/* Functions to support general ended bitmaps. Copyright (C) 1997-2014 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 . */ #ifndef GCC_BITMAP_H #define GCC_BITMAP_H /* Implementation of sparse integer sets as a linked list. This sparse set representation is suitable for sparse sets with an unknown (a priori) universe. The set is represented as a double-linked list of container nodes (struct bitmap_element). Each 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. The elements 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. 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 downside is that many 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: * clear : bitmap_clear * choose_one : (not implemented, but could be implemented in constant time) The following operations can be performed in O(E) time worst-case (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 * remove_member : bitmap_clear_bit The following operations can be performed in O(E) time: * cardinality : bitmap_count_bits * set_size : bitmap_last_set_bit (but this could in constant time with a pointer to the last element in the chain) 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 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 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). 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.). 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. 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. For random-access sets of unknown universe, a hash table or a balanced binary tree representation is likely to be a more suitable choice. Traversing linked lists is usually cache-unfriendly, even with the last accessed element cached. Cache performance can be improved by keeping the elements 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. */ #include "hashtab.h" #include "statistics.h" #include "obstack.h" /* 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 GTY (()) bitmap_obstack { struct bitmap_element *elements; struct bitmap_head *heads; struct obstack GTY ((skip)) 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"), chain_prev ("%h.prev"))) bitmap_element { struct bitmap_element *next; /* Next element. */ struct bitmap_element *prev; /* Previous element. */ unsigned int indx; /* regno/BITMAP_ELEMENT_ALL_BITS. */ BITMAP_WORD bits[BITMAP_ELEMENT_WORDS]; /* Bits that are set. */ }; /* Head of bitmap linked list. The 'current' member points to something already pointed to by the chain started by first, so GTY((skip)) it. */ struct GTY(()) bitmap_head { unsigned int indx; /* Index of last element looked at. */ unsigned int descriptor_id; /* Unique identifier for the allocation site of this bitmap, for detailed statistics gathering. */ bitmap_element *first; /* First element in linked list. */ bitmap_element * GTY((skip(""))) current; /* Last element looked at. */ bitmap_obstack *obstack; /* Obstack to allocate elements from. If NULL, then use GGC allocation. */ }; /* Global data */ extern bitmap_element bitmap_zero_bits; /* Zero bitmap element */ extern bitmap_obstack bitmap_default_obstack; /* Default bitmap obstack */ /* 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); /* 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); /* 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 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 register is set in a register set. */ extern int bitmap_bit_p (bitmap, int); /* Debug functions to print a bitmap linked list. */ 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. */ static inline void bitmap_initialize_stat (bitmap head, bitmap_obstack *obstack MEM_STAT_DECL) { head->first = head->current = NULL; head->obstack = obstack; if (GATHER_STATISTICS) bitmap_register (head PASS_MEM_STAT); } #define bitmap_initialize(h,o) bitmap_initialize_stat (h,o MEM_STAT_INFO) /* Allocate and free bitmaps from obstack, malloc and gc'd memory. */ extern bitmap bitmap_obstack_alloc_stat (bitmap_obstack *obstack MEM_STAT_DECL); #define bitmap_obstack_alloc(t) bitmap_obstack_alloc_stat (t MEM_STAT_INFO) extern bitmap bitmap_gc_alloc_stat (ALONE_MEM_STAT_DECL); #define bitmap_gc_alloc() bitmap_gc_alloc_stat (ALONE_MEM_STAT_INFO) 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_last_set_bit (const_bitmap); /* Compute bitmap hash (for purposes of hashing etc.) */ extern hashval_t bitmap_hash (const_bitmap); /* Allocate a bitmap from a bit obstack. */ #define BITMAP_ALLOC(OBSTACK) bitmap_obstack_alloc (OBSTACK) /* Allocate a gc'd bitmap. */ #define BITMAP_GGC_ALLOC() bitmap_gc_alloc () /* 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. */ static 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; /* 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. */ static 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; /* 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. */ static 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; /* 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. */ static inline void bmp_iter_next (bitmap_iterator *bi, unsigned *bit_no) { bi->bits >>= 1; *bit_no += 1; } /* Advance to first set bit in BI. */ static 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. */ static 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++; } /* 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. */ static 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 { /* 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); /* 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. */ static 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++; } /* Advance to the next element of elt1. */ bi->elt1 = bi->elt1->next; if (!bi->elt1) return false; /* 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; } } /* 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))) #endif /* GCC_BITMAP_H */