q) && !(FLAG_MANY & (word)GET_OH_BG_PTR(p))) {
	if (GC_print_stats)
	GC_printf2("Found bogus pointer from 0x%lx to 0x%lx\n", q, p);
	/* Reachable object "points to" unreachable one. */
	/* Could be caused by our lax treatment of GC descriptors. */
	this_height = 1;
	} else {
	this_height = backwards_height(q);
	}
	if (this_height >= result) result = this_height + 1;
	});
	be -> height = result;
	be -> height_gc_no = GC_gc_no;
	return result;
	}

	word GC_max_height;
	ptr_t GC_deepest_obj;

	/* Compute the maximum height of every unreachable predecessor p of a */
	/* reachable object. Arrange to save the heights of all such objects p */
	/* so that they can be used in calculating the height of objects in the */
	/* next GC. */
	/* Set GC_max_height to be the maximum height we encounter, and */
	/* GC_deepest_obj to be the corresponding object. */
	static void update_max_height(ptr_t p, word n_words, word gc_descr)
	{
	if (GC_is_marked(p) && GC_HAS_DEBUG_INFO(p)) {
	int i;
	word p_height = 0;
	ptr_t p_deepest_obj = 0;
	ptr_t back_ptr;
	back_edges *be = 0;

	/* If we remembered a height last time, use it as a minimum. */
	/* It may have increased due to newly unreachable chains pointing */
	/* to p, but it can't have decreased. */
	back_ptr = GET_OH_BG_PTR(p);
	if (0 != back_ptr && ((word)back_ptr & FLAG_MANY)) {
	be = (back_edges *)((word)back_ptr & ~FLAG_MANY);
	if (be -> height != HEIGHT_UNKNOWN) p_height = be -> height;
	}
	FOR_EACH_PRED(q, p, {
	if (!GC_is_marked(q) && GC_HAS_DEBUG_INFO(q)) {
	word q_height;

	q_height = backwards_height(q);
	if (q_height > p_height) {
	p_height = q_height;
	p_deepest_obj = q;
	}
	}
	});
	if (p_height > 0) {
	/* Remember the height for next time. */
	if (be == 0) {
	ensure_struct(p);
	back_ptr = GET_OH_BG_PTR(p);
	be = (back_edges *)((word)back_ptr & ~FLAG_MANY);
	}
	be -> flags \|= RETAIN;
	be -> height = p_height;
	be -> height_gc_no = GC_gc_no;
	}
	if (p_height > GC_max_height) {
	GC_max_height = p_height;
	GC_deepest_obj = p_deepest_obj;
	}
	}
	}

	word GC_max_max_height = 0;

	void GC_traverse_back_graph(void)
	{
	GC_max_height = 0;
	GC_apply_to_each_object(update_max_height);
	}

	void GC_print_back_graph_stats(void)
	{
	GC_printf2("Maximum backwards height of reachable objects at GC %lu is %ld\n",
	(unsigned long) GC_gc_no, GC_max_height);
	if (GC_max_height > GC_max_max_height) {
	GC_max_max_height = GC_max_height;
	GC_printf0("The following unreachable object is last in a longest chain "
	"of unreachable objects:\n");
	GC_print_heap_obj(GC_deepest_obj);
	}
	if (GC_print_stats) {
	GC_printf1("Needed max total of %ld back-edge structs\n",
	GC_n_back_edge_structs);
	}
	GC_apply_to_each_object(reset_back_edge);
	GC_deepest_obj = 0;
	}

	#endif /* MAKE_BACK_GRAPH */