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+// SPDX-License-Identifier: GPL-2.0-or-later
+/*
+ * decompress_common.c - Code shared by the XPRESS and LZX decompressors
+ *
+ * Copyright (C) 2015 Eric Biggers
+ */
+
+#include "decompress_common.h"
+
+/*
+ * make_huffman_decode_table() -
+ *
+ * Build a decoding table for a canonical prefix code, or "Huffman code".
+ *
+ * This is an internal function, not part of the library API!
+ *
+ * This takes as input the length of the codeword for each symbol in the
+ * alphabet and produces as output a table that can be used for fast
+ * decoding of prefix-encoded symbols using read_huffsym().
+ *
+ * Strictly speaking, a canonical prefix code might not be a Huffman
+ * code. But this algorithm will work either way; and in fact, since
+ * Huffman codes are defined in terms of symbol frequencies, there is no
+ * way for the decompressor to know whether the code is a true Huffman
+ * code or not until all symbols have been decoded.
+ *
+ * Because the prefix code is assumed to be "canonical", it can be
+ * reconstructed directly from the codeword lengths. A prefix code is
+ * canonical if and only if a longer codeword never lexicographically
+ * precedes a shorter codeword, and the lexicographic ordering of
+ * codewords of the same length is the same as the lexicographic ordering
+ * of the corresponding symbols. Consequently, we can sort the symbols
+ * primarily by codeword length and secondarily by symbol value, then
+ * reconstruct the prefix code by generating codewords lexicographically
+ * in that order.
+ *
+ * This function does not, however, generate the prefix code explicitly.
+ * Instead, it directly builds a table for decoding symbols using the
+ * code. The basic idea is this: given the next 'max_codeword_len' bits
+ * in the input, we can look up the decoded symbol by indexing a table
+ * containing 2**max_codeword_len entries. A codeword with length
+ * 'max_codeword_len' will have exactly one entry in this table, whereas
+ * a codeword shorter than 'max_codeword_len' will have multiple entries
+ * in this table. Precisely, a codeword of length n will be represented
+ * by 2**(max_codeword_len - n) entries in this table. The 0-based index
+ * of each such entry will contain the corresponding codeword as a prefix
+ * when zero-padded on the left to 'max_codeword_len' binary digits.
+ *
+ * That's the basic idea, but we implement two optimizations regarding
+ * the format of the decode table itself:
+ *
+ * - For many compression formats, the maximum codeword length is too
+ * long for it to be efficient to build the full decoding table
+ * whenever a new prefix code is used. Instead, we can build the table
+ * using only 2**table_bits entries, where 'table_bits' is some number
+ * less than or equal to 'max_codeword_len'. Then, only codewords of
+ * length 'table_bits' and shorter can be directly looked up. For
+ * longer codewords, the direct lookup instead produces the root of a
+ * binary tree. Using this tree, the decoder can do traditional
+ * bit-by-bit decoding of the remainder of the codeword. Child nodes
+ * are allocated in extra entries at the end of the table; leaf nodes
+ * contain symbols. Note that the long-codeword case is, in general,
+ * not performance critical, since in Huffman codes the most frequently
+ * used symbols are assigned the shortest codeword lengths.
+ *
+ * - When we decode a symbol using a direct lookup of the table, we still
+ * need to know its length so that the bitstream can be advanced by the
+ * appropriate number of bits. The simple solution is to simply retain
+ * the 'lens' array and use the decoded symbol as an index into it.
+ * However, this requires two separate array accesses in the fast path.
+ * The optimization is to store the length directly in the decode
+ * table. We use the bottom 11 bits for the symbol and the top 5 bits
+ * for the length. In addition, to combine this optimization with the
+ * previous one, we introduce a special case where the top 2 bits of
+ * the length are both set if the entry is actually the root of a
+ * binary tree.
+ *
+ * @decode_table:
+ * The array in which to create the decoding table. This must have
+ * a length of at least ((2**table_bits) + 2 * num_syms) entries.
+ *
+ * @num_syms:
+ * The number of symbols in the alphabet; also, the length of the
+ * 'lens' array. Must be less than or equal to 2048.
+ *
+ * @table_bits:
+ * The order of the decode table size, as explained above. Must be
+ * less than or equal to 13.
+ *
+ * @lens:
+ * An array of length @num_syms, indexable by symbol, that gives the
+ * length of the codeword, in bits, for that symbol. The length can
+ * be 0, which means that the symbol does not have a codeword
+ * assigned.
+ *
+ * @max_codeword_len:
+ * The longest codeword length allowed in the compression format.
+ * All entries in 'lens' must be less than or equal to this value.
+ * This must be less than or equal to 23.
+ *
+ * @working_space
+ * A temporary array of length '2 * (max_codeword_len + 1) +
+ * num_syms'.
+ *
+ * Returns 0 on success, or -1 if the lengths do not form a valid prefix
+ * code.
+ */
+int make_huffman_decode_table(u16 decode_table[], const u32 num_syms,
+ const u32 table_bits, const u8 lens[],
+ const u32 max_codeword_len,
+ u16 working_space[])
+{
+ const u32 table_num_entries = 1 << table_bits;
+ u16 * const len_counts = &working_space[0];
+ u16 * const offsets = &working_space[1 * (max_codeword_len + 1)];
+ u16 * const sorted_syms = &working_space[2 * (max_codeword_len + 1)];
+ int left;
+ void *decode_table_ptr;
+ u32 sym_idx;
+ u32 codeword_len;
+ u32 stores_per_loop;
+ u32 decode_table_pos;
+ u32 len;
+ u32 sym;
+
+ /* Count how many symbols have each possible codeword length.
+ * Note that a length of 0 indicates the corresponding symbol is not
+ * used in the code and therefore does not have a codeword.
+ */
+ for (len = 0; len <= max_codeword_len; len++)
+ len_counts[len] = 0;
+ for (sym = 0; sym < num_syms; sym++)
+ len_counts[lens[sym]]++;
+
+ /* We can assume all lengths are <= max_codeword_len, but we
+ * cannot assume they form a valid prefix code. A codeword of
+ * length n should require a proportion of the codespace equaling
+ * (1/2)^n. The code is valid if and only if the codespace is
+ * exactly filled by the lengths, by this measure.
+ */
+ left = 1;
+ for (len = 1; len <= max_codeword_len; len++) {
+ left <<= 1;
+ left -= len_counts[len];
+ if (left < 0) {
+ /* The lengths overflow the codespace; that is, the code
+ * is over-subscribed.
+ */
+ return -1;
+ }
+ }
+
+ if (left) {
+ /* The lengths do not fill the codespace; that is, they form an
+ * incomplete set.
+ */
+ if (left == (1 << max_codeword_len)) {
+ /* The code is completely empty. This is arguably
+ * invalid, but in fact it is valid in LZX and XPRESS,
+ * so we must allow it. By definition, no symbols can
+ * be decoded with an empty code. Consequently, we
+ * technically don't even need to fill in the decode
+ * table. However, to avoid accessing uninitialized
+ * memory if the algorithm nevertheless attempts to
+ * decode symbols using such a code, we zero out the
+ * decode table.
+ */
+ memset(decode_table, 0,
+ table_num_entries * sizeof(decode_table[0]));
+ return 0;
+ }
+ return -1;
+ }
+
+ /* Sort the symbols primarily by length and secondarily by symbol order.
+ */
+
+ /* Initialize 'offsets' so that offsets[len] for 1 <= len <=
+ * max_codeword_len is the number of codewords shorter than 'len' bits.
+ */
+ offsets[1] = 0;
+ for (len = 1; len < max_codeword_len; len++)
+ offsets[len + 1] = offsets[len] + len_counts[len];
+
+ /* Use the 'offsets' array to sort the symbols. Note that we do not
+ * include symbols that are not used in the code. Consequently, fewer
+ * than 'num_syms' entries in 'sorted_syms' may be filled.
+ */
+ for (sym = 0; sym < num_syms; sym++)
+ if (lens[sym])
+ sorted_syms[offsets[lens[sym]]++] = sym;
+
+ /* Fill entries for codewords with length <= table_bits
+ * --- that is, those short enough for a direct mapping.
+ *
+ * The table will start with entries for the shortest codeword(s), which
+ * have the most entries. From there, the number of entries per
+ * codeword will decrease.
+ */
+ decode_table_ptr = decode_table;
+ sym_idx = 0;
+ codeword_len = 1;
+ stores_per_loop = (1 << (table_bits - codeword_len));
+ for (; stores_per_loop != 0; codeword_len++, stores_per_loop >>= 1) {
+ u32 end_sym_idx = sym_idx + len_counts[codeword_len];
+
+ for (; sym_idx < end_sym_idx; sym_idx++) {
+ u16 entry;
+ u16 *p;
+ u32 n;
+
+ entry = ((u32)codeword_len << 11) | sorted_syms[sym_idx];
+ p = (u16 *)decode_table_ptr;
+ n = stores_per_loop;
+
+ do {
+ *p++ = entry;
+ } while (--n);
+
+ decode_table_ptr = p;
+ }
+ }
+
+ /* If we've filled in the entire table, we are done. Otherwise,
+ * there are codewords longer than table_bits for which we must
+ * generate binary trees.
+ */
+ decode_table_pos = (u16 *)decode_table_ptr - decode_table;
+ if (decode_table_pos != table_num_entries) {
+ u32 j;
+ u32 next_free_tree_slot;
+ u32 cur_codeword;
+
+ /* First, zero out the remaining entries. This is
+ * necessary so that these entries appear as
+ * "unallocated" in the next part. Each of these entries
+ * will eventually be filled with the representation of
+ * the root node of a binary tree.
+ */
+ j = decode_table_pos;
+ do {
+ decode_table[j] = 0;
+ } while (++j != table_num_entries);
+
+ /* We allocate child nodes starting at the end of the
+ * direct lookup table. Note that there should be
+ * 2*num_syms extra entries for this purpose, although
+ * fewer than this may actually be needed.
+ */
+ next_free_tree_slot = table_num_entries;
+
+ /* Iterate through each codeword with length greater than
+ * 'table_bits', primarily in order of codeword length
+ * and secondarily in order of symbol.
+ */
+ for (cur_codeword = decode_table_pos << 1;
+ codeword_len <= max_codeword_len;
+ codeword_len++, cur_codeword <<= 1) {
+ u32 end_sym_idx = sym_idx + len_counts[codeword_len];
+
+ for (; sym_idx < end_sym_idx; sym_idx++, cur_codeword++) {
+ /* 'sorted_sym' is the symbol represented by the
+ * codeword.
+ */
+ u32 sorted_sym = sorted_syms[sym_idx];
+ u32 extra_bits = codeword_len - table_bits;
+ u32 node_idx = cur_codeword >> extra_bits;
+
+ /* Go through each bit of the current codeword
+ * beyond the prefix of length @table_bits and
+ * walk the appropriate binary tree, allocating
+ * any slots that have not yet been allocated.
+ *
+ * Note that the 'pointer' entry to the binary
+ * tree, which is stored in the direct lookup
+ * portion of the table, is represented
+ * identically to other internal (non-leaf)
+ * nodes of the binary tree; it can be thought
+ * of as simply the root of the tree. The
+ * representation of these internal nodes is
+ * simply the index of the left child combined
+ * with the special bits 0xC000 to distinguish
+ * the entry from direct mapping and leaf node
+ * entries.
+ */
+ do {
+ /* At least one bit remains in the
+ * codeword, but the current node is an
+ * unallocated leaf. Change it to an
+ * internal node.
+ */
+ if (decode_table[node_idx] == 0) {
+ decode_table[node_idx] =
+ next_free_tree_slot | 0xC000;
+ decode_table[next_free_tree_slot++] = 0;
+ decode_table[next_free_tree_slot++] = 0;
+ }
+
+ /* Go to the left child if the next bit
+ * in the codeword is 0; otherwise go to
+ * the right child.
+ */
+ node_idx = decode_table[node_idx] & 0x3FFF;
+ --extra_bits;
+ node_idx += (cur_codeword >> extra_bits) & 1;
+ } while (extra_bits != 0);
+
+ /* We've traversed the tree using the entire
+ * codeword, and we're now at the entry where
+ * the actual symbol will be stored. This is
+ * distinguished from internal nodes by not
+ * having its high two bits set.
+ */
+ decode_table[node_idx] = sorted_sym;
+ }
+ }
+ }
+ return 0;
+}