avl_tree: Optimize first iteration of insertion rebalance loop

[wimlib] / src / compress_common.c

/*
 * compress_common.c
 *
 * Code for compression shared among multiple compression formats.
 */

/*
 * Copyright (C) 2012, 2013 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/.
 */

#ifdef HAVE_CONFIG_H
#  include "config.h"
#endif

#include "wimlib/assert.h"
#include "wimlib/endianness.h"
#include "wimlib/compiler.h"
#include "wimlib/compress_common.h"
#include "wimlib/util.h"

#include <stdlib.h>
#include <string.h>

/* Writes @num_bits bits, given by the @num_bits least significant bits of
 * @bits, to the output @ostream. */
void
bitstream_put_bits(struct output_bitstream *ostream, u32 bits,
                   unsigned num_bits)
{
        bits &= (1U << num_bits) - 1;
        while (num_bits > ostream->free_bits) {
                /* Buffer variable does not have space for the new bits.  It
                 * needs to be flushed as a 16-bit integer.  Bits in the second
                 * byte logically precede those in the first byte
                 * (little-endian), but within each byte the bits are ordered
                 * from high to low.  This is true for both XPRESS and LZX
                 * compression.  */

                /* There must be at least 2 bytes of space remaining.  */
                if (unlikely(ostream->bytes_remaining < 2)) {
                        ostream->overrun = true;
                        return;
                }

                /* Fill the buffer with as many bits that fit.  */
                unsigned fill_bits = ostream->free_bits;

                ostream->bitbuf <<= fill_bits;
                ostream->bitbuf |= bits >> (num_bits - fill_bits);

                *(le16*)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->bytes_remaining -= 2;

                ostream->free_bits = 16;
                num_bits -= fill_bits;
                bits &= (1U << num_bits) - 1;
        }

        /* Buffer variable has space for the new bits.  */
        ostream->bitbuf = (ostream->bitbuf << num_bits) | bits;
        ostream->free_bits -= num_bits;
}

void
bitstream_put_byte(struct output_bitstream *ostream, u8 n)
{
        if (unlikely(ostream->bytes_remaining < 1)) {
                ostream->overrun = true;
                return;
        }
        *ostream->output++ = n;
        ostream->bytes_remaining--;
}

/* Flushes any remaining bits to the output bitstream.
 *
 * Returns -1 if the stream has overrun; otherwise returns the total number of
 * bytes in the output.  */
input_idx_t
flush_output_bitstream(struct output_bitstream *ostream)
{
        if (unlikely(ostream->overrun))
                return ~(input_idx_t)0;

        *(le16*)ostream->bit_output =
                cpu_to_le16((u16)((u32)ostream->bitbuf << ostream->free_bits));
        *(le16*)ostream->next_bit_output =
                cpu_to_le16(0);

        return ostream->output - ostream->output_start;
}

/* 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, unsigned num_bytes)
{
        wimlib_assert(num_bytes >= 4);

        ostream->bitbuf              = 0;
        ostream->free_bits           = 16;
        ostream->output_start        = data;
        ostream->bit_output          = data;
        ostream->next_bit_output     = data + 2;
        ostream->output              = data + 4;
        ostream->bytes_remaining     = num_bytes - 4;
        ostream->overrun             = false;
}

typedef struct {
        input_idx_t freq;
        u16 sym;
        union {
                u16 path_len;
                u16 height;
        };
} HuffmanNode;

typedef struct HuffmanIntermediateNode {
        HuffmanNode node_base;
        HuffmanNode *left_child;
        HuffmanNode *right_child;
} HuffmanIntermediateNode;


/* Comparator function for HuffmanNodes.  Sorts primarily by symbol
 * frequency and secondarily by symbol value. */
static int
cmp_nodes_by_freq(const void *_leaf1, const void *_leaf2)
{
        const HuffmanNode *leaf1 = _leaf1;
        const HuffmanNode *leaf2 = _leaf2;

        if (leaf1->freq > leaf2->freq)
                return 1;
        else if (leaf1->freq < leaf2->freq)
                return -1;
        else
                return (int)leaf1->sym - (int)leaf2->sym;
}

/* Comparator function for HuffmanNodes.  Sorts primarily by code length and
 * secondarily by symbol value. */
static int
cmp_nodes_by_code_len(const void *_leaf1, const void *_leaf2)
{
        const HuffmanNode *leaf1 = _leaf1;
        const HuffmanNode *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;
}

#define INVALID_SYMBOL 0xffff

/* Recursive function to calculate the depth of the leaves in a Huffman tree.
 * */
static void
huffman_tree_compute_path_lengths(HuffmanNode *base_node, u16 cur_len)
{
        if (base_node->sym == INVALID_SYMBOL) {
                /* Intermediate node. */
                HuffmanIntermediateNode *node = (HuffmanIntermediateNode*)base_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. */
                base_node->path_len = cur_len;
        }
}

/* make_canonical_huffman_code: - 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(unsigned num_syms,
                            unsigned max_codeword_len,
                            const input_idx_t freq_tab[restrict],
                            u8 lens[restrict],
                            u16 codewords[restrict])
{
        /* 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 && num_syms < INVALID_SYMBOL);

        /* 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. */
        unsigned num_used_symbols = 0;
        for (unsigned 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. */
        HuffmanNode leaves[num_used_symbols];
        unsigned leaf_idx = 0;
        for (unsigned 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. */

                        unsigned 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.  */
        HuffmanIntermediateNode 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. */
        HuffmanNode *cur_leaf;

        /* Pointer past the end of the array of leaves. */
        HuffmanNode *end_leaf = &leaves[num_used_symbols];

        /* Pointer to the intermediate node of lowest frequency. */
        HuffmanIntermediateNode     *cur_inode;

        /* Pointer to the next unallocated intermediate node. */
        HuffmanIntermediateNode     *next_inode;

        /* 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_nodes_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;

                /* Second lowest frequency node. */
                HuffmanNode *f2;

                /* 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->node_base.freq)) {
                        f1 = cur_leaf++;
                } else if (cur_inode != next_inode) {
                        f1 = (HuffmanNode*)cur_inode++;
                }

                if (cur_leaf != end_leaf && (cur_inode == next_inode ||
                                        cur_leaf->freq <= cur_inode->node_base.freq)) {
                        f2 = cur_leaf++;
                } else if (cur_inode != next_inode) {
                        f2 = (HuffmanNode*)cur_inode++;
                } else {
                        /* All nodes used up! */
                        break;
                }

                /* next_inode becomes the parent of f1 and f2. */

                next_inode->node_base.freq = f1->freq + f2->freq;
                next_inode->node_base.sym  = 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->node_base.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->node_base.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 (unsigned i = 0; i < num_used_symbols; i++)
                                leaves[i].freq = (leaves[i].freq + 1) >> 1;

                        goto try_building_tree_again;
                }
                next_inode++;
        }

        /* The Huffman tree is now complete, and its height is no more than
         * max_codeword_len.  */

        HuffmanIntermediateNode *root = next_inode - 1;
        wimlib_assert(root->node_base.height <= max_codeword_len);

        /* Compute the path lengths for the leaf nodes. */
        huffman_tree_compute_path_lengths(&root->node_base, 0);

        /* Sort the leaf nodes primarily by code length and secondarily by
         * symbol.  */
        qsort(leaves, num_used_symbols, sizeof(leaves[0]), cmp_nodes_by_code_len);

        u16 cur_codeword = 0;
        unsigned cur_codeword_len = 0;
        for (unsigned 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.  */

                unsigned 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++;
        }
}