/* bit_array.c project: bit array C library url: https://github.com/noporpoise/BitArray/ maintainer: Isaac Turner license: Public Domain, no warranty date: Aug 2014 */ // 64 bit words // Array length can be zero // Unused top bits must be zero #include #include #include #include // ULONG_MAX #include #include // needed for abort() #include // memset() #include #include // needed for seeding rand() #include // need for getpid() for seeding rand number #include // need for tolower() #include // perror() #include // for seeding random // Windows includes #if defined(_WIN32) #include #endif #include "bit_array.h" #include "bit_macros.h" // // Tables of constants // // byte reverse look up table static const word_t reverse_table[256] = { 0x00, 0x80, 0x40, 0xC0, 0x20, 0xA0, 0x60, 0xE0, 0x10, 0x90, 0x50, 0xD0, 0x30, 0xB0, 0x70, 0xF0, 0x08, 0x88, 0x48, 0xC8, 0x28, 0xA8, 0x68, 0xE8, 0x18, 0x98, 0x58, 0xD8, 0x38, 0xB8, 0x78, 0xF8, 0x04, 0x84, 0x44, 0xC4, 0x24, 0xA4, 0x64, 0xE4, 0x14, 0x94, 0x54, 0xD4, 0x34, 0xB4, 0x74, 0xF4, 0x0C, 0x8C, 0x4C, 0xCC, 0x2C, 0xAC, 0x6C, 0xEC, 0x1C, 0x9C, 0x5C, 0xDC, 0x3C, 0xBC, 0x7C, 0xFC, 0x02, 0x82, 0x42, 0xC2, 0x22, 0xA2, 0x62, 0xE2, 0x12, 0x92, 0x52, 0xD2, 0x32, 0xB2, 0x72, 0xF2, 0x0A, 0x8A, 0x4A, 0xCA, 0x2A, 0xAA, 0x6A, 0xEA, 0x1A, 0x9A, 0x5A, 0xDA, 0x3A, 0xBA, 0x7A, 0xFA, 0x06, 0x86, 0x46, 0xC6, 0x26, 0xA6, 0x66, 0xE6, 0x16, 0x96, 0x56, 0xD6, 0x36, 0xB6, 0x76, 0xF6, 0x0E, 0x8E, 0x4E, 0xCE, 0x2E, 0xAE, 0x6E, 0xEE, 0x1E, 0x9E, 0x5E, 0xDE, 0x3E, 0xBE, 0x7E, 0xFE, 0x01, 0x81, 0x41, 0xC1, 0x21, 0xA1, 0x61, 0xE1, 0x11, 0x91, 0x51, 0xD1, 0x31, 0xB1, 0x71, 0xF1, 0x09, 0x89, 0x49, 0xC9, 0x29, 0xA9, 0x69, 0xE9, 0x19, 0x99, 0x59, 0xD9, 0x39, 0xB9, 0x79, 0xF9, 0x05, 0x85, 0x45, 0xC5, 0x25, 0xA5, 0x65, 0xE5, 0x15, 0x95, 0x55, 0xD5, 0x35, 0xB5, 0x75, 0xF5, 0x0D, 0x8D, 0x4D, 0xCD, 0x2D, 0xAD, 0x6D, 0xED, 0x1D, 0x9D, 0x5D, 0xDD, 0x3D, 0xBD, 0x7D, 0xFD, 0x03, 0x83, 0x43, 0xC3, 0x23, 0xA3, 0x63, 0xE3, 0x13, 0x93, 0x53, 0xD3, 0x33, 0xB3, 0x73, 0xF3, 0x0B, 0x8B, 0x4B, 0xCB, 0x2B, 0xAB, 0x6B, 0xEB, 0x1B, 0x9B, 0x5B, 0xDB, 0x3B, 0xBB, 0x7B, 0xFB, 0x07, 0x87, 0x47, 0xC7, 0x27, 0xA7, 0x67, 0xE7, 0x17, 0x97, 0x57, 0xD7, 0x37, 0xB7, 0x77, 0xF7, 0x0F, 0x8F, 0x4F, 0xCF, 0x2F, 0xAF, 0x6F, 0xEF, 0x1F, 0x9F, 0x5F, 0xDF, 0x3F, 0xBF, 0x7F, 0xFF, }; // Morton table for interleaving bytes static const word_t morton_table0[256] = { 0x0000, 0x0001, 0x0004, 0x0005, 0x0010, 0x0011, 0x0014, 0x0015, 0x0040, 0x0041, 0x0044, 0x0045, 0x0050, 0x0051, 0x0054, 0x0055, 0x0100, 0x0101, 0x0104, 0x0105, 0x0110, 0x0111, 0x0114, 0x0115, 0x0140, 0x0141, 0x0144, 0x0145, 0x0150, 0x0151, 0x0154, 0x0155, 0x0400, 0x0401, 0x0404, 0x0405, 0x0410, 0x0411, 0x0414, 0x0415, 0x0440, 0x0441, 0x0444, 0x0445, 0x0450, 0x0451, 0x0454, 0x0455, 0x0500, 0x0501, 0x0504, 0x0505, 0x0510, 0x0511, 0x0514, 0x0515, 0x0540, 0x0541, 0x0544, 0x0545, 0x0550, 0x0551, 0x0554, 0x0555, 0x1000, 0x1001, 0x1004, 0x1005, 0x1010, 0x1011, 0x1014, 0x1015, 0x1040, 0x1041, 0x1044, 0x1045, 0x1050, 0x1051, 0x1054, 0x1055, 0x1100, 0x1101, 0x1104, 0x1105, 0x1110, 0x1111, 0x1114, 0x1115, 0x1140, 0x1141, 0x1144, 0x1145, 0x1150, 0x1151, 0x1154, 0x1155, 0x1400, 0x1401, 0x1404, 0x1405, 0x1410, 0x1411, 0x1414, 0x1415, 0x1440, 0x1441, 0x1444, 0x1445, 0x1450, 0x1451, 0x1454, 0x1455, 0x1500, 0x1501, 0x1504, 0x1505, 0x1510, 0x1511, 0x1514, 0x1515, 0x1540, 0x1541, 0x1544, 0x1545, 0x1550, 0x1551, 0x1554, 0x1555, 0x4000, 0x4001, 0x4004, 0x4005, 0x4010, 0x4011, 0x4014, 0x4015, 0x4040, 0x4041, 0x4044, 0x4045, 0x4050, 0x4051, 0x4054, 0x4055, 0x4100, 0x4101, 0x4104, 0x4105, 0x4110, 0x4111, 0x4114, 0x4115, 0x4140, 0x4141, 0x4144, 0x4145, 0x4150, 0x4151, 0x4154, 0x4155, 0x4400, 0x4401, 0x4404, 0x4405, 0x4410, 0x4411, 0x4414, 0x4415, 0x4440, 0x4441, 0x4444, 0x4445, 0x4450, 0x4451, 0x4454, 0x4455, 0x4500, 0x4501, 0x4504, 0x4505, 0x4510, 0x4511, 0x4514, 0x4515, 0x4540, 0x4541, 0x4544, 0x4545, 0x4550, 0x4551, 0x4554, 0x4555, 0x5000, 0x5001, 0x5004, 0x5005, 0x5010, 0x5011, 0x5014, 0x5015, 0x5040, 0x5041, 0x5044, 0x5045, 0x5050, 0x5051, 0x5054, 0x5055, 0x5100, 0x5101, 0x5104, 0x5105, 0x5110, 0x5111, 0x5114, 0x5115, 0x5140, 0x5141, 0x5144, 0x5145, 0x5150, 0x5151, 0x5154, 0x5155, 0x5400, 0x5401, 0x5404, 0x5405, 0x5410, 0x5411, 0x5414, 0x5415, 0x5440, 0x5441, 0x5444, 0x5445, 0x5450, 0x5451, 0x5454, 0x5455, 0x5500, 0x5501, 0x5504, 0x5505, 0x5510, 0x5511, 0x5514, 0x5515, 0x5540, 0x5541, 0x5544, 0x5545, 0x5550, 0x5551, 0x5554, 0x5555, }; // Morton table for interleaving bytes, shifted left 1 bit static const word_t morton_table1[256] = { 0x0000, 0x0002, 0x0008, 0x000A, 0x0020, 0x0022, 0x0028, 0x002A, 0x0080, 0x0082, 0x0088, 0x008A, 0x00A0, 0x00A2, 0x00A8, 0x00AA, 0x0200, 0x0202, 0x0208, 0x020A, 0x0220, 0x0222, 0x0228, 0x022A, 0x0280, 0x0282, 0x0288, 0x028A, 0x02A0, 0x02A2, 0x02A8, 0x02AA, 0x0800, 0x0802, 0x0808, 0x080A, 0x0820, 0x0822, 0x0828, 0x082A, 0x0880, 0x0882, 0x0888, 0x088A, 0x08A0, 0x08A2, 0x08A8, 0x08AA, 0x0A00, 0x0A02, 0x0A08, 0x0A0A, 0x0A20, 0x0A22, 0x0A28, 0x0A2A, 0x0A80, 0x0A82, 0x0A88, 0x0A8A, 0x0AA0, 0x0AA2, 0x0AA8, 0x0AAA, 0x2000, 0x2002, 0x2008, 0x200A, 0x2020, 0x2022, 0x2028, 0x202A, 0x2080, 0x2082, 0x2088, 0x208A, 0x20A0, 0x20A2, 0x20A8, 0x20AA, 0x2200, 0x2202, 0x2208, 0x220A, 0x2220, 0x2222, 0x2228, 0x222A, 0x2280, 0x2282, 0x2288, 0x228A, 0x22A0, 0x22A2, 0x22A8, 0x22AA, 0x2800, 0x2802, 0x2808, 0x280A, 0x2820, 0x2822, 0x2828, 0x282A, 0x2880, 0x2882, 0x2888, 0x288A, 0x28A0, 0x28A2, 0x28A8, 0x28AA, 0x2A00, 0x2A02, 0x2A08, 0x2A0A, 0x2A20, 0x2A22, 0x2A28, 0x2A2A, 0x2A80, 0x2A82, 0x2A88, 0x2A8A, 0x2AA0, 0x2AA2, 0x2AA8, 0x2AAA, 0x8000, 0x8002, 0x8008, 0x800A, 0x8020, 0x8022, 0x8028, 0x802A, 0x8080, 0x8082, 0x8088, 0x808A, 0x80A0, 0x80A2, 0x80A8, 0x80AA, 0x8200, 0x8202, 0x8208, 0x820A, 0x8220, 0x8222, 0x8228, 0x822A, 0x8280, 0x8282, 0x8288, 0x828A, 0x82A0, 0x82A2, 0x82A8, 0x82AA, 0x8800, 0x8802, 0x8808, 0x880A, 0x8820, 0x8822, 0x8828, 0x882A, 0x8880, 0x8882, 0x8888, 0x888A, 0x88A0, 0x88A2, 0x88A8, 0x88AA, 0x8A00, 0x8A02, 0x8A08, 0x8A0A, 0x8A20, 0x8A22, 0x8A28, 0x8A2A, 0x8A80, 0x8A82, 0x8A88, 0x8A8A, 0x8AA0, 0x8AA2, 0x8AA8, 0x8AAA, 0xA000, 0xA002, 0xA008, 0xA00A, 0xA020, 0xA022, 0xA028, 0xA02A, 0xA080, 0xA082, 0xA088, 0xA08A, 0xA0A0, 0xA0A2, 0xA0A8, 0xA0AA, 0xA200, 0xA202, 0xA208, 0xA20A, 0xA220, 0xA222, 0xA228, 0xA22A, 0xA280, 0xA282, 0xA288, 0xA28A, 0xA2A0, 0xA2A2, 0xA2A8, 0xA2AA, 0xA800, 0xA802, 0xA808, 0xA80A, 0xA820, 0xA822, 0xA828, 0xA82A, 0xA880, 0xA882, 0xA888, 0xA88A, 0xA8A0, 0xA8A2, 0xA8A8, 0xA8AA, 0xAA00, 0xAA02, 0xAA08, 0xAA0A, 0xAA20, 0xAA22, 0xAA28, 0xAA2A, 0xAA80, 0xAA82, 0xAA88, 0xAA8A, 0xAAA0, 0xAAA2, 0xAAA8, 0xAAAA, }; // // Macros // // WORD_SIZE is the number of bits per word // sizeof gives size in bytes (8 bits per byte) #define WORD_SIZE 64 // #define WORD_SIZE (sizeof(word_t) * 8) // POPCOUNT is number of bits set #if defined(_WIN32) // See http://graphics.stanford.edu/~seander/bithacks.html#CountBitsSetParallel static word_t __inline windows_popcount(word_t w) { w = w - ((w >> 1) & (word_t)~(word_t)0/3); w = (w & (word_t)~(word_t)0/15*3) + ((w >> 2) & (word_t)~(word_t)0/15*3); w = (w + (w >> 4)) & (word_t)~(word_t)0/255*15; c = (word_t)(w * ((word_t)~(word_t)0/255)) >> (sizeof(word_t) - 1) * 8; } static word_t __inline windows_parity(word_t w) { w ^= w >> 1; w ^= w >> 2; w = (w & 0x1111111111111111UL) * 0x1111111111111111UL; return (w >> 60) & 1; } #define POPCOUNT(x) windows_popcountl(x) #define PARITY(x) windows_parity(x) #else #define POPCOUNT(x) (unsigned)__builtin_popcountll(x) #define PARITY(x) (unsigned)__builtin_parityll(x) #endif #define MIN(a, b) (((a) <= (b)) ? (a) : (b)) #define MAX(a, b) (((a) >= (b)) ? (a) : (b)) // Make this a power of two #define INIT_CAPACITY_WORDS 2 // word of all 1s #define WORD_MAX (~(word_t)0) #define SET_REGION(arr,start,len) _set_region((arr),(start),(len),FILL_REGION) #define CLEAR_REGION(arr,start,len) _set_region((arr),(start),(len),ZERO_REGION) #define TOGGLE_REGION(arr,start,len) _set_region((arr),(start),(len),SWAP_REGION) // Have we initialised with srand() ? static char rand_initiated = 0; static void _seed_rand() { if(!rand_initiated) { // Initialise random number generator struct timeval time; gettimeofday(&time, NULL); srand((((time.tv_sec ^ getpid()) * 1000001) + time.tv_usec)); rand_initiated = 1; } } // // Common internal functions // #define bits_in_top_word(nbits) ((nbits) ? bitset64_idx((nbits) - 1) + 1 : 0) // Mostly used for debugging static inline void _print_word(word_t word, FILE* out) { word_offset_t i; for(i = 0; i < WORD_SIZE; i++) { fprintf(out, "%c", ((word >> i) & (word_t)0x1) == 0 ? '0' : '1'); } } // prints right to left static inline char* _word_to_str(word_t word, char str[WORD_SIZE+1]) __attribute__((unused)); static inline char* _word_to_str(word_t word, char str[WORD_SIZE+1]) { word_offset_t i; for(i = 0; i < WORD_SIZE; i++) { str[WORD_SIZE-i-1] = ((word >> i) & (word_t)0x1) == 0 ? '0' : '1'; } str[WORD_SIZE] = '\0'; return str; } // Used in debugging #ifdef DEBUG #define DEBUG_PRINT(msg,...) printf("[%s:%i] "msg, __FILE__, __LINE__, ##__VA_ARGS__); #define DEBUG_VALIDATE(a) validate_bitarr((a), __FILE__, __LINE__) #else #define DEBUG_PRINT(msg,...) #define DEBUG_VALIDATE(a) #endif void validate_bitarr(BIT_ARRAY *arr, const char *file, int lineno) { // Check top word is masked word_addr_t tw = arr->num_of_words == 0 ? 0 : arr->num_of_words - 1; bit_index_t top_bits = bits_in_top_word(arr->num_of_bits); int err = 0; if(arr->words[tw] > bitmask64(top_bits)) { _print_word(arr->words[tw], stderr); fprintf(stderr, "\n[%s:%i] Expected %i bits in top word[%i]\n", file, lineno, (int)top_bits, (int)tw); err = 1; } // Check num of words is correct word_addr_t num_words = roundup_bits2words64(arr->num_of_bits); if(num_words != arr->num_of_words) { fprintf(stderr, "\n[%s:%i] num of words wrong " "[bits: %i, word: %i, actual words: %i]\n", file, lineno, (int)arr->num_of_bits, (int)num_words, (int)arr->num_of_words); err = 1; } if(err) abort(); } // Reverse a word static inline word_t _reverse_word(word_t word) { word_t reverse = (reverse_table[(word) & 0xff] << 56) | (reverse_table[(word >> 8) & 0xff] << 48) | (reverse_table[(word >> 16) & 0xff] << 40) | (reverse_table[(word >> 24) & 0xff] << 32) | (reverse_table[(word >> 32) & 0xff] << 24) | (reverse_table[(word >> 40) & 0xff] << 16) | (reverse_table[(word >> 48) & 0xff] << 8) | (reverse_table[(word >> 56) & 0xff]); return reverse; } static inline void _mask_top_word(BIT_ARRAY* bitarr) { // Mask top word word_addr_t num_of_words = MAX(1, bitarr->num_of_words); word_offset_t bits_active = bits_in_top_word(bitarr->num_of_bits); bitarr->words[num_of_words-1] &= bitmask64(bits_active); } // // Get and set words (internal use only -- no bounds checking) // static inline word_t _get_word(const BIT_ARRAY* bitarr, bit_index_t start) { word_addr_t word_index = bitset64_wrd(start); word_offset_t word_offset = bitset64_idx(start); word_t result = bitarr->words[word_index] >> word_offset; word_offset_t bits_taken = WORD_SIZE - word_offset; // word_offset is now the number of bits we need from the next word // Check the next word has at least some bits if(word_offset > 0 && start + bits_taken < bitarr->num_of_bits) { result |= bitarr->words[word_index+1] << (WORD_SIZE - word_offset); } return result; } // Set 64 bits from a particular start position // Doesn't extend bit array static inline void _set_word(BIT_ARRAY* bitarr, bit_index_t start, word_t word) { word_addr_t word_index = bitset64_wrd(start); word_offset_t word_offset = bitset64_idx(start); if(word_offset == 0) { bitarr->words[word_index] = word; } else { bitarr->words[word_index] = (word << word_offset) | (bitarr->words[word_index] & bitmask64(word_offset)); if(word_index+1 < bitarr->num_of_words) { bitarr->words[word_index+1] = (word >> (WORD_SIZE - word_offset)) | (bitarr->words[word_index+1] & (WORD_MAX << word_offset)); } } // Mask top word _mask_top_word(bitarr); DEBUG_VALIDATE(bitarr); } static inline void _set_byte(BIT_ARRAY *bitarr, bit_index_t start, uint8_t byte) { word_t w = _get_word(bitarr, start); _set_word(bitarr, start, (w & ~(word_t)0xff) | byte); } // 4 bits static inline void _set_nibble(BIT_ARRAY *bitarr, bit_index_t start, uint8_t nibble) { word_t w = _get_word(bitarr, start); _set_word(bitarr, start, (w & ~(word_t)0xf) | nibble); } // Wrap around static inline word_t _get_word_cyclic(const BIT_ARRAY* bitarr, bit_index_t start) { word_t word = _get_word(bitarr, start); bit_index_t bits_taken = bitarr->num_of_bits - start; if(bits_taken < WORD_SIZE) { word |= (bitarr->words[0] << bits_taken); if(bitarr->num_of_bits < (bit_index_t)WORD_SIZE) { // Mask word to prevent repetition of the same bits word = word & bitmask64(bitarr->num_of_bits); } } return word; } // Wrap around static inline void _set_word_cyclic(BIT_ARRAY* bitarr, bit_index_t start, word_t word) { _set_word(bitarr, start, word); bit_index_t bits_set = bitarr->num_of_bits - start; if(bits_set < WORD_SIZE && start > 0) { word >>= bits_set; // Prevent overwriting the bits we've just set // by setting 'start' as the upper bound for the number of bits to write word_offset_t bits_remaining = MIN(WORD_SIZE - bits_set, start); word_t mask = bitmask64(bits_remaining); bitarr->words[0] = bitmask_merge(word, bitarr->words[0], mask); } } // // Fill a region (internal use only) // // FillAction is fill with 0 or 1 or toggle typedef enum {ZERO_REGION, FILL_REGION, SWAP_REGION} FillAction; static inline void _set_region(BIT_ARRAY* bitarr, bit_index_t start, bit_index_t length, FillAction action) { if(length == 0) return; word_addr_t first_word = bitset64_wrd(start); word_addr_t last_word = bitset64_wrd(start+length-1); word_offset_t foffset = bitset64_idx(start); word_offset_t loffset = bitset64_idx(start+length-1); if(first_word == last_word) { word_t mask = bitmask64(length) << foffset; switch(action) { case ZERO_REGION: bitarr->words[first_word] &= ~mask; break; case FILL_REGION: bitarr->words[first_word] |= mask; break; case SWAP_REGION: bitarr->words[first_word] ^= mask; break; } } else { // Set first word switch(action) { case ZERO_REGION: bitarr->words[first_word] &= bitmask64(foffset); break; case FILL_REGION: bitarr->words[first_word] |= ~bitmask64(foffset); break; case SWAP_REGION: bitarr->words[first_word] ^= ~bitmask64(foffset); break; } word_addr_t i; // Set whole words switch(action) { case ZERO_REGION: for(i = first_word + 1; i < last_word; i++) bitarr->words[i] = (word_t)0; break; case FILL_REGION: for(i = first_word + 1; i < last_word; i++) bitarr->words[i] = WORD_MAX; break; case SWAP_REGION: for(i = first_word + 1; i < last_word; i++) bitarr->words[i] ^= WORD_MAX; break; } // Set last word switch(action) { case ZERO_REGION: bitarr->words[last_word] &= ~bitmask64(loffset+1); break; case FILL_REGION: bitarr->words[last_word] |= bitmask64(loffset+1); break; case SWAP_REGION: bitarr->words[last_word] ^= bitmask64(loffset+1); break; } } } // // Constructor // // If cannot allocate memory, set errno to ENOMEM, return NULL BIT_ARRAY* bit_array_alloc(BIT_ARRAY* bitarr, bit_index_t nbits) { bitarr->num_of_bits = nbits; bitarr->num_of_words = roundup_bits2words64(nbits); bitarr->capacity_in_words = MAX(8, roundup2pow(bitarr->num_of_words)); bitarr->words = (word_t*)calloc(bitarr->capacity_in_words, sizeof(word_t)); if(bitarr->words == NULL) { errno = ENOMEM; return NULL; } return bitarr; } void bit_array_dealloc(BIT_ARRAY* bitarr) { free(bitarr->words); memset(bitarr, 0, sizeof(BIT_ARRAY)); } // If cannot allocate memory, set errno to ENOMEM, return NULL BIT_ARRAY* bit_array_create(bit_index_t nbits) { BIT_ARRAY* bitarr = (BIT_ARRAY*)malloc(sizeof(BIT_ARRAY)); // error if could not allocate enough memory if(bitarr == NULL || bit_array_alloc(bitarr, nbits) == NULL) { if(bitarr != NULL) free(bitarr); errno = ENOMEM; return NULL; } DEBUG_PRINT("Creating BIT_ARRAY (bits: %lu; allocated words: %lu; " "using words: %lu; WORD_SIZE: %i)\n", (unsigned long)nbits, (unsigned long)bitarr->capacity_in_words, (unsigned long)roundup_bits2words64(nbits), (int)WORD_SIZE); DEBUG_VALIDATE(bitarr); return bitarr; } // // Destructor // void bit_array_free(BIT_ARRAY* bitarr) { if(bitarr->words != NULL) free(bitarr->words); free(bitarr); } bit_index_t bit_array_length(const BIT_ARRAY* bit_arr) { return bit_arr->num_of_bits; } // Change the size of a bit array. Enlarging an array will add zeros // to the end of it. Returns 1 on success, 0 on failure (e.g. not enough memory) char bit_array_resize(BIT_ARRAY* bitarr, bit_index_t new_num_of_bits) { word_addr_t old_num_of_words = bitarr->num_of_words; word_addr_t new_num_of_words = roundup_bits2words64(new_num_of_bits); bitarr->num_of_bits = new_num_of_bits; bitarr->num_of_words = new_num_of_words; DEBUG_PRINT("Resize: old_num_of_words: %i; new_num_of_words: %i capacity: %i\n", (int)old_num_of_words, (int)new_num_of_words, (int)bitarr->capacity_in_words); if(new_num_of_words > bitarr->capacity_in_words) { // Need to change the amount of memory used word_addr_t old_capacity_in_words = bitarr->capacity_in_words; size_t old_capacity_in_bytes = old_capacity_in_words * sizeof(word_t); bitarr->capacity_in_words = roundup2pow(new_num_of_words); bitarr->capacity_in_words = MAX(8, bitarr->capacity_in_words); size_t new_capacity_in_bytes = bitarr->capacity_in_words * sizeof(word_t); bitarr->words = (word_t*)realloc(bitarr->words, new_capacity_in_bytes); if(bitarr->words == NULL) { // error - could not allocate enough memory perror("resize realloc"); errno = ENOMEM; return 0; } // Need to zero new memory size_t num_bytes_to_zero = new_capacity_in_bytes - old_capacity_in_bytes; memset(bitarr->words + old_capacity_in_words, 0, num_bytes_to_zero); DEBUG_PRINT("zeroing from word %i for %i bytes\n", (int)old_capacity_in_words, (int)num_bytes_to_zero); } else if(new_num_of_words < old_num_of_words) { // Shrunk -- need to zero old memory size_t num_bytes_to_zero = (old_num_of_words - new_num_of_words)*sizeof(word_t); memset(bitarr->words + new_num_of_words, 0, num_bytes_to_zero); } // Mask top word _mask_top_word(bitarr); DEBUG_VALIDATE(bitarr); return 1; } void bit_array_resize_critical(BIT_ARRAY* bitarr, bit_index_t num_of_bits) { bit_index_t old_num_of_bits = bitarr->num_of_bits; if(!bit_array_resize(bitarr, num_of_bits)) { fprintf(stderr, "Ran out of memory resizing [%lu -> %lu]", (unsigned long)old_num_of_bits, (unsigned long)num_of_bits); abort(); } } // If bitarr length < num_bits, resizes to num_bits char bit_array_ensure_size(BIT_ARRAY* bitarr, bit_index_t ensure_num_of_bits) { if(bitarr->num_of_bits < ensure_num_of_bits) { return bit_array_resize(bitarr, ensure_num_of_bits); } return 1; } void bit_array_ensure_size_critical(BIT_ARRAY* bitarr, bit_index_t num_of_bits) { if(num_of_bits > bitarr->num_of_bits) { bit_array_resize_critical(bitarr, num_of_bits); } } static inline void _bit_array_ensure_nwords(BIT_ARRAY* bitarr, word_addr_t nwords, const char *file, int lineno, const char *func) { size_t newmem, oldmem; if(bitarr->capacity_in_words < nwords) { oldmem = bitarr->capacity_in_words * sizeof(word_t); bitarr->capacity_in_words = roundup2pow(nwords); newmem = bitarr->capacity_in_words * sizeof(word_t); bitarr->words = (word_t*)realloc(bitarr->words, newmem); if(bitarr->words == NULL) { fprintf(stderr, "[%s:%i:%s()] Ran out of memory resizing [%zu -> %zu]", file, lineno, func, oldmem, newmem); abort(); } DEBUG_PRINT("Ensure nwords realloc %zu -> %zu\n", oldmem, newmem); } } // // Get, set, clear, assign and toggle individual bits // // Get the value of a bit (returns 0 or 1) char bit_array_get_bit(const BIT_ARRAY* bitarr, bit_index_t b) { assert(b < bitarr->num_of_bits); return bit_array_get(bitarr, b); } // set a bit (to 1) at position b void bit_array_set_bit(BIT_ARRAY* bitarr, bit_index_t b) { assert(b < bitarr->num_of_bits); bit_array_set(bitarr,b); DEBUG_VALIDATE(bitarr); } // clear a bit (to 0) at position b void bit_array_clear_bit(BIT_ARRAY* bitarr, bit_index_t b) { assert(b < bitarr->num_of_bits); bit_array_clear(bitarr, b); DEBUG_VALIDATE(bitarr); } // If bit is 0 -> 1, if bit is 1 -> 0. AKA 'flip' void bit_array_toggle_bit(BIT_ARRAY* bitarr, bit_index_t b) { assert(b < bitarr->num_of_bits); bit_array_toggle(bitarr, b); DEBUG_VALIDATE(bitarr); } // If char c != 0, set bit; otherwise clear bit void bit_array_assign_bit(BIT_ARRAY* bitarr, bit_index_t b, char c) { assert(b < bitarr->num_of_bits); bit_array_assign(bitarr, b, c ? 1 : 0); DEBUG_VALIDATE(bitarr); } // // Get, set etc with resize // // Get the value of a bit (returns 0 or 1) char bit_array_rget(BIT_ARRAY* bitarr, bit_index_t b) { bit_array_ensure_size_critical(bitarr, b+1); return bit_array_get(bitarr, b); } // set a bit (to 1) at position b void bit_array_rset(BIT_ARRAY* bitarr, bit_index_t b) { bit_array_ensure_size_critical(bitarr, b+1); bit_array_set(bitarr,b); DEBUG_VALIDATE(bitarr); } // clear a bit (to 0) at position b void bit_array_rclear(BIT_ARRAY* bitarr, bit_index_t b) { bit_array_ensure_size_critical(bitarr, b+1); bit_array_clear(bitarr, b); DEBUG_VALIDATE(bitarr); } // If bit is 0 -> 1, if bit is 1 -> 0. AKA 'flip' void bit_array_rtoggle(BIT_ARRAY* bitarr, bit_index_t b) { bit_array_ensure_size_critical(bitarr, b+1); bit_array_toggle(bitarr, b); DEBUG_VALIDATE(bitarr); } // If char c != 0, set bit; otherwise clear bit void bit_array_rassign(BIT_ARRAY* bitarr, bit_index_t b, char c) { bit_array_ensure_size_critical(bitarr, b+1); bit_array_assign(bitarr, b, c ? 1 : 0); DEBUG_VALIDATE(bitarr); } // // Set, clear and toggle several bits at once // // Set multiple bits at once. // e.g. set bits 1, 20 & 31: bit_array_set_bits(bitarr, 3, 1,20,31); void bit_array_set_bits(BIT_ARRAY* bitarr, size_t n, ...) { size_t i; va_list argptr; va_start(argptr, n); for(i = 0; i < n; i++) { unsigned int bit_index = va_arg(argptr, unsigned int); bit_array_set_bit(bitarr, bit_index); } va_end(argptr); DEBUG_VALIDATE(bitarr); } // Clear multiple bits at once. // e.g. clear bits 1, 20 & 31: bit_array_clear_bits(bitarr, 3, 1,20,31); void bit_array_clear_bits(BIT_ARRAY* bitarr, size_t n, ...) { size_t i; va_list argptr; va_start(argptr, n); for(i = 0; i < n; i++) { unsigned int bit_index = va_arg(argptr, unsigned int); bit_array_clear_bit(bitarr, bit_index); } va_end(argptr); DEBUG_VALIDATE(bitarr); } // Toggle multiple bits at once // e.g. toggle bits 1, 20 & 31: bit_array_toggle_bits(bitarr, 3, 1,20,31); void bit_array_toggle_bits(BIT_ARRAY* bitarr, size_t n, ...) { size_t i; va_list argptr; va_start(argptr, n); for(i = 0; i < n; i++) { unsigned int bit_index = va_arg(argptr, unsigned int); bit_array_toggle_bit(bitarr, bit_index); } va_end(argptr); DEBUG_VALIDATE(bitarr); } // // Set, clear and toggle all bits in a region // // Set all the bits in a region void bit_array_set_region(BIT_ARRAY* bitarr, bit_index_t start, bit_index_t len) { assert(start + len <= bitarr->num_of_bits); SET_REGION(bitarr, start, len); DEBUG_VALIDATE(bitarr); } // Clear all the bits in a region void bit_array_clear_region(BIT_ARRAY* bitarr, bit_index_t start, bit_index_t len) { assert(start + len <= bitarr->num_of_bits); CLEAR_REGION(bitarr, start, len); DEBUG_VALIDATE(bitarr); } // Toggle all the bits in a region void bit_array_toggle_region(BIT_ARRAY* bitarr, bit_index_t start, bit_index_t len) { assert(start + len <= bitarr->num_of_bits); TOGGLE_REGION(bitarr, start, len); DEBUG_VALIDATE(bitarr); } // // Set, clear and toggle all bits at once // // set all elements of data to one void bit_array_set_all(BIT_ARRAY* bitarr) { bit_index_t num_of_bytes = bitarr->num_of_words * sizeof(word_t); memset(bitarr->words, 0xFF, num_of_bytes); _mask_top_word(bitarr); DEBUG_VALIDATE(bitarr); } // set all elements of data to zero void bit_array_clear_all(BIT_ARRAY* bitarr) { memset(bitarr->words, 0, bitarr->num_of_words * sizeof(word_t)); DEBUG_VALIDATE(bitarr); } // Set all 1 bits to 0, and all 0 bits to 1. AKA flip void bit_array_toggle_all(BIT_ARRAY* bitarr) { word_addr_t i; for(i = 0; i < bitarr->num_of_words; i++) { bitarr->words[i] ^= WORD_MAX; } _mask_top_word(bitarr); DEBUG_VALIDATE(bitarr); } // // Get a word at a time // uint64_t bit_array_get_word64(const BIT_ARRAY* bitarr, bit_index_t start) { assert(start < bitarr->num_of_bits); return (uint64_t)_get_word(bitarr, start); } uint32_t bit_array_get_word32(const BIT_ARRAY* bitarr, bit_index_t start) { assert(start < bitarr->num_of_bits); return (uint32_t)_get_word(bitarr, start); } uint16_t bit_array_get_word16(const BIT_ARRAY* bitarr, bit_index_t start) { assert(start < bitarr->num_of_bits); return (uint16_t)_get_word(bitarr, start); } uint8_t bit_array_get_word8(const BIT_ARRAY* bitarr, bit_index_t start) { assert(start < bitarr->num_of_bits); return (uint8_t)_get_word(bitarr, start); } uint64_t bit_array_get_wordn(const BIT_ARRAY* bitarr, bit_index_t start, int n) { assert(start < bitarr->num_of_bits); assert(n <= 64); return (uint64_t)(_get_word(bitarr, start) & bitmask64(n)); } // // Set a word at a time // void bit_array_set_word64(BIT_ARRAY* bitarr, bit_index_t start, uint64_t word) { assert(start < bitarr->num_of_bits); _set_word(bitarr, start, (word_t)word); } void bit_array_set_word32(BIT_ARRAY* bitarr, bit_index_t start, uint32_t word) { assert(start < bitarr->num_of_bits); word_t w = _get_word(bitarr, start); _set_word(bitarr, start, (w & ~(word_t)0xffffffff) | word); } void bit_array_set_word16(BIT_ARRAY* bitarr, bit_index_t start, uint16_t word) { assert(start < bitarr->num_of_bits); word_t w = _get_word(bitarr, start); _set_word(bitarr, start, (w & ~(word_t)0xffff) | word); } void bit_array_set_word8(BIT_ARRAY* bitarr, bit_index_t start, uint8_t byte) { assert(start < bitarr->num_of_bits); _set_byte(bitarr, start, byte); } void bit_array_set_wordn(BIT_ARRAY* bitarr, bit_index_t start, uint64_t word, int n) { assert(start < bitarr->num_of_bits); assert(n <= 64); word_t w = _get_word(bitarr, start), m = bitmask64(n); _set_word(bitarr, start, bitmask_merge(word,w,m)); } // // Number of bits set // // Get the number of bits set (hamming weight) bit_index_t bit_array_num_bits_set(const BIT_ARRAY* bitarr) { word_addr_t i; bit_index_t num_of_bits_set = 0; for(i = 0; i < bitarr->num_of_words; i++) { if(bitarr->words[i] > 0) { num_of_bits_set += POPCOUNT(bitarr->words[i]); } } return num_of_bits_set; } // Get the number of bits not set (1 - hamming weight) bit_index_t bit_array_num_bits_cleared(const BIT_ARRAY* bitarr) { return bitarr->num_of_bits - bit_array_num_bits_set(bitarr); } // Get the number of bits set in on array and not the other. This is equivalent // to hamming weight of the XOR when the two arrays are the same length. // e.g. 10101 vs 00111 => hamming distance 2 (XOR is 10010) bit_index_t bit_array_hamming_distance(const BIT_ARRAY* arr1, const BIT_ARRAY* arr2) { word_addr_t min_words = MIN(arr1->num_of_words, arr2->num_of_words); word_addr_t max_words = MAX(arr1->num_of_words, arr2->num_of_words); bit_index_t hamming_distance = 0; word_addr_t i; for(i = 0; i < min_words; i++) { hamming_distance += POPCOUNT(arr1->words[i] ^ arr2->words[i]); } if(min_words != max_words) { const BIT_ARRAY* long_arr = (arr1->num_of_words > arr2->num_of_words ? arr1 : arr2); for(i = min_words; i < max_words; i++) { hamming_distance += POPCOUNT(long_arr->words[i]); } } return hamming_distance; } // Parity - returns 1 if odd number of bits set, 0 if even char bit_array_parity(const BIT_ARRAY* bitarr) { word_addr_t w; unsigned int parity = 0; for(w = 0; w < bitarr->num_of_words; w++) { parity ^= PARITY(bitarr->words[w]); } return (char)parity; } // // Find indices of set/clear bits // // Find the index of the next bit that is set/clear, at or after `offset` // Returns 1 if such a bit is found, otherwise 0 // Index is stored in the integer pointed to by `result` // If no such bit is found, value at `result` is not changed #define _next_bit_func_def(FUNC,GET) \ char FUNC(const BIT_ARRAY* bitarr, bit_index_t offset, bit_index_t* result) \ { \ assert(offset < bitarr->num_of_bits); \ if(bitarr->num_of_bits == 0 || offset >= bitarr->num_of_bits) { return 0; } \ \ /* Find first word that is greater than zero */ \ word_addr_t i = bitset64_wrd(offset); \ word_t w = GET(bitarr->words[i]) & ~bitmask64(bitset64_idx(offset)); \ \ while(1) { \ if(w > 0) { \ bit_index_t pos = i * WORD_SIZE + trailing_zeros(w); \ if(pos < bitarr->num_of_bits) { *result = pos; return 1; } \ else { return 0; } \ } \ i++; \ if(i >= bitarr->num_of_words) break; \ w = GET(bitarr->words[i]); \ } \ \ return 0; \ } // Find the index of the previous bit that is set/clear, before `offset`. // Returns 1 if such a bit is found, otherwise 0 // Index is stored in the integer pointed to by `result` // If no such bit is found, value at `result` is not changed #define _prev_bit_func_def(FUNC,GET) \ char FUNC(const BIT_ARRAY* bitarr, bit_index_t offset, bit_index_t* result) \ { \ assert(offset <= bitarr->num_of_bits); \ if(bitarr->num_of_bits == 0 || offset == 0) { return 0; } \ \ /* Find prev word that is greater than zero */ \ word_addr_t i = bitset64_wrd(offset-1); \ word_t w = GET(bitarr->words[i]) & bitmask64(bitset64_idx(offset-1)+1); \ \ if(w > 0) { *result = (i+1) * WORD_SIZE - leading_zeros(w) - 1; return 1; } \ \ /* i is unsigned so have to use break when i == 0 */ \ for(--i; i != BIT_INDEX_MAX; i--) { \ w = GET(bitarr->words[i]); \ if(w > 0) { \ *result = (i+1) * WORD_SIZE - leading_zeros(w) - 1; \ return 1; \ } \ } \ \ return 0; \ } #define GET_WORD(x) (x) #define NEG_WORD(x) (~(x)) _next_bit_func_def(bit_array_find_next_set_bit, GET_WORD); _next_bit_func_def(bit_array_find_next_clear_bit,NEG_WORD); _prev_bit_func_def(bit_array_find_prev_set_bit, GET_WORD); _prev_bit_func_def(bit_array_find_prev_clear_bit,NEG_WORD); // Find the index of the first bit that is set. // Returns 1 if a bit is set, otherwise 0 // Index of first set bit is stored in the integer pointed to by result // If no bits are set, value at `result` is not changed char bit_array_find_first_set_bit(const BIT_ARRAY* bitarr, bit_index_t* result) { return bit_array_find_next_set_bit(bitarr, 0, result); } // same same char bit_array_find_first_clear_bit(const BIT_ARRAY* bitarr, bit_index_t* result) { return bit_array_find_next_clear_bit(bitarr, 0, result); } // Find the index of the last bit that is set. // Returns 1 if a bit is set, otherwise 0 // Index of last set bit is stored in the integer pointed to by `result` // If no bits are set, value at `result` is not changed char bit_array_find_last_set_bit(const BIT_ARRAY* bitarr, bit_index_t* result) { return bit_array_find_prev_set_bit(bitarr, bitarr->num_of_bits, result); } // same same char bit_array_find_last_clear_bit(const BIT_ARRAY* bitarr, bit_index_t* result) { return bit_array_find_prev_clear_bit(bitarr, bitarr->num_of_bits, result); } // // "Sorting" bits // // Put all the 0s before all the 1s void bit_array_sort_bits(BIT_ARRAY* bitarr) { bit_index_t num_of_bits_set = bit_array_num_bits_set(bitarr); bit_index_t num_of_bits_cleared = bitarr->num_of_bits - num_of_bits_set; bit_array_set_all(bitarr); CLEAR_REGION(bitarr, 0, num_of_bits_cleared); DEBUG_VALIDATE(bitarr); } // Put all the 1s before all the 0s void bit_array_sort_bits_rev(BIT_ARRAY* bitarr) { bit_index_t num_of_bits_set = bit_array_num_bits_set(bitarr); bit_array_clear_all(bitarr); SET_REGION(bitarr, 0, num_of_bits_set); DEBUG_VALIDATE(bitarr); } // // Strings and printing // // Construct a BIT_ARRAY from a substring with given on and off characters. void bit_array_from_substr(BIT_ARRAY* bitarr, bit_index_t offset, const char *str, size_t len, const char *on, const char *off, char left_to_right) { bit_array_ensure_size(bitarr, offset + len); bit_array_clear_region(bitarr, offset, len); // BitArray region is now all 0s -- just set the 1s size_t i; bit_index_t j; for(i = 0; i < len; i++) { if(strchr(on, str[i]) != NULL) { j = offset + (left_to_right ? i : len - i - 1); bit_array_set(bitarr, j); } else { assert(strchr(off, str[i]) != NULL); } } DEBUG_VALIDATE(bitarr); } // From string method void bit_array_from_str(BIT_ARRAY* bitarr, const char* str) { bit_array_from_substr(bitarr, 0, str, strlen(str), "1", "0", 1); } // Takes a char array to write to. `str` must be bitarr->num_of_bits+1 in length // Terminates string with '\0' char* bit_array_to_str(const BIT_ARRAY* bitarr, char* str) { bit_index_t i; for(i = 0; i < bitarr->num_of_bits; i++) { str[i] = bit_array_get(bitarr, i) ? '1' : '0'; } str[bitarr->num_of_bits] = '\0'; return str; } char* bit_array_to_str_rev(const BIT_ARRAY* bitarr, char* str) { bit_index_t i; for(i = 0; i < bitarr->num_of_bits; i++) { str[i] = bit_array_get(bitarr, bitarr->num_of_bits-i-1) ? '1' : '0'; } str[bitarr->num_of_bits] = '\0'; return str; } // Get a string representations for a given region, using given on/off characters. // Note: does not null-terminate void bit_array_to_substr(const BIT_ARRAY* bitarr, bit_index_t start, bit_index_t length, char* str, char on, char off, char left_to_right) { assert(start + length <= bitarr->num_of_bits); bit_index_t i, j; bit_index_t end = start + length - 1; for(i = 0; i < length; i++) { j = (left_to_right ? start + i : end - i); str[i] = bit_array_get(bitarr, j) ? on : off; } // str[length] = '\0'; } // Print this array to a file stream. Prints '0's and '1'. Doesn't print newline. void bit_array_print(const BIT_ARRAY* bitarr, FILE* fout) { bit_index_t i; for(i = 0; i < bitarr->num_of_bits; i++) { fprintf(fout, "%c", bit_array_get(bitarr, i) ? '1' : '0'); } } // Print a string representations for a given region, using given on/off characters. void bit_array_print_substr(const BIT_ARRAY* bitarr, bit_index_t start, bit_index_t length, FILE* fout, char on, char off, char left_to_right) { assert(start + length <= bitarr->num_of_bits); bit_index_t i, j; bit_index_t end = start + length - 1; for(i = 0; i < length; i++) { j = (left_to_right ? start + i : end - i); fprintf(fout, "%c", bit_array_get(bitarr, j) ? on : off); } } // // Decimal // // Get bit array as decimal str (e.g. 0b1101 -> "13") // len is the length of str char array -- will write at most len-1 chars // returns the number of characters needed // return is the same as strlen(str) size_t bit_array_to_decimal(const BIT_ARRAY *bitarr, char *str, size_t len) { size_t i = 0; if(bit_array_cmp_uint64(bitarr, 0) == 0) { if(len >= 2) { *str = '0'; *(str+1) = '\0'; } return 1; } BIT_ARRAY *tmp = bit_array_clone(bitarr); uint64_t rem; str[len-1] = '\0'; while(bit_array_cmp_uint64(tmp, 0) != 0) { bit_array_div_uint64(tmp, 10, &rem); if(i < len-1) { str[len-2-i] = '0' + rem; } i++; } if(i < len-1) { // Moves null-terminator as well memmove(str, str+len-i-1, i+1); } bit_array_free(tmp); return i; } // Get bit array from decimal str (e.g. "13" -> 0b1101) // Returns number of characters used size_t bit_array_from_decimal(BIT_ARRAY *bitarr, const char* decimal) { bit_array_clear_all(bitarr); size_t i = 0; if(decimal[0] == '\0' || decimal[0] < '0' || decimal[0] > '9') { return 0; } bit_array_add_uint64(bitarr, decimal[i] - '0'); i++; while(decimal[i] != '\0' && decimal[i] >= '0' && decimal[i] <= '9') { bit_array_mul_uint64(bitarr, 10); bit_array_add_uint64(bitarr, decimal[i] - '0'); i++; } return i; } // // Hexidecimal // char bit_array_hex_to_nibble(char c, uint8_t *b) { c = tolower(c); if(c >= '0' && c <= '9') { *b = c - '0'; return 1; } else if(c >= 'a' && c <= 'f') { *b = 0xa + (c - 'a'); return 1; } else { return 0; } } char bit_array_nibble_to_hex(uint8_t b, char uppercase) { if(b <= 9) { return '0' + b; } else { return (uppercase ? 'A' : 'a') + (b - 0xa); } } // Loads array from hex string // Returns the number of bits loaded (will be chars rounded up to multiple of 4) // (0 on failure) bit_index_t bit_array_from_hex(BIT_ARRAY* bitarr, bit_index_t offset, const char* str, size_t len) { if(str[0] == '0' && tolower(str[1]) == 'x') { str += 2; len -= 2; } size_t i; for(i = 0; i < len; i++, offset += 4) { uint8_t b; if(bit_array_hex_to_nibble(str[i], &b)) { bit_array_ensure_size(bitarr, offset + 4); _set_nibble(bitarr, offset, b); } else { break; } } return 4 * i; } // Returns number of characters written size_t bit_array_to_hex(const BIT_ARRAY* bitarr, bit_index_t start, bit_index_t length, char* str, char uppercase) { assert(start + length <= bitarr->num_of_bits); size_t k = 0; bit_index_t offset, end = start + length; for(offset = start; offset + WORD_SIZE <= end; offset += WORD_SIZE) { word_t w = _get_word(bitarr, offset); word_offset_t j; for(j = 0; j < 64; j += 4) { str[k++] = bit_array_nibble_to_hex((w>>j) & 0xf, uppercase); } } if(offset < end) { // Remaining full nibbles (4 bits) word_t w = _get_word(bitarr, offset); for(; offset + 4 <= end; offset += 4) { str[k++] = bit_array_nibble_to_hex(w & 0xf, uppercase); w >>= 4; } if(offset < end) { // Remaining bits str[k++] = bit_array_nibble_to_hex(w & bitmask64(end - offset), uppercase); } } str[k] = '\0'; // Return number of characters written return k; } // Print bit array as hex size_t bit_array_print_hex(const BIT_ARRAY* bitarr, bit_index_t start, bit_index_t length, FILE* fout, char uppercase) { assert(start + length <= bitarr->num_of_bits); size_t k = 0; bit_index_t offset, end = start + length; for(offset = start; offset + WORD_SIZE <= end; offset += WORD_SIZE) { word_t w = _get_word(bitarr, offset); word_offset_t j; for(j = 0; j < 64; j += 4) { fprintf(fout, "%c", bit_array_nibble_to_hex((w>>j) & 0xf, uppercase)); k++; } } if(offset < end) { // Remaining full nibbles (4 bits) word_t w = _get_word(bitarr, offset); for(; offset + 4 <= end; offset += 4) { fprintf(fout, "%c", bit_array_nibble_to_hex(w & 0xf, uppercase)); w >>= 4; k++; } if(offset < end) { // Remaining bits char hex = bit_array_nibble_to_hex(w & bitmask64(end - offset), uppercase); fprintf(fout, "%c", hex); k++; } } return k; } // // Clone and copy // // Returns NULL if cannot malloc BIT_ARRAY* bit_array_clone(const BIT_ARRAY* bitarr) { BIT_ARRAY* cpy = bit_array_create(bitarr->num_of_bits); if(cpy == NULL) { return NULL; } // Copy across bits memcpy(cpy->words, bitarr->words, bitarr->num_of_words * sizeof(word_t)); DEBUG_VALIDATE(cpy); return cpy; } // destination and source may be the same bit_array // and src/dst regions may overlap static void _array_copy(BIT_ARRAY* dst, bit_index_t dstindx, const BIT_ARRAY* src, bit_index_t srcindx, bit_index_t length) { DEBUG_PRINT("bit_array_copy(dst: %zu, src: %zu, length: %zu)\n", (size_t)dstindx, (size_t)srcindx, (size_t)length); // Num of full words to copy word_addr_t num_of_full_words = length / WORD_SIZE; word_addr_t i; word_offset_t bits_in_last_word = bits_in_top_word(length); if(dst == src && srcindx > dstindx) { // Work left to right DEBUG_PRINT("work left to right\n"); for(i = 0; i < num_of_full_words; i++) { word_t word = _get_word(src, srcindx+i*WORD_SIZE); _set_word(dst, dstindx+i*WORD_SIZE, word); } if(bits_in_last_word > 0) { word_t src_word = _get_word(src, srcindx+i*WORD_SIZE); word_t dst_word = _get_word(dst, dstindx+i*WORD_SIZE); word_t mask = bitmask64(bits_in_last_word); word_t word = bitmask_merge(src_word, dst_word, mask); _set_word(dst, dstindx+num_of_full_words*WORD_SIZE, word); } } else { // Work right to left DEBUG_PRINT("work right to left\n"); for(i = 0; i < num_of_full_words; i++) { word_t word = _get_word(src, srcindx+length-(i+1)*WORD_SIZE); _set_word(dst, dstindx+length-(i+1)*WORD_SIZE, word); } DEBUG_PRINT("Copy %i,%i to %i\n", (int)srcindx, (int)bits_in_last_word, (int)dstindx); if(bits_in_last_word > 0) { word_t src_word = _get_word(src, srcindx); word_t dst_word = _get_word(dst, dstindx); word_t mask = bitmask64(bits_in_last_word); word_t word = bitmask_merge(src_word, dst_word, mask); _set_word(dst, dstindx, word); } } _mask_top_word(dst); } // destination and source may be the same bit_array // and src/dst regions may overlap void bit_array_copy(BIT_ARRAY* dst, bit_index_t dstindx, const BIT_ARRAY* src, bit_index_t srcindx, bit_index_t length) { assert(srcindx + length <= src->num_of_bits); assert(dstindx <= dst->num_of_bits); _array_copy(dst, dstindx, src, srcindx, length); DEBUG_VALIDATE(dst); } // Clone `src` into `dst`. Resizes `dst`. void bit_array_copy_all(BIT_ARRAY* dst, const BIT_ARRAY* src) { bit_array_resize_critical(dst, src->num_of_bits); memmove(dst->words, src->words, src->num_of_words * sizeof(word_t)); DEBUG_VALIDATE(dst); } // // Logic operators // // Destination can be the same as one or both of the sources void bit_array_and(BIT_ARRAY* dst, const BIT_ARRAY* src1, const BIT_ARRAY* src2) { // Ensure dst array is big enough word_addr_t max_bits = MAX(src1->num_of_bits, src2->num_of_bits); bit_array_ensure_size_critical(dst, max_bits); word_addr_t min_words = MIN(src1->num_of_words, src2->num_of_words); word_addr_t i; for(i = 0; i < min_words; i++) { dst->words[i] = src1->words[i] & src2->words[i]; } // Set remaining bits to zero for(i = min_words; i < dst->num_of_words; i++) { dst->words[i] = (word_t)0; } DEBUG_VALIDATE(dst); } // Destination can be the same as one or both of the sources static void _logical_or_xor(BIT_ARRAY* dst, const BIT_ARRAY* src1, const BIT_ARRAY* src2, char use_xor) { // Ensure dst array is big enough bit_array_ensure_size_critical(dst, MAX(src1->num_of_bits, src2->num_of_bits)); word_addr_t min_words = MIN(src1->num_of_words, src2->num_of_words); word_addr_t max_words = MAX(src1->num_of_words, src2->num_of_words); word_addr_t i; if(use_xor) { for(i = 0; i < min_words; i++) dst->words[i] = src1->words[i] ^ src2->words[i]; } else { for(i = 0; i < min_words; i++) dst->words[i] = src1->words[i] | src2->words[i]; } // Copy remaining bits from longer src array if(min_words != max_words) { const BIT_ARRAY* longer = src1->num_of_words > src2->num_of_words ? src1 : src2; for(i = min_words; i < max_words; i++) { dst->words[i] = longer->words[i]; } } // Set remaining bits to zero size_t size = (dst->num_of_words - max_words) * sizeof(word_t); memset(dst->words + max_words, 0, size); DEBUG_VALIDATE(dst); } void bit_array_or(BIT_ARRAY* dst, const BIT_ARRAY* src1, const BIT_ARRAY* src2) { _logical_or_xor(dst, src1, src2, 0); } // Destination can be the same as one or both of the sources void bit_array_xor(BIT_ARRAY* dst, const BIT_ARRAY* src1, const BIT_ARRAY* src2) { _logical_or_xor(dst, src1, src2, 1); } // If dst is longer than src, top bits are set to 1 void bit_array_not(BIT_ARRAY* dst, const BIT_ARRAY* src) { bit_array_ensure_size_critical(dst, src->num_of_bits); word_addr_t i; for(i = 0; i < src->num_of_words; i++) { dst->words[i] = ~(src->words[i]); } // Set remaining words to 1s for(i = src->num_of_words; i < dst->num_of_words; i++) { dst->words[i] = WORD_MAX; } _mask_top_word(dst); DEBUG_VALIDATE(dst); } // // Comparisons // // Compare two bit arrays by value stored, with index 0 being the Least // Significant Bit (LSB). Arrays do not have to be the same length. // Example: ..0101 (5) > ...0011 (3) [index 0 is LSB at right hand side] // Sorts on length if all zeros: (0,0) < (0,0,0) // returns: // >0 iff bitarr1 > bitarr2 // 0 iff bitarr1 == bitarr2 // <0 iff bitarr1 < bitarr2 int bit_array_cmp(const BIT_ARRAY* bitarr1, const BIT_ARRAY* bitarr2) { word_addr_t i; word_t word1, word2; word_addr_t min_words = bitarr1->num_of_words; // i is unsigned so break when i == 0 if(bitarr1->num_of_words > bitarr2->num_of_words) { min_words = bitarr2->num_of_words; for(i = bitarr1->num_of_words-1; ; i--) { if(bitarr1->words[i]) return 1; if(i == bitarr2->num_of_words) break; } } else if(bitarr1->num_of_words < bitarr2->num_of_words) { for(i = bitarr2->num_of_words-1; ; i--) { if(bitarr2->words[i]) return 1; if(i == bitarr1->num_of_words) break; } } if(min_words == 0) return 0; for(i = min_words-1; ; i--) { word1 = bitarr1->words[i]; word2 = bitarr2->words[i]; if(word1 != word2) return (word1 > word2 ? 1 : -1); if(i == 0) break; } if(bitarr1->num_of_bits == bitarr2->num_of_bits) return 0; return bitarr1->num_of_bits > bitarr2->num_of_bits ? 1 : -1; } // Compare two bit arrays by value stored, with index 0 being the Most // Significant Bit (MSB). Arrays do not have to be the same length. // Example: 10.. > 01.. [index 0 is MSB at left hand side] // Sorts on length if all zeros: (0,0) < (0,0,0) // returns: // >0 iff bitarr1 > bitarr2 // 0 iff bitarr1 == bitarr2 // <0 iff bitarr1 < bitarr2 int bit_array_cmp_big_endian(const BIT_ARRAY* bitarr1, const BIT_ARRAY* bitarr2) { word_addr_t min_words = MAX(bitarr1->num_of_words, bitarr2->num_of_words); word_addr_t i; word_t word1, word2; for(i = 0; i < min_words; i++) { word1 = _reverse_word(bitarr1->words[i]); word2 = _reverse_word(bitarr2->words[i]); if(word1 != word2) return (word1 > word2 ? 1 : -1); } // Check remaining words. Only one of these loops will execute for(; i < bitarr1->num_of_words; i++) if(bitarr1->words[i]) return 1; for(; i < bitarr2->num_of_words; i++) if(bitarr2->words[i]) return -1; if(bitarr1->num_of_bits == bitarr2->num_of_bits) return 0; return bitarr1->num_of_bits > bitarr2->num_of_bits ? 1 : -1; } // compare bitarr with (bitarr2 << pos) // bit_array_cmp(bitarr1, bitarr2<0 iff bitarr1 > bitarr2 // 0 iff bitarr1 == bitarr2 // <0 iff bitarr1 < bitarr2 int bit_array_cmp_words(const BIT_ARRAY *arr1, bit_index_t pos, const BIT_ARRAY *arr2) { if(arr1->num_of_bits == 0 && arr2->num_of_bits == 0) { return 0; } bit_index_t top_bit1 = 0, top_bit2 = 0; char arr1_zero = !bit_array_find_last_set_bit(arr1, &top_bit1); char arr2_zero = !bit_array_find_last_set_bit(arr2, &top_bit2); if(arr1_zero && arr2_zero) return 0; if(arr1_zero) return -1; if(arr2_zero) return 1; bit_index_t top_bit2_offset = top_bit2 + pos; if(top_bit1 != top_bit2_offset) { return top_bit1 > top_bit2_offset ? 1 : -1; } word_addr_t i; word_t word1, word2; for(i = top_bit2 / WORD_SIZE; i > 0; i--) { word1 = _get_word(arr1, pos + i * WORD_SIZE); word2 = arr2->words[i]; if(word1 > word2) return 1; if(word1 < word2) return -1; } word1 = _get_word(arr1, pos); word2 = arr2->words[0]; if(word1 > word2) return 1; if(word1 < word2) return -1; // return 1 if arr1[0..pos] != 0, 0 otherwise // Whole words word_addr_t num_words = pos / WORD_SIZE; for(i = 0; i < num_words; i++) { if(arr1->words[i] > 0) { return 1; } } word_offset_t bits_remaining = pos - num_words * WORD_SIZE; if(arr1->words[num_words] & bitmask64(bits_remaining)) { return 1; } return 0; } // // Reverse -- coords may wrap around // // No bounds checking // length cannot be zero static void _reverse_region(BIT_ARRAY* bitarr, bit_index_t start, bit_index_t length) { bit_index_t left = start; bit_index_t right = (start + length - WORD_SIZE) % bitarr->num_of_bits; while(length >= 2 * WORD_SIZE) { // Swap entire words word_t left_word = _get_word_cyclic(bitarr, left); word_t right_word = _get_word_cyclic(bitarr, right); // reverse words individually left_word = _reverse_word(left_word); right_word = _reverse_word(right_word); // Swap _set_word_cyclic(bitarr, left, right_word); _set_word_cyclic(bitarr, right, left_word); // Update left = (left + WORD_SIZE) % bitarr->num_of_bits; right = (right < WORD_SIZE ? right + bitarr->num_of_bits : right) - WORD_SIZE; length -= 2 * WORD_SIZE; } word_t word, rev; if(length == 0) { return; } else if(length > WORD_SIZE) { // Words overlap word_t left_word = _get_word_cyclic(bitarr, left); word_t right_word = _get_word_cyclic(bitarr, right); rev = _reverse_word(left_word); right_word = _reverse_word(right_word); // fill left 64 bits with right word rev _set_word_cyclic(bitarr, left, right_word); // Now do remaining bits (length is between 1 and 64 bits) left += WORD_SIZE; length -= WORD_SIZE; word = _get_word_cyclic(bitarr, left); } else { word = _get_word_cyclic(bitarr, left); rev = _reverse_word(word); } rev >>= WORD_SIZE - length; word_t mask = bitmask64(length); word = bitmask_merge(rev, word, mask); _set_word_cyclic(bitarr, left, word); } void bit_array_reverse_region(BIT_ARRAY* bitarr, bit_index_t start, bit_index_t len) { assert(start + len <= bitarr->num_of_bits); if(len > 0) _reverse_region(bitarr, start, len); DEBUG_VALIDATE(bitarr); } void bit_array_reverse(BIT_ARRAY* bitarr) { if(bitarr->num_of_bits > 0) _reverse_region(bitarr, 0, bitarr->num_of_bits); DEBUG_VALIDATE(bitarr); } // // Shift left / right // // Shift towards MSB / higher index void bit_array_shift_left(BIT_ARRAY* bitarr, bit_index_t shift_dist, char fill) { if(shift_dist >= bitarr->num_of_bits) { fill ? bit_array_set_all(bitarr) : bit_array_clear_all(bitarr); return; } else if(shift_dist == 0) { return; } FillAction action = fill ? FILL_REGION : ZERO_REGION; bit_index_t cpy_length = bitarr->num_of_bits - shift_dist; _array_copy(bitarr, shift_dist, bitarr, 0, cpy_length); _set_region(bitarr, 0, shift_dist, action); } // shift left extend - don't truncate bits when shifting UP, instead // make room for them. void bit_array_shift_left_extend(BIT_ARRAY* bitarr, bit_index_t shift_dist, char fill) { bit_index_t newlen = bitarr->num_of_bits + shift_dist; bit_index_t cpy_length = bitarr->num_of_bits; if(shift_dist == 0) { return; } bit_array_resize_critical(bitarr, newlen); FillAction action = fill ? FILL_REGION : ZERO_REGION; _array_copy(bitarr, shift_dist, bitarr, 0, cpy_length); _set_region(bitarr, 0, shift_dist, action); } // Shift towards LSB / lower index void bit_array_shift_right(BIT_ARRAY* bitarr, bit_index_t shift_dist, char fill) { if(shift_dist >= bitarr->num_of_bits) { fill ? bit_array_set_all(bitarr) : bit_array_clear_all(bitarr); return; } else if(shift_dist == 0) { return; } FillAction action = fill ? FILL_REGION : ZERO_REGION; bit_index_t cpy_length = bitarr->num_of_bits - shift_dist; bit_array_copy(bitarr, 0, bitarr, shift_dist, cpy_length); _set_region(bitarr, cpy_length, shift_dist, action); } // // Cycle // // Cycle towards index 0 void bit_array_cycle_right(BIT_ARRAY* bitarr, bit_index_t cycle_dist) { if(bitarr->num_of_bits == 0) { return; } cycle_dist = cycle_dist % bitarr->num_of_bits; if(cycle_dist == 0) { return; } bit_index_t len1 = cycle_dist; bit_index_t len2 = bitarr->num_of_bits - cycle_dist; _reverse_region(bitarr, 0, len1); _reverse_region(bitarr, len1, len2); bit_array_reverse(bitarr); } // Cycle away from index 0 void bit_array_cycle_left(BIT_ARRAY* bitarr, bit_index_t cycle_dist) { if(bitarr->num_of_bits == 0) { return; } cycle_dist = cycle_dist % bitarr->num_of_bits; if(cycle_dist == 0) { return; } bit_index_t len1 = bitarr->num_of_bits - cycle_dist; bit_index_t len2 = cycle_dist; _reverse_region(bitarr, 0, len1); _reverse_region(bitarr, len1, len2); bit_array_reverse(bitarr); } // // Next permutation // static word_t _next_permutation(word_t v) { // From http://graphics.stanford.edu/~seander/bithacks.html#NextBitPermutation word_t t = v | (v - 1); // t gets v's least significant 0 bits set to 1 // Next set to 1 the most significant bit to change, // set to 0 the least significant ones, and add the necessary 1 bits. return (t+1) | (((~t & (t+1)) - 1) >> (trailing_zeros(v) + 1)); } // Get the next permutation of an array with a fixed size and given number of // bits set. Also known as next lexicographic permutation. // Given a bit array find the next lexicographic orginisation of the bits // Number of possible combinations given by (size choose bits_set) i.e. nCk // 00011 -> 00101 -> 00110 -> 01001 -> 01010 -> // 01100 -> 10001 -> 10010 -> 10100 -> 11000 -> 00011 (back to start) void bit_array_next_permutation(BIT_ARRAY* bitarr) { if(bitarr->num_of_bits == 0) { return; } word_addr_t w; char carry = 0; word_offset_t top_bits = bitset64_idx(bitarr->num_of_bits); for(w = 0; w < bitarr->num_of_words; w++) { word_t mask = (w < bitarr->num_of_words - 1 || top_bits == 0) ? WORD_MAX : bitmask64(top_bits); if(bitarr->words[w] > 0 && (bitarr->words[w] | (bitarr->words[w]-1)) == mask) { // Bits in this word cannot be moved forward carry = 1; } else if(carry) { // 0111 -> 1000, 1000 -> 1001 word_t tmp = bitarr->words[w] + 1; // Count bits previously set bit_index_t bits_previously_set = POPCOUNT(bitarr->words[w]); // set new word bitarr->words[w] = tmp; // note: w is unsigned // Zero words while counting bits set while(w > 0) { bits_previously_set += POPCOUNT(bitarr->words[w-1]); bitarr->words[w-1] = 0; w--; } // Set bits at the beginning SET_REGION(bitarr, 0, bits_previously_set - POPCOUNT(tmp)); carry = 0; break; } else if(bitarr->words[w] > 0) { bitarr->words[w] = _next_permutation(bitarr->words[w]); break; } } if(carry) { // Loop around bit_index_t num_bits_set = bit_array_num_bits_set(bitarr); bit_array_clear_all(bitarr); SET_REGION(bitarr, 0, num_bits_set); } DEBUG_VALIDATE(bitarr); } // // Interleave // // dst cannot point to the same bit array as src1 or src2 // src1, src2 may point to the same bit array // abcd 1234 -> a1b2c3d4 // 0011 0000 -> 00001010 // 1111 0000 -> 10101010 // 0101 1010 -> 01100110 void bit_array_interleave(BIT_ARRAY* dst, const BIT_ARRAY* src1, const BIT_ARRAY* src2) { // dst cannot be either src1 or src2 assert(dst != src1 && dst != src2); // Behaviour undefined when src1 length != src2 length", assert(src1->num_of_bits == src2->num_of_bits); // Need at least src1->num_of_words + src2->num_of_words size_t nwords = MIN(src1->num_of_words + src2->num_of_words, 2); _bit_array_ensure_nwords(dst, nwords, __FILE__, __LINE__, __func__); dst->num_of_bits = src1->num_of_bits + src2->num_of_bits; dst->num_of_words = roundup_bits2words64(dst->num_of_bits); word_addr_t i, j; for(i = 0, j = 0; i < src1->num_of_words; i++) { word_t a = src1->words[i]; word_t b = src2->words[i]; dst->words[j++] = morton_table0[(a ) & 0xff] | morton_table1[(b ) & 0xff] | (morton_table0[(a >> 8) & 0xff] << 16) | (morton_table1[(b >> 8) & 0xff] << 16) | (morton_table0[(a >> 16) & 0xff] << 32) | (morton_table1[(b >> 16) & 0xff] << 32) | (morton_table0[(a >> 24) & 0xff] << 48) | (morton_table1[(b >> 24) & 0xff] << 48); dst->words[j++] = morton_table0[(a >> 32) & 0xff] | morton_table1[(b >> 32) & 0xff] | (morton_table0[(a >> 40) & 0xff] << 16) | (morton_table1[(b >> 40) & 0xff] << 16) | (morton_table0[(a >> 48) & 0xff] << 32) | (morton_table1[(b >> 48) & 0xff] << 32) | (morton_table0[(a >> 56) ] << 48) | (morton_table1[(b >> 56) ] << 48); } DEBUG_VALIDATE(dst); } // // Random // // Set bits randomly with probability prob : 0 <= prob <= 1 void bit_array_random(BIT_ARRAY* bitarr, float prob) { assert(prob >= 0 && prob <= 1); if(bitarr->num_of_bits == 0) { return; } else if(prob == 1) { bit_array_set_all(bitarr); return; } // rand() generates number between 0 and RAND_MAX inclusive // therefore we want to check if rand() <= p long p = RAND_MAX * prob; _seed_rand(); word_addr_t w; word_offset_t o; // Initialise to zero memset(bitarr->words, 0, bitarr->num_of_words * sizeof(word_t)); for(w = 0; w < bitarr->num_of_words - 1; w++) { for(o = 0; o < WORD_SIZE; o++) { if(rand() <= p) { bitarr->words[w] |= ((word_t)0x1 << o); } } } // Top word word_offset_t bits_in_last_word = bits_in_top_word(bitarr->num_of_bits); w = bitarr->num_of_words - 1; for(o = 0; o < bits_in_last_word; o++) { if(rand() <= p) { bitarr->words[w] |= ((word_t)0x1 << o); } } DEBUG_VALIDATE(bitarr); } // Shuffle the bits in an array randomly void bit_array_shuffle(BIT_ARRAY* bitarr) { if(bitarr->num_of_bits == 0) return; _seed_rand(); bit_index_t i, j; for(i = bitarr->num_of_bits - 1; i > 0; i--) { j = (bit_index_t)rand() % i; // Swap i and j char x = (bitarr->words[bitset64_wrd(i)] >> bitset64_idx(i)) & 0x1; char y = (bitarr->words[bitset64_wrd(j)] >> bitset64_idx(j)) & 0x1; if(!y) bitarr->words[bitset64_wrd(i)] &= ~((word_t)0x1 << bitset64_idx(i)); else bitarr->words[bitset64_wrd(i)] |= (word_t)0x1 << bitset64_idx(i); if(!x) bitarr->words[bitset64_wrd(j)] &= ~((word_t)0x1 << bitset64_idx(j)); else bitarr->words[bitset64_wrd(j)] |= (word_t)0x1 << bitset64_idx(j); } DEBUG_VALIDATE(bitarr); } // // Arithmetic // // Returns 1 on sucess, 0 if value in array is too big char bit_array_as_num(const BIT_ARRAY* bitarr, uint64_t* result) { if(bitarr->num_of_bits == 0) { *result = 0; return 1; } word_addr_t w; for(w = bitarr->num_of_words-1; w > 0; w--) { if(bitarr->words[w] > 0) { return 0; } } *result = bitarr->words[0]; return 1; } // 1 iff bitarr > value // 0 iff bitarr == value // -1 iff bitarr < value int bit_array_cmp_uint64(const BIT_ARRAY* bitarr, uint64_t value) { uint64_t arr_num = 0; // If cannot put bitarr in uint64, it is > value if(!bit_array_as_num(bitarr, &arr_num)) return 1; if(arr_num > value) return 1; else if(arr_num < value) return -1; else return 0; } // If value is zero, no change is made void bit_array_add_uint64(BIT_ARRAY* bitarr, uint64_t value) { if(value == 0) { return; } else if(bitarr->num_of_bits == 0) { bit_array_resize_critical(bitarr, WORD_SIZE - leading_zeros(value)); bitarr->words[0] = (word_t)value; return; } char carry = 0; word_addr_t i; for(i = 0; i < bitarr->num_of_words; i++) { if(WORD_MAX - bitarr->words[i] < value) { carry = 1; bitarr->words[i] += value; } else { // Carry is absorbed bitarr->words[i] += value; carry = 0; break; } } if(carry) { // Bit array full, need another bit after all words filled bit_array_resize_critical(bitarr, bitarr->num_of_words * WORD_SIZE + 1); // Set top word to 1 bitarr->words[bitarr->num_of_words-1] = 1; } else { word_t final_word = bitarr->words[bitarr->num_of_words-1]; word_offset_t expected_bits = bits_in_top_word(bitarr->num_of_bits); word_offset_t actual_bits = WORD_SIZE - leading_zeros(final_word); if(actual_bits > expected_bits) { // num_of_bits has increased -- num_of_words has not bitarr->num_of_bits += (actual_bits - expected_bits); } } } // If value is greater than bitarr, bitarr is not changed and 0 is returned // Returns 1 on success, 0 if value > bitarr char bit_array_sub_uint64(BIT_ARRAY* bitarr, uint64_t value) { if(value == 0) { return 1; } else if(bitarr->words[0] >= value) { bitarr->words[0] -= value; return 1; } value -= bitarr->words[0]; word_addr_t i; for(i = 1; i < bitarr->num_of_words; i++) { if(bitarr->words[i] > 0) { // deduct one bitarr->words[i]--; for(; i > 0; i--) { bitarr->words[i] = WORD_MAX; } // -1 since we've already deducted 1 bitarr->words[0] = WORD_MAX - value - 1; return 1; } } // subtract value is greater than array return 0; } // // Arithmetic between bit arrays // // src1, src2 and dst can all be the same BIT_ARRAY static void _arithmetic(BIT_ARRAY* dst, const BIT_ARRAY* src1, const BIT_ARRAY* src2, char subtract) { word_addr_t max_words = MAX(src1->num_of_words, src2->num_of_words); // Adding: dst_words >= max(src1 words, src2 words) // Subtracting: dst_words is >= src1->num_of_words char carry = subtract ? 1 : 0; word_addr_t i; word_t word1, word2; for(i = 0; i < max_words; i++) { word1 = (i < src1->num_of_words ? src1->words[i] : 0); word2 = (i < src2->num_of_words ? src2->words[i] : 0); if(subtract) word2 = ~word2; dst->words[i] = word1 + word2 + carry; // Update carry carry = WORD_MAX - word1 < word2 || WORD_MAX - word1 - word2 < (word_t)carry; } if(subtract) { carry = 0; } else { // Check last word word_offset_t bits_on_last_word = bits_in_top_word(dst->num_of_bits); if(bits_on_last_word < WORD_SIZE) { word_t mask = bitmask64(bits_on_last_word); if(dst->words[max_words-1] > mask) { // Array has overflowed, increase size dst->num_of_bits++; } } else if(carry) { // Carry onto a new word if(dst->num_of_words == max_words) { // Need to resize for the carry bit bit_array_resize_critical(dst, dst->num_of_bits+1); } dst->words[max_words] = (word_t)1; } } // Zero the rest of dst array for(i = max_words+carry; i < dst->num_of_words; i++) { dst->words[i] = (word_t)0; } DEBUG_VALIDATE(dst); } // src1, src2 and dst can all be the same BIT_ARRAY // If dst is shorter than either of src1, src2, it is enlarged void bit_array_add(BIT_ARRAY* dst, const BIT_ARRAY* src1, const BIT_ARRAY* src2) { bit_array_ensure_size_critical(dst, MAX(src1->num_of_bits, src2->num_of_bits)); _arithmetic(dst, src1, src2, 0); } // dst = src1 - src2 // src1, src2 and dst can all be the same BIT_ARRAY // If dst is shorter than src1, it will be extended to be as long as src1 // src1 must be greater than or equal to src2 (src1 >= src2) void bit_array_subtract(BIT_ARRAY* dst, const BIT_ARRAY* src1, const BIT_ARRAY* src2) { // subtraction by method of complements: // a - b = a + ~b + 1 = src1 + ~src2 +1 assert(bit_array_cmp(src1, src2) >= 0); // Require src1 >= src2 bit_array_ensure_size_critical(dst, src1->num_of_bits); _arithmetic(dst, src1, src2, 1); } // Add `add` to `bitarr` at `pos` // Bounds checking not needed as out of bounds is valid void bit_array_add_word(BIT_ARRAY *bitarr, bit_index_t pos, uint64_t add) { DEBUG_VALIDATE(bitarr); if(add == 0) { return; } else if(pos >= bitarr->num_of_bits) { // Resize and add! bit_index_t num_bits_required = pos + (WORD_SIZE - leading_zeros(add)); bit_array_resize_critical(bitarr, num_bits_required); _set_word(bitarr, pos, (word_t)add); return; } /* char str[1000]; printf(" add_word: %s\n", bit_array_to_str_rev(bitarr, str)); printf(" word: %s [pos: %i]\n", _word_to_str(add, str), (int)pos); */ word_t w = _get_word(bitarr, pos); word_t sum = w + add; char carry = WORD_MAX - w < add; // Ensure array is big enough bit_index_t num_bits_required = pos + (carry ? WORD_SIZE + 1 : (WORD_SIZE - leading_zeros(sum))); bit_array_ensure_size(bitarr, num_bits_required); _set_word(bitarr, pos, sum); pos += WORD_SIZE; if(carry) { word_offset_t offset = pos % WORD_SIZE; word_addr_t addr = bitset64_wrd(pos); add = (word_t)0x1 << offset; carry = (WORD_MAX - bitarr->words[addr] < add); sum = bitarr->words[addr] + add; num_bits_required = addr * WORD_SIZE + (carry ? WORD_SIZE + 1 : (WORD_SIZE - leading_zeros(sum))); bit_array_ensure_size(bitarr, num_bits_required); bitarr->words[addr++] = sum; if(carry) { while(addr < bitarr->num_of_words && bitarr->words[addr] == WORD_MAX) { bitarr->words[addr++] = 0; } if(addr == bitarr->num_of_words) { bit_array_resize_critical(bitarr, addr * WORD_SIZE + 1); } else if(addr == bitarr->num_of_words-1 && bitarr->words[addr] == bitmask64(bits_in_top_word(bitarr->num_of_bits))) { bit_array_resize_critical(bitarr, bitarr->num_of_bits + 1); } bitarr->words[addr]++; } } DEBUG_VALIDATE(bitarr); } // Add `add` to `bitarr` at `pos` // Bounds checking not needed as out of bounds is valid void bit_array_add_words(BIT_ARRAY *bitarr, bit_index_t pos, const BIT_ARRAY *add) { assert(bitarr != add); // bitarr and add cannot point to the same bit array bit_index_t add_top_bit_set; if(!bit_array_find_last_set_bit(add, &add_top_bit_set)) { // No bits set in add return; } else if(pos >= bitarr->num_of_bits) { // Just resize and copy! bit_index_t num_bits_required = pos + add_top_bit_set + 1; bit_array_resize_critical(bitarr, num_bits_required); _array_copy(bitarr, pos, add, 0, add->num_of_bits); return; } else if(pos == 0) { bit_array_add(bitarr, bitarr, add); return; } /* char str[1000]; printf(" add_words1: %s\n", bit_array_to_str_rev(bitarr, str)); printf(" add_words2: %s\n", bit_array_to_str_rev(add, str)); printf(" [pos: %i]\n", (int)pos); */ bit_index_t num_bits_required = pos + add_top_bit_set + 1; bit_array_ensure_size(bitarr, num_bits_required); word_addr_t first_word = bitset64_wrd(pos); word_offset_t first_offset = bitset64_idx(pos); word_t w = add->words[0] << first_offset; unsigned char carry = (WORD_MAX - bitarr->words[first_word] < w); bitarr->words[first_word] += w; word_addr_t i = first_word + 1; bit_index_t offset = WORD_SIZE - first_offset; for(; carry || offset <= add_top_bit_set; i++, offset += WORD_SIZE) { w = offset < add->num_of_bits ? _get_word(add, offset) : (word_t)0; if(i >= bitarr->num_of_words) { // Extend by a word bit_array_resize_critical(bitarr, (bit_index_t)(i+1)*WORD_SIZE+1); } word_t prev = bitarr->words[i]; bitarr->words[i] += w + carry; carry = (WORD_MAX - prev < w || (carry && prev + w == WORD_MAX)) ? 1 : 0; } word_offset_t top_bits = WORD_SIZE - leading_zeros(bitarr->words[bitarr->num_of_words-1]); bit_index_t min_bits = (bitarr->num_of_words-1)*WORD_SIZE + top_bits; if(bitarr->num_of_bits < min_bits) { // Extend within the last word bitarr->num_of_bits = min_bits; } DEBUG_VALIDATE(bitarr); } char bit_array_sub_word(BIT_ARRAY* bitarr, bit_index_t pos, word_t minus) { DEBUG_VALIDATE(bitarr); if(minus == 0) { return 1; } word_t w = _get_word(bitarr, pos); if(w >= minus) { _set_word(bitarr, pos, w - minus); DEBUG_VALIDATE(bitarr); return 1; } minus -= w; bit_index_t offset; for(offset = pos + WORD_SIZE; offset < bitarr->num_of_bits; offset += WORD_SIZE) { w = _get_word(bitarr, offset); if(w > 0) { // deduct one _set_word(bitarr, offset, w - 1); SET_REGION(bitarr, pos, offset-pos); // -1 since we've already deducted 1 minus--; _set_word(bitarr, pos, WORD_MAX - minus); DEBUG_VALIDATE(bitarr); return 1; } } DEBUG_VALIDATE(bitarr); return 0; } char bit_array_sub_words(BIT_ARRAY* bitarr, bit_index_t pos, BIT_ARRAY* minus) { assert(bitarr != minus); // bitarr and minus cannot point to the same bit array int cmp = bit_array_cmp_words(bitarr, pos, minus); if(cmp == 0) { bit_array_clear_all(bitarr); return 1; } else if(cmp < 0) { return 0; } bit_index_t bitarr_length = bitarr->num_of_bits; bit_index_t bitarr_top_bit_set; bit_array_find_last_set_bit(bitarr, &bitarr_top_bit_set); // subtraction by method of complements: // a - b = a + ~b + 1 = src1 + ~src2 +1 bit_array_not(minus, minus); bit_array_add_words(bitarr, pos, minus); bit_array_add_word(bitarr, pos, (word_t)1); bit_array_sub_word(bitarr, pos+minus->num_of_bits, 1); bit_array_resize(bitarr, bitarr_length); bit_array_not(minus, minus); DEBUG_VALIDATE(bitarr); return 1; } void bit_array_mul_uint64(BIT_ARRAY *bitarr, uint64_t multiplier) { if(bitarr->num_of_bits == 0 || multiplier == 1) { return; } else if(multiplier == 0) { bit_array_clear_all(bitarr); return; } bit_index_t i; for(i = bitarr->num_of_bits; i > 0; i--) { if(bit_array_get(bitarr, i-1)) { bit_array_clear(bitarr, i-1); bit_array_add_word(bitarr, i-1, multiplier); } } DEBUG_VALIDATE(bitarr); } void bit_array_multiply(BIT_ARRAY *dst, BIT_ARRAY *src1, BIT_ARRAY *src2) { if(src1->num_of_bits == 0 || src2->num_of_bits == 0) { bit_array_clear_all(dst); return; } // Cannot pass the same array as dst, src1 AND src2 assert(dst != src1 || dst != src2); // Dev: multiplier == 1? BIT_ARRAY *read_arr, *add_arr; if(src1 == dst) { read_arr = src1; add_arr = src2; } else { read_arr = src2; add_arr = src1; } if(dst != src1 && dst != src2) { bit_array_clear_all(dst); } bit_index_t i; for(i = read_arr->num_of_bits; i > 0; i--) { if(bit_array_get(read_arr, i-1)) { bit_array_clear(dst, i-1); bit_array_add_words(dst, i-1, add_arr); } } DEBUG_VALIDATE(dst); } // bitarr = round_down(bitarr / divisor) // rem = bitarr % divisor void bit_array_div_uint64(BIT_ARRAY *bitarr, uint64_t divisor, uint64_t *rem) { assert(divisor != 0); // cannot divide by zero bit_index_t div_top_bit = 63 - leading_zeros(divisor); bit_index_t bitarr_top_bit; if(!bit_array_find_last_set_bit(bitarr, &bitarr_top_bit)) { *rem = 0; return; } if(bitarr_top_bit < div_top_bit) { *rem = bitarr->words[0]; bit_array_clear_all(bitarr); return; } // When div is shifted by offset, their top set bits are aligned bit_index_t offset = bitarr_top_bit - div_top_bit; uint64_t tmp = _get_word(bitarr, offset); _set_word(bitarr, offset, (word_t)0); // Carry if 1 if the top bit was set before left shift char carry = 0; // offset unsigned so break when offset == 0 while(1) { if(carry) { // (carry:tmp) - divisor = (WORD_MAX+1+tmp)-divisor tmp = WORD_MAX - divisor + tmp + 1; bit_array_set(bitarr, offset); } else if(tmp >= divisor) { tmp -= divisor; bit_array_set(bitarr, offset); } else { bit_array_clear(bitarr, offset); } if(offset == 0) break; offset--; // Is the top bit set (that we're about to shift off)? carry = tmp & 0x8000000000000000; tmp <<= 1; tmp |= bit_array_get(bitarr, offset); } *rem = tmp; } // Results in: // quotient = dividend / divisor // dividend = dividend % divisor // (dividend is used to return the remainder) void bit_array_divide(BIT_ARRAY *dividend, BIT_ARRAY *quotient, BIT_ARRAY *divisor) { assert(bit_array_cmp_uint64(divisor, 0) != 0); // Cannot divide by zero bit_array_clear_all(quotient); int cmp = bit_array_cmp(dividend, divisor); if(cmp == 0) { bit_array_ensure_size(quotient, 1); bit_array_set(quotient, 0); bit_array_clear_all(dividend); return; } else if(cmp < 0) { // dividend is < divisor, quotient is zero -- done return; } // now we know: dividend > divisor, quotient is zero'd, // dividend != 0, divisor != 0 bit_index_t dividend_top_bit = 0, div_top_bit = 0; bit_array_find_last_set_bit(dividend, ÷nd_top_bit); bit_array_find_last_set_bit(divisor, &div_top_bit); // When divisor is shifted by offset, their top set bits are aligned bit_index_t offset = dividend_top_bit - div_top_bit; // offset unsigned so break when offset == 0 for(; ; offset--) { if(bit_array_cmp_words(dividend, offset, divisor) >= 0) { bit_array_sub_words(dividend, offset, divisor); bit_array_ensure_size(quotient, offset+1); bit_array_set(quotient, offset); } if(offset == 0) break; } } // // Read/Write from files // // file format is [8 bytes: for number of elements in array][data] // data is written in little endian order (least sig byte first) // // Saves bit array to a file. Returns the number of bytes written // number of bytes returned should be 8+(bitarr->num_of_bits+7)/8 bit_index_t bit_array_save(const BIT_ARRAY* bitarr, FILE* f) { bit_index_t num_of_bytes = roundup_bits2bytes(bitarr->num_of_bits); bit_index_t bytes_written = 0; const int endian = 1; if(*(uint8_t*)&endian == 1) { // Little endian machine // Write 8 bytes to store the number of bits in the array bytes_written += fwrite(&bitarr->num_of_bits, 1, 8, f); // Write the array bytes_written += fwrite(bitarr->words, 1, num_of_bytes, f); } else { // Big endian machine uint64_t i, w, whole_words = num_of_bytes/sizeof(word_t); uint64_t rem_bytes = num_of_bytes - whole_words*sizeof(word_t); uint64_t n_bits = byteswap64(bitarr->num_of_bits); // Write 8 bytes to store the number of bits in the array bytes_written += fwrite(&n_bits, 1, 8, f); // Write the array for(i = 0; i < whole_words; i++) { w = byteswap64(bitarr->words[i]); bytes_written += fwrite(&w, 1, 8, f); } if(rem_bytes > 0) { w = byteswap64(bitarr->words[whole_words]); bytes_written += fwrite(&w, 1, rem_bytes, f); } } return bytes_written; } // Load a uint64 from little endian format. // Works for both big and little endian architectures static inline uint64_t le64_to_cpu(const uint8_t *x) { return (((uint64_t)(x[0])) | ((uint64_t)(x[1]) << 8) | ((uint64_t)(x[2]) << 16) | ((uint64_t)(x[3]) << 24) | ((uint64_t)(x[4]) << 32) | ((uint64_t)(x[5]) << 40) | ((uint64_t)(x[6]) << 48) | ((uint64_t)(x[7]) << 56)); } // Reads bit array from a file. bitarr is resized and filled. // Returns 1 on success, 0 on failure char bit_array_load(BIT_ARRAY* bitarr, FILE* f) { // Read in number of bits, return 0 if we can't read in bit_index_t num_bits; if(fread(&num_bits, 1, 8, f) != 8) return 0; num_bits = le64_to_cpu((uint8_t*)&num_bits); // Resize bit_array_resize_critical(bitarr, num_bits); // Have to calculate how many bytes are needed for the file // (Note: this may be different from num_of_words * sizeof(word_t)) bit_index_t num_of_bytes = roundup_bits2bytes(bitarr->num_of_bits); if(fread(bitarr->words, 1, num_of_bytes, f) != num_of_bytes) return 0; // Fix endianness word_addr_t i; for(i = 0; i < bitarr->num_of_words; i++) bitarr->words[i] = le64_to_cpu((uint8_t*)&bitarr->words[i]); // Mask top word _mask_top_word(bitarr); DEBUG_VALIDATE(bitarr); return 1; } // // Hash function // /* From: lookup3.c, by Bob Jenkins, May 2006, Public Domain. */ #define hashsize(n) ((uint32_t)1<<(n)) #define hashmask(n) (hashsize(n)-1) #define rot(x,k) (((x)<<(k)) | ((x)>>(32-(k)))) /* From: lookup3.c, by Bob Jenkins, May 2006, Public Domain. */ #define mix(a,b,c) \ { \ a -= c; a ^= rot(c, 4); c += b; \ b -= a; b ^= rot(a, 6); a += c; \ c -= b; c ^= rot(b, 8); b += a; \ a -= c; a ^= rot(c,16); c += b; \ b -= a; b ^= rot(a,19); a += c; \ c -= b; c ^= rot(b, 4); b += a; \ } /* From: lookup3.c, by Bob Jenkins, May 2006, Public Domain. */ #define final(a,b,c) \ { \ c ^= b; c -= rot(b,14); \ a ^= c; a -= rot(c,11); \ b ^= a; b -= rot(a,25); \ c ^= b; c -= rot(b,16); \ a ^= c; a -= rot(c,4); \ b ^= a; b -= rot(a,14); \ c ^= b; c -= rot(b,24); \ } /* From: lookup3.c, by Bob Jenkins, May 2006, Public Domain. -------------------------------------------------------------------- hashword2() -- same as hashword(), but take two seeds and return two 32-bit values. pc and pb must both be nonnull, and *pc and *pb must both be initialized with seeds. If you pass in (*pb)==0, the output (*pc) will be the same as the return value from hashword(). -------------------------------------------------------------------- */ static void hashword2 ( const uint32_t *k, /* the key, an array of uint32_t values */ size_t length, /* the length of the key, in uint32_ts */ uint32_t *pc, /* IN: seed OUT: primary hash value */ uint32_t *pb) /* IN: more seed OUT: secondary hash value */ { uint32_t a,b,c; /* Set up the internal state */ a = b = c = 0xdeadbeef + ((uint32_t)(length<<2)) + *pc; c += *pb; /*------------------------------------------------- handle most of the key */ while (length > 3) { a += k[0]; b += k[1]; c += k[2]; mix(a,b,c); length -= 3; k += 3; } /*------------------------------------------- handle the last 3 uint32_t's */ switch(length) /* all the case statements fall through */ { case 3 : c+=k[2]; case 2 : b+=k[1]; case 1 : a+=k[0]; final(a,b,c); case 0: /* case 0: nothing left to add */ break; } /*------------------------------------------------------ report the result */ *pc=c; *pb=b; } // Pass seed as 0 on first call, pass previous hash value if rehashing due // to a collision // Using bob jenkins hash lookup3 uint64_t bit_array_hash(const BIT_ARRAY* bitarr, uint64_t seed) { uint32_t seed32[2]; memcpy(seed32, &seed, sizeof(uint32_t)*2); // Round up length to number 32bit words hashword2((uint32_t*)bitarr->words, (bitarr->num_of_bits + 31) / 32, &seed32[0], &seed32[1]); // XOR with array length. This ensures arrays with different length but same // contents have different hash values seed ^= bitarr->num_of_bits; return seed; } // // Generally useful functions // // Generalised 'binary to string' function // Adds bits to the string in order of lsb to msb // e.g. 0b11010 (26 in decimal) would come out as "01011" char* bit_array_word2str(const void *ptr, size_t num_of_bits, char *str) { const uint8_t* d = (const uint8_t*)ptr; size_t i; for(i = 0; i < num_of_bits; i++) { uint8_t bit = (d[i/8] >> (i % 8)) & 0x1; str[i] = bit ? '1' : '0'; } str[num_of_bits] = '\0'; return str; } char* bit_array_word2str_rev(const void *ptr, size_t num_of_bits, char *str) { const uint8_t* d = (const uint8_t*)ptr; size_t i; for(i = 0; i < num_of_bits; i++) { uint8_t bit = (d[i/8] >> (i % 8)) & 0x1; str[num_of_bits-1-i] = bit ? '1' : '0'; } str[num_of_bits] = '\0'; return str; }