bitmap.h

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/* Functions to support general ended bitmaps.
   Copyright (C) 1997-2024 Free Software Foundation, Inc.
 
This file is part of GCC.
 
GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 3, or (at your option) any later
version.
 
GCC is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
for more details.
 
You should have received a copy of the GNU General Public License
along with GCC; see the file COPYING3.  If not see
<http://www.gnu.org/licenses/>.  */
 
#ifndef GCC_BITMAP_H
#define GCC_BITMAP_H
 
/* Implementation of sparse integer sets as a linked list or tree.
 
   This sparse set representation is suitable for sparse sets with an
   unknown (a priori) universe.
 
   Sets are represented as double-linked lists of container nodes of
   type "struct bitmap_element" or as a binary trees of the same
   container nodes.  Each container node consists of an index for the
   first member that could be held in the container, a small array of
   integers that represent the members in the container, and pointers
   to the next and previous element in the linked list, or left and
   right children in the tree.  In linked-list form, the container
   nodes in the list are sorted in ascending order, i.e. the head of
   the list holds the element with the smallest member of the set.
   In tree form, nodes to the left have a smaller container index.
 
   For a given member I in the set:
     - the element for I will have index is I / (bits per element)
     - the position for I within element is I % (bits per element)
 
   This representation is very space-efficient for large sparse sets, and
   the size of the set can be changed dynamically without much overhead.
   An important parameter is the number of bits per element.  In this
   implementation, there are 128 bits per element.  This results in a
   high storage overhead *per element*, but a small overall overhead if
   the set is very sparse.
 
   The storage requirements for linked-list sparse sets are O(E), with E->N
   in the worst case (a sparse set with large distances between the values
   of the set members).
 
   This representation also works well for data flow problems where the size
   of the set may grow dynamically, but care must be taken that the member_p,
   add_member, and remove_member operations occur with a suitable access
   pattern.
 
   The linked-list set representation works well for problems involving very
   sparse sets.  The canonical example in GCC is, of course, the "set of
   sets" for some CFG-based data flow problems (liveness analysis, dominance
   frontiers, etc.).
   
   For random-access sparse sets of unknown universe, the binary tree
   representation is likely to be a more suitable choice.  Theoretical
   access times for the binary tree representation are better than those
   for the linked-list, but in practice this is only true for truely
   random access.
 
   Often the most suitable representation during construction of the set
   is not the best choice for the usage of the set.  For such cases, the
   "view" of the set can be changed from one representation to the other.
   This is an O(E) operation:
 
     * from list to tree view   : bitmap_tree_view
     * from tree to list view   : bitmap_list_view
 
   Traversing linked lists or trees can be cache-unfriendly.  Performance
   can be improved by keeping container nodes in the set grouped together
   in  memory, using a dedicated obstack for a set (or group of related
   sets).  Elements allocated on obstacks are released to a free-list and
   taken off the free list.  If multiple sets are allocated on the same
   obstack, elements freed from one set may be re-used for one of the other
   sets.  This usually helps avoid cache misses.
 
   A single free-list is used for all sets allocated in GGC space.  This is
   bad for persistent sets, so persistent sets should be allocated on an
   obstack whenever possible.
 
   For random-access sets with a known, relatively small universe size, the
   SparseSet or simple bitmap representations may be more efficient than a
   linked-list set.
 
 
   LINKED LIST FORM
   ================
 
   In linked-list form, in-order iterations of the set can be executed
   efficiently.  The downside is that many random-access operations are
   relatively slow, because the linked list has to be traversed to test
   membership (i.e. member_p/ add_member/remove_member).
   
   To improve the performance of this set representation, the last
   accessed element and its index are cached.  For membership tests on
   members close to recently accessed members, the cached last element
   improves membership test to a constant-time operation.
 
   The following operations can always be performed in O(1) time in
   list view:
 
     * clear                    : bitmap_clear
     * smallest_member          : bitmap_first_set_bit
     * pop_smallest             : bitmap_clear_first_set_bit
     * choose_one               : (not implemented, but could be
                                   in constant time)
 
   The following operations can be performed in O(E) time worst-case in
   list view (with E the number of elements in the linked list), but in
   O(1) time with a suitable access patterns:
 
     * member_p                 : bitmap_bit_p
     * add_member               : bitmap_set_bit / bitmap_set_range
     * remove_member            : bitmap_clear_bit / bitmap_clear_range
 
   The following operations can be performed in O(E) time in list view:
 
     * cardinality              : bitmap_count_bits
     * largest_member           : bitmap_last_set_bit (but this could
                                  in constant time with a pointer to
                                  the last element in the chain)
     * set_size                 : bitmap_last_set_bit
 
   In tree view the following operations can all be performed in O(log E)
   amortized time with O(E) worst-case behavior.
 
     * smallest_member
     * pop_smallest
     * largest_member
     * set_size
     * member_p
     * add_member
     * remove_member
 
   Additionally, the linked-list sparse set representation supports
   enumeration of the members in O(E) time:
 
     * forall                   : EXECUTE_IF_SET_IN_BITMAP
     * set_copy                 : bitmap_copy
     * set_intersection         : bitmap_intersect_p /
                                  bitmap_and / bitmap_and_into /
                                  EXECUTE_IF_AND_IN_BITMAP
     * set_union                : bitmap_ior / bitmap_ior_into
     * set_difference           : bitmap_intersect_compl_p /
                                  bitmap_and_comp / bitmap_and_comp_into /
                                  EXECUTE_IF_AND_COMPL_IN_BITMAP
     * set_disjuction           : bitmap_xor_comp / bitmap_xor_comp_into
     * set_compare              : bitmap_equal_p
 
   Some operations on 3 sets that occur frequently in data flow problems
   are also implemented:
 
     * A | (B & C)              : bitmap_ior_and_into
     * A | (B & ~C)             : bitmap_ior_and_compl /
                                  bitmap_ior_and_compl_into
 
 
   BINARY TREE FORM
   ================
   An alternate "view" of a bitmap is its binary tree representation.
   For this representation, splay trees are used because they can be
   implemented using the same data structures as the linked list, with
   no overhead for meta-data (like color, or rank) on the tree nodes.
 
   In binary tree form, random-access to the set is much more efficient
   than for the linked-list representation.  Downsides are the high cost
   of clearing the set, and the relatively large number of operations
   necessary to balance the tree.  Also, iterating the set members is
   not supported.
   
   As for the linked-list representation, the last accessed element and
   its index are cached, so that membership tests on the latest accessed
   members is a constant-time operation.  Other lookups take O(logE)
   time amortized (but O(E) time worst-case).
 
   The following operations can always be performed in O(1) time:
 
     * choose_one               : (not implemented, but could be
                                   implemented in constant time)
 
   The following operations can be performed in O(logE) time amortized
   but O(E) time worst-case, but in O(1) time if the same element is
   accessed.
 
     * member_p                 : bitmap_bit_p
     * add_member               : bitmap_set_bit
     * remove_member            : bitmap_clear_bit
 
   The following operations can be performed in O(logE) time amortized
   but O(E) time worst-case:
 
     * smallest_member          : bitmap_first_set_bit
     * largest_member           : bitmap_last_set_bit
     * set_size                 : bitmap_last_set_bit
 
   The following operations can be performed in O(E) time:
 
     * clear                    : bitmap_clear
 
   The binary tree sparse set representation does *not* support any form
   of enumeration, and does also *not* support logical operations on sets.
   The binary tree representation is only supposed to be used for sets
   on which many random-access membership tests will happen.  */
 
#include "obstack.h"
#include "array-traits.h"
 
/* Bitmap memory usage.  */
class bitmap_usage: public mem_usage
{
public:
  /* Default contructor.  */
  bitmap_usage (): m_nsearches (0), m_search_iter (0) {}
  /* Constructor.  */
  bitmap_usage (size_t allocated, size_t times, size_t peak,
             uint64_t nsearches, uint64_t search_iter)
    : mem_usage (allocated, times, peak),
    m_nsearches (nsearches), m_search_iter (search_iter) {}
 
  /* Sum the usage with SECOND usage.  */
  bitmap_usage
  operator+ (const bitmap_usage &second)
  {
    return bitmap_usage (m_allocated + second.m_allocated,
                             m_times + second.m_times,
                             m_peak + second.m_peak,
                             m_nsearches + second.m_nsearches,
                             m_search_iter + second.m_search_iter);
  }
 
  /* Dump usage coupled to LOC location, where TOTAL is sum of all rows.  */
  inline void
  dump (mem_location *loc, const mem_usage &total) const
  {
    char *location_string = loc->to_string ();
 
    fprintf (stderr, "%-48s " PRsa (9) ":%5.1f%%"
             PRsa (9) PRsa (9) ":%5.1f%%"
             PRsa (11) PRsa (11) "%10s\n",
             location_string, SIZE_AMOUNT (m_allocated),
             get_percent (m_allocated, total.m_allocated),
             SIZE_AMOUNT (m_peak), SIZE_AMOUNT (m_times),
             get_percent (m_times, total.m_times),
             SIZE_AMOUNT (m_nsearches), SIZE_AMOUNT (m_search_iter),
             loc->m_ggc ? "ggc" : "heap");
 
    free (location_string);
  }
 
  /* Dump header with NAME.  */
  static inline void
  dump_header (const char *name)
  {
    fprintf (stderr, "%-48s %11s%16s%17s%12s%12s%10s\n", name, "Leak", "Peak",
             "Times", "N searches", "Search iter", "Type");
  }
 
  /* Number search operations.  */
  uint64_t m_nsearches;
  /* Number of search iterations.  */
  uint64_t m_search_iter;
};
 
/* Bitmap memory description.  */
extern mem_alloc_description<bitmap_usage> bitmap_mem_desc;
 
/* Fundamental storage type for bitmap.  */
 
typedef unsigned long BITMAP_WORD;
/* BITMAP_WORD_BITS needs to be unsigned, but cannot contain casts as
   it is used in preprocessor directives -- hence the 1u.  */
#define BITMAP_WORD_BITS (CHAR_BIT * SIZEOF_LONG * 1u)
 
/* Number of words to use for each element in the linked list.  */
 
#ifndef BITMAP_ELEMENT_WORDS
#define BITMAP_ELEMENT_WORDS ((128 + BITMAP_WORD_BITS - 1) / BITMAP_WORD_BITS)
#endif
 
/* Number of bits in each actual element of a bitmap.  */
 
#define BITMAP_ELEMENT_ALL_BITS (BITMAP_ELEMENT_WORDS * BITMAP_WORD_BITS)
 
/* Obstack for allocating bitmaps and elements from.  */
struct bitmap_obstack {
  struct bitmap_element *elements;
  bitmap_head *heads;
  struct obstack obstack;
};
 
/* Bitmap set element.  We use a linked list to hold only the bits that
   are set.  This allows for use to grow the bitset dynamically without
   having to realloc and copy a giant bit array.
 
   The free list is implemented as a list of lists.  There is one
   outer list connected together by prev fields.  Each element of that
   outer is an inner list (that may consist only of the outer list
   element) that are connected by the next fields.  The prev pointer
   is undefined for interior elements.  This allows
   bitmap_elt_clear_from to be implemented in unit time rather than
   linear in the number of elements to be freed.  */
 
struct GTY((chain_next ("%h.next"))) bitmap_element {
  /* In list form, the next element in the linked list;
     in tree form, the left child node in the tree.  */
  struct bitmap_element *next;
  /* In list form, the previous element in the linked list;
     in tree form, the right child node in the tree.  */
  struct bitmap_element *prev;
  /* regno/BITMAP_ELEMENT_ALL_BITS.  */
  unsigned int indx;
  /* Bits that are set, counting from INDX, inclusive  */
  BITMAP_WORD bits[BITMAP_ELEMENT_WORDS];
};
 
/* Head of bitmap linked list.  The 'current' member points to something
   already pointed to by the chain started by first, so GTY((skip)) it.  */
 
class GTY(()) bitmap_head {
public:
  static bitmap_obstack crashme;
  /* Poison obstack to not make it not a valid initialized GC bitmap.  */
  CONSTEXPR bitmap_head()
    : indx (0), tree_form (false), padding (0), alloc_descriptor (0), first (NULL),
      current (NULL), obstack (&crashme)
  {}
  /* Index of last element looked at.  */
  unsigned int indx;
  /* False if the bitmap is in list form; true if the bitmap is in tree form.
     Bitmap iterators only work on bitmaps in list form.  */
  unsigned tree_form: 1;
  /* Next integer is shifted, so padding is needed.  */
  unsigned padding: 2;
  /* Bitmap UID used for memory allocation statistics.  */
  unsigned alloc_descriptor: 29;
  /* In list form, the first element in the linked list;
     in tree form, the root of the tree.   */
  bitmap_element *first;
  /* Last element looked at.  */
  bitmap_element * GTY((skip(""))) current;
  /* Obstack to allocate elements from.  If NULL, then use GGC allocation.  */
  bitmap_obstack * GTY((skip(""))) obstack;
 
  /* Dump bitmap.  */
  void dump ();
 
  /* Get bitmap descriptor UID casted to an unsigned integer pointer.
     Shift the descriptor because pointer_hash<Type>::hash is
     doing >> 3 shift operation.  */
  unsigned *get_descriptor ()
  {
    return (unsigned *)(ptrdiff_t)(alloc_descriptor << 3);
  }
};
 
/* Global data */
extern bitmap_element bitmap_zero_bits; /* Zero bitmap element */
extern bitmap_obstack bitmap_default_obstack;   /* Default bitmap obstack */
 
/* Change the view of the bitmap to list, or tree.  */
void bitmap_list_view (bitmap);
void bitmap_tree_view (bitmap);
 
/* Clear a bitmap by freeing up the linked list.  */
extern void bitmap_clear (bitmap);
 
/* Copy a bitmap to another bitmap.  */
extern void bitmap_copy (bitmap, const_bitmap);
 
/* Move a bitmap to another bitmap.  */
extern void bitmap_move (bitmap, bitmap);
 
/* True if two bitmaps are identical.  */
extern bool bitmap_equal_p (const_bitmap, const_bitmap);
 
/* True if the bitmaps intersect (their AND is non-empty).  */
extern bool bitmap_intersect_p (const_bitmap, const_bitmap);
 
/* True if the complement of the second intersects the first (their
   AND_COMPL is non-empty).  */
extern bool bitmap_intersect_compl_p (const_bitmap, const_bitmap);
 
/* True if MAP is an empty bitmap.  */
inline bool bitmap_empty_p (const_bitmap map)
{
  return !map->first;
}
 
/* True if the bitmap has only a single bit set.  */
extern bool bitmap_single_bit_set_p (const_bitmap);
 
/* Count the number of bits set in the bitmap.  */
extern unsigned long bitmap_count_bits (const_bitmap);
 
/* Count the number of unique bits set across the two bitmaps.  */
extern unsigned long bitmap_count_unique_bits (const_bitmap, const_bitmap);
 
/* Boolean operations on bitmaps.  The _into variants are two operand
   versions that modify the first source operand.  The other variants
   are three operand versions that to not destroy the source bitmaps.
   The operations supported are &, & ~, |, ^.  */
extern void bitmap_and (bitmap, const_bitmap, const_bitmap);
extern bool bitmap_and_into (bitmap, const_bitmap);
extern bool bitmap_and_compl (bitmap, const_bitmap, const_bitmap);
extern bool bitmap_and_compl_into (bitmap, const_bitmap);
#define bitmap_compl_and(DST, A, B) bitmap_and_compl (DST, B, A)
extern void bitmap_compl_and_into (bitmap, const_bitmap);
extern void bitmap_clear_range (bitmap, unsigned int, unsigned int);
extern void bitmap_set_range (bitmap, unsigned int, unsigned int);
extern bool bitmap_ior (bitmap, const_bitmap, const_bitmap);
extern bool bitmap_ior_into (bitmap, const_bitmap);
extern bool bitmap_ior_into_and_free (bitmap, bitmap *);
extern void bitmap_xor (bitmap, const_bitmap, const_bitmap);
extern void bitmap_xor_into (bitmap, const_bitmap);
 
/* DST = A | (B & C).  Return true if DST changes.  */
extern bool bitmap_ior_and_into (bitmap DST, const_bitmap B, const_bitmap C);
/* DST = A | (B & ~C).  Return true if DST changes.  */
extern bool bitmap_ior_and_compl (bitmap DST, const_bitmap A,
                                  const_bitmap B, const_bitmap C);
/* A |= (B & ~C).  Return true if A changes.  */
extern bool bitmap_ior_and_compl_into (bitmap A,
                                       const_bitmap B, const_bitmap C);
 
/* Clear a single bit in a bitmap.  Return true if the bit changed.  */
extern bool bitmap_clear_bit (bitmap, int);
 
/* Set a single bit in a bitmap.  Return true if the bit changed.  */
extern bool bitmap_set_bit (bitmap, int);
 
/* Return true if a bit is set in a bitmap.  */
extern bool bitmap_bit_p (const_bitmap, int);
 
/* Set and get multiple bit values in a sparse bitmap.  This allows a bitmap to
   function as a sparse array of bit patterns where the patterns are
   multiples of power of 2. This is more efficient than performing this as
   multiple individual operations.  */
void bitmap_set_aligned_chunk (bitmap, unsigned int, unsigned int, BITMAP_WORD);
BITMAP_WORD bitmap_get_aligned_chunk (const_bitmap, unsigned int, unsigned int);
 
/* Debug functions to print a bitmap.  */
extern void debug_bitmap (const_bitmap);
extern void debug_bitmap_file (FILE *, const_bitmap);
 
/* Print a bitmap.  */
extern void bitmap_print (FILE *, const_bitmap, const char *, const char *);
 
/* Initialize and release a bitmap obstack.  */
extern void bitmap_obstack_initialize (bitmap_obstack *);
extern void bitmap_obstack_release (bitmap_obstack *);
extern void bitmap_register (bitmap MEM_STAT_DECL);
extern void dump_bitmap_statistics (void);
 
/* Initialize a bitmap header.  OBSTACK indicates the bitmap obstack
   to allocate from, NULL for GC'd bitmap.  */
 
inline void
bitmap_initialize (bitmap head, bitmap_obstack *obstack CXX_MEM_STAT_INFO)
{
  head->first = head->current = NULL;
  head->indx = head->tree_form = 0;
  head->padding = 0;
  head->alloc_descriptor = 0;
  head->obstack = obstack;
  if (GATHER_STATISTICS)
    bitmap_register (head PASS_MEM_STAT);
}
 
/* Release a bitmap (but not its head).  This is suitable for pairing with
   bitmap_initialize.  */
 
inline void
bitmap_release (bitmap head)
{
  bitmap_clear (head);
  /* Poison the obstack pointer so the obstack can be safely released.
     Do not zero it as the bitmap then becomes initialized GC.  */
  head->obstack = &bitmap_head::crashme;
}
 
/* Allocate and free bitmaps from obstack, malloc and gc'd memory.  */
extern bitmap bitmap_alloc (bitmap_obstack *obstack CXX_MEM_STAT_INFO);
#define BITMAP_ALLOC bitmap_alloc
extern bitmap bitmap_gc_alloc (ALONE_CXX_MEM_STAT_INFO);
#define BITMAP_GGC_ALLOC bitmap_gc_alloc
extern void bitmap_obstack_free (bitmap);
 
/* A few compatibility/functions macros for compatibility with sbitmaps */
inline void dump_bitmap (FILE *file, const_bitmap map)
{
  bitmap_print (file, map, "", "\n");
}
extern void debug (const bitmap_head &ref);
extern void debug (const bitmap_head *ptr);
 
extern unsigned bitmap_first_set_bit (const_bitmap);
extern unsigned bitmap_clear_first_set_bit (bitmap);
extern unsigned bitmap_last_set_bit (const_bitmap);
 
/* Compute bitmap hash (for purposes of hashing etc.)  */
extern hashval_t bitmap_hash (const_bitmap);
 
/* Do any cleanup needed on a bitmap when it is no longer used.  */
#define BITMAP_FREE(BITMAP) \
       ((void) (bitmap_obstack_free ((bitmap) BITMAP), (BITMAP) = (bitmap) NULL))
 
/* Iterator for bitmaps.  */
 
struct bitmap_iterator
{
  /* Pointer to the current bitmap element.  */
  bitmap_element *elt1;
 
  /* Pointer to 2nd bitmap element when two are involved.  */
  bitmap_element *elt2;
 
  /* Word within the current element.  */
  unsigned word_no;
 
  /* Contents of the actually processed word.  When finding next bit
     it is shifted right, so that the actual bit is always the least
     significant bit of ACTUAL.  */
  BITMAP_WORD bits;
};
 
/* Initialize a single bitmap iterator.  START_BIT is the first bit to
   iterate from.  */
 
inline void
bmp_iter_set_init (bitmap_iterator *bi, const_bitmap map,
                   unsigned start_bit, unsigned *bit_no)
{
  bi->elt1 = map->first;
  bi->elt2 = NULL;
 
  gcc_checking_assert (!map->tree_form);
 
  /* Advance elt1 until it is not before the block containing start_bit.  */
  while (1)
    {
      if (!bi->elt1)
        {
          bi->elt1 = &bitmap_zero_bits;
          break;
        }
 
      if (bi->elt1->indx >= start_bit / BITMAP_ELEMENT_ALL_BITS)
        break;
      bi->elt1 = bi->elt1->next;
    }
 
  /* We might have gone past the start bit, so reinitialize it.  */
  if (bi->elt1->indx != start_bit / BITMAP_ELEMENT_ALL_BITS)
    start_bit = bi->elt1->indx * BITMAP_ELEMENT_ALL_BITS;
 
  /* Initialize for what is now start_bit.  */
  bi->word_no = start_bit / BITMAP_WORD_BITS % BITMAP_ELEMENT_WORDS;
  bi->bits = bi->elt1->bits[bi->word_no];
  bi->bits >>= start_bit % BITMAP_WORD_BITS;
 
  /* If this word is zero, we must make sure we're not pointing at the
     first bit, otherwise our incrementing to the next word boundary
     will fail.  It won't matter if this increment moves us into the
     next word.  */
  start_bit += !bi->bits;
 
  *bit_no = start_bit;
}
 
/* Initialize an iterator to iterate over the intersection of two
   bitmaps.  START_BIT is the bit to commence from.  */
 
inline void
bmp_iter_and_init (bitmap_iterator *bi, const_bitmap map1, const_bitmap map2,
                   unsigned start_bit, unsigned *bit_no)
{
  bi->elt1 = map1->first;
  bi->elt2 = map2->first;
 
  gcc_checking_assert (!map1->tree_form && !map2->tree_form);
 
  /* Advance elt1 until it is not before the block containing
     start_bit.  */
  while (1)
    {
      if (!bi->elt1)
        {
          bi->elt2 = NULL;
          break;
        }
 
      if (bi->elt1->indx >= start_bit / BITMAP_ELEMENT_ALL_BITS)
        break;
      bi->elt1 = bi->elt1->next;
    }
 
  /* Advance elt2 until it is not before elt1.  */
  while (1)
    {
      if (!bi->elt2)
        {
          bi->elt1 = bi->elt2 = &bitmap_zero_bits;
          break;
        }
 
      if (bi->elt2->indx >= bi->elt1->indx)
        break;
      bi->elt2 = bi->elt2->next;
    }
 
  /* If we're at the same index, then we have some intersecting bits.  */
  if (bi->elt1->indx == bi->elt2->indx)
    {
      /* We might have advanced beyond the start_bit, so reinitialize
         for that.  */
      if (bi->elt1->indx != start_bit / BITMAP_ELEMENT_ALL_BITS)
        start_bit = bi->elt1->indx * BITMAP_ELEMENT_ALL_BITS;
 
      bi->word_no = start_bit / BITMAP_WORD_BITS % BITMAP_ELEMENT_WORDS;
      bi->bits = bi->elt1->bits[bi->word_no] & bi->elt2->bits[bi->word_no];
      bi->bits >>= start_bit % BITMAP_WORD_BITS;
    }
  else
    {
      /* Otherwise we must immediately advance elt1, so initialize for
         that.  */
      bi->word_no = BITMAP_ELEMENT_WORDS - 1;
      bi->bits = 0;
    }
 
  /* If this word is zero, we must make sure we're not pointing at the
     first bit, otherwise our incrementing to the next word boundary
     will fail.  It won't matter if this increment moves us into the
     next word.  */
  start_bit += !bi->bits;
 
  *bit_no = start_bit;
}
 
/* Initialize an iterator to iterate over the bits in MAP1 & ~MAP2.  */
 
inline void
bmp_iter_and_compl_init (bitmap_iterator *bi,
                         const_bitmap map1, const_bitmap map2,
                         unsigned start_bit, unsigned *bit_no)
{
  bi->elt1 = map1->first;
  bi->elt2 = map2->first;
 
  gcc_checking_assert (!map1->tree_form && !map2->tree_form);
 
  /* Advance elt1 until it is not before the block containing start_bit.  */
  while (1)
    {
      if (!bi->elt1)
        {
          bi->elt1 = &bitmap_zero_bits;
          break;
        }
 
      if (bi->elt1->indx >= start_bit / BITMAP_ELEMENT_ALL_BITS)
        break;
      bi->elt1 = bi->elt1->next;
    }
 
  /* Advance elt2 until it is not before elt1.  */
  while (bi->elt2 && bi->elt2->indx < bi->elt1->indx)
    bi->elt2 = bi->elt2->next;
 
  /* We might have advanced beyond the start_bit, so reinitialize for
     that.  */
  if (bi->elt1->indx != start_bit / BITMAP_ELEMENT_ALL_BITS)
    start_bit = bi->elt1->indx * BITMAP_ELEMENT_ALL_BITS;
 
  bi->word_no = start_bit / BITMAP_WORD_BITS % BITMAP_ELEMENT_WORDS;
  bi->bits = bi->elt1->bits[bi->word_no];
  if (bi->elt2 && bi->elt1->indx == bi->elt2->indx)
    bi->bits &= ~bi->elt2->bits[bi->word_no];
  bi->bits >>= start_bit % BITMAP_WORD_BITS;
 
  /* If this word is zero, we must make sure we're not pointing at the
     first bit, otherwise our incrementing to the next word boundary
     will fail.  It won't matter if this increment moves us into the
     next word.  */
  start_bit += !bi->bits;
 
  *bit_no = start_bit;
}
 
/* Advance to the next bit in BI.  We don't advance to the next
   nonzero bit yet.  */
 
inline void
bmp_iter_next (bitmap_iterator *bi, unsigned *bit_no)
{
  bi->bits >>= 1;
  *bit_no += 1;
}
 
/* Advance to first set bit in BI.  */
 
inline void
bmp_iter_next_bit (bitmap_iterator * bi, unsigned *bit_no)
{
#if (GCC_VERSION >= 3004)
  {
    unsigned int n = __builtin_ctzl (bi->bits);
    gcc_assert (sizeof (unsigned long) == sizeof (BITMAP_WORD));
    bi->bits >>= n;
    *bit_no += n;
  }
#else
  while (!(bi->bits & 1))
    {
      bi->bits >>= 1;
      *bit_no += 1;
    }
#endif
}
 
/* Advance to the next nonzero bit of a single bitmap, we will have
   already advanced past the just iterated bit.  Return true if there
   is a bit to iterate.  */
 
inline bool
bmp_iter_set (bitmap_iterator *bi, unsigned *bit_no)
{
  /* If our current word is nonzero, it contains the bit we want.  */
  if (bi->bits)
    {
    next_bit:
      bmp_iter_next_bit (bi, bit_no);
      return true;
    }
 
  /* Round up to the word boundary.  We might have just iterated past
     the end of the last word, hence the -1.  It is not possible for
     bit_no to point at the beginning of the now last word.  */
  *bit_no = ((*bit_no + BITMAP_WORD_BITS - 1)
             / BITMAP_WORD_BITS * BITMAP_WORD_BITS);
  bi->word_no++;
 
  while (1)
    {
      /* Find the next nonzero word in this elt.  */
      while (bi->word_no != BITMAP_ELEMENT_WORDS)
        {
          bi->bits = bi->elt1->bits[bi->word_no];
          if (bi->bits)
            goto next_bit;
          *bit_no += BITMAP_WORD_BITS;
          bi->word_no++;
        }
 
      /* Make sure we didn't remove the element while iterating.  */
      gcc_checking_assert (bi->elt1->indx != -1U);
 
      /* Advance to the next element.  */
      bi->elt1 = bi->elt1->next;
      if (!bi->elt1)
        return false;
      *bit_no = bi->elt1->indx * BITMAP_ELEMENT_ALL_BITS;
      bi->word_no = 0;
    }
}
 
/* Advance to the next nonzero bit of an intersecting pair of
   bitmaps.  We will have already advanced past the just iterated bit.
   Return true if there is a bit to iterate.  */
 
inline bool
bmp_iter_and (bitmap_iterator *bi, unsigned *bit_no)
{
  /* If our current word is nonzero, it contains the bit we want.  */
  if (bi->bits)
    {
    next_bit:
      bmp_iter_next_bit (bi, bit_no);
      return true;
    }
 
  /* Round up to the word boundary.  We might have just iterated past
     the end of the last word, hence the -1.  It is not possible for
     bit_no to point at the beginning of the now last word.  */
  *bit_no = ((*bit_no + BITMAP_WORD_BITS - 1)
             / BITMAP_WORD_BITS * BITMAP_WORD_BITS);
  bi->word_no++;
 
  while (1)
    {
      /* Find the next nonzero word in this elt.  */
      while (bi->word_no != BITMAP_ELEMENT_WORDS)
        {
          bi->bits = bi->elt1->bits[bi->word_no] & bi->elt2->bits[bi->word_no];
          if (bi->bits)
            goto next_bit;
          *bit_no += BITMAP_WORD_BITS;
          bi->word_no++;
        }
 
      /* Advance to the next identical element.  */
      do
        {
          /* Make sure we didn't remove the element while iterating.  */
          gcc_checking_assert (bi->elt1->indx != -1U);
 
          /* Advance elt1 while it is less than elt2.  We always want
             to advance one elt.  */
          do
            {
              bi->elt1 = bi->elt1->next;
              if (!bi->elt1)
                return false;
            }
          while (bi->elt1->indx < bi->elt2->indx);
 
          /* Make sure we didn't remove the element while iterating.  */
          gcc_checking_assert (bi->elt2->indx != -1U);
 
          /* Advance elt2 to be no less than elt1.  This might not
             advance.  */
          while (bi->elt2->indx < bi->elt1->indx)
            {
              bi->elt2 = bi->elt2->next;
              if (!bi->elt2)
                return false;
            }
        }
      while (bi->elt1->indx != bi->elt2->indx);
 
      *bit_no = bi->elt1->indx * BITMAP_ELEMENT_ALL_BITS;
      bi->word_no = 0;
    }
}
 
/* Advance to the next nonzero bit in the intersection of
   complemented bitmaps.  We will have already advanced past the just
   iterated bit.  */
 
inline bool
bmp_iter_and_compl (bitmap_iterator *bi, unsigned *bit_no)
{
  /* If our current word is nonzero, it contains the bit we want.  */
  if (bi->bits)
    {
    next_bit:
      bmp_iter_next_bit (bi, bit_no);
      return true;
    }
 
  /* Round up to the word boundary.  We might have just iterated past
     the end of the last word, hence the -1.  It is not possible for
     bit_no to point at the beginning of the now last word.  */
  *bit_no = ((*bit_no + BITMAP_WORD_BITS - 1)
             / BITMAP_WORD_BITS * BITMAP_WORD_BITS);
  bi->word_no++;
 
  while (1)
    {
      /* Find the next nonzero word in this elt.  */
      while (bi->word_no != BITMAP_ELEMENT_WORDS)
        {
          bi->bits = bi->elt1->bits[bi->word_no];
          if (bi->elt2 && bi->elt2->indx == bi->elt1->indx)
            bi->bits &= ~bi->elt2->bits[bi->word_no];
          if (bi->bits)
            goto next_bit;
          *bit_no += BITMAP_WORD_BITS;
          bi->word_no++;
        }
 
      /* Make sure we didn't remove the element while iterating.  */
      gcc_checking_assert (bi->elt1->indx != -1U);
 
      /* Advance to the next element of elt1.  */
      bi->elt1 = bi->elt1->next;
      if (!bi->elt1)
        return false;
 
      /* Make sure we didn't remove the element while iterating.  */
      gcc_checking_assert (! bi->elt2 || bi->elt2->indx != -1U);
 
      /* Advance elt2 until it is no less than elt1.  */
      while (bi->elt2 && bi->elt2->indx < bi->elt1->indx)
        bi->elt2 = bi->elt2->next;
 
      *bit_no = bi->elt1->indx * BITMAP_ELEMENT_ALL_BITS;
      bi->word_no = 0;
    }
}
 
/* If you are modifying a bitmap you are currently iterating over you
   have to ensure to
     - never remove the current bit;
     - if you set or clear a bit before the current bit this operation
       will not affect the set of bits you are visiting during the iteration;
     - if you set or clear a bit after the current bit it is unspecified
       whether that affects the set of bits you are visiting during the
       iteration.
   If you want to remove the current bit you can delay this to the next
   iteration (and after the iteration in case the last iteration is
   affected).  */
 
/* Loop over all bits set in BITMAP, starting with MIN and setting
   BITNUM to the bit number.  ITER is a bitmap iterator.  BITNUM
   should be treated as a read-only variable as it contains loop
   state.  */
 
#ifndef EXECUTE_IF_SET_IN_BITMAP
/* See sbitmap.h for the other definition of EXECUTE_IF_SET_IN_BITMAP.  */
#define EXECUTE_IF_SET_IN_BITMAP(BITMAP, MIN, BITNUM, ITER)             \
  for (bmp_iter_set_init (&(ITER), (BITMAP), (MIN), &(BITNUM));         \
       bmp_iter_set (&(ITER), &(BITNUM));                               \
       bmp_iter_next (&(ITER), &(BITNUM)))
#endif
 
/* Loop over all the bits set in BITMAP1 & BITMAP2, starting with MIN
   and setting BITNUM to the bit number.  ITER is a bitmap iterator.
   BITNUM should be treated as a read-only variable as it contains
   loop state.  */
 
#define EXECUTE_IF_AND_IN_BITMAP(BITMAP1, BITMAP2, MIN, BITNUM, ITER)   \
  for (bmp_iter_and_init (&(ITER), (BITMAP1), (BITMAP2), (MIN),         \
                          &(BITNUM));                                   \
       bmp_iter_and (&(ITER), &(BITNUM));                               \
       bmp_iter_next (&(ITER), &(BITNUM)))
 
/* Loop over all the bits set in BITMAP1 & ~BITMAP2, starting with MIN
   and setting BITNUM to the bit number.  ITER is a bitmap iterator.
   BITNUM should be treated as a read-only variable as it contains
   loop state.  */
 
#define EXECUTE_IF_AND_COMPL_IN_BITMAP(BITMAP1, BITMAP2, MIN, BITNUM, ITER) \
  for (bmp_iter_and_compl_init (&(ITER), (BITMAP1), (BITMAP2), (MIN),   \
                                &(BITNUM));                             \
       bmp_iter_and_compl (&(ITER), &(BITNUM));                         \
       bmp_iter_next (&(ITER), &(BITNUM)))
 
/* A class that ties the lifetime of a bitmap to its scope.  */
class auto_bitmap
{
 public:
  auto_bitmap (ALONE_CXX_MEM_STAT_INFO)
    { bitmap_initialize (&m_bits, &bitmap_default_obstack PASS_MEM_STAT); }
  explicit auto_bitmap (bitmap_obstack *o CXX_MEM_STAT_INFO)
    { bitmap_initialize (&m_bits, o PASS_MEM_STAT); }
  ~auto_bitmap () { bitmap_clear (&m_bits); }
  // Allow calling bitmap functions on our bitmap.
  operator bitmap () { return &m_bits; }
 
 private:
  // Prevent making a copy that references our bitmap.
  auto_bitmap (const auto_bitmap &) = delete;
  auto_bitmap &operator = (const auto_bitmap &) = delete;
  auto_bitmap (auto_bitmap &&) = delete;
  auto_bitmap &operator = (auto_bitmap &&) = delete;
 
  bitmap_head m_bits;
};
 
extern void debug (const auto_bitmap &ref);
extern void debug (const auto_bitmap *ptr);
 
/* Base class for bitmap_view; see there for details.  */
template<typename T, typename Traits = array_traits<T> >
class base_bitmap_view
{
public:
  typedef typename Traits::element_type array_element_type;
 
  base_bitmap_view (const T &, bitmap_element *);
  operator const_bitmap () const { return &m_head; }
 
private:
  base_bitmap_view (const base_bitmap_view &);
 
  bitmap_head m_head;
};
 
/* Provides a read-only bitmap view of a single integer bitmask or a
   constant-sized array of integer bitmasks, or of a wrapper around such
   bitmasks.  */
template<typename T, typename Traits>
class bitmap_view<T, Traits, true> : public base_bitmap_view<T, Traits>
{
public:
  bitmap_view (const T &array)
    : base_bitmap_view<T, Traits> (array, m_bitmap_elements) {}
 
private:
  /* How many bitmap_elements we need to hold a full T.  */
  static const size_t num_bitmap_elements
    = CEIL (CHAR_BIT
            * sizeof (typename Traits::element_type)
            * Traits::constant_size,
            BITMAP_ELEMENT_ALL_BITS);
  bitmap_element m_bitmap_elements[num_bitmap_elements];
};
 
/* Initialize the view for array ARRAY, using the array of bitmap
   elements in BITMAP_ELEMENTS (which is known to contain enough
   entries).  */
template<typename T, typename Traits>
base_bitmap_view<T, Traits>::base_bitmap_view (const T &array,
                                               bitmap_element *bitmap_elements)
{
  m_head.obstack = NULL;
 
  /* The code currently assumes that each element of ARRAY corresponds
     to exactly one bitmap_element.  */
  const size_t array_element_bits = CHAR_BIT * sizeof (array_element_type);
  STATIC_ASSERT (BITMAP_ELEMENT_ALL_BITS % array_element_bits == 0);
  size_t array_step = BITMAP_ELEMENT_ALL_BITS / array_element_bits;
  size_t array_size = Traits::size (array);
 
  /* Process each potential bitmap_element in turn.  The loop is written
     this way rather than per array element because usually there are
     only a small number of array elements per bitmap element (typically
     two or four).  The inner loops should therefore unroll completely.  */
  const array_element_type *array_elements = Traits::base (array);
  unsigned int indx = 0;
  for (size_t array_base = 0;
       array_base < array_size;
       array_base += array_step, indx += 1)
    {
      /* How many array elements are in this particular bitmap_element.  */
      unsigned int array_count
        = (STATIC_CONSTANT_P (array_size % array_step == 0)
           ? array_step : MIN (array_step, array_size - array_base));
 
      /* See whether we need this bitmap element.  */
      array_element_type ior = array_elements[array_base];
      for (size_t i = 1; i < array_count; ++i)
        ior |= array_elements[array_base + i];
      if (ior == 0)
        continue;
 
      /* Grab the next bitmap element and chain it.  */
      bitmap_element *bitmap_element = bitmap_elements++;
      if (m_head.current)
        m_head.current->next = bitmap_element;
      else
        m_head.first = bitmap_element;
      bitmap_element->prev = m_head.current;
      bitmap_element->next = NULL;
      bitmap_element->indx = indx;
      m_head.current = bitmap_element;
      m_head.indx = indx;
 
      /* Fill in the bits of the bitmap element.  */
      if (array_element_bits < BITMAP_WORD_BITS)
        {
          /* Multiple array elements fit in one element of
             bitmap_element->bits.  */
          size_t array_i = array_base;
          for (unsigned int word_i = 0; word_i < BITMAP_ELEMENT_WORDS;
               ++word_i)
            {
              BITMAP_WORD word = 0;
              for (unsigned int shift = 0;
                   shift < BITMAP_WORD_BITS && array_i < array_size;
                   shift += array_element_bits)
                word |= array_elements[array_i++] << shift;
              bitmap_element->bits[word_i] = word;
            }
        }
      else
        {
          /* Array elements are the same size as elements of
             bitmap_element->bits, or are an exact multiple of that size.  */
          unsigned int word_i = 0;
          for (unsigned int i = 0; i < array_count; ++i)
            for (unsigned int shift = 0; shift < array_element_bits;
                 shift += BITMAP_WORD_BITS)
              bitmap_element->bits[word_i++]
                = array_elements[array_base + i] >> shift;
          while (word_i < BITMAP_ELEMENT_WORDS)
            bitmap_element->bits[word_i++] = 0;
        }
    }
}
 
#endif /* GCC_BITMAP_H */