}
/*
- * Builds a fast huffman decoding table from a canonical huffman code lengths
- * table. Based on code written by David Tritscher.
+ * Builds a fast huffman decoding table from an array that gives the length of
+ * the codeword for each symbol in the alphabet. Originally based on code
+ * written by David Tritscher (taken the original LZX decompression code); also
+ * heavily modified to add some optimizations used in the zlib code, as well as
+ * more comments.
*
* @decode_table: The array in which to create the fast huffman decoding
- * table. It must have a length of at least
- * (2**num_bits) + 2 * num_syms to guarantee
- * that there is enough space.
+ * table. It must have a length of at least
+ * (2**table_bits) + 2 * num_syms to guarantee
+ * that there is enough space.
*
- * @num_syms: Total number of symbols in the Huffman tree.
+ * @num_syms: Total number of symbols in the Huffman tree.
*
- * @num_bits: Any symbols with a code length of num_bits or less can be
- * decoded in one lookup of the table. 2**num_bits
+ * @table_bits: Any symbols with a code length of table_bits or less can
+ * be decoded in one lookup of the table. 2**table_bits
* must be greater than or equal to @num_syms if there are
- * any Huffman codes longer than @num_bits.
+ * any Huffman codes longer than @table_bits.
*
- * @lens: An array of length @num_syms, indexable by symbol, that
- * gives the length of that symbol. Because the Huffman
- * tree is in canonical form, it can be reconstructed by
- * only knowing the length of the code for each symbol.
+ * @lens: An array of length @num_syms, indexable by symbol, that
+ * gives the length of the Huffman codeward for that
+ * symbol. Because the Huffman tree is in canonical form,
+ * it can be reconstructed by only knowing the length of
+ * the codeword for each symbol. It is assumed, but not
+ * checked, that every length is less than
+ * @max_codeword_len.
*
- * @make_codeword_len: An integer that gives the longest possible codeword
- * length.
+ * @max_codeword_len: The longest codeword length allowed in the compression
+ * format.
*
- * Returns 0 on success; returns 1 if the length values do not correspond to a
- * valid Huffman tree, or if there are codes of length greater than @num_bits
- * but 2**num_bits < num_syms.
+ * Returns 0 on success; returns -1 if the length values do not correspond to a
+ * valid Huffman tree.
*
- * What exactly is the format of the fast Huffman decoding table? The first
- * (1 << num_bits) entries of the table are indexed by chunks of the input of
- * size @num_bits. If the next Huffman code in the input happens to have a
- * length of exactly @num_bits, the symbol is simply read directly from the
- * decoding table. Alternatively, if the next Huffman code has length _less
- * than_ @num_bits, the symbol is also read directly from the decode table; this
- * is possible because every entry in the table that is indexed by an integer
- * that has the shorter code as a binary prefix is filled in with the
- * appropriate symbol. If a code has length n <= num_bits, it will have
- * 2**(num_bits - n) possible suffixes, and thus that many entries in the
+ * The format of the Huffamn decoding table is as follows. The first (1 <<
+ * table_bits) entries of the table are indexed by chunks of the input of size
+ * @table_bits. If the next Huffman codeword in the input happens to have a
+ * length of exactly @table_bits, the symbol is simply read directly from the
+ * decoding table. Alternatively, if the next Huffman codeword has length _less
+ * than_ @table_bits, the symbol is also read directly from the decode table;
+ * this is possible because every entry in the table that is indexed by an
+ * integer that has the shorter codeword as a binary prefix is filled in with
+ * the appropriate symbol. If a codeword has length n <= table_bits, it will
+ * have 2**(table_bits - n) possible suffixes, and thus that many entries in the
* decoding table.
*
- * It's a bit more complicated if the next Huffman code has length of more than
- * @num_bits. The table entry indexed by the first @num_bits of that code
- * cannot give the appropriate symbol directly, because that entry is guaranteed
- * to be referenced by the Huffman codes for multiple symbols. And while the
- * LZX compression format does not allow codes longer than 16 bits, a table of
- * size (2 ** 16) = 65536 entries would be too slow to create.
+ * It's a bit more complicated if the next Huffman codeword has length of more
+ * than @table_bits. The table entry indexed by the first @table_bits of that
+ * codeword cannot give the appropriate symbol directly, because that entry is
+ * guaranteed to be referenced by the Huffman codewords of multiple symbols.
+ * And while the LZX compression format does not allow codes longer than 16
+ * bits, a table of size (2 ** 16) = 65536 entries would be too slow to create.
*
* There are several different ways to make it possible to look up the symbols
- * for codes longer than @num_bits. A common way is to make the entries for the
- * prefixes of length @num_bits of those entries be pointers to additional
+ * for codewords longer than @table_bits. One way is to make the entries for
+ * the prefixes of length @table_bits of those entries be pointers to additional
* decoding tables that are indexed by some number of additional bits of the
- * code symbol. The technique used here is a bit simpler, however. We just
- * store the needed subtrees of the Huffman tree in the decoding table after the
- * lookup entries, beginning at index (2**num_bits). Real pointers are
- * replaced by indices into the decoding table, and we distinguish symbol
- * entries from pointers by the fact that values less than @num_syms must be
- * symbol values.
+ * codeword. The technique used here is a bit simpler, however: just store the
+ * needed subtrees of the Huffman tree in the decoding table after the lookup
+ * entries, beginning at index (2**table_bits). Real pointers are replaced by
+ * indices into the decoding table, and symbol entries are distinguished from
+ * pointers by the fact that values less than @num_syms must be symbol values.
*/
int make_huffman_decode_table(u16 decode_table[], unsigned num_syms,
- unsigned num_bits, const u8 lens[],
- unsigned max_code_len)
+ unsigned table_bits, const u8 lens[],
+ unsigned max_codeword_len)
{
- /* Number of entries in the decode table. */
- u32 table_num_entries = 1 << num_bits;
-
- /* Current position in the decode table. */
- u32 decode_table_pos = 0;
-
- /* Fill entries for codes short enough for a direct mapping. Here we
- * are taking advantage of the ordering of the codes, since they are for
- * a canonical Huffman tree. It must be the case that all the codes of
- * some length @code_length, zero-extended or one-extended, numerically
- * precede all the codes of length @code_length + 1. Furthermore, if we
- * have 2 symbols A and B, such that A is listed before B in the lens
- * array, and both symbols have the same code length, then we know that
- * the code for A numerically precedes the code for B.
- * */
- for (unsigned code_len = 1; code_len <= num_bits; code_len++) {
-
- /* Number of entries that a code of length @code_length would
- * need. */
- u32 code_num_entries = 1 << (num_bits - code_len);
-
-
- /* For each symbol of length @code_len, fill in its entries in
- * the decode table. */
- for (unsigned sym = 0; sym < num_syms; sym++) {
-
- if (lens[sym] != code_len)
- continue;
-
-
- /* Check for table overrun. This can only happen if the
- * given lengths do not correspond to a valid Huffman
- * tree. */
- if (decode_table_pos >= table_num_entries) {
- ERROR("Huffman decoding table overrun: "
- "pos = %u, num_entries = %u",
- decode_table_pos, table_num_entries);
- return 1;
- }
-
- /* Fill all possible lookups of this symbol with
- * the symbol itself. */
- for (unsigned i = 0; i < code_num_entries; i++)
- decode_table[decode_table_pos + i] = sym;
+ unsigned len_counts[max_codeword_len + 1];
+ u16 sorted_syms[num_syms];
+ unsigned offsets[max_codeword_len + 1];
+ const unsigned table_num_entries = 1 << table_bits;
+
+ /* accumulate lengths for codes */
+ for (unsigned i = 0; i <= max_codeword_len; i++)
+ len_counts[i] = 0;
+
+ for (unsigned sym = 0; sym < num_syms; sym++) {
+ wimlib_assert2(lens[sym] <= max_codeword_len);
+ len_counts[lens[sym]]++;
+ }
- /* Increment the position in the decode table by
- * the number of entries that were just filled
- * in. */
- decode_table_pos += code_num_entries;
+ /* check for an over-subscribed or incomplete set of lengths */
+ int left = 1;
+ for (unsigned len = 1; len <= max_codeword_len; len++) {
+ left <<= 1;
+ left -= len_counts[len];
+ if (left < 0) { /* over-subscribed */
+ ERROR("Invalid Huffman code (over-subscribed)");
+ return -1;
+ }
+ }
+ if (left != 0) /* incomplete set */{
+ if (left == 1 << max_codeword_len) {
+ /* Empty code--- okay in XPRESS and LZX */
+ memset(decode_table, 0,
+ table_num_entries * sizeof(decode_table[0]));
+ return 0;
+ } else {
+ ERROR("Invalid Huffman code (incomplete set)");
+ return -1;
}
}
- /* If all entries of the decode table have been filled in, there are no
- * codes longer than num_bits, so we are done filling in the decode
- * table. */
- if (decode_table_pos == table_num_entries)
- return 0;
+ /* Generate offsets into symbol table for each length for sorting */
+ offsets[1] = 0;
+ for (unsigned len = 1; len < max_codeword_len; len++)
+ offsets[len + 1] = offsets[len] + len_counts[len];
+
+ /* Sort symbols primarily by length and secondarily by symbol order.
+ * This is basically a count-sort over the codeword lengths.
+ * In the process, calculate the number of symbols that have nonzero
+ * length and are therefore used in the symbol stream. */
+ unsigned num_used_syms = 0;
+ for (unsigned sym = 0; sym < num_syms; sym++) {
+ if (lens[sym] != 0) {
+ sorted_syms[offsets[lens[sym]]++] = sym;
+ num_used_syms++;
+ }
+ }
- /* Otherwise, fill in the remaining entries, which correspond to codes longer
- * than @num_bits. */
+ /* Fill entries for codewords short enough for a direct mapping. We can
+ * take advantage of the ordering of the codewords, since the Huffman
+ * code is canonical. It must be the case that all the codewords of
+ * some length L numerically precede all the codewords of length L + 1.
+ * Furthermore, if we have 2 symbols A and B with the same codeword
+ * length but symbol A is sorted before symbol B, then then we know that
+ * the codeword for A numerically precedes the codeword for B. */
+ unsigned decode_table_pos = 0;
+ unsigned i = 0;
+
+ wimlib_assert2(num_used_syms != 0);
+ while (1) {
+ unsigned sym = sorted_syms[i];
+ unsigned codeword_len = lens[sym];
+ if (codeword_len > table_bits)
+ break;
+
+ unsigned num_entries = 1 << (table_bits - codeword_len);
+ if (num_entries >=
+ (sizeof(unsigned long) / sizeof(decode_table[0])))
+ {
+ wimlib_assert2(decode_table_pos % 4 == 0);
+ BUILD_BUG_ON(sizeof(unsigned long) != 4 &&
+ sizeof(unsigned long) != 8);
+
+ unsigned long *p = (unsigned long *)&decode_table[decode_table_pos];
+ unsigned long n = num_entries /
+ (sizeof(unsigned long) /
+ sizeof(decode_table[0]));
+ unsigned long v = sym;
+ if (sizeof(unsigned long) >= 4)
+ v |= v << 16;
+ if (sizeof(unsigned long) >= 8)
+ v |= v << 32;
+ do {
+ *p++ = v;
+ } while (--n);
+
+ decode_table_pos += num_entries;
+ } else {
+ do {
+ decode_table[decode_table_pos++] = sym;
+ } while (--num_entries);
+ }
+ wimlib_assert2(decode_table_pos <= table_num_entries);
+ if (++i == num_used_syms) {
+ wimlib_assert2(decode_table_pos == table_num_entries);
+ /* No codewords were longer than @table_bits, so the
+ * table is now entirely filled with the codewords. */
+ return 0;
+ }
+ }
+ wimlib_assert2(i < num_used_syms);
+ wimlib_assert2(decode_table_pos < table_num_entries);
- /* First, zero out the rest of the entries; this is necessary so
- * that the entries appear as "unallocated" in the next part. */
- for (unsigned i = decode_table_pos; i < table_num_entries; i++)
- decode_table[i] = 0;
+ /* Fill in the remaining entries, which correspond to codes longer than
+ * @table_bits.
+ *
+ * First, zero out the rest of the entries. This is necessary so that
+ * the entries appear as "unallocated" in the next part. */
+ {
+ unsigned j = decode_table_pos;
+ do {
+ decode_table[j] = 0;
+ } while (++j != table_num_entries);
+ }
- /* Assert that 2**num_bits is at least num_syms. If this wasn't the
+ /* Assert that 2**table_bits is at least num_syms. If this wasn't the
* case, we wouldn't be able to distinguish pointer entries from symbol
* entries. */
- wimlib_assert((1 << num_bits) >= num_syms);
-
+ wimlib_assert2(table_num_entries >= num_syms);
- /* The current Huffman code. */
- unsigned current_code = decode_table_pos;
+ /* The current Huffman codeword */
+ unsigned cur_codeword = decode_table_pos;
- /* The tree nodes are allocated starting at
- * decode_table[table_num_entries]. Remember that the full size of the
- * table, including the extra space for the tree nodes, is actually
- * 2**num_bits + 2 * num_syms slots, while table_num_entries is only
- * 2**num_bits. */
+ /* The tree nodes are allocated starting at decode_table[1 <<
+ * table_bits]. Remember that the full size of the table, including the
+ * extra space for the tree nodes, is actually 2**table_bits + 2 *
+ * num_syms slots, while table_num_entries is only 2**table_Bits. */
unsigned next_free_tree_slot = table_num_entries;
- /* Go through every codeword of length greater than @num_bits. Note:
- * the LZX format guarantees that the codeword length can be at most 16
- * bits. */
- for (unsigned code_len = num_bits + 1; code_len <= max_code_len;
- code_len++)
- {
- current_code <<= 1;
- for (unsigned sym = 0; sym < num_syms; sym++) {
- if (lens[sym] != code_len)
- continue;
-
-
- /* i is the index of the current node; find it from the
- * prefix of the current Huffman code. */
- unsigned i = current_code >> (code_len - num_bits);
-
- if (i >= (1 << num_bits)) {
- ERROR("Invalid canonical Huffman code");
- return 1;
- }
+ /* Go through every codeword of length greater than @table_bits,
+ * primarily in order of codeword length and secondarily in order of
+ * symbol. */
+ unsigned prev_codeword_len = table_bits;
+ do {
+ unsigned sym = sorted_syms[i];
+ unsigned codeword_len = lens[sym];
+ unsigned extra_bits = codeword_len - table_bits;
+ unsigned extra_mask;
+
+ cur_codeword <<= (codeword_len - prev_codeword_len);
+ prev_codeword_len = codeword_len;
+
+ /* index of the current node; find it from the prefix of the
+ * current Huffman codeword. */
+ unsigned node_idx = cur_codeword >> extra_bits;
+ wimlib_assert2(node_idx < table_num_entries);
+
+ /* Go through each bit of the current Huffman codeword beyond
+ * the prefix of length @table_bits and walk the tree,
+ * allocating any slots that have not yet been allocated. */
+ do {
- /* Go through each bit of the current Huffman code
- * beyond the prefix of length num_bits and walk the
- * tree, "allocating" slots that have not yet been
- * allocated. */
- for (int bit_num = num_bits + 1; bit_num <= code_len; bit_num++) {
-
- /* If the current tree node points to nowhere
- * but we need to follow it, allocate a new node
- * for it to point to. */
- if (decode_table[i] == 0) {
- decode_table[i] = next_free_tree_slot;
- decode_table[next_free_tree_slot++] = 0;
- decode_table[next_free_tree_slot++] = 0;
- }
-
- i = decode_table[i];
-
- /* Is the next bit 0 or 1? If 0, go left;
- * otherwise, go right (by incrementing i by 1) */
- int bit_pos = code_len - bit_num;
-
- int bit = (current_code & (1 << bit_pos)) >>
- bit_pos;
- i += bit;
+ /* If the current tree node points to nowhere
+ * but we need to follow it, allocate a new node
+ * for it to point to. */
+ if (decode_table[node_idx] == 0) {
+ decode_table[node_idx] = next_free_tree_slot;
+ decode_table[next_free_tree_slot++] = 0;
+ decode_table[next_free_tree_slot++] = 0;
+ wimlib_assert2(next_free_tree_slot <=
+ table_num_entries + 2 * num_syms);
}
- /* i is now the index of the leaf entry into which the
- * actual symbol will go. */
- decode_table[i] = sym;
-
- /* Increment decode_table_pos only if the prefix of the
- * Huffman code changes. */
- if (current_code >> (code_len - num_bits) !=
- (current_code + 1) >> (code_len - num_bits))
- decode_table_pos++;
-
- /* current_code is always incremented because this is
- * how canonical Huffman codes are generated (add 1 for
- * each code, then left shift whenever the code length
- * increases) */
- current_code++;
- }
- }
-
-
- /* If the lengths really represented a valid Huffman tree, all
- * @table_num_entries in the table will have been filled. However, it
- * is also possible that the tree is completely empty (as noted
- * earlier) with all 0 lengths, and this is expected to succeed. */
-
- if (decode_table_pos != table_num_entries) {
-
- for (unsigned i = 0; i < num_syms; i++) {
- if (lens[i] != 0) {
- ERROR("Lengths do not form a valid canonical "
- "Huffman tree (only filled %u of %u "
- "decode table slots)",
- decode_table_pos, table_num_entries);
- return 1;
- }
- }
- }
+ /* Set node_idx to left child */
+ node_idx = decode_table[node_idx];
+
+ /* Is the next bit 0 or 1? If 0, go left (already done).
+ * If 1, go right by incrementing node_idx. */
+ --extra_bits;
+ node_idx += (cur_codeword >> extra_bits) & 1;
+ } while (extra_bits != 0);
+
+ /* node_idx is now the index of the leaf entry into which the
+ * actual symbol will go. */
+ decode_table[node_idx] = sym;
+
+ /* cur_codeword is always incremented because this is
+ * how canonical Huffman codes are generated (add 1 for
+ * each code, then left shift whenever the code length
+ * increases) */
+ cur_codeword++;
+ } while (++i != num_used_syms);
return 0;
}
git://wimlib.net / wimlib / commitdiff