Allow changing WIM compression type

[wimlib] / src / lzx-compress.c

/*
 * lzx-compress.c
 *
 * LZX compression routines
 */

/*
 * Copyright (C) 2012, 2013 Eric Biggers
 *
 * This file is part of wimlib, a library for working with WIM files.
 *
 * wimlib is free software; you can redistribute it and/or modify it under the
 * terms of the GNU General Public License as published by the Free
 * Software Foundation; either version 3 of the License, or (at your option)
 * any later version.
 *
 * wimlib is distributed in the hope that it will be useful, but WITHOUT ANY
 * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
 * A PARTICULAR PURPOSE. See the GNU General Public License for more
 * details.
 *
 * You should have received a copy of the GNU General Public License
 * along with wimlib; if not, see http://www.gnu.org/licenses/.
 */


/*
 * This file contains a compressor for the LZX compression format, as used in
 * the WIM file format.
 *
 * Format
 * ======
 *
 * First, the primary reference for the LZX compression format is the
 * specification released by Microsoft.
 *
 * Second, the comments in lzx-decompress.c provide some more information about
 * the LZX compression format, including errors in the Microsoft specification.
 *
 * Do note that LZX shares many similarities with DEFLATE, the algorithm used by
 * zlib and gzip.  Both LZX and DEFLATE use LZ77 matching and Huffman coding,
 * and certain other details are quite similar, such as the method for storing
 * Huffman codes.  However, some of 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; however it does have two types of
 *   dynamic Huffman blocks ("aligned offset" and "verbatim").
 * - 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.
 *
 * Algorithms
 * ==========
 *
 * There are actually two distinct overall algorithms implemented here.  We
 * shall refer to them as the "slow" algorithm and the "fast" algorithm.  The
 * "slow" algorithm spends more time compressing to achieve a higher compression
 * ratio compared to the "fast" algorithm.  More details are presented below.
 *
 * Slow algorithm
 * --------------
 *
 * The "slow" algorithm to generate LZX-compressed data is roughly as follows:
 *
 * 1. Preprocess the input data to translate the targets of x86 call instructions
 *    to absolute offsets.
 *
 * 2. Build the suffix array and inverse suffix array for the input data.  The
 *    suffix array contains the indices of all suffixes of the input data,
 *    sorted lexcographically by the corresponding suffixes.  The "position" of
 *    a suffix is the index of that suffix in the original string, whereas the
 *    "rank" of a suffix is the index at which that suffix's position is found
 *    in the suffix array.
 *
 * 3. Build the longest common prefix array corresponding to the suffix array.
 *
 * 4. For each suffix, find the highest lower ranked suffix that has a
 *    lower position, the lowest higher ranked suffix that has a lower position,
 *    and the length of the common prefix shared between each.   This
 *    information is later used to link suffix ranks into a doubly-linked list
 *    for searching the suffix array.
 *
 * 5. Set a default cost model for matches/literals.
 *
 * 6. Determine the lowest cost sequence of LZ77 matches ((offset, length) pairs)
 *    and literal bytes to divide the input into.  Raw match-finding is done by
 *    searching the suffix array using a linked list to avoid considering any
 *    suffixes that start after the current position.  Each run of the
 *    match-finder returns the approximate lowest-cost longest match as well as
 *    any shorter matches that have even lower approximate costs.  Each such run
 *    also adds the suffix rank of the current position into the linked list
 *    being used to search the suffix array.  Parsing, or match-choosing, is
 *    solved as a minimum-cost path problem using a forward "optimal parsing"
 *    algorithm based on the Deflate encoder from 7-Zip.  This algorithm moves
 *    forward calculating the minimum cost to reach each byte until either a
 *    very long match is found or until a position is found at which no matches
 *    start or overlap.
 *
 * 7. Build the Huffman codes needed to output the matches/literals.
 *
 * 8. Up to a certain number of iterations, use the resulting Huffman codes to
 *    refine a cost model and go back to Step #6 to determine an improved
 *    sequence of matches and literals.
 *
 * 9. Output the resulting block using the match/literal sequences and the
 *    Huffman codes that were computed for the block.
 *
 * Note: the algorithm does not yet attempt to split the input into multiple LZX
 * blocks.
 *
 * Fast algorithm
 * --------------
 *
 * The fast algorithm (and the only one available in wimlib v1.5.1 and earlier)
 * spends much less time on the main bottlenecks of the compression process ---
 * that is, the match finding and match choosing.  Matches are found and chosen
 * with hash chains using a greedy parse with one position of look-ahead.  No
 * block splitting is done; only compressing the full input into an aligned
 * offset block is considered.
 *
 * API
 * ===
 *
 * The old API (retained for backward compatibility) consists of just one function:
 *
 *      wimlib_lzx_compress()
 *
 * The new compressor has more potential parameters and needs more memory, so
 * the new API ties up memory allocations and compression parameters into a
 * context:
 *
 *      wimlib_lzx_alloc_context()
 *      wimlib_lzx_compress2()
 *      wimlib_lzx_free_context()
 *      wimlib_lzx_set_default_params()
 *
 * Both wimlib_lzx_compress() and wimlib_lzx_compress2() are designed to
 * compress an in-memory buffer of up to 32768 bytes.  There is no sliding
 * window.  This is suitable for the WIM format, which uses fixed-size chunks
 * that are seemingly always 32768 bytes.  If needed, the compressor potentially
 * could be extended to support a larger and/or sliding window.
 *
 * Both wimlib_lzx_compress() and wimlib_lzx_compress2() return 0 if the data
 * could not be compressed to less than the size of the uncompressed data.
 * Again, this is suitable for the WIM format, which stores such data chunks
 * uncompressed.
 *
 * The functions in this LZX compression API are exported from the library,
 * although with the possible exception of wimlib_lzx_set_default_params(), this
 * is only in case other programs happen to have uses for it other than WIM
 * reading/writing as already handled through the rest of the library.
 *
 * Acknowledgments
 * ===============
 *
 * Acknowledgments to several open-source projects and research papers that made
 * it possible to implement this code:
 *
 * - divsufsort (author: Yuta Mori), for the suffix array construction code,
 *   located in a separate directory (divsufsort/).
 *
 * - "Linear-Time Longest-Common-Prefix Computation in Suffix Arrays and Its
 *   Applications" (Kasai et al. 2001), for the LCP array computation.
 *
 * - "LPF computation revisited" (Crochemore et al. 2009) for the prev and next
 *   array computations.
 *
 * - 7-Zip (author: Igor Pavlov) for the algorithm for forward optimal parsing
 *   (match-choosing).
 *
 * - zlib (author: Jean-loup Gailly and Mark Adler), for the hash table
 *   match-finding algorithm (used in lz77.c).
 *
 * - lzx-compress (author: Matthew T. Russotto), on which some parts of this
 *   code were originally based.
 */

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

#include "wimlib.h"
#include "wimlib/compress.h"
#include "wimlib/error.h"
#include "wimlib/lzx.h"
#include "wimlib/util.h"
#include <pthread.h>
#include <math.h>
#include <string.h>

#ifdef ENABLE_LZX_DEBUG
#  include <wimlib/decompress.h>
#endif

#include "divsufsort/divsufsort.h"

typedef freq_t input_idx_t;
typedef u32 block_cost_t;
#define INFINITE_BLOCK_COST     ((block_cost_t)~0U)

#define LZX_OPTIM_ARRAY_SIZE    4096

/* Currently, this constant can't simply be changed because the code currently
 * uses a static number of position slots (and may make other assumptions as
 * well).  */
#define LZX_MAX_WINDOW_SIZE     32768

/* This may be WIM-specific  */
#define LZX_DEFAULT_BLOCK_SIZE  32768

#define LZX_MAX_CACHE_PER_POS   10

/* Codewords for the LZX main, length, and aligned offset Huffman codes  */
struct lzx_codewords {
        u16 main[LZX_MAINCODE_NUM_SYMBOLS];
        u16 len[LZX_LENCODE_NUM_SYMBOLS];
        u16 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_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 times.  */
struct lzx_costs {
        u8 main[LZX_MAINCODE_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 {
        freq_t main[LZX_MAINCODE_NUM_SYMBOLS];
        freq_t len[LZX_LENCODE_NUM_SYMBOLS];
        freq_t aligned[LZX_ALIGNEDCODE_NUM_SYMBOLS];
};

/* LZX intermediate match/literal format  */
struct lzx_match {
        /* 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_NUM_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;
};

/* Raw LZ match/literal format: just a length and offset.
 *
 * The length is the number of bytes of the match, and the offset is the number
 * of bytes back in the input the match is from the current position.
 *
 * If @len < LZX_MIN_MATCH_LEN, then it's really just a literal byte and @offset is
 * meaningless.  */
struct raw_match {
        u16 len;
        input_idx_t offset;
};

/* 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.  */
        input_idx_t window_pos;

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

        /* The position in the 'chosen_matches' array in the `struct
         * lzx_compressor' at which the match/literal specifications for
         * this block begin.  */
        input_idx_t chosen_matches_start_pos;

        /* The number of match/literal specifications for this block.  */
        input_idx_t num_chosen_matches;

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

/*
 * 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_optimal {
        /* The approximate minimum cost, in bits, to reach this position in the
         * window which has been found so far.  */
        block_cost_t cost;

        /* 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.  */
                        input_idx_t 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.  */
                        input_idx_t match_offset;
                } prev;
                struct {
                        /* Position at which the match or literal starting at
                         * this position ends in the minimum-cost parse.  */
                        input_idx_t link;

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

        /* The match offset LRU queue that will exist when the approximate
         * minimum-cost path to reach this position is taken.  */
        struct lzx_lru_queue queue;
};

/* Suffix array link  */
struct salink {
        /* Rank of highest ranked suffix that has rank lower than the suffix
         * corresponding to this structure and either has a lower position
         * (initially) or has a position lower than the highest position at
         * which matches have been searched for so far, or -1 if there is no
         * such suffix.  */
        input_idx_t prev;

        /* Rank of lowest ranked suffix that has rank greater than the suffix
         * corresponding to this structure and either has a lower position
         * (intially) or has a position lower than the highest position at which
         * matches have been searched for so far, or -1 if there is no such
         * suffix.  */
        input_idx_t next;

        /* Length of longest common prefix between the suffix corresponding to
         * this structure and the suffix with rank @prev, or 0 if @prev is -1.
         */
        input_idx_t lcpprev;

        /* Length of longest common prefix between the suffix corresponding to
         * this structure and the suffix with rank @next, or 0 if @next is -1.
         */
        input_idx_t lcpnext;
};

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

        /* The parameters that were used to create the compressor.  */
        struct wimlib_lzx_params params;

        /* 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 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.
         *
         * We reserve a few extra bytes to potentially allow reading off the end
         * of the array in the match-finding code for optimization purposes.
         */
        u8 window[LZX_MAX_WINDOW_SIZE + 12];

        /* Number of bytes of data to be compressed, which is the number of
         * bytes of data in @window that are actually valid.  */
        input_idx_t window_size;

        /* 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_match *chosen_matches;

        /* 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;

        /* Suffix array for window.
         * This is a mapping from suffix rank to suffix position.  */
        input_idx_t *SA;

        /* Inverse suffix array for window.
         * This is a mapping from suffix position to suffix rank.
         * If 0 <= r < window_size, then ISA[SA[r]] == r.  */
        input_idx_t *ISA;

        /* Suffix array links.
         *
         * During a linear scan of the input string to find matches, this array
         * used to keep track of which rank suffixes in the suffix array appear
         * before the current position.  Instead of searching in the original
         * suffix array, scans for matches at a given position traverse a linked
         * list containing only suffixes that appear before that position.  */
        struct salink *salink;

        /* Position in window of next match to return.
         * Note: This cannot simply be modified, as the match-finder must still
         * be synchronized on the same position.  To seek forwards or backwards,
         * use lzx_lz_skip_bytes() or lzx_lz_rewind_matchfinder(), respectively.
         */
        input_idx_t match_window_pos;

        /* The match-finder shall ensure the length of matches does not exceed
         * this position in the input.  */
        input_idx_t match_window_end;

        /* 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 raw_match *cached_matches;
        unsigned cached_matches_pos;
        bool matches_cached;

        /* Slow algorithm only: Temporary space used for match-choosing
         * algorithm.
         *
         * The size of this array must be at least LZX_MAX_MATCH_LEN but
         * otherwise is arbitrary.  More space simply allows the match-choosing
         * algorithm to potentially find better matches (depending on the input,
         * as always).  */
        struct lzx_optimal *optimum;

        /* Slow algorithm only: Variables used by the match-choosing algorithm.
         *
         * 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.  */
        u32 optimum_cur_idx;
        u32 optimum_end_idx;
};

/* Returns the LZX position slot that corresponds to a given formatted offset.
 *
 * Logically, this returns the smallest i such that
 * formatted_offset >= lzx_position_base[i].
 *
 * The actual implementation below takes advantage of the regularity of the
 * numbers in the lzx_position_base array to calculate the slot directly from
 * the formatted offset without actually looking at the array.
 */
static unsigned
lzx_get_position_slot_raw(unsigned formatted_offset)
{
#if 0
        /*
         * Slots 36-49 (formatted_offset >= 262144) can be found by
         * (formatted_offset/131072) + 34 == (formatted_offset >> 17) + 34;
         * however, this check for formatted_offset >= 262144 is commented out
         * because WIM chunks cannot be that large.
         */
        if (formatted_offset >= 262144) {
                return (formatted_offset >> 17) + 34;
        } else
#endif
        {
                /* Note: this part here only works if:
                 *
                 *    2 <= formatted_offset < 655360
                 *
                 * It is < 655360 because the frequency of the position bases
                 * increases starting at the 655360 entry, and it is >= 2
                 * because the below calculation fails if the most significant
                 * bit is lower than the 2's place. */
                LZX_ASSERT(2 <= formatted_offset && formatted_offset < 655360);
                unsigned mssb_idx = bsr32(formatted_offset);
                return (mssb_idx << 1) |
                        ((formatted_offset >> (mssb_idx - 1)) & 1);
        }
}


/* 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(unsigned offset, struct lzx_lru_queue *queue)
{
        unsigned position_slot;

        /* See if the offset was recently used.  */
        for (unsigned 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 (unsigned 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)
{
        make_canonical_huffman_code(LZX_MAINCODE_NUM_SYMBOLS,
                                    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 an LZX match.
 *
 * @out:         The bitstream to write the match to.
 * @block_type:  The type of the LZX block (LZX_BLOCKTYPE_ALIGNED or LZX_BLOCKTYPE_VERBATIM)
 * @match:       The match.
 * @codes:       Pointer to a structure that contains the codewords for the
 *               main, length, and aligned offset Huffman codes.
 */
static void
lzx_write_match(struct output_bitstream *out, int block_type,
                struct lzx_match match, const struct lzx_codes *codes)
{
        /* low 8 bits are the match length minus 2 */
        unsigned match_len_minus_2 = match.data & 0xff;
        /* Next 17 bits are the position footer */
        unsigned position_footer = (match.data >> 8) & 0x1ffff; /* 17 bits */
        /* Next 6 bits are the position slot. */
        unsigned position_slot = (match.data >> 25) & 0x3f;     /* 6 bits */
        unsigned len_header;
        unsigned len_footer;
        unsigned main_symbol;
        unsigned num_extra_bits;
        unsigned verbatim_bits;
        unsigned aligned_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;
                /* No length footer-- mark it with a special
                 * value. */
                len_footer = (unsigned)(-1);
        } 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 tree.
         *
         * 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. */
        bitstream_put_bits(out, codes->codewords.main[main_symbol],
                           codes->lens.main[main_symbol]);

        /* If there is a length footer, output it using the
         * length Huffman code. */
        if (len_footer != (unsigned)(-1)) {
                bitstream_put_bits(out, codes->codewords.len[len_footer],
                                   codes->lens.len[len_footer]);
        }

        num_extra_bits = lzx_get_num_extra_bits(position_slot);

        /* For aligned offset blocks with at least 3 extra bits, output the
         * verbatim bits literally, then the aligned bits encoded using the
         * aligned offset tree.  Otherwise, only the verbatim bits need to be
         * output. */
        if ((block_type == LZX_BLOCKTYPE_ALIGNED) && (num_extra_bits >= 3)) {

                verbatim_bits = position_footer >> 3;
                bitstream_put_bits(out, verbatim_bits,
                                   num_extra_bits - 3);

                aligned_bits = (position_footer & 7);
                bitstream_put_bits(out,
                                   codes->codewords.aligned[aligned_bits],
                                   codes->lens.aligned[aligned_bits]);
        } else {
                /* verbatim bits is the same as the position
                 * footer, in this case. */
                bitstream_put_bits(out, position_footer, num_extra_bits);
        }
}

static unsigned
lzx_build_precode(const u8 lens[restrict],
                  const u8 prev_lens[restrict],
                  const unsigned num_syms,
                  freq_t precode_freqs[restrict LZX_PRECODE_NUM_SYMBOLS],
                  u8 output_syms[restrict num_syms],
                  u8 precode_lens[restrict LZX_PRECODE_NUM_SYMBOLS],
                  u16 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 pre-tree.
         *
         * 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 tree.
                         * */
                        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 tree. */
                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;
}

/*
 * Writes a compressed Huffman code to the output, preceded by the precode for
 * it.
 *
 * The Huffman code is represented in the output as a series of path lengths
 * from which the canonical Huffman code can be reconstructed.  The path lengths
 * themselves are compressed using a separate Huffman code, the precode, which
 * consists of LZX_PRECODE_NUM_SYMBOLS (= 20) symbols that cover all possible
 * code lengths, plus extra codes for repeated lengths.  The path lengths of the
 * precode precede the path lengths of the larger code and are uncompressed,
 * consisting of 20 entries of 4 bits each.
 *
 * @out:                Bitstream to write the code to.
 * @lens:               The code lengths for the Huffman code, indexed by symbol.
 * @prev_lens:          Code lengths for this Huffman code, indexed by symbol,
 *                      in the *previous block*, or all zeroes if this is the
 *                      first block.
 * @num_syms:           The number of symbols in the code.
 */
static void
lzx_write_compressed_code(struct output_bitstream *out,
                          const u8 lens[restrict],
                          const u8 prev_lens[restrict],
                          unsigned num_syms)
{
        freq_t precode_freqs[LZX_PRECODE_NUM_SYMBOLS];
        u8 output_syms[num_syms];
        u8 precode_lens[LZX_PRECODE_NUM_SYMBOLS];
        u16 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++)
                bitstream_put_bits(out, 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++];

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

/*
 * Writes all compressed matches and literal bytes in an LZX block to the the
 * output bitstream.
 *
 * @ostream
 *      The output bitstream.
 * @block_type
 *      The type of the block (LZX_BLOCKTYPE_ALIGNED or LZX_BLOCKTYPE_VERBATIM).
 * @match_tab
 *      The array of matches/literals that will be output (length @match_count).
 * @match_count
 *      Number of matches/literals to be output.
 * @codes
 *      Pointer to a structure that contains the codewords for the main, length,
 *      and aligned offset Huffman codes.
 */
static void
lzx_write_matches_and_literals(struct output_bitstream *ostream,
                               int block_type,
                               const struct lzx_match match_tab[],
                               unsigned match_count,
                               const struct lzx_codes *codes)
{
        for (unsigned i = 0; i < match_count; i++) {
                struct lzx_match match = match_tab[i];

                /* High bit of the match indicates whether the match is an
                 * actual match (1) or a literal uncompressed byte (0)  */
                if (match.data & 0x80000000) {
                        /* match */
                        lzx_write_match(ostream, block_type,
                                        match, codes);
                } else {
                        /* literal byte */
                        bitstream_put_bits(ostream,
                                           codes->codewords.main[match.data],
                                           codes->lens.main[match.data]);
                }
        }
}

static void
lzx_assert_codes_valid(const struct lzx_codes * codes)
{
#ifdef ENABLE_LZX_DEBUG
        unsigned i;

        for (i = 0; i < LZX_MAINCODE_NUM_SYMBOLS; i++)
                LZX_ASSERT(codes->lens.main[i] <= LZX_MAX_MAIN_CODEWORD_LEN);

        for (i = 0; i < LZX_LENCODE_NUM_SYMBOLS; i++)
                LZX_ASSERT(codes->lens.len[i] <= LZX_MAX_LEN_CODEWORD_LEN);

        for (i = 0; i < LZX_ALIGNEDCODE_NUM_SYMBOLS; i++)
                LZX_ASSERT(codes->lens.aligned[i] <= LZX_MAX_ALIGNED_CODEWORD_LEN);

        const unsigned tablebits = 10;
        u16 decode_table[(1 << tablebits) +
                         (2 * max(LZX_MAINCODE_NUM_SYMBOLS, LZX_LENCODE_NUM_SYMBOLS))]
                         _aligned_attribute(DECODE_TABLE_ALIGNMENT);
        LZX_ASSERT(0 == make_huffman_decode_table(decode_table,
                                                  LZX_MAINCODE_NUM_SYMBOLS,
                                                  min(tablebits, LZX_MAINCODE_TABLEBITS),
                                                  codes->lens.main,
                                                  LZX_MAX_MAIN_CODEWORD_LEN));
        LZX_ASSERT(0 == make_huffman_decode_table(decode_table,
                                                  LZX_LENCODE_NUM_SYMBOLS,
                                                  min(tablebits, LZX_LENCODE_TABLEBITS),
                                                  codes->lens.len,
                                                  LZX_MAX_LEN_CODEWORD_LEN));
        LZX_ASSERT(0 == make_huffman_decode_table(decode_table,
                                                  LZX_ALIGNEDCODE_NUM_SYMBOLS,
                                                  min(tablebits, LZX_ALIGNEDCODE_TABLEBITS),
                                                  codes->lens.aligned,
                                                  LZX_MAX_ALIGNED_CODEWORD_LEN));
#endif /* ENABLE_LZX_DEBUG */
}

/* Write an LZX aligned offset or verbatim block to the output.  */
static void
lzx_write_compressed_block(int block_type,
                           unsigned block_size,
                           struct lzx_match * chosen_matches,
                           unsigned num_chosen_matches,
                           const struct lzx_codes * codes,
                           const struct lzx_codes * prev_codes,
                           struct output_bitstream * ostream)
{
        unsigned i;

        LZX_ASSERT(block_type == LZX_BLOCKTYPE_ALIGNED ||
                   block_type == LZX_BLOCKTYPE_VERBATIM);
        LZX_ASSERT(block_size <= LZX_MAX_WINDOW_SIZE);
        LZX_ASSERT(num_chosen_matches <= LZX_MAX_WINDOW_SIZE);
        lzx_assert_codes_valid(codes);

        /* The first three bits indicate the type of block and are one of the
         * LZX_BLOCKTYPE_* constants.  */
        bitstream_put_bits(ostream, block_type, LZX_BLOCKTYPE_NBITS);

        /* The next bit indicates whether the block size is the default (32768),
         * indicated by a 1 bit, or whether the block size is given by the next
         * 16 bits, indicated by a 0 bit.  */
        if (block_size == LZX_DEFAULT_BLOCK_SIZE) {
                bitstream_put_bits(ostream, 1, 1);
        } else {
                bitstream_put_bits(ostream, 0, 1);
                bitstream_put_bits(ostream, block_size, LZX_BLOCKSIZE_NBITS);
        }

        /* Write out lengths of the main code. Note that the LZX specification
         * incorrectly states that the aligned offset code comes after the
         * length code, but in fact it is the very first tree to be written
         * (before the main code).  */
        if (block_type == LZX_BLOCKTYPE_ALIGNED)
                for (i = 0; i < LZX_ALIGNEDCODE_NUM_SYMBOLS; i++)
                        bitstream_put_bits(ostream, codes->lens.aligned[i],
                                           LZX_ALIGNEDCODE_ELEMENT_SIZE);

        LZX_DEBUG("Writing main code...");

        /* Write the pre-tree and lengths for the first LZX_NUM_CHARS symbols in
         * the main code, which are the codewords for literal bytes.  */
        lzx_write_compressed_code(ostream,
                                  codes->lens.main,
                                  prev_codes->lens.main,
                                  LZX_NUM_CHARS);

        /* Write the pre-tree and lengths for the rest of the main code, which
         * are the codewords for match headers.  */
        lzx_write_compressed_code(ostream,
                                  codes->lens.main + LZX_NUM_CHARS,
                                  prev_codes->lens.main + LZX_NUM_CHARS,
                                  LZX_MAINCODE_NUM_SYMBOLS - LZX_NUM_CHARS);

        LZX_DEBUG("Writing length code...");

        /* Write the pre-tree and lengths for the length code.  */
        lzx_write_compressed_code(ostream,
                                  codes->lens.len,
                                  prev_codes->lens.len,
                                  LZX_LENCODE_NUM_SYMBOLS);

        LZX_DEBUG("Writing matches and literals...");

        /* Write the actual matches and literals.  */
        lzx_write_matches_and_literals(ostream, block_type,
                                       chosen_matches, num_chosen_matches,
                                       codes);

        LZX_DEBUG("Done writing block.");
}

/* Write out the LZX blocks that were computed.  */
static void
lzx_write_all_blocks(struct lzx_compressor *ctx, struct output_bitstream *ostream)
{
        const struct lzx_codes *prev_codes = &ctx->zero_codes;
        for (unsigned i = 0; i < ctx->num_blocks; i++) {
                const struct lzx_block_spec *spec = &ctx->block_specs[i];

                LZX_DEBUG("Writing block %u/%u (type=%d, size=%u, num_chosen_matches=%u)...",
                          i + 1, ctx->num_blocks,
                          spec->block_type, spec->block_size,
                          spec->num_chosen_matches);

                lzx_write_compressed_block(spec->block_type,
                                           spec->block_size,
                                           &ctx->chosen_matches[spec->chosen_matches_start_pos],
                                           spec->num_chosen_matches,
                                           &spec->codes,
                                           prev_codes,
                                           ostream);
                prev_codes = &spec->codes;
        }
}

/* Constructs an LZX match from a literal byte and updates the main code symbol
 * frequencies.  */
static u32
lzx_record_literal(u8 literal, void *_freqs)
{
        struct lzx_freqs *freqs = _freqs;

        freqs->main[literal]++;

        return (u32)literal;
}

/* 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 u32
lzx_record_match(unsigned match_offset, unsigned match_len,
                 void *_freqs, void *_queue)
{
        struct lzx_freqs *freqs = _freqs;
        struct lzx_lru_queue *queue = _queue;
        unsigned position_slot;
        unsigned 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) &
                                ((1U << 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.
         *
         * bits    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_NUM_POSITION_SLOTS - 1] is 17).
         *
         * 0-7     length of match, offset by 2.  This can be at most
         *         (LZX_MAX_MATCH_LEN - 2) == 255, so it will fit in 8 bits.  */
        BUILD_BUG_ON(LZX_NUM_POSITION_SLOTS > 64);
        LZX_ASSERT(lzx_get_num_extra_bits(LZX_NUM_POSITION_SLOTS - 1) <= 17);
        BUILD_BUG_ON(LZX_MAX_MATCH_LEN - LZX_MIN_MATCH_LEN + 1 > 256);
        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 unsigned
lzx_literal_cost(u8 c, const struct lzx_costs * costs)
{
        return costs->main[c];
}

/* Given a (length, offset) pair that could be turned into a valid LZX match as
 * well as costs for the codewords in the main, length, and aligned Huffman
 * codes, return the approximate number of bits it will take to represent this
 * match in the compressed output.  Take into account the match offset LRU
 * queue and optionally update it.  */
static unsigned
lzx_match_cost(unsigned length, unsigned offset, const struct lzx_costs *costs,
               struct lzx_lru_queue *queue)
{
        unsigned position_slot;
        unsigned len_header, main_symbol;
        unsigned cost = 0;

        position_slot = lzx_get_position_slot(offset, queue);

        len_header = min(length - 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 position information.  */
        unsigned num_extra_bits = lzx_get_num_extra_bits(position_slot);
        if (num_extra_bits >= 3) {
                cost += num_extra_bits - 3;
                cost += costs->aligned[(offset + LZX_OFFSET_OFFSET) & 7];
        } else {
                cost += num_extra_bits;
        }

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

        return cost;

}

/* Fast heuristic cost evaluation to use in the inner loop of the match-finder.
 * Unlike lzx_match_cost() which does a true cost evaluation, this simply
 * prioritize matches based on their offset.  */
static block_cost_t
lzx_match_cost_fast(unsigned offset, const struct lzx_lru_queue *queue)
{
        /* It seems well worth it to take the time to give priority to recently
         * used offsets.  */
        for (unsigned i = 0; i < LZX_NUM_RECENT_OFFSETS; i++)
                if (offset == queue->R[i])
                        return i;

        BUILD_BUG_ON(LZX_MAX_WINDOW_SIZE >= (block_cost_t)~0U);
        return offset;
}

/* Set the cost model @ctx->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 * ctx, const struct lzx_lens * lens)
{
        unsigned i;

        /* Main code  */
        for (i = 0; i < LZX_MAINCODE_NUM_SYMBOLS; i++) {
                ctx->costs.main[i] = lens->main[i];
                if (ctx->costs.main[i] == 0)
                        ctx->costs.main[i] = ctx->params.alg_params.slow.main_nostat_cost;
        }

        /* Length code  */
        for (i = 0; i < LZX_LENCODE_NUM_SYMBOLS; i++) {
                ctx->costs.len[i] = lens->len[i];
                if (ctx->costs.len[i] == 0)
                        ctx->costs.len[i] = ctx->params.alg_params.slow.len_nostat_cost;
        }

        /* Aligned offset code  */
        for (i = 0; i < LZX_ALIGNEDCODE_NUM_SYMBOLS; i++) {
                ctx->costs.aligned[i] = lens->aligned[i];
                if (ctx->costs.aligned[i] == 0)
                        ctx->costs.aligned[i] = ctx->params.alg_params.slow.aligned_nostat_cost;
        }
}

/* Advance the suffix array match-finder to the next position.  */
static void
lzx_lz_update_salink(input_idx_t i,
                     const input_idx_t SA[restrict],
                     const input_idx_t ISA[restrict],
                     struct salink link[restrict])
{
        /* r = Rank of the suffix at the current position.  */
        const input_idx_t r = ISA[i];

        /* next = rank of LOWEST ranked suffix that is ranked HIGHER than the
         * current suffix AND has a LOWER position, or -1 if none exists.  */
        const input_idx_t next = link[r].next;

        /* prev = rank of HIGHEST ranked suffix that is ranked LOWER than the
         * current suffix AND has a LOWER position, or -1 if none exists.  */
        const input_idx_t prev = link[r].prev;

        /* Link the suffix at the current position into the linked list that
         * contains all suffixes in the suffix array that are appear at or
         * before the current position, sorted by rank.
         *
         * Save the values of all fields we overwrite so that rollback is
         * possible.  */
        if (next != (input_idx_t)~0U) {

                link[next].prev = r;
                link[next].lcpprev = link[r].lcpnext;
        }

        if (prev != (input_idx_t)~0U) {

                link[prev].next = r;
                link[prev].lcpnext = link[r].lcpprev;
        }
}

/* Rewind the suffix array match-finder to the specified position.
 *
 * This undoes a series of updates by lzx_lz_update_salink().  */
static void
lzx_lz_rewind_matchfinder(struct lzx_compressor *ctx,
                          const unsigned orig_pos)
{
        LZX_DEBUG("Rewind match-finder %u => %u", ctx->match_window_pos, orig_pos);

        if (ctx->match_window_pos == orig_pos)
                return;

        /* NOTE: this has been optimized for the current algorithm where no
         * block-splitting is done and matches are cached, so that the suffix
         * array match-finder only runs through the input one time.  Generalized
         * rewinds of the suffix array match-finder are possible, but require
         * incrementally saving fields being overwritten in
         * lzx_lz_update_salink(), then restoring them here in reverse order.
         */

        LZX_ASSERT(ctx->match_window_pos > orig_pos);
        LZX_ASSERT(orig_pos == 0);
        ctx->matches_cached = true;
        ctx->cached_matches_pos = 0;
        ctx->match_window_pos = orig_pos;
}

/*
 * Use the suffix array match-finder to retrieve a list of LZ matches at the
 * current position.
 *
 * [in]    @i           Current position in the window.
 * [in]    @SA          Suffix array for the window.
 * [in]    @ISA         Inverse suffix array for the window.
 * [inout] @link        Suffix array links used internally by the match-finder.
 * [out]   @matches     The (length, offset) pairs of the resulting matches will
 *                              be written here, sorted in decreasing order by
 *                              length.  All returned lengths will be unique.
 * [in]    @queue       Recently used match offsets, used when evaluating the
 *                              cost of matches.
 * [in]    @min_match_len       Minimum match length to return.
 * [in]    @max_matches_to_consider     Maximum number of matches to consider at
 *                                      the position.
 * [in]    @max_matches_to_return       Maximum number of matches to return.
 *
 * The return value is the number of matches found and written to @matches.
 */
static unsigned
lzx_lz_get_matches(const input_idx_t i,
                   const input_idx_t SA[const restrict],
                   const input_idx_t ISA[const restrict],
                   struct salink link[const restrict],
                   struct raw_match matches[const restrict],
                   const struct lzx_lru_queue * const restrict queue,
                   const unsigned min_match_len,
                   const uint32_t max_matches_to_consider,
                   const uint32_t max_matches_to_return)
{
        /* r = Rank of the suffix at the current position.  */
        const input_idx_t r = ISA[i];

        /* Prepare for searching the current position.  */
        lzx_lz_update_salink(i, SA, ISA, link);

        /* L = rank of next suffix to the left;
         * R = rank of next suffix to the right;
         * lenL = length of match between current position and the suffix with rank L;
         * lenR = length of match between current position and the suffix with rank R.
         *
         * This is left and right relative to the rank of the current suffix.
         * Since the suffixes in the suffix array are sorted, the longest
         * matches are immediately to the left and right (using the linked list
         * to ignore all suffixes that occur later in the window).  The match
         * length decreases the farther left and right we go.  We shall keep the
         * length on both sides in sync in order to choose the lowest-cost match
         * of each length.
         */
        input_idx_t L = link[r].prev;
        input_idx_t R = link[r].next;
        input_idx_t lenL = link[r].lcpprev;
        input_idx_t lenR = link[r].lcpnext;

        /* nmatches = number of matches found so far.  */
        unsigned nmatches = 0;

        /* best_cost = cost of lowest-cost match found so far.
         *
         * We keep track of this so that we can ignore shorter matches that do
         * not have lower costs than a longer matches already found.
         */
        block_cost_t best_cost = INFINITE_BLOCK_COST;

        /* count_remaining = maximum number of possible matches remaining to be
         * considered.  */
        uint32_t count_remaining = max_matches_to_consider;

        /* pending = match currently being considered for a specific length.  */
        struct raw_match pending;
        block_cost_t pending_cost;

        while (lenL >= min_match_len || lenR >= min_match_len)
        {
                pending.len = lenL;
                pending_cost = INFINITE_BLOCK_COST;
                block_cost_t cost;

                /* Extend left.  */
                if (lenL >= min_match_len && lenL >= lenR) {
                        for (;;) {

                                if (--count_remaining == 0)
                                        goto out_save_pending;

                                input_idx_t offset = i - SA[L];

                                /* Save match if it has smaller cost.  */
                                cost = lzx_match_cost_fast(offset, queue);
                                if (cost < pending_cost) {
                                        pending.offset = offset;
                                        pending_cost = cost;
                                }

                                if (link[L].lcpprev < lenL) {
                                        /* Match length decreased.  */

                                        lenL = link[L].lcpprev;

                                        /* Save the pending match unless the
                                         * right side still may have matches of
                                         * this length to be scanned, or if a
                                         * previous (longer) match had lower
                                         * cost.  */
                                        if (pending.len > lenR) {
                                                if (pending_cost < best_cost) {
                                                        best_cost = pending_cost;
                                                        matches[nmatches++] = pending;
                                                        if (nmatches == max_matches_to_return)
                                                                return nmatches;
                                                }
                                                pending.len = lenL;
                                                pending_cost = INFINITE_BLOCK_COST;
                                        }
                                        if (lenL < min_match_len || lenL < lenR)
                                                break;
                                }
                                L = link[L].prev;
                        }
                }

                pending.len = lenR;

                /* Extend right.  */
                if (lenR >= min_match_len && lenR > lenL) {
                        for (;;) {

                                if (--count_remaining == 0)
                                        goto out_save_pending;

                                input_idx_t offset = i - SA[R];

                                /* Save match if it has smaller cost.  */
                                cost = lzx_match_cost_fast(offset, queue);
                                if (cost < pending_cost) {
                                        pending.offset = offset;
                                        pending_cost = cost;
                                }

                                if (link[R].lcpnext < lenR) {
                                        /* Match length decreased.  */

                                        lenR = link[R].lcpnext;

                                        /* Save the pending match unless a
                                         * previous (longer) match had lower
                                         * cost.  */
                                        if (pending_cost < best_cost) {
                                                matches[nmatches++] = pending;
                                                best_cost = pending_cost;
                                                if (nmatches == max_matches_to_return)
                                                        return nmatches;
                                        }

                                        if (lenR < min_match_len || lenR <= lenL)
                                                break;

                                        pending.len = lenR;
                                        pending_cost = INFINITE_BLOCK_COST;
                                }
                                R = link[R].next;
                        }
                }
        }
        goto out;

out_save_pending:
        if (pending_cost != INFINITE_BLOCK_COST)
                matches[nmatches++] = pending;

out:
        return nmatches;
}


/* Tell the match-finder to skip the specified number of bytes (@n) in the
 * input.  */
static void
lzx_lz_skip_bytes(struct lzx_compressor *ctx, unsigned n)
{
        LZX_ASSERT(n <= ctx->match_window_end - ctx->match_window_pos);
        if (ctx->matches_cached) {
                ctx->match_window_pos += n;
                while (n--) {
                        ctx->cached_matches_pos +=
                                ctx->cached_matches[ctx->cached_matches_pos].len + 1;
                }
        } else {
                while (n--) {
                        ctx->cached_matches[ctx->cached_matches_pos++].len = 0;
                        lzx_lz_update_salink(ctx->match_window_pos++, ctx->SA,
                                             ctx->ISA, ctx->salink);
                }
        }
}

/* Retrieve a list of matches available at the next position in the input.
 *
 * The matches are written to ctx->matches in decreasing order of length, and
 * the return value is the number of matches found.  */
static unsigned
lzx_lz_get_matches_caching(struct lzx_compressor *ctx,
                           const struct lzx_lru_queue *queue,
                           struct raw_match **matches_ret)
{
        unsigned num_matches;
        struct raw_match *matches;

        LZX_ASSERT(ctx->match_window_pos <= ctx->match_window_end);

        matches = &ctx->cached_matches[ctx->cached_matches_pos + 1];

        if (ctx->matches_cached) {
                num_matches = matches[-1].len;
        } else {
                unsigned min_match_len = LZX_MIN_MATCH_LEN;
                if (!ctx->params.alg_params.slow.use_len2_matches)
                        min_match_len = max(min_match_len, 3);
                const uint32_t max_search_depth = ctx->params.alg_params.slow.max_search_depth;
                const uint32_t max_matches_per_pos = ctx->params.alg_params.slow.max_matches_per_pos;

                if (unlikely(max_search_depth == 0 || max_matches_per_pos == 0))
                        num_matches = 0;
                else
                        num_matches = lzx_lz_get_matches(ctx->match_window_pos,
                                                         ctx->SA,
                                                         ctx->ISA,
                                                         ctx->salink,
                                                         matches,
                                                         queue,
                                                         min_match_len,
                                                         max_search_depth,
                                                         max_matches_per_pos);
                matches[-1].len = num_matches;
        }
        ctx->cached_matches_pos += num_matches + 1;
        *matches_ret = matches;

        /* Cap the length of returned matches to the number of bytes remaining,
         * if it is not the whole window.  */
        if (ctx->match_window_end < ctx->window_size) {
                unsigned maxlen = ctx->match_window_end - ctx->match_window_pos;
                for (unsigned i = 0; i < num_matches; i++)
                        if (matches[i].len > maxlen)
                                matches[i].len = maxlen;
        }
#if 0
        fprintf(stderr, "Pos %u/%u: %u matches\n",
                ctx->match_window_pos, ctx->match_window_end, num_matches);
        for (unsigned i = 0; i < num_matches; i++)
                fprintf(stderr, "\tLen %u Offset %u\n", matches[i].len, matches[i].offset);
#endif

#ifdef ENABLE_LZX_DEBUG
        for (unsigned i = 0; i < num_matches; i++) {
                LZX_ASSERT(matches[i].len >= LZX_MIN_MATCH_LEN);
                LZX_ASSERT(matches[i].len <= LZX_MAX_MATCH_LEN);
                LZX_ASSERT(matches[i].len <= ctx->match_window_end - ctx->match_window_pos);
                LZX_ASSERT(matches[i].offset > 0);
                LZX_ASSERT(matches[i].offset <= ctx->match_window_pos);
                LZX_ASSERT(!memcmp(&ctx->window[ctx->match_window_pos],
                                   &ctx->window[ctx->match_window_pos - matches[i].offset],
                                   matches[i].len));
        }
#endif

        ctx->match_window_pos++;
        return num_matches;
}

/*
 * 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 raw_match
lzx_lz_reverse_near_optimal_match_list(struct lzx_compressor *ctx,
                                       unsigned cur_pos)
{
        unsigned prev_link, saved_prev_link;
        unsigned prev_match_offset, saved_prev_match_offset;

        ctx->optimum_end_idx = cur_pos;

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

        do {
                prev_link = saved_prev_link;
                prev_match_offset = saved_prev_match_offset;

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

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

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

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

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

/*
 * lzx_lz_get_near_optimal_match() -
 *
 * Choose the optimal match or literal to use at the next position in the input.
 *
 * Unlike a greedy parser that always takes the longest match, or even a
 * parser with one match/literal look-ahead like zlib, the algorithm used here
 * may look ahead many matches/literals to determine the optimal match/literal to
 * output 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 Huffman code cost
 * model rather than simply assuming that longer is better.
 *
 * Still, this is not truly an optimal parser because very long matches are
 * taken immediately, and the raw match-finder takes some shortcuts.  This is
 * done to avoid considering many different alternatives that are unlikely to
 * be significantly better.
 *
 * This algorithm is based on that used in 7-Zip's DEFLATE encoder.
 *
 * Each call to this function does one of two things:
 *
 * 1. Build a near-optimal sequence of 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;
 *
 * This function relies on the following state in the compressor context:
 *
 *      ctx->window          (read-only: preprocessed data being compressed)
 *      ctx->cost            (read-only: cost model to use)
 *      ctx->optimum         (internal state; leave uninitialized)
 *      ctx->optimum_cur_idx (must set to 0 before first call)
 *      ctx->optimum_end_idx (must set to 0 before first call)
 *
 *      Plus any state used by the raw match-finder.
 *
 * The return value is a (length, offset) pair specifying the match or literal
 * chosen.  For literals, the length is less than LZX_MIN_MATCH_LEN and the
 * offset is meaningless.
 */
static struct raw_match
lzx_lz_get_near_optimal_match(struct lzx_compressor * ctx)
{
        unsigned num_possible_matches;
        struct raw_match *possible_matches;
        struct raw_match match;
        unsigned longest_match_len;

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

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

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

        ctx->optimum_cur_idx = 0;
        ctx->optimum_end_idx = 0;

        /* Get matches at this position.  */
        num_possible_matches = lzx_lz_get_matches_caching(ctx, &ctx->queue, &possible_matches);

        /* If no matches found, return literal.  */
        if (num_possible_matches == 0)
                return (struct raw_match){ .len = 0 };

        /* The matches that were found are sorted in decreasing order by length.
         * Get the length of the longest one.  */
        longest_match_len = possible_matches[0].len;

        /* Greedy heuristic:  if the longest match that was found is greater
         * than the number of fast bytes, return it immediately; don't both
         * doing more work.  */
        if (longest_match_len > ctx->params.alg_params.slow.num_fast_bytes) {
                lzx_lz_skip_bytes(ctx, longest_match_len - 1);
                return possible_matches[0];
        }

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

        /* Calculate the cost to reach any position up to and including that
         * reached by the longest match, using the shortest (i.e. closest) match
         * that reaches each position.  */
        BUILD_BUG_ON(LZX_MIN_MATCH_LEN != 2);
        for (unsigned len = LZX_MIN_MATCH_LEN, match_idx = num_possible_matches - 1;
             len <= longest_match_len; len++) {

                LZX_ASSERT(match_idx < num_possible_matches);

                ctx->optimum[len].queue = ctx->optimum[0].queue;
                ctx->optimum[len].prev.link = 0;
                ctx->optimum[len].prev.match_offset = possible_matches[match_idx].offset;
                ctx->optimum[len].cost = lzx_match_cost(len,
                                                        possible_matches[match_idx].offset,
                                                        &ctx->costs,
                                                        &ctx->optimum[len].queue);
                if (len == possible_matches[match_idx].len)
                        match_idx--;
        }

        unsigned cur_pos = 0;

        /* len_end: greatest index forward at which costs have been calculated
         * so far  */
        unsigned len_end = longest_match_len;

        for (;;) {
                /* Advance to next position.  */
                cur_pos++;

                if (cur_pos == len_end || cur_pos == LZX_OPTIM_ARRAY_SIZE)
                        return lzx_lz_reverse_near_optimal_match_list(ctx, cur_pos);

                /* retrieve the number of matches available at this position  */
                num_possible_matches = lzx_lz_get_matches_caching(ctx, &ctx->optimum[cur_pos].queue,
                                                                  &possible_matches);

                unsigned new_len = 0;

                if (num_possible_matches != 0) {
                        new_len = possible_matches[0].len;

                        /* Greedy heuristic:  if we found a match greater than
                         * the number of fast bytes, stop immediately.  */
                        if (new_len > ctx->params.alg_params.slow.num_fast_bytes) {

                                /* Build the list of matches to return and get
                                 * the first one.  */
                                match = lzx_lz_reverse_near_optimal_match_list(ctx, cur_pos);

                                /* Append the long match to the end of the list.  */
                                ctx->optimum[cur_pos].next.match_offset =
                                        possible_matches[0].offset;
                                ctx->optimum[cur_pos].next.link = cur_pos + new_len;
                                ctx->optimum_end_idx = cur_pos + new_len;

                                /* Skip over the remaining bytes of the long match.  */
                                lzx_lz_skip_bytes(ctx, new_len - 1);

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

                /* Consider proceeding with a literal byte.  */
                block_cost_t cur_cost = ctx->optimum[cur_pos].cost;
                block_cost_t cur_plus_literal_cost = cur_cost +
                        lzx_literal_cost(ctx->window[ctx->match_window_pos - 1],
                                         &ctx->costs);
                if (cur_plus_literal_cost < ctx->optimum[cur_pos + 1].cost) {
                        ctx->optimum[cur_pos + 1].cost = cur_plus_literal_cost;
                        ctx->optimum[cur_pos + 1].prev.link = cur_pos;
                        ctx->optimum[cur_pos + 1].queue = ctx->optimum[cur_pos].queue;
                }

                if (num_possible_matches == 0)
                        continue;

                /* Consider proceeding with a match.  */

                while (len_end < cur_pos + new_len)
                        ctx->optimum[++len_end].cost = INFINITE_BLOCK_COST;

                for (unsigned len = LZX_MIN_MATCH_LEN, match_idx = num_possible_matches - 1;
                     len <= new_len; len++) {
                        LZX_ASSERT(match_idx < num_possible_matches);
                        struct lzx_lru_queue q = ctx->optimum[cur_pos].queue;
                        block_cost_t cost = cur_cost + lzx_match_cost(len,
                                                                      possible_matches[match_idx].offset,
                                                                      &ctx->costs,
                                                                      &q);

                        if (cost < ctx->optimum[cur_pos + len].cost) {
                                ctx->optimum[cur_pos + len].cost = cost;
                                ctx->optimum[cur_pos + len].prev.link = cur_pos;
                                ctx->optimum[cur_pos + len].prev.match_offset =
                                                possible_matches[match_idx].offset;
                                ctx->optimum[cur_pos + len].queue = q;
                        }

                        if (len == possible_matches[match_idx].len)
                                match_idx--;
                }
        }
}

/*
 * Set default symbol costs.
 */
static void
lzx_set_default_costs(struct lzx_costs * costs)
{
        unsigned i;

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

        /* Match header symbols  */
        for (; i < LZX_MAINCODE_NUM_SYMBOLS; i++)
                costs->main[i] = 10;

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

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

/* Given the frequencies of symbols in a 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 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 near-optimal sequence of matches/literals with which to output the
 * specified LZX block, then set its type to that which has the minimum cost to
 * output.  */
static void
lzx_optimize_block(struct lzx_compressor *ctx, struct lzx_block_spec *spec,
                   unsigned num_passes)
{
        const struct lzx_lru_queue orig_queue = ctx->queue;
        struct lzx_freqs freqs;

        ctx->match_window_end = spec->window_pos + spec->block_size;
        spec->chosen_matches_start_pos = spec->window_pos;

        LZX_ASSERT(num_passes >= 1);

        /* The first optimal parsing pass is done using the cost model already
         * set in ctx->costs.  Each later pass is done using a cost model
         * computed from the previous pass.  */
        for (unsigned pass = 0; pass < num_passes; pass++) {

                lzx_lz_rewind_matchfinder(ctx, spec->window_pos);
                ctx->queue = orig_queue;
                spec->num_chosen_matches = 0;
                memset(&freqs, 0, sizeof(freqs));

                for (unsigned i = spec->window_pos; i < spec->window_pos + spec->block_size; ) {
                        struct raw_match raw_match;
                        struct lzx_match lzx_match;

                        raw_match = lzx_lz_get_near_optimal_match(ctx);
                        if (raw_match.len >= LZX_MIN_MATCH_LEN) {
                                lzx_match.data = lzx_record_match(raw_match.offset, raw_match.len,
                                                                  &freqs, &ctx->queue);
                                i += raw_match.len;
                        } else {
                                lzx_match.data = lzx_record_literal(ctx->window[i], &freqs);
                                i += 1;
                        }
                        ctx->chosen_matches[spec->chosen_matches_start_pos +
                                            spec->num_chosen_matches++] = lzx_match;
                }

                lzx_make_huffman_codes(&freqs, &spec->codes);
                if (pass < num_passes - 1)
                        lzx_set_costs(ctx, &spec->codes.lens);
        }
        spec->block_type = lzx_choose_verbatim_or_aligned(&freqs, &spec->codes);
}

static void
lzx_optimize_blocks(struct lzx_compressor *ctx)
{
        lzx_lru_queue_init(&ctx->queue);
        ctx->optimum_cur_idx = 0;
        ctx->optimum_end_idx = 0;

        const unsigned num_passes = ctx->params.alg_params.slow.num_optim_passes;

        for (unsigned i = 0; i < ctx->num_blocks; i++)
                lzx_optimize_block(ctx, &ctx->block_specs[i], num_passes);
}

/* Initialize the suffix array match-finder for the specified input.  */
static void
lzx_lz_init_matchfinder(const u8 T[const restrict],
                        const input_idx_t n,
                        input_idx_t SA[const restrict],
                        input_idx_t ISA[const restrict],
                        struct salink link[const restrict],
                        const unsigned max_match_len)
{
        /* Compute SA (Suffix Array).  */

        {
                saidx_t sa[n];
                /* ISA and link are used as temporary space.  */
                BUILD_BUG_ON(LZX_MAX_WINDOW_SIZE * sizeof(ISA[0]) < 256 * sizeof(saidx_t));
                BUILD_BUG_ON(LZX_MAX_WINDOW_SIZE * 2 * sizeof(link[0]) < 256 * 256 * sizeof(saidx_t));
                divsufsort(T, sa, n, (saidx_t*)ISA, (saidx_t*)link);
                for (input_idx_t i = 0; i < n; i++)
                        SA[i] = sa[i];
        }

#ifdef ENABLE_LZX_DEBUG

        LZX_ASSERT(n > 0);

        /* Verify suffix array.  */
        {
                bool found[n];
                ZERO_ARRAY(found);
                for (input_idx_t r = 0; r < n; r++) {
                        input_idx_t i = SA[r];
                        LZX_ASSERT(i < n);
                        LZX_ASSERT(!found[i]);
                        found[i] = true;
                }
        }

        for (input_idx_t r = 0; r < n - 1; r++) {

                input_idx_t i1 = SA[r];
                input_idx_t i2 = SA[r + 1];

                input_idx_t n1 = n - i1;
                input_idx_t n2 = n - i2;

                LZX_ASSERT(memcmp(&T[i1], &T[i2], min(n1, n2)) <= 0);
        }
        LZX_DEBUG("Verified SA (len %u)", n);
#endif /* ENABLE_LZX_DEBUG */

        /* Compute ISA (Inverse Suffix Array)  */
        for (input_idx_t r = 0; r < n; r++)
                ISA[SA[r]] = r;

        {
                input_idx_t LCP[n];
                /* Compute LCP (longest common prefix) array.
                 *
                 * Algorithm adapted from Kasai et al. 2001: "Linear-Time
                 * Longest-Common-Prefix Computation in Suffix Arrays and Its
                 * Applications".  */
                {
                        input_idx_t h = 0;
                        for (input_idx_t i = 0; i < n; i++) {
                                input_idx_t r = ISA[i];
                                if (r > 0) {
                                        input_idx_t j = SA[r - 1];

                                        input_idx_t lim = min(n - i, n - j);

                                        while (h < lim && T[i + h] == T[j + h])
                                                h++;
                                        LCP[r] = h;
                                        if (h > 0)
                                                h--;
                                }
                        }
                }

        #ifdef ENABLE_LZX_DEBUG
                /* Verify LCP array.  */
                for (input_idx_t r = 0; r < n - 1; r++) {
                        LZX_ASSERT(ISA[SA[r]] == r);
                        LZX_ASSERT(ISA[SA[r + 1]] == r + 1);

                        input_idx_t i1 = SA[r];
                        input_idx_t i2 = SA[r + 1];
                        input_idx_t lcp = LCP[r + 1];

                        input_idx_t n1 = n - i1;
                        input_idx_t n2 = n - i2;

                        LZX_ASSERT(lcp <= min(n1, n2));

                        LZX_ASSERT(memcmp(&T[i1], &T[i2], lcp) == 0);
                        if (lcp < min(n1, n2))
                                LZX_ASSERT(T[i1 + lcp] != T[i2 + lcp]);
                }
        #endif /* ENABLE_LZX_DEBUG */

                /* Compute salink.next and salink.lcpnext.
                 *
                 * Algorithm adapted from Crochemore et al. 2009:
                 * "LPF computation revisited".
                 *
                 * Note: we cap lcpnext to the maximum match length so that the
                 * match-finder need not worry about it later.  */
                link[n - 1].next = (input_idx_t)~0U;
                link[n - 1].prev = (input_idx_t)~0U;
                link[n - 1].lcpnext = 0;
                link[n - 1].lcpprev = 0;
                for (input_idx_t r = n - 2; r != (input_idx_t)~0U; r--) {
                        input_idx_t t = r + 1;
                        input_idx_t l = LCP[t];
                        while (t != (input_idx_t)~0 && SA[t] > SA[r]) {
                                l = min(l, link[t].lcpnext);
                                t = link[t].next;
                        }
                        link[r].next = t;
                        link[r].lcpnext = min(l, max_match_len);
                        LZX_ASSERT(t == (input_idx_t)~0U || l <= n - SA[t]);
                        LZX_ASSERT(l <= n - SA[r]);
                        LZX_ASSERT(memcmp(&T[SA[r]], &T[SA[t]], l) == 0);
                }

                /* Compute salink.prev and salink.lcpprev.
                 *
                 * Algorithm adapted from Crochemore et al. 2009:
                 * "LPF computation revisited".
                 *
                 * Note: we cap lcpprev to the maximum match length so that the
                 * match-finder need not worry about it later.  */
                link[0].prev = (input_idx_t)~0;
                link[0].next = (input_idx_t)~0;
                link[0].lcpprev = 0;
                link[0].lcpnext = 0;
                for (input_idx_t r = 1; r < n; r++) {
                        input_idx_t t = r - 1;
                        input_idx_t l = LCP[r];
                        while (t != (input_idx_t)~0 && SA[t] > SA[r]) {
                                l = min(l, link[t].lcpprev);
                                t = link[t].prev;
                        }
                        link[r].prev = t;
                        link[r].lcpprev = min(l, max_match_len);
                        LZX_ASSERT(t == (input_idx_t)~0 || l <= n - SA[t]);
                        LZX_ASSERT(l <= n - SA[r]);
                        LZX_ASSERT(memcmp(&T[SA[r]], &T[SA[t]], l) == 0);
                }
        }
}

/* Prepare the input window into one or more LZX blocks ready to be output.  */
static void
lzx_prepare_blocks(struct lzx_compressor * ctx)
{
        /* Initialize the match-finder.  */
        lzx_lz_init_matchfinder(ctx->window, ctx->window_size,
                                ctx->SA, ctx->ISA, ctx->salink,
                                LZX_MAX_MATCH_LEN);
        ctx->cached_matches_pos = 0;
        ctx->matches_cached = false;
        ctx->match_window_pos = 0;

        /* Set up a default cost model.  */
        lzx_set_default_costs(&ctx->costs);

        /* Assume that the entire input will be one LZX block.  */
        ctx->block_specs[0].window_pos = 0;
        ctx->block_specs[0].block_size = ctx->window_size;
        ctx->num_blocks = 1;

        /* Determine sequence of matches/literals to output for each block.  */
        lzx_optimize_blocks(ctx);
}

/*
 * This is the fast version of lzx_prepare_blocks().  This version "quickly"
 * prepares a single compressed block containing the entire input.  See the
 * description of the "Fast algorithm" at the beginning of this file for more
 * information.
 *
 * Input ---  the preprocessed data:
 *
 *      ctx->window[]
 *      ctx->window_size
 *
 * Working space:
 *      ctx->queue
 *
 * Output --- the block specification and the corresponding match/literal data:
 *
 *      ctx->block_specs[]
 *      ctx->num_blocks
 *      ctx->chosen_matches[]
 */
static void
lzx_prepare_block_fast(struct lzx_compressor * ctx)
{
        unsigned num_matches;
        struct lzx_freqs freqs;
        struct lzx_block_spec *spec;

        /* Parameters to hash chain LZ match finder
         * (lazy with 1 match lookahead)  */
        static const struct lz_params lzx_lz_params = {
                /* Although LZX_MIN_MATCH_LEN == 2, length 2 matches typically
                 * aren't worth choosing when using greedy or lazy parsing.  */
                .min_match      = 3,
                .max_match      = LZX_MAX_MATCH_LEN,
                .good_match     = LZX_MAX_MATCH_LEN,
                .nice_match     = LZX_MAX_MATCH_LEN,
                .max_chain_len  = LZX_MAX_MATCH_LEN,
                .max_lazy_match = LZX_MAX_MATCH_LEN,
                .too_far        = 4096,
        };

        /* Initialize symbol frequencies and match offset LRU queue.  */
        memset(&freqs, 0, sizeof(struct lzx_freqs));
        lzx_lru_queue_init(&ctx->queue);

        /* Determine series of matches/literals to output.  */
        num_matches = lz_analyze_block(ctx->window,
                                       ctx->window_size,
                                       (u32*)ctx->chosen_matches,
                                       lzx_record_match,
                                       lzx_record_literal,
                                       &freqs,
                                       &ctx->queue,
                                       &freqs,
                                       &lzx_lz_params);


        /* Set up block specification.  */
        spec = &ctx->block_specs[0];
        spec->block_type = LZX_BLOCKTYPE_ALIGNED;
        spec->window_pos = 0;
        spec->block_size = ctx->window_size;
        spec->num_chosen_matches = num_matches;
        spec->chosen_matches_start_pos = 0;
        lzx_make_huffman_codes(&freqs, &spec->codes);
        ctx->num_blocks = 1;
}

static void
do_call_insn_translation(u32 *call_insn_target, int input_pos,
                         s32 file_size)
{
        s32 abs_offset;
        s32 rel_offset;

        rel_offset = le32_to_cpu(*call_insn_target);
        if (rel_offset >= -input_pos && rel_offset < file_size) {
                if (rel_offset < file_size - input_pos) {
                        /* "good translation" */
                        abs_offset = rel_offset + input_pos;
                } else {
                        /* "compensating translation" */
                        abs_offset = rel_offset - file_size;
                }
                *call_insn_target = cpu_to_le32(abs_offset);
        }
}

/* This is the reverse of undo_call_insn_preprocessing() in lzx-decompress.c.
 * See the comment above that function for more information.  */
static void
do_call_insn_preprocessing(u8 data[], int size)
{
        for (int i = 0; i < size - 10; i++) {
                if (data[i] == 0xe8) {
                        do_call_insn_translation((u32*)&data[i + 1], i,
                                                 LZX_WIM_MAGIC_FILESIZE);
                        i += 4;
                }
        }
}

/* API function documented in wimlib.h  */
WIMLIBAPI unsigned
wimlib_lzx_compress2(const void                 * const restrict uncompressed_data,
                     unsigned                     const          uncompressed_len,
                     void                       * const restrict compressed_data,
                     struct wimlib_lzx_context  * const restrict lzx_ctx)
{
        struct lzx_compressor *ctx = (struct lzx_compressor*)lzx_ctx;
        struct output_bitstream ostream;
        unsigned compressed_len;

        if (uncompressed_len < 100) {
                LZX_DEBUG("Too small to bother compressing.");
                return 0;
        }

        if (uncompressed_len > 32768) {
                LZX_DEBUG("Only up to 32768 bytes of uncompressed data are supported.");
                return 0;
        }

        wimlib_assert(lzx_ctx != NULL);

        LZX_DEBUG("Attempting to compress %u bytes...", uncompressed_len);

        /* The input data must be preprocessed.  To avoid changing the original
         * input, copy it to a temporary buffer.  */
        memcpy(ctx->window, uncompressed_data, uncompressed_len);
        ctx->window_size = uncompressed_len;

        /* This line is unnecessary; it just avoids inconsequential accesses of
         * uninitialized memory that would show up in memory-checking tools such
         * as valgrind.  */
        memset(&ctx->window[ctx->window_size], 0, 12);

        LZX_DEBUG("Preprocessing data...");

        /* Before doing any actual compression, do the call instruction (0xe8
         * byte) translation on the uncompressed data.  */
        do_call_insn_preprocessing(ctx->window, ctx->window_size);

        LZX_DEBUG("Preparing blocks...");

        /* Prepare the compressed data.  */
        if (ctx->params.algorithm == WIMLIB_LZX_ALGORITHM_FAST)
                lzx_prepare_block_fast(ctx);
        else
                lzx_prepare_blocks(ctx);

        LZX_DEBUG("Writing compressed blocks...");

        /* Generate the compressed data.  */
        init_output_bitstream(&ostream, compressed_data, ctx->window_size - 1);
        lzx_write_all_blocks(ctx, &ostream);

        LZX_DEBUG("Flushing bitstream...");
        if (flush_output_bitstream(&ostream)) {
                /* If the bitstream cannot be flushed, then the output space was
                 * exhausted.  */
                LZX_DEBUG("Data did not compress to less than original length!");
                return 0;
        }

        /* Compute the length of the compressed data.  */
        compressed_len = ostream.bit_output - (u8*)compressed_data;

        LZX_DEBUG("Done: compressed %u => %u bytes.",
                  uncompressed_len, compressed_len);

        /* Verify that we really get the same thing back when decompressing.
         * Although this could be disabled by default in all cases, it only
         * takes around 2-3% of the running time of the slow algorithm to do the
         * verification.  */
        if (ctx->params.algorithm == WIMLIB_LZX_ALGORITHM_SLOW
        #if defined(ENABLE_LZX_DEBUG) || defined(ENABLE_VERIFY_COMPRESSION)
            || 1
        #endif
            )
        {
                u8 buf[uncompressed_len];
                int ret;

                ret = wimlib_lzx_decompress(compressed_data, compressed_len,
                                            buf, uncompressed_len);
                if (ret) {
                        ERROR("Failed to decompress data we "
                              "compressed using LZX algorithm");
                        wimlib_assert(0);
                        return 0;
                }

                if (memcmp(uncompressed_data, buf, uncompressed_len)) {
                        ERROR("Data we compressed using LZX algorithm "
                              "didn't decompress to original");
                        wimlib_assert(0);
                        return 0;
                }
        }
        return compressed_len;
}

static bool
lzx_params_compatible(const struct wimlib_lzx_params *oldparams,
                      const struct wimlib_lzx_params *newparams)
{
        return 0 == memcmp(oldparams, newparams, sizeof(struct wimlib_lzx_params));
}

static struct wimlib_lzx_params lzx_user_default_params;
static struct wimlib_lzx_params *lzx_user_default_params_ptr;

static bool
lzx_params_valid(const struct wimlib_lzx_params *params)
{
        /* Validate parameters.  */
        if (params->size_of_this != sizeof(struct wimlib_lzx_params)) {
                LZX_DEBUG("Invalid parameter structure size!");
                return false;
        }

        if (params->algorithm != WIMLIB_LZX_ALGORITHM_SLOW &&
            params->algorithm != WIMLIB_LZX_ALGORITHM_FAST)
        {
                LZX_DEBUG("Invalid algorithm.");
                return false;
        }

        if (params->algorithm == WIMLIB_LZX_ALGORITHM_SLOW) {
                if (params->alg_params.slow.num_optim_passes < 1)
                {
                        LZX_DEBUG("Invalid number of optimization passes!");
                        return false;
                }

                if (params->alg_params.slow.main_nostat_cost < 1 ||
                    params->alg_params.slow.main_nostat_cost > 16)
                {
                        LZX_DEBUG("Invalid main_nostat_cost!");
                        return false;
                }

                if (params->alg_params.slow.len_nostat_cost < 1 ||
                    params->alg_params.slow.len_nostat_cost > 16)
                {
                        LZX_DEBUG("Invalid len_nostat_cost!");
                        return false;
                }

                if (params->alg_params.slow.aligned_nostat_cost < 1 ||
                    params->alg_params.slow.aligned_nostat_cost > 8)
                {
                        LZX_DEBUG("Invalid aligned_nostat_cost!");
                        return false;
                }
        }
        return true;
}

/* API function documented in wimlib.h  */
WIMLIBAPI int
wimlib_lzx_set_default_params(const struct wimlib_lzx_params * params)
{
        if (params) {
                if (!lzx_params_valid(params))
                        return WIMLIB_ERR_INVALID_PARAM;
                lzx_user_default_params = *params;
                lzx_user_default_params_ptr = &lzx_user_default_params;
        } else {
                lzx_user_default_params_ptr = NULL;
        }
        return 0;
}

/* API function documented in wimlib.h  */
WIMLIBAPI int
wimlib_lzx_alloc_context(const struct wimlib_lzx_params *params,
                         struct wimlib_lzx_context **ctx_pp)
{

        LZX_DEBUG("Allocating LZX context...");

        struct lzx_compressor *ctx;

        static const struct wimlib_lzx_params fast_default = {
                .size_of_this = sizeof(struct wimlib_lzx_params),
                .algorithm = WIMLIB_LZX_ALGORITHM_FAST,
                .use_defaults = 0,
                .alg_params = {
                        .fast = {
                        },
                },
        };
        static const struct wimlib_lzx_params slow_default = {
                .size_of_this = sizeof(struct wimlib_lzx_params),
                .algorithm = WIMLIB_LZX_ALGORITHM_SLOW,
                .use_defaults = 0,
                .alg_params = {
                        .slow = {
                                .use_len2_matches = 1,
                                .num_fast_bytes = 32,
                                .num_optim_passes = 2,
                                .max_search_depth = 50,
                                .max_matches_per_pos = 3,
                                .main_nostat_cost = 15,
                                .len_nostat_cost = 15,
                                .aligned_nostat_cost = 7,
                        },
                },
        };

        if (params) {
                if (!lzx_params_valid(params))
                        return WIMLIB_ERR_INVALID_PARAM;
        } else {
                LZX_DEBUG("Using default algorithm and parameters.");
                if (lzx_user_default_params_ptr)
                        params = lzx_user_default_params_ptr;
                else
                        params = &slow_default;
        }

        if (params->use_defaults) {
                if (params->algorithm == WIMLIB_LZX_ALGORITHM_SLOW)
                        params = &slow_default;
                else
                        params = &fast_default;
        }

        if (ctx_pp) {
                ctx = *(struct lzx_compressor**)ctx_pp;

                if (ctx && lzx_params_compatible(&ctx->params, params))
                        return 0;
        } else {
                LZX_DEBUG("Check parameters only.");
                return 0;
        }

        LZX_DEBUG("Allocating memory.");

        ctx = MALLOC(sizeof(struct lzx_compressor));
        if (ctx == NULL)
                goto err;

        size_t block_specs_length;

#if 0
        if (params->algorithm == WIMLIB_LZX_ALGORITHM_SLOW)
                block_specs_length = 1U << params->alg_params.slow.num_split_passes;
        else
#endif
                block_specs_length = 1U;
        ctx->block_specs = MALLOC(block_specs_length * sizeof(ctx->block_specs[0]));
        if (ctx->block_specs == NULL)
                goto err_free_ctx;

        if (params->algorithm == WIMLIB_LZX_ALGORITHM_SLOW) {
                ctx->SA = MALLOC(3U * LZX_MAX_WINDOW_SIZE * sizeof(ctx->SA[0]));
                if (ctx->SA == NULL)
                        goto err_free_block_specs;
                ctx->ISA = ctx->SA + LZX_MAX_WINDOW_SIZE;
                ctx->salink = MALLOC(LZX_MAX_WINDOW_SIZE * sizeof(ctx->salink[0]));
                if (ctx->salink == NULL)
                        goto err_free_SA;
        } else {
                ctx->SA = NULL;
                ctx->ISA = NULL;
                ctx->salink = NULL;
        }

        if (params->algorithm == WIMLIB_LZX_ALGORITHM_SLOW) {
                ctx->optimum = MALLOC((LZX_OPTIM_ARRAY_SIZE + LZX_MAX_MATCH_LEN) *
                                       sizeof(ctx->optimum[0]));
                if (ctx->optimum == NULL)
                        goto err_free_salink;
        } else {
                ctx->optimum = NULL;
        }

        if (params->algorithm == WIMLIB_LZX_ALGORITHM_SLOW) {
                uint32_t cache_per_pos;

                cache_per_pos = params->alg_params.slow.max_matches_per_pos;
                if (cache_per_pos > LZX_MAX_CACHE_PER_POS)
                        cache_per_pos = LZX_MAX_CACHE_PER_POS;

                ctx->cached_matches = MALLOC(LZX_MAX_WINDOW_SIZE * (cache_per_pos + 1) *
                                             sizeof(ctx->cached_matches[0]));
                if (ctx->cached_matches == NULL)
                        goto err_free_optimum;
        } else {
                ctx->cached_matches = NULL;
        }

        ctx->chosen_matches = MALLOC(LZX_MAX_WINDOW_SIZE *
                                     sizeof(ctx->chosen_matches[0]));
        if (ctx->chosen_matches == NULL)
                goto err_free_cached_matches;

        memcpy(&ctx->params, params, sizeof(struct wimlib_lzx_params));
        memset(&ctx->zero_codes, 0, sizeof(ctx->zero_codes));

        LZX_DEBUG("Successfully allocated new LZX context.");

        wimlib_lzx_free_context(*ctx_pp);
        *ctx_pp = (struct wimlib_lzx_context*)ctx;
        return 0;

err_free_cached_matches:
        FREE(ctx->cached_matches);
err_free_optimum:
        FREE(ctx->optimum);
err_free_salink:
        FREE(ctx->salink);
err_free_SA:
        FREE(ctx->SA);
err_free_block_specs:
        FREE(ctx->block_specs);
err_free_ctx:
        FREE(ctx);
err:
        LZX_DEBUG("Ran out of memory.");
        return WIMLIB_ERR_NOMEM;
}

/* API function documented in wimlib.h  */
WIMLIBAPI void
wimlib_lzx_free_context(struct wimlib_lzx_context *_ctx)
{
        struct lzx_compressor *ctx = (struct lzx_compressor*)_ctx;

        if (ctx) {
                FREE(ctx->chosen_matches);
                FREE(ctx->cached_matches);
                FREE(ctx->optimum);
                FREE(ctx->salink);
                FREE(ctx->SA);
                FREE(ctx->block_specs);
                FREE(ctx);
        }
}

/* API function documented in wimlib.h  */
WIMLIBAPI unsigned
wimlib_lzx_compress(const void * const restrict uncompressed_data,
                    unsigned     const          uncompressed_len,
                    void       * const restrict compressed_data)
{
        int ret;
        struct wimlib_lzx_context *ctx = NULL;
        unsigned compressed_len;

        ret = wimlib_lzx_alloc_context(NULL, &ctx);
        if (ret) {
                wimlib_assert(ret != WIMLIB_ERR_INVALID_PARAM);
                WARNING("Couldn't allocate LZX compression context: %"TS"",
                        wimlib_get_error_string(ret));
                return 0;
        }

        compressed_len = wimlib_lzx_compress2(uncompressed_data,
                                              uncompressed_len,
                                              compressed_data,
                                              ctx);

        wimlib_lzx_free_context(ctx);

        return compressed_len;
}