X-Git-Url: https://wimlib.net/git/?a=blobdiff_plain;f=src%2Fcomp.c;h=2db66022d4a33432e58810754887cc5d2044e02c;hb=5577584b8a50baa958f832ddb9418986e3e38847;hp=206a2b85a007951e7003d98e5cb282b4212be5a3;hpb=885632f08c75c1d7bb5d25436231c78f6ad7e0c0;p=wimlib

diff --git a/src/comp.c b/src/comp.c
index 206a2b85..2db66022 100644
--- a/src/comp.c
+++ b/src/comp.c
@@ -1,27 +1,31 @@
 /*
  * comp.c
  *
- * Functions too long to declare as inline in comp.h.
- *
+ * Functions used for compression.
+ */
+
+/*
  * Copyright (C) 2012 Eric Biggers
  *
- * wimlib - Library for working with WIM files 
+ * This file is part of wimlib, a library for working with WIM files.
  *
- * This library is free software; you can redistribute it and/or modify it under
- * the terms of the GNU Lesser General Public License as published by the Free
- * Software Foundation; either version 2.1 of the License, or (at your option) any
- * later version.
+ * wimlib is free software; you can redistribute it and/or modify it under the
+ * terms of the GNU Lesser General Public License as published by the Free
+ * Software Foundation; either version 2.1 of the License, or (at your option)
+ * any later version.
  *
- * This library is distributed in the hope that it will be useful, but WITHOUT ANY
- * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A
- * PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.
+ * wimlib is distributed in the hope that it will be useful, but WITHOUT ANY
+ * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
+ * A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
+ * details.
  *
- * You should have received a copy of the GNU Lesser General Public License along
- * with this library; if not, write to the Free Software Foundation, Inc., 59
- * Temple Place, Suite 330, Boston, MA 02111-1307 USA 
+ * You should have received a copy of the GNU Lesser General Public License
+ * along with wimlib; if not, see http://www.gnu.org/licenses/.
  */
 
 #include "comp.h"
+#include <stdlib.h>
+#include <string.h>
 
 static inline void flush_bits(struct output_bitstream *ostream)
 {
@@ -93,3 +97,347 @@ void init_output_bitstream(struct output_bitstream *ostream, void *data,
 	ostream->output              = (u8*)data + 4;
 	ostream->num_bytes_remaining = num_bytes - 4;
 }
+
+/* Intermediate (non-leaf) node in a Huffman tree. */
+typedef struct HuffmanNode {
+	u32 freq;
+	u16 sym;
+	union {
+		u16 path_len;
+		u16 height;
+	};
+	struct HuffmanNode *left_child;
+	struct HuffmanNode *right_child;
+} HuffmanNode;
+
+/* Leaf node in a Huffman tree.  The fields are in the same order as the
+ * HuffmanNode, so it can be cast to a HuffmanNode.  There are no pointers to
+ * the children in the leaf node. */
+typedef struct {
+	u32 freq;
+	u16 sym;
+	union {
+		u16 path_len;
+		u16 height;
+	};
+} HuffmanLeafNode;
+
+/* Comparator function for HuffmanLeafNodes.  Sorts primarily by symbol
+ * frequency and secondarily by symbol value. */
+static int cmp_leaves_by_freq(const void *__leaf1, const void *__leaf2)
+{
+	const HuffmanLeafNode *leaf1 = __leaf1;
+	const HuffmanLeafNode *leaf2 = __leaf2;
+
+	int freq_diff = (int)leaf1->freq - (int)leaf2->freq;
+
+	if (freq_diff == 0)
+		return (int)leaf1->sym - (int)leaf2->sym;
+	else
+		return freq_diff;
+}
+
+/* Comparator function for HuffmanLeafNodes.  Sorts primarily by code length and
+ * secondarily by symbol value. */
+static int cmp_leaves_by_code_len(const void *__leaf1, const void *__leaf2)
+{
+	const HuffmanLeafNode *leaf1 = __leaf1;
+	const HuffmanLeafNode *leaf2 = __leaf2;
+
+	int code_len_diff = (int)leaf1->path_len - (int)leaf2->path_len;
+
+	if (code_len_diff == 0)
+		return (int)leaf1->sym - (int)leaf2->sym;
+	else
+		return code_len_diff;
+}
+
+/* Recursive function to calculate the depth of the leaves in a Huffman tree.
+ * */
+static void huffman_tree_compute_path_lengths(HuffmanNode *node, u16 cur_len)
+{
+	if (node->sym == (u16)(-1)) {
+		/* Intermediate node. */
+		huffman_tree_compute_path_lengths(node->left_child, cur_len + 1);
+		huffman_tree_compute_path_lengths(node->right_child, cur_len + 1);
+	} else {
+		/* Leaf node. */
+		node->path_len = cur_len;
+	}
+}
+
+/* Creates a canonical Huffman code from an array of symbol frequencies. 
+ *
+ * The algorithm used is similar to the well-known algorithm that builds a
+ * Huffman tree using a minheap.  In that algorithm, the leaf nodes are
+ * initialized and inserted into the minheap with the frequency as the key.
+ * Repeatedly, the top two nodes (nodes with the lowest frequency) are taken out
+ * of the heap and made the children of a new node that has a frequency equal to
+ * the sum of the two frequencies of its children.  This new node is inserted
+ * into the heap.  When all the nodes have been removed from the heap, what
+ * remains is the Huffman tree. The Huffman code for a symbol is given by the
+ * path to it in the tree, where each left pointer is mapped to a 0 bit and each
+ * right pointer is mapped to a 1 bit.
+ *
+ * The algorithm used here uses an optimization that removes the need to
+ * actually use a heap.  The leaf nodes are first sorted by frequency, as
+ * opposed to being made into a heap.  Note that this sorting step takes O(n log
+ * n) time vs.  O(n) time for heapifying the array, where n is the number of
+ * symbols.  However, the heapless method is probably faster overall, due to the
+ * time saved later.  In the heapless method, whenever an intermediate node is
+ * created, it is not inserted into the sorted array.  Instead, the intermediate
+ * nodes are kept in a separate array, which is easily kept sorted because every
+ * time an intermediate node is initialized, it will have a frequency at least
+ * as high as that of the previous intermediate node that was initialized.  So
+ * whenever we want the 2 nodes, leaf or intermediate, that have the lowest
+ * frequency, we check the low-frequency ends of both arrays, which is an O(1)
+ * operation.
+ *
+ * The function builds a canonical Huffman code, not just any Huffman code.  A
+ * Huffman code is canonical if the codeword for each symbol numerically
+ * precedes the codeword for all other symbols of the same length that are
+ * numbered higher than the symbol, and additionally, all shorter codewords,
+ * 0-extended, numerically precede longer codewords.  A canonical Huffman code
+ * is useful because it can be reconstructed by only knowing the path lengths in
+ * the tree.  See the make_huffman_decode_table() function to see how to
+ * reconstruct a canonical Huffman code from only the lengths of the codes.
+ *
+ * @num_syms:  The number of symbols in the alphabet.
+ *
+ * @max_codeword_len:  The maximum allowed length of a codeword in the code.
+ * 			Note that if the code being created runs up against
+ * 			this restriction, the code ultimately created will be
+ * 			suboptimal, although there are some advantages for
+ * 			limiting the length of the codewords.
+ *
+ * @freq_tab:  An array of length @num_syms that contains the frequencies
+ * 			of each symbol in the uncompressed data.
+ *
+ * @lens:	   An array of length @num_syms into which the lengths of the
+ * 			codewords for each symbol will be written.
+ *
+ * @codewords:	   An array of @num_syms short integers into which the
+ * 			codewords for each symbol will be written.  The first 
+ * 			lens[i] bits of codewords[i] will contain the codeword 
+ * 			for symbol i.
+ */
+void make_canonical_huffman_code(uint num_syms, uint max_codeword_len, 
+				 const u32 freq_tab[], u8 lens[], 
+				 u16 codewords[])
+{
+	/* We require at least 2 possible symbols in the alphabet to produce a
+	 * valid Huffman decoding table. It is allowed that fewer than 2 symbols
+	 * are actually used, though. */
+	wimlib_assert(num_syms >= 2);
+
+	/* Initialize the lengths and codewords to 0 */
+	memset(lens, 0, num_syms * sizeof(lens[0]));
+	memset(codewords, 0, num_syms * sizeof(codewords[0]));
+
+	/* Calculate how many symbols have non-zero frequency.  These are the
+	 * symbols that actually appeared in the input. */
+	uint num_used_symbols = 0;
+	for (uint i = 0; i < num_syms; i++)
+		if (freq_tab[i] != 0)
+			num_used_symbols++;
+
+
+	/* It is impossible to make a code for num_used_symbols symbols if there
+	 * aren't enough code bits to uniquely represent all of them. */
+	wimlib_assert((1 << max_codeword_len) > num_used_symbols);
+
+	/* Initialize the array of leaf nodes with the symbols and their
+	 * frequencies. */
+	HuffmanLeafNode leaves[num_used_symbols];
+	uint leaf_idx = 0;
+	for (uint i = 0; i < num_syms; i++) {
+		if (freq_tab[i] != 0) {
+			leaves[leaf_idx].freq = freq_tab[i];
+			leaves[leaf_idx].sym  = i;
+			leaves[leaf_idx].height = 0;
+			leaf_idx++;
+		}
+	}
+
+	/* Deal with the special cases where num_used_symbols < 2. */
+	if (num_used_symbols < 2) {
+		if (num_used_symbols == 0) {
+			/* If num_used_symbols is 0, there are no symbols in the
+			 * input, so it must be empty.  This should be an error,
+			 * but the LZX format expects this case to succeed.  All
+			 * the codeword lengths are simply marked as 0 (which
+			 * was already done.) */
+		} else {
+			/* If only one symbol is present, the LZX format
+			 * requires that the Huffman code include two codewords.
+			 * One is not used.  Note that this doesn't make the
+			 * encoded data take up more room anyway, since binary
+			 * data itself has 2 symbols. */
+
+			uint sym = leaves[0].sym;
+
+			codewords[0] = 0;
+			lens[0]      = 1;
+			if (sym == 0) {
+				/* dummy symbol is 1, real symbol is 0 */
+				codewords[1] = 1;
+				lens[1]      = 1;
+			} else {
+				/* dummy symbol is 0, real symbol is sym */
+				codewords[sym] = 1;
+				lens[sym]      = 1;
+			}
+		}
+		return;
+	}
+
+	/* Otherwise, there are at least 2 symbols in the input, so we need to
+	 * find a real Huffman code. */
+
+
+	/* Declare the array of intermediate nodes.  An intermediate node is not
+	 * associated with a symbol. Instead, it represents some binary code
+	 * prefix that is shared between at least 2 codewords.  There can be at
+	 * most num_used_symbols - 1 intermediate nodes when creating a Huffman
+	 * code.  This is because if there were at least num_used_symbols nodes,
+	 * the code would be suboptimal because there would be at least one
+	 * unnecessary intermediate node.  
+	 *
+	 * The worst case (greatest number of intermediate nodes) would be if
+	 * all the intermediate nodes were chained together.  This results in
+	 * num_used_symbols - 1 intermediate nodes.  If num_used_symbols is at
+	 * least 17, this configuration would not be allowed because the LZX
+	 * format constrains codes to 16 bits or less each.  However, it is
+	 * still possible for there to be more than 16 intermediate nodes, as
+	 * long as no leaf has a depth of more than 16.  */
+	HuffmanNode inodes[num_used_symbols - 1];
+
+
+	/* Pointer to the leaf node of lowest frequency that hasn't already been
+	 * added as the child of some intermediate note. */
+	HuffmanLeafNode *cur_leaf = &leaves[0];
+
+	/* Pointer past the end of the array of leaves. */
+	HuffmanLeafNode *end_leaf = &leaves[num_used_symbols];
+
+	/* Pointer to the intermediate node of lowest frequency. */
+	HuffmanNode     *cur_inode = &inodes[0];
+
+	/* Pointer to the next unallocated intermediate node. */
+	HuffmanNode     *next_inode = &inodes[0];
+
+	/* Only jump back to here if the maximum length of the codewords allowed
+	 * by the LZX format (16 bits) is exceeded. */
+try_building_tree_again:
+
+	/* Sort the leaves from those that correspond to the least frequent
+	 * symbol, to those that correspond to the most frequent symbol.  If two
+	 * leaves have the same frequency, they are sorted by symbol. */
+	qsort(leaves, num_used_symbols, sizeof(leaves[0]), cmp_leaves_by_freq);
+
+	cur_leaf   = &leaves[0];
+	cur_inode  = &inodes[0];
+	next_inode = &inodes[0];
+
+	/* The following loop takes the two lowest frequency nodes of those
+	 * remaining and makes them the children of the next available
+	 * intermediate node.  It continues until all the leaf nodes and
+	 * intermediate nodes have been used up, or the maximum allowed length
+	 * for the codewords is exceeded.  For the latter case, we must adjust
+	 * the frequencies to be more equal and then execute this loop again. */
+	while (1) {
+
+		/* Lowest frequency node. */
+		HuffmanNode *f1 = NULL; 
+
+		/* Second lowest frequency node. */
+		HuffmanNode *f2 = NULL;
+
+		/* Get the lowest and second lowest frequency nodes from
+		 * the remaining leaves or from the intermediate nodes.
+		 * */
+
+		if (cur_leaf != end_leaf && (cur_inode == next_inode || 
+					cur_leaf->freq <= cur_inode->freq)) {
+			f1 = (HuffmanNode*)cur_leaf++;
+		} else if (cur_inode != next_inode) {
+			f1 = cur_inode++;
+		}
+
+		if (cur_leaf != end_leaf && (cur_inode == next_inode || 
+					cur_leaf->freq <= cur_inode->freq)) {
+			f2 = (HuffmanNode*)cur_leaf++;
+		} else if (cur_inode != next_inode) {
+			f2 = cur_inode++;
+		}
+
+		/* All nodes used up! */
+		if (f1 == NULL || f2 == NULL)
+			break;
+
+		/* next_inode becomes the parent of f1 and f2. */
+
+		next_inode->freq   = f1->freq + f2->freq;
+		next_inode->sym    = (u16)(-1); /* Invalid symbol. */
+		next_inode->left_child   = f1;
+		next_inode->right_child  = f2;
+
+		/* We need to keep track of the height so that we can detect if
+		 * the length of a codeword has execeed max_codeword_len.   The
+		 * parent node has a height one higher than the maximum height
+		 * of its children. */
+		next_inode->height = max(f1->height, f2->height) + 1;
+
+		/* Check to see if the code length of the leaf farthest away
+		 * from next_inode has exceeded the maximum code length. */
+		if (next_inode->height > max_codeword_len) {
+			/* The code lengths can be made more uniform by making
+			 * the frequencies more uniform.  Divide all the
+			 * frequencies by 2, leaving 1 as the minimum frequency.
+			 * If this keeps happening, the symbol frequencies will
+			 * approach equality, which makes their Huffman
+			 * codewords approach the length
+			 * log_2(num_used_symbols).
+			 * */
+			for (uint i = 0; i < num_used_symbols; i++)
+				if (leaves[i].freq > 1)
+					leaves[i].freq >>= 1;
+			goto try_building_tree_again;
+		} 
+		next_inode++;
+	}
+
+	/* The Huffman tree is now complete, and its height is no more than
+	 * max_codeword_len.  */
+
+	HuffmanNode *root = next_inode - 1;
+	wimlib_assert(root->height <= max_codeword_len);
+
+	/* Compute the path lengths for the leaf nodes. */
+	huffman_tree_compute_path_lengths(root, 0);
+
+	/* Sort the leaf nodes primarily by code length and secondarily by
+	 * symbol.  */
+	qsort(leaves, num_used_symbols, sizeof(leaves[0]), cmp_leaves_by_code_len);
+
+	u16 cur_codeword = 0;
+	uint cur_codeword_len = 0;
+	for (uint i = 0; i < num_used_symbols; i++) {
+
+		/* Each time a codeword becomes one longer, the current codeword
+		 * is left shifted by one place.  This is part of the procedure
+		 * for enumerating the canonical Huffman code.  Additionally,
+		 * whenever a codeword is used, 1 is added to the current
+		 * codeword.  */
+
+		uint len_diff = leaves[i].path_len - cur_codeword_len;
+		cur_codeword <<= len_diff;
+		cur_codeword_len += len_diff;
+
+		u16 sym = leaves[i].sym;
+		codewords[sym] = cur_codeword;
+		lens[sym] = cur_codeword_len;
+
+		cur_codeword++;
+	}
+}