Wimlib LZX

/*
 * lzx_compress.c
 *
 * A compressor for the LZX compression format, as used in WIM archives.
 */

/*
 * Copyright (C) 2012-2017 Eric Biggers
 *
 * This file is free software; you can redistribute it and/or modify it under
 * the terms of the GNU Lesser General Public License as published by the Free
 * Software Foundation; either version 3 of the License, or (at your option) any
 * later version.
 *
 * This file is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
 * FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
 * details.
 *
 * You should have received a copy of the GNU Lesser General Public License
 * along with this file; if not, see http://www.gnu.org/licenses/.
 */


/*
 * This file contains a compressor for the LZX ("Lempel-Ziv eXtended")
 * compression format, as used in the WIM (Windows IMaging) file format.
 *
 * Two different LZX-compatible algorithms are implemented: "near-optimal" and
 * "lazy".  "Near-optimal" is significantly slower than "lazy", but results in a
 * better compression ratio.  The "near-optimal" algorithm is used at the
 * default compression level.
 *
 * This file may need some slight modifications to be used outside of the WIM
 * format.  In particular, in other situations the LZX block header might be
 * slightly different, and sliding window support might be required.
 *
 * LZX is a compression format derived from DEFLATE, the format used by zlib and
 * gzip.  Both LZX and DEFLATE use LZ77 matching and Huffman coding.  Certain
 * details are quite similar, such as the method for storing Huffman codes.
 * However, the main differences are:
 *
 * - LZX preprocesses the data to attempt to make x86 machine code slightly more
 *   compressible before attempting to compress it further.
 *
 * - LZX uses a "main" alphabet which combines literals and matches, with the
 *   match symbols containing a "length header" (giving all or part of the match
 *   length) and an "offset slot" (giving, roughly speaking, the order of
 *   magnitude of the match offset).
 *
 * - LZX does not have static Huffman blocks (that is, the kind with preset
 *   Huffman codes); however it does have two types of dynamic Huffman blocks
 *   ("verbatim" and "aligned").
 *
 * - LZX has a minimum match length of 2 rather than 3.  Length 2 matches can be
 *   useful, but generally only if the compressor is smart about choosing them.
 *
 * - In LZX, offset slots 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.
 */

/******************************************************************************/
/*                            General parameters                              */
/*----------------------------------------------------------------------------*/

/*
 * The compressor uses the faster algorithm at levels <= MAX_FAST_LEVEL.  It
 * uses the slower algorithm at levels > MAX_FAST_LEVEL.
 */
#define MAX_FAST_LEVEL              34

/*
 * The compressor-side limits on the codeword lengths (in bits) for each Huffman
 * code.  To make outputting bits slightly faster, some of these limits are
 * lower than the limits defined by the LZX format.  This does not significantly
 * affect the compression ratio.
 */
#define MAIN_CODEWORD_LIMIT         16
#define LENGTH_CODEWORD_LIMIT           12
#define ALIGNED_CODEWORD_LIMIT          7
#define PRE_CODEWORD_LIMIT          7


/******************************************************************************/
/*                         Block splitting parameters                         */
/*----------------------------------------------------------------------------*/

/*
 * The compressor always outputs blocks of at least this size in bytes, except
 * for the last block which may need to be smaller.
 */
#define MIN_BLOCK_SIZE              6500

/*
 * The compressor attempts to end a block when it reaches this size in bytes.
 * The final size might be slightly larger due to matches extending beyond the
 * end of the block.  Specifically:
 *
 *  - The near-optimal compressor may choose a match of up to LZX_MAX_MATCH_LEN
 *    bytes starting at position 'SOFT_MAX_BLOCK_SIZE - 1'.
 *
 *  - The lazy compressor may choose a sequence of literals starting at position
 *    'SOFT_MAX_BLOCK_SIZE - 1' when it sees a sequence of increasingly better
 *    matches.  The final match may be up to LZX_MAX_MATCH_LEN bytes.  The
 *    length of the literal sequence is approximately limited by the "nice match
 *    length" parameter.
 */
#define SOFT_MAX_BLOCK_SIZE         100000

/*
 * The number of observed items (matches and literals) that represents
 * sufficient data for the compressor to decide whether the current block should
 * be ended or not.
 */
#define NUM_OBSERVATIONS_PER_BLOCK_CHECK    400


/******************************************************************************/
/*                      Parameters for slower algorithm                       */
/*----------------------------------------------------------------------------*/

/*
 * The log base 2 of the number of entries in the hash table for finding length
 * 2 matches.  This could be as high as 16, but using a smaller hash table
 * speeds up compression due to reduced cache pressure.
 */
#define BT_MATCHFINDER_HASH2_ORDER      12

/*
 * The number of lz_match structures in the match cache, excluding the extra
 * "overflow" entries.  This value should be high enough so that nearly the
 * time, all matches found in a given block can fit in the match cache.
 * However, fallback behavior (immediately terminating the block) on cache
 * overflow is still required.
 */
#define CACHE_LENGTH                (SOFT_MAX_BLOCK_SIZE * 5)

/*
 * An upper bound on the number of matches that can ever be saved in the match
 * cache for a single position.  Since each match we save for a single position
 * has a distinct length, we can use the number of possible match lengths in LZX
 * as this bound.  This bound is guaranteed to be valid in all cases, although
 * if 'nice_match_length < LZX_MAX_MATCH_LEN', then it will never actually be
 * reached.
 */
#define MAX_MATCHES_PER_POS         LZX_NUM_LENS

/*
 * A scaling factor that makes it possible to consider fractional bit costs.  A
 * single bit has a cost of BIT_COST.
 *
 * Note: this is only useful as a statistical trick for when the true costs are
 * unknown.  Ultimately, each token in LZX requires a whole number of bits to
 * output.
 */
#define BIT_COST                64

/*
 * Should the compressor take into account the costs of aligned offset symbols
 * instead of assuming that all are equally likely?
 */
#define CONSIDER_ALIGNED_COSTS          1

/*
 * Should the "minimum" cost path search algorithm consider "gap" matches, where
 * a normal match is followed by a literal, then by a match with the same
 * offset?  This is one specific, somewhat common situation in which the true
 * minimum cost path is often different from the path found by looking only one
 * edge ahead.
 */
#define CONSIDER_GAP_MATCHES            1

/******************************************************************************/
/*                                  Includes                                  */
/*----------------------------------------------------------------------------*/

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

#include "wimlib/compress_common.h"
#include "wimlib/compressor_ops.h"
#include "wimlib/error.h"
#include "wimlib/lz_extend.h"
#include "wimlib/lzx_common.h"
#include "wimlib/unaligned.h"
#include "wimlib/util.h"

/* Note: BT_MATCHFINDER_HASH2_ORDER must be defined before including
 * bt_matchfinder.h. */

/* Matchfinders with 16-bit positions */
#define mf_pos_t    u16
#define MF_SUFFIX   _16
#include "wimlib/bt_matchfinder.h"
#include "wimlib/hc_matchfinder.h"

/* Matchfinders with 32-bit positions */
#undef mf_pos_t
#undef MF_SUFFIX
#define mf_pos_t    u32
#define MF_SUFFIX   _32
#include "wimlib/bt_matchfinder.h"
#include "wimlib/hc_matchfinder.h"

/******************************************************************************/
/*                            Compressor structure                            */
/*----------------------------------------------------------------------------*/

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

/*
 * Codeword lengths, in bits, for the Huffman codes.
 *
 * A codeword length of 0 means the corresponding codeword has zero frequency.
 *
 * The main and length codes each have one extra entry for use as a sentinel.
 * See lzx_write_compressed_code().
 */
struct lzx_lens {
    u8 main[LZX_MAINCODE_MAX_NUM_SYMBOLS + 1];
    u8 len[LZX_LENCODE_NUM_SYMBOLS + 1];
    u8 aligned[LZX_ALIGNEDCODE_NUM_SYMBOLS];
};

/* Codewords and lengths for the Huffman codes */
struct lzx_codes {
    struct lzx_codewords codewords;
    struct lzx_lens lens;
};

/* Symbol frequency counters for the Huffman-encoded alphabets */
struct lzx_freqs {
    u32 main[LZX_MAINCODE_MAX_NUM_SYMBOLS];
    u32 len[LZX_LENCODE_NUM_SYMBOLS];
    u32 aligned[LZX_ALIGNEDCODE_NUM_SYMBOLS];
};

/* Block split statistics.  See the "Block splitting algorithm" section later in
 * this file for details. */
#define NUM_LITERAL_OBSERVATION_TYPES 8
#define NUM_MATCH_OBSERVATION_TYPES 2
#define NUM_OBSERVATION_TYPES (NUM_LITERAL_OBSERVATION_TYPES + \
                   NUM_MATCH_OBSERVATION_TYPES)
struct lzx_block_split_stats {
    u32 new_observations[NUM_OBSERVATION_TYPES];
    u32 observations[NUM_OBSERVATION_TYPES];
    u32 num_new_observations;
    u32 num_observations;
};

/*
 * Represents a run of literals followed by a match or end-of-block.  This
 * structure is needed to temporarily store items chosen by the compressor,
 * since items cannot be written until all items for the block have been chosen
 * and the block's Huffman codes have been computed.
 */
struct lzx_sequence {

    /*
     * Bits 9..31: the number of literals in this run.  This may be 0 and
     * can be at most about SOFT_MAX_BLOCK_LENGTH.  The literals are not
     * stored explicitly in this structure; instead, they are read directly
     * from the uncompressed data.
     *
     * Bits 0..8: the length of the match which follows the literals, or 0
     * if this literal run was the last in the block, so there is no match
     * which follows it.  This can be at most LZX_MAX_MATCH_LEN.
     */
    u32 litrunlen_and_matchlen;
#define SEQ_MATCHLEN_BITS   9
#define SEQ_MATCHLEN_MASK   (((u32)1 << SEQ_MATCHLEN_BITS) - 1)

    /*
     * If 'matchlen' doesn't indicate end-of-block, then this contains:
     *
     * Bits 10..31: either the offset plus LZX_OFFSET_ADJUSTMENT or a recent
     * offset code, depending on the offset slot encoded in the main symbol.
     *
     * Bits 0..9: the main symbol.
     */
    u32 adjusted_offset_and_mainsym;
#define SEQ_MAINSYM_BITS    10
#define SEQ_MAINSYM_MASK    (((u32)1 << SEQ_MAINSYM_BITS) - 1)
} _aligned_attribute(8);

/*
 * This structure represents a byte position in the input buffer and a node in
 * the graph of possible match/literal choices.
 *
 * Logically, each incoming edge to this node is labeled with a literal or a
 * match that can be taken to reach this position from an earlier position; and
 * each outgoing edge from this node is labeled with a literal or a match that
 * can be taken to advance from this position to a later position.
 */
struct lzx_optimum_node {

    /* The cost, in bits, of the lowest-cost path that has been found to
     * reach this position.  This can change as progressively lower cost
     * paths are found to reach this position.  */
    u32 cost;

    /*
     * The best arrival to this node, i.e. the match or literal that was
     * used to arrive to this position at the given 'cost'.  This can change
     * as progressively lower cost paths are found to reach this position.
     *
     * For non-gap matches, this variable is divided into two bitfields
     * whose meanings depend on the item type:
     *
     * Literals:
     *  Low bits are 0, high bits are the literal.
     *
     * Explicit offset matches:
     *  Low bits are the match length, high bits are the offset plus
     *  LZX_OFFSET_ADJUSTMENT.
     *
     * Repeat offset matches:
     *  Low bits are the match length, high bits are the queue index.
     *
     * For gap matches, identified by OPTIMUM_GAP_MATCH set, special
     * behavior applies --- see the code.
     */
    u32 item;
#define OPTIMUM_OFFSET_SHIFT    SEQ_MATCHLEN_BITS
#define OPTIMUM_LEN_MASK    SEQ_MATCHLEN_MASK
#if CONSIDER_GAP_MATCHES
#  define OPTIMUM_GAP_MATCH 0x80000000
#endif

} _aligned_attribute(8);

/* The cost model for near-optimal parsing */
struct lzx_costs {

    /*
     * 'match_cost[offset_slot][len - LZX_MIN_MATCH_LEN]' is the cost of a
     * length 'len' match which has an offset belonging to 'offset_slot'.
     * The cost includes the main symbol, the length symbol if required, and
     * the extra offset bits if any, excluding any entropy-coded bits
     * (aligned offset bits).  It does *not* include the cost of the aligned
     * offset symbol which may be required.
     */
    u16 match_cost[LZX_MAX_OFFSET_SLOTS][LZX_NUM_LENS];

    /* Cost of each symbol in the main code */
    u32 main[LZX_MAINCODE_MAX_NUM_SYMBOLS];

    /* Cost of each symbol in the length code */
    u32 len[LZX_LENCODE_NUM_SYMBOLS];

#if CONSIDER_ALIGNED_COSTS
    /* Cost of each symbol in the aligned offset code */
    u32 aligned[LZX_ALIGNEDCODE_NUM_SYMBOLS];
#endif
};

struct lzx_output_bitstream;

/* The main LZX compressor structure */
struct lzx_compressor {

    /* The buffer for preprocessed input data, if not using destructive
     * compression */
    void *in_buffer;

    /* If true, then the compressor need not preserve the input buffer if it
     * compresses the data successfully */
    bool destructive;

    /* Pointer to the compress() implementation chosen at allocation time */
    void (*impl)(struct lzx_compressor *, const u8 *, size_t,
             struct lzx_output_bitstream *);

    /* The log base 2 of the window size for match offset encoding purposes.
     * This will be >= LZX_MIN_WINDOW_ORDER and <= LZX_MAX_WINDOW_ORDER. */
    unsigned window_order;

    /* The number of symbols in the main alphabet.  This depends on the
     * window order, since the window order determines the maximum possible
     * match offset. */
    unsigned num_main_syms;

    /* The "nice" match length: if a match of this length is found, then it
     * is chosen immediately without further consideration. */
    unsigned nice_match_length;

    /* The maximum search depth: at most this many potential matches are
     * considered at each position. */
    unsigned max_search_depth;

    /* The number of optimization passes per block */
    unsigned num_optim_passes;

    /* The symbol frequency counters for the current block */
    struct lzx_freqs freqs;

    /* Block split statistics for the current block */
    struct lzx_block_split_stats split_stats;

    /* The Huffman codes for the current and previous blocks.  The one with
     * index 'codes_index' is for the current block, and the other one is
     * for the previous block. */
    struct lzx_codes codes[2];
    unsigned codes_index;

    /* The matches and literals that the compressor has chosen for the
     * current block.  The required length of this array is limited by the
     * maximum number of matches that can ever be chosen for a single block,
     * plus one for the special entry at the end. */
    struct lzx_sequence chosen_sequences[
               DIV_ROUND_UP(SOFT_MAX_BLOCK_SIZE, LZX_MIN_MATCH_LEN) + 1];

    /* Tables for mapping adjusted offsets to offset slots */
    u8 offset_slot_tab_1[32768]; /* offset slots [0, 29] */
    u8 offset_slot_tab_2[128]; /* offset slots [30, 49] */

    union {
        /* Data for lzx_compress_lazy() */
        struct {
            /* Hash chains matchfinder (MUST BE LAST!!!) */
            union {
                struct hc_matchfinder_16 hc_mf_16;
                struct hc_matchfinder_32 hc_mf_32;
            };
        };

        /* Data for lzx_compress_near_optimal() */
        struct {
            /*
             * Array of nodes, one per position, for running the
             * minimum-cost path algorithm.
             *
             * This array must be large enough to accommodate the
             * worst-case number of nodes, which occurs if the
             * compressor finds a match of length LZX_MAX_MATCH_LEN
             * at position 'SOFT_MAX_BLOCK_SIZE - 1', producing a
             * block of size 'SOFT_MAX_BLOCK_SIZE - 1 +
             * LZX_MAX_MATCH_LEN'.  Add one for the end-of-block
             * node.
             */
            struct lzx_optimum_node optimum_nodes[
                            SOFT_MAX_BLOCK_SIZE - 1 +
                            LZX_MAX_MATCH_LEN + 1];

            /* The cost model for the current optimization pass */
            struct lzx_costs costs;

            /*
             * Cached matches for the current block.  This array
             * contains the matches that were found at each position
             * in the block.  Specifically, for each position, there
             * is a special 'struct lz_match' whose 'length' field
             * contains the number of matches that were found at
             * that position; this is followed by the matches
             * themselves, if any, sorted by strictly increasing
             * length.
             *
             * Note: in rare cases, there will be a very high number
             * of matches in the block and this array will overflow.
             * If this happens, we force the end of the current
             * block.  CACHE_LENGTH is the length at which we
             * actually check for overflow.  The extra slots beyond
             * this are enough to absorb the worst case overflow,
             * which occurs if starting at &match_cache[CACHE_LENGTH
             * - 1], we write the match count header, then write
             * MAX_MATCHES_PER_POS matches, then skip searching for
             * matches at 'LZX_MAX_MATCH_LEN - 1' positions and
             * write the match count header for each.
             */
            struct lz_match match_cache[CACHE_LENGTH +
                            MAX_MATCHES_PER_POS +
                            LZX_MAX_MATCH_LEN - 1];

            /* Binary trees matchfinder (MUST BE LAST!!!) */
            union {
                struct bt_matchfinder_16 bt_mf_16;
                struct bt_matchfinder_32 bt_mf_32;
            };
        };
    };
};

/******************************************************************************/
/*                            Matchfinder utilities                           */
/*----------------------------------------------------------------------------*/

/*
 * Will a matchfinder using 16-bit positions be sufficient for compressing
 * buffers of up to the specified size?  The limit could be 65536 bytes, but we
 * also want to optimize out the use of offset_slot_tab_2 in the 16-bit case.
 * This requires that the limit be no more than the length of offset_slot_tab_1
 * (currently 32768).
 */
static forceinline bool
lzx_is_16_bit(size_t max_bufsize)
{
    STATIC_ASSERT(ARRAY_LEN(((struct lzx_compressor *)0)->offset_slot_tab_1) == 32768);
    return max_bufsize <= 32768;
}

/*
 * Return the offset slot for the specified adjusted match offset.
 */
static forceinline unsigned
lzx_get_offset_slot(struct lzx_compressor *c, u32 adjusted_offset,
            bool is_16_bit)
{
    if (__builtin_constant_p(adjusted_offset) &&
        adjusted_offset < LZX_NUM_RECENT_OFFSETS)
        return adjusted_offset;
    if (is_16_bit || adjusted_offset < ARRAY_LEN(c->offset_slot_tab_1))
        return c->offset_slot_tab_1[adjusted_offset];
    return c->offset_slot_tab_2[adjusted_offset >> 14];
}

/*
 * For a match that has the specified length and adjusted offset, tally its main
 * symbol, and if needed its length symbol; then return its main symbol.
 */
static forceinline unsigned
lzx_tally_main_and_lensyms(struct lzx_compressor *c, unsigned length,
               u32 adjusted_offset, bool is_16_bit)
{
    unsigned mainsym;

    if (length >= LZX_MIN_SECONDARY_LEN) {
        /* Length symbol needed */
        c->freqs.len[length - LZX_MIN_SECONDARY_LEN]++;
        mainsym = LZX_NUM_CHARS + LZX_NUM_PRIMARY_LENS;
    } else {
        /* No length symbol needed */
        mainsym = LZX_NUM_CHARS + length - LZX_MIN_MATCH_LEN;
    }

    mainsym += LZX_NUM_LEN_HEADERS *
           lzx_get_offset_slot(c, adjusted_offset, is_16_bit);
    c->freqs.main[mainsym]++;
    return mainsym;
}

/*
 * The following macros call either the 16-bit or the 32-bit version of a
 * matchfinder function based on the value of 'is_16_bit', which will be known
 * at compilation time.
 */

#define CALL_HC_MF(is_16_bit, c, funcname, ...)                   \
    ((is_16_bit) ? CONCAT(funcname, _16)(&(c)->hc_mf_16, ##__VA_ARGS__) : \
               CONCAT(funcname, _32)(&(c)->hc_mf_32, ##__VA_ARGS__));

#define CALL_BT_MF(is_16_bit, c, funcname, ...)                   \
    ((is_16_bit) ? CONCAT(funcname, _16)(&(c)->bt_mf_16, ##__VA_ARGS__) : \
               CONCAT(funcname, _32)(&(c)->bt_mf_32, ##__VA_ARGS__));

/******************************************************************************/
/*                             Output bitstream                               */
/*----------------------------------------------------------------------------*/

/*
 * The LZX bitstream is encoded as a sequence of little endian 16-bit coding
 * units.  Bits are ordered from most significant to least significant within
 * each coding unit.
 */

/*
 * Structure to keep track of the current state of sending bits to the
 * compressed output buffer.
 */
struct lzx_output_bitstream {

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

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

    /* Pointer to the start of the output buffer */
    u8 *start;

    /* Pointer to the position in the output buffer at which the next coding
     * unit should be written */
    u8 *next;

    /* Pointer to just past the end of the output buffer, rounded down by
     * one byte if needed to make 'end - start' a multiple of 2 */
    u8 *end;
};

/* Can the specified number of bits always be added to 'bitbuf' after all
 * pending 16-bit coding units have been flushed?  */
#define CAN_BUFFER(n)   ((n) <= WORDBITS - 15)

/* Initialize the output bitstream to write to the specified buffer. */
static void
lzx_init_output(struct lzx_output_bitstream *os, void *buffer, size_t size)
{
    os->bitbuf = 0;
    os->bitcount = 0;
    os->start = buffer;
    os->next = buffer;
    os->end = (u8 *)buffer + (size & ~1);
}

/*
 * Add some bits to the bitbuffer variable of the output bitstream.  The caller
 * must make sure there is enough room.
 */
static forceinline void
lzx_add_bits(struct lzx_output_bitstream *os, u32 bits, unsigned num_bits)
{
    os->bitbuf = (os->bitbuf << num_bits) | bits;
    os->bitcount += num_bits;
}

/*
 * Flush bits from the bitbuffer variable to the output buffer.  'max_num_bits'
 * specifies the maximum number of bits that may have been added since the last
 * flush.
 */
static forceinline void
lzx_flush_bits(struct lzx_output_bitstream *os, unsigned max_num_bits)
{
    /* Masking the number of bits to shift is only needed to avoid undefined
     * behavior; we don't actually care about the results of bad shifts.  On
     * x86, the explicit masking generates no extra code.  */
    const u32 shift_mask = WORDBITS - 1;

    if (os->end - os->next < 6)
        return;
    put_unaligned_le16(os->bitbuf >> ((os->bitcount - 16) &
                        shift_mask), os->next + 0);
    if (max_num_bits > 16)
        put_unaligned_le16(os->bitbuf >> ((os->bitcount - 32) &
                        shift_mask), os->next + 2);
    if (max_num_bits > 32)
        put_unaligned_le16(os->bitbuf >> ((os->bitcount - 48) &
                        shift_mask), os->next + 4);
    os->next += (os->bitcount >> 4) << 1;
    os->bitcount &= 15;
}

/* Add at most 16 bits to the bitbuffer and flush it.  */
static forceinline void
lzx_write_bits(struct lzx_output_bitstream *os, u32 bits, unsigned num_bits)
{
    lzx_add_bits(os, bits, num_bits);
    lzx_flush_bits(os, 16);
}

/*
 * Flush the last coding unit to the output buffer if needed.  Return the total
 * number of bytes written to the output buffer, or 0 if an overflow occurred.
 */
static size_t
lzx_flush_output(struct lzx_output_bitstream *os)
{
    if (os->end - os->next < 6)
        return 0;

    if (os->bitcount != 0) {
        put_unaligned_le16(os->bitbuf << (16 - os->bitcount), os->next);
        os->next += 2;
    }

    return os->next - os->start;
}

/******************************************************************************/
/*                           Preparing Huffman codes                          */
/*----------------------------------------------------------------------------*/

/*
 * Build the Huffman codes.  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_build_huffman_codes(struct lzx_compressor *c)
{
    const struct lzx_freqs *freqs = &c->freqs;
    struct lzx_codes *codes = &c->codes[c->codes_index];

    STATIC_ASSERT(MAIN_CODEWORD_LIMIT >= 9 &&
              MAIN_CODEWORD_LIMIT <= LZX_MAX_MAIN_CODEWORD_LEN);
    make_canonical_huffman_code(c->num_main_syms,
                    MAIN_CODEWORD_LIMIT,
                    freqs->main,
                    codes->lens.main,
                    codes->codewords.main);

    STATIC_ASSERT(LENGTH_CODEWORD_LIMIT >= 8 &&
              LENGTH_CODEWORD_LIMIT <= LZX_MAX_LEN_CODEWORD_LEN);
    make_canonical_huffman_code(LZX_LENCODE_NUM_SYMBOLS,
                    LENGTH_CODEWORD_LIMIT,
                    freqs->len,
                    codes->lens.len,
                    codes->codewords.len);

    STATIC_ASSERT(ALIGNED_CODEWORD_LIMIT >= LZX_NUM_ALIGNED_OFFSET_BITS &&
              ALIGNED_CODEWORD_LIMIT <= LZX_MAX_ALIGNED_CODEWORD_LEN);
    make_canonical_huffman_code(LZX_ALIGNEDCODE_NUM_SYMBOLS,
                    ALIGNED_CODEWORD_LIMIT,
                    freqs->aligned,
                    codes->lens.aligned,
                    codes->codewords.aligned);
}

/* Reset the symbol frequencies for the current block. */
static void
lzx_reset_symbol_frequencies(struct lzx_compressor *c)
{
    memset(&c->freqs, 0, sizeof(c->freqs));
}

static unsigned
lzx_compute_precode_items(const u8 lens[],
              const u8 prev_lens[],
              u32 precode_freqs[],
              unsigned precode_items[])
{
    unsigned *itemptr;
    unsigned run_start;
    unsigned run_end;
    unsigned extra_bits;
    int delta;
    u8 len;

    itemptr = precode_items;
    run_start = 0;

    while (!((len = lens[run_start]) & 0x80)) {

        /* len = the length being repeated  */

        /* Find the next run of codeword lengths.  */

        run_end = run_start + 1;

        /* Fast case for a single length.  */
        if (likely(len != lens[run_end])) {
            delta = prev_lens[run_start] - len;
            if (delta < 0)
                delta += 17;
            precode_freqs[delta]++;
            *itemptr++ = delta;
            run_start++;
            continue;
        }

        /* Extend the run.  */
        do {
            run_end++;
        } while (len == lens[run_end]);

        if (len == 0) {
            /* Run of zeroes.  */

            /* Symbol 18: RLE 20 to 51 zeroes at a time.  */
            while ((run_end - run_start) >= 20) {
                extra_bits = min((run_end - run_start) - 20, 0x1F);
                precode_freqs[18]++;
                *itemptr++ = 18 | (extra_bits << 5);
                run_start += 20 + extra_bits;
            }

            /* Symbol 17: RLE 4 to 19 zeroes at a time.  */
            if ((run_end - run_start) >= 4) {
                extra_bits = min((run_end - run_start) - 4, 0xF);
                precode_freqs[17]++;
                *itemptr++ = 17 | (extra_bits << 5);
                run_start += 4 + extra_bits;
            }
        } else {

            /* A run of nonzero lengths. */

            /* Symbol 19: RLE 4 to 5 of any length at a time.  */
            while ((run_end - run_start) >= 4) {
                extra_bits = (run_end - run_start) > 4;
                delta = prev_lens[run_start] - len;
                if (delta < 0)
                    delta += 17;
                precode_freqs[19]++;
                precode_freqs[delta]++;
                *itemptr++ = 19 | (extra_bits << 5) | (delta << 6);
                run_start += 4 + extra_bits;
            }
        }

        /* Output any remaining lengths without RLE.  */
        while (run_start != run_end) {
            delta = prev_lens[run_start] - len;
            if (delta < 0)
                delta += 17;
            precode_freqs[delta]++;
            *itemptr++ = delta;
            run_start++;
        }
    }

    return itemptr - precode_items;
}

/******************************************************************************/
/*                          Outputting compressed data                        */
/*----------------------------------------------------------------------------*/

/*
 * Output a Huffman code in the compressed form used in LZX.
 *
 * The Huffman code is represented in the output as a logical series of codeword
 * lengths from which the Huffman code, which must be in canonical form, can be
 * reconstructed.
 *
 * The codeword lengths are themselves compressed using a separate Huffman code,
 * the "precode", which contains a symbol for each possible codeword length in
 * the larger code as well as several special symbols to represent repeated
 * codeword lengths (a form of run-length encoding).  The precode is itself
 * constructed in canonical form, and its codeword lengths are represented
 * literally in 20 4-bit fields that immediately precede the compressed codeword
 * lengths of the larger code.
 *
 * Furthermore, the codeword lengths of the larger code are actually represented
 * as deltas from the codeword lengths of the corresponding code in the previous
 * block.
 *
 * @os:
 *  Bitstream to which to write the compressed Huffman code.
 * @lens:
 *  The codeword lengths, indexed by symbol, in the Huffman code.
 * @prev_lens:
 *  The codeword lengths, indexed by symbol, in the corresponding Huffman
 *  code in the previous block, or all zeroes if this is the first block.
 * @num_lens:
 *  The number of symbols in the Huffman code.
 */
static void
lzx_write_compressed_code(struct lzx_output_bitstream *os,
              const u8 lens[],
              const u8 prev_lens[],
              unsigned num_lens)
{
    u32 precode_freqs[LZX_PRECODE_NUM_SYMBOLS];
    u8 precode_lens[LZX_PRECODE_NUM_SYMBOLS];
    u32 precode_codewords[LZX_PRECODE_NUM_SYMBOLS];
    unsigned precode_items[num_lens];
    unsigned num_precode_items;
    unsigned precode_item;
    unsigned precode_sym;
    unsigned i;
    u8 saved = lens[num_lens];
    *(u8 *)(lens + num_lens) = 0x80;

    for (i = 0; i < LZX_PRECODE_NUM_SYMBOLS; i++)
        precode_freqs[i] = 0;

    /* Compute the "items" (RLE / literal tokens and extra bits) with which
     * the codeword lengths in the larger code will be output.  */
    num_precode_items = lzx_compute_precode_items(lens,
                              prev_lens,
                              precode_freqs,
                              precode_items);

    /* Build the precode.  */
    STATIC_ASSERT(PRE_CODEWORD_LIMIT >= 5 &&
              PRE_CODEWORD_LIMIT <= LZX_MAX_PRE_CODEWORD_LEN);
    make_canonical_huffman_code(LZX_PRECODE_NUM_SYMBOLS, PRE_CODEWORD_LIMIT,
                    precode_freqs, precode_lens,
                    precode_codewords);

    /* Output the lengths of the codewords in the precode.  */
    for (i = 0; i < LZX_PRECODE_NUM_SYMBOLS; i++)
        lzx_write_bits(os, precode_lens[i], LZX_PRECODE_ELEMENT_SIZE);

    /* Output the encoded lengths of the codewords in the larger code.  */
    for (i = 0; i < num_precode_items; i++) {
        precode_item = precode_items[i];
        precode_sym = precode_item & 0x1F;
        lzx_add_bits(os, precode_codewords[precode_sym],
                 precode_lens[precode_sym]);
        if (precode_sym >= 17) {
            if (precode_sym == 17) {
                lzx_add_bits(os, precode_item >> 5, 4);
            } else if (precode_sym == 18) {
                lzx_add_bits(os, precode_item >> 5, 5);
            } else {
                lzx_add_bits(os, (precode_item >> 5) & 1, 1);
                precode_sym = precode_item >> 6;
                lzx_add_bits(os, precode_codewords[precode_sym],
                         precode_lens[precode_sym]);
            }
        }
        STATIC_ASSERT(CAN_BUFFER(2 * PRE_CODEWORD_LIMIT + 1));
        lzx_flush_bits(os, 2 * PRE_CODEWORD_LIMIT + 1);
    }

    *(u8 *)(lens + num_lens) = saved;
}

/*
 * Write all matches and literal bytes (which were precomputed) in an LZX
 * compressed block to the output bitstream in the final compressed
 * representation.
 *
 * @os
 *  The output bitstream.
 * @block_type
 *  The chosen type of the LZX compressed block (LZX_BLOCKTYPE_ALIGNED or
 *  LZX_BLOCKTYPE_VERBATIM).
 * @block_data
 *  The uncompressed data of the block.
 * @sequences
 *  The matches and literals to output, given as a series of sequences.
 * @codes
 *  The main, length, and aligned offset Huffman codes for the block.
 */
static void
lzx_write_sequences(struct lzx_output_bitstream *os, int block_type,
            const u8 *block_data, const struct lzx_sequence sequences[],
            const struct lzx_codes *codes)
{
    const struct lzx_sequence *seq = sequences;
    unsigned min_aligned_offset_slot;

    if (block_type == LZX_BLOCKTYPE_ALIGNED)
        min_aligned_offset_slot = LZX_MIN_ALIGNED_OFFSET_SLOT;
    else
        min_aligned_offset_slot = LZX_MAX_OFFSET_SLOTS;

    for (;;) {
        /* Output the next sequence.  */

        u32 litrunlen = seq->litrunlen_and_matchlen >> SEQ_MATCHLEN_BITS;
        unsigned matchlen = seq->litrunlen_and_matchlen & SEQ_MATCHLEN_MASK;
        STATIC_ASSERT((u32)~SEQ_MATCHLEN_MASK >> SEQ_MATCHLEN_BITS >=
                  SOFT_MAX_BLOCK_SIZE);
        u32 adjusted_offset;
        unsigned main_symbol;
        unsigned offset_slot;
        unsigned num_extra_bits;
        u32 extra_bits;

        /* Output the literal run of the sequence.  */

        if (litrunlen) {  /* Is the literal run nonempty?  */

            /* Verify optimization is enabled on 64-bit  */
            STATIC_ASSERT(WORDBITS < 64 ||
                      CAN_BUFFER(3 * MAIN_CODEWORD_LIMIT));

            if (CAN_BUFFER(3 * MAIN_CODEWORD_LIMIT)) {

                /* 64-bit: write 3 literals at a time.  */
                while (litrunlen >= 3) {
                    unsigned lit0 = block_data[0];
                    unsigned lit1 = block_data[1];
                    unsigned lit2 = block_data[2];
                    lzx_add_bits(os, codes->codewords.main[lit0],
                             codes->lens.main[lit0]);
                    lzx_add_bits(os, codes->codewords.main[lit1],
                             codes->lens.main[lit1]);
                    lzx_add_bits(os, codes->codewords.main[lit2],
                             codes->lens.main[lit2]);
                    lzx_flush_bits(os, 3 * MAIN_CODEWORD_LIMIT);
                    block_data += 3;
                    litrunlen -= 3;
                }
                if (litrunlen--) {
                    unsigned lit = *block_data++;
                    lzx_add_bits(os, codes->codewords.main[lit],
                             codes->lens.main[lit]);
                    if (litrunlen--) {
                        unsigned lit = *block_data++;
                        lzx_add_bits(os, codes->codewords.main[lit],
                                 codes->lens.main[lit]);
                        lzx_flush_bits(os, 2 * MAIN_CODEWORD_LIMIT);
                    } else {
                        lzx_flush_bits(os, 1 * MAIN_CODEWORD_LIMIT);
                    }
                }
            } else {
                /* 32-bit: write 1 literal at a time.  */
                do {
                    unsigned lit = *block_data++;
                    lzx_add_bits(os, codes->codewords.main[lit],
                             codes->lens.main[lit]);
                    lzx_flush_bits(os, MAIN_CODEWORD_LIMIT);
                } while (--litrunlen);
            }
        }

        /* Was this the last literal run?  */
        if (matchlen == 0)
            return;

        /* Nope; output the match.  */

        block_data += matchlen;

        adjusted_offset = seq->adjusted_offset_and_mainsym >> SEQ_MAINSYM_BITS;
        main_symbol = seq->adjusted_offset_and_mainsym & SEQ_MAINSYM_MASK;

        offset_slot = (main_symbol - LZX_NUM_CHARS) / LZX_NUM_LEN_HEADERS;
        num_extra_bits = lzx_extra_offset_bits[offset_slot];
        extra_bits = adjusted_offset - (lzx_offset_slot_base[offset_slot] +
                        LZX_OFFSET_ADJUSTMENT);

    #define MAX_MATCH_BITS (MAIN_CODEWORD_LIMIT +       \
                LENGTH_CODEWORD_LIMIT +     \
                LZX_MAX_NUM_EXTRA_BITS -    \
                LZX_NUM_ALIGNED_OFFSET_BITS +   \
                ALIGNED_CODEWORD_LIMIT)

        /* Verify optimization is enabled on 64-bit  */
        STATIC_ASSERT(WORDBITS < 64 || CAN_BUFFER(MAX_MATCH_BITS));

        /* Output the main symbol for the match.  */

        lzx_add_bits(os, codes->codewords.main[main_symbol],
                 codes->lens.main[main_symbol]);
        if (!CAN_BUFFER(MAX_MATCH_BITS))
            lzx_flush_bits(os, MAIN_CODEWORD_LIMIT);

        /* If needed, output the length symbol for the match.  */

        if (matchlen >= LZX_MIN_SECONDARY_LEN) {
            lzx_add_bits(os, codes->codewords.len[matchlen -
                                  LZX_MIN_SECONDARY_LEN],
                     codes->lens.len[matchlen -
                             LZX_MIN_SECONDARY_LEN]);
            if (!CAN_BUFFER(MAX_MATCH_BITS))
                lzx_flush_bits(os, LENGTH_CODEWORD_LIMIT);
        }

        /* Output the extra offset bits for the match.  In aligned
         * offset blocks, the lowest 3 bits of the adjusted offset are
         * Huffman-encoded using the aligned offset code, provided that
         * there are at least extra 3 offset bits required.  All other
         * extra offset bits are output verbatim.  */

        if (offset_slot >= min_aligned_offset_slot) {

            lzx_add_bits(os, extra_bits >> LZX_NUM_ALIGNED_OFFSET_BITS,
                     num_extra_bits - LZX_NUM_ALIGNED_OFFSET_BITS);
            if (!CAN_BUFFER(MAX_MATCH_BITS))
                lzx_flush_bits(os, LZX_MAX_NUM_EXTRA_BITS -
                           LZX_NUM_ALIGNED_OFFSET_BITS);

            lzx_add_bits(os, codes->codewords.aligned[adjusted_offset &
                                  LZX_ALIGNED_OFFSET_BITMASK],
                     codes->lens.aligned[adjusted_offset &
                             LZX_ALIGNED_OFFSET_BITMASK]);
            if (!CAN_BUFFER(MAX_MATCH_BITS))
                lzx_flush_bits(os, ALIGNED_CODEWORD_LIMIT);
        } else {
            STATIC_ASSERT(CAN_BUFFER(LZX_MAX_NUM_EXTRA_BITS));

            lzx_add_bits(os, extra_bits, num_extra_bits);
            if (!CAN_BUFFER(MAX_MATCH_BITS))
                lzx_flush_bits(os, LZX_MAX_NUM_EXTRA_BITS);
        }

        if (CAN_BUFFER(MAX_MATCH_BITS))
            lzx_flush_bits(os, MAX_MATCH_BITS);

        /* Advance to the next sequence.  */
        seq++;
    }
}

static void
lzx_write_compressed_block(const u8 *block_begin,
               int block_type,
               u32 block_size,
               unsigned window_order,
               unsigned num_main_syms,
               const struct lzx_sequence sequences[],
               const struct lzx_codes * codes,
               const struct lzx_lens * prev_lens,
               struct lzx_output_bitstream * os)
{
    /* The first three bits indicate the type of block and are one of the
     * LZX_BLOCKTYPE_* constants.  */
    lzx_write_bits(os, block_type, 3);

    /*
     * Output the block size.
     *
     * The original LZX format encoded the block size in 24 bits.  However,
     * the LZX format used in WIM archives uses 1 bit to specify whether the
     * block has the default size of 32768 bytes, then optionally 16 bits to
     * specify a non-default size.  This works fine for Microsoft's WIM
     * software (WIMGAPI), which never compresses more than 32768 bytes at a
     * time with LZX.  However, as an extension, our LZX compressor supports
     * compressing up to 2097152 bytes, with a corresponding increase in
     * window size.  It is possible for blocks in these larger buffers to
     * exceed 65535 bytes; such blocks cannot have their size represented in
     * 16 bits.
     *
     * The chosen solution was to use 24 bits for the block size when
     * possibly required --- specifically, when the compressor has been
     * allocated to be capable of compressing more than 32768 bytes at once
     * (which also causes the number of main symbols to be increased).
     */
    if (block_size == LZX_DEFAULT_BLOCK_SIZE) {
        lzx_write_bits(os, 1, 1);
    } else {
        lzx_write_bits(os, 0, 1);

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

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

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

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

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

    /* Output the compressed matches and literals.  */
    lzx_write_sequences(os, block_type, block_begin, sequences, codes);
}

/*
 * Given the frequencies of symbols in an LZX-compressed block and the
 * corresponding Huffman codes, return LZX_BLOCKTYPE_ALIGNED or
 * LZX_BLOCKTYPE_VERBATIM if an aligned offset or verbatim block, respectively,
 * will take fewer bits to output.
 */
static int
lzx_choose_verbatim_or_aligned(const struct lzx_freqs * freqs,
                   const struct lzx_codes * codes)
{
    u32 verbatim_cost = 0;
    u32 aligned_cost = 0;

    /* A verbatim block requires 3 bits in each place that an aligned offset
     * symbol would be used in an aligned offset block.  */
    for (unsigned i = 0; i < LZX_ALIGNEDCODE_NUM_SYMBOLS; i++) {
        verbatim_cost += LZX_NUM_ALIGNED_OFFSET_BITS * freqs->aligned[i];
        aligned_cost += codes->lens.aligned[i] * freqs->aligned[i];
    }

    /* Account for the cost of sending the codeword lengths of the aligned
     * offset code.  */
    aligned_cost += LZX_ALIGNEDCODE_ELEMENT_SIZE *
            LZX_ALIGNEDCODE_NUM_SYMBOLS;

    if (aligned_cost < verbatim_cost)
        return LZX_BLOCKTYPE_ALIGNED;
    else
        return LZX_BLOCKTYPE_VERBATIM;
}

/*
 * Flush an LZX block:
 *
 * 1. Build the Huffman codes.
 * 2. Decide whether to output the block as VERBATIM or ALIGNED.
 * 3. Write the block.
 * 4. Swap the indices of the current and previous Huffman codes.
 *
 * Note: we never output UNCOMPRESSED blocks.  This probably should be
 * implemented sometime, but it doesn't make much difference.
 */
static void
lzx_flush_block(struct lzx_compressor *c, struct lzx_output_bitstream *os,
        const u8 *block_begin, u32 block_size, u32 seq_idx)
{
    int block_type;

    lzx_build_huffman_codes(c);

    block_type = lzx_choose_verbatim_or_aligned(&c->freqs,
                            &c->codes[c->codes_index]);
    lzx_write_compressed_block(block_begin,
                   block_type,
                   block_size,
                   c->window_order,
                   c->num_main_syms,
                   &c->chosen_sequences[seq_idx],
                   &c->codes[c->codes_index],
                   &c->codes[c->codes_index ^ 1].lens,
                   os);
    c->codes_index ^= 1;
}

/******************************************************************************/
/*                          Block splitting algorithm                         */
/*----------------------------------------------------------------------------*/

/*
 * The problem of block splitting is to decide when it is worthwhile to start a
 * new block with new entropy codes.  There is a theoretically optimal solution:
 * recursively consider every possible block split, considering the exact cost
 * of each block, and choose the minimum cost approach.  But this is far too
 * slow.  Instead, as an approximation, we can count symbols and after every N
 * symbols, compare the expected distribution of symbols based on the previous
 * data with the actual distribution.  If they differ "by enough", then start a
 * new block.
 *
 * As an optimization and heuristic, we don't distinguish between every symbol
 * but rather we combine many symbols into a single "observation type".  For
 * literals we only look at the high bits and low bits, and for matches we only
 * look at whether the match is long or not.  The assumption is that for typical
 * "real" data, places that are good block boundaries will tend to be noticable
 * based only on changes in these aggregate frequencies, without looking for
 * subtle differences in individual symbols.  For example, a change from ASCII
 * bytes to non-ASCII bytes, or from few matches (generally less compressible)
 * to many matches (generally more compressible), would be easily noticed based
 * on the aggregates.
 *
 * For determining whether the frequency distributions are "different enough" to
 * start a new block, the simply heuristic of splitting when the sum of absolute
 * differences exceeds a constant seems to be good enough.
 *
 * Finally, for an approximation, it is not strictly necessary that the exact
 * symbols being used are considered.  With "near-optimal parsing", for example,
 * the actual symbols that will be used are unknown until after the block
 * boundary is chosen and the block has been optimized.  Since the final choices
 * cannot be used, we can use preliminary "greedy" choices instead.
 */

/* Initialize the block split statistics when starting a new block. */
static void
lzx_init_block_split_stats(struct lzx_block_split_stats *stats)
{
    memset(stats, 0, sizeof(*stats));
}

/* Literal observation.  Heuristic: use the top 2 bits and low 1 bits of the
 * literal, for 8 possible literal observation types.  */
static forceinline void
lzx_observe_literal(struct lzx_block_split_stats *stats, u8 lit)
{
    stats->new_observations[((lit >> 5) & 0x6) | (lit & 1)]++;
    stats->num_new_observations++;
}

/* Match observation.  Heuristic: use one observation type for "short match" and
 * one observation type for "long match".  */
static forceinline void
lzx_observe_match(struct lzx_block_split_stats *stats, unsigned length)
{
    stats->new_observations[NUM_LITERAL_OBSERVATION_TYPES + (length >= 5)]++;
    stats->num_new_observations++;
}

static bool
lzx_should_end_block(struct lzx_block_split_stats *stats)
{
    if (stats->num_observations > 0) {

        /* Note: to avoid slow divisions, we do not divide by
         * 'num_observations', but rather do all math with the numbers
         * multiplied by 'num_observations'. */
        u32 total_delta = 0;
        for (int i = 0; i < NUM_OBSERVATION_TYPES; i++) {
            u32 expected = stats->observations[i] *
                       stats->num_new_observations;
            u32 actual = stats->new_observations[i] *
                     stats->num_observations;
            u32 delta = (actual > expected) ? actual - expected :
                              expected - actual;
            total_delta += delta;
        }

        /* Ready to end the block? */
        if (total_delta >=
            stats->num_new_observations * 7 / 8 * stats->num_observations)
            return true;
    }

    for (int i = 0; i < NUM_OBSERVATION_TYPES; i++) {
        stats->num_observations += stats->new_observations[i];
        stats->observations[i] += stats->new_observations[i];
        stats->new_observations[i] = 0;
    }
    stats->num_new_observations = 0;
    return false;
}

/******************************************************************************/
/*                   Slower ("near-optimal") compression algorithm            */
/*----------------------------------------------------------------------------*/

/*
 * Least-recently-used queue for match offsets.
 *
 * This is represented as a 64-bit integer for efficiency.  There are three
 * offsets of 21 bits each.  Bit 64 is garbage.
 */
struct lzx_lru_queue {
    u64 R;
} _aligned_attribute(8);

#define LZX_QUEUE_OFFSET_SHIFT  21
#define LZX_QUEUE_OFFSET_MASK   (((u64)1 << LZX_QUEUE_OFFSET_SHIFT) - 1)

#define LZX_QUEUE_R0_SHIFT (0 * LZX_QUEUE_OFFSET_SHIFT)
#define LZX_QUEUE_R1_SHIFT (1 * LZX_QUEUE_OFFSET_SHIFT)
#define LZX_QUEUE_R2_SHIFT (2 * LZX_QUEUE_OFFSET_SHIFT)

#define LZX_QUEUE_R0_MASK (LZX_QUEUE_OFFSET_MASK << LZX_QUEUE_R0_SHIFT)
#define LZX_QUEUE_R1_MASK (LZX_QUEUE_OFFSET_MASK << LZX_QUEUE_R1_SHIFT)
#define LZX_QUEUE_R2_MASK (LZX_QUEUE_OFFSET_MASK << LZX_QUEUE_R2_SHIFT)

#define LZX_QUEUE_INITIALIZER {         \
    ((u64)1 << LZX_QUEUE_R0_SHIFT) |    \
    ((u64)1 << LZX_QUEUE_R1_SHIFT) |    \
    ((u64)1 << LZX_QUEUE_R2_SHIFT) }

static forceinline u64
lzx_lru_queue_R0(struct lzx_lru_queue queue)
{
    return (queue.R >> LZX_QUEUE_R0_SHIFT) & LZX_QUEUE_OFFSET_MASK;
}

static forceinline u64
lzx_lru_queue_R1(struct lzx_lru_queue queue)
{
    return (queue.R >> LZX_QUEUE_R1_SHIFT) & LZX_QUEUE_OFFSET_MASK;
}

static forceinline u64
lzx_lru_queue_R2(struct lzx_lru_queue queue)
{
    return (queue.R >> LZX_QUEUE_R2_SHIFT) & LZX_QUEUE_OFFSET_MASK;
}

/* Push a match offset onto the front (most recently used) end of the queue.  */
static forceinline struct lzx_lru_queue
lzx_lru_queue_push(struct lzx_lru_queue queue, u32 offset)
{
    return (struct lzx_lru_queue) {
        .R = (queue.R << LZX_QUEUE_OFFSET_SHIFT) | offset,
    };
}

/* Swap a match offset to the front of the queue.  */
static forceinline struct lzx_lru_queue
lzx_lru_queue_swap(struct lzx_lru_queue queue, unsigned idx)
{
    unsigned shift = idx * 21;
    const u64 mask = LZX_QUEUE_R0_MASK;
    const u64 mask_high = mask << shift;

    return (struct lzx_lru_queue) {
        (queue.R & ~(mask | mask_high)) |
        ((queue.R & mask_high) >> shift) |
        ((queue.R & mask) << shift)
    };
}

static forceinline u32
lzx_walk_item_list(struct lzx_compressor *c, u32 block_size, bool is_16_bit,
           bool record)
{
    struct lzx_sequence *seq =
        &c->chosen_sequences[ARRAY_LEN(c->chosen_sequences) - 1];
    u32 node_idx = block_size;
    u32 litrun_end; /* if record=true: end of the current literal run */

    if (record) {
        /* The last sequence has matchlen 0 */
        seq->litrunlen_and_matchlen = 0;
        litrun_end = node_idx;
    }

    for (;;) {
        u32 item;
        unsigned matchlen;
        u32 adjusted_offset;
        unsigned mainsym;

        /* Tally literals until either a match or the beginning of the
         * block is reached.  Note: the item in the node at the
         * beginning of the block (c->optimum_nodes[0]) has all bits
         * set, causing this loop to end when it is reached. */
        for (;;) {
            item = c->optimum_nodes[node_idx].item;
            if (item & OPTIMUM_LEN_MASK)
                break;
            c->freqs.main[item >> OPTIMUM_OFFSET_SHIFT]++;
            node_idx--;
        }

    #if CONSIDER_GAP_MATCHES
        if (item & OPTIMUM_GAP_MATCH) {
            if (node_idx == 0)
                break;
            /* Tally/record the rep0 match after the gap. */
            matchlen = item & OPTIMUM_LEN_MASK;
            mainsym = lzx_tally_main_and_lensyms(c, matchlen, 0,
                                 is_16_bit);
            if (record) {
                seq->litrunlen_and_matchlen |=
                    (litrun_end - node_idx) <<
                     SEQ_MATCHLEN_BITS;
                seq--;
                seq->litrunlen_and_matchlen = matchlen;
                seq->adjusted_offset_and_mainsym = mainsym;
                litrun_end = node_idx - matchlen;
            }

            /* Tally the literal in the gap. */
            c->freqs.main[(u8)(item >> OPTIMUM_OFFSET_SHIFT)]++;

            /* Fall through and tally the match before the gap.
             * (It was temporarily saved in the 'cost' field of the
             * previous node, which was free to reuse.) */
            item = c->optimum_nodes[--node_idx].cost;
            node_idx -= matchlen;
        }
    #else /* CONSIDER_GAP_MATCHES */
        if (node_idx == 0)
            break;
    #endif /* !CONSIDER_GAP_MATCHES */

        /* Tally/record a match. */
        matchlen = item & OPTIMUM_LEN_MASK;
        adjusted_offset = item >> OPTIMUM_OFFSET_SHIFT;
        mainsym = lzx_tally_main_and_lensyms(c, matchlen,
                             adjusted_offset,
                             is_16_bit);
        if (adjusted_offset >= LZX_MIN_ALIGNED_OFFSET +
                       LZX_OFFSET_ADJUSTMENT)
            c->freqs.aligned[adjusted_offset &
                     LZX_ALIGNED_OFFSET_BITMASK]++;
        if (record) {
            seq->litrunlen_and_matchlen |=
                (litrun_end - node_idx) << SEQ_MATCHLEN_BITS;
            seq--;
            seq->litrunlen_and_matchlen = matchlen;
            seq->adjusted_offset_and_mainsym =
                (adjusted_offset << SEQ_MAINSYM_BITS) | mainsym;
            litrun_end = node_idx - matchlen;
        }
        node_idx -= matchlen;
    }

    /* Record the literal run length for the first sequence. */
    if (record) {
        seq->litrunlen_and_matchlen |=
            (litrun_end - node_idx) << SEQ_MATCHLEN_BITS;
    }

    /* Return the index in chosen_sequences at which the sequences begin. */
    return seq - &c->chosen_sequences[0];
}

/*
 * Given the minimum-cost path computed through the item graph for the current
 * block, walk the path and count how many of each symbol in each Huffman-coded
 * alphabet would be required to output the items (matches and literals) along
 * the path.
 *
 * Note that the path will be walked backwards (from the end of the block to the
 * beginning of the block), but this doesn't matter because this function only
 * computes frequencies.
 */
static forceinline void
lzx_tally_item_list(struct lzx_compressor *c, u32 block_size, bool is_16_bit)
{
    lzx_walk_item_list(c, block_size, is_16_bit, false);
}

/*
 * Like lzx_tally_item_list(), but this function also generates the list of
 * lzx_sequences for the minimum-cost path and writes it to c->chosen_sequences,
 * ready to be output to the bitstream after the Huffman codes are computed.
 * The lzx_sequences will be written to decreasing memory addresses as the path
 * is walked backwards, which means they will end up in the expected
 * first-to-last order.  The return value is the index in c->chosen_sequences at
 * which the lzx_sequences begin.
 */
static forceinline u32
lzx_record_item_list(struct lzx_compressor *c, u32 block_size, bool is_16_bit)
{
    return lzx_walk_item_list(c, block_size, is_16_bit, true);
}

/*
 * Find an inexpensive path through the graph of possible match/literal choices
 * for the current block.  The nodes of the graph are
 * c->optimum_nodes[0...block_size].  They correspond directly to the bytes in
 * the current block, plus one extra node for end-of-block.  The edges of the
 * graph are matches and literals.  The goal is to find the minimum cost path
 * from 'c->optimum_nodes[0]' to 'c->optimum_nodes[block_size]', given the cost
 * model 'c->costs'.
 *
 * The algorithm works forwards, starting at 'c->optimum_nodes[0]' and
 * proceeding forwards one node at a time.  At each node, a selection of matches
 * (len >= 2), as well as the literal byte (len = 1), is considered.  An item of
 * length 'len' provides a new path to reach the node 'len' bytes later.  If
 * such a path is the lowest cost found so far to reach that later node, then
 * that later node is updated with the new cost and the "arrival" which provided
 * that cost.
 *
 * Note that although this algorithm is based on minimum cost path search, due
 * to various simplifying assumptions the result is not guaranteed to be the
 * true minimum cost, or "optimal", path over the graph of all valid LZX
 * representations of this block.
 *
 * Also, note that because of the presence of the recent offsets queue (which is
 * a type of adaptive state), the algorithm cannot work backwards and compute
 * "cost to end" instead of "cost to beginning".  Furthermore, the way the
 * algorithm handles this adaptive state in the "minimum cost" parse is actually
 * only an approximation.  It's possible for the globally optimal, minimum cost
 * path to contain a prefix, ending at a position, where that path prefix is
 * *not* the minimum cost path to that position.  This can happen if such a path
 * prefix results in a different adaptive state which results in lower costs
 * later.  The algorithm does not solve this problem in general; it only looks
 * one step ahead, with the exception of special consideration for "gap
 * matches".
 */
static forceinline struct lzx_lru_queue
lzx_find_min_cost_path(struct lzx_compressor * const  c,
               const u8 * const  block_begin,
               const u32 block_size,
               const struct lzx_lru_queue initial_queue,
               bool is_16_bit)
{
    struct lzx_optimum_node *cur_node = c->optimum_nodes;
    struct lzx_optimum_node * const end_node = cur_node + block_size;
    struct lz_match *cache_ptr = c->match_cache;
    const u8 *in_next = block_begin;
    const u8 * const block_end = block_begin + block_size;

    /*
     * Instead of storing the match offset LRU queues in the
     * 'lzx_optimum_node' structures, we save memory (and cache lines) by
     * storing them in a smaller array.  This works because the algorithm
     * only requires a limited history of the adaptive state.  Once a given
     * state is more than LZX_MAX_MATCH_LEN bytes behind the current node
     * (more if gap match consideration is enabled; we just round up to 512
     * so it's a power of 2), it is no longer needed.
     *
     * The QUEUE() macro finds the queue for the given node.  This macro has
     * been optimized by taking advantage of 'struct lzx_lru_queue' and
     * 'struct lzx_optimum_node' both being 8 bytes in size and alignment.
     */
    struct lzx_lru_queue queues[512];
    STATIC_ASSERT(ARRAY_LEN(queues) >= LZX_MAX_MATCH_LEN + 1);
    STATIC_ASSERT(sizeof(c->optimum_nodes[0]) == sizeof(queues[0]));
#define QUEUE(node) \
    (*(struct lzx_lru_queue *)((char *)queues + \
            ((uintptr_t)(node) % (ARRAY_LEN(queues) * sizeof(queues[0])))))
    /*(queues[(uintptr_t)(node) / sizeof(*(node)) % ARRAY_LEN(queues)])*/

#if CONSIDER_GAP_MATCHES
    u32 matches_before_gap[ARRAY_LEN(queues)];
#define MATCH_BEFORE_GAP(node) \
    (matches_before_gap[(uintptr_t)(node) / sizeof(*(node)) % \
                ARRAY_LEN(matches_before_gap)])
#endif

    /*
     * Initially, the cost to reach each node is "infinity".
     *
     * The first node actually should have cost 0, but "infinity"
     * (0xFFFFFFFF) works just as well because it immediately overflows.
     *
     * The following statement also intentionally sets the 'item' of the
     * first node, which would otherwise have no meaning, to 0xFFFFFFFF for
     * use as a sentinel.  See lzx_walk_item_list().
     */
    memset(c->optimum_nodes, 0xFF,
           (block_size + 1) * sizeof(c->optimum_nodes[0]));

    /* Initialize the recent offsets queue for the first node. */
    QUEUE(cur_node) = initial_queue;

    do { /* For each node in the block in position order... */

        unsigned num_matches;
        unsigned literal;
        u32 cost;

        /*
         * A selection of matches for the block was already saved in
         * memory so that we don't have to run the uncompressed data
         * through the matchfinder on every optimization pass.  However,
         * we still search for repeat offset matches during each
         * optimization pass because we cannot predict the state of the
         * recent offsets queue.  But as a heuristic, we don't bother
         * searching for repeat offset matches if the general-purpose
         * matchfinder failed to find any matches.
         *
         * Note that a match of length n at some offset implies there is
         * also a match of length l for LZX_MIN_MATCH_LEN <= l <= n at
         * that same offset.  In other words, we don't necessarily need
         * to use the full length of a match.  The key heuristic that
         * saves a significicant amount of time is that for each
         * distinct length, we only consider the smallest offset for
         * which that length is available.  This heuristic also applies
         * to repeat offsets, which we order specially: R0 < R1 < R2 <
         * any explicit offset.  Of course, this heuristic may be
         * produce suboptimal results because offset slots in LZX are
         * subject to entropy encoding, but in practice this is a useful
         * heuristic.
         */

        num_matches = cache_ptr->length;
        cache_ptr++;

        if (num_matches) {
            struct lz_match *end_matches = cache_ptr + num_matches;
            unsigned next_len = LZX_MIN_MATCH_LEN;
            unsigned max_len = min(block_end - in_next, LZX_MAX_MATCH_LEN);
            const u8 *matchptr;

            /* Consider rep0 matches. */
            matchptr = in_next - lzx_lru_queue_R0(QUEUE(cur_node));
            if (load_u16_unaligned(matchptr) != load_u16_unaligned(in_next))
                goto rep0_done;
            STATIC_ASSERT(LZX_MIN_MATCH_LEN == 2);
            do {
                u32 cost = cur_node->cost +
                       c->costs.match_cost[0][
                            next_len - LZX_MIN_MATCH_LEN];
                if (cost <= (cur_node + next_len)->cost) {
                    (cur_node + next_len)->cost = cost;
                    (cur_node + next_len)->item =
                        (0 << OPTIMUM_OFFSET_SHIFT) | next_len;
                }
                if (unlikely(++next_len > max_len)) {
                    cache_ptr = end_matches;
                    goto done_matches;
                }
            } while (in_next[next_len - 1] == matchptr[next_len - 1]);

        rep0_done:

            /* Consider rep1 matches. */
            matchptr = in_next - lzx_lru_queue_R1(QUEUE(cur_node));
            if (load_u16_unaligned(matchptr) != load_u16_unaligned(in_next))
                goto rep1_done;
            if (matchptr[next_len - 1] != in_next[next_len - 1])
                goto rep1_done;
            for (unsigned len = 2; len < next_len - 1; len++)
                if (matchptr[len] != in_next[len])
                    goto rep1_done;
            do {
                u32 cost = cur_node->cost +
                       c->costs.match_cost[1][
                            next_len - LZX_MIN_MATCH_LEN];
                if (cost <= (cur_node + next_len)->cost) {
                    (cur_node + next_len)->cost = cost;
                    (cur_node + next_len)->item =
                        (1 << OPTIMUM_OFFSET_SHIFT) | next_len;
                }
                if (unlikely(++next_len > max_len)) {
                    cache_ptr = end_matches;
                    goto done_matches;
                }
            } while (in_next[next_len - 1] == matchptr[next_len - 1]);

        rep1_done:

            /* Consider rep2 matches. */
            matchptr = in_next - lzx_lru_queue_R2(QUEUE(cur_node));
            if (load_u16_unaligned(matchptr) != load_u16_unaligned(in_next))
                goto rep2_done;
            if (matchptr[next_len - 1] != in_next[next_len - 1])
                goto rep2_done;
            for (unsigned len = 2; len < next_len - 1; len++)
                if (matchptr[len] != in_next[len])
                    goto rep2_done;
            do {
                u32 cost = cur_node->cost +
                       c->costs.match_cost[2][
                            next_len - LZX_MIN_MATCH_LEN];
                if (cost <= (cur_node + next_len)->cost) {
                    (cur_node + next_len)->cost = cost;
                    (cur_node + next_len)->item =
                        (2 << OPTIMUM_OFFSET_SHIFT) | next_len;
                }
                if (unlikely(++next_len > max_len)) {
                    cache_ptr = end_matches;
                    goto done_matches;
                }
            } while (in_next[next_len - 1] == matchptr[next_len - 1]);

        rep2_done:

            while (next_len > cache_ptr->length)
                if (++cache_ptr == end_matches)
                    goto done_matches;

            /* Consider explicit offset matches. */
            for (;;) {
                u32 offset = cache_ptr->offset;
                u32 adjusted_offset = offset + LZX_OFFSET_ADJUSTMENT;
                unsigned offset_slot = lzx_get_offset_slot(c, adjusted_offset, is_16_bit);
                u32 base_cost = cur_node->cost;
                u32 cost;

            #if CONSIDER_ALIGNED_COSTS
                if (offset >= LZX_MIN_ALIGNED_OFFSET)
                    base_cost += c->costs.aligned[adjusted_offset &
                                      LZX_ALIGNED_OFFSET_BITMASK];
            #endif
                do {
                    cost = base_cost +
                           c->costs.match_cost[offset_slot][
                                next_len - LZX_MIN_MATCH_LEN];
                    if (cost < (cur_node + next_len)->cost) {
                        (cur_node + next_len)->cost = cost;
                        (cur_node + next_len)->item =
                            (adjusted_offset << OPTIMUM_OFFSET_SHIFT) | next_len;
                    }
                } while (++next_len <= cache_ptr->length);

                if (++cache_ptr == end_matches) {
                #if CONSIDER_GAP_MATCHES
                    /* Also consider the longest explicit
                     * offset match as a "gap match": match
                     * + lit + rep0. */
                    s32 remaining = (block_end - in_next) - (s32)next_len;
                    if (likely(remaining >= 2)) {
                        const u8 *strptr = in_next + next_len;
                        const u8 *matchptr = strptr - offset;
                        if (load_u16_unaligned(strptr) == load_u16_unaligned(matchptr)) {
                            STATIC_ASSERT(ARRAY_LEN(queues) - LZX_MAX_MATCH_LEN - 2 >= 250);
                            STATIC_ASSERT(ARRAY_LEN(queues) == ARRAY_LEN(matches_before_gap));
                            unsigned limit = min(remaining,
                                         min(ARRAY_LEN(queues) - LZX_MAX_MATCH_LEN - 2,
                                         LZX_MAX_MATCH_LEN));
                            unsigned rep0_len = lz_extend(strptr, matchptr, 2, limit);
                            u8 lit = strptr[-1];
                            cost += c->costs.main[lit] +
                                c->costs.match_cost[0][rep0_len - LZX_MIN_MATCH_LEN];
                            unsigned total_len = next_len + rep0_len;
                            if (cost < (cur_node + total_len)->cost) {
                                (cur_node + total_len)->cost = cost;
                                (cur_node + total_len)->item =
                                    OPTIMUM_GAP_MATCH |
                                    ((u32)lit << OPTIMUM_OFFSET_SHIFT) |
                                    rep0_len;
                                MATCH_BEFORE_GAP(cur_node + total_len) =
                                    (adjusted_offset << OPTIMUM_OFFSET_SHIFT) |
                                    (next_len - 1);
                            }
                        }
                    }
                #endif /* CONSIDER_GAP_MATCHES */
                    break;
                }
            }
        }

    done_matches:

        /* Consider coding a literal.

         * To avoid an extra branch, actually checking the preferability
         * of coding the literal is integrated into the queue update
         * code below. */
        literal = *in_next++;
        cost = cur_node->cost + c->costs.main[literal];

        /* Advance to the next position. */
        cur_node++;

        /* The lowest-cost path to the current position is now known.
         * Finalize the recent offsets queue that results from taking
         * this lowest-cost path. */

        if (cost <= cur_node->cost) {
            /* Literal: queue remains unchanged. */
            cur_node->cost = cost;
            cur_node->item = (u32)literal << OPTIMUM_OFFSET_SHIFT;
            QUEUE(cur_node) = QUEUE(cur_node - 1);
        } else {
            /* Match: queue update is needed. */
            unsigned len = cur_node->item & OPTIMUM_LEN_MASK;
        #if CONSIDER_GAP_MATCHES
            s32 adjusted_offset = (s32)cur_node->item >> OPTIMUM_OFFSET_SHIFT;
            STATIC_ASSERT(OPTIMUM_GAP_MATCH == 0x80000000); /* assuming sign extension */
        #else
            u32 adjusted_offset = cur_node->item >> OPTIMUM_OFFSET_SHIFT;
        #endif

            if (adjusted_offset >= LZX_NUM_RECENT_OFFSETS) {
                /* Explicit offset match: insert offset at front. */
                QUEUE(cur_node) =
                    lzx_lru_queue_push(QUEUE(cur_node - len),
                               adjusted_offset - LZX_OFFSET_ADJUSTMENT);
            }
        #if CONSIDER_GAP_MATCHES
            else if (adjusted_offset < 0) {
                /* "Gap match": Explicit offset match, then a
                 * literal, then rep0 match.  Save the explicit
                 * offset match information in the cost field of
                 * the previous node, which isn't needed
                 * anymore.  Then insert the offset at the front
                 * of the queue. */
                u32 match_before_gap = MATCH_BEFORE_GAP(cur_node);
                (cur_node - 1)->cost = match_before_gap;
                QUEUE(cur_node) =
                    lzx_lru_queue_push(QUEUE(cur_node - len - 1 -
                                 (match_before_gap & OPTIMUM_LEN_MASK)),
                               (match_before_gap >> OPTIMUM_OFFSET_SHIFT) -
                               LZX_OFFSET_ADJUSTMENT);
            }
        #endif
            else {
                /* Repeat offset match: swap offset to front. */
                QUEUE(cur_node) =
                    lzx_lru_queue_swap(QUEUE(cur_node - len),
                               adjusted_offset);
            }
        }
    } while (cur_node != end_node);

    /* Return the recent offsets queue at the end of the path. */
    return QUEUE(cur_node);
}

/*
 * Given the costs for the main and length codewords (c->costs.main and
 * c->costs.len), initialize the match cost array (c->costs.match_cost) which
 * directly provides the cost of every possible (length, offset slot) pair.
 */
static void
lzx_compute_match_costs(struct lzx_compressor *c)
{
    unsigned num_offset_slots = (c->num_main_syms - LZX_NUM_CHARS) /
                    LZX_NUM_LEN_HEADERS;
    struct lzx_costs *costs = &c->costs;
    unsigned main_symbol = LZX_NUM_CHARS;

    for (unsigned offset_slot = 0; offset_slot < num_offset_slots;
         offset_slot++)
    {
        u32 extra_cost = lzx_extra_offset_bits[offset_slot] * BIT_COST;
        unsigned i;

    #if CONSIDER_ALIGNED_COSTS
        if (offset_slot >= LZX_MIN_ALIGNED_OFFSET_SLOT)
            extra_cost -= LZX_NUM_ALIGNED_OFFSET_BITS * BIT_COST;
    #endif

        for (i = 0; i < LZX_NUM_PRIMARY_LENS; i++) {
            costs->match_cost[offset_slot][i] =
                costs->main[main_symbol++] + extra_cost;
        }

        extra_cost += costs->main[main_symbol++];

        for (; i < LZX_NUM_LENS; i++) {
            costs->match_cost[offset_slot][i] =
                costs->len[i - LZX_NUM_PRIMARY_LENS] +
                extra_cost;
        }
    }
}

/*
 * Fast approximation for log2f(x).  This is not as accurate as the standard C
 * version.  It does not need to be perfectly accurate because it is only used
 * for estimating symbol costs, which is very approximate anyway.
 */
static float
log2f_fast(float x)
{
        union {
        float f;
        s32 i;
    } u = { .f = x };

    /* Extract the exponent and subtract 127 to remove the bias.  This gives
     * the integer part of the result. */
        float res = ((u.i >> 23) & 0xFF) - 127;

    /* Set the exponent to 0 (plus bias of 127).  This transforms the number
     * to the range [1, 2) while retaining the same mantissa. */
    u.i = (u.i & ~(0xFF << 23)) | (127 << 23);

    /*
     * Approximate the log2 of the transformed number using a degree 2
     * interpolating polynomial for log2(x) over the interval [1, 2).  Then
     * add this to the extracted exponent to produce the final approximation
     * of log2(x).
     *
     * The coefficients of the interpolating polynomial used here were found
     * using the script tools/log2_interpolation.r.
     */
        return res - 1.653124006f + u.f * (1.9941812f - u.f * 0.3347490189f);

}

/*
 * Return the estimated cost of a symbol which has been estimated to have the
 * given probability.
 */
static u32
lzx_cost_for_probability(float prob)
{
    /*
     * The basic formula is:
     *
     *  entropy = -log2(probability)
     *
     * Use this to get the cost in fractional bits.  Then multiply by our
     * scaling factor of BIT_COST and convert to an integer.
     *
     * In addition, the minimum cost is BIT_COST (one bit) because the
     * entropy coding method will be Huffman codes.
     *
     * Careful: even though 'prob' should be <= 1.0, 'log2f_fast(prob)' may
     * be positive due to inaccuracy in our log2 approximation.  Therefore,
     * we cannot, in general, assume the computed cost is non-negative, and
     * we should make sure negative costs get rounded up correctly.
     */
    s32 cost = -log2f_fast(prob) * BIT_COST;
    return max(cost, BIT_COST);
}

/*
 * Mapping: number of used literals => heuristic probability of a literal times
 * 6870.  Generated by running this R command:
 *
 *  cat(paste(round(6870*2^-((304+(0:256))/64)), collapse=", "))
 */
static const u8 literal_scaled_probs[257] = {
    255, 253, 250, 247, 244, 242, 239, 237, 234, 232, 229, 227, 224, 222,
    219, 217, 215, 212, 210, 208, 206, 203, 201, 199, 197, 195, 193, 191,
    189, 186, 184, 182, 181, 179, 177, 175, 173, 171, 169, 167, 166, 164,
    162, 160, 159, 157, 155, 153, 152, 150, 149, 147, 145, 144, 142, 141,
    139, 138, 136, 135, 133, 132, 130, 129, 128, 126, 125, 124, 122, 121,
    120, 118, 117, 116, 115, 113, 112, 111, 110, 109, 107, 106, 105, 104,
    103, 102, 101, 100, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86,
    86, 85, 84, 83, 82, 81, 80, 79, 78, 78, 77, 76, 75, 74, 73, 73, 72, 71,
    70, 70, 69, 68, 67, 67, 66, 65, 65, 64, 63, 62, 62, 61, 60, 60, 59, 59,
    58, 57, 57, 56, 55, 55, 54, 54, 53, 53, 52, 51, 51, 50, 50, 49, 49, 48,
    48, 47, 47, 46, 46, 45, 45, 44, 44, 43, 43, 42, 42, 41, 41, 40, 40, 40,
    39, 39, 38, 38, 38, 37, 37, 36, 36, 36, 35, 35, 34, 34, 34, 33, 33, 33,
    32, 32, 32, 31, 31, 31, 30, 30, 30, 29, 29, 29, 28, 28, 28, 27, 27, 27,
    27, 26, 26, 26, 25, 25, 25, 25, 24, 24, 24, 24, 23, 23, 23, 23, 22, 22,
    22, 22, 21, 21, 21, 21, 20, 20, 20, 20, 20, 19, 19, 19, 19, 19, 18, 18,
    18, 18, 18, 17, 17, 17, 17, 17, 16, 16, 16, 16
};

/*
 * Mapping: length symbol => default cost of that symbol.  This is derived from
 * sample data but has been slightly edited to add more bias towards the
 * shortest lengths, which are the most common.
 */
static const u16 lzx_default_len_costs[LZX_LENCODE_NUM_SYMBOLS] = {
    300, 310, 320, 330, 360, 396, 399, 416, 451, 448, 463, 466, 505, 492,
    503, 514, 547, 531, 566, 561, 589, 563, 592, 586, 623, 602, 639, 627,
    659, 643, 657, 650, 685, 662, 661, 672, 685, 686, 696, 680, 657, 682,
    666, 699, 674, 699, 679, 709, 688, 712, 692, 714, 694, 716, 698, 712,
    706, 727, 714, 727, 713, 723, 712, 718, 719, 719, 720, 735, 725, 735,
    728, 740, 727, 739, 727, 742, 716, 733, 733, 740, 738, 746, 737, 747,
    738, 745, 736, 748, 742, 749, 745, 749, 743, 748, 741, 752, 745, 752,
    747, 750, 747, 752, 748, 753, 750, 752, 753, 753, 749, 744, 752, 755,
    753, 756, 745, 748, 746, 745, 723, 757, 755, 758, 755, 758, 752, 757,
    754, 757, 755, 759, 755, 758, 753, 755, 755, 758, 757, 761, 755, 750,
    758, 759, 759, 760, 758, 751, 757, 757, 759, 759, 758, 759, 758, 761,
    750, 761, 758, 760, 759, 761, 758, 761, 760, 752, 759, 760, 759, 759,
    757, 762, 760, 761, 761, 748, 761, 760, 762, 763, 752, 762, 762, 763,
    762, 762, 763, 763, 762, 763, 762, 763, 762, 763, 763, 764, 763, 762,
    763, 762, 762, 762, 764, 764, 763, 764, 763, 763, 763, 762, 763, 763,
    762, 764, 764, 763, 762, 763, 763, 763, 763, 762, 764, 763, 762, 764,
    764, 763, 763, 765, 764, 764, 762, 763, 764, 765, 763, 764, 763, 764,
    762, 764, 764, 754, 763, 764, 763, 763, 762, 763, 584,
};

/* Set default costs to bootstrap the iterative optimization algorithm. */
static void
lzx_set_default_costs(struct lzx_compressor *c)
{
    unsigned i;
    u32 num_literals = 0;
    u32 num_used_literals = 0;
    float inv_num_matches = 1.0f / c->freqs.main[LZX_NUM_CHARS];
    float inv_num_items;
    float prob_match = 1.0f;
    u32 match_cost;
    float base_literal_prob;

    /* Some numbers here have been hardcoded to assume a bit cost of 64. */
    STATIC_ASSERT(BIT_COST == 64);

    /* Estimate the number of literals that will used.  'num_literals' is
     * the total number, whereas 'num_used_literals' is the number of
     * distinct symbols. */
    for (i = 0; i < LZX_NUM_CHARS; i++) {
        num_literals += c->freqs.main[i];
        num_used_literals += (c->freqs.main[i] != 0);
    }

    /* Note: all match headers were tallied as symbol 'LZX_NUM_CHARS'.  We
     * don't attempt to estimate which ones will be used. */

    inv_num_items = 1.0f / (num_literals + c->freqs.main[LZX_NUM_CHARS]);
    base_literal_prob = literal_scaled_probs[num_used_literals] *
                (1.0f / 6870.0f);

    /* Literal costs.  We use two different methods to compute the
     * probability of each literal and mix together their results. */
    for (i = 0; i < LZX_NUM_CHARS; i++) {
        u32 freq = c->freqs.main[i];
        if (freq != 0) {
            float prob = 0.5f * ((freq * inv_num_items) +
                         base_literal_prob);
            c->costs.main[i] = lzx_cost_for_probability(prob);
            prob_match -= prob;
        } else {
            c->costs.main[i] = 11 * BIT_COST;
        }
    }

    /* Match header costs.  We just assume that all match headers are
     * equally probable, but we do take into account the relative cost of a
     * match header vs. a literal depending on how common matches are
     * expected to be vs. literals. */
    prob_match = max(prob_match, 0.15f);
    match_cost = lzx_cost_for_probability(prob_match / (c->num_main_syms -
                                LZX_NUM_CHARS));
    for (; i < c->num_main_syms; i++)
        c->costs.main[i] = match_cost;

    /* Length symbol costs.  These are just set to fixed values which
     * reflect the fact the smallest lengths are typically the most common,
     * and therefore are typically the cheapest. */
    for (i = 0; i < LZX_LENCODE_NUM_SYMBOLS; i++)
        c->costs.len[i] = lzx_default_len_costs[i];

#if CONSIDER_ALIGNED_COSTS
    /* Aligned offset symbol costs.  These are derived from the estimated
     * probability of each aligned offset symbol. */
    for (i = 0; i < LZX_ALIGNEDCODE_NUM_SYMBOLS; i++) {
        /* We intentionally tallied the frequencies in the wrong slots,
         * not accounting for LZX_OFFSET_ADJUSTMENT, since doing the
         * fixup here is faster: a constant 8 subtractions here vs. one
         * addition for every match. */
        unsigned j = (i - LZX_OFFSET_ADJUSTMENT) & LZX_ALIGNED_OFFSET_BITMASK;
        if (c->freqs.aligned[j] != 0) {
            float prob = c->freqs.aligned[j] * inv_num_matches;
            c->costs.aligned[i] = lzx_cost_for_probability(prob);
        } else {
            c->costs.aligned[i] =
                (2 * LZX_NUM_ALIGNED_OFFSET_BITS) * BIT_COST;
        }
    }
#endif
}

/* Update the current cost model to reflect the computed Huffman codes.  */
static void
lzx_set_costs_from_codes(struct lzx_compressor *c)
{
    unsigned i;
    const struct lzx_lens *lens = &c->codes[c->codes_index].lens;

    for (i = 0; i < c->num_main_syms; i++) {
        c->costs.main[i] = (lens->main[i] ? lens->main[i] :
                    MAIN_CODEWORD_LIMIT) * BIT_COST;
    }

    for (i = 0; i < LZX_LENCODE_NUM_SYMBOLS; i++) {
        c->costs.len[i] = (lens->len[i] ? lens->len[i] :
                   LENGTH_CODEWORD_LIMIT) * BIT_COST;
    }

#if CONSIDER_ALIGNED_COSTS
    for (i = 0; i < LZX_ALIGNEDCODE_NUM_SYMBOLS; i++) {
        c->costs.aligned[i] = (lens->aligned[i] ? lens->aligned[i] :
                       ALIGNED_CODEWORD_LIMIT) * BIT_COST;
    }
#endif
}

/*
 * Choose a "near-optimal" literal/match sequence to use for the current block,
 * then flush the block.  Because the cost of each Huffman symbol is unknown
 * until the Huffman codes have been built and the Huffman codes themselves
 * depend on the symbol frequencies, this uses an iterative optimization
 * algorithm to approximate an optimal solution.  The first optimization pass
 * for the block uses default costs; additional passes use costs derived from
 * the Huffman codes computed in the previous pass.
 */
static forceinline struct lzx_lru_queue
lzx_optimize_and_flush_block(struct lzx_compressor * const  c,
                 struct lzx_output_bitstream * const  os,
                 const u8 * const  block_begin,
                 const u32 block_size,
                 const struct lzx_lru_queue initial_queue,
                 bool is_16_bit)
{
    unsigned num_passes_remaining = c->num_optim_passes;
    struct lzx_lru_queue new_queue;
    u32 seq_idx;

    lzx_set_default_costs(c);

    for (;;) {
        lzx_compute_match_costs(c);
        new_queue = lzx_find_min_cost_path(c, block_begin, block_size,
                           initial_queue, is_16_bit);

        if (--num_passes_remaining == 0)
            break;

        /* At least one optimization pass remains.  Update the costs. */
        lzx_reset_symbol_frequencies(c);
        lzx_tally_item_list(c, block_size, is_16_bit);
        lzx_build_huffman_codes(c);
        lzx_set_costs_from_codes(c);
    }

    /* Done optimizing.  Generate the sequence list and flush the block. */
    lzx_reset_symbol_frequencies(c);
    seq_idx = lzx_record_item_list(c, block_size, is_16_bit);
    lzx_flush_block(c, os, block_begin, block_size, seq_idx);
    return new_queue;
}

/*
 * This is the "near-optimal" LZX compressor.
 *
 * For each block, it performs a relatively thorough graph search to find an
 * inexpensive (in terms of compressed size) way to output the block.
 *
 * Note: there are actually many things this algorithm leaves on the table in
 * terms of compression ratio.  So although it may be "near-optimal", it is
 * certainly not "optimal".  The goal is not to produce the optimal compression
 * ratio, which for LZX is probably impossible within any practical amount of
 * time, but rather to produce a compression ratio significantly better than a
 * simpler "greedy" or "lazy" parse while still being relatively fast.
 */
static forceinline void
lzx_compress_near_optimal(struct lzx_compressor *  c,
              const u8 * const  in_begin, size_t in_nbytes,
              struct lzx_output_bitstream *  os,
              bool is_16_bit)
{
    const u8 *   in_next = in_begin;
    const u8 * const in_end  = in_begin + in_nbytes;
    u32 max_len = LZX_MAX_MATCH_LEN;
    u32 nice_len = min(c->nice_match_length, max_len);
    u32 next_hashes[2] = {0, 0};
    struct lzx_lru_queue queue = LZX_QUEUE_INITIALIZER;

    /* Initialize the matchfinder. */
    CALL_BT_MF(is_16_bit, c, bt_matchfinder_init);

    do {
        /* Starting a new block */

        const u8 * const in_block_begin = in_next;
        const u8 * const in_max_block_end =
            in_next + min(SOFT_MAX_BLOCK_SIZE, in_end - in_next);
        struct lz_match *cache_ptr = c->match_cache;
        const u8 *next_search_pos = in_next;
        const u8 *next_observation = in_next;
        const u8 *next_pause_point =
            min(in_next + min(MIN_BLOCK_SIZE,
                      in_max_block_end - in_next),
                in_max_block_end - min(LZX_MAX_MATCH_LEN - 1,
                           in_max_block_end - in_next));

        lzx_init_block_split_stats(&c->split_stats);
        lzx_reset_symbol_frequencies(c);

        if (in_next >= next_pause_point)
            goto pause;

        /*
         * Run the input buffer through the matchfinder, caching the
         * matches, until we decide to end the block.
         *
         * For a tighter matchfinding loop, we compute a "pause point",
         * which is the next position at which we may need to check
         * whether to end the block or to decrease max_len.  We then
         * only do these extra checks upon reaching the pause point.
         */
    resume_matchfinding:
        do {
            if (in_next >= next_search_pos) {
                /* Search for matches at this position. */
                struct lz_match *lz_matchptr;
                u32 best_len;

                lz_matchptr = CALL_BT_MF(is_16_bit, c,
                             bt_matchfinder_get_matches,
                             in_begin,
                             in_next - in_begin,
                             max_len,
                             nice_len,
                             c->max_search_depth,
                             next_hashes,
                             &best_len,
                             cache_ptr + 1);
                cache_ptr->length = lz_matchptr - (cache_ptr + 1);
                cache_ptr = lz_matchptr;

                /* Accumulate literal/match statistics for block
                 * splitting and for generating the initial cost
                 * model. */
                if (in_next >= next_observation) {
                    best_len = cache_ptr[-1].length;
                    if (best_len >= 3) {
                        /* Match (len >= 3) */

                        /*
                         * Note: for performance reasons this has
                         * been simplified significantly:
                         *
                         * - We wait until later to account for
                         *   LZX_OFFSET_ADJUSTMENT.
                         * - We don't account for repeat offsets.
                         * - We don't account for different match headers.
                         */
                        c->freqs.aligned[cache_ptr[-1].offset &
                            LZX_ALIGNED_OFFSET_BITMASK]++;
                        c->freqs.main[LZX_NUM_CHARS]++;

                        lzx_observe_match(&c->split_stats, best_len);
                        next_observation = in_next + best_len;
                    } else {
                        /* Literal */
                        c->freqs.main[*in_next]++;
                        lzx_observe_literal(&c->split_stats, *in_next);
                        next_observation = in_next + 1;
                    }
                }

                /*
                 * If there was a very long match found, then
                 * don't cache any matches for the bytes covered
                 * by that match.  This avoids degenerate
                 * behavior when compressing highly redundant
                 * data, where the number of matches can be very
                 * large.
                 *
                 * This heuristic doesn't actually hurt the
                 * compression ratio *too* much.  If there's a
                 * long match, then the data must be highly
                 * compressible, so it doesn't matter as much
                 * what we do.
                 */
                if (best_len >= nice_len)
                    next_search_pos = in_next + best_len;
            } else {
                /* Don't search for matches at this position. */
                CALL_BT_MF(is_16_bit, c,
                       bt_matchfinder_skip_position,
                       in_begin,
                       in_next - in_begin,
                       nice_len,
                       c->max_search_depth,
                       next_hashes);
                cache_ptr->length = 0;
                cache_ptr++;
            }
        } while (++in_next < next_pause_point &&
             likely(cache_ptr < &c->match_cache[CACHE_LENGTH]));

    pause:

        /* Adjust max_len and nice_len if we're nearing the end of the
         * input buffer.  In addition, if we are so close to the end of
         * the input buffer that there cannot be any more matches, then
         * just advance through the last few positions and record no
         * matches. */
        if (unlikely(max_len > in_end - in_next)) {
            max_len = in_end - in_next;
            nice_len = min(max_len, nice_len);
            if (max_len < BT_MATCHFINDER_REQUIRED_NBYTES) {
                while (in_next != in_end) {
                    cache_ptr->length = 0;
                    cache_ptr++;
                    in_next++;
                }
            }
        }

        /* End the block if the match cache may overflow. */
        if (unlikely(cache_ptr >= &c->match_cache[CACHE_LENGTH]))
            goto end_block;

        /* End the block if the soft maximum size has been reached. */
        if (in_next >= in_max_block_end)
            goto end_block;

        /* End the block if the block splitting algorithm thinks this is
         * a good place to do so. */
        if (c->split_stats.num_new_observations >=
                NUM_OBSERVATIONS_PER_BLOCK_CHECK &&
            in_max_block_end - in_next >= MIN_BLOCK_SIZE &&
            lzx_should_end_block(&c->split_stats))
            goto end_block;

        /* It's not time to end the block yet.  Compute the next pause
         * point and resume matchfinding. */
        next_pause_point =
            min(in_next + min(NUM_OBSERVATIONS_PER_BLOCK_CHECK * 2 -
                        c->split_stats.num_new_observations,
                      in_max_block_end - in_next),
                in_max_block_end - min(LZX_MAX_MATCH_LEN - 1,
                           in_max_block_end - in_next));
        goto resume_matchfinding;

    end_block:
        /* We've decided on a block boundary and cached matches.  Now
         * choose a match/literal sequence and flush the block. */
        queue = lzx_optimize_and_flush_block(c, os, in_block_begin,
                             in_next - in_block_begin,
                             queue, is_16_bit);
    } while (in_next != in_end);
}

static void
lzx_compress_near_optimal_16(struct lzx_compressor *c, const u8 *in,
                 size_t in_nbytes, struct lzx_output_bitstream *os)
{
    lzx_compress_near_optimal(c, in, in_nbytes, os, true);
}

static void
lzx_compress_near_optimal_32(struct lzx_compressor *c, const u8 *in,
                 size_t in_nbytes, struct lzx_output_bitstream *os)
{
    lzx_compress_near_optimal(c, in, in_nbytes, os, false);
}

/******************************************************************************/
/*                     Faster ("lazy") compression algorithm                  */
/*----------------------------------------------------------------------------*/

/*
 * Called when the compressor chooses to use a literal.  This tallies the
 * Huffman symbol for the literal, increments the current literal run length,
 * and "observes" the literal for the block split statistics.
 */
static forceinline void
lzx_choose_literal(struct lzx_compressor *c, unsigned literal, u32 *litrunlen_p)
{
    lzx_observe_literal(&c->split_stats, literal);
    c->freqs.main[literal]++;
    ++*litrunlen_p;
}

/*
 * Called when the compressor chooses to use a match.  This tallies the Huffman
 * symbol(s) for a match, saves the match data and the length of the preceding
 * literal run, updates the recent offsets queue, and "observes" the match for
 * the block split statistics.
 */
static forceinline void
lzx_choose_match(struct lzx_compressor *c, unsigned length, u32 adjusted_offset,
         u32 recent_offsets[LZX_NUM_RECENT_OFFSETS], bool is_16_bit,
         u32 *litrunlen_p, struct lzx_sequence **next_seq_p)
{
    struct lzx_sequence *next_seq = *next_seq_p;
    unsigned mainsym;

    lzx_observe_match(&c->split_stats, length);

    mainsym = lzx_tally_main_and_lensyms(c, length, adjusted_offset,
                         is_16_bit);
    next_seq->litrunlen_and_matchlen =
        (*litrunlen_p << SEQ_MATCHLEN_BITS) | length;
    next_seq->adjusted_offset_and_mainsym =
        (adjusted_offset << SEQ_MAINSYM_BITS) | mainsym;

    /* Update the recent offsets queue. */
    if (adjusted_offset < LZX_NUM_RECENT_OFFSETS) {
        /* Repeat offset match. */
        swap(recent_offsets[0], recent_offsets[adjusted_offset]);
    } else {
        /* Explicit offset match. */

        /* Tally the aligned offset symbol if needed. */
        if (adjusted_offset >= LZX_MIN_ALIGNED_OFFSET + LZX_OFFSET_ADJUSTMENT)
            c->freqs.aligned[adjusted_offset & LZX_ALIGNED_OFFSET_BITMASK]++;

        recent_offsets[2] = recent_offsets[1];
        recent_offsets[1] = recent_offsets[0];
        recent_offsets[0] = adjusted_offset - LZX_OFFSET_ADJUSTMENT;
    }

    /* Reset the literal run length and advance to the next sequence. */
    *next_seq_p = next_seq + 1;
    *litrunlen_p = 0;
}

/*
 * Called when the compressor ends a block.  This finshes the last lzx_sequence,
 * which is just a literal run with no following match.  This literal run might
 * be empty.
 */
static forceinline void
lzx_finish_sequence(struct lzx_sequence *last_seq, u32 litrunlen)
{
    last_seq->litrunlen_and_matchlen = litrunlen << SEQ_MATCHLEN_BITS;
}

/*
 * Find the longest repeat offset match with the current position.  If a match
 * is found, return its length and set *best_rep_idx_ret to the index of its
 * offset in @recent_offsets.  Otherwise, return 0.
 *
 * Don't bother with length 2 matches; consider matches of length >= 3 only.
 * Also assume that max_len >= 3.
 */
static unsigned
lzx_find_longest_repeat_offset_match(const u8 * const in_next,
                     const u32 recent_offsets[],
                     const unsigned max_len,
                     unsigned *best_rep_idx_ret)
{
    STATIC_ASSERT(LZX_NUM_RECENT_OFFSETS == 3); /* loop is unrolled */

    const u32 seq3 = load_u24_unaligned(in_next);
    const u8 *matchptr;
    unsigned best_rep_len = 0;
    unsigned best_rep_idx = 0;
    unsigned rep_len;

    /* Check for rep0 match (most recent offset) */
    matchptr = in_next - recent_offsets[0];
    if (load_u24_unaligned(matchptr) == seq3)
        best_rep_len = lz_extend(in_next, matchptr, 3, max_len);

    /* Check for rep1 match (second most recent offset) */
    matchptr = in_next - recent_offsets[1];
    if (load_u24_unaligned(matchptr) == seq3) {
        rep_len = lz_extend(in_next, matchptr, 3, max_len);
        if (rep_len > best_rep_len) {
            best_rep_len = rep_len;
            best_rep_idx = 1;
        }
    }

    /* Check for rep2 match (third most recent offset) */
    matchptr = in_next - recent_offsets[2];
    if (load_u24_unaligned(matchptr) == seq3) {
        rep_len = lz_extend(in_next, matchptr, 3, max_len);
        if (rep_len > best_rep_len) {
            best_rep_len = rep_len;
            best_rep_idx = 2;
        }
    }

    *best_rep_idx_ret = best_rep_idx;
    return best_rep_len;
}

/*
 * Fast heuristic scoring for lazy parsing: how "good" is this match?
 * This is mainly determined by the length: longer matches are better.
 * However, we also give a bonus to close (small offset) matches and to repeat
 * offset matches, since those require fewer bits to encode.
 */

static forceinline unsigned
lzx_explicit_offset_match_score(unsigned len, u32 adjusted_offset)
{
    unsigned score = len;

    if (adjusted_offset < 4096)
        score++;
    if (adjusted_offset < 256)
        score++;

    return score;
}

static forceinline unsigned
lzx_repeat_offset_match_score(unsigned rep_len, unsigned rep_idx)
{
    return rep_len + 3;
}

/*
 * This is the "lazy" LZX compressor.  The basic idea is that before it chooses
 * a match, it checks to see if there's a longer match at the next position.  If
 * yes, it chooses a literal and continues to the next position.  If no, it
 * chooses the match.
 *
 * Some additional heuristics are used as well.  Repeat offset matches are
 * considered favorably and sometimes are chosen immediately.  In addition, long
 * matches (at least "nice_len" bytes) are chosen immediately as well.  Finally,
 * when we decide whether a match is "better" than another, we take the offset
 * into consideration as well as the length.
 */
static forceinline void
lzx_compress_lazy(struct lzx_compressor *  c,
          const u8 * const  in_begin, size_t in_nbytes,
          struct lzx_output_bitstream *  os, bool is_16_bit)
{
    const u8 *   in_next = in_begin;
    const u8 * const in_end  = in_begin + in_nbytes;
    unsigned max_len = LZX_MAX_MATCH_LEN;
    unsigned nice_len = min(c->nice_match_length, max_len);
    STATIC_ASSERT(LZX_NUM_RECENT_OFFSETS == 3);
    u32 recent_offsets[LZX_NUM_RECENT_OFFSETS] = {1, 1, 1};
    u32 next_hashes[2] = {0, 0};

    /* Initialize the matchfinder. */
    CALL_HC_MF(is_16_bit, c, hc_matchfinder_init);

    do {
        /* Starting a new block */

        const u8 * const in_block_begin = in_next;
        const u8 * const in_max_block_end =
            in_next + min(SOFT_MAX_BLOCK_SIZE, in_end - in_next);
        struct lzx_sequence *next_seq = c->chosen_sequences;
        u32 litrunlen = 0;
        unsigned cur_len;
        u32 cur_offset;
        u32 cur_adjusted_offset;
        unsigned cur_score;
        unsigned next_len;
        u32 next_offset;
        u32 next_adjusted_offset;
        unsigned next_score;
        unsigned best_rep_len;
        unsigned best_rep_idx;
        unsigned rep_score;
        unsigned skip_len;

        lzx_reset_symbol_frequencies(c);
        lzx_init_block_split_stats(&c->split_stats);

        do {
            /* Adjust max_len and nice_len if we're nearing the end
             * of the input buffer. */
            if (unlikely(max_len > in_end - in_next)) {
                max_len = in_end - in_next;
                nice_len = min(max_len, nice_len);
            }

            /* Find the longest match (subject to the
             * max_search_depth cutoff parameter) with the current
             * position.  Don't bother with length 2 matches; only
             * look for matches of length >= 3. */
            cur_len = CALL_HC_MF(is_16_bit, c,
                         hc_matchfinder_longest_match,
                         in_begin,
                         in_next - in_begin,
                         2,
                         max_len,
                         nice_len,
                         c->max_search_depth,
                         next_hashes,
                         &cur_offset);

            /* If there was no match found, or the only match found
             * was a distant short match, then choose a literal. */
            if (cur_len < 3 ||
                (cur_len == 3 &&
                 cur_offset >= 8192 - LZX_OFFSET_ADJUSTMENT &&
                 cur_offset != recent_offsets[0] &&
                 cur_offset != recent_offsets[1] &&
                 cur_offset != recent_offsets[2]))
            {
                lzx_choose_literal(c, *in_next, &litrunlen);
                in_next++;
                continue;
            }

            /* Heuristic: if this match has the most recent offset,
             * then go ahead and choose it as a rep0 match. */
            if (cur_offset == recent_offsets[0]) {
                in_next++;
                skip_len = cur_len - 1;
                cur_adjusted_offset = 0;
                goto choose_cur_match;
            }

            /* Compute the longest match's score as an explicit
             * offset match. */
            cur_adjusted_offset = cur_offset + LZX_OFFSET_ADJUSTMENT;
            cur_score = lzx_explicit_offset_match_score(cur_len, cur_adjusted_offset);

            /* Find the longest repeat offset match at this
             * position.  If we find one and it's "better" than the
             * explicit offset match we found, then go ahead and
             * choose the repeat offset match immediately. */
            best_rep_len = lzx_find_longest_repeat_offset_match(in_next,
                                        recent_offsets,
                                        max_len,
                                        &best_rep_idx);
            in_next++;

            if (best_rep_len != 0 &&
                (rep_score = lzx_repeat_offset_match_score(best_rep_len,
                                       best_rep_idx)) >= cur_score)
            {
                cur_len = best_rep_len;
                cur_adjusted_offset = best_rep_idx;
                skip_len = best_rep_len - 1;
                goto choose_cur_match;
            }

        have_cur_match:
            /*
             * We have a match at the current position.  If the
             * match is very long, then choose it immediately.
             * Otherwise, see if there's a better match at the next
             * position.
             */

            if (cur_len >= nice_len) {
                skip_len = cur_len - 1;
                goto choose_cur_match;
            }

            if (unlikely(max_len > in_end - in_next)) {
                max_len = in_end - in_next;
                nice_len = min(max_len, nice_len);
            }

            next_len = CALL_HC_MF(is_16_bit, c,
                          hc_matchfinder_longest_match,
                          in_begin,
                          in_next - in_begin,
                          cur_len - 2,
                          max_len,
                          nice_len,
                          c->max_search_depth / 2,
                          next_hashes,
                          &next_offset);

            if (next_len <= cur_len - 2) {
                /* No potentially better match was found. */
                in_next++;
                skip_len = cur_len - 2;
                goto choose_cur_match;
            }

            next_adjusted_offset = next_offset + LZX_OFFSET_ADJUSTMENT;
            next_score = lzx_explicit_offset_match_score(next_len, next_adjusted_offset);

            best_rep_len = lzx_find_longest_repeat_offset_match(in_next,
                                        recent_offsets,
                                        max_len,
                                        &best_rep_idx);
            in_next++;

            if (best_rep_len != 0 &&
                (rep_score = lzx_repeat_offset_match_score(best_rep_len,
                                       best_rep_idx)) >= next_score)
            {

                if (rep_score > cur_score) {
                    /* The next match is better, and it's a
                     * repeat offset match. */
                    lzx_choose_literal(c, *(in_next - 2),
                               &litrunlen);
                    cur_len = best_rep_len;
                    cur_adjusted_offset = best_rep_idx;
                    skip_len = cur_len - 1;
                    goto choose_cur_match;
                }
            } else {
                if (next_score > cur_score) {
                    /* The next match is better, and it's an
                     * explicit offset match. */
                    lzx_choose_literal(c, *(in_next - 2),
                               &litrunlen);
                    cur_len = next_len;
                    cur_adjusted_offset = next_adjusted_offset;
                    cur_score = next_score;
                    goto have_cur_match;
                }
            }

            /* The original match was better; choose it. */
            skip_len = cur_len - 2;

        choose_cur_match:
            /* Choose a match and have the matchfinder skip over its
             * remaining bytes. */
            lzx_choose_match(c, cur_len, cur_adjusted_offset,
                     recent_offsets, is_16_bit,
                     &litrunlen, &next_seq);
            in_next = CALL_HC_MF(is_16_bit, c,
                         hc_matchfinder_skip_positions,
                         in_begin,
                         in_next - in_begin,
                         in_end - in_begin,
                         skip_len,
                         next_hashes);

            /* Keep going until it's time to end the block. */
        } while (in_next < in_max_block_end &&
             !(c->split_stats.num_new_observations >=
                    NUM_OBSERVATIONS_PER_BLOCK_CHECK &&
               in_next - in_block_begin >= MIN_BLOCK_SIZE &&
               in_end - in_next >= MIN_BLOCK_SIZE &&
               lzx_should_end_block(&c->split_stats)));

        /* Flush the block. */
        lzx_finish_sequence(next_seq, litrunlen);
        lzx_flush_block(c, os, in_block_begin, in_next - in_block_begin, 0);

        /* Keep going until we've reached the end of the input buffer. */
    } while (in_next != in_end);
}

static void
lzx_compress_lazy_16(struct lzx_compressor *c, const u8 *in, size_t in_nbytes,
             struct lzx_output_bitstream *os)
{
    lzx_compress_lazy(c, in, in_nbytes, os, true);
}

static void
lzx_compress_lazy_32(struct lzx_compressor *c, const u8 *in, size_t in_nbytes,
             struct lzx_output_bitstream *os)
{
    lzx_compress_lazy(c, in, in_nbytes, os, false);
}

/******************************************************************************/
/*                          Compressor operations                             */
/*----------------------------------------------------------------------------*/

/*
 * Generate tables for mapping match offsets (actually, "adjusted" match
 * offsets) to offset slots.
 */
static void
lzx_init_offset_slot_tabs(struct lzx_compressor *c)
{
    u32 adjusted_offset = 0;
    unsigned slot = 0;

    /* slots [0, 29] */
    for (; adjusted_offset < ARRAY_LEN(c->offset_slot_tab_1);
         adjusted_offset++)
    {
        if (adjusted_offset >= lzx_offset_slot_base[slot + 1] +
                       LZX_OFFSET_ADJUSTMENT)
            slot++;
        c->offset_slot_tab_1[adjusted_offset] = slot;
    }

    /* slots [30, 49] */
    for (; adjusted_offset < LZX_MAX_WINDOW_SIZE;
         adjusted_offset += (u32)1 << 14)
    {
        if (adjusted_offset >= lzx_offset_slot_base[slot + 1] +
                       LZX_OFFSET_ADJUSTMENT)
            slot++;
        c->offset_slot_tab_2[adjusted_offset >> 14] = slot;
    }
}

static size_t
lzx_get_compressor_size(size_t max_bufsize, unsigned compression_level)
{
    if (compression_level <= MAX_FAST_LEVEL) {
        if (lzx_is_16_bit(max_bufsize))
            return offsetof(struct lzx_compressor, hc_mf_16) +
                   hc_matchfinder_size_16(max_bufsize);
        else
            return offsetof(struct lzx_compressor, hc_mf_32) +
                   hc_matchfinder_size_32(max_bufsize);
    } else {
        if (lzx_is_16_bit(max_bufsize))
            return offsetof(struct lzx_compressor, bt_mf_16) +
                   bt_matchfinder_size_16(max_bufsize);
        else
            return offsetof(struct lzx_compressor, bt_mf_32) +
                   bt_matchfinder_size_32(max_bufsize);
    }
}

/* Compute the amount of memory needed to allocate an LZX compressor. */
static u64
lzx_get_needed_memory(size_t max_bufsize, unsigned compression_level,
              bool destructive)
{
    u64 size = 0;

    if (max_bufsize > LZX_MAX_WINDOW_SIZE)
        return 0;

    size += lzx_get_compressor_size(max_bufsize, compression_level);
    if (!destructive)
        size += max_bufsize; /* account for in_buffer */
    return size;
}

/* Allocate an LZX compressor. */
__declspec(dllexport) int
lzx_create_compressor(size_t max_bufsize, unsigned compression_level,
              bool destructive, void **c_ret)
{
    unsigned window_order;
    struct lzx_compressor *c;

    /* Validate the maximum buffer size and get the window order from it. */
    window_order = lzx_get_window_order(max_bufsize);
    if (window_order == 0)
        return WIMLIB_ERR_INVALID_PARAM;

    /* Allocate the compressor. */
    c = MALLOC(lzx_get_compressor_size(max_bufsize, compression_level));
    if (!c)
        goto oom0;

    c->window_order = window_order;
    c->num_main_syms = lzx_get_num_main_syms(window_order);
    c->destructive = destructive;

    /* Allocate the buffer for preprocessed data if needed. */
    if (!c->destructive) {
        c->in_buffer = MALLOC(max_bufsize);
        if (!c->in_buffer)
            goto oom1;
    }

    if (compression_level <= MAX_FAST_LEVEL) {

        /* Fast compression: Use lazy parsing. */
        if (lzx_is_16_bit(max_bufsize))
            c->impl = lzx_compress_lazy_16;
        else
            c->impl = lzx_compress_lazy_32;

        /* Scale max_search_depth and nice_match_length with the
         * compression level. */
        c->max_search_depth = (60 * compression_level) / 20;
        c->nice_match_length = (80 * compression_level) / 20;

        /* lzx_compress_lazy() needs max_search_depth >= 2 because it
         * halves the max_search_depth when attempting a lazy match, and
         * max_search_depth must be at least 1. */
        c->max_search_depth = max(c->max_search_depth, 2);
    } else {

        /* Normal / high compression: Use near-optimal parsing. */
        if (lzx_is_16_bit(max_bufsize))
            c->impl = lzx_compress_near_optimal_16;
        else
            c->impl = lzx_compress_near_optimal_32;

        /* Scale max_search_depth and nice_match_length with the
         * compression level. */
        c->max_search_depth = (24 * compression_level) / 50;
        c->nice_match_length = (48 * compression_level) / 50;

        /* Also scale num_optim_passes with the compression level.  But
         * the more passes there are, the less they help --- so don't
         * add them linearly.  */
        c->num_optim_passes = 1;
        c->num_optim_passes += (compression_level >= 45);
        c->num_optim_passes += (compression_level >= 70);
        c->num_optim_passes += (compression_level >= 100);
        c->num_optim_passes += (compression_level >= 150);
        c->num_optim_passes += (compression_level >= 200);
        c->num_optim_passes += (compression_level >= 300);

        /* max_search_depth must be at least 1. */
        c->max_search_depth = max(c->max_search_depth, 1);
    }

    /* Prepare the offset => offset slot mapping. */
    lzx_init_offset_slot_tabs(c);

    *c_ret = c;
    return 0;

oom1:
    FREE(c);
oom0:
    return WIMLIB_ERR_NOMEM;
}

/* Compress a buffer of data. */
__declspec(dllexport) size_t
lzx_compress(const void * in, size_t in_nbytes,
         void * out, size_t out_nbytes_avail, void * _c)
{
    struct lzx_compressor *c = _c;
    struct lzx_output_bitstream os;
    size_t result;

    /* Don't bother trying to compress very small inputs. */
    if (in_nbytes < 64)
        return 0;

    /* If the compressor is in "destructive" mode, then we can directly
     * preprocess the input data.  Otherwise, we need to copy it into an
     * internal buffer first. */
    if (!c->destructive) {
        memcpy(c->in_buffer, in, in_nbytes);
        in = c->in_buffer;
    }

    /* Preprocess the input data. */
    lzx_preprocess((void *)in, in_nbytes);

    /* Initially, the previous Huffman codeword lengths are all zeroes. */
    c->codes_index = 0;
    memset(&c->codes[1].lens, 0, sizeof(struct lzx_lens));

    /* Initialize the output bitstream. */
    lzx_init_output(&os, out, out_nbytes_avail);

    /* Call the compression level-specific compress() function. */
    (*c->impl)(c, in, in_nbytes, &os);

    /* Flush the output bitstream. */
    result = lzx_flush_output(&os);

    /* If the data did not compress to less than its original size and we
     * preprocessed the original buffer, then postprocess it to restore it
     * to its original state. */
    if (result == 0 && c->destructive)
        lzx_postprocess((void *)in, in_nbytes);

    /* Return the number of compressed bytes, or 0 if the input did not
     * compress to less than its original size. */
    return result;
}

/* Free an LZX compressor. */
__declspec(dllexport) void
lzx_free_compressor(void *_c)
{
    struct lzx_compressor *c = _c;

    if (!c->destructive)
        FREE(c->in_buffer);
    FREE(c);
}

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