1// SPDX-License-Identifier: GPL-2.0-or-later 2/* 3 * decompress_common.c - Code shared by the XPRESS and LZX decompressors 4 * 5 * Copyright (C) 2015 Eric Biggers 6 */ 7 8#include "decompress_common.h" 9 10/* 11 * make_huffman_decode_table() - 12 * 13 * Build a decoding table for a canonical prefix code, or "Huffman code". 14 * 15 * This is an internal function, not part of the library API! 16 * 17 * This takes as input the length of the codeword for each symbol in the 18 * alphabet and produces as output a table that can be used for fast 19 * decoding of prefix-encoded symbols using read_huffsym(). 20 * 21 * Strictly speaking, a canonical prefix code might not be a Huffman 22 * code. But this algorithm will work either way; and in fact, since 23 * Huffman codes are defined in terms of symbol frequencies, there is no 24 * way for the decompressor to know whether the code is a true Huffman 25 * code or not until all symbols have been decoded. 26 * 27 * Because the prefix code is assumed to be "canonical", it can be 28 * reconstructed directly from the codeword lengths. A prefix code is 29 * canonical if and only if a longer codeword never lexicographically 30 * precedes a shorter codeword, and the lexicographic ordering of 31 * codewords of the same length is the same as the lexicographic ordering 32 * of the corresponding symbols. Consequently, we can sort the symbols 33 * primarily by codeword length and secondarily by symbol value, then 34 * reconstruct the prefix code by generating codewords lexicographically 35 * in that order. 36 * 37 * This function does not, however, generate the prefix code explicitly. 38 * Instead, it directly builds a table for decoding symbols using the 39 * code. The basic idea is this: given the next 'max_codeword_len' bits 40 * in the input, we can look up the decoded symbol by indexing a table 41 * containing 2**max_codeword_len entries. A codeword with length 42 * 'max_codeword_len' will have exactly one entry in this table, whereas 43 * a codeword shorter than 'max_codeword_len' will have multiple entries 44 * in this table. Precisely, a codeword of length n will be represented 45 * by 2**(max_codeword_len - n) entries in this table. The 0-based index 46 * of each such entry will contain the corresponding codeword as a prefix 47 * when zero-padded on the left to 'max_codeword_len' binary digits. 48 * 49 * That's the basic idea, but we implement two optimizations regarding 50 * the format of the decode table itself: 51 * 52 * - For many compression formats, the maximum codeword length is too 53 * long for it to be efficient to build the full decoding table 54 * whenever a new prefix code is used. Instead, we can build the table 55 * using only 2**table_bits entries, where 'table_bits' is some number 56 * less than or equal to 'max_codeword_len'. Then, only codewords of 57 * length 'table_bits' and shorter can be directly looked up. For 58 * longer codewords, the direct lookup instead produces the root of a 59 * binary tree. Using this tree, the decoder can do traditional 60 * bit-by-bit decoding of the remainder of the codeword. Child nodes 61 * are allocated in extra entries at the end of the table; leaf nodes 62 * contain symbols. Note that the long-codeword case is, in general, 63 * not performance critical, since in Huffman codes the most frequently 64 * used symbols are assigned the shortest codeword lengths. 65 * 66 * - When we decode a symbol using a direct lookup of the table, we still 67 * need to know its length so that the bitstream can be advanced by the 68 * appropriate number of bits. The simple solution is to simply retain 69 * the 'lens' array and use the decoded symbol as an index into it. 70 * However, this requires two separate array accesses in the fast path. 71 * The optimization is to store the length directly in the decode 72 * table. We use the bottom 11 bits for the symbol and the top 5 bits 73 * for the length. In addition, to combine this optimization with the 74 * previous one, we introduce a special case where the top 2 bits of 75 * the length are both set if the entry is actually the root of a 76 * binary tree. 77 * 78 * @decode_table: 79 * The array in which to create the decoding table. This must have 80 * a length of at least ((2**table_bits) + 2 * num_syms) entries. 81 * 82 * @num_syms: 83 * The number of symbols in the alphabet; also, the length of the 84 * 'lens' array. Must be less than or equal to 2048. 85 * 86 * @table_bits: 87 * The order of the decode table size, as explained above. Must be 88 * less than or equal to 13. 89 * 90 * @lens: 91 * An array of length @num_syms, indexable by symbol, that gives the 92 * length of the codeword, in bits, for that symbol. The length can 93 * be 0, which means that the symbol does not have a codeword 94 * assigned. 95 * 96 * @max_codeword_len: 97 * The longest codeword length allowed in the compression format. 98 * All entries in 'lens' must be less than or equal to this value. 99 * This must be less than or equal to 23. 100 * 101 * @working_space 102 * A temporary array of length '2 * (max_codeword_len + 1) + 103 * num_syms'. 104 * 105 * Returns 0 on success, or -1 if the lengths do not form a valid prefix 106 * code. 107 */ 108int make_huffman_decode_table(u16 decode_table[], const u32 num_syms, 109 const u32 table_bits, const u8 lens[], 110 const u32 max_codeword_len, 111 u16 working_space[]) 112{ 113 const u32 table_num_entries = 1 << table_bits; 114 u16 * const len_counts = &working_space[0]; 115 u16 * const offsets = &working_space[1 * (max_codeword_len + 1)]; 116 u16 * const sorted_syms = &working_space[2 * (max_codeword_len + 1)]; 117 int left; 118 void *decode_table_ptr; 119 u32 sym_idx; 120 u32 codeword_len; 121 u32 stores_per_loop; 122 u32 decode_table_pos; 123 u32 len; 124 u32 sym; 125 126 /* Count how many symbols have each possible codeword length. 127 * Note that a length of 0 indicates the corresponding symbol is not 128 * used in the code and therefore does not have a codeword. 129 */ 130 for (len = 0; len <= max_codeword_len; len++) 131 len_counts[len] = 0; 132 for (sym = 0; sym < num_syms; sym++) 133 len_counts[lens[sym]]++; 134 135 /* We can assume all lengths are <= max_codeword_len, but we 136 * cannot assume they form a valid prefix code. A codeword of 137 * length n should require a proportion of the codespace equaling 138 * (1/2)^n. The code is valid if and only if the codespace is 139 * exactly filled by the lengths, by this measure. 140 */ 141 left = 1; 142 for (len = 1; len <= max_codeword_len; len++) { 143 left <<= 1; 144 left -= len_counts[len]; 145 if (left < 0) { 146 /* The lengths overflow the codespace; that is, the code 147 * is over-subscribed. 148 */ 149 return -1; 150 } 151 } 152 153 if (left) { 154 /* The lengths do not fill the codespace; that is, they form an 155 * incomplete set. 156 */ 157 if (left == (1 << max_codeword_len)) { 158 /* The code is completely empty. This is arguably 159 * invalid, but in fact it is valid in LZX and XPRESS, 160 * so we must allow it. By definition, no symbols can 161 * be decoded with an empty code. Consequently, we 162 * technically don't even need to fill in the decode 163 * table. However, to avoid accessing uninitialized 164 * memory if the algorithm nevertheless attempts to 165 * decode symbols using such a code, we zero out the 166 * decode table. 167 */ 168 memset(decode_table, 0, 169 table_num_entries * sizeof(decode_table[0])); 170 return 0; 171 } 172 return -1; 173 } 174 175 /* Sort the symbols primarily by length and secondarily by symbol order. 176 */ 177 178 /* Initialize 'offsets' so that offsets[len] for 1 <= len <= 179 * max_codeword_len is the number of codewords shorter than 'len' bits. 180 */ 181 offsets[1] = 0; 182 for (len = 1; len < max_codeword_len; len++) 183 offsets[len + 1] = offsets[len] + len_counts[len]; 184 185 /* Use the 'offsets' array to sort the symbols. Note that we do not 186 * include symbols that are not used in the code. Consequently, fewer 187 * than 'num_syms' entries in 'sorted_syms' may be filled. 188 */ 189 for (sym = 0; sym < num_syms; sym++) 190 if (lens[sym]) 191 sorted_syms[offsets[lens[sym]]++] = sym; 192 193 /* Fill entries for codewords with length <= table_bits 194 * --- that is, those short enough for a direct mapping. 195 * 196 * The table will start with entries for the shortest codeword(s), which 197 * have the most entries. From there, the number of entries per 198 * codeword will decrease. 199 */ 200 decode_table_ptr = decode_table; 201 sym_idx = 0; 202 codeword_len = 1; 203 stores_per_loop = (1 << (table_bits - codeword_len)); 204 for (; stores_per_loop != 0; codeword_len++, stores_per_loop >>= 1) { 205 u32 end_sym_idx = sym_idx + len_counts[codeword_len]; 206 207 for (; sym_idx < end_sym_idx; sym_idx++) { 208 u16 entry; 209 u16 *p; 210 u32 n; 211 212 entry = ((u32)codeword_len << 11) | sorted_syms[sym_idx]; 213 p = (u16 *)decode_table_ptr; 214 n = stores_per_loop; 215 216 do { 217 *p++ = entry; 218 } while (--n); 219 220 decode_table_ptr = p; 221 } 222 } 223 224 /* If we've filled in the entire table, we are done. Otherwise, 225 * there are codewords longer than table_bits for which we must 226 * generate binary trees. 227 */ 228 decode_table_pos = (u16 *)decode_table_ptr - decode_table; 229 if (decode_table_pos != table_num_entries) { 230 u32 j; 231 u32 next_free_tree_slot; 232 u32 cur_codeword; 233 234 /* First, zero out the remaining entries. This is 235 * necessary so that these entries appear as 236 * "unallocated" in the next part. Each of these entries 237 * will eventually be filled with the representation of 238 * the root node of a binary tree. 239 */ 240 j = decode_table_pos; 241 do { 242 decode_table[j] = 0; 243 } while (++j != table_num_entries); 244 245 /* We allocate child nodes starting at the end of the 246 * direct lookup table. Note that there should be 247 * 2*num_syms extra entries for this purpose, although 248 * fewer than this may actually be needed. 249 */ 250 next_free_tree_slot = table_num_entries; 251 252 /* Iterate through each codeword with length greater than 253 * 'table_bits', primarily in order of codeword length 254 * and secondarily in order of symbol. 255 */ 256 for (cur_codeword = decode_table_pos << 1; 257 codeword_len <= max_codeword_len; 258 codeword_len++, cur_codeword <<= 1) { 259 u32 end_sym_idx = sym_idx + len_counts[codeword_len]; 260 261 for (; sym_idx < end_sym_idx; sym_idx++, cur_codeword++) { 262 /* 'sorted_sym' is the symbol represented by the 263 * codeword. 264 */ 265 u32 sorted_sym = sorted_syms[sym_idx]; 266 u32 extra_bits = codeword_len - table_bits; 267 u32 node_idx = cur_codeword >> extra_bits; 268 269 /* Go through each bit of the current codeword 270 * beyond the prefix of length @table_bits and 271 * walk the appropriate binary tree, allocating 272 * any slots that have not yet been allocated. 273 * 274 * Note that the 'pointer' entry to the binary 275 * tree, which is stored in the direct lookup 276 * portion of the table, is represented 277 * identically to other internal (non-leaf) 278 * nodes of the binary tree; it can be thought 279 * of as simply the root of the tree. The 280 * representation of these internal nodes is 281 * simply the index of the left child combined 282 * with the special bits 0xC000 to distinguish 283 * the entry from direct mapping and leaf node 284 * entries. 285 */ 286 do { 287 /* At least one bit remains in the 288 * codeword, but the current node is an 289 * unallocated leaf. Change it to an 290 * internal node. 291 */ 292 if (decode_table[node_idx] == 0) { 293 decode_table[node_idx] = 294 next_free_tree_slot | 0xC000; 295 decode_table[next_free_tree_slot++] = 0; 296 decode_table[next_free_tree_slot++] = 0; 297 } 298 299 /* Go to the left child if the next bit 300 * in the codeword is 0; otherwise go to 301 * the right child. 302 */ 303 node_idx = decode_table[node_idx] & 0x3FFF; 304 --extra_bits; 305 node_idx += (cur_codeword >> extra_bits) & 1; 306 } while (extra_bits != 0); 307 308 /* We've traversed the tree using the entire 309 * codeword, and we're now at the entry where 310 * the actual symbol will be stored. This is 311 * distinguished from internal nodes by not 312 * having its high two bits set. 313 */ 314 decode_table[node_idx] = sorted_sym; 315 } 316 } 317 } 318 return 0; 319} 320