[wimlib] / src / comp.c

/*
 * comp.c
 *
 * Functions used for compression.
 */

/*
 * Copyright (C) 2012 Eric Biggers
 *
 * This file is part of wimlib, a library for working with WIM files.
 *
 * wimlib is free software; you can redistribute it and/or modify it under the
 * terms of the GNU General Public License as published by the Free
 * Software Foundation; either version 3 of the License, or (at your option)
 * any later version.
 *
 * 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 General Public License for more
 * details.
 *
 * You should have received a copy of the GNU 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)
{
        *(u16*)ostream->bit_output = cpu_to_le16(ostream->bitbuf);
        ostream->bit_output = ostream->next_bit_output;
        ostream->next_bit_output = ostream->output;
        ostream->output += 2;
        ostream->num_bytes_remaining -= 2;
}

/* Writes @num_bits bits, given by the @num_bits least significant bits of
 * @bits, to the output @ostream. */
int bitstream_put_bits(struct output_bitstream *ostream, output_bitbuf_t bits, 
                       uint num_bits)
{
        uint rem_bits;

        wimlib_assert(num_bits <= 16);
        if (num_bits <= ostream->free_bits) {
                ostream->bitbuf = (ostream->bitbuf << num_bits) | bits;
                ostream->free_bits -= num_bits;
        } else {

                if (ostream->num_bytes_remaining + (ostream->output - 
                                                ostream->bit_output) < 2)
                        return 1;

                /* It is tricky to output the bits correctly.  The correct way
                 * is to output little-endian 2-byte words, such that the bits
                 * in the SECOND byte logically precede those in the FIRST byte.
                 * While the byte order is little-endian, the bit order is
                 * big-endian; the first bit in a byte is the high-order one.
                 * Any multi-bit numbers are in bit-big-endian form, so the
                 * low-order bit of a multi-bit number is the LAST bit to be
                 * output. */
                rem_bits = num_bits - ostream->free_bits;
                ostream->bitbuf <<= ostream->free_bits;
                ostream->bitbuf |= bits >> rem_bits;
                flush_bits(ostream);
                ostream->free_bits = 16 - rem_bits;
                ostream->bitbuf = bits;

        }
        return 0;
}

/* Flushes any remaining bits in the output buffer to the output byte stream. */
int flush_output_bitstream(struct output_bitstream *ostream)
{
        if (ostream->num_bytes_remaining + (ostream->output - 
                                        ostream->bit_output) < 2)
                return 1;
        if (ostream->free_bits != 16) {
                ostream->bitbuf <<= ostream->free_bits;
                flush_bits(ostream);
        }
        return 0;
}

/* Initializes an output bit buffer to write its output to the memory location
 * pointer to by @data. */
void init_output_bitstream(struct output_bitstream *ostream, void *data, 
                           uint num_bytes)
{
        ostream->bitbuf              = 0;
        ostream->free_bits           = 16;
        ostream->bit_output          = (u8*)data;
        ostream->next_bit_output     = (u8*)data + 2;
        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++;
        }
}