decompress_common.c revision 989e795b
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