Contributors: 3
Author Tokens Token Proportion Commits Commit Proportion
Konstantin Komarov 645 99.69% 1 33.33%
Colin Ian King 1 0.15% 1 33.33%
Kari Argillander 1 0.15% 1 33.33%
Total 647 3 


// 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;
}