[wimlib] / src / lzx-compress.c

/*
 * lzx-compress.c
 *
 * A compressor that produces output compatible with the LZX compression format.
 */

/*
 * Copyright (C) 2012, 2013, 2014 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/.
 */


/*
 * This file contains a compressor for the LZX ("Lempel-Ziv eXtended"?)
 * compression format, as used in the WIM (Windows IMaging) file format.  This
 * code may need some slight modifications to be used outside of the WIM format.
 * In particular, in other situations the LZX block header might be slightly
 * different, and a sliding window rather than a fixed-size window might be
 * required.
 *
 * ----------------------------------------------------------------------------
 *
 *                               Format Overview
 *
 * The primary reference for LZX is the specification released by Microsoft.
 * However, the comments in lzx-decompress.c provide more information about LZX
 * and note some errors in the Microsoft specification.
 *
 * LZX shares many similarities with DEFLATE, the format used by zlib and gzip.
 * Both LZX and DEFLATE use LZ77 matching and Huffman coding.  Certain details
 * are quite similar, such as the method for storing Huffman codes.  However,
 * the main differences are:
 *
 * - LZX preprocesses the data to attempt to make x86 machine code slightly more
 *   compressible before attempting to compress it further.
 *
 * - LZX uses a "main" alphabet which combines literals and matches, with the
 *   match symbols containing a "length header" (giving all or part of the match
 *   length) and a "position slot" (giving, roughly speaking, the order of
 *   magnitude of the match offset).
 *
 * - LZX does not have static Huffman blocks (that is, the kind with preset
 *   Huffman codes); however it does have two types of dynamic Huffman blocks
 *   ("verbatim" and "aligned").
 *
 * - LZX has a minimum match length of 2 rather than 3.
 *
 * - In LZX, match offsets 0 through 2 actually represent entries in an LRU
 *   queue of match offsets.  This is very useful for certain types of files,
 *   such as binary files that have repeating records.
 *
 * ----------------------------------------------------------------------------
 *
 *                            Algorithmic Overview
 *
 * At a high level, any implementation of LZX compression must operate as
 * follows:
 *
 * 1. Preprocess the input data to translate the targets of 32-bit x86 call
 *    instructions to absolute offsets.  (Actually, this is required for WIM,
 *    but might not be in other places LZX is used.)
 *
 * 2. Find a sequence of LZ77-style matches and literal bytes that expands to
 *    the preprocessed data.
 *
 * 3. Divide the match/literal sequence into one or more LZX blocks, each of
 *    which may be "uncompressed", "verbatim", or "aligned".
 *
 * 4. Output each LZX block.
 *
 * Step (1) is fairly straightforward.  It requires looking for 0xe8 bytes in
 * the input data and performing a translation on the 4 bytes following each
 * one.
 *
 * Step (4) is complicated, but it is mostly determined by the LZX format.  The
 * only real choice we have is what algorithm to use to build the length-limited
 * canonical Huffman codes.  See lzx_write_all_blocks() for details.
 *
 * That leaves steps (2) and (3) as where all the hard stuff happens.  Focusing
 * on step (2), we need to do LZ77-style parsing on the input data, or "window",
 * to divide it into a sequence of matches and literals.  Each position in the
 * window might have multiple matches associated with it, and we need to choose
 * which one, if any, to actually use.  Therefore, the problem can really be
 * divided into two areas of concern: (a) finding matches at a given position,
 * which we shall call "match-finding", and (b) choosing whether to use a
 * match or a literal at a given position, and if using a match, which one (if
 * there is more than one available).  We shall call this "match-choosing".  We
 * first consider match-finding, then match-choosing.
 *
 * ----------------------------------------------------------------------------
 *
 *                               Match-finding
 *
 * Given a position in the window, we want to find LZ77-style "matches" with
 * that position at previous positions in the window.  With LZX, the minimum
 * match length is 2 and the maximum match length is 257.  The only restriction
 * on offsets is that LZX does not allow the last 2 bytes of the window to match
 * the beginning of the window.
 *
 * There are a number of algorithms that can be used for this, including hash
 * chains, binary trees, and suffix arrays.  Binary trees generally work well
 * for LZX compression since it uses medium-size windows (2^15 to 2^21 bytes).
 * However, when compressing in a fast mode where many positions are skipped
 * (not searched for matches), hash chains are faster.
 *
 * Since the match-finders are not specific to LZX, I will not explain them in
 * detail here.  Instead, see lz_hash_chains.c and lz_binary_trees.c.
 *
 * ----------------------------------------------------------------------------
 *
 *                               Match-choosing
 *
 * Usually, choosing the longest match is best because it encodes the most data
 * in that one item.  However, sometimes the longest match is not optimal
 * because (a) choosing a long match now might prevent using an even longer
 * match later, or (b) more generally, what we actually care about is the number
 * of bits it will ultimately take to output each match or literal, which is
 * actually dependent on the entropy encoding using by the underlying
 * compression format.  Consequently, a longer match usually, but not always,
 * takes fewer bits to encode than multiple shorter matches or literals that
 * cover the same data.
 *
 * This problem of choosing the truly best match/literal sequence is probably
 * impossible to solve efficiently when combined with entropy encoding.  If we
 * knew how many bits it takes to output each match/literal, then we could
 * choose the optimal sequence using shortest-path search a la Dijkstra's
 * algorithm.  However, with entropy encoding, the chosen match/literal sequence
 * affects its own encoding.  Therefore, we can't know how many bits it will
 * take to actually output any one match or literal until we have actually
 * chosen the full sequence of matches and literals.
 *
 * Notwithstanding the entropy encoding problem, we also aren't guaranteed to
 * choose the optimal match/literal sequence unless the match-finder (see
 * section "Match-finder") provides the match-chooser with all possible matches
 * at each position.  However, this is not computationally efficient.  For
 * example, there might be many matches of the same length, and usually (but not
 * always) the best choice is the one with the smallest offset.  So in practice,
 * it's fine to only consider the smallest offset for a given match length at a
 * given position.  (Actually, for LZX, it's also worth considering repeat
 * offsets.)
 *
 * In addition, as mentioned earlier, in LZX we have the choice of using
 * multiple blocks, each of which resets the Huffman codes.  This expands the
 * search space even further.  Therefore, to simplify the problem, we currently
 * we don't attempt to actually choose the LZX blocks based on the data.
 * Instead, we just divide the data into fixed-size blocks of LZX_DIV_BLOCK_SIZE
 * bytes each, and always use verbatim or aligned blocks (never uncompressed).
 * A previous version of this code recursively split the input data into
 * equal-sized blocks, up to a maximum depth, and chose the lowest-cost block
 * divisions.  However, this made compression much slower and did not actually
 * help very much.  It remains an open question whether a sufficiently fast and
 * useful block-splitting algorithm is possible for LZX.  Essentially the same
 * problem also applies to DEFLATE.  The Microsoft LZX compressor seemingly does
 * do block splitting, although I don't know how fast or useful it is,
 * specifically.
 *
 * Now, back to the entropy encoding problem.  The "solution" is to use an
 * iterative approach to compute a good, but not necessarily optimal,
 * match/literal sequence.  Start with a fixed assignment of symbol costs and
 * choose an "optimal" match/literal sequence based on those costs, using
 * shortest-path seach a la Dijkstra's algorithm.  Then, for each iteration of
 * the optimization, update the costs based on the entropy encoding of the
 * current match/literal sequence, then choose a new match/literal sequence
 * based on the updated costs.  Usually, the actual cost to output the current
 * match/literal sequence will decrease in each iteration until it converges on
 * a fixed point.  This result may not be the truly optimal match/literal
 * sequence, but it usually is much better than one chosen by doing a "greedy"
 * parse where we always chooe the longest match.
 *
 * An alternative to both greedy parsing and iterative, near-optimal parsing is
 * "lazy" parsing.  Briefly, "lazy" parsing considers just the longest match at
 * each position, but it waits to choose that match until it has also examined
 * the next position.  This is actually a useful approach; it's used by zlib,
 * for example.  Therefore, for fast compression we combine lazy parsing with
 * the hash chain max-finder.  For normal/high compression we combine
 * near-optimal parsing with the binary tree match-finder.
 */

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

#include "wimlib/compressor_ops.h"
#include "wimlib/compress_common.h"
#include "wimlib/endianness.h"
#include "wimlib/error.h"
#include "wimlib/lz_extend.h"
#include "wimlib/lz_mf.h"
#include "wimlib/lzx.h"
#include "wimlib/util.h"
#include <string.h>

#define LZX_OPTIM_ARRAY_LENGTH  4096

#define LZX_DIV_BLOCK_SIZE      32768

#define LZX_CACHE_PER_POS       8

#define LZX_MAX_MATCHES_PER_POS (LZX_MAX_MATCH_LEN - LZX_MIN_MATCH_LEN + 1)

#define LZX_CACHE_LEN (LZX_DIV_BLOCK_SIZE * (LZX_CACHE_PER_POS + 1))

/* Codewords for the LZX main, length, and aligned offset Huffman codes  */
struct lzx_codewords {
        u32 main[LZX_MAINCODE_MAX_NUM_SYMBOLS];
        u32 len[LZX_LENCODE_NUM_SYMBOLS];
        u32 aligned[LZX_ALIGNEDCODE_NUM_SYMBOLS];
};

/* Codeword lengths (in bits) for the LZX main, length, and aligned offset
 * Huffman codes.
 *
 * A 0 length means the codeword has zero frequency.
 */
struct lzx_lens {
        u8 main[LZX_MAINCODE_MAX_NUM_SYMBOLS];
        u8 len[LZX_LENCODE_NUM_SYMBOLS];
        u8 aligned[LZX_ALIGNEDCODE_NUM_SYMBOLS];
};

/* Costs for the LZX main, length, and aligned offset Huffman symbols.
 *
 * If a codeword has zero frequency, it must still be assigned some nonzero cost
 * --- generally a high cost, since even if it gets used in the next iteration,
 * it probably will not be used very many times.  */
struct lzx_costs {
        u8 main[LZX_MAINCODE_MAX_NUM_SYMBOLS];
        u8 len[LZX_LENCODE_NUM_SYMBOLS];
        u8 aligned[LZX_ALIGNEDCODE_NUM_SYMBOLS];
};

/* The LZX main, length, and aligned offset Huffman codes  */
struct lzx_codes {
        struct lzx_codewords codewords;
        struct lzx_lens lens;
};

/* Tables for tallying symbol frequencies in the three LZX alphabets  */
struct lzx_freqs {
        u32 main[LZX_MAINCODE_MAX_NUM_SYMBOLS];
        u32 len[LZX_LENCODE_NUM_SYMBOLS];
        u32 aligned[LZX_ALIGNEDCODE_NUM_SYMBOLS];
};

/* LZX intermediate match/literal format  */
struct lzx_item {
        /* Bit     Description
         *
         * 31      1 if a match, 0 if a literal.
         *
         * 30-25   position slot.  This can be at most 50, so it will fit in 6
         *         bits.
         *
         * 8-24    position footer.  This is the offset of the real formatted
         *         offset from the position base.  This can be at most 17 bits
         *         (since lzx_extra_bits[LZX_MAX_POSITION_SLOTS - 1] is 17).
         *
         * 0-7     length of match, minus 2.  This can be at most
         *         (LZX_MAX_MATCH_LEN - 2) == 255, so it will fit in 8 bits.  */
        u32 data;
};

/* Specification for an LZX block.  */
struct lzx_block_spec {

        /* One of the LZX_BLOCKTYPE_* constants indicating which type of this
         * block.  */
        int block_type;

        /* 0-based position in the window at which this block starts.  */
        u32 window_pos;

        /* The number of bytes of uncompressed data this block represents.  */
        u32 block_size;

        /* The match/literal sequence for this block.  */
        struct lzx_item *chosen_items;

        /* The length of the @chosen_items sequence.  */
        u32 num_chosen_items;

        /* Huffman codes for this block.  */
        struct lzx_codes codes;
};

struct lzx_compressor;

struct lzx_compressor_params {
        struct lz_match (*choose_item_func)(struct lzx_compressor *);
        enum lz_mf_algo mf_algo;
        u32 num_optim_passes;
        u32 min_match_length;
        u32 nice_match_length;
        u32 max_search_depth;
};

/* State of the LZX compressor.  */
struct lzx_compressor {

        /* The buffer of data to be compressed.
         *
         * 0xe8 byte preprocessing is done directly on the data here before
         * further compression.
         *
         * Note that this compressor does *not* use a real sliding window!!!!
         * It's not needed in the WIM format, since every chunk is compressed
         * independently.  This is by design, to allow random access to the
         * chunks.  */
        u8 *cur_window;

        /* Number of bytes of data to be compressed, which is the number of
         * bytes of data in @cur_window that are actually valid.  */
        u32 cur_window_size;

        /* Allocated size of @cur_window.  */
        u32 max_window_size;

        /* log2 order of the LZX window size for LZ match offset encoding
         * purposes.  Will be >= LZX_MIN_WINDOW_ORDER and <=
         * LZX_MAX_WINDOW_ORDER.
         *
         * Note: 1 << @window_order is normally equal to @max_window_size, but
         * it will be greater than @max_window_size in the event that the
         * compressor was created with a non-power-of-2 block size.  (See
         * lzx_get_window_order().)  */
        unsigned window_order;

        /* Compression parameters.  */
        struct lzx_compressor_params params;

        unsigned (*get_matches_func)(struct lzx_compressor *, const struct lz_match **);
        void (*skip_bytes_func)(struct lzx_compressor *, unsigned n);

        /* Number of symbols in the main alphabet (depends on the @window_order
         * since it determines the maximum allowed offset).  */
        unsigned num_main_syms;

        /* The current match offset LRU queue.  */
        struct lzx_lru_queue queue;

        /* Space for the sequences of matches/literals that were chosen for each
         * block.  */
        struct lzx_item *chosen_items;

        /* Information about the LZX blocks the preprocessed input was divided
         * into.  */
        struct lzx_block_spec *block_specs;

        /* Number of LZX blocks the input was divided into; a.k.a. the number of
         * elements of @block_specs that are valid.  */
        unsigned num_blocks;

        /* This is simply filled in with zeroes and used to avoid special-casing
         * the output of the first compressed Huffman code, which conceptually
         * has a delta taken from a code with all symbols having zero-length
         * codewords.  */
        struct lzx_codes zero_codes;

        /* The current cost model.  */
        struct lzx_costs costs;

        /* Lempel-Ziv match-finder.  */
        struct lz_mf *mf;

        /* Position in window of next match to return.  */
        u32 match_window_pos;

        /* The end-of-block position.  We can't allow any matches to span this
         * position.  */
        u32 match_window_end;

        /* When doing more than one match-choosing pass over the data, matches
         * found by the match-finder are cached in the following array to
         * achieve a slight speedup when the same matches are needed on
         * subsequent passes.  This is suboptimal because different matches may
         * be preferred with different cost models, but seems to be a worthwhile
         * speedup.  */
        struct lz_match *cached_matches;
        struct lz_match *cache_ptr;
        struct lz_match *cache_limit;

        /* Match-chooser state, used when doing near-optimal parsing.
         *
         * When matches have been chosen, optimum_cur_idx is set to the position
         * in the window of the next match/literal to return and optimum_end_idx
         * is set to the position in the window at the end of the last
         * match/literal to return.  */
        struct lzx_mc_pos_data *optimum;
        unsigned optimum_cur_idx;
        unsigned optimum_end_idx;

        /* Previous match, used when doing lazy parsing.  */
        struct lz_match prev_match;
};

/*
 * Match chooser position data:
 *
 * An array of these structures is used during the match-choosing algorithm.
 * They correspond to consecutive positions in the window and are used to keep
 * track of the cost to reach each position, and the match/literal choices that
 * need to be chosen to reach that position.
 */
struct lzx_mc_pos_data {
        /* The approximate minimum cost, in bits, to reach this position in the
         * window which has been found so far.  */
        u32 cost;
#define MC_INFINITE_COST ((u32)~0UL)

        /* The union here is just for clarity, since the fields are used in two
         * slightly different ways.  Initially, the @prev structure is filled in
         * first, and links go from later in the window to earlier in the
         * window.  Later, @next structure is filled in and links go from
         * earlier in the window to later in the window.  */
        union {
                struct {
                        /* Position of the start of the match or literal that
                         * was taken to get to this position in the approximate
                         * minimum-cost parse.  */
                        u32 link;

                        /* Offset (as in an LZ (length, offset) pair) of the
                         * match or literal that was taken to get to this
                         * position in the approximate minimum-cost parse.  */
                        u32 match_offset;
                } prev;
                struct {
                        /* Position at which the match or literal starting at
                         * this position ends in the minimum-cost parse.  */
                        u32 link;

                        /* Offset (as in an LZ (length, offset) pair) of the
                         * match or literal starting at this position in the
                         * approximate minimum-cost parse.  */
                        u32 match_offset;
                } next;
        };

        /* Adaptive state that exists after an approximate minimum-cost path to
         * reach this position is taken.
         *
         * Note: we update this whenever we update the pending minimum-cost
         * path.  This is in contrast to LZMA, which also has an optimal parser
         * that maintains a repeat offset queue per position, but will only
         * compute the queue once that position is actually reached in the
         * parse, meaning that matches are being considered *starting* at that
         * position.  However, the two methods seem to have approximately the
         * same performance if appropriate optimizations are used.  Intuitively
         * the LZMA method seems faster, but it actually suffers from 1-2 extra
         * hard-to-predict branches at each position.  Probably it works better
         * for LZMA than LZX because LZMA has a larger adaptive state than LZX,
         * and the LZMA encoder considers more possibilities.  */
        struct lzx_lru_queue queue;
};


/*
 * Structure to keep track of the current state of sending bits to the
 * compressed output buffer.
 *
 * The LZX bitstream is encoded as a sequence of 16-bit coding units.
 */
struct lzx_output_bitstream {

        /* Bits that haven't yet been written to the output buffer.  */
        u32 bitbuf;

        /* Number of bits currently held in @bitbuf.  */
        u32 bitcount;

        /* Pointer to the start of the output buffer.  */
        le16 *start;

        /* Pointer to the position in the output buffer at which the next coding
         * unit should be written.  */
        le16 *next;

        /* Pointer past the end of the output buffer.  */
        le16 *end;
};

/*
 * Initialize the output bitstream.
 *
 * @os
 *      The output bitstream structure to initialize.
 * @buffer
 *      The buffer being written to.
 * @size
 *      Size of @buffer, in bytes.
 */
static void
lzx_init_output(struct lzx_output_bitstream *os, void *buffer, u32 size)
{
        os->bitbuf = 0;
        os->bitcount = 0;
        os->start = buffer;
        os->next = os->start;
        os->end = os->start + size / sizeof(le16);
}

/*
 * Write some bits to the output bitstream.
 *
 * The bits are given by the low-order @num_bits bits of @bits.  Higher-order
 * bits in @bits cannot be set.  At most 17 bits can be written at once.
 *
 * @max_bits is a compile-time constant that specifies the maximum number of
 * bits that can ever be written at the call site.  Currently, it is used to
 * optimize away the conditional code for writing a second 16-bit coding unit
 * when writing fewer than 17 bits.
 *
 * If the output buffer space is exhausted, then the bits will be ignored, and
 * lzx_flush_output() will return 0 when it gets called.
 */
static _always_inline_attribute void
lzx_write_varbits(struct lzx_output_bitstream *os,
                  const u32 bits, const unsigned int num_bits,
                  const unsigned int max_num_bits)
{
        /* This code is optimized for LZX, which never needs to write more than
         * 17 bits at once.  */
        LZX_ASSERT(num_bits <= 17);
        LZX_ASSERT(num_bits <= max_num_bits);
        LZX_ASSERT(os->bitcount <= 15);

        /* Add the bits to the bit buffer variable.  @bitcount will be at most
         * 15, so there will be just enough space for the maximum possible
         * @num_bits of 17.  */
        os->bitcount += num_bits;
        os->bitbuf = (os->bitbuf << num_bits) | bits;

        /* Check whether any coding units need to be written.  */
        if (os->bitcount >= 16) {

                os->bitcount -= 16;

                /* Write a coding unit, unless it would overflow the buffer.  */
                if (os->next != os->end)
                        *os->next++ = cpu_to_le16(os->bitbuf >> os->bitcount);

                /* If writing 17 bits, a second coding unit might need to be
                 * written.  But because 'max_num_bits' is a compile-time
                 * constant, the compiler will optimize away this code at most
                 * call sites.  */
                if (max_num_bits == 17 && os->bitcount == 16) {
                        if (os->next != os->end)
                                *os->next++ = cpu_to_le16(os->bitbuf);
                        os->bitcount = 0;
                }
        }
}

/* Use when @num_bits is a compile-time constant.  Otherwise use
 * lzx_write_varbits().  */
static _always_inline_attribute void
lzx_write_bits(struct lzx_output_bitstream *os,
               const u32 bits, const unsigned int num_bits)
{
        lzx_write_varbits(os, bits, num_bits, num_bits);
}

/*
 * Flush the last coding unit to the output buffer if needed.  Return the total
 * number of bytes written to the output buffer, or 0 if an overflow occurred.
 */
static u32
lzx_flush_output(struct lzx_output_bitstream *os)
{
        if (os->next == os->end)
                return 0;

        if (os->bitcount != 0)
                *os->next++ = cpu_to_le16(os->bitbuf << (16 - os->bitcount));

        return (const u8 *)os->next - (const u8 *)os->start;
}

/* Returns the LZX position slot that corresponds to a given match offset,
 * taking into account the recent offset queue and updating it if the offset is
 * found in it.  */
static unsigned
lzx_get_position_slot(u32 offset, struct lzx_lru_queue *queue)
{
        unsigned position_slot;

        /* See if the offset was recently used.  */
        for (int i = 0; i < LZX_NUM_RECENT_OFFSETS; i++) {
                if (offset == queue->R[i]) {
                        /* Found it.  */

                        /* Bring the repeat offset to the front of the
                         * queue.  Note: this is, in fact, not a real
                         * LRU queue because repeat matches are simply
                         * swapped to the front.  */
                        swap(queue->R[0], queue->R[i]);

                        /* The resulting position slot is simply the first index
                         * at which the offset was found in the queue.  */
                        return i;
                }
        }

        /* The offset was not recently used; look up its real position slot.  */
        position_slot = lzx_get_position_slot_raw(offset + LZX_OFFSET_OFFSET);

        /* Bring the new offset to the front of the queue.  */
        for (int i = LZX_NUM_RECENT_OFFSETS - 1; i > 0; i--)
                queue->R[i] = queue->R[i - 1];
        queue->R[0] = offset;

        return position_slot;
}

/* Build the main, length, and aligned offset Huffman codes used in LZX.
 *
 * This takes as input the frequency tables for each code and produces as output
 * a set of tables that map symbols to codewords and codeword lengths.  */
static void
lzx_make_huffman_codes(const struct lzx_freqs *freqs,
                       struct lzx_codes *codes,
                       unsigned num_main_syms)
{
        make_canonical_huffman_code(num_main_syms,
                                    LZX_MAX_MAIN_CODEWORD_LEN,
                                    freqs->main,
                                    codes->lens.main,
                                    codes->codewords.main);

        make_canonical_huffman_code(LZX_LENCODE_NUM_SYMBOLS,
                                    LZX_MAX_LEN_CODEWORD_LEN,
                                    freqs->len,
                                    codes->lens.len,
                                    codes->codewords.len);

        make_canonical_huffman_code(LZX_ALIGNEDCODE_NUM_SYMBOLS,
                                    LZX_MAX_ALIGNED_CODEWORD_LEN,
                                    freqs->aligned,
                                    codes->lens.aligned,
                                    codes->codewords.aligned);
}

/*
 * Output a precomputed LZX match.
 *
 * @os:
 *      The bitstream to which to write the match.
 * @block_type:
 *      The type of the LZX block (LZX_BLOCKTYPE_ALIGNED or
 *      LZX_BLOCKTYPE_VERBATIM)
 * @match:
 *      The match data.
 * @codes:
 *      Pointer to a structure that contains the codewords for the main, length,
 *      and aligned offset Huffman codes for the current LZX compressed block.
 */
static void
lzx_write_match(struct lzx_output_bitstream *os, int block_type,
                struct lzx_item match, const struct lzx_codes *codes)
{
        unsigned match_len_minus_2 = match.data & 0xff;
        u32 position_footer = (match.data >> 8) & 0x1ffff;
        unsigned position_slot = (match.data >> 25) & 0x3f;
        unsigned len_header;
        unsigned len_footer;
        unsigned main_symbol;
        unsigned num_extra_bits;

        /* If the match length is less than MIN_MATCH_LEN (= 2) +
         * NUM_PRIMARY_LENS (= 7), the length header contains the match length
         * minus MIN_MATCH_LEN, and there is no length footer.
         *
         * Otherwise, the length header contains NUM_PRIMARY_LENS, and the
         * length footer contains the match length minus NUM_PRIMARY_LENS minus
         * MIN_MATCH_LEN. */
        if (match_len_minus_2 < LZX_NUM_PRIMARY_LENS) {
                len_header = match_len_minus_2;
        } else {
                len_header = LZX_NUM_PRIMARY_LENS;
                len_footer = match_len_minus_2 - LZX_NUM_PRIMARY_LENS;
        }

        /* Combine the position slot with the length header into a single symbol
         * that will be encoded with the main code.
         *
         * The actual main symbol is offset by LZX_NUM_CHARS because values
         * under LZX_NUM_CHARS are used to indicate a literal byte rather than a
         * match.  */
        main_symbol = ((position_slot << 3) | len_header) + LZX_NUM_CHARS;

        /* Output main symbol. */
        lzx_write_varbits(os, codes->codewords.main[main_symbol],
                          codes->lens.main[main_symbol],
                          LZX_MAX_MAIN_CODEWORD_LEN);

        /* If there is a length footer, output it using the
         * length Huffman code. */
        if (len_header == LZX_NUM_PRIMARY_LENS) {
                lzx_write_varbits(os, codes->codewords.len[len_footer],
                                  codes->lens.len[len_footer],
                                  LZX_MAX_LEN_CODEWORD_LEN);
        }

        /* Output the position footer.  */

        num_extra_bits = lzx_get_num_extra_bits(position_slot);

        if ((block_type == LZX_BLOCKTYPE_ALIGNED) && (num_extra_bits >= 3)) {

                /* Aligned offset blocks: The low 3 bits of the position footer
                 * are Huffman-encoded using the aligned offset code.  The
                 * remaining bits are output literally.  */

                lzx_write_varbits(os,
                                  position_footer >> 3, num_extra_bits - 3, 14);

                lzx_write_varbits(os,
                                  codes->codewords.aligned[position_footer & 7],
                                  codes->lens.aligned[position_footer & 7],
                                  LZX_MAX_ALIGNED_CODEWORD_LEN);
        } else {
                /* Verbatim blocks, or fewer than 3 extra bits:  All position
                 * footer bits are output literally.  */
                lzx_write_varbits(os, position_footer, num_extra_bits, 17);
        }
}

/* Output an LZX literal (encoded with the main Huffman code).  */
static void
lzx_write_literal(struct lzx_output_bitstream *os, unsigned literal,
                  const struct lzx_codes *codes)
{
        lzx_write_varbits(os, codes->codewords.main[literal],
                          codes->lens.main[literal], LZX_MAX_MAIN_CODEWORD_LEN);
}

static unsigned
lzx_build_precode(const u8 lens[restrict],
                  const u8 prev_lens[restrict],
                  const unsigned num_syms,
                  u32 precode_freqs[restrict LZX_PRECODE_NUM_SYMBOLS],
                  u8 output_syms[restrict num_syms],
                  u8 precode_lens[restrict LZX_PRECODE_NUM_SYMBOLS],
                  u32 precode_codewords[restrict LZX_PRECODE_NUM_SYMBOLS],
                  unsigned *num_additional_bits_ret)
{
        memset(precode_freqs, 0,
               LZX_PRECODE_NUM_SYMBOLS * sizeof(precode_freqs[0]));

        /* Since the code word lengths use a form of RLE encoding, the goal here
         * is to find each run of identical lengths when going through them in
         * symbol order (including runs of length 1).  For each run, as many
         * lengths are encoded using RLE as possible, and the rest are output
         * literally.
         *
         * output_syms[] will be filled in with the length symbols that will be
         * output, including RLE codes, not yet encoded using the precode.
         *
         * cur_run_len keeps track of how many code word lengths are in the
         * current run of identical lengths.  */
        unsigned output_syms_idx = 0;
        unsigned cur_run_len = 1;
        unsigned num_additional_bits = 0;
        for (unsigned i = 1; i <= num_syms; i++) {

                if (i != num_syms && lens[i] == lens[i - 1]) {
                        /* Still in a run--- keep going. */
                        cur_run_len++;
                        continue;
                }

                /* Run ended! Check if it is a run of zeroes or a run of
                 * nonzeroes. */

                /* The symbol that was repeated in the run--- not to be confused
                 * with the length *of* the run (cur_run_len) */
                unsigned len_in_run = lens[i - 1];

                if (len_in_run == 0) {
                        /* A run of 0's.  Encode it in as few length
                         * codes as we can. */

                        /* The magic length 18 indicates a run of 20 + n zeroes,
                         * where n is an uncompressed literal 5-bit integer that
                         * follows the magic length. */
                        while (cur_run_len >= 20) {
                                unsigned additional_bits;

                                additional_bits = min(cur_run_len - 20, 0x1f);
                                num_additional_bits += 5;
                                precode_freqs[18]++;
                                output_syms[output_syms_idx++] = 18;
                                output_syms[output_syms_idx++] = additional_bits;
                                cur_run_len -= 20 + additional_bits;
                        }

                        /* The magic length 17 indicates a run of 4 + n zeroes,
                         * where n is an uncompressed literal 4-bit integer that
                         * follows the magic length. */
                        while (cur_run_len >= 4) {
                                unsigned additional_bits;

                                additional_bits = min(cur_run_len - 4, 0xf);
                                num_additional_bits += 4;
                                precode_freqs[17]++;
                                output_syms[output_syms_idx++] = 17;
                                output_syms[output_syms_idx++] = additional_bits;
                                cur_run_len -= 4 + additional_bits;
                        }

                } else {

                        /* A run of nonzero lengths. */

                        /* The magic length 19 indicates a run of 4 + n
                         * nonzeroes, where n is a literal bit that follows the
                         * magic length, and where the value of the lengths in
                         * the run is given by an extra length symbol, encoded
                         * with the precode, that follows the literal bit.
                         *
                         * The extra length symbol is encoded as a difference
                         * from the length of the codeword for the first symbol
                         * in the run in the previous code.
                         * */
                        while (cur_run_len >= 4) {
                                unsigned additional_bits;
                                signed char delta;

                                additional_bits = (cur_run_len > 4);
                                num_additional_bits += 1;
                                delta = (signed char)prev_lens[i - cur_run_len] -
                                        (signed char)len_in_run;
                                if (delta < 0)
                                        delta += 17;
                                precode_freqs[19]++;
                                precode_freqs[(unsigned char)delta]++;
                                output_syms[output_syms_idx++] = 19;
                                output_syms[output_syms_idx++] = additional_bits;
                                output_syms[output_syms_idx++] = delta;
                                cur_run_len -= 4 + additional_bits;
                        }
                }

                /* Any remaining lengths in the run are outputted without RLE,
                 * as a difference from the length of that codeword in the
                 * previous code. */
                while (cur_run_len > 0) {
                        signed char delta;

                        delta = (signed char)prev_lens[i - cur_run_len] -
                                (signed char)len_in_run;
                        if (delta < 0)
                                delta += 17;

                        precode_freqs[(unsigned char)delta]++;
                        output_syms[output_syms_idx++] = delta;
                        cur_run_len--;
                }

                cur_run_len = 1;
        }

        /* Build the precode from the frequencies of the length symbols. */

        make_canonical_huffman_code(LZX_PRECODE_NUM_SYMBOLS,
                                    LZX_MAX_PRE_CODEWORD_LEN,
                                    precode_freqs, precode_lens,
                                    precode_codewords);

        *num_additional_bits_ret = num_additional_bits;

        return output_syms_idx;
}

/*
 * Output a Huffman code in the compressed form used in LZX.
 *
 * The Huffman code is represented in the output as a logical series of codeword
 * lengths from which the Huffman code, which must be in canonical form, can be
 * reconstructed.
 *
 * The codeword lengths are themselves compressed using a separate Huffman code,
 * the "precode", which contains a symbol for each possible codeword length in
 * the larger code as well as several special symbols to represent repeated
 * codeword lengths (a form of run-length encoding).  The precode is itself
 * constructed in canonical form, and its codeword lengths are represented
 * literally in 20 4-bit fields that immediately precede the compressed codeword
 * lengths of the larger code.
 *
 * Furthermore, the codeword lengths of the larger code are actually represented
 * as deltas from the codeword lengths of the corresponding code in the previous
 * block.
 *
 * @os:
 *      Bitstream to which to write the compressed Huffman code.
 * @lens:
 *      The codeword lengths, indexed by symbol, in the Huffman code.
 * @prev_lens:
 *      The codeword lengths, indexed by symbol, in the corresponding Huffman
 *      code in the previous block, or all zeroes if this is the first block.
 * @num_syms:
 *      The number of symbols in the Huffman code.
 */
static void
lzx_write_compressed_code(struct lzx_output_bitstream *os,
                          const u8 lens[restrict],
                          const u8 prev_lens[restrict],
                          unsigned num_syms)
{
        u32 precode_freqs[LZX_PRECODE_NUM_SYMBOLS];
        u8 output_syms[num_syms];
        u8 precode_lens[LZX_PRECODE_NUM_SYMBOLS];
        u32 precode_codewords[LZX_PRECODE_NUM_SYMBOLS];
        unsigned i;
        unsigned num_output_syms;
        u8 precode_sym;
        unsigned dummy;

        num_output_syms = lzx_build_precode(lens,
                                            prev_lens,
                                            num_syms,
                                            precode_freqs,
                                            output_syms,
                                            precode_lens,
                                            precode_codewords,
                                            &dummy);

        /* Write the lengths of the precode codes to the output. */
        for (i = 0; i < LZX_PRECODE_NUM_SYMBOLS; i++)
                lzx_write_bits(os, precode_lens[i], LZX_PRECODE_ELEMENT_SIZE);

        /* Write the length symbols, encoded with the precode, to the output. */

        for (i = 0; i < num_output_syms; ) {
                precode_sym = output_syms[i++];

                lzx_write_varbits(os, precode_codewords[precode_sym],
                                  precode_lens[precode_sym],
                                  LZX_MAX_PRE_CODEWORD_LEN);
                switch (precode_sym) {
                case 17:
                        lzx_write_bits(os, output_syms[i++], 4);
                        break;
                case 18:
                        lzx_write_bits(os, output_syms[i++], 5);
                        break;
                case 19:
                        lzx_write_bits(os, output_syms[i++], 1);
                        lzx_write_varbits(os, precode_codewords[output_syms[i]],
                                          precode_lens[output_syms[i]],
                                          LZX_MAX_PRE_CODEWORD_LEN);
                        i++;
                        break;
                default:
                        break;
                }
        }
}

/*
 * Write all matches and literal bytes (which were precomputed) in an LZX
 * compressed block to the output bitstream in the final compressed
 * representation.
 *
 * @os
 *      The output bitstream.
 * @block_type
 *      The chosen type of the LZX compressed block (LZX_BLOCKTYPE_ALIGNED or
 *      LZX_BLOCKTYPE_VERBATIM).
 * @items
 *      The array of matches/literals to output.
 * @num_items
 *      Number of matches/literals to output (length of @items).
 * @codes
 *      The main, length, and aligned offset Huffman codes for the current
 *      LZX compressed block.
 */
static void
lzx_write_items(struct lzx_output_bitstream *os, int block_type,
                const struct lzx_item items[], u32 num_items,
                const struct lzx_codes *codes)
{
        for (u32 i = 0; i < num_items; i++) {
                /* The high bit of the 32-bit intermediate representation
                 * indicates whether the item is an actual LZ-style match (1) or
                 * a literal byte (0).  */
                if (items[i].data & 0x80000000)
                        lzx_write_match(os, block_type, items[i], codes);
                else
                        lzx_write_literal(os, items[i].data, codes);
        }
}

/* Write an LZX aligned offset or verbatim block to the output.  */
static void
lzx_write_compressed_block(int block_type,
                           u32 block_size,
                           unsigned window_order,
                           unsigned num_main_syms,
                           struct lzx_item * chosen_items,
                           u32 num_chosen_items,
                           const struct lzx_codes * codes,
                           const struct lzx_codes * prev_codes,
                           struct lzx_output_bitstream * os)
{
        LZX_ASSERT(block_type == LZX_BLOCKTYPE_ALIGNED ||
                   block_type == LZX_BLOCKTYPE_VERBATIM);

        /* The first three bits indicate the type of block and are one of the
         * LZX_BLOCKTYPE_* constants.  */
        lzx_write_bits(os, block_type, 3);

        /* Output the block size.
         *
         * The original LZX format seemed to always encode the block size in 3
         * bytes.  However, the implementation in WIMGAPI, as used in WIM files,
         * uses the first bit to indicate whether the block is the default size
         * (32768) or a different size given explicitly by the next 16 bits.
         *
         * By default, this compressor uses a window size of 32768 and therefore
         * follows the WIMGAPI behavior.  However, this compressor also supports
         * window sizes greater than 32768 bytes, which do not appear to be
         * supported by WIMGAPI.  In such cases, we retain the default size bit
         * to mean a size of 32768 bytes but output non-default block size in 24
         * bits rather than 16.  The compatibility of this behavior is unknown
         * because WIMs created with chunk size greater than 32768 can seemingly
         * only be opened by wimlib anyway.  */
        if (block_size == LZX_DEFAULT_BLOCK_SIZE) {
                lzx_write_bits(os, 1, 1);
        } else {
                lzx_write_bits(os, 0, 1);

                if (window_order >= 16)
                        lzx_write_bits(os, block_size >> 16, 8);

                lzx_write_bits(os, block_size & 0xFFFF, 16);
        }

        /* Output the aligned offset code.  */
        if (block_type == LZX_BLOCKTYPE_ALIGNED) {
                for (int i = 0; i < LZX_ALIGNEDCODE_NUM_SYMBOLS; i++) {
                        lzx_write_bits(os, codes->lens.aligned[i],
                                       LZX_ALIGNEDCODE_ELEMENT_SIZE);
                }
        }

        /* Output the main code (two parts).  */
        lzx_write_compressed_code(os, codes->lens.main,
                                  prev_codes->lens.main,
                                  LZX_NUM_CHARS);
        lzx_write_compressed_code(os, codes->lens.main + LZX_NUM_CHARS,
                                  prev_codes->lens.main + LZX_NUM_CHARS,
                                  num_main_syms - LZX_NUM_CHARS);

        /* Output the length code.  */
        lzx_write_compressed_code(os, codes->lens.len,
                                  prev_codes->lens.len,
                                  LZX_LENCODE_NUM_SYMBOLS);

        /* Output the compressed matches and literals.  */
        lzx_write_items(os, block_type, chosen_items, num_chosen_items, codes);
}

/* Write out the LZX blocks that were computed.  */
static void
lzx_write_all_blocks(struct lzx_compressor *c, struct lzx_output_bitstream *os)
{

        const struct lzx_codes *prev_codes = &c->zero_codes;
        for (unsigned i = 0; i < c->num_blocks; i++) {
                const struct lzx_block_spec *spec = &c->block_specs[i];

                lzx_write_compressed_block(spec->block_type,
                                           spec->block_size,
                                           c->window_order,
                                           c->num_main_syms,
                                           spec->chosen_items,
                                           spec->num_chosen_items,
                                           &spec->codes,
                                           prev_codes,
                                           os);

                prev_codes = &spec->codes;
        }
}

/* Constructs an LZX match from a literal byte and updates the main code symbol
 * frequencies.  */
static inline u32
lzx_tally_literal(u8 lit, struct lzx_freqs *freqs)
{
        freqs->main[lit]++;
        return (u32)lit;
}

/* Constructs an LZX match from an offset and a length, and updates the LRU
 * queue and the frequency of symbols in the main, length, and aligned offset
 * alphabets.  The return value is a 32-bit number that provides the match in an
 * intermediate representation documented below.  */
static inline u32
lzx_tally_match(unsigned match_len, u32 match_offset,
                struct lzx_freqs *freqs, struct lzx_lru_queue *queue)
{
        unsigned position_slot;
        u32 position_footer;
        u32 len_header;
        unsigned main_symbol;
        unsigned len_footer;
        unsigned adjusted_match_len;

        LZX_ASSERT(match_len >= LZX_MIN_MATCH_LEN && match_len <= LZX_MAX_MATCH_LEN);

        /* The match offset shall be encoded as a position slot (itself encoded
         * as part of the main symbol) and a position footer.  */
        position_slot = lzx_get_position_slot(match_offset, queue);
        position_footer = (match_offset + LZX_OFFSET_OFFSET) &
                                (((u32)1 << lzx_get_num_extra_bits(position_slot)) - 1);

        /* The match length shall be encoded as a length header (itself encoded
         * as part of the main symbol) and an optional length footer.  */
        adjusted_match_len = match_len - LZX_MIN_MATCH_LEN;
        if (adjusted_match_len < LZX_NUM_PRIMARY_LENS) {
                /* No length footer needed.  */
                len_header = adjusted_match_len;
        } else {
                /* Length footer needed.  It will be encoded using the length
                 * code.  */
                len_header = LZX_NUM_PRIMARY_LENS;
                len_footer = adjusted_match_len - LZX_NUM_PRIMARY_LENS;
                freqs->len[len_footer]++;
        }

        /* Account for the main symbol.  */
        main_symbol = ((position_slot << 3) | len_header) + LZX_NUM_CHARS;

        freqs->main[main_symbol]++;

        /* In an aligned offset block, 3 bits of the position footer are output
         * as an aligned offset symbol.  Account for this, although we may
         * ultimately decide to output the block as verbatim.  */

        /* The following check is equivalent to:
         *
         * if (lzx_extra_bits[position_slot] >= 3)
         *
         * Note that this correctly excludes position slots that correspond to
         * recent offsets.  */
        if (position_slot >= 8)
                freqs->aligned[position_footer & 7]++;

        /* Pack the position slot, position footer, and match length into an
         * intermediate representation.  See `struct lzx_item' for details.
         */
        LZX_ASSERT(LZX_MAX_POSITION_SLOTS <= 64);
        LZX_ASSERT(lzx_get_num_extra_bits(LZX_MAX_POSITION_SLOTS - 1) <= 17);
        LZX_ASSERT(LZX_MAX_MATCH_LEN - LZX_MIN_MATCH_LEN + 1 <= 256);

        LZX_ASSERT(position_slot      <= (1U << (31 - 25)) - 1);
        LZX_ASSERT(position_footer    <= (1U << (25 -  8)) - 1);
        LZX_ASSERT(adjusted_match_len <= (1U << (8  -  0)) - 1);
        return 0x80000000 |
                (position_slot << 25) |
                (position_footer << 8) |
                (adjusted_match_len);
}

/* Returns the cost, in bits, to output a literal byte using the specified cost
 * model.  */
static u32
lzx_literal_cost(u8 c, const struct lzx_costs * costs)
{
        return costs->main[c];
}

/* Returns the cost, in bits, to output a repeat offset match of the specified
 * length and position slot (repeat index) using the specified cost model.  */
static u32
lzx_repmatch_cost(u32 len, unsigned position_slot, const struct lzx_costs *costs)
{
        unsigned len_header, main_symbol;
        u32 cost = 0;

        len_header = min(len - LZX_MIN_MATCH_LEN, LZX_NUM_PRIMARY_LENS);
        main_symbol = ((position_slot << 3) | len_header) + LZX_NUM_CHARS;

        /* Account for main symbol.  */
        cost += costs->main[main_symbol];

        /* Account for extra length information.  */
        if (len_header == LZX_NUM_PRIMARY_LENS)
                cost += costs->len[len - LZX_MIN_MATCH_LEN - LZX_NUM_PRIMARY_LENS];

        return cost;
}

/* Set the cost model @c->costs from the Huffman codeword lengths specified in
 * @lens.
 *
 * The cost model and codeword lengths are almost the same thing, but the
 * Huffman codewords with length 0 correspond to symbols with zero frequency
 * that still need to be assigned actual costs.  The specific values assigned
 * are arbitrary, but they should be fairly high (near the maximum codeword
 * length) to take into account the fact that uses of these symbols are expected
 * to be rare.  */
static void
lzx_set_costs(struct lzx_compressor *c, const struct lzx_lens * lens,
              unsigned nostat)
{
        unsigned i;

        /* Main code  */
        for (i = 0; i < c->num_main_syms; i++)
                c->costs.main[i] = lens->main[i] ? lens->main[i] : nostat;

        /* Length code  */
        for (i = 0; i < LZX_LENCODE_NUM_SYMBOLS; i++)
                c->costs.len[i] = lens->len[i] ? lens->len[i] : nostat;

        /* Aligned offset code  */
        for (i = 0; i < LZX_ALIGNEDCODE_NUM_SYMBOLS; i++)
                c->costs.aligned[i] = lens->aligned[i] ? lens->aligned[i] : nostat / 2;
}

/* Don't allow matches to span the end of an LZX block.  */
static inline u32
maybe_truncate_matches(struct lz_match matches[], u32 num_matches,
                       struct lzx_compressor *c)
{
        if (c->match_window_end < c->cur_window_size && num_matches != 0) {
                u32 limit = c->match_window_end - c->match_window_pos;

                if (limit >= LZX_MIN_MATCH_LEN) {

                        u32 i = num_matches - 1;
                        do {
                                if (matches[i].len >= limit) {
                                        matches[i].len = limit;

                                        /* Truncation might produce multiple
                                         * matches with length 'limit'.  Keep at
                                         * most 1.  */
                                        num_matches = i + 1;
                                }
                        } while (i--);
                } else {
                        num_matches = 0;
                }
        }
        return num_matches;
}

static unsigned
lzx_get_matches_fillcache_singleblock(struct lzx_compressor *c,
                                      const struct lz_match **matches_ret)
{
        struct lz_match *cache_ptr;
        struct lz_match *matches;
        unsigned num_matches;

        cache_ptr = c->cache_ptr;
        matches = cache_ptr + 1;
        if (likely(cache_ptr <= c->cache_limit)) {
                num_matches = lz_mf_get_matches(c->mf, matches);
                cache_ptr->len = num_matches;
                c->cache_ptr = matches + num_matches;
        } else {
                num_matches = 0;
        }
        c->match_window_pos++;
        *matches_ret = matches;
        return num_matches;
}

static unsigned
lzx_get_matches_fillcache_multiblock(struct lzx_compressor *c,
                                     const struct lz_match **matches_ret)
{
        struct lz_match *cache_ptr;
        struct lz_match *matches;
        unsigned num_matches;

        cache_ptr = c->cache_ptr;
        matches = cache_ptr + 1;
        if (likely(cache_ptr <= c->cache_limit)) {
                num_matches = lz_mf_get_matches(c->mf, matches);
                num_matches = maybe_truncate_matches(matches, num_matches, c);
                cache_ptr->len = num_matches;
                c->cache_ptr = matches + num_matches;
        } else {
                num_matches = 0;
        }
        c->match_window_pos++;
        *matches_ret = matches;
        return num_matches;
}

static unsigned
lzx_get_matches_usecache(struct lzx_compressor *c,
                         const struct lz_match **matches_ret)
{
        struct lz_match *cache_ptr;
        struct lz_match *matches;
        unsigned num_matches;

        cache_ptr = c->cache_ptr;
        matches = cache_ptr + 1;
        if (cache_ptr <= c->cache_limit) {
                num_matches = cache_ptr->len;
                c->cache_ptr = matches + num_matches;
        } else {
                num_matches = 0;
        }
        c->match_window_pos++;
        *matches_ret = matches;
        return num_matches;
}

static unsigned
lzx_get_matches_usecache_nocheck(struct lzx_compressor *c,
                                 const struct lz_match **matches_ret)
{
        struct lz_match *cache_ptr;
        struct lz_match *matches;
        unsigned num_matches;

        cache_ptr = c->cache_ptr;
        matches = cache_ptr + 1;
        num_matches = cache_ptr->len;
        c->cache_ptr = matches + num_matches;
        c->match_window_pos++;
        *matches_ret = matches;
        return num_matches;
}

static unsigned
lzx_get_matches_nocache_singleblock(struct lzx_compressor *c,
                                    const struct lz_match **matches_ret)
{
        struct lz_match *matches;
        unsigned num_matches;

        matches = c->cache_ptr;
        num_matches = lz_mf_get_matches(c->mf, matches);
        c->match_window_pos++;
        *matches_ret = matches;
        return num_matches;
}

static unsigned
lzx_get_matches_nocache_multiblock(struct lzx_compressor *c,
                                   const struct lz_match **matches_ret)
{
        struct lz_match *matches;
        unsigned num_matches;

        matches = c->cache_ptr;
        num_matches = lz_mf_get_matches(c->mf, matches);
        num_matches = maybe_truncate_matches(matches, num_matches, c);
        c->match_window_pos++;
        *matches_ret = matches;
        return num_matches;
}

/*
 * Find matches at the next position in the window.
 *
 * Returns the number of matches found and sets *matches_ret to point to the
 * matches array.  The matches will be sorted by strictly increasing length and
 * offset.
 */
static inline unsigned
lzx_get_matches(struct lzx_compressor *c,
                const struct lz_match **matches_ret)
{
        return (*c->get_matches_func)(c, matches_ret);
}

static void
lzx_skip_bytes_fillcache(struct lzx_compressor *c, unsigned n)
{
        struct lz_match *cache_ptr;

        cache_ptr = c->cache_ptr;
        c->match_window_pos += n;
        lz_mf_skip_positions(c->mf, n);
        if (cache_ptr <= c->cache_limit) {
                do {
                        cache_ptr->len = 0;
                        cache_ptr += 1;
                } while (--n && cache_ptr <= c->cache_limit);
        }
        c->cache_ptr = cache_ptr;
}

static void
lzx_skip_bytes_usecache(struct lzx_compressor *c, unsigned n)
{
        struct lz_match *cache_ptr;

        cache_ptr = c->cache_ptr;
        c->match_window_pos += n;
        if (cache_ptr <= c->cache_limit) {
                do {
                        cache_ptr += 1 + cache_ptr->len;
                } while (--n && cache_ptr <= c->cache_limit);
        }
        c->cache_ptr = cache_ptr;
}

static void
lzx_skip_bytes_usecache_nocheck(struct lzx_compressor *c, unsigned n)
{
        struct lz_match *cache_ptr;

        cache_ptr = c->cache_ptr;
        c->match_window_pos += n;
        do {
                cache_ptr += 1 + cache_ptr->len;
        } while (--n);
        c->cache_ptr = cache_ptr;
}

static void
lzx_skip_bytes_nocache(struct lzx_compressor *c, unsigned n)
{
        c->match_window_pos += n;
        lz_mf_skip_positions(c->mf, n);
}

/*
 * Skip the specified number of positions in the window (don't search for
 * matches at them).
 */
static inline void
lzx_skip_bytes(struct lzx_compressor *c, unsigned n)
{
        return (*c->skip_bytes_func)(c, n);
}

/*
 * Reverse the linked list of near-optimal matches so that they can be returned
 * in forwards order.
 *
 * Returns the first match in the list.
 */
static struct lz_match
lzx_match_chooser_reverse_list(struct lzx_compressor *c, unsigned cur_pos)
{
        unsigned prev_link, saved_prev_link;
        unsigned prev_match_offset, saved_prev_match_offset;

        c->optimum_end_idx = cur_pos;

        saved_prev_link = c->optimum[cur_pos].prev.link;
        saved_prev_match_offset = c->optimum[cur_pos].prev.match_offset;

        do {
                prev_link = saved_prev_link;
                prev_match_offset = saved_prev_match_offset;

                saved_prev_link = c->optimum[prev_link].prev.link;
                saved_prev_match_offset = c->optimum[prev_link].prev.match_offset;

                c->optimum[prev_link].next.link = cur_pos;
                c->optimum[prev_link].next.match_offset = prev_match_offset;

                cur_pos = prev_link;
        } while (cur_pos != 0);

        c->optimum_cur_idx = c->optimum[0].next.link;

        return (struct lz_match)
                { .len = c->optimum_cur_idx,
                  .offset = c->optimum[0].next.match_offset,
                };
}

/*
 * Find the longest repeat offset match.
 *
 * If no match of at least LZX_MIN_MATCH_LEN bytes is found, then return 0.
 *
 * If a match of at least LZX_MIN_MATCH_LEN bytes is found, then return its
 * length and set *slot_ret to the index of its offset in @queue.
 */
static inline u32
lzx_repsearch(const u8 * const strptr, const u32 bytes_remaining,
              const struct lzx_lru_queue *queue, unsigned *slot_ret)
{
        u32 best_len = 0;

        BUILD_BUG_ON(LZX_MIN_MATCH_LEN != 2);
        if (likely(bytes_remaining >= 2)) {
                const u32 max_len = min(LZX_MAX_MATCH_LEN, bytes_remaining);
                const u16 str = *(const u16 *)strptr;
                for (unsigned i = 0; i < LZX_NUM_RECENT_OFFSETS; i++) {
                        const u8 * const matchptr = strptr - queue->R[i];

                        /* Check the first two bytes.  If they match, then
                         * extend the match to its full length.  */
                        if (*(const u16 *)matchptr == str) {
                                const u32 len = lz_extend(strptr, matchptr,
                                                          2, max_len);
                                if (len > best_len) {
                                        best_len = len;
                                        *slot_ret = i;
                                }
                        }
                }
        }
        return best_len;
}

/*
 * lzx_choose_near_optimal_match() -
 *
 * Choose an approximately optimal match or literal to use at the next position
 * in the string, or "window", being LZ-encoded.
 *
 * This is based on algorithms used in 7-Zip, including the DEFLATE encoder
 * and the LZMA encoder, written by Igor Pavlov.
 *
 * Unlike a greedy parser that always takes the longest match, or even a "lazy"
 * parser with one match/literal look-ahead like zlib, the algorithm used here
 * may look ahead many matches/literals to determine the approximately optimal
 * match/literal to code next.  The motivation is that the compression ratio is
 * improved if the compressor can do things like use a shorter-than-possible
 * match in order to allow a longer match later, and also take into account the
 * estimated real cost of coding each match/literal based on the underlying
 * entropy encoding.
 *
 * Still, this is not a true optimal parser for several reasons:
 *
 * - Real compression formats use entropy encoding of the literal/match
 *   sequence, so the real cost of coding each match or literal is unknown until
 *   the parse is fully determined.  It can be approximated based on iterative
 *   parses, but the end result is not guaranteed to be globally optimal.
 *
 * - Very long matches are chosen immediately.  This is because locations with
 *   long matches are likely to have many possible alternatives that would cause
 *   slow optimal parsing, but also such locations are already highly
 *   compressible so it is not too harmful to just grab the longest match.
 *
 * - Not all possible matches at each location are considered because the
 *   underlying match-finder limits the number and type of matches produced at
 *   each position.  For example, for a given match length it's usually not
 *   worth it to only consider matches other than the lowest-offset match,
 *   except in the case of a repeat offset.
 *
 * - Although we take into account the adaptive state (in LZX, the recent offset
 *   queue), coding decisions made with respect to the adaptive state will be
 *   locally optimal but will not necessarily be globally optimal.  This is
 *   because the algorithm only keeps the least-costly path to get to a given
 *   location and does not take into account that a slightly more costly path
 *   could result in a different adaptive state that ultimately results in a
 *   lower global cost.
 *
 * - The array space used by this function is bounded, so in degenerate cases it
 *   is forced to start returning matches/literals before the algorithm has
 *   really finished.
 *
 * Each call to this function does one of two things:
 *
 * 1. Build a sequence of near-optimal matches/literals, up to some point, that
 *    will be returned by subsequent calls to this function, then return the
 *    first one.
 *
 * OR
 *
 * 2. Return the next match/literal previously computed by a call to this
 *    function.
 *
 * The return value is a (length, offset) pair specifying the match or literal
 * chosen.  For literals, the length is 0 or 1 and the offset is meaningless.
 */
static struct lz_match
lzx_choose_near_optimal_item(struct lzx_compressor *c)
{
        unsigned num_matches;
        const struct lz_match *matches;
        struct lz_match match;
        u32 longest_len;
        u32 longest_rep_len;
        unsigned longest_rep_slot;
        unsigned cur_pos;
        unsigned end_pos;
        struct lzx_mc_pos_data *optimum = c->optimum;

        if (c->optimum_cur_idx != c->optimum_end_idx) {
                /* Case 2: Return the next match/literal already found.  */
                match.len = optimum[c->optimum_cur_idx].next.link -
                                    c->optimum_cur_idx;
                match.offset = optimum[c->optimum_cur_idx].next.match_offset;

                c->optimum_cur_idx = optimum[c->optimum_cur_idx].next.link;
                return match;
        }

        /* Case 1:  Compute a new list of matches/literals to return.  */

        c->optimum_cur_idx = 0;
        c->optimum_end_idx = 0;

        /* Search for matches at repeat offsets.  As a heuristic, we only keep
         * the one with the longest match length.  */
        if (likely(c->match_window_pos >= 1)) {
                longest_rep_len = lzx_repsearch(&c->cur_window[c->match_window_pos],
                                                c->match_window_end - c->match_window_pos,
                                                &c->queue,
                                                &longest_rep_slot);
        } else {
                longest_rep_len = 0;
        }

        /* If there's a long match with a repeat offset, choose it immediately.  */
        if (longest_rep_len >= c->params.nice_match_length) {
                lzx_skip_bytes(c, longest_rep_len);
                return (struct lz_match) {
                        .len = longest_rep_len,
                        .offset = c->queue.R[longest_rep_slot],
                };
        }

        /* Find other matches.  */
        num_matches = lzx_get_matches(c, &matches);

        /* If there's a long match, choose it immediately.  */
        if (num_matches) {
                longest_len = matches[num_matches - 1].len;
                if (longest_len >= c->params.nice_match_length) {
                        lzx_skip_bytes(c, longest_len - 1);
                        return matches[num_matches - 1];
                }
        } else {
                longest_len = 1;
        }

        /* Calculate the cost to reach the next position by coding a literal.  */
        optimum[1].queue = c->queue;
        optimum[1].cost = lzx_literal_cost(c->cur_window[c->match_window_pos - 1],
                                              &c->costs);
        optimum[1].prev.link = 0;

        /* Calculate the cost to reach any position up to and including that
         * reached by the longest match.
         *
         * Note: We consider only the lowest-offset match that reaches each
         * position.
         *
         * Note: Some of the cost calculation stays the same for each offset,
         * regardless of how many lengths it gets used for.  Therefore, to
         * improve performance, we hand-code the cost calculation instead of
         * calling lzx_match_cost() to do a from-scratch cost evaluation at each
         * length.  */
        for (unsigned i = 0, len = 2; i < num_matches; i++) {
                u32 offset;
                struct lzx_lru_queue queue;
                u32 position_cost;
                unsigned position_slot;
                unsigned num_extra_bits;

                offset = matches[i].offset;
                queue = c->queue;
                position_cost = 0;

                position_slot = lzx_get_position_slot(offset, &queue);
                num_extra_bits = lzx_get_num_extra_bits(position_slot);
                if (num_extra_bits >= 3) {
                        position_cost += num_extra_bits - 3;
                        position_cost += c->costs.aligned[(offset + LZX_OFFSET_OFFSET) & 7];
                } else {
                        position_cost += num_extra_bits;
                }

                do {
                        unsigned len_header;
                        unsigned main_symbol;
                        u32 cost;

                        cost = position_cost;

                        len_header = min(len - LZX_MIN_MATCH_LEN, LZX_NUM_PRIMARY_LENS);
                        main_symbol = ((position_slot << 3) | len_header) + LZX_NUM_CHARS;
                        cost += c->costs.main[main_symbol];
                        if (len_header == LZX_NUM_PRIMARY_LENS)
                                cost += c->costs.len[len - LZX_MIN_MATCH_LEN - LZX_NUM_PRIMARY_LENS];

                        optimum[len].queue = queue;
                        optimum[len].prev.link = 0;
                        optimum[len].prev.match_offset = offset;
                        optimum[len].cost = cost;
                } while (++len <= matches[i].len);
        }
        end_pos = longest_len;

        if (longest_rep_len) {

                LZX_ASSERT(longest_rep_len >= LZX_MIN_MATCH_LEN);

                u32 cost;

                while (end_pos < longest_rep_len)
                        optimum[++end_pos].cost = MC_INFINITE_COST;

                cost = lzx_repmatch_cost(longest_rep_len, longest_rep_slot,
                                         &c->costs);
                if (cost <= optimum[longest_rep_len].cost) {
                        optimum[longest_rep_len].queue = c->queue;
                        swap(optimum[longest_rep_len].queue.R[0],
                             optimum[longest_rep_len].queue.R[longest_rep_slot]);
                        optimum[longest_rep_len].prev.link = 0;
                        optimum[longest_rep_len].prev.match_offset =
                                optimum[longest_rep_len].queue.R[0];
                        optimum[longest_rep_len].cost = cost;
                }
        }

        /* Step forward, calculating the estimated minimum cost to reach each
         * position.  The algorithm may find multiple paths to reach each
         * position; only the lowest-cost path is saved.
         *
         * The progress of the parse is tracked in the @optimum array, which for
         * each position contains the minimum cost to reach that position, the
         * index of the start of the match/literal taken to reach that position
         * through the minimum-cost path, the offset of the match taken (not
         * relevant for literals), and the adaptive state that will exist at
         * that position after the minimum-cost path is taken.  The @cur_pos
         * variable stores the position at which the algorithm is currently
         * considering coding choices, and the @end_pos variable stores the
         * greatest position at which the costs of coding choices have been
         * saved.
         *
         * The loop terminates when any one of the following conditions occurs:
         *
         * 1. A match with length greater than or equal to @nice_match_length is
         *    found.  When this occurs, the algorithm chooses this match
         *    unconditionally, and consequently the near-optimal match/literal
         *    sequence up to and including that match is fully determined and it
         *    can begin returning the match/literal list.
         *
         * 2. @cur_pos reaches a position not overlapped by a preceding match.
         *    In such cases, the near-optimal match/literal sequence up to
         *    @cur_pos is fully determined and it can begin returning the
         *    match/literal list.
         *
         * 3. Failing either of the above in a degenerate case, the loop
         *    terminates when space in the @optimum array is exhausted.
         *    This terminates the algorithm and forces it to start returning
         *    matches/literals even though they may not be globally optimal.
         *
         * Upon loop termination, a nonempty list of matches/literals will have
         * been produced and stored in the @optimum array.  These
         * matches/literals are linked in reverse order, so the last thing this
         * function does is reverse this list and return the first
         * match/literal, leaving the rest to be returned immediately by
         * subsequent calls to this function.
         */
        cur_pos = 0;
        for (;;) {
                u32 cost;

                /* Advance to next position.  */
                cur_pos++;

                /* Check termination conditions (2) and (3) noted above.  */
                if (cur_pos == end_pos || cur_pos == LZX_OPTIM_ARRAY_LENGTH)
                        return lzx_match_chooser_reverse_list(c, cur_pos);

                /* Search for matches at repeat offsets.  Again, as a heuristic
                 * we only keep the longest one.  */
                longest_rep_len = lzx_repsearch(&c->cur_window[c->match_window_pos],
                                                c->match_window_end - c->match_window_pos,
                                                &optimum[cur_pos].queue,
                                                &longest_rep_slot);

                /* If we found a long match at a repeat offset, choose it
                 * immediately.  */
                if (longest_rep_len >= c->params.nice_match_length) {
                        /* Build the list of matches to return and get
                         * the first one.  */
                        match = lzx_match_chooser_reverse_list(c, cur_pos);

                        /* Append the long match to the end of the list.  */
                        optimum[cur_pos].next.match_offset =
                                optimum[cur_pos].queue.R[longest_rep_slot];
                        optimum[cur_pos].next.link = cur_pos + longest_rep_len;
                        c->optimum_end_idx = cur_pos + longest_rep_len;

                        /* Skip over the remaining bytes of the long match.  */
                        lzx_skip_bytes(c, longest_rep_len);

                        /* Return first match in the list.  */
                        return match;
                }

                /* Find other matches.  */
                num_matches = lzx_get_matches(c, &matches);

                /* If there's a long match, choose it immediately.  */
                if (num_matches) {
                        longest_len = matches[num_matches - 1].len;
                        if (longest_len >= c->params.nice_match_length) {
                                /* Build the list of matches to return and get
                                 * the first one.  */
                                match = lzx_match_chooser_reverse_list(c, cur_pos);

                                /* Append the long match to the end of the list.  */
                                optimum[cur_pos].next.match_offset =
                                        matches[num_matches - 1].offset;
                                optimum[cur_pos].next.link = cur_pos + longest_len;
                                c->optimum_end_idx = cur_pos + longest_len;

                                /* Skip over the remaining bytes of the long match.  */
                                lzx_skip_bytes(c, longest_len - 1);

                                /* Return first match in the list.  */
                                return match;
                        }
                } else {
                        longest_len = 1;
                }

                /* If we are reaching any positions for the first time, we need
                 * to initialize their costs to infinity.  */
                while (end_pos < cur_pos + longest_len)
                        optimum[++end_pos].cost = MC_INFINITE_COST;

                /* Consider coding a literal.  */
                cost = optimum[cur_pos].cost +
                        lzx_literal_cost(c->cur_window[c->match_window_pos - 1],
                                         &c->costs);
                if (cost < optimum[cur_pos + 1].cost) {
                        optimum[cur_pos + 1].queue = optimum[cur_pos].queue;
                        optimum[cur_pos + 1].cost = cost;
                        optimum[cur_pos + 1].prev.link = cur_pos;
                }

                /* Consider coding a match.
                 *
                 * The hard-coded cost calculation is done for the same reason
                 * stated in the comment for the similar loop earlier.
                 * Actually, it is *this* one that has the biggest effect on
                 * performance; overall LZX compression is > 10% faster with
                 * this code compared to calling lzx_match_cost() with each
                 * length.  */
                for (unsigned i = 0, len = 2; i < num_matches; i++) {
                        u32 offset;
                        u32 position_cost;
                        unsigned position_slot;
                        unsigned num_extra_bits;

                        offset = matches[i].offset;
                        position_cost = optimum[cur_pos].cost;

                        /* Yet another optimization: instead of calling
                         * lzx_get_position_slot(), hand-inline the search of
                         * the repeat offset queue.  Then we can omit the
                         * extra_bits calculation for repeat offset matches, and
                         * also only compute the updated queue if we actually do
                         * find a new lowest cost path.  */
                        for (position_slot = 0; position_slot < LZX_NUM_RECENT_OFFSETS; position_slot++)
                                if (offset == optimum[cur_pos].queue.R[position_slot])
                                        goto have_position_cost;

                        position_slot = lzx_get_position_slot_raw(offset + LZX_OFFSET_OFFSET);

                        num_extra_bits = lzx_get_num_extra_bits(position_slot);
                        if (num_extra_bits >= 3) {
                                position_cost += num_extra_bits - 3;
                                position_cost += c->costs.aligned[
                                                (offset + LZX_OFFSET_OFFSET) & 7];
                        } else {
                                position_cost += num_extra_bits;
                        }

                have_position_cost:

                        do {
                                unsigned len_header;
                                unsigned main_symbol;
                                u32 cost;

                                cost = position_cost;

                                len_header = min(len - LZX_MIN_MATCH_LEN,
                                                 LZX_NUM_PRIMARY_LENS);
                                main_symbol = ((position_slot << 3) | len_header) +
                                                LZX_NUM_CHARS;
                                cost += c->costs.main[main_symbol];
                                if (len_header == LZX_NUM_PRIMARY_LENS) {
                                        cost += c->costs.len[len -
                                                        LZX_MIN_MATCH_LEN -
                                                        LZX_NUM_PRIMARY_LENS];
                                }
                                if (cost < optimum[cur_pos + len].cost) {
                                        if (position_slot < LZX_NUM_RECENT_OFFSETS) {
                                                optimum[cur_pos + len].queue = optimum[cur_pos].queue;
                                                swap(optimum[cur_pos + len].queue.R[0],
                                                     optimum[cur_pos + len].queue.R[position_slot]);
                                        } else {
                                                optimum[cur_pos + len].queue.R[0] = offset;
                                                optimum[cur_pos + len].queue.R[1] = optimum[cur_pos].queue.R[0];
                                                optimum[cur_pos + len].queue.R[2] = optimum[cur_pos].queue.R[1];
                                        }
                                        optimum[cur_pos + len].prev.link = cur_pos;
                                        optimum[cur_pos + len].prev.match_offset = offset;
                                        optimum[cur_pos + len].cost = cost;
                                }
                        } while (++len <= matches[i].len);
                }

                /* Consider coding a repeat offset match.
                 *
                 * As a heuristic, we only consider the longest length of the
                 * longest repeat offset match.  This does not, however,
                 * necessarily mean that we will never consider any other repeat
                 * offsets, because above we detect repeat offset matches that
                 * were found by the regular match-finder.  Therefore, this
                 * special handling of the longest repeat-offset match is only
                 * helpful for coding a repeat offset match that was *not* found
                 * by the match-finder, e.g. due to being obscured by a less
                 * distant match that is at least as long.
                 *
                 * Note: an alternative, used in LZMA, is to consider every
                 * length of every repeat offset match.  This is a more thorough
                 * search, and it makes it unnecessary to detect repeat offset
                 * matches that were found by the regular match-finder.  But by
                 * my tests, for LZX the LZMA method slows down the compressor
                 * by ~10% and doesn't actually help the compression ratio too
                 * much.
                 *
                 * Also tested a compromise approach: consider every 3rd length
                 * of the longest repeat offset match.  Still didn't seem quite
                 * worth it, though.
                 */
                if (longest_rep_len) {

                        LZX_ASSERT(longest_rep_len >= LZX_MIN_MATCH_LEN);

                        while (end_pos < cur_pos + longest_rep_len)
                                optimum[++end_pos].cost = MC_INFINITE_COST;

                        cost = optimum[cur_pos].cost +
                                lzx_repmatch_cost(longest_rep_len, longest_rep_slot,
                                                  &c->costs);
                        if (cost <= optimum[cur_pos + longest_rep_len].cost) {
                                optimum[cur_pos + longest_rep_len].queue =
                                        optimum[cur_pos].queue;
                                swap(optimum[cur_pos + longest_rep_len].queue.R[0],
                                     optimum[cur_pos + longest_rep_len].queue.R[longest_rep_slot]);
                                optimum[cur_pos + longest_rep_len].prev.link =
                                        cur_pos;
                                optimum[cur_pos + longest_rep_len].prev.match_offset =
                                        optimum[cur_pos + longest_rep_len].queue.R[0];
                                optimum[cur_pos + longest_rep_len].cost =
                                        cost;
                        }
                }
        }
}

static struct lz_match
lzx_choose_lazy_item(struct lzx_compressor *c)
{
        const struct lz_match *matches;
        struct lz_match cur_match;
        struct lz_match next_match;
        u32 num_matches;

        if (c->prev_match.len) {
                cur_match = c->prev_match;
                c->prev_match.len = 0;
        } else {
                num_matches = lzx_get_matches(c, &matches);
                if (num_matches == 0 ||
                    (matches[num_matches - 1].len <= 3 &&
                     (matches[num_matches - 1].len <= 2 ||
                      matches[num_matches - 1].offset > 4096)))
                {
                        return (struct lz_match) { };
                }

                cur_match = matches[num_matches - 1];
        }

        if (cur_match.len >= c->params.nice_match_length) {
                lzx_skip_bytes(c, cur_match.len - 1);
                return cur_match;
        }

        num_matches = lzx_get_matches(c, &matches);
        if (num_matches == 0 ||
            (matches[num_matches - 1].len <= 3 &&
             (matches[num_matches - 1].len <= 2 ||
              matches[num_matches - 1].offset > 4096)))
        {
                lzx_skip_bytes(c, cur_match.len - 2);
                return cur_match;
        }

        next_match = matches[num_matches - 1];

        if (next_match.len <= cur_match.len) {
                lzx_skip_bytes(c, cur_match.len - 2);
                return cur_match;
        } else {
                c->prev_match = next_match;
                return (struct lz_match) { };
        }
}

/*
 * Return the next match or literal to use, delegating to the currently selected
 * match-choosing algorithm.
 *
 * If the length of the returned 'struct lz_match' is less than
 * LZX_MIN_MATCH_LEN, then it is really a literal.
 */
static inline struct lz_match
lzx_choose_item(struct lzx_compressor *c)
{
        return (*c->params.choose_item_func)(c);
}

/* Set default symbol costs for the LZX Huffman codes.  */
static void
lzx_set_default_costs(struct lzx_costs * costs, unsigned num_main_syms)
{
        unsigned i;

        /* Main code (part 1): Literal symbols  */
        for (i = 0; i < LZX_NUM_CHARS; i++)
                costs->main[i] = 8;

        /* Main code (part 2): Match header symbols  */
        for (; i < num_main_syms; i++)
                costs->main[i] = 10;

        /* Length code  */
        for (i = 0; i < LZX_LENCODE_NUM_SYMBOLS; i++)
                costs->len[i] = 8;

        /* Aligned offset code  */
        for (i = 0; i < LZX_ALIGNEDCODE_NUM_SYMBOLS; i++)
                costs->aligned[i] = 3;
}

/* Given the frequencies of symbols in an LZX-compressed block and the
 * corresponding Huffman codes, return LZX_BLOCKTYPE_ALIGNED or
 * LZX_BLOCKTYPE_VERBATIM if an aligned offset or verbatim block, respectively,
 * will take fewer bits to output.  */
static int
lzx_choose_verbatim_or_aligned(const struct lzx_freqs * freqs,
                               const struct lzx_codes * codes)
{
        unsigned aligned_cost = 0;
        unsigned verbatim_cost = 0;

        /* Verbatim blocks have a constant 3 bits per position footer.  Aligned
         * offset blocks have an aligned offset symbol per position footer, plus
         * an extra 24 bits per block to output the lengths necessary to
         * reconstruct the aligned offset code itself.  */
        for (unsigned i = 0; i < LZX_ALIGNEDCODE_NUM_SYMBOLS; i++) {
                verbatim_cost += 3 * freqs->aligned[i];
                aligned_cost += codes->lens.aligned[i] * freqs->aligned[i];
        }
        aligned_cost += LZX_ALIGNEDCODE_ELEMENT_SIZE * LZX_ALIGNEDCODE_NUM_SYMBOLS;
        if (aligned_cost < verbatim_cost)
                return LZX_BLOCKTYPE_ALIGNED;
        else
                return LZX_BLOCKTYPE_VERBATIM;
}

/* Find a sequence of matches/literals with which to output the specified LZX
 * block, then set the block's type to that which has the minimum cost to output
 * (either verbatim or aligned).  */
static void
lzx_choose_items_for_block(struct lzx_compressor *c, struct lzx_block_spec *spec)
{
        const struct lzx_lru_queue orig_queue = c->queue;
        u32 num_passes_remaining = c->params.num_optim_passes;
        struct lzx_freqs freqs;
        const u8 *window_ptr;
        const u8 *window_end;
        struct lzx_item *next_chosen_item;
        struct lz_match lz_match;
        struct lzx_item lzx_item;

        LZX_ASSERT(num_passes_remaining >= 1);
        LZX_ASSERT(lz_mf_get_position(c->mf) == spec->window_pos);

        c->match_window_end = spec->window_pos + spec->block_size;

        if (c->params.num_optim_passes > 1) {
                if (spec->block_size == c->cur_window_size)
                        c->get_matches_func = lzx_get_matches_fillcache_singleblock;
                else
                        c->get_matches_func = lzx_get_matches_fillcache_multiblock;
                c->skip_bytes_func = lzx_skip_bytes_fillcache;
        } else {
                if (spec->block_size == c->cur_window_size)
                        c->get_matches_func = lzx_get_matches_nocache_singleblock;
                else
                        c->get_matches_func = lzx_get_matches_nocache_multiblock;
                c->skip_bytes_func = lzx_skip_bytes_nocache;
        }

        /* The first optimal parsing pass is done using the cost model already
         * set in c->costs.  Each later pass is done using a cost model
         * computed from the previous pass.
         *
         * To improve performance we only generate the array containing the
         * matches and literals in intermediate form on the final pass.  */

        while (--num_passes_remaining) {
                c->match_window_pos = spec->window_pos;
                c->cache_ptr = c->cached_matches;
                memset(&freqs, 0, sizeof(freqs));
                window_ptr = &c->cur_window[spec->window_pos];
                window_end = window_ptr + spec->block_size;

                while (window_ptr != window_end) {

                        lz_match = lzx_choose_item(c);

                        LZX_ASSERT(!(lz_match.len == LZX_MIN_MATCH_LEN &&
                                     lz_match.offset == c->max_window_size -
                                                         LZX_MIN_MATCH_LEN));
                        if (lz_match.len >= LZX_MIN_MATCH_LEN) {
                                lzx_tally_match(lz_match.len, lz_match.offset,
                                                &freqs, &c->queue);
                                window_ptr += lz_match.len;
                        } else {
                                lzx_tally_literal(*window_ptr, &freqs);
                                window_ptr += 1;
                        }
                }
                lzx_make_huffman_codes(&freqs, &spec->codes, c->num_main_syms);
                lzx_set_costs(c, &spec->codes.lens, 15);
                c->queue = orig_queue;
                if (c->cache_ptr <= c->cache_limit) {
                        c->get_matches_func = lzx_get_matches_usecache_nocheck;
                        c->skip_bytes_func = lzx_skip_bytes_usecache_nocheck;
                } else {
                        c->get_matches_func = lzx_get_matches_usecache;
                        c->skip_bytes_func = lzx_skip_bytes_usecache;
                }
        }

        c->match_window_pos = spec->window_pos;
        c->cache_ptr = c->cached_matches;
        memset(&freqs, 0, sizeof(freqs));
        window_ptr = &c->cur_window[spec->window_pos];
        window_end = window_ptr + spec->block_size;

        spec->chosen_items = &c->chosen_items[spec->window_pos];
        next_chosen_item = spec->chosen_items;

        unsigned unseen_cost = 9;
        while (window_ptr != window_end) {

                lz_match = lzx_choose_item(c);

                LZX_ASSERT(!(lz_match.len == LZX_MIN_MATCH_LEN &&
                             lz_match.offset == c->max_window_size -
                                                 LZX_MIN_MATCH_LEN));
                if (lz_match.len >= LZX_MIN_MATCH_LEN) {
                        lzx_item.data = lzx_tally_match(lz_match.len,
                                                         lz_match.offset,
                                                         &freqs, &c->queue);
                        window_ptr += lz_match.len;
                } else {
                        lzx_item.data = lzx_tally_literal(*window_ptr, &freqs);
                        window_ptr += 1;
                }
                *next_chosen_item++ = lzx_item;

                /* When doing one-pass "near-optimal" parsing, update the cost
                 * model occassionally.  */
                if (unlikely((next_chosen_item - spec->chosen_items) % 2048 == 0) &&
                    c->params.choose_item_func == lzx_choose_near_optimal_item &&
                    c->params.num_optim_passes == 1)
                {
                        lzx_make_huffman_codes(&freqs, &spec->codes, c->num_main_syms);
                        lzx_set_costs(c, &spec->codes.lens, unseen_cost);
                        if (unseen_cost < 15)
                                unseen_cost++;
                }
        }
        spec->num_chosen_items = next_chosen_item - spec->chosen_items;
        lzx_make_huffman_codes(&freqs, &spec->codes, c->num_main_syms);
        spec->block_type = lzx_choose_verbatim_or_aligned(&freqs, &spec->codes);
}

/* Prepare the input window into one or more LZX blocks ready to be output.  */
static void
lzx_prepare_blocks(struct lzx_compressor *c)
{
        /* Set up a default cost model.  */
        if (c->params.choose_item_func == lzx_choose_near_optimal_item)
                lzx_set_default_costs(&c->costs, c->num_main_syms);

        /* Set up the block specifications.
         * TODO: The compression ratio could be slightly improved by performing
         * data-dependent block splitting instead of using fixed-size blocks.
         * Doing so well is a computationally hard problem, however.  */
        c->num_blocks = DIV_ROUND_UP(c->cur_window_size, LZX_DIV_BLOCK_SIZE);
        for (unsigned i = 0; i < c->num_blocks; i++) {
                u32 pos = LZX_DIV_BLOCK_SIZE * i;
                c->block_specs[i].window_pos = pos;
                c->block_specs[i].block_size = min(c->cur_window_size - pos,
                                                   LZX_DIV_BLOCK_SIZE);
        }

        /* Load the window into the match-finder.  */
        lz_mf_load_window(c->mf, c->cur_window, c->cur_window_size);

        /* Determine sequence of matches/literals to output for each block.  */
        lzx_lru_queue_init(&c->queue);
        c->optimum_cur_idx = 0;
        c->optimum_end_idx = 0;
        c->prev_match.len = 0;
        for (unsigned i = 0; i < c->num_blocks; i++)
                lzx_choose_items_for_block(c, &c->block_specs[i]);
}

static void
lzx_build_params(unsigned int compression_level,
                 u32 max_window_size,
                 struct lzx_compressor_params *lzx_params)
{
        if (compression_level < 25) {
                lzx_params->choose_item_func = lzx_choose_lazy_item;
                lzx_params->num_optim_passes  = 1;
                if (max_window_size <= 262144)
                        lzx_params->mf_algo = LZ_MF_HASH_CHAINS;
                else
                        lzx_params->mf_algo = LZ_MF_BINARY_TREES;
                lzx_params->min_match_length  = 3;
                lzx_params->nice_match_length = 25 + compression_level * 2;
                lzx_params->max_search_depth  = 25 + compression_level;
        } else {
                lzx_params->choose_item_func = lzx_choose_near_optimal_item;
                lzx_params->num_optim_passes  = compression_level / 20;
                if (max_window_size <= 32768 && lzx_params->num_optim_passes == 1)
                        lzx_params->mf_algo = LZ_MF_HASH_CHAINS;
                else
                        lzx_params->mf_algo = LZ_MF_BINARY_TREES;
                lzx_params->min_match_length  = (compression_level >= 45) ? 2 : 3;
                lzx_params->nice_match_length = min(((u64)compression_level * 32) / 50,
                                                    LZX_MAX_MATCH_LEN);
                lzx_params->max_search_depth  = min(((u64)compression_level * 50) / 50,
                                                    LZX_MAX_MATCH_LEN);
        }
}

static void
lzx_build_mf_params(const struct lzx_compressor_params *lzx_params,
                    u32 max_window_size, struct lz_mf_params *mf_params)
{
        memset(mf_params, 0, sizeof(*mf_params));

        mf_params->algorithm = lzx_params->mf_algo;
        mf_params->max_window_size = max_window_size;
        mf_params->min_match_len = lzx_params->min_match_length;
        mf_params->max_match_len = LZX_MAX_MATCH_LEN;
        mf_params->max_search_depth = lzx_params->max_search_depth;
        mf_params->nice_match_len = lzx_params->nice_match_length;
}

static void
lzx_free_compressor(void *_c);

static u64
lzx_get_needed_memory(size_t max_block_size, unsigned int compression_level)
{
        struct lzx_compressor_params params;
        u64 size = 0;
        unsigned window_order;
        u32 max_window_size;

        window_order = lzx_get_window_order(max_block_size);
        if (window_order == 0)
                return 0;
        max_window_size = max_block_size;

        lzx_build_params(compression_level, max_window_size, &params);

        size += sizeof(struct lzx_compressor);

        size += max_window_size;

        size += DIV_ROUND_UP(max_window_size, LZX_DIV_BLOCK_SIZE) *
                sizeof(struct lzx_block_spec);

        size += max_window_size * sizeof(struct lzx_item);

        size += lz_mf_get_needed_memory(params.mf_algo, max_window_size);
        if (params.choose_item_func == lzx_choose_near_optimal_item) {
                size += (LZX_OPTIM_ARRAY_LENGTH + params.nice_match_length) *
                        sizeof(struct lzx_mc_pos_data);
        }
        if (params.num_optim_passes > 1)
                size += LZX_CACHE_LEN * sizeof(struct lz_match);
        else
                size += LZX_MAX_MATCHES_PER_POS * sizeof(struct lz_match);
        return size;
}

static int
lzx_create_compressor(size_t max_block_size, unsigned int compression_level,
                      void **c_ret)
{
        struct lzx_compressor *c;
        struct lzx_compressor_params params;
        struct lz_mf_params mf_params;
        unsigned window_order;
        u32 max_window_size;

        window_order = lzx_get_window_order(max_block_size);
        if (window_order == 0)
                return WIMLIB_ERR_INVALID_PARAM;
        max_window_size = max_block_size;

        lzx_build_params(compression_level, max_window_size, &params);
        lzx_build_mf_params(&params, max_window_size, &mf_params);
        if (!lz_mf_params_valid(&mf_params))
                return WIMLIB_ERR_INVALID_PARAM;

        c = CALLOC(1, sizeof(struct lzx_compressor));
        if (!c)
                goto oom;

        c->params = params;
        c->num_main_syms = lzx_get_num_main_syms(window_order);
        c->max_window_size = max_window_size;
        c->window_order = window_order;

        c->cur_window = ALIGNED_MALLOC(max_window_size, 16);
        if (!c->cur_window)
                goto oom;

        c->block_specs = MALLOC(DIV_ROUND_UP(max_window_size,
                                             LZX_DIV_BLOCK_SIZE) *
                                sizeof(struct lzx_block_spec));
        if (!c->block_specs)
                goto oom;

        c->chosen_items = MALLOC(max_window_size * sizeof(struct lzx_item));
        if (!c->chosen_items)
                goto oom;

        c->mf = lz_mf_alloc(&mf_params);
        if (!c->mf)
                goto oom;

        if (params.choose_item_func == lzx_choose_near_optimal_item) {
                c->optimum = MALLOC((LZX_OPTIM_ARRAY_LENGTH +
                                     params.nice_match_length) *
                                    sizeof(struct lzx_mc_pos_data));
                if (!c->optimum)
                        goto oom;
        }

        if (params.num_optim_passes > 1) {
                c->cached_matches = MALLOC(LZX_CACHE_LEN *
                                           sizeof(struct lz_match));
                if (!c->cached_matches)
                        goto oom;
                c->cache_limit = c->cached_matches + LZX_CACHE_LEN -
                                 (LZX_MAX_MATCHES_PER_POS + 1);
        } else {
                c->cached_matches = MALLOC(LZX_MAX_MATCHES_PER_POS *
                                           sizeof(struct lz_match));
                if (!c->cached_matches)
                        goto oom;
        }

        *c_ret = c;
        return 0;

oom:
        lzx_free_compressor(c);
        return WIMLIB_ERR_NOMEM;
}

static size_t
lzx_compress(const void *uncompressed_data, size_t uncompressed_size,
             void *compressed_data, size_t compressed_size_avail, void *_c)
{
        struct lzx_compressor *c = _c;
        struct lzx_output_bitstream os;

        /* Don't bother compressing very small inputs.  */
        if (uncompressed_size < 100)
                return 0;

        /* The input data must be preprocessed.  To avoid changing the original
         * input, copy it to a temporary buffer.  */
        memcpy(c->cur_window, uncompressed_data, uncompressed_size);
        c->cur_window_size = uncompressed_size;

        /* Preprocess the data.  */
        lzx_do_e8_preprocessing(c->cur_window, c->cur_window_size);

        /* Prepare the compressed data.  */
        lzx_prepare_blocks(c);

        /* Generate the compressed data and return its size, or 0 if an overflow
         * occurred.  */
        lzx_init_output(&os, compressed_data, compressed_size_avail);
        lzx_write_all_blocks(c, &os);
        return lzx_flush_output(&os);
}

static void
lzx_free_compressor(void *_c)
{
        struct lzx_compressor *c = _c;

        if (c) {
                ALIGNED_FREE(c->cur_window);
                FREE(c->block_specs);
                FREE(c->chosen_items);
                lz_mf_free(c->mf);
                FREE(c->optimum);
                FREE(c->cached_matches);
                FREE(c);
        }
}

const struct compressor_ops lzx_compressor_ops = {
        .get_needed_memory  = lzx_get_needed_memory,
        .create_compressor  = lzx_create_compressor,
        .compress           = lzx_compress,
        .free_compressor    = lzx_free_compressor,
};