lzx lcpit

[wimlib] / src / lzx_compress.c

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

/*
 * Copyright (C) 2012-2016 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 parsing 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.
 *
 * Note: 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 parser 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.
 */

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

/*
 * The compressor always chooses a block of at least MIN_BLOCK_LENGTH bytes,
 * except if the last block has to be shorter.
 */
#define MIN_BLOCK_LENGTH                6500

/*
 * The compressor attempts to end blocks after SOFT_MAX_BLOCK_LENGTH bytes, but
 * the final size might be larger due to matches extending beyond the end of the
 * block.  Specifically:
 *
 *  - The greedy parser may choose an arbitrarily long match starting at the
 *    SOFT_MAX_BLOCK_LENGTH'th byte.
 *
 *  - The lazy parser may choose a sequence of literals starting at the
 *    SOFT_MAX_BLOCK_LENGTH'th byte when it sees a sequence of increasing good
 *    matches.  The final match may be of arbitrary length.  The length of the
 *    literal sequence is approximately limited by the "nice match length"
 *    parameter.
 */
#define SOFT_MAX_BLOCK_LENGTH   100000

/*
 * The number of observed matches or literals that represents sufficient data to
 * decide whether the current block should be terminated or not.
 */
#define NUM_OBSERVATIONS_PER_BLOCK_CHECK        500

/*
 * LZX_CACHE_LENGTH is 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 LZX_CACHE_LENGTH        (SOFT_MAX_BLOCK_LENGTH * 5)

/*
 * LZX_MAX_MATCHES_PER_POS is 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 LZX_MAX_MATCHES_PER_POS LZX_NUM_LENS

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

/*
 * Should the compressor take into account the costs of aligned offset symbols?
 */
#define LZX_CONSIDER_ALIGNED_COSTS      1

/*
 * LZX_MAX_FAST_LEVEL is the maximum compression level at which we use the
 * faster algorithm.
 */
#define LZX_MAX_FAST_LEVEL      34

/*
 * BT_MATCHFINDER_HASH2_ORDER is 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

/*
 * These are the compressor-side limits on the codeword lengths 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, at least for the block lengths we use.
 */
#define MAIN_CODEWORD_LIMIT     16
#define LENGTH_CODEWORD_LIMIT   12
#define ALIGNED_CODEWORD_LIMIT  7
#define PRE_CODEWORD_LIMIT      7

#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"

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

struct lzx_output_bitstream;

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

/* Codeword lengths (in bits) for the LZX Huffman codes.
 * A zero length means the corresponding codeword has zero frequency.  */
struct lzx_lens {
        u8 main[LZX_MAINCODE_MAX_NUM_SYMBOLS + 1];
        u8 len[LZX_LENCODE_NUM_SYMBOLS + 1];
        u8 aligned[LZX_ALIGNEDCODE_NUM_SYMBOLS];
};

/* Cost model for near-optimal parsing  */
struct lzx_costs {

        /* 'match_cost[offset_slot][len - LZX_MIN_MATCH_LEN]' is the cost for a
         * length 'len' match that has an offset belonging to 'offset_slot'.  */
        u32 match_cost[LZX_MAX_OFFSET_SLOTS][LZX_NUM_LENS];

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

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

#if LZX_CONSIDER_ALIGNED_COSTS
        /* Cost for each symbol in the aligned code  */
        u32 aligned[LZX_ALIGNEDCODE_NUM_SYMBOLS];
#endif
};

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

/* Symbol frequency counters for the LZX Huffman codes.  */
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 "Block splitting algorithm" below. */
#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 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
 * struct is needed to temporarily store items chosen by the parser, 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 {

        /* The number of literals in the run.  This may be 0.  The literals are
         * not stored explicitly in this structure; instead, they are read
         * directly from the uncompressed data.  */
        u16 litrunlen;

        /* If the next field doesn't indicate end-of-block, then this is the
         * match length minus LZX_MIN_MATCH_LEN.  */
        u16 adjusted_length;

        /* If bit 31 is clear, then this field contains the match header in bits
         * 0-8, and either the match offset plus LZX_OFFSET_ADJUSTMENT or a
         * recent offset code in bits 9-30.  Otherwise (if bit 31 is set), this
         * sequence's literal run was the last literal run in the block, so
         * there is no match that follows it.  */
        u32 adjusted_offset_and_match_hdr;
};

/*
 * 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 match or literal that was taken to reach this position.  This can
         * change as progressively lower cost paths are found to reach this
         * position.
         *
         * This variable is divided into two bitfields.
         *
         * 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 2.
         *
         * Repeat offset matches:
         *      Low bits are the match length, high bits are the queue index.
         */
        u32 item;
#define OPTIMUM_OFFSET_SHIFT 9
#define OPTIMUM_LEN_MASK ((1 << OPTIMUM_OFFSET_SHIFT) - 1)
#define OPTIMUM_EXTRA_FLAG 0x80000000
        u32 extra_match;
        u32 extra_literal;
} _aligned_attribute(8);

/*
 * 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;
};

#define LZX_QUEUE64_OFFSET_SHIFT 21
#define LZX_QUEUE64_OFFSET_MASK (((u64)1 << LZX_QUEUE64_OFFSET_SHIFT) - 1)

#define LZX_QUEUE64_R0_SHIFT (0 * LZX_QUEUE64_OFFSET_SHIFT)
#define LZX_QUEUE64_R1_SHIFT (1 * LZX_QUEUE64_OFFSET_SHIFT)
#define LZX_QUEUE64_R2_SHIFT (2 * LZX_QUEUE64_OFFSET_SHIFT)

#define LZX_QUEUE64_R0_MASK (LZX_QUEUE64_OFFSET_MASK << LZX_QUEUE64_R0_SHIFT)
#define LZX_QUEUE64_R1_MASK (LZX_QUEUE64_OFFSET_MASK << LZX_QUEUE64_R1_SHIFT)
#define LZX_QUEUE64_R2_MASK (LZX_QUEUE64_OFFSET_MASK << LZX_QUEUE64_R2_SHIFT)

static inline void
lzx_lru_queue_init(struct lzx_lru_queue *queue)
{
        queue->R = ((u64)1 << LZX_QUEUE64_R0_SHIFT) |
                   ((u64)1 << LZX_QUEUE64_R1_SHIFT) |
                   ((u64)1 << LZX_QUEUE64_R2_SHIFT);
}

static inline u64
lzx_lru_queue_R0(struct lzx_lru_queue queue)
{
        return (queue.R >> LZX_QUEUE64_R0_SHIFT) & LZX_QUEUE64_OFFSET_MASK;
}

static inline u64
lzx_lru_queue_R1(struct lzx_lru_queue queue)
{
        return (queue.R >> LZX_QUEUE64_R1_SHIFT) & LZX_QUEUE64_OFFSET_MASK;
}

static inline u64
lzx_lru_queue_R2(struct lzx_lru_queue queue)
{
        return (queue.R >> LZX_QUEUE64_R2_SHIFT) & LZX_QUEUE64_OFFSET_MASK;
}

/* Push a match offset onto the front (most recently used) end of the queue.  */
static inline struct lzx_lru_queue
lzx_lru_queue_push(struct lzx_lru_queue queue, u32 offset)
{
        return (struct lzx_lru_queue) {
                .R = (queue.R << LZX_QUEUE64_OFFSET_SHIFT) | offset,
        };
}

/* Swap a match offset to the front of the queue.  */
static inline struct lzx_lru_queue
lzx_lru_queue_swap(struct lzx_lru_queue queue, unsigned idx)
{
        if (idx == 0)
                return queue;

        if (idx == 1)
                return (struct lzx_lru_queue) {
                        .R = (lzx_lru_queue_R1(queue) << LZX_QUEUE64_R0_SHIFT) |
                             (lzx_lru_queue_R0(queue) << LZX_QUEUE64_R1_SHIFT) |
                             (queue.R & LZX_QUEUE64_R2_MASK),
                };

        return (struct lzx_lru_queue) {
                .R = (lzx_lru_queue_R2(queue) << LZX_QUEUE64_R0_SHIFT) |
                     (queue.R & LZX_QUEUE64_R1_MASK) |
                     (lzx_lru_queue_R0(queue) << LZX_QUEUE64_R2_SHIFT),
        };
}

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

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

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

        /* The log base 2 of the LZX window size for LZ 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
         * @window_order, since @window_order determines the maximum possible
         * offset.  */
        unsigned num_main_syms;

        /* Number of optimization passes per block  */
        unsigned num_optim_passes;

        /* The preprocessed buffer of data being compressed  */
        u8 *in_buffer;

        /* The number of bytes of data to be compressed, which is the number of
         * bytes of data in @in_buffer that are actually valid.  */
        size_t in_nbytes;

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

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

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

        /* Block split statistics.  */
        struct 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 parser 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_LENGTH, LZX_MIN_MATCH_LEN) + 1];

        /* Tables for mapping adjusted offsets to offset slots  */

        /* offset slots [0, 29]  */
        u8 offset_slot_tab_1[32768];

        /* offset slots [30, 49]  */
        u8 offset_slot_tab_2[128];

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

                /* Data for near-optimal parsing  */
                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 we find a
                         * match of length LZX_MAX_MATCH_LEN at position
                         * SOFT_MAX_BLOCK_LENGTH - 1, producing a block of length
                         * SOFT_MAX_BLOCK_LENGTH - 1 + LZX_MAX_MATCH_LEN.  Add one
                         * for the end-of-block node.
                         */
                        struct lzx_optimum_node optimum_nodes[SOFT_MAX_BLOCK_LENGTH - 1 +
                                                              LZX_MAX_MATCH_LEN + 1];

                        /* The cost model for the current block  */
                        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.  LZX_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[LZX_CACHE_LENGTH - 1], we write the
                         * match count header, then write
                         * LZX_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[LZX_CACHE_LENGTH +
                                                    LZX_MAX_MATCHES_PER_POS +
                                                    LZX_MAX_MATCH_LEN - 1];

                        struct lcpit_matchfinder lcpit_mf;
                };
        };
};

/*
 * 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 inline 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;
}

/*
 * 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__));

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

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

        /* Number of bits currently held in @bitbuf.  */
        u32 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 just past the end of the output buffer, rounded down to a
         * 2-byte boundary.  */
        u8 *end;
};

/* Can the specified number of bits always be added to 'bitbuf' after any
 * pending 16-bit coding units have been flushed?  */
#define CAN_BUFFER(n)   ((n) <= (8 * sizeof(machine_word_t)) - 15)

/*
 * Initialize the output bitstream.
 *
 * @os
 *      The output bitstream structure to initialize.
 * @buffer
 *      The buffer being written to.
 * @size
 *      Size of @buffer, in bytes.
 */
static void
lzx_init_output(struct lzx_output_bitstream *os, void *buffer, size_t size)
{
        os->bitbuf = 0;
        os->bitcount = 0;
        os->start = buffer;
        os->next = os->start;
        os->end = os->start + (size & ~1);
}

/* Add some bits to the bitbuffer variable of the output bitstream.  The caller
 * must make sure there is enough room.  */
static inline 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 inline 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 = 8 * sizeof(os->bitbuf) - 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 inline 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 u32
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;
}

/*
 * Build the main, length, and aligned offset Huffman codes used in LZX.
 *
 * This takes as input the frequency tables for each code and produces as output
 * a set of tables that map symbols to codewords and codeword lengths.
 */
static void
lzx_make_huffman_codes(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);
        STATIC_ASSERT(LENGTH_CODEWORD_LIMIT >= 8 &&
                      LENGTH_CODEWORD_LIMIT <= LZX_MAX_LEN_CODEWORD_LEN);
        STATIC_ASSERT(ALIGNED_CODEWORD_LIMIT >= LZX_NUM_ALIGNED_OFFSET_BITS &&
                      ALIGNED_CODEWORD_LIMIT <= LZX_MAX_ALIGNED_CODEWORD_LEN);

        make_canonical_huffman_code(c->num_main_syms,
                                    MAIN_CODEWORD_LIMIT,
                                    freqs->main,
                                    codes->lens.main,
                                    codes->codewords.main);

        make_canonical_huffman_code(LZX_LENCODE_NUM_SYMBOLS,
                                    LENGTH_CODEWORD_LIMIT,
                                    freqs->len,
                                    codes->lens.len,
                                    codes->codewords.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 LZX Huffman codes.  */
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[restrict],
                          const u8 prev_lens[restrict],
                          u32 precode_freqs[restrict],
                          unsigned precode_items[restrict])
{
        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;
}

/*
 * 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[restrict],
                          const u8 prev_lens[restrict],
                          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 current
 *      LZX compressed 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;
        u32 ones_if_aligned = 0 - (block_type == LZX_BLOCKTYPE_ALIGNED);

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

                unsigned litrunlen = seq->litrunlen;
                unsigned match_hdr;
                unsigned main_symbol;
                unsigned adjusted_length;
                u32 adjusted_offset;
                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(sizeof(machine_word_t) < 8 ||
                                      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 (seq->adjusted_offset_and_match_hdr & 0x80000000)
                        return;

                /* Nope; output the match.  */

                match_hdr = seq->adjusted_offset_and_match_hdr & 0x1FF;
                main_symbol = LZX_NUM_CHARS + match_hdr;
                adjusted_length = seq->adjusted_length;

                block_data += adjusted_length + LZX_MIN_MATCH_LEN;

                offset_slot = match_hdr / LZX_NUM_LEN_HEADERS;
                adjusted_offset = seq->adjusted_offset_and_match_hdr >> 9;

                num_extra_bits = lzx_extra_offset_bits[offset_slot];
                extra_bits = adjusted_offset - lzx_offset_slot_base[offset_slot];

        #define MAX_MATCH_BITS  (MAIN_CODEWORD_LIMIT + LENGTH_CODEWORD_LIMIT + \
                                 14 + ALIGNED_CODEWORD_LIMIT)

                /* Verify optimization is enabled on 64-bit  */
                STATIC_ASSERT(sizeof(machine_word_t) < 8 || 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 (adjusted_length >= LZX_NUM_PRIMARY_LENS) {
                        lzx_add_bits(os, codes->codewords.len[adjusted_length -
                                                              LZX_NUM_PRIMARY_LENS],
                                     codes->lens.len[adjusted_length -
                                                     LZX_NUM_PRIMARY_LENS]);
                        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 ((adjusted_offset & ones_if_aligned) >= 16) {

                        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, 14);

                        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(17));

                        lzx_add_bits(os, extra_bits, num_extra_bits);
                        if (!CAN_BUFFER(MAX_MATCH_BITS))
                                lzx_flush_bits(os, 17);
                }

                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_length,
                           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 length.
         *
         * The original LZX format seemed to always encode the block length in 3
         * bytes.  However, the implementation in WIMGAPI, as used in WIM files,
         * uses the first bit to indicate whether the block is the default
         * length (32768) or a different length given explicitly by the next 16
         * bits.
         *
         * By default, this compressor uses a window size of 32768 and therefore
         * follows the WIMGAPI behavior.  However, this compressor also supports
         * window sizes greater than 32768 bytes, which do not appear to be
         * supported by WIMGAPI.  In such cases, we retain the default size bit
         * to mean a size of 32768 bytes but output non-default block length in
         * 24 bits rather than 16.  The compatibility of this behavior is
         * unknown because WIMs created with chunk size greater than 32768 can
         * seemingly only be opened by wimlib anyway.
         */
        if (block_length == 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_length >> 16, 8);

                lzx_write_bits(os, block_length & 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 aligned_cost = 0;
        u32 verbatim_cost = 0;

        /* A verbatim block requires 3 bits in each place that an aligned 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 output 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;
}

/*
 * Return the offset slot for the specified adjusted match offset, using the
 * compressor's acceleration tables to speed up the mapping.
 */
static inline unsigned
lzx_comp_get_offset_slot(struct lzx_compressor *c, u32 adjusted_offset,
                         bool is_16_bit)
{
        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];
}

/*
 * 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.
 */
static void
lzx_flush_block(struct lzx_compressor *c, struct lzx_output_bitstream *os,
                const u8 *block_begin, u32 block_length, u32 seq_idx)
{
        int block_type;

        lzx_make_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_length,
                                   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;
}

/* Tally the Huffman symbol for a literal and increment the literal run length.
 */
static inline void
lzx_record_literal(struct lzx_compressor *c, unsigned literal, u32 *litrunlen_p)
{
        c->freqs.main[literal]++;
        ++*litrunlen_p;
}

/* Tally the Huffman symbol for a match, save the match data and the length of
 * the preceding literal run in the next lzx_sequence, and update the recent
 * offsets queue.  */
static inline void
lzx_record_match(struct lzx_compressor *c, unsigned length, u32 offset_data,
                 u32 recent_offsets[LZX_NUM_RECENT_OFFSETS], bool is_16_bit,
                 u32 *litrunlen_p, struct lzx_sequence **next_seq_p)
{
        u32 litrunlen = *litrunlen_p;
        struct lzx_sequence *next_seq = *next_seq_p;
        unsigned offset_slot;
        unsigned v;

        v = length - LZX_MIN_MATCH_LEN;

        /* Save the literal run length and adjusted length.  */
        next_seq->litrunlen = litrunlen;
        next_seq->adjusted_length = v;

        /* Compute the length header and tally the length symbol if needed  */
        if (v >= LZX_NUM_PRIMARY_LENS) {
                c->freqs.len[v - LZX_NUM_PRIMARY_LENS]++;
                v = LZX_NUM_PRIMARY_LENS;
        }

        /* Compute the offset slot  */
        offset_slot = lzx_comp_get_offset_slot(c, offset_data, is_16_bit);

        /* Compute the match header.  */
        v += offset_slot * LZX_NUM_LEN_HEADERS;

        /* Save the adjusted offset and match header.  */
        next_seq->adjusted_offset_and_match_hdr = (offset_data << 9) | v;

        /* Tally the main symbol.  */
        c->freqs.main[LZX_NUM_CHARS + v]++;

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

                /* Tally the aligned offset symbol if needed  */
                if (offset_data >= 16)
                        c->freqs.aligned[offset_data & LZX_ALIGNED_OFFSET_BITMASK]++;

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

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

/* Finish the last lzx_sequence.  The last lzx_sequence is just a literal run;
 * there is no match.  This literal run may be empty.  */
static inline void
lzx_finish_sequence(struct lzx_sequence *last_seq, u32 litrunlen)
{
        last_seq->litrunlen = litrunlen;

        /* Special value to mark last sequence  */
        last_seq->adjusted_offset_and_match_hdr = 0x80000000;
}

/******************************************************************************/

/*
 * Block splitting algorithm.  The problem 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.  We also add a number
 * proportional to the block length so that the algorithm is more likely to end
 * long blocks than short blocks.  This reflects the general expectation that it
 * will become increasingly beneficial to start a new block as the current
 * blocks grows larger.
 *
 * 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
init_block_split_stats(struct block_split_stats *stats)
{
        for (int i = 0; i < NUM_OBSERVATION_TYPES; i++) {
                stats->new_observations[i] = 0;
                stats->observations[i] = 0;
        }
        stats->num_new_observations = 0;
        stats->num_observations = 0;
}

/* Literal observation.  Heuristic: use the top 2 bits and low 1 bits of the
 * literal, for 8 possible literal observation types.  */
static inline void
observe_literal(struct 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 inline void
observe_match(struct block_split_stats *stats, unsigned length)
{
        stats->new_observations[NUM_LITERAL_OBSERVATION_TYPES + (length >= 5)]++;
        stats->num_new_observations++;
}

static bool
do_end_block_check(struct block_split_stats *stats, u32 block_length)
{
        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 + (block_length / 1024) * stats->num_observations >=
                    stats->num_new_observations * 51 / 64 * 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;
}

static inline bool
should_end_block(struct block_split_stats *stats,
                 const u8 *in_block_begin, const u8 *in_next, const u8 *in_end)
{
        /* Ready to check block split statistics? */
        if (stats->num_new_observations < NUM_OBSERVATIONS_PER_BLOCK_CHECK ||
            in_next - in_block_begin < MIN_BLOCK_LENGTH ||
            in_end - in_next < MIN_BLOCK_LENGTH)
                return false;

        return do_end_block_check(stats, in_next - in_block_begin);
}

/******************************************************************************/

/*
 * 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 inline void
lzx_tally_item_list(struct lzx_compressor *c, u32 block_length, bool is_16_bit)
{
        u32 node_idx = block_length;

        for (;;) {
                u32 item;
                u32 len;
                u32 offset_data;
                unsigned v;
                unsigned offset_slot;

                /* Tally literals until either a match or the beginning of the
                 * block 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 (item & OPTIMUM_EXTRA_FLAG) {

                        if (node_idx == 0)
                                break;

                        /* Tally a rep0 match.  */
                        len = item & OPTIMUM_LEN_MASK;
                        v = len - LZX_MIN_MATCH_LEN;
                        if (v >= LZX_NUM_PRIMARY_LENS) {
                                c->freqs.len[v - LZX_NUM_PRIMARY_LENS]++;
                                v = LZX_NUM_PRIMARY_LENS;
                        }
                        c->freqs.main[LZX_NUM_CHARS + v]++;

                        /* Tally a literal.  */
                        c->freqs.main[c->optimum_nodes[node_idx].extra_literal]++;

                        item = c->optimum_nodes[node_idx].extra_match;
                        node_idx -= len + 1;
                }

                len = item & OPTIMUM_LEN_MASK;
                offset_data = item >> OPTIMUM_OFFSET_SHIFT;

                node_idx -= len;

                /* Tally a match.  */

                /* Tally the aligned offset symbol if needed.  */
                if (offset_data >= 16)
                        c->freqs.aligned[offset_data & LZX_ALIGNED_OFFSET_BITMASK]++;

                /* Tally the length symbol if needed.  */
                v = len - LZX_MIN_MATCH_LEN;;
                if (v >= LZX_NUM_PRIMARY_LENS) {
                        c->freqs.len[v - LZX_NUM_PRIMARY_LENS]++;
                        v = LZX_NUM_PRIMARY_LENS;
                }

                /* Tally the main symbol.  */
                offset_slot = lzx_comp_get_offset_slot(c, offset_data, is_16_bit);
                v += offset_slot * LZX_NUM_LEN_HEADERS;
                c->freqs.main[LZX_NUM_CHARS + v]++;
        }
}

/*
 * 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 inline u32
lzx_record_item_list(struct lzx_compressor *c, u32 block_length, bool is_16_bit)
{
        u32 node_idx = block_length;
        u32 seq_idx = ARRAY_LEN(c->chosen_sequences) - 1;
        u32 lit_start_node;

        /* Special value to mark last sequence  */
        c->chosen_sequences[seq_idx].adjusted_offset_and_match_hdr = 0x80000000;

        lit_start_node = node_idx;
        for (;;) {
                u32 item;
                u32 len;
                u32 offset_data;
                unsigned v;
                unsigned offset_slot;

                /* Tally literals until either a match or the beginning of the
                 * block 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 (item & OPTIMUM_EXTRA_FLAG) {

                        if (node_idx == 0)
                                break;

                        /* Save the literal run length for the next sequence
                         * (the "previous sequence" when walking backwards).  */
                        len = item & OPTIMUM_LEN_MASK;
                        c->chosen_sequences[seq_idx].litrunlen = lit_start_node - node_idx;
                        seq_idx--;
                        lit_start_node = node_idx - len;

                        /* Tally a rep0 match.  */
                        v = len - LZX_MIN_MATCH_LEN;
                        c->chosen_sequences[seq_idx].adjusted_length = v;
                        if (v >= LZX_NUM_PRIMARY_LENS) {
                                c->freqs.len[v - LZX_NUM_PRIMARY_LENS]++;
                                v = LZX_NUM_PRIMARY_LENS;
                        }
                        c->freqs.main[LZX_NUM_CHARS + v]++;
                        c->chosen_sequences[seq_idx].adjusted_offset_and_match_hdr = v;

                        /* Tally a literal.  */
                        c->freqs.main[c->optimum_nodes[node_idx].extra_literal]++;

                        item = c->optimum_nodes[node_idx].extra_match;
                        node_idx -= len + 1;
                }

                len = item & OPTIMUM_LEN_MASK;
                offset_data = item >> OPTIMUM_OFFSET_SHIFT;

                /* Save the literal run length for the next sequence (the
                 * "previous sequence" when walking backwards).  */
                c->chosen_sequences[seq_idx--].litrunlen = lit_start_node - node_idx;
                node_idx -= len;
                lit_start_node = node_idx;

                /* Record a match.  */

                /* Tally the aligned offset symbol if needed.  */
                if (offset_data >= 16)
                        c->freqs.aligned[offset_data & LZX_ALIGNED_OFFSET_BITMASK]++;

                /* Save the adjusted length.  */
                v = len - LZX_MIN_MATCH_LEN;
                c->chosen_sequences[seq_idx].adjusted_length = v;

                /* Tally the length symbol if needed.  */
                if (v >= LZX_NUM_PRIMARY_LENS) {
                        c->freqs.len[v - LZX_NUM_PRIMARY_LENS]++;
                        v = LZX_NUM_PRIMARY_LENS;
                }

                /* Tally the main symbol.  */
                offset_slot = lzx_comp_get_offset_slot(c, offset_data, is_16_bit);
                v += offset_slot * LZX_NUM_LEN_HEADERS;
                c->freqs.main[LZX_NUM_CHARS + v]++;

                /* Save the adjusted offset and match header.  */
                c->chosen_sequences[seq_idx].adjusted_offset_and_match_hdr =
                                (offset_data << 9) | v;
        }

        /* Save the literal run length for the first sequence.  */
        c->chosen_sequences[seq_idx].litrunlen = lit_start_node - node_idx;

        /* Return the index in c->chosen_sequences at which the lzx_sequences
         * begin.  */
        return seq_idx;
}

/*
 * 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_length].  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_length]', 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 path.
 *
 * 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; it only considers the
 * lowest cost to reach each individual position.
 */
static inline struct lzx_lru_queue
lzx_find_min_cost_path(struct lzx_compressor * const restrict c,
                       const u8 * const restrict block_begin,
                       const u32 block_length,
                       const struct lzx_lru_queue initial_queue,
                       bool is_16_bit)
{
        struct lzx_optimum_node *cur_node = c->optimum_nodes;
        struct lz_match *cache_ptr = c->match_cache;
        const u8 *in_next = block_begin;
        const u8 * const block_end = block_begin + block_length;

        /* 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,
         * it is no longer needed.  */
        struct lzx_lru_queue queues[512];

        STATIC_ASSERT(ARRAY_LEN(queues) >= LZX_MAX_MATCH_LEN + 1);
#define QUEUE(in) (queues[(uintptr_t)(in) % ARRAY_LEN(queues)])

        /* Initially, the cost to reach each node is "infinity".  */
        memset(c->optimum_nodes, 0xFF,
               (block_length + 1) * sizeof(c->optimum_nodes[0]));

        QUEUE(block_begin) = initial_queue;

        /* The following loop runs 'block_length' iterations, one per node.  */
        do {
                unsigned num_matches;
                unsigned literal;
                u32 cost;
                struct lz_match *matches;

                /*
                 * 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++;
                matches = cache_ptr;

                if (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 R0 match  */
                        matchptr = in_next - lzx_lru_queue_R0(QUEUE(in_next));
                        if (load_u16_unaligned(matchptr) != load_u16_unaligned(in_next))
                                goto R0_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))
                                        goto done_matches;
                        } while (in_next[next_len - 1] == matchptr[next_len - 1]);

                R0_done:

                        /* Consider R1 match  */
                        matchptr = in_next - lzx_lru_queue_R1(QUEUE(in_next));
                        if (load_u16_unaligned(matchptr) != load_u16_unaligned(in_next))
                                goto R1_done;
                        if (matchptr[next_len - 1] != in_next[next_len - 1])
                                goto R1_done;
                        for (unsigned len = 2; len < next_len - 1; len++)
                                if (matchptr[len] != in_next[len])
                                        goto R1_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))
                                        goto done_matches;
                        } while (in_next[next_len - 1] == matchptr[next_len - 1]);

                R1_done:

                        /* Consider R2 match  */
                        matchptr = in_next - lzx_lru_queue_R2(QUEUE(in_next));
                        if (load_u16_unaligned(matchptr) != load_u16_unaligned(in_next))
                                goto R2_done;
                        if (matchptr[next_len - 1] != in_next[next_len - 1])
                                goto R2_done;
                        for (unsigned len = 2; len < next_len - 1; len++)
                                if (matchptr[len] != in_next[len])
                                        goto R2_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))
                                        goto done_matches;
                        } while (in_next[next_len - 1] == matchptr[next_len - 1]);

                R2_done:
                        matches = cache_ptr;
                        cache_ptr += num_matches - 1;
                        while (next_len > cache_ptr->length) {
                                if (cache_ptr == matches)
                                        goto done_matches;
                                cache_ptr--;
                        }

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

                        #if LZX_CONSIDER_ALIGNED_COSTS
                                if (offset_data >= 16)
                                        base_cost += c->costs.aligned[offset_data &
                                                                      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 =
                                                        (offset_data << OPTIMUM_OFFSET_SHIFT) | next_len;
                                        }
                                } while (++next_len <= cache_ptr->length);

                                if (cache_ptr == matches) {
                                        /* Consider match + lit + rep0 */
                                        u32 remaining = block_end - (in_next + next_len);
                                        if (likely(remaining >= 2)) {
                                                const u8 *strptr = in_next + next_len;
                                                const u8 *matchptr = strptr - offset;
                                                if (unlikely(load_u16_unaligned(strptr) == load_u16_unaligned(matchptr))) {
                                                        u32 rep0_len = lz_extend(strptr, matchptr, 2,
                                                                                 min(remaining, LZX_MAX_MATCH_LEN));
                                                        u8 lit = strptr[-1];
                                                        cost += c->costs.main[lit] +
                                                                c->costs.match_cost[0][rep0_len - LZX_MIN_MATCH_LEN];
                                                        u32 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_EXTRA_FLAG | rep0_len;
                                                                (cur_node + total_len)->extra_literal = lit;
                                                                (cur_node + total_len)->extra_match =
                                                                        (offset_data << OPTIMUM_OFFSET_SHIFT) | (next_len - 1);
                                                        }
                                                }
                                        }
                                        break;
                                }
                                cache_ptr--;
                        }
                }

        done_matches:
                cache_ptr = matches + num_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(in_next) = QUEUE(in_next - 1);
                } else {
                        /* Match: queue update is needed.  */
                        unsigned len = cur_node->item & OPTIMUM_LEN_MASK;
                        u32 offset_data = (cur_node->item &
                                           ~OPTIMUM_EXTRA_FLAG) >> OPTIMUM_OFFSET_SHIFT;
                        if (offset_data >= LZX_NUM_RECENT_OFFSETS) {
                                /* Explicit offset match: insert offset at front  */
                                QUEUE(in_next) =
                                        lzx_lru_queue_push(QUEUE(in_next - len),
                                                           offset_data - LZX_OFFSET_ADJUSTMENT);
                        } else if (cur_node->item & OPTIMUM_EXTRA_FLAG) {
                                /* Explicit offset match, then literal, then
                                 * rep0 match: insert offset at front  */
                                len += 1 + (cur_node->extra_match & OPTIMUM_LEN_MASK);
                                QUEUE(in_next) =
                                        lzx_lru_queue_push(QUEUE(in_next - len),
                                                           (cur_node->extra_match >> OPTIMUM_OFFSET_SHIFT) -
                                                           LZX_OFFSET_ADJUSTMENT);
                        } else {
                                /* Repeat offset match: swap offset to front  */
                                QUEUE(in_next) =
                                        lzx_lru_queue_swap(QUEUE(in_next - len),
                                                           offset_data);
                        }
                }
        } while (in_next != block_end);

        /* Return the match offset queue at the end of the minimum cost path. */
        return QUEUE(block_end);
}

/* Given the costs for the main and length codewords, compute 'match_costs'.  */
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;

        for (unsigned offset_slot = 0; offset_slot < num_offset_slots; offset_slot++) {

                u32 extra_cost = (u32)lzx_extra_offset_bits[offset_slot] * LZX_BIT_COST;
                unsigned main_symbol = LZX_NUM_CHARS + (offset_slot *
                                                        LZX_NUM_LEN_HEADERS);
                unsigned i;

        #if LZX_CONSIDER_ALIGNED_COSTS
                if (offset_slot >= 8)
                        extra_cost -= LZX_NUM_ALIGNED_OFFSET_BITS * LZX_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;
        }
}

/* Set default LZX Huffman symbol costs to bootstrap the iterative optimization
 * algorithm.  */
static void
lzx_set_default_costs(struct lzx_compressor *c, const u8 *block, u32 block_length)
{
        u32 i;
        bool have_byte[256];
        unsigned num_used_bytes;

        /* The costs below are hard coded to use a scaling factor of 64.  */
        STATIC_ASSERT(LZX_BIT_COST == 64);

        /*
         * Heuristics:
         *
         * - Use smaller initial costs for literal symbols when the input buffer
         *   contains fewer distinct bytes.
         *
         * - Assume that match symbols are more costly than literal symbols.
         *
         * - Assume that length symbols for shorter lengths are less costly than
         *   length symbols for longer lengths.
         */

        for (i = 0; i < 256; i++)
                have_byte[i] = false;

        for (i = 0; i < block_length; i++)
                have_byte[block[i]] = true;

        num_used_bytes = 0;
        for (i = 0; i < 256; i++)
                num_used_bytes += have_byte[i];

        for (i = 0; i < 256; i++)
                c->costs.main[i] = 560 - (256 - num_used_bytes);

        for (; i < c->num_main_syms; i++)
                c->costs.main[i] = 680;

        for (i = 0; i < LZX_LENCODE_NUM_SYMBOLS; i++)
                c->costs.len[i] = 412 + i;

#if LZX_CONSIDER_ALIGNED_COSTS
        for (i = 0; i < LZX_ALIGNEDCODE_NUM_SYMBOLS; i++)
                c->costs.aligned[i] = LZX_NUM_ALIGNED_OFFSET_BITS * LZX_BIT_COST;
#endif

        lzx_compute_match_costs(c);
}

/* 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) * LZX_BIT_COST;
        }

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

#if LZX_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) * LZX_BIT_COST;
        }
#endif

        lzx_compute_match_costs(c);
}

/*
 * Choose a "near-optimal" literal/match sequence to use for the current 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 taken from the Huffman codes computed in
 * the previous pass.
 */
static inline struct lzx_lru_queue
lzx_optimize_and_write_block(struct lzx_compressor * const restrict c,
                             struct lzx_output_bitstream * const restrict os,
                             const u8 * const restrict block_begin,
                             const u32 block_length,
                             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, block_begin, block_length);

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

                if (--num_passes_remaining == 0)
                        break;

                /* At least one iteration remains; update the costs. */
                lzx_reset_symbol_frequencies(c);
                lzx_tally_item_list(c, block_length, is_16_bit);
                lzx_make_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_length, is_16_bit);
        lzx_flush_block(c, os, block_begin, block_length, 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 that 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 inline void
lzx_compress_near_optimal(struct lzx_compressor * restrict c,
                          const u8 * const restrict in_begin,
                          struct lzx_output_bitstream * restrict os,
                          bool is_16_bit)
{
        const u8 *       in_next = in_begin;
        const u8 * const in_end  = in_begin + c->in_nbytes;
        struct lzx_lru_queue queue;

        lcpit_matchfinder_load_buffer(&c->lcpit_mf, in_begin, c->in_nbytes);
        lzx_lru_queue_init(&queue);

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

                init_block_split_stats(&c->split_stats);

                /* Run the block through the matchfinder and cache the matches. */
        enter_mf_loop:
                do {
                        u32 num_matches;
                        u32 best_len = 0;

                        num_matches = lcpit_matchfinder_get_matches(&c->lcpit_mf, cache_ptr + 1);
                        cache_ptr->length = num_matches;
                        if (num_matches)
                                best_len = cache_ptr[1].length;

                        if (in_next >= next_observation) {
                                if (best_len) {
                                        observe_match(&c->split_stats, best_len);
                                        next_observation = in_next + best_len;
                                } else {
                                        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 very 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 >= c->nice_match_length) {
                                best_len = lz_extend(in_next, in_next - cache_ptr[1].offset,
                                                     best_len,
                                                     min(LZX_MAX_MATCH_LEN,
                                                         in_end - in_next));
                                cache_ptr[1].length = best_len;
                                lcpit_matchfinder_skip_bytes(&c->lcpit_mf, best_len - 1);
                                cache_ptr += 1 + num_matches;
                                for (u32 i = 0; i < best_len - 1; i++) {
                                        cache_ptr->length = 0;
                                        cache_ptr++;
                                }
                                in_next += best_len;
                                next_observation = in_next;
                        } else {
                                cache_ptr += 1 + num_matches;
                                in_next++;
                        }
                } while (in_next < next_pause_point &&
                         likely(cache_ptr < &c->match_cache[LZX_CACHE_LENGTH]));

                if (unlikely(cache_ptr >= &c->match_cache[LZX_CACHE_LENGTH]))
                        goto flush_block;

                if (in_next >= in_max_block_end)
                        goto flush_block;

                if (c->split_stats.num_new_observations >= NUM_OBSERVATIONS_PER_BLOCK_CHECK) {
                        if (do_end_block_check(&c->split_stats, in_next - in_block_begin))
                                goto flush_block;
                        if (in_max_block_end - in_next <= MIN_BLOCK_LENGTH)
                                next_observation = in_max_block_end;
                }

                next_pause_point = min(in_next +
                                       NUM_OBSERVATIONS_PER_BLOCK_CHECK * 2 -
                                       c->split_stats.num_new_observations,
                                       in_max_block_end - LZX_MAX_MATCH_LEN - 1);
                goto enter_mf_loop;

        flush_block:
                /* We've finished running the block through the matchfinder.
                 * Now choose a match/literal sequence and write the block.  */

                queue = lzx_optimize_and_write_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,
                             struct lzx_output_bitstream *os)
{
        lzx_compress_near_optimal(c, c->in_buffer, os, true);
}

static void
lzx_compress_near_optimal_32(struct lzx_compressor *c,
                             struct lzx_output_bitstream *os)
{
        lzx_compress_near_optimal(c, c->in_buffer, os, false);
}

/*
 * Given a pointer to the current byte sequence and the current list of recent
 * match offsets, find the longest repeat offset match.
 *
 * If no match of at least 2 bytes is found, then return 0.
 *
 * If a match of at least 2 bytes is found, then return its length and set
 * *rep_max_idx_ret to the index of its offset in @queue.
*/
static unsigned
lzx_find_longest_repeat_offset_match(const u8 * const in_next,
                                     const u32 bytes_remaining,
                                     const u32 recent_offsets[LZX_NUM_RECENT_OFFSETS],
                                     unsigned *rep_max_idx_ret)
{
        STATIC_ASSERT(LZX_NUM_RECENT_OFFSETS == 3);

        const unsigned max_len = min(bytes_remaining, LZX_MAX_MATCH_LEN);
        const u16 next_2_bytes = load_u16_unaligned(in_next);
        const u8 *matchptr;
        unsigned rep_max_len;
        unsigned rep_max_idx;
        unsigned rep_len;

        matchptr = in_next - recent_offsets[0];
        if (load_u16_unaligned(matchptr) == next_2_bytes)
                rep_max_len = lz_extend(in_next, matchptr, 2, max_len);
        else
                rep_max_len = 0;
        rep_max_idx = 0;

        matchptr = in_next - recent_offsets[1];
        if (load_u16_unaligned(matchptr) == next_2_bytes) {
                rep_len = lz_extend(in_next, matchptr, 2, max_len);
                if (rep_len > rep_max_len) {
                        rep_max_len = rep_len;
                        rep_max_idx = 1;
                }
        }

        matchptr = in_next - recent_offsets[2];
        if (load_u16_unaligned(matchptr) == next_2_bytes) {
                rep_len = lz_extend(in_next, matchptr, 2, max_len);
                if (rep_len > rep_max_len) {
                        rep_max_len = rep_len;
                        rep_max_idx = 2;
                }
        }

        *rep_max_idx_ret = rep_max_idx;
        return rep_max_len;
}

/* Fast heuristic scoring for lazy parsing: how "good" is this match?  */
static inline 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 inline unsigned
lzx_repeat_offset_match_score(unsigned rep_len, unsigned rep_idx)
{
        return rep_len + 3;
}

/* This is the "lazy" LZX compressor.  */
static inline void
lzx_compress_lazy(struct lzx_compressor *c, struct lzx_output_bitstream *os,
                  bool is_16_bit)
{
        const u8 * const in_begin = c->in_buffer;
        const u8 *       in_next = in_begin;
        const u8 * const in_end  = in_begin + c->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[3] = {1, 1, 1};
        u32 next_hashes[2] = {};

        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_LENGTH, in_end - in_next);
                struct lzx_sequence *next_seq = c->chosen_sequences;
                unsigned cur_len;
                u32 cur_offset;
                u32 cur_offset_data;
                unsigned cur_score;
                unsigned next_len;
                u32 next_offset;
                u32 next_offset_data;
                unsigned next_score;
                unsigned rep_max_len;
                unsigned rep_max_idx;
                unsigned rep_score;
                unsigned skip_len;
                u32 litrunlen = 0;

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

                do {
                        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 at the current position.  */

                        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 (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]))
                        {
                                /* There was no match found, or the only match found
                                 * was a distant length 3 match.  Output a literal.  */
                                lzx_record_literal(c, *in_next, &litrunlen);
                                observe_literal(&c->split_stats, *in_next);
                                in_next++;
                                continue;
                        }

                        observe_match(&c->split_stats, cur_len);

                        if (cur_offset == recent_offsets[0]) {
                                in_next++;
                                cur_offset_data = 0;
                                skip_len = cur_len - 1;
                                goto choose_cur_match;
                        }

                        cur_offset_data = cur_offset + LZX_OFFSET_ADJUSTMENT;
                        cur_score = lzx_explicit_offset_match_score(cur_len, cur_offset_data);

                        /* Consider a repeat offset match  */
                        rep_max_len = lzx_find_longest_repeat_offset_match(in_next,
                                                                           in_end - in_next,
                                                                           recent_offsets,
                                                                           &rep_max_idx);
                        in_next++;

                        if (rep_max_len >= 3 &&
                            (rep_score = lzx_repeat_offset_match_score(rep_max_len,
                                                                       rep_max_idx)) >= cur_score)
                        {
                                cur_len = rep_max_len;
                                cur_offset_data = rep_max_idx;
                                skip_len = rep_max_len - 1;
                                goto choose_cur_match;
                        }

                have_cur_match:

                        /* We have a match at the current position.  */

                        /* If we have a very long match, choose it immediately.  */
                        if (cur_len >= nice_len) {
                                skip_len = cur_len - 1;
                                goto choose_cur_match;
                        }

                        /* See if there's a better match at the next position.  */

                        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) {
                                in_next++;
                                skip_len = cur_len - 2;
                                goto choose_cur_match;
                        }

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

                        rep_max_len = lzx_find_longest_repeat_offset_match(in_next,
                                                                           in_end - in_next,
                                                                           recent_offsets,
                                                                           &rep_max_idx);
                        in_next++;

                        if (rep_max_len >= 3 &&
                            (rep_score = lzx_repeat_offset_match_score(rep_max_len,
                                                                       rep_max_idx)) >= next_score)
                        {

                                if (rep_score > cur_score) {
                                        /* The next match is better, and it's a
                                         * repeat offset match.  */
                                        lzx_record_literal(c, *(in_next - 2),
                                                           &litrunlen);
                                        cur_len = rep_max_len;
                                        cur_offset_data = rep_max_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_record_literal(c, *(in_next - 2),
                                                           &litrunlen);
                                        cur_len = next_len;
                                        cur_offset_data = next_offset_data;
                                        cur_score = next_score;
                                        goto have_cur_match;
                                }
                        }

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

                choose_cur_match:
                        lzx_record_match(c, cur_len, cur_offset_data,
                                         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);
                } while (in_next < in_max_block_end &&
                         !should_end_block(&c->split_stats, in_block_begin, in_next, in_end));

                lzx_finish_sequence(next_seq, litrunlen);

                lzx_flush_block(c, os, in_block_begin, in_next - in_block_begin, 0);

        } while (in_next != in_end);
}

static void
lzx_compress_lazy_16(struct lzx_compressor *c, struct lzx_output_bitstream *os)
{
        lzx_compress_lazy(c, os, true);
}

static void
lzx_compress_lazy_32(struct lzx_compressor *c, struct lzx_output_bitstream *os)
{
        lzx_compress_lazy(c, os, false);
}

/* Generate the acceleration tables for 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])
                        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])
                        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 <= LZX_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, lcpit_mf) +
                               sizeof(struct lcpit_matchfinder);
                else
                        return offsetof(struct lzx_compressor, lcpit_mf) +
                               sizeof(struct lcpit_matchfinder);
        }
}

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; /* in_buffer */
        if (compression_level > LZX_MAX_FAST_LEVEL)
                size += lcpit_matchfinder_get_needed_memory(max_bufsize);
        return size;
}

static int
lzx_create_compressor(size_t max_bufsize, unsigned compression_level,
                      bool destructive, void **c_ret)
{
        unsigned window_order;
        struct lzx_compressor *c;

        window_order = lzx_get_window_order(max_bufsize);
        if (window_order == 0)
                return WIMLIB_ERR_INVALID_PARAM;

        c = MALLOC(lzx_get_compressor_size(max_bufsize, compression_level));
        if (!c)
                goto oom0;

        c->destructive = destructive;

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

        if (!c->destructive) {
                c->in_buffer = MALLOC(max_bufsize);
                if (!c->in_buffer)
                        goto oom1;
        }

        if (compression_level <= LZX_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;
                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 cannot be 0.  */
                if (c->max_search_depth < 2)
                        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 nice_match_length and max_search_depth with the
                 * compression level.  */
                c->max_search_depth = (24 * compression_level) / 50;
                c->nice_match_length = (48 * compression_level) / 50;

                /* Set a number of optimization passes appropriate for the
                 * compression level.  */

                c->num_optim_passes = 1;

                if (compression_level >= 45)
                        c->num_optim_passes++;

                /* Use more optimization passes for higher compression levels.
                 * But the more passes there are, the less they help --- so
                 * don't add them linearly.  */
                if (compression_level >= 70) {
                        c->num_optim_passes++;
                        if (compression_level >= 100)
                                c->num_optim_passes++;
                        if (compression_level >= 150)
                                c->num_optim_passes++;
                        if (compression_level >= 200)
                                c->num_optim_passes++;
                        if (compression_level >= 300)
                                c->num_optim_passes++;
                }
        }

        /* max_search_depth == 0 is invalid.  */
        if (c->max_search_depth < 1)
                c->max_search_depth = 1;

        if (c->nice_match_length > LZX_MAX_MATCH_LEN)
                c->nice_match_length = LZX_MAX_MATCH_LEN;

        if (!lcpit_matchfinder_init(&c->lcpit_mf, max_bufsize,
                                    LZX_MIN_MATCH_LEN, c->nice_match_length))
                goto oom2;

        lzx_init_offset_slot_tabs(c);
        *c_ret = c;
        return 0;

oom2:
        if (!c->destructive)
                FREE(c->in_buffer);
oom1:
        FREE(c);
oom0:
        return WIMLIB_ERR_NOMEM;
}

static size_t
lzx_compress(const void *restrict in, size_t in_nbytes,
             void *restrict out, size_t out_nbytes_avail, void *restrict _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 < 100)
                return 0;

        /* Copy the input data into the internal buffer and preprocess it.  */
        if (c->destructive)
                c->in_buffer = (void *)in;
        else
                memcpy(c->in_buffer, in, in_nbytes);
        c->in_nbytes = in_nbytes;
        lzx_preprocess(c->in_buffer, 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, &os);

        /* Flush the output bitstream and return the compressed size or 0.  */
        result = lzx_flush_output(&os);
        if (!result && c->destructive)
                lzx_postprocess(c->in_buffer, c->in_nbytes);
        return result;
}

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

        lcpit_matchfinder_destroy(&c->lcpit_mf);
        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,
};