LZX compressor improvements
authorEric Biggers <ebiggers3@gmail.com>
Sat, 2 Jul 2016 03:31:17 +0000 (22:31 -0500)
committerEric Biggers <ebiggers3@gmail.com>
Sat, 2 Jul 2016 15:04:13 +0000 (10:04 -0500)
- Improved block splitting algorithm
- Consider gap matches
- Improved default cost initialization
- Other improvements and cleanups

src/lzx_compress.c
tools/log2_interpolation.r [new file with mode: 0644]

index 588b81d..f0c3c52 100644 (file)
@@ -1,11 +1,11 @@
 /*
  * lzx_compress.c
  *
- * A compressor for the LZX compression format, as used in WIM files.
+ * A compressor for the LZX compression format, as used in WIM archives.
  */
 
 /*
- * Copyright (C) 2012, 2013, 2014, 2015 Eric Biggers
+ * 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
  * 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.
+ * Two different LZX-compatible algorithms are implemented: "near-optimal" and
+ * "lazy".  "Near-optimal" is significantly slower than "lazy", but results in a
+ * better compression ratio.  The "near-optimal" algorithm is used at the
+ * default compression level.
  *
  * This file may need some slight modifications to be used outside of the WIM
  * format.  In particular, in other situations the LZX block header might be
  * slightly different, and sliding window support might be required.
  *
- * 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 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.
  *   ("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.
+ *   useful, but generally only if the compressor is smart about choosing them.
  *
  * - In LZX, offset slots 0 through 2 actually represent entries in an LRU queue
  *   of match offsets.  This is very useful for certain types of files, such as
  *   binary files that have repeating records.
  */
 
-#ifdef HAVE_CONFIG_H
-#  include "config.h"
-#endif
+/******************************************************************************/
+/*                            General parameters                              */
+/*----------------------------------------------------------------------------*/
+
+/*
+ * The compressor uses the faster algorithm at levels <= MAX_FAST_LEVEL.  It
+ * uses the slower algorithm at levels > MAX_FAST_LEVEL.
+ */
+#define MAX_FAST_LEVEL                         34
+
+/*
+ * The compressor-side limits on the codeword lengths (in bits) for each Huffman
+ * code.  To make outputting bits slightly faster, some of these limits are
+ * lower than the limits defined by the LZX format.  This does not significantly
+ * affect the compression ratio.
+ */
+#define MAIN_CODEWORD_LIMIT                    16
+#define LENGTH_CODEWORD_LIMIT                  12
+#define ALIGNED_CODEWORD_LIMIT                 7
+#define PRE_CODEWORD_LIMIT                     7
+
+
+/******************************************************************************/
+/*                         Block splitting parameters                         */
+/*----------------------------------------------------------------------------*/
+
+/*
+ * The compressor always outputs blocks of at least this size in bytes, except
+ * for the last block which may need to be smaller.
+ */
+#define MIN_BLOCK_SIZE                         6500
 
 /*
- * Start a new LZX block (with new Huffman codes) after this many bytes.
+ * The compressor attempts to end a block when it reaches this size in bytes.
+ * The final size might be slightly larger due to matches extending beyond the
+ * end of the block.  Specifically:
  *
- * Note: actual block sizes may slightly exceed this value.
+ *  - The near-optimal compressor may choose a match of up to LZX_MAX_MATCH_LEN
+ *    bytes starting at position 'SOFT_MAX_BLOCK_SIZE - 1'.
  *
- * TODO: recursive splitting and cost evaluation might be good for an extremely
- * high compression mode, but otherwise it is almost always far too slow for how
- * much it helps.  Perhaps some sort of heuristic would be useful?
+ *  - The lazy compressor may choose a sequence of literals starting at position
+ *    'SOFT_MAX_BLOCK_SIZE - 1' when it sees a sequence of increasingly better
+ *    matches.  The final match may be up to LZX_MAX_MATCH_LEN bytes.  The
+ *    length of the literal sequence is approximately limited by the "nice match
+ *    length" parameter.
  */
-#define LZX_DIV_BLOCK_SIZE     32768
+#define SOFT_MAX_BLOCK_SIZE                    100000
 
 /*
- * LZX_CACHE_PER_POS is the number of lz_match structures to reserve in the
- * match cache for each byte position.  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.
+ * The number of observed items (matches and literals) that represents
+ * sufficient data for the compressor to decide whether the current block should
+ * be ended or not.
  */
-#define LZX_CACHE_PER_POS      7
+#define NUM_OBSERVATIONS_PER_BLOCK_CHECK       400
+
+
+/******************************************************************************/
+/*                      Parameters for slower algorithm                       */
+/*----------------------------------------------------------------------------*/
+
+/*
+ * The log base 2 of the number of entries in the hash table for finding length
+ * 2 matches.  This could be as high as 16, but using a smaller hash table
+ * speeds up compression due to reduced cache pressure.
+ */
+#define BT_MATCHFINDER_HASH2_ORDER             12
 
 /*
- * LZX_CACHE_LENGTH is the number of lz_match structures in the match cache,
- * excluding the extra "overflow" entries.  The per-position multiplier is '1 +
- * LZX_CACHE_PER_POS' instead of 'LZX_CACHE_PER_POS' because there is an
- * overhead of one lz_match per position, used to hold the match count at that
- * position.
+ * 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       (LZX_DIV_BLOCK_SIZE * (1 + LZX_CACHE_PER_POS))
+#define CACHE_LENGTH                           (SOFT_MAX_BLOCK_SIZE * 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.
+ * 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
+#define 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.
+ * A scaling factor that makes it possible to consider fractional bit costs.  A
+ * single bit has a cost of BIT_COST.
  *
  * Note: this is only useful as a statistical trick for when the true costs are
- * unknown.  In reality, each token in LZX requires a whole number of bits to
+ * unknown.  Ultimately, each token in LZX requires a whole number of bits to
  * output.
  */
-#define LZX_BIT_COST           16
+#define BIT_COST                               64
 
 /*
- * Should the compressor take into account the costs of aligned offset symbols?
+ * Should the compressor take into account the costs of aligned offset symbols
+ * instead of assuming that all are equally likely?
  */
-#define LZX_CONSIDER_ALIGNED_COSTS     1
+#define CONSIDER_ALIGNED_COSTS                 1
 
 /*
- * LZX_MAX_FAST_LEVEL is the maximum compression level at which we use the
- * faster algorithm.
+ * Should the "minimum" cost path search algorithm consider "gap" matches, where
+ * a normal match is followed by a literal, then by a match with the same
+ * offset?  This is one specific, somewhat common situation in which the true
+ * minimum cost path is often different from the path found by looking only one
+ * edge ahead.
  */
-#define LZX_MAX_FAST_LEVEL     34
+#define CONSIDER_GAP_MATCHES                   1
 
-/*
- * 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
+/******************************************************************************/
+/*                                  Includes                                  */
+/*----------------------------------------------------------------------------*/
 
-/*
- * 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 sizes we use.
- */
-#define MAIN_CODEWORD_LIMIT    12      /* 64-bit: can buffer 4 main symbols  */
-#define LENGTH_CODEWORD_LIMIT  12
-#define ALIGNED_CODEWORD_LIMIT 7
-#define PRE_CODEWORD_LIMIT     7
+#ifdef HAVE_CONFIG_H
+#  include "config.h"
+#endif
 
 #include "wimlib/compress_common.h"
 #include "wimlib/compressor_ops.h"
 #include "wimlib/unaligned.h"
 #include "wimlib/util.h"
 
-/* Matchfinders with 16-bit positions  */
+/* Note: BT_MATCHFINDER_HASH2_ORDER must be defined before including
+ * bt_matchfinder.h. */
+
+/* Matchfinders with 16-bit positions */
 #define mf_pos_t       u16
 #define MF_SUFFIX      _16
 #include "wimlib/bt_matchfinder.h"
 #include "wimlib/hc_matchfinder.h"
 
-/* Matchfinders with 32-bit positions  */
+/* Matchfinders with 32-bit positions */
 #undef mf_pos_t
 #undef MF_SUFFIX
 #define mf_pos_t       u32
 #include "wimlib/bt_matchfinder.h"
 #include "wimlib/hc_matchfinder.h"
 
-struct lzx_output_bitstream;
+/******************************************************************************/
+/*                            Compressor structure                            */
+/*----------------------------------------------------------------------------*/
 
-/* Codewords for the LZX Huffman codes.  */
+/* Codewords for the Huffman codes */
 struct lzx_codewords {
        u32 main[LZX_MAINCODE_MAX_NUM_SYMBOLS];
        u32 len[LZX_LENCODE_NUM_SYMBOLS];
        u32 aligned[LZX_ALIGNEDCODE_NUM_SYMBOLS];
 };
 
-/* Codeword lengths (in bits) for the LZX Huffman codes.
- * A zero length means the corresponding codeword has zero frequency.  */
+/*
+ * Codeword lengths, in bits, for the Huffman codes.
+ *
+ * A codeword length of 0 means the corresponding codeword has zero frequency.
+ *
+ * The main and length codes each have one extra entry for use as a sentinel.
+ * See lzx_write_compressed_code().
+ */
 struct lzx_lens {
        u8 main[LZX_MAINCODE_MAX_NUM_SYMBOLS + 1];
        u8 len[LZX_LENCODE_NUM_SYMBOLS + 1];
        u8 aligned[LZX_ALIGNEDCODE_NUM_SYMBOLS];
 };
 
-/* 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.  */
+/* Codewords and lengths for the Huffman codes */
 struct lzx_codes {
        struct lzx_codewords codewords;
        struct lzx_lens lens;
 };
 
-/* Symbol frequency counters for the LZX Huffman codes.  */
+/* Symbol frequency counters for the Huffman-encoded alphabets */
 struct lzx_freqs {
        u32 main[LZX_MAINCODE_MAX_NUM_SYMBOLS];
        u32 len[LZX_LENCODE_NUM_SYMBOLS];
        u32 aligned[LZX_ALIGNEDCODE_NUM_SYMBOLS];
 };
 
+/* Block split statistics.  See the "Block splitting algorithm" section later in
+ * this file for details. */
+#define NUM_LITERAL_OBSERVATION_TYPES 8
+#define NUM_MATCH_OBSERVATION_TYPES 2
+#define NUM_OBSERVATION_TYPES (NUM_LITERAL_OBSERVATION_TYPES + \
+                              NUM_MATCH_OBSERVATION_TYPES)
+struct lzx_block_split_stats {
+       u32 new_observations[NUM_OBSERVATION_TYPES];
+       u32 observations[NUM_OBSERVATION_TYPES];
+       u32 num_new_observations;
+       u32 num_observations;
+};
+
 /*
  * Represents a run of literals followed by a match or end-of-block.  This
- * 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.
+ * structure is needed to temporarily store items chosen by the compressor,
+ * since items cannot be written until all items for the block have been chosen
+ * and the block's Huffman codes have been computed.
  */
 struct lzx_sequence {
 
@@ -256,198 +297,149 @@ struct lzx_optimum_node {
        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.
+        * The best arrival to this node, i.e. the match or literal that was
+        * used to arrive to this position at the given 'cost'.  This can change
+        * as progressively lower cost paths are found to reach this position.
         *
-        * This variable is divided into two bitfields.
+        * For non-gap matches, this variable is divided into two bitfields
+        * whose meanings depend on the item type:
         *
         * Literals:
         *      Low bits are 0, high bits are the literal.
         *
         * Explicit offset matches:
-        *      Low bits are the match length, high bits are the offset plus 2.
+        *      Low bits are the match length, high bits are the offset plus
+        *      LZX_OFFSET_ADJUSTMENT.
         *
         * Repeat offset matches:
         *      Low bits are the match length, high bits are the queue index.
+        *
+        * For gap matches, identified by OPTIMUM_GAP_MATCH set, special
+        * behavior applies --- see the code.
         */
        u32 item;
 #define OPTIMUM_OFFSET_SHIFT 9
 #define OPTIMUM_LEN_MASK ((1 << OPTIMUM_OFFSET_SHIFT) - 1)
+#if CONSIDER_GAP_MATCHES
+#  define OPTIMUM_GAP_MATCH 0x80000000
+#endif
+
 } _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;
-};
+/* The cost model for near-optimal parsing */
+struct lzx_costs {
 
-#define LZX_QUEUE64_OFFSET_SHIFT 21
-#define LZX_QUEUE64_OFFSET_MASK        (((u64)1 << LZX_QUEUE64_OFFSET_SHIFT) - 1)
+       /*
+        * 'match_cost[offset_slot][len - LZX_MIN_MATCH_LEN]' is the cost of a
+        * length 'len' match which has an offset belonging to 'offset_slot'.
+        * The cost includes the main symbol, the length symbol if required, and
+        * the extra offset bits if any, excluding any entropy-coded bits
+        * (aligned offset bits).  It does *not* include the cost of the aligned
+        * offset symbol which may be required.
+        */
+       u16 match_cost[LZX_MAX_OFFSET_SLOTS][LZX_NUM_LENS];
 
-#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)
+       /* Cost of each symbol in the main code */
+       u32 main[LZX_MAINCODE_MAX_NUM_SYMBOLS];
 
-#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)
+       /* Cost of each symbol in the length code */
+       u32 len[LZX_LENCODE_NUM_SYMBOLS];
 
-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);
-}
+#if CONSIDER_ALIGNED_COSTS
+       /* Cost of each symbol in the aligned offset code */
+       u32 aligned[LZX_ALIGNEDCODE_NUM_SYMBOLS];
+#endif
+};
 
-static inline u64
-lzx_lru_queue_R0(struct lzx_lru_queue queue)
-{
-       return (queue.R >> LZX_QUEUE64_R0_SHIFT) & LZX_QUEUE64_OFFSET_MASK;
-}
+struct lzx_output_bitstream;
 
-static inline u64
-lzx_lru_queue_R1(struct lzx_lru_queue queue)
-{
-       return (queue.R >> LZX_QUEUE64_R1_SHIFT) & LZX_QUEUE64_OFFSET_MASK;
-}
+/* The main LZX compressor structure */
+struct lzx_compressor {
 
-static inline u64
-lzx_lru_queue_R2(struct lzx_lru_queue queue)
-{
-       return (queue.R >> LZX_QUEUE64_R2_SHIFT) & LZX_QUEUE64_OFFSET_MASK;
-}
+       /* The buffer for preprocessed input data, if not using destructive
+        * compression */
+       void *in_buffer;
 
-/* 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,
-       };
-}
+       /* If true, then the compressor need not preserve the input buffer if it
+        * compresses the data successfully */
+       bool destructive;
 
-/* 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),
-               };
+       /* Pointer to the compress() implementation chosen at allocation time */
+       void (*impl)(struct lzx_compressor *, const u8 *, size_t,
+                    struct lzx_output_bitstream *);
 
-       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 log base 2 of the window size for match offset encoding purposes.
+        * This will be >= LZX_MIN_WINDOW_ORDER and <= LZX_MAX_WINDOW_ORDER. */
+       unsigned window_order;
 
-/* The main LZX compressor structure  */
-struct lzx_compressor {
+       /* The number of symbols in the main alphabet.  This depends on the
+        * window order, since the window order determines the maximum possible
+        * match offset. */
+       unsigned num_main_syms;
 
-       /* The "nice" match length: if a match of this length is found, then
-        * choose it immediately without further consideration.  */
+       /* The "nice" match length: if a match of this length is found, then it
+        * is chosen immediately without further consideration. */
        unsigned nice_match_length;
 
-       /* The maximum search depth: consider at most this many potential
-        * matches at each position.  */
+       /* The maximum search depth: at most this many potential matches are
+        * considered 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  */
+       /* The 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.  */
+       /* The symbol frequency counters for the current block */
        struct lzx_freqs freqs;
 
+       /* Block split statistics for the current block */
+       struct lzx_block_split_stats split_stats;
+
        /* The Huffman codes for the current and previous blocks.  The one with
         * index 'codes_index' is for the current block, and the other one is
-        * for the previous block.  */
+        * 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.  */
+       /* The matches and literals that the compressor has chosen for the
+        * current block.  The required length of this array is limited by the
+        * maximum number of matches that can ever be chosen for a single block,
+        * plus one for the special entry at the end. */
        struct lzx_sequence chosen_sequences[
-                      DIV_ROUND_UP(LZX_DIV_BLOCK_SIZE, LZX_MIN_MATCH_LEN) + 1];
-
-       /* Tables for mapping adjusted offsets to offset slots  */
+                      DIV_ROUND_UP(SOFT_MAX_BLOCK_SIZE, LZX_MIN_MATCH_LEN) + 1];
 
-       /* offset slots [0, 29]  */
-       u8 offset_slot_tab_1[32768];
-
-       /* offset slots [30, 49]  */
-       u8 offset_slot_tab_2[128];
+       /* Tables for mapping adjusted offsets to offset slots */
+       u8 offset_slot_tab_1[32768]; /* offset slots [0, 29] */
+       u8 offset_slot_tab_2[128]; /* offset slots [30, 49] */
 
        union {
-               /* Data for greedy or lazy parsing  */
+               /* Data for lzx_compress_lazy() */
                struct {
-                       /* Hash chains matchfinder (MUST BE LAST!!!)  */
+                       /* 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  */
+               /* Data for lzx_compress_near_optimal() */
                struct {
                        /*
-                        * The graph nodes for the current block.
-                        *
-                        * We need at least 'LZX_DIV_BLOCK_SIZE +
-                        * LZX_MAX_MATCH_LEN - 1' nodes because that is the
-                        * maximum block size that may be used.  Add 1 because
-                        * we need a node to represent end-of-block.
+                        * Array of nodes, one per position, for running the
+                        * minimum-cost path algorithm.
                         *
-                        * It is possible that nodes past end-of-block are
-                        * accessed during match consideration, but this can
-                        * only occur if the block was truncated at
-                        * LZX_DIV_BLOCK_SIZE.  So the same bound still applies.
-                        * Note that since nodes past the end of the block will
-                        * never actually have an effect on the items that are
-                        * chosen for the block, it makes no difference what
-                        * their costs are initialized to (if anything).
+                        * This array must be large enough to accommodate the
+                        * worst-case number of nodes, which occurs if the
+                        * compressor finds a match of length LZX_MAX_MATCH_LEN
+                        * at position 'SOFT_MAX_BLOCK_SIZE - 1', producing a
+                        * block of size 'SOFT_MAX_BLOCK_SIZE - 1 +
+                        * LZX_MAX_MATCH_LEN'.  Add one for the end-of-block
+                        * node.
                         */
-                       struct lzx_optimum_node optimum_nodes[LZX_DIV_BLOCK_SIZE +
-                                                             LZX_MAX_MATCH_LEN - 1 + 1];
+                       struct lzx_optimum_node optimum_nodes[
+                                                   SOFT_MAX_BLOCK_SIZE - 1 +
+                                                   LZX_MAX_MATCH_LEN + 1];
 
-                       /* The cost model for the current block  */
+                       /* The cost model for the current optimization pass */
                        struct lzx_costs costs;
 
                        /*
@@ -463,21 +455,20 @@ struct lzx_compressor {
                         * 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
+                        * block.  CACHE_LENGTH is the length at which we
                         * actually check for overflow.  The extra slots beyond
                         * this are enough to absorb the worst case overflow,
-                        * which occurs if starting at
-                        * &match_cache[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
+                        * which occurs if starting at &match_cache[CACHE_LENGTH
+                        * - 1], we write the match count header, then write
+                        * MAX_MATCHES_PER_POS matches, then skip searching for
+                        * matches at 'LZX_MAX_MATCH_LEN - 1' positions and
                         * write the match count header for each.
                         */
-                       struct lz_match match_cache[LZX_CACHE_LENGTH +
-                                                   LZX_MAX_MATCHES_PER_POS +
+                       struct lz_match match_cache[CACHE_LENGTH +
+                                                   MAX_MATCHES_PER_POS +
                                                    LZX_MAX_MATCH_LEN - 1];
 
-                       /* Binary trees matchfinder (MUST BE LAST!!!)  */
+                       /* Binary trees matchfinder (MUST BE LAST!!!) */
                        union {
                                struct bt_matchfinder_16 bt_mf_16;
                                struct bt_matchfinder_32 bt_mf_32;
@@ -486,6 +477,10 @@ struct lzx_compressor {
        };
 };
 
+/******************************************************************************/
+/*                            Matchfinder utilities                           */
+/*----------------------------------------------------------------------------*/
+
 /*
  * Will a matchfinder using 16-bit positions be sufficient for compressing
  * buffers of up to the specified size?  The limit could be 65536 bytes, but we
@@ -501,6 +496,18 @@ lzx_is_16_bit(size_t max_bufsize)
 }
 
 /*
+ * Return the offset slot for the specified adjusted match offset.
+ */
+static inline unsigned
+lzx_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];
+}
+
+/*
  * 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.
@@ -514,58 +521,59 @@ lzx_is_16_bit(size_t max_bufsize)
        ((is_16_bit) ? CONCAT(funcname, _16)(&(c)->bt_mf_16, ##__VA_ARGS__) : \
                       CONCAT(funcname, _32)(&(c)->bt_mf_32, ##__VA_ARGS__));
 
+/******************************************************************************/
+/*                             Output bitstream                               */
+/*----------------------------------------------------------------------------*/
+
+/*
+ * The LZX bitstream is encoded as a sequence of little endian 16-bit coding
+ * units.  Bits are ordered from most significant to least significant within
+ * each coding unit.
+ */
+
 /*
  * Structure to keep track of the current state of sending bits to the
  * compressed output buffer.
- *
- * 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 */
+       /* Bits that haven't yet been written to the output buffer */
        machine_word_t bitbuf;
 
-       /* Number of bits currently held in @bitbuf */
-       u32 bitcount;
+       /* Number of bits currently held in @bitbuf */
+       machine_word_t bitcount;
 
-       /* Pointer to the start of the output buffer */
+       /* 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 */
+        * unit should be written */
        u8 *next;
 
-       /* Pointer just past the end of the output buffer, rounded down to a
-        * 2-byte boundary.  */
+       /* Pointer to just past the end of the output buffer, rounded down by
+        * one byte if needed to make 'end - start' a multiple of 2 */
        u8 *end;
 };
 
-/* Can the specified number of bits always be added to 'bitbuf' after any
+/* Can the specified number of bits always be added to 'bitbuf' after all
  * pending 16-bit coding units have been flushed?  */
 #define CAN_BUFFER(n)  ((n) <= WORDBITS - 15)
 
-/*
- * Initialize the output bitstream.
- *
- * @os
- *     The output bitstream structure to initialize.
- * @buffer
- *     The buffer being written to.
- * @size
- *     Size of @buffer, in bytes.
- */
+/* Initialize the output bitstream to write to the specified buffer. */
 static void
 lzx_init_output(struct lzx_output_bitstream *os, void *buffer, size_t size)
 {
        os->bitbuf = 0;
        os->bitcount = 0;
        os->start = buffer;
-       os->next = os->start;
-       os->end = os->start + (size & ~1);
+       os->next = buffer;
+       os->end = (u8 *)buffer + (size & ~1);
 }
 
-/* Add some bits to the bitbuffer variable of the output bitstream.  The caller
- * must make sure there is enough room.  */
+/*
+ * 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)
 {
@@ -573,16 +581,18 @@ lzx_add_bits(struct lzx_output_bitstream *os, u32 bits, unsigned num_bits)
        os->bitcount += num_bits;
 }
 
-/* Flush bits from the bitbuffer variable to the output buffer.  'max_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.  */
+ * 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;
+       const u32 shift_mask = WORDBITS - 1;
 
        if (os->end - os->next < 6)
                return;
@@ -610,7 +620,7 @@ lzx_write_bits(struct lzx_output_bitstream *os, u32 bits, unsigned num_bits)
  * Flush the last coding unit to the output buffer if needed.  Return the total
  * number of bytes written to the output buffer, or 0 if an overflow occurred.
  */
-static u32
+static size_t
 lzx_flush_output(struct lzx_output_bitstream *os)
 {
        if (os->end - os->next < 6)
@@ -624,35 +634,39 @@ lzx_flush_output(struct lzx_output_bitstream *os)
        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.  */
+/******************************************************************************/
+/*                           Preparing Huffman codes                          */
+/*----------------------------------------------------------------------------*/
+
+/*
+ * Build the Huffman codes.  This takes as input the frequency tables for each
+ * code and produces as output a set of tables that map symbols to codewords and
+ * codeword lengths.
+ */
 static void
-lzx_make_huffman_codes(struct lzx_compressor *c)
+lzx_build_huffman_codes(struct lzx_compressor *c)
 {
        const struct lzx_freqs *freqs = &c->freqs;
        struct lzx_codes *codes = &c->codes[c->codes_index];
 
        STATIC_ASSERT(MAIN_CODEWORD_LIMIT >= 9 &&
                      MAIN_CODEWORD_LIMIT <= LZX_MAX_MAIN_CODEWORD_LEN);
-       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);
 
+       STATIC_ASSERT(LENGTH_CODEWORD_LIMIT >= 8 &&
+                     LENGTH_CODEWORD_LIMIT <= LZX_MAX_LEN_CODEWORD_LEN);
        make_canonical_huffman_code(LZX_LENCODE_NUM_SYMBOLS,
                                    LENGTH_CODEWORD_LIMIT,
                                    freqs->len,
                                    codes->lens.len,
                                    codes->codewords.len);
 
+       STATIC_ASSERT(ALIGNED_CODEWORD_LIMIT >= LZX_NUM_ALIGNED_OFFSET_BITS &&
+                     ALIGNED_CODEWORD_LIMIT <= LZX_MAX_ALIGNED_CODEWORD_LEN);
        make_canonical_huffman_code(LZX_ALIGNEDCODE_NUM_SYMBOLS,
                                    ALIGNED_CODEWORD_LIMIT,
                                    freqs->aligned,
@@ -660,7 +674,7 @@ lzx_make_huffman_codes(struct lzx_compressor *c)
                                    codes->codewords.aligned);
 }
 
-/* Reset the symbol frequencies for the LZX Huffman codes.  */
+/* Reset the symbol frequencies for the current block. */
 static void
 lzx_reset_symbol_frequencies(struct lzx_compressor *c)
 {
@@ -712,7 +726,7 @@ lzx_compute_precode_items(const u8 lens[restrict],
 
                        /* 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);
+                               extra_bits = min((run_end - run_start) - 20, 0x1F);
                                precode_freqs[18]++;
                                *itemptr++ = 18 | (extra_bits << 5);
                                run_start += 20 + extra_bits;
@@ -720,7 +734,7 @@ lzx_compute_precode_items(const u8 lens[restrict],
 
                        /* 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);
+                               extra_bits = min((run_end - run_start) - 4, 0xF);
                                precode_freqs[17]++;
                                *itemptr++ = 17 | (extra_bits << 5);
                                run_start += 4 + extra_bits;
@@ -756,6 +770,10 @@ lzx_compute_precode_items(const u8 lens[restrict],
        return itemptr - precode_items;
 }
 
+/******************************************************************************/
+/*                          Outputting compressed data                        */
+/*----------------------------------------------------------------------------*/
+
 /*
  * Output a Huffman code in the compressed form used in LZX.
  *
@@ -815,8 +833,7 @@ lzx_write_compressed_code(struct lzx_output_bitstream *os,
        /* 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,
+       make_canonical_huffman_code(LZX_PRECODE_NUM_SYMBOLS, PRE_CODEWORD_LIMIT,
                                    precode_freqs, precode_lens,
                                    precode_codewords);
 
@@ -864,8 +881,7 @@ lzx_write_compressed_code(struct lzx_output_bitstream *os,
  * @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.
+ *     The main, length, and aligned offset Huffman codes for the block.
  */
 static void
 lzx_write_sequences(struct lzx_output_bitstream *os, int block_type,
@@ -893,27 +909,24 @@ lzx_write_sequences(struct lzx_output_bitstream *os, int block_type,
 
                        /* Verify optimization is enabled on 64-bit  */
                        STATIC_ASSERT(WORDBITS < 64 ||
-                                     CAN_BUFFER(4 * MAIN_CODEWORD_LIMIT));
+                                     CAN_BUFFER(3 * MAIN_CODEWORD_LIMIT));
 
-                       if (CAN_BUFFER(4 * MAIN_CODEWORD_LIMIT)) {
+                       if (CAN_BUFFER(3 * MAIN_CODEWORD_LIMIT)) {
 
-                               /* 64-bit: write 4 literals at a time.  */
-                               while (litrunlen >= 4) {
+                               /* 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];
-                                       unsigned lit3 = block_data[3];
                                        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_add_bits(os, codes->codewords.main[lit3],
-                                                    codes->lens.main[lit3]);
-                                       lzx_flush_bits(os, 4 * MAIN_CODEWORD_LIMIT);
-                                       block_data += 4;
-                                       litrunlen -= 4;
+                                       lzx_flush_bits(os, 3 * MAIN_CODEWORD_LIMIT);
+                                       block_data += 3;
+                                       litrunlen -= 3;
                                }
                                if (litrunlen--) {
                                        unsigned lit = *block_data++;
@@ -923,14 +936,7 @@ lzx_write_sequences(struct lzx_output_bitstream *os, int block_type,
                                                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, 3 * MAIN_CODEWORD_LIMIT);
-                                               } else {
-                                                       lzx_flush_bits(os, 2 * MAIN_CODEWORD_LIMIT);
-                                               }
+                                               lzx_flush_bits(os, 2 * MAIN_CODEWORD_LIMIT);
                                        } else {
                                                lzx_flush_bits(os, 1 * MAIN_CODEWORD_LIMIT);
                                        }
@@ -1038,21 +1044,25 @@ lzx_write_compressed_block(const u8 *block_begin,
         * LZX_BLOCKTYPE_* constants.  */
        lzx_write_bits(os, block_type, 3);
 
-       /* Output the block size.
+       /*
+        * Output the block size.
         *
-        * The original LZX format seemed to always encode the block size in 3
-        * bytes.  However, the implementation in WIMGAPI, as used in WIM files,
-        * uses the first bit to indicate whether the block is the default size
-        * (32768) or a different size given explicitly by the next 16 bits.
+        * The original LZX format encoded the block size in 24 bits.  However,
+        * the LZX format used in WIM archives uses 1 bit to specify whether the
+        * block has the default size of 32768 bytes, then optionally 16 bits to
+        * specify a non-default size.  This works fine for Microsoft's WIM
+        * software (WIMGAPI), which never compresses more than 32768 bytes at a
+        * time with LZX.  However, as an extension, our LZX compressor supports
+        * compressing up to 2097152 bytes, with a corresponding increase in
+        * window size.  It is possible for blocks in these larger buffers to
+        * exceed 65535 bytes; such blocks cannot have their size represented in
+        * 16 bits.
         *
-        * By default, this compressor uses a window size of 32768 and therefore
-        * follows the WIMGAPI behavior.  However, this compressor also supports
-        * window sizes greater than 32768 bytes, which do not appear to be
-        * supported by WIMGAPI.  In such cases, we retain the default size bit
-        * to mean a size of 32768 bytes but output non-default block size in 24
-        * bits rather than 16.  The compatibility of this behavior is unknown
-        * because WIMs created with chunk size greater than 32768 can seemingly
-        * only be opened by wimlib anyway.  */
+        * The chosen solution was to use 24 bits for the block size when
+        * possibly required --- specifically, when the compressor has been
+        * allocated to be capable of compressing more than 32768 bytes at once
+        * (which also causes the number of main symbols to be increased).
+        */
        if (block_size == LZX_DEFAULT_BLOCK_SIZE) {
                lzx_write_bits(os, 1, 1);
        } else {
@@ -1089,26 +1099,30 @@ lzx_write_compressed_block(const u8 *block_begin,
        lzx_write_sequences(os, block_type, block_begin, sequences, codes);
 }
 
-/* Given the frequencies of symbols in an LZX-compressed block and the
+/*
+ * 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.  */
+ * 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;
+       u32 aligned_cost = 0;
 
-       /* A verbatim block requires 3 bits in each place that an aligned symbol
-        * would be used in an aligned offset block.  */
+       /* A verbatim block requires 3 bits in each place that an aligned offset
+        * symbol would be used in an aligned offset block.  */
        for (unsigned i = 0; i < LZX_ALIGNEDCODE_NUM_SYMBOLS; i++) {
                verbatim_cost += LZX_NUM_ALIGNED_OFFSET_BITS * freqs->aligned[i];
                aligned_cost += codes->lens.aligned[i] * freqs->aligned[i];
        }
 
-       /* Account for output of the aligned offset code.  */
-       aligned_cost += LZX_ALIGNEDCODE_ELEMENT_SIZE * LZX_ALIGNEDCODE_NUM_SYMBOLS;
+       /* Account for the cost of sending the codeword lengths of the aligned
+        * offset code.  */
+       aligned_cost += LZX_ALIGNEDCODE_ELEMENT_SIZE *
+                       LZX_ALIGNEDCODE_NUM_SYMBOLS;
 
        if (aligned_cost < verbatim_cost)
                return LZX_BLOCKTYPE_ALIGNED;
@@ -1117,33 +1131,23 @@ lzx_choose_verbatim_or_aligned(const struct lzx_freqs * freqs,
 }
 
 /*
- * 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];
-}
-
-/*
- * Finish an LZX block:
+ * 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.
  *
- * - build the Huffman codes
- * - decide whether to output the block as VERBATIM or ALIGNED
- * - output the block
- * - swap the indices of the current and previous Huffman codes
+ * Note: we never output UNCOMPRESSED blocks.  This probably should be
+ * implemented sometime, but it doesn't make much difference.
  */
 static void
-lzx_finish_block(struct lzx_compressor *c, struct lzx_output_bitstream *os,
-                const u8 *block_begin, u32 block_size, u32 seq_idx)
+lzx_flush_block(struct lzx_compressor *c, struct lzx_output_bitstream *os,
+               const u8 *block_begin, u32 block_size, u32 seq_idx)
 {
        int block_type;
 
-       lzx_make_huffman_codes(c);
+       lzx_build_huffman_codes(c);
 
        block_type = lzx_choose_verbatim_or_aligned(&c->freqs,
                                                    &c->codes[c->codes_index]);
@@ -1159,249 +1163,345 @@ lzx_finish_block(struct lzx_compressor *c, struct lzx_output_bitstream *os,
        c->codes_index ^= 1;
 }
 
-/* Tally the Huffman symbol for a literal and increment the literal run length.
+/******************************************************************************/
+/*                          Block splitting algorithm                         */
+/*----------------------------------------------------------------------------*/
+
+/*
+ * The problem of block splitting is to decide when it is worthwhile to start a
+ * new block with new entropy codes.  There is a theoretically optimal solution:
+ * recursively consider every possible block split, considering the exact cost
+ * of each block, and choose the minimum cost approach.  But this is far too
+ * slow.  Instead, as an approximation, we can count symbols and after every N
+ * symbols, compare the expected distribution of symbols based on the previous
+ * data with the actual distribution.  If they differ "by enough", then start a
+ * new block.
+ *
+ * As an optimization and heuristic, we don't distinguish between every symbol
+ * but rather we combine many symbols into a single "observation type".  For
+ * literals we only look at the high bits and low bits, and for matches we only
+ * look at whether the match is long or not.  The assumption is that for typical
+ * "real" data, places that are good block boundaries will tend to be noticable
+ * based only on changes in these aggregate frequencies, without looking for
+ * subtle differences in individual symbols.  For example, a change from ASCII
+ * bytes to non-ASCII bytes, or from few matches (generally less compressible)
+ * to many matches (generally more compressible), would be easily noticed based
+ * on the aggregates.
+ *
+ * For determining whether the frequency distributions are "different enough" to
+ * start a new block, the simply heuristic of splitting when the sum of absolute
+ * differences exceeds a constant seems to be good enough.
+ *
+ * Finally, for an approximation, it is not strictly necessary that the exact
+ * symbols being used are considered.  With "near-optimal parsing", for example,
+ * the actual symbols that will be used are unknown until after the block
+ * boundary is chosen and the block has been optimized.  Since the final choices
+ * cannot be used, we can use preliminary "greedy" choices instead.
  */
-static inline void
-lzx_record_literal(struct lzx_compressor *c, unsigned literal, u32 *litrunlen_p)
+
+/* Initialize the block split statistics when starting a new block. */
+static void
+lzx_init_block_split_stats(struct lzx_block_split_stats *stats)
 {
-       c->freqs.main[literal]++;
-       ++*litrunlen_p;
+       memset(stats, 0, sizeof(*stats));
 }
 
-/* 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.  */
+/* Literal observation.  Heuristic: use the top 2 bits and low 1 bits of the
+ * literal, for 8 possible literal observation types.  */
 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)
+lzx_observe_literal(struct lzx_block_split_stats *stats, u8 lit)
 {
-       u32 litrunlen = *litrunlen_p;
-       struct lzx_sequence *next_seq = *next_seq_p;
-       unsigned offset_slot;
-       unsigned v;
+       stats->new_observations[((lit >> 5) & 0x6) | (lit & 1)]++;
+       stats->num_new_observations++;
+}
 
-       v = length - LZX_MIN_MATCH_LEN;
+/* Match observation.  Heuristic: use one observation type for "short match" and
+ * one observation type for "long match".  */
+static inline void
+lzx_observe_match(struct lzx_block_split_stats *stats, unsigned length)
+{
+       stats->new_observations[NUM_LITERAL_OBSERVATION_TYPES + (length >= 5)]++;
+       stats->num_new_observations++;
+}
 
-       /* Save the literal run length and adjusted length.  */
-       next_seq->litrunlen = litrunlen;
-       next_seq->adjusted_length = v;
+static bool
+lzx_should_end_block(struct lzx_block_split_stats *stats)
+{
+       if (stats->num_observations > 0) {
+
+               /* Note: to avoid slow divisions, we do not divide by
+                * 'num_observations', but rather do all math with the numbers
+                * multiplied by 'num_observations'. */
+               u32 total_delta = 0;
+               for (int i = 0; i < NUM_OBSERVATION_TYPES; i++) {
+                       u32 expected = stats->observations[i] *
+                                      stats->num_new_observations;
+                       u32 actual = stats->new_observations[i] *
+                                    stats->num_observations;
+                       u32 delta = (actual > expected) ? actual - expected :
+                                                         expected - actual;
+                       total_delta += delta;
+               }
 
-       /* 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;
+               /* Ready to end the block? */
+               if (total_delta >=
+                   stats->num_new_observations * 7 / 8 * stats->num_observations)
+                       return true;
        }
 
-       /* Compute the offset slot  */
-       offset_slot = lzx_comp_get_offset_slot(c, offset_data, is_16_bit);
+       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;
+}
 
-       /* Compute the match header.  */
-       v += offset_slot * LZX_NUM_LEN_HEADERS;
+/******************************************************************************/
+/*                   Slower ("near-optimal") compression algorithm            */
+/*----------------------------------------------------------------------------*/
 
-       /* Save the adjusted offset and match header.  */
-       next_seq->adjusted_offset_and_match_hdr = (offset_data << 9) | v;
+/*
+ * Least-recently-used queue for match offsets.
+ *
+ * This is represented as a 64-bit integer for efficiency.  There are three
+ * offsets of 21 bits each.  Bit 64 is garbage.
+ */
+struct lzx_lru_queue {
+       u64 R;
+} _aligned_attribute(8);
 
-       /* Tally the main symbol.  */
-       c->freqs.main[LZX_NUM_CHARS + v]++;
+#define LZX_QUEUE_OFFSET_SHIFT 21
+#define LZX_QUEUE_OFFSET_MASK  (((u64)1 << LZX_QUEUE_OFFSET_SHIFT) - 1)
 
-       /* 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  */
+#define LZX_QUEUE_R0_SHIFT (0 * LZX_QUEUE_OFFSET_SHIFT)
+#define LZX_QUEUE_R1_SHIFT (1 * LZX_QUEUE_OFFSET_SHIFT)
+#define LZX_QUEUE_R2_SHIFT (2 * LZX_QUEUE_OFFSET_SHIFT)
 
-               /* Tally the aligned offset symbol if needed  */
-               if (offset_data >= 16)
-                       c->freqs.aligned[offset_data & LZX_ALIGNED_OFFSET_BITMASK]++;
+#define LZX_QUEUE_R0_MASK (LZX_QUEUE_OFFSET_MASK << LZX_QUEUE_R0_SHIFT)
+#define LZX_QUEUE_R1_MASK (LZX_QUEUE_OFFSET_MASK << LZX_QUEUE_R1_SHIFT)
+#define LZX_QUEUE_R2_MASK (LZX_QUEUE_OFFSET_MASK << LZX_QUEUE_R2_SHIFT)
 
-               recent_offsets[2] = recent_offsets[1];
-               recent_offsets[1] = recent_offsets[0];
-               recent_offsets[0] = offset_data - LZX_OFFSET_ADJUSTMENT;
-       }
+#define LZX_QUEUE_INITIALIZER {                        \
+       ((u64)1 << LZX_QUEUE_R0_SHIFT) |        \
+       ((u64)1 << LZX_QUEUE_R1_SHIFT) |        \
+       ((u64)1 << LZX_QUEUE_R2_SHIFT) }
 
-       /* Reset the literal run length and advance to the next sequence.  */
-       *next_seq_p = next_seq + 1;
-       *litrunlen_p = 0;
+static inline u64
+lzx_lru_queue_R0(struct lzx_lru_queue queue)
+{
+       return (queue.R >> LZX_QUEUE_R0_SHIFT) & LZX_QUEUE_OFFSET_MASK;
 }
 
-/* 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)
+static inline u64
+lzx_lru_queue_R1(struct lzx_lru_queue queue)
 {
-       last_seq->litrunlen = litrunlen;
-
-       /* Special value to mark last sequence  */
-       last_seq->adjusted_offset_and_match_hdr = 0x80000000;
+       return (queue.R >> LZX_QUEUE_R1_SHIFT) & LZX_QUEUE_OFFSET_MASK;
 }
 
-/*
- * 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_size, bool is_16_bit)
+static inline u64
+lzx_lru_queue_R2(struct lzx_lru_queue queue)
 {
-       u32 node_idx = block_size;
-       for (;;) {
-               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 (;;) {
-                       u32 item = c->optimum_nodes[node_idx].item;
+       return (queue.R >> LZX_QUEUE_R2_SHIFT) & LZX_QUEUE_OFFSET_MASK;
+}
 
-                       len = item & OPTIMUM_LEN_MASK;
-                       offset_data = item >> OPTIMUM_OFFSET_SHIFT;
-
-                       if (len != 0)  /* Not a literal?  */
-                               break;
-
-                       /* Tally the main symbol for the literal.  */
-                       c->freqs.main[offset_data]++;
-
-                       if (--node_idx == 0) /* Beginning of block was reached?  */
-                               return;
-               }
-
-               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;
-               }
+/* 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_QUEUE_OFFSET_SHIFT) | offset,
+       };
+}
 
-               /* 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]++;
+/* 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)
+{
+       unsigned shift = idx * 21;
+       const u64 mask = LZX_QUEUE_R0_MASK;
+       const u64 mask_high = mask << shift;
 
-               if (node_idx == 0) /* Beginning of block was reached?  */
-                       return;
-       }
+       return (struct lzx_lru_queue) {
+               (queue.R & ~(mask | mask_high)) |
+               ((queue.R & mask_high) >> shift) |
+               ((queue.R & mask) << shift)
+       };
 }
 
-/*
- * 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_size, bool is_16_bit)
+lzx_walk_item_list(struct lzx_compressor *c, u32 block_size, bool is_16_bit,
+                  bool record)
 {
        u32 node_idx = block_size;
        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;
+       if (record) {
+               /* Special value to mark last sequence  */
+               c->chosen_sequences[seq_idx].adjusted_offset_and_match_hdr = 0x80000000;
+               lit_start_node = node_idx;
+       }
 
-       lit_start_node = node_idx;
        for (;;) {
+               u32 item;
                u32 len;
-               u32 offset_data;
+               u32 adjusted_offset;
                unsigned v;
                unsigned offset_slot;
 
-               /* Record literals until either a match or the beginning of the
-                * block is reached.  */
+               /* Tally literals until either a match or the beginning of the
+                * block is reached.  Note: the item in the node at the
+                * beginning of the block has all bits set, causing this loop to
+                * end when it is reached. */
                for (;;) {
-                       u32 item = c->optimum_nodes[node_idx].item;
+                       item = c->optimum_nodes[node_idx].item;
+                       if (item & OPTIMUM_LEN_MASK)
+                               break;
+                       c->freqs.main[item >> OPTIMUM_OFFSET_SHIFT]++;
+                       node_idx--;
+               }
 
-                       len = item & OPTIMUM_LEN_MASK;
-                       offset_data = item >> OPTIMUM_OFFSET_SHIFT;
+       #if CONSIDER_GAP_MATCHES
+               if (item & OPTIMUM_GAP_MATCH) {
 
-                       if (len != 0) /* Not a literal?  */
+                       if (node_idx == 0)
                                break;
 
-                       /* Tally the main symbol for the literal.  */
-                       c->freqs.main[offset_data]++;
+                       /* Record the literal run length for the next sequence
+                        * (the "previous sequence" when walking backwards). */
+                       len = item & OPTIMUM_LEN_MASK;
+                       if (record) {
+                               c->chosen_sequences[seq_idx--].litrunlen =
+                                               lit_start_node - node_idx;
+                               lit_start_node = node_idx - len;
+                       }
 
-                       if (--node_idx == 0) /* Beginning of block was reached?  */
-                               goto out;
+                       /* Tally the rep0 match after the gap. */
+                       v = len - LZX_MIN_MATCH_LEN;
+                       if (record)
+                               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]++;
+                       if (record)
+                               c->chosen_sequences[seq_idx].adjusted_offset_and_match_hdr = v;
+
+                       /* Tally the literal in the gap. */
+                       c->freqs.main[(u8)(item >> OPTIMUM_OFFSET_SHIFT)]++;
+
+                       /* Fall through and tally the match before the gap.
+                        * (It was temporarily saved in the 'cost' field of the
+                        * previous node, which was free to reuse.) */
+                       item = c->optimum_nodes[--node_idx].cost;
+                       node_idx -= len;
+               }
+       #else /* CONSIDER_GAP_MATCHES */
+               if (node_idx == 0)
+                       break;
+       #endif /* !CONSIDER_GAP_MATCHES */
+
+               len = item & OPTIMUM_LEN_MASK;
+               adjusted_offset = item >> OPTIMUM_OFFSET_SHIFT;
+
+               /* Record the literal run length for the next sequence (the
+                * "previous sequence" when walking backwards). */
+               if (record) {
+                       c->chosen_sequences[seq_idx--].litrunlen =
+                                       lit_start_node - node_idx;
+                       node_idx -= len;
+                       lit_start_node = node_idx;
+               } else {
+                       node_idx -= len;
                }
 
-               /* 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.  */
+               /* Record a match. */
 
-               /* Tally the aligned offset symbol if needed.  */
-               if (offset_data >= 16)
-                       c->freqs.aligned[offset_data & LZX_ALIGNED_OFFSET_BITMASK]++;
+               /* Tally the aligned offset symbol if needed. */
+               if (adjusted_offset >= 16)
+                       c->freqs.aligned[adjusted_offset & LZX_ALIGNED_OFFSET_BITMASK]++;
 
-               /* Save the adjusted length.  */
+               /* Record the adjusted length. */
                v = len - LZX_MIN_MATCH_LEN;
-               c->chosen_sequences[seq_idx].adjusted_length = v;
+               if (record)
+                       c->chosen_sequences[seq_idx].adjusted_length = v;
 
-               /* Tally the length symbol if needed.  */
+               /* 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);
+               /* Tally the main symbol. */
+               offset_slot = lzx_get_offset_slot(c, adjusted_offset, 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;
-
-               if (node_idx == 0) /* Beginning of block was reached?  */
-                       goto out;
+               /* Record the adjusted offset and match header. */
+               if (record) {
+                       c->chosen_sequences[seq_idx].adjusted_offset_and_match_hdr =
+                                       (adjusted_offset << 9) | v;
+               }
        }
 
-out:
-       /* Save the literal run length for the first sequence.  */
-       c->chosen_sequences[seq_idx].litrunlen = lit_start_node - node_idx;
+       /* Record the literal run length for the first sequence. */
+       if (record)
+               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 the index in chosen_sequences at which the sequences begin. */
        return seq_idx;
 }
 
 /*
+ * 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_size, bool is_16_bit)
+{
+       lzx_walk_item_list(c, block_size, is_16_bit, false);
+}
+
+/*
+ * Like lzx_tally_item_list(), but this function also generates the list of
+ * lzx_sequences for the minimum-cost path and writes it to c->chosen_sequences,
+ * ready to be output to the bitstream after the Huffman codes are computed.
+ * The lzx_sequences will be written to decreasing memory addresses as the path
+ * is walked backwards, which means they will end up in the expected
+ * first-to-last order.  The return value is the index in c->chosen_sequences at
+ * which the lzx_sequences begin.
+ */
+static inline u32
+lzx_record_item_list(struct lzx_compressor *c, u32 block_size, bool is_16_bit)
+{
+       return lzx_walk_item_list(c, block_size, is_16_bit, true);
+}
+
+/*
  * Find an inexpensive path through the graph of possible match/literal choices
  * for the current block.  The nodes of the graph are
  * c->optimum_nodes[0...block_size].  They correspond directly to the bytes in
  * the current block, plus one extra node for end-of-block.  The edges of the
  * graph are matches and literals.  The goal is to find the minimum cost path
- * from 'c->optimum_nodes[0]' to 'c->optimum_nodes[block_size]'.
+ * from 'c->optimum_nodes[0]' to 'c->optimum_nodes[block_size]', given the cost
+ * model 'c->costs'.
  *
  * The algorithm works forwards, starting at 'c->optimum_nodes[0]' and
  * proceeding forwards one node at a time.  At each node, a selection of matches
  * (len >= 2), as well as the literal byte (len = 1), is considered.  An item of
  * length 'len' provides a new path to reach the node 'len' bytes later.  If
  * such a path is the lowest cost found so far to reach that later node, then
- * that later node is updated with the new path.
+ * that later node is updated with the new cost and the "arrival" which provided
+ * that cost.
  *
  * Note that although this algorithm is based on minimum cost path search, due
  * to various simplifying assumptions the result is not guaranteed to be the
@@ -1416,8 +1516,9 @@ out:
  * 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.
+ * later.  The algorithm does not solve this problem in general; it only looks
+ * one step ahead, with the exception of special consideration for "gap
+ * matches".
  */
 static inline struct lzx_lru_queue
 lzx_find_min_cost_path(struct lzx_compressor * const restrict c,
@@ -1427,30 +1528,57 @@ lzx_find_min_cost_path(struct lzx_compressor * const restrict c,
                       bool is_16_bit)
 {
        struct lzx_optimum_node *cur_node = c->optimum_nodes;
-       struct lzx_optimum_node * const end_node = &c->optimum_nodes[block_size];
+       struct lzx_optimum_node * const end_node = cur_node + block_size;
        struct lz_match *cache_ptr = c->match_cache;
        const u8 *in_next = block_begin;
        const u8 * const block_end = block_begin + block_size;
 
-       /* Instead of storing the match offset LRU queues in the
+       /*
+        * 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.  */
+        * state is more than LZX_MAX_MATCH_LEN bytes behind the current node
+        * (more if gap match consideration is enabled; we just round up to 512
+        * so it's a power of 2), it is no longer needed.
+        *
+        * The QUEUE() macro finds the queue for the given node.  This macro has
+        * been optimized by taking advantage of 'struct lzx_lru_queue' and
+        * 'struct lzx_optimum_node' both being 8 bytes in size and alignment.
+        */
        struct lzx_lru_queue queues[512];
-
        STATIC_ASSERT(ARRAY_LEN(queues) >= LZX_MAX_MATCH_LEN + 1);
-#define QUEUE(in) (queues[(uintptr_t)(in) % ARRAY_LEN(queues)])
+       STATIC_ASSERT(sizeof(c->optimum_nodes[0]) == sizeof(queues[0]));
+#define QUEUE(node) \
+       (*(struct lzx_lru_queue *)((char *)queues + \
+                       ((uintptr_t)(node) % (ARRAY_LEN(queues) * sizeof(queues[0])))))
+       /*(queues[(uintptr_t)(node) / sizeof(*(node)) % ARRAY_LEN(queues)])*/
+
+#if CONSIDER_GAP_MATCHES
+       u32 matches_before_gap[ARRAY_LEN(queues)];
+#define MATCH_BEFORE_GAP(node) \
+       (matches_before_gap[(uintptr_t)(node) / sizeof(*(node)) % \
+                           ARRAY_LEN(matches_before_gap)])
+#endif
 
-       /* Initially, the cost to reach each node is "infinity".  */
+       /*
+        * Initially, the cost to reach each node is "infinity".
+        *
+        * The first node actually should have cost 0, but "infinity"
+        * (0xFFFFFFFF) works just as well because it immediately overflows.
+        *
+        * The following statement also intentionally sets the 'item' of the
+        * first node, which would otherwise have no meaning, to 0xFFFFFFFF for
+        * use as a sentinel.  See lzx_walk_item_list().
+        */
        memset(c->optimum_nodes, 0xFF,
               (block_size + 1) * sizeof(c->optimum_nodes[0]));
 
-       QUEUE(block_begin) = initial_queue;
+       /* Initialize the recent offsets queue for the first node. */
+       QUEUE(cur_node) = initial_queue;
+
+       do { /* For each node in the block in position order... */
 
-       /* The following loop runs 'block_size' iterations, one per node.  */
-       do {
                unsigned num_matches;
                unsigned literal;
                u32 cost;
@@ -1488,10 +1616,10 @@ lzx_find_min_cost_path(struct lzx_compressor * const restrict c,
                        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));
+                       /* Consider rep0 matches. */
+                       matchptr = in_next - lzx_lru_queue_R0(QUEUE(cur_node));
                        if (load_u16_unaligned(matchptr) != load_u16_unaligned(in_next))
-                               goto R0_done;
+                               goto rep0_done;
                        STATIC_ASSERT(LZX_MIN_MATCH_LEN == 2);
                        do {
                                u32 cost = cur_node->cost +
@@ -1508,17 +1636,17 @@ lzx_find_min_cost_path(struct lzx_compressor * const restrict c,
                                }
                        } while (in_next[next_len - 1] == matchptr[next_len - 1]);
 
-               R0_done:
+               rep0_done:
 
-                       /* Consider R1 match  */
-                       matchptr = in_next - lzx_lru_queue_R1(QUEUE(in_next));
+                       /* Consider rep1 matches. */
+                       matchptr = in_next - lzx_lru_queue_R1(QUEUE(cur_node));
                        if (load_u16_unaligned(matchptr) != load_u16_unaligned(in_next))
-                               goto R1_done;
+                               goto rep1_done;
                        if (matchptr[next_len - 1] != in_next[next_len - 1])
-                               goto R1_done;
+                               goto rep1_done;
                        for (unsigned len = 2; len < next_len - 1; len++)
                                if (matchptr[len] != in_next[len])
-                                       goto R1_done;
+                                       goto rep1_done;
                        do {
                                u32 cost = cur_node->cost +
                                           c->costs.match_cost[1][
@@ -1534,17 +1662,17 @@ lzx_find_min_cost_path(struct lzx_compressor * const restrict c,
                                }
                        } while (in_next[next_len - 1] == matchptr[next_len - 1]);
 
-               R1_done:
+               rep1_done:
 
-                       /* Consider R2 match  */
-                       matchptr = in_next - lzx_lru_queue_R2(QUEUE(in_next));
+                       /* Consider rep2 matches. */
+                       matchptr = in_next - lzx_lru_queue_R2(QUEUE(cur_node));
                        if (load_u16_unaligned(matchptr) != load_u16_unaligned(in_next))
-                               goto R2_done;
+                               goto rep2_done;
                        if (matchptr[next_len - 1] != in_next[next_len - 1])
-                               goto R2_done;
+                               goto rep2_done;
                        for (unsigned len = 2; len < next_len - 1; len++)
                                if (matchptr[len] != in_next[len])
-                                       goto R2_done;
+                                       goto rep2_done;
                        do {
                                u32 cost = cur_node->cost +
                                           c->costs.match_cost[2][
@@ -1560,37 +1688,72 @@ lzx_find_min_cost_path(struct lzx_compressor * const restrict c,
                                }
                        } while (in_next[next_len - 1] == matchptr[next_len - 1]);
 
-               R2_done:
+               rep2_done:
 
                        while (next_len > cache_ptr->length)
                                if (++cache_ptr == end_matches)
                                        goto done_matches;
 
-                       /* Consider explicit offset matches  */
-                       do {
+                       /* 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 adjusted_offset = offset + LZX_OFFSET_ADJUSTMENT;
+                               unsigned offset_slot = lzx_get_offset_slot(c, adjusted_offset, is_16_bit);
                                u32 base_cost = cur_node->cost;
+                               u32 cost;
 
-                       #if LZX_CONSIDER_ALIGNED_COSTS
-                               if (offset_data >= 16)
-                                       base_cost += c->costs.aligned[offset_data &
+                       #if CONSIDER_ALIGNED_COSTS
+                               if (offset >= 16 - LZX_OFFSET_ADJUSTMENT)
+                                       base_cost += c->costs.aligned[adjusted_offset &
                                                                      LZX_ALIGNED_OFFSET_BITMASK];
                        #endif
-
                                do {
-                                       u32 cost = base_cost +
-                                                  c->costs.match_cost[offset_slot][
+                                       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;
+                                                       (adjusted_offset << OPTIMUM_OFFSET_SHIFT) | next_len;
                                        }
                                } while (++next_len <= cache_ptr->length);
-                       } while (++cache_ptr != end_matches);
+
+                               if (++cache_ptr == end_matches) {
+                               #if CONSIDER_GAP_MATCHES
+                                       /* Also consider the longest explicit
+                                        * offset match as a "gap match": match
+                                        * + lit + rep0. */
+                                       s32 remaining = (block_end - in_next) - (s32)next_len;
+                                       if (likely(remaining >= 2)) {
+                                               const u8 *strptr = in_next + next_len;
+                                               const u8 *matchptr = strptr - offset;
+                                               if (load_u16_unaligned(strptr) == load_u16_unaligned(matchptr)) {
+                                                       STATIC_ASSERT(ARRAY_LEN(queues) - LZX_MAX_MATCH_LEN - 2 >= 250);
+                                                       STATIC_ASSERT(ARRAY_LEN(queues) == ARRAY_LEN(matches_before_gap));
+                                                       unsigned limit = min(remaining,
+                                                                            min(ARRAY_LEN(queues) - LZX_MAX_MATCH_LEN - 2,
+                                                                                LZX_MAX_MATCH_LEN));
+                                                       unsigned rep0_len = lz_extend(strptr, matchptr, 2, limit);
+                                                       u8 lit = strptr[-1];
+                                                       cost += c->costs.main[lit] +
+                                                               c->costs.match_cost[0][rep0_len - LZX_MIN_MATCH_LEN];
+                                                       unsigned total_len = next_len + rep0_len;
+                                                       if (cost < (cur_node + total_len)->cost) {
+                                                               (cur_node + total_len)->cost = cost;
+                                                               (cur_node + total_len)->item =
+                                                                       OPTIMUM_GAP_MATCH |
+                                                                       ((u32)lit << OPTIMUM_OFFSET_SHIFT) |
+                                                                       rep0_len;
+                                                               MATCH_BEFORE_GAP(cur_node + total_len) =
+                                                                       (adjusted_offset << OPTIMUM_OFFSET_SHIFT) |
+                                                                       (next_len - 1);
+                                                       }
+                                               }
+                                       }
+                               #endif /* CONSIDER_GAP_MATCHES */
+                                       break;
+                               }
+                       }
                }
 
        done_matches:
@@ -1599,156 +1762,331 @@ lzx_find_min_cost_path(struct lzx_compressor * const restrict c,
 
                 * To avoid an extra branch, actually checking the preferability
                 * of coding the literal is integrated into the queue update
-                * code below.  */
+                * code below. */
                literal = *in_next++;
                cost = cur_node->cost + c->costs.main[literal];
 
-               /* Advance to the next position.  */
+               /* 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.  */
+                * this lowest-cost path. */
 
                if (cost <= cur_node->cost) {
-                       /* Literal: queue remains unchanged.  */
+                       /* Literal: queue remains unchanged. */
                        cur_node->cost = cost;
                        cur_node->item = (u32)literal << OPTIMUM_OFFSET_SHIFT;
-                       QUEUE(in_next) = QUEUE(in_next - 1);
+                       QUEUE(cur_node) = QUEUE(cur_node - 1);
                } else {
-                       /* Match: queue update is needed.  */
+                       /* Match: queue update is needed. */
                        unsigned len = cur_node->item & OPTIMUM_LEN_MASK;
-                       u32 offset_data = cur_node->item >> 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 {
-                               /* Repeat offset match: swap offset to front  */
-                               QUEUE(in_next) =
-                                       lzx_lru_queue_swap(QUEUE(in_next - len),
-                                                          offset_data);
+               #if CONSIDER_GAP_MATCHES
+                       s32 adjusted_offset = (s32)cur_node->item >> OPTIMUM_OFFSET_SHIFT;
+                       STATIC_ASSERT(OPTIMUM_GAP_MATCH == 0x80000000); /* assuming sign extension */
+               #else
+                       u32 adjusted_offset = cur_node->item >> OPTIMUM_OFFSET_SHIFT;
+               #endif
+
+                       if (adjusted_offset >= LZX_NUM_RECENT_OFFSETS) {
+                               /* Explicit offset match: insert offset at front. */
+                               QUEUE(cur_node) =
+                                       lzx_lru_queue_push(QUEUE(cur_node - len),
+                                                          adjusted_offset - LZX_OFFSET_ADJUSTMENT);
+                       }
+               #if CONSIDER_GAP_MATCHES
+                       else if (adjusted_offset < 0) {
+                               /* "Gap match": Explicit offset match, then a
+                                * literal, then rep0 match.  Save the explicit
+                                * offset match information in the cost field of
+                                * the previous node, which isn't needed
+                                * anymore.  Then insert the offset at the front
+                                * of the queue. */
+                               u32 match_before_gap = MATCH_BEFORE_GAP(cur_node);
+                               (cur_node - 1)->cost = match_before_gap;
+                               QUEUE(cur_node) =
+                                       lzx_lru_queue_push(QUEUE(cur_node - len - 1 -
+                                                                (match_before_gap & OPTIMUM_LEN_MASK)),
+                                                          (match_before_gap >> OPTIMUM_OFFSET_SHIFT) -
+                                                          LZX_OFFSET_ADJUSTMENT);
+                       }
+               #endif
+                       else {
+                               /* Repeat offset match: swap offset to front. */
+                               QUEUE(cur_node) =
+                                       lzx_lru_queue_swap(QUEUE(cur_node - len),
+                                                          adjusted_offset);
                        }
                }
        } while (cur_node != end_node);
 
-       /* Return the match offset queue at the end of the minimum cost path. */
-       return QUEUE(block_end);
+       /* Return the recent offsets queue at the end of the path. */
+       return QUEUE(cur_node);
 }
 
-/* Given the costs for the main and length codewords, compute 'match_costs'.  */
+/*
+ * Given the costs for the main and length codewords (c->costs.main and
+ * c->costs.len), initialize the match cost array (c->costs.match_cost) which
+ * directly provides the cost of every possible (length, offset slot) pair.
+ */
 static void
 lzx_compute_match_costs(struct lzx_compressor *c)
 {
        unsigned num_offset_slots = (c->num_main_syms - LZX_NUM_CHARS) /
                                        LZX_NUM_LEN_HEADERS;
        struct lzx_costs *costs = &c->costs;
+       unsigned main_symbol = LZX_NUM_CHARS;
 
-       for (unsigned offset_slot = 0; offset_slot < num_offset_slots; offset_slot++) {
-
-               u32 extra_cost = (u32)lzx_extra_offset_bits[offset_slot] * LZX_BIT_COST;
-               unsigned main_symbol = LZX_NUM_CHARS + (offset_slot *
-                                                       LZX_NUM_LEN_HEADERS);
+       for (unsigned offset_slot = 0; offset_slot < num_offset_slots;
+            offset_slot++)
+       {
+               u32 extra_cost = lzx_extra_offset_bits[offset_slot] * BIT_COST;
                unsigned i;
 
-       #if LZX_CONSIDER_ALIGNED_COSTS
+       #if CONSIDER_ALIGNED_COSTS
                if (offset_slot >= 8)
-                       extra_cost -= LZX_NUM_ALIGNED_OFFSET_BITS * LZX_BIT_COST;
+                       extra_cost -= LZX_NUM_ALIGNED_OFFSET_BITS * BIT_COST;
        #endif
 
-               for (i = 0; i < LZX_NUM_PRIMARY_LENS; i++)
+               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];
+               extra_cost += costs->main[main_symbol++];
 
-               for (; i < LZX_NUM_LENS; i++)
+               for (; i < LZX_NUM_LENS; i++) {
                        costs->match_cost[offset_slot][i] =
-                               costs->len[i - LZX_NUM_PRIMARY_LENS] + extra_cost;
+                               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_size)
+/*
+ * Fast approximation for log2f(x).  This is not as accurate as the standard C
+ * version.  It does not need to be perfectly accurate because it is only used
+ * for estimating symbol costs, which is very approximate anyway.
+ */
+static float
+log2f_fast(float x)
 {
-       u32 i;
-       bool have_byte[256];
-       unsigned num_used_bytes;
+        union {
+               float f;
+               s32 i;
+       } u = { .f = x };
 
-       /* The costs below are hard coded to use a scaling factor of 16.  */
-       STATIC_ASSERT(LZX_BIT_COST == 16);
+       /* Extract the exponent and subtract 127 to remove the bias.  This gives
+        * the integer part of the result. */
+        float res = ((u.i >> 23) & 0xFF) - 127;
+
+       /* Set the exponent to 0 (plus bias of 127).  This transforms the number
+        * to the range [1, 2) while retaining the same mantissa. */
+       u.i = (u.i & ~(0xFF << 23)) | (127 << 23);
 
        /*
-        * Heuristics:
+        * Approximate the log2 of the transformed number using a degree 2
+        * interpolating polynomial for log2(x) over the interval [1, 2).  Then
+        * add this to the extracted exponent to produce the final approximation
+        * of log2(x).
         *
-        * - Use smaller initial costs for literal symbols when the input buffer
-        *   contains fewer distinct bytes.
+        * The coefficients of the interpolating polynomial used here were found
+        * using the script tools/log2_interpolation.r.
+        */
+        return res - 1.653124006f + u.f * (1.9941812f - u.f * 0.3347490189f);
+
+}
+
+/*
+ * Return the estimated cost of a symbol which has been estimated to have the
+ * given probability.
+ */
+static u32
+lzx_cost_for_probability(float prob)
+{
+       /*
+        * The basic formula is:
         *
-        * - Assume that match symbols are more costly than literal symbols.
+        *      entropy = -log2(probability)
         *
-        * - Assume that length symbols for shorter lengths are less costly than
-        *   length symbols for longer lengths.
+        * Use this to get the cost in fractional bits.  Then multiply by our
+        * scaling factor of BIT_COST and truncate to a u32.
+        *
+        * In addition, the minimum cost is BIT_COST (one bit) because the
+        * entropy coding method will be Huffman codes.
         */
+       u32 cost = -log2f_fast(prob) * BIT_COST;
+       return max(cost, BIT_COST);
+}
 
-       for (i = 0; i < 256; i++)
-               have_byte[i] = false;
+/*
+ * Mapping: number of used literals => heuristic probability of a literal times
+ * 6870.  Generated by running this R command:
+ *
+ *     cat(paste(round(6870*2^-((304+(0:256))/64)), collapse=", "))
+ */
+static const u8 literal_scaled_probs[257] = {
+       255, 253, 250, 247, 244, 242, 239, 237, 234, 232, 229, 227, 224, 222,
+       219, 217, 215, 212, 210, 208, 206, 203, 201, 199, 197, 195, 193, 191,
+       189, 186, 184, 182, 181, 179, 177, 175, 173, 171, 169, 167, 166, 164,
+       162, 160, 159, 157, 155, 153, 152, 150, 149, 147, 145, 144, 142, 141,
+       139, 138, 136, 135, 133, 132, 130, 129, 128, 126, 125, 124, 122, 121,
+       120, 118, 117, 116, 115, 113, 112, 111, 110, 109, 107, 106, 105, 104,
+       103, 102, 101, 100, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86,
+       86, 85, 84, 83, 82, 81, 80, 79, 78, 78, 77, 76, 75, 74, 73, 73, 72, 71,
+       70, 70, 69, 68, 67, 67, 66, 65, 65, 64, 63, 62, 62, 61, 60, 60, 59, 59,
+       58, 57, 57, 56, 55, 55, 54, 54, 53, 53, 52, 51, 51, 50, 50, 49, 49, 48,
+       48, 47, 47, 46, 46, 45, 45, 44, 44, 43, 43, 42, 42, 41, 41, 40, 40, 40,
+       39, 39, 38, 38, 38, 37, 37, 36, 36, 36, 35, 35, 34, 34, 34, 33, 33, 33,
+       32, 32, 32, 31, 31, 31, 30, 30, 30, 29, 29, 29, 28, 28, 28, 27, 27, 27,
+       27, 26, 26, 26, 25, 25, 25, 25, 24, 24, 24, 24, 23, 23, 23, 23, 22, 22,
+       22, 22, 21, 21, 21, 21, 20, 20, 20, 20, 20, 19, 19, 19, 19, 19, 18, 18,
+       18, 18, 18, 17, 17, 17, 17, 17, 16, 16, 16, 16
+};
 
-       for (i = 0; i < block_size; i++)
-               have_byte[block[i]] = true;
+/*
+ * Mapping: length symbol => default cost of that symbol.  This is derived from
+ * sample data but has been slightly edited to add more bias towards the
+ * shortest lengths, which are the most common.
+ */
+static const u16 lzx_default_len_costs[LZX_LENCODE_NUM_SYMBOLS] = {
+       300, 310, 320, 330, 360, 396, 399, 416, 451, 448, 463, 466, 505, 492,
+       503, 514, 547, 531, 566, 561, 589, 563, 592, 586, 623, 602, 639, 627,
+       659, 643, 657, 650, 685, 662, 661, 672, 685, 686, 696, 680, 657, 682,
+       666, 699, 674, 699, 679, 709, 688, 712, 692, 714, 694, 716, 698, 712,
+       706, 727, 714, 727, 713, 723, 712, 718, 719, 719, 720, 735, 725, 735,
+       728, 740, 727, 739, 727, 742, 716, 733, 733, 740, 738, 746, 737, 747,
+       738, 745, 736, 748, 742, 749, 745, 749, 743, 748, 741, 752, 745, 752,
+       747, 750, 747, 752, 748, 753, 750, 752, 753, 753, 749, 744, 752, 755,
+       753, 756, 745, 748, 746, 745, 723, 757, 755, 758, 755, 758, 752, 757,
+       754, 757, 755, 759, 755, 758, 753, 755, 755, 758, 757, 761, 755, 750,
+       758, 759, 759, 760, 758, 751, 757, 757, 759, 759, 758, 759, 758, 761,
+       750, 761, 758, 760, 759, 761, 758, 761, 760, 752, 759, 760, 759, 759,
+       757, 762, 760, 761, 761, 748, 761, 760, 762, 763, 752, 762, 762, 763,
+       762, 762, 763, 763, 762, 763, 762, 763, 762, 763, 763, 764, 763, 762,
+       763, 762, 762, 762, 764, 764, 763, 764, 763, 763, 763, 762, 763, 763,
+       762, 764, 764, 763, 762, 763, 763, 763, 763, 762, 764, 763, 762, 764,
+       764, 763, 763, 765, 764, 764, 762, 763, 764, 765, 763, 764, 763, 764,
+       762, 764, 764, 754, 763, 764, 763, 763, 762, 763, 584,
+};
 
-       num_used_bytes = 0;
-       for (i = 0; i < 256; i++)
-               num_used_bytes += have_byte[i];
+/* Set default costs to bootstrap the iterative optimization algorithm. */
+static void
+lzx_set_default_costs(struct lzx_compressor *c)
+{
+       unsigned i;
+       u32 num_literals = 0;
+       u32 num_used_literals = 0;
+       float inv_num_matches = 1.0f / c->freqs.main[LZX_NUM_CHARS];
+       float inv_num_items;
+       float prob_match = 1.0f;
+       u32 match_cost;
+       float base_literal_prob;
+
+       /* Some numbers here have been hardcoded to assume a bit cost of 64. */
+       STATIC_ASSERT(BIT_COST == 64);
+
+       /* Estimate the number of literals that will used.  'num_literals' is
+        * the total number, whereas 'num_used_literals' is the number of
+        * distinct symbols. */
+       for (i = 0; i < LZX_NUM_CHARS; i++) {
+               num_literals += c->freqs.main[i];
+               num_used_literals += (c->freqs.main[i] != 0);
+       }
 
-       for (i = 0; i < 256; i++)
-               c->costs.main[i] = 140 - (256 - num_used_bytes) / 4;
+       /* Note: all match headers were tallied as symbol 'LZX_NUM_CHARS'.  We
+        * don't attempt to estimate which ones will be used. */
+
+       inv_num_items = 1.0f / (num_literals + c->freqs.main[LZX_NUM_CHARS]);
+       base_literal_prob = literal_scaled_probs[num_used_literals] *
+                           (1.0f / 6870.0f);
+
+       /* Literal costs.  We use two different methods to compute the
+        * probability of each literal and mix together their results. */
+       for (i = 0; i < LZX_NUM_CHARS; i++) {
+               u32 freq = c->freqs.main[i];
+               if (freq != 0) {
+                       float prob = 0.5f * ((freq * inv_num_items) +
+                                            base_literal_prob);
+                       c->costs.main[i] = lzx_cost_for_probability(prob);
+                       prob_match -= prob;
+               } else {
+                       c->costs.main[i] = 11 * BIT_COST;
+               }
+       }
 
+       /* Match header costs.  We just assume that all match headers are
+        * equally probable, but we do take into account the relative cost of a
+        * match header vs. a literal depending on how common matches are
+        * expected to be vs. literals. */
+       prob_match = max(prob_match, 0.15f);
+       match_cost = lzx_cost_for_probability(prob_match / (c->num_main_syms -
+                                                           LZX_NUM_CHARS));
        for (; i < c->num_main_syms; i++)
-               c->costs.main[i] = 170;
+               c->costs.main[i] = match_cost;
 
+       /* Length symbol costs.  These are just set to fixed values which
+        * reflect the fact the smallest lengths are typically the most common,
+        * and therefore are typically the cheapest. */
        for (i = 0; i < LZX_LENCODE_NUM_SYMBOLS; i++)
-               c->costs.len[i] = 103 + (i / 4);
+               c->costs.len[i] = lzx_default_len_costs[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;
+#if CONSIDER_ALIGNED_COSTS
+       /* Aligned offset symbol costs.  These are derived from the estimated
+        * probability of each aligned offset symbol. */
+       for (i = 0; i < LZX_ALIGNEDCODE_NUM_SYMBOLS; i++) {
+               /* We intentionally tallied the frequencies in the wrong slots,
+                * not accounting for LZX_OFFSET_ADJUSTMENT, since doing the
+                * fixup here is faster: a constant 8 subtractions here vs. one
+                * addition for every match. */
+               unsigned j = (i - LZX_OFFSET_ADJUSTMENT) & LZX_ALIGNED_OFFSET_BITMASK;
+               if (c->freqs.aligned[j] != 0) {
+                       float prob = c->freqs.aligned[j] * inv_num_matches;
+                       c->costs.aligned[i] = lzx_cost_for_probability(prob);
+               } else {
+                       c->costs.aligned[i] =
+                               (2 * LZX_NUM_ALIGNED_OFFSET_BITS) * BIT_COST;
+               }
+       }
 #endif
-
-       lzx_compute_match_costs(c);
 }
 
 /* Update the current cost model to reflect the computed Huffman codes.  */
 static void
-lzx_update_costs(struct lzx_compressor *c)
+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;
+                                   MAIN_CODEWORD_LIMIT) * BIT_COST;
        }
 
        for (i = 0; i < LZX_LENCODE_NUM_SYMBOLS; i++) {
                c->costs.len[i] = (lens->len[i] ? lens->len[i] :
-                                  LENGTH_CODEWORD_LIMIT) * LZX_BIT_COST;
+                                  LENGTH_CODEWORD_LIMIT) * BIT_COST;
        }
 
-#if LZX_CONSIDER_ALIGNED_COSTS
+#if CONSIDER_ALIGNED_COSTS
        for (i = 0; i < LZX_ALIGNEDCODE_NUM_SYMBOLS; i++) {
                c->costs.aligned[i] = (lens->aligned[i] ? lens->aligned[i] :
-                                      ALIGNED_CODEWORD_LIMIT) * LZX_BIT_COST;
+                                      ALIGNED_CODEWORD_LIMIT) * BIT_COST;
        }
 #endif
-
-       lzx_compute_match_costs(c);
 }
 
+/*
+ * Choose a "near-optimal" literal/match sequence to use for the current block,
+ * then flush the block.  Because the cost of each Huffman symbol is unknown
+ * until the Huffman codes have been built and the Huffman codes themselves
+ * depend on the symbol frequencies, this uses an iterative optimization
+ * algorithm to approximate an optimal solution.  The first optimization pass
+ * for the block uses default costs; additional passes use costs derived from
+ * the Huffman codes computed in the previous pass.
+ */
 static inline struct lzx_lru_queue
-lzx_optimize_and_write_block(struct lzx_compressor * const restrict c,
+lzx_optimize_and_flush_block(struct lzx_compressor * const restrict c,
                             struct lzx_output_bitstream * const restrict os,
                             const u8 * const restrict block_begin,
                             const u32 block_size,
@@ -1759,25 +2097,27 @@ lzx_optimize_and_write_block(struct lzx_compressor * const restrict c,
        struct lzx_lru_queue new_queue;
        u32 seq_idx;
 
-       /* The first optimization pass uses a default cost model.  Each
-        * additional optimization pass uses a cost model derived from the
-        * Huffman code computed in the previous pass.  */
+       lzx_set_default_costs(c);
 
-       lzx_set_default_costs(c, block_begin, block_size);
-       lzx_reset_symbol_frequencies(c);
-       do {
+       for (;;) {
+               lzx_compute_match_costs(c);
                new_queue = lzx_find_min_cost_path(c, block_begin, block_size,
                                                   initial_queue, is_16_bit);
-               if (num_passes_remaining > 1) {
-                       lzx_tally_item_list(c, block_size, is_16_bit);
-                       lzx_make_huffman_codes(c);
-                       lzx_update_costs(c);
-                       lzx_reset_symbol_frequencies(c);
-               }
-       } while (--num_passes_remaining);
 
+               if (--num_passes_remaining == 0)
+                       break;
+
+               /* At least one optimization pass remains.  Update the costs. */
+               lzx_reset_symbol_frequencies(c);
+               lzx_tally_item_list(c, block_size, is_16_bit);
+               lzx_build_huffman_codes(c);
+               lzx_set_costs_from_codes(c);
+       }
+
+       /* Done optimizing.  Generate the sequence list and flush the block. */
+       lzx_reset_symbol_frequencies(c);
        seq_idx = lzx_record_item_list(c, block_size, is_16_bit);
-       lzx_finish_block(c, os, block_begin, block_size, seq_idx);
+       lzx_flush_block(c, os, block_begin, block_size, seq_idx);
        return new_queue;
 }
 
@@ -1785,7 +2125,7 @@ lzx_optimize_and_write_block(struct lzx_compressor * const restrict c,
  * 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.
+ * inexpensive (in terms of compressed size) way to output the block.
  *
  * Note: there are actually many things this algorithm leaves on the table in
  * terms of compression ratio.  So although it may be "near-optimal", it is
@@ -1795,182 +2135,353 @@ lzx_optimize_and_write_block(struct lzx_compressor * const restrict c,
  * simpler "greedy" or "lazy" parse while still being relatively fast.
  */
 static inline void
-lzx_compress_near_optimal(struct lzx_compressor *c,
-                         struct lzx_output_bitstream *os,
+lzx_compress_near_optimal(struct lzx_compressor * restrict c,
+                         const u8 * const restrict in_begin, size_t in_nbytes,
+                         struct lzx_output_bitstream * restrict 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;
+       const u8 * const in_end  = in_begin + in_nbytes;
        u32 max_len = LZX_MAX_MATCH_LEN;
        u32 nice_len = min(c->nice_match_length, max_len);
-       u32 next_hashes[2] = {};
-       struct lzx_lru_queue queue;
+       u32 next_hashes[2] = {0, 0};
+       struct lzx_lru_queue queue = LZX_QUEUE_INITIALIZER;
 
+       /* Initialize the matchfinder. */
        CALL_BT_MF(is_16_bit, c, bt_matchfinder_init);
-       lzx_lru_queue_init(&queue);
 
        do {
-               /* Starting a new block  */
-               const u8 * const in_block_begin = in_next;
-               const u8 * const in_block_end =
-                       in_next + min(LZX_DIV_BLOCK_SIZE, in_end - in_next);
+               /* Starting a new block */
 
-               /* Run the block through the matchfinder and cache the matches. */
+               const u8 * const in_block_begin = in_next;
+               const u8 * const in_max_block_end =
+                       in_next + min(SOFT_MAX_BLOCK_SIZE, in_end - in_next);
                struct lz_match *cache_ptr = c->match_cache;
-               do {
-                       struct lz_match *lz_matchptr;
-                       u32 best_len;
-
-                       /* If approaching the end of the input buffer, adjust
-                        * 'max_len' and 'nice_len' accordingly.  */
-                       if (unlikely(max_len > in_end - in_next)) {
-                               max_len = in_end - in_next;
-                               nice_len = min(max_len, nice_len);
-                               if (unlikely(max_len <
-                                            BT_MATCHFINDER_REQUIRED_NBYTES))
-                               {
-                                       in_next++;
-                                       cache_ptr->length = 0;
-                                       cache_ptr++;
-                                       continue;
-                               }
-                       }
+               const u8 *next_search_pos = in_next;
+               const u8 *next_observation = in_next;
+               const u8 *next_pause_point =
+                       min(in_next + min(MIN_BLOCK_SIZE,
+                                         in_max_block_end - in_next),
+                           in_max_block_end - min(LZX_MAX_MATCH_LEN - 1,
+                                                  in_max_block_end - in_next));
+
+               lzx_init_block_split_stats(&c->split_stats);
+               lzx_reset_symbol_frequencies(c);
 
-                       /* Check for matches.  */
-                       lz_matchptr = CALL_BT_MF(is_16_bit, c,
-                                                bt_matchfinder_get_matches,
-                                                in_begin,
-                                                in_next - in_begin,
-                                                max_len,
-                                                nice_len,
-                                                c->max_search_depth,
-                                                next_hashes,
-                                                &best_len,
-                                                cache_ptr + 1);
-                       in_next++;
-                       cache_ptr->length = lz_matchptr - (cache_ptr + 1);
-                       cache_ptr = lz_matchptr;
+               if (in_next >= next_pause_point)
+                       goto pause;
 
-                       /*
-                        * 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 >= nice_len) {
-                               --best_len;
-                               do {
-                                       if (unlikely(max_len > in_end - in_next)) {
-                                               max_len = in_end - in_next;
-                                               nice_len = min(max_len, nice_len);
-                                               if (unlikely(max_len <
-                                                            BT_MATCHFINDER_REQUIRED_NBYTES))
-                                               {
-                                                       in_next++;
-                                                       cache_ptr->length = 0;
-                                                       cache_ptr++;
-                                                       continue;
-                                               }
+               /*
+                * Run the input buffer through the matchfinder, caching the
+                * matches, until we decide to end the block.
+                *
+                * For a tighter matchfinding loop, we compute a "pause point",
+                * which is the next position at which we may need to check
+                * whether to end the block or to decrease max_len.  We then
+                * only do these extra checks upon reaching the pause point.
+                */
+       resume_matchfinding:
+               do {
+                       if (in_next >= next_search_pos) {
+                               /* Search for matches at this position. */
+                               struct lz_match *lz_matchptr;
+                               u32 best_len;
+
+                               lz_matchptr = CALL_BT_MF(is_16_bit, c,
+                                                        bt_matchfinder_get_matches,
+                                                        in_begin,
+                                                        in_next - in_begin,
+                                                        max_len,
+                                                        nice_len,
+                                                        c->max_search_depth,
+                                                        next_hashes,
+                                                        &best_len,
+                                                        cache_ptr + 1);
+                               cache_ptr->length = lz_matchptr - (cache_ptr + 1);
+                               cache_ptr = lz_matchptr;
+
+                               /* Accumulate literal/match statistics for block
+                                * splitting and for generating the initial cost
+                                * model. */
+                               if (in_next >= next_observation) {
+                                       best_len = cache_ptr[-1].length;
+                                       if (best_len >= 3) {
+                                               /* Match (len >= 3) */
+
+                                               /*
+                                                * Note: for performance reasons this has
+                                                * been simplified significantly:
+                                                *
+                                                * - We wait until later to account for
+                                                *   LZX_OFFSET_ADJUSTMENT.
+                                                * - We don't account for repeat offsets.
+                                                * - We don't account for different match headers.
+                                                */
+                                               c->freqs.aligned[cache_ptr[-1].offset &
+                                                       LZX_ALIGNED_OFFSET_BITMASK]++;
+                                               c->freqs.main[LZX_NUM_CHARS]++;
+
+                                               lzx_observe_match(&c->split_stats, best_len);
+                                               next_observation = in_next + best_len;
+                                       } else {
+                                               /* Literal */
+                                               c->freqs.main[*in_next]++;
+                                               lzx_observe_literal(&c->split_stats, *in_next);
+                                               next_observation = in_next + 1;
                                        }
-                                       CALL_BT_MF(is_16_bit, c,
-                                                  bt_matchfinder_skip_position,
-                                                  in_begin,
-                                                  in_next - in_begin,
-                                                  nice_len,
-                                                  c->max_search_depth,
-                                                  next_hashes);
-                                       in_next++;
+                               }
+
+                               /*
+                                * If there was a very long match found, then
+                                * don't cache any matches for the bytes covered
+                                * by that match.  This avoids degenerate
+                                * behavior when compressing highly redundant
+                                * data, where the number of matches can be very
+                                * large.
+                                *
+                                * This heuristic doesn't actually hurt the
+                                * compression ratio *too* much.  If there's a
+                                * long match, then the data must be highly
+                                * compressible, so it doesn't matter as much
+                                * what we do.
+                                */
+                               if (best_len >= nice_len)
+                                       next_search_pos = in_next + best_len;
+                       } else {
+                               /* Don't search for matches at this position. */
+                               CALL_BT_MF(is_16_bit, c,
+                                          bt_matchfinder_skip_position,
+                                          in_begin,
+                                          in_next - in_begin,
+                                          nice_len,
+                                          c->max_search_depth,
+                                          next_hashes);
+                               cache_ptr->length = 0;
+                               cache_ptr++;
+                       }
+               } while (++in_next < next_pause_point &&
+                        likely(cache_ptr < &c->match_cache[CACHE_LENGTH]));
+
+       pause:
+
+               /* Adjust max_len and nice_len if we're nearing the end of the
+                * input buffer.  In addition, if we are so close to the end of
+                * the input buffer that there cannot be any more matches, then
+                * just advance through the last few positions and record no
+                * matches. */
+               if (unlikely(max_len > in_end - in_next)) {
+                       max_len = in_end - in_next;
+                       nice_len = min(max_len, nice_len);
+                       if (max_len < BT_MATCHFINDER_REQUIRED_NBYTES) {
+                               while (in_next != in_end) {
                                        cache_ptr->length = 0;
                                        cache_ptr++;
-                               } while (--best_len);
+                                       in_next++;
+                               }
                        }
-               } while (in_next < in_block_end &&
-                        likely(cache_ptr < &c->match_cache[LZX_CACHE_LENGTH]));
-
-               /* 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,
+               /* End the block if the match cache may overflow. */
+               if (unlikely(cache_ptr >= &c->match_cache[CACHE_LENGTH]))
+                       goto end_block;
+
+               /* End the block if the soft maximum size has been reached. */
+               if (in_next >= in_max_block_end)
+                       goto end_block;
+
+               /* End the block if the block splitting algorithm thinks this is
+                * a good place to do so. */
+               if (c->split_stats.num_new_observations >=
+                               NUM_OBSERVATIONS_PER_BLOCK_CHECK &&
+                   in_max_block_end - in_next >= MIN_BLOCK_SIZE &&
+                   lzx_should_end_block(&c->split_stats))
+                       goto end_block;
+
+               /* It's not time to end the block yet.  Compute the next pause
+                * point and resume matchfinding. */
+               next_pause_point =
+                       min(in_next + min(NUM_OBSERVATIONS_PER_BLOCK_CHECK * 2 -
+                                           c->split_stats.num_new_observations,
+                                         in_max_block_end - in_next),
+                           in_max_block_end - min(LZX_MAX_MATCH_LEN - 1,
+                                                  in_max_block_end - in_next));
+               goto resume_matchfinding;
+
+       end_block:
+               /* We've decided on a block boundary and cached matches.  Now
+                * choose a match/literal sequence and flush the block. */
+               queue = lzx_optimize_and_flush_block(c, os, in_block_begin,
                                                     in_next - in_block_begin,
                                                     queue, is_16_bit);
        } while (in_next != in_end);
 }
 
 static void
-lzx_compress_near_optimal_16(struct lzx_compressor *c,
-                            struct lzx_output_bitstream *os)
+lzx_compress_near_optimal_16(struct lzx_compressor *c, const u8 *in,
+                            size_t in_nbytes, struct lzx_output_bitstream *os)
 {
-       lzx_compress_near_optimal(c, os, true);
+       lzx_compress_near_optimal(c, in, in_nbytes, os, true);
 }
 
 static void
-lzx_compress_near_optimal_32(struct lzx_compressor *c,
-                            struct lzx_output_bitstream *os)
+lzx_compress_near_optimal_32(struct lzx_compressor *c, const u8 *in,
+                            size_t in_nbytes, struct lzx_output_bitstream *os)
 {
-       lzx_compress_near_optimal(c, os, false);
+       lzx_compress_near_optimal(c, in, in_nbytes, os, false);
 }
 
+/******************************************************************************/
+/*                     Faster ("lazy") compression algorithm                  */
+/*----------------------------------------------------------------------------*/
+
 /*
- * 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.
+ * Called when the compressor chooses to use a literal.  This tallies the
+ * Huffman symbol for the literal, increments the current literal run length,
+ * and "observes" the literal for the block split statistics.
+ */
+static inline void
+lzx_choose_literal(struct lzx_compressor *c, unsigned literal, u32 *litrunlen_p)
+{
+       lzx_observe_literal(&c->split_stats, literal);
+       c->freqs.main[literal]++;
+       ++*litrunlen_p;
+}
+
+/*
+ * Called when the compressor chooses to use a match.  This tallies the Huffman
+ * symbol(s) for a match, saves the match data and the length of the preceding
+ * literal run, updates the recent offsets queue, and "observes" the match for
+ * the block split statistics.
+ */
+static inline void
+lzx_choose_match(struct lzx_compressor *c, unsigned length, u32 adjusted_offset,
+                u32 recent_offsets[LZX_NUM_RECENT_OFFSETS], bool is_16_bit,
+                u32 *litrunlen_p, struct lzx_sequence **next_seq_p)
+{
+       u32 litrunlen = *litrunlen_p;
+       struct lzx_sequence *next_seq = *next_seq_p;
+       unsigned offset_slot;
+       unsigned v;
+
+       lzx_observe_match(&c->split_stats, length);
+
+       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, then 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_get_offset_slot(c, adjusted_offset, 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 = (adjusted_offset << 9) | v;
+
+       /* Tally the main symbol. */
+       c->freqs.main[LZX_NUM_CHARS + v]++;
+
+       /* Update the recent offsets queue. */
+       if (adjusted_offset < LZX_NUM_RECENT_OFFSETS) {
+               /* Repeat offset match. */
+               swap(recent_offsets[0], recent_offsets[adjusted_offset]);
+       } else {
+               /* Explicit offset match. */
+
+               /* Tally the aligned offset symbol if needed. */
+               if (adjusted_offset >= 16)
+                       c->freqs.aligned[adjusted_offset & LZX_ALIGNED_OFFSET_BITMASK]++;
+
+               recent_offsets[2] = recent_offsets[1];
+               recent_offsets[1] = recent_offsets[0];
+               recent_offsets[0] = adjusted_offset - LZX_OFFSET_ADJUSTMENT;
+       }
+
+       /* Reset the literal run length and advance to the next sequence. */
+       *next_seq_p = next_seq + 1;
+       *litrunlen_p = 0;
+}
+
+/*
+ * Called when the compressor ends a block.  This finshes the last lzx_sequence,
+ * which is just a literal run with no following match.  This literal run might
+ * be empty.
+ */
+static 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;
+}
+
+/*
+ * Find the longest repeat offset match with the current position.  If a match
+ * is found, return its length and set *best_rep_idx_ret to the index of its
+ * offset in @recent_offsets.  Otherwise, return 0.
  *
- * 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.
-*/
+ * Don't bother with length 2 matches; consider matches of length >= 3 only.
+ * Also assume that max_len >= 3.
+ */
 static unsigned
 lzx_find_longest_repeat_offset_match(const u8 * const in_next,
-                                    const u32 bytes_remaining,
-                                    const u32 recent_offsets[LZX_NUM_RECENT_OFFSETS],
-                                    unsigned *rep_max_idx_ret)
+                                    const u32 recent_offsets[],
+                                    const unsigned max_len,
+                                    unsigned *best_rep_idx_ret)
 {
-       STATIC_ASSERT(LZX_NUM_RECENT_OFFSETS == 3);
+       STATIC_ASSERT(LZX_NUM_RECENT_OFFSETS == 3); /* loop is unrolled */
 
-       const unsigned max_len = min(bytes_remaining, LZX_MAX_MATCH_LEN);
-       const u16 next_2_bytes = load_u16_unaligned(in_next);
+       const u32 seq3 = load_u24_unaligned(in_next);
        const u8 *matchptr;
-       unsigned rep_max_len;
-       unsigned rep_max_idx;
+       unsigned best_rep_len = 0;
+       unsigned best_rep_idx = 0;
        unsigned rep_len;
 
+       /* Check for rep0 match (most recent offset) */
        matchptr = in_next - recent_offsets[0];
-       if (load_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;
+       if (load_u24_unaligned(matchptr) == seq3)
+               best_rep_len = lz_extend(in_next, matchptr, 3, max_len);
 
+       /* Check for rep1 match (second most recent offset) */
        matchptr = in_next - recent_offsets[1];
-       if (load_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;
+       if (load_u24_unaligned(matchptr) == seq3) {
+               rep_len = lz_extend(in_next, matchptr, 3, max_len);
+               if (rep_len > best_rep_len) {
+                       best_rep_len = rep_len;
+                       best_rep_idx = 1;
                }
        }
 
+       /* Check for rep2 match (third most recent offset) */
        matchptr = in_next - recent_offsets[2];
-       if (load_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;
+       if (load_u24_unaligned(matchptr) == seq3) {
+               rep_len = lz_extend(in_next, matchptr, 3, max_len);
+               if (rep_len > best_rep_len) {
+                       best_rep_len = rep_len;
+                       best_rep_idx = 2;
                }
        }
 
-       *rep_max_idx_ret = rep_max_idx;
-       return rep_max_len;
+       *best_rep_idx_ret = best_rep_idx;
+       return best_rep_len;
 }
 
-/* Fast heuristic scoring for lazy parsing: how "good" is this match?  */
+/*
+ * Fast heuristic scoring for lazy parsing: how "good" is this match?
+ * This is mainly determined by the length: longer matches are better.
+ * However, we also give a bonus to close (small offset) matches and to repeat
+ * offset matches, since those require fewer bits to encode.
+ */
+
 static inline unsigned
 lzx_explicit_offset_match_score(unsigned len, u32 adjusted_offset)
 {
@@ -1978,7 +2489,6 @@ lzx_explicit_offset_match_score(unsigned len, u32 adjusted_offset)
 
        if (adjusted_offset < 4096)
                score++;
-
        if (adjusted_offset < 256)
                score++;
 
@@ -1991,53 +2501,70 @@ lzx_repeat_offset_match_score(unsigned rep_len, unsigned rep_idx)
        return rep_len + 3;
 }
 
-/* This is the "lazy" LZX compressor.  */
+/*
+ * This is the "lazy" LZX compressor.  The basic idea is that before it chooses
+ * a match, it checks to see if there's a longer match at the next position.  If
+ * yes, it chooses a literal and continues to the next position.  If no, it
+ * chooses the match.
+ *
+ * Some additional heuristics are used as well.  Repeat offset matches are
+ * considered favorably and sometimes are chosen immediately.  In addition, long
+ * matches (at least "nice_len" bytes) are chosen immediately as well.  Finally,
+ * when we decide whether a match is "better" than another, we take the offset
+ * into consideration as well as the length.
+ */
 static inline void
-lzx_compress_lazy(struct lzx_compressor *c, struct lzx_output_bitstream *os,
-                 bool is_16_bit)
+lzx_compress_lazy(struct lzx_compressor * restrict c,
+                 const u8 * const restrict in_begin, size_t in_nbytes,
+                 struct lzx_output_bitstream * restrict 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;
+       const u8 * const in_end  = in_begin + in_nbytes;
        unsigned max_len = LZX_MAX_MATCH_LEN;
        unsigned nice_len = min(c->nice_match_length, max_len);
        STATIC_ASSERT(LZX_NUM_RECENT_OFFSETS == 3);
-       u32 recent_offsets[3] = {1, 1, 1};
-       u32 next_hashes[2] = {};
+       u32 recent_offsets[LZX_NUM_RECENT_OFFSETS] = {1, 1, 1};
+       u32 next_hashes[2] = {0, 0};
 
+       /* Initialize the matchfinder. */
        CALL_HC_MF(is_16_bit, c, hc_matchfinder_init);
 
        do {
-               /* Starting a new block  */
+               /* Starting a new block */
 
                const u8 * const in_block_begin = in_next;
-               const u8 * const in_block_end =
-                       in_next + min(LZX_DIV_BLOCK_SIZE, in_end - in_next);
+               const u8 * const in_max_block_end =
+                       in_next + min(SOFT_MAX_BLOCK_SIZE, in_end - in_next);
                struct lzx_sequence *next_seq = c->chosen_sequences;
+               u32 litrunlen = 0;
                unsigned cur_len;
                u32 cur_offset;
-               u32 cur_offset_data;
+               u32 cur_adjusted_offset;
                unsigned cur_score;
                unsigned next_len;
                u32 next_offset;
-               u32 next_offset_data;
+               u32 next_adjusted_offset;
                unsigned next_score;
-               unsigned rep_max_len;
-               unsigned rep_max_idx;
+               unsigned best_rep_len;
+               unsigned best_rep_idx;
                unsigned rep_score;
                unsigned skip_len;
-               u32 litrunlen = 0;
 
                lzx_reset_symbol_frequencies(c);
+               lzx_init_block_split_stats(&c->split_stats);
 
                do {
+                       /* Adjust max_len and nice_len if we're nearing the end
+                        * of the input buffer. */
                        if (unlikely(max_len > in_end - in_next)) {
                                max_len = in_end - in_next;
                                nice_len = min(max_len, nice_len);
                        }
 
-                       /* Find the longest match at the current position.  */
-
+                       /* Find the longest match (subject to the
+                        * max_search_depth cutoff parameter) with the current
+                        * position.  Don't bother with length 2 matches; only
+                        * look for matches of length >= 3. */
                        cur_len = CALL_HC_MF(is_16_bit, c,
                                             hc_matchfinder_longest_match,
                                             in_begin,
@@ -2048,6 +2575,9 @@ lzx_compress_lazy(struct lzx_compressor *c, struct lzx_output_bitstream *os,
                                             c->max_search_depth,
                                             next_hashes,
                                             &cur_offset);
+
+                       /* If there was no match found, or the only match found
+                        * was a distant short match, then choose a literal. */
                        if (cur_len < 3 ||
                            (cur_len == 3 &&
                             cur_offset >= 8192 - LZX_OFFSET_ADJUSTMENT &&
@@ -2055,51 +2585,58 @@ lzx_compress_lazy(struct lzx_compressor *c, struct lzx_output_bitstream *os,
                             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);
+                               lzx_choose_literal(c, *in_next, &litrunlen);
+                               in_next++;
                                continue;
                        }
 
+                       /* Heuristic: if this match has the most recent offset,
+                        * then go ahead and choose it as a rep0 match. */
                        if (cur_offset == recent_offsets[0]) {
                                in_next++;
-                               cur_offset_data = 0;
                                skip_len = cur_len - 1;
+                               cur_adjusted_offset = 0;
                                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);
+                       /* Compute the longest match's score as an explicit
+                        * offset match. */
+                       cur_adjusted_offset = cur_offset + LZX_OFFSET_ADJUSTMENT;
+                       cur_score = lzx_explicit_offset_match_score(cur_len, cur_adjusted_offset);
+
+                       /* Find the longest repeat offset match at this
+                        * position.  If we find one and it's "better" than the
+                        * explicit offset match we found, then go ahead and
+                        * choose the repeat offset match immediately. */
+                       best_rep_len = lzx_find_longest_repeat_offset_match(in_next,
+                                                                           recent_offsets,
+                                                                           max_len,
+                                                                           &best_rep_idx);
                        in_next++;
 
-                       if (rep_max_len >= 3 &&
-                           (rep_score = lzx_repeat_offset_match_score(rep_max_len,
-                                                                      rep_max_idx)) >= cur_score)
+                       if (best_rep_len != 0 &&
+                           (rep_score = lzx_repeat_offset_match_score(best_rep_len,
+                                                                      best_rep_idx)) >= cur_score)
                        {
-                               cur_len = rep_max_len;
-                               cur_offset_data = rep_max_idx;
-                               skip_len = rep_max_len - 1;
+                               cur_len = best_rep_len;
+                               cur_adjusted_offset = best_rep_idx;
+                               skip_len = best_rep_len - 1;
                                goto choose_cur_match;
                        }
 
                have_cur_match:
+                       /*
+                        * We have a match at the current position.  If the
+                        * match is very long, then choose it immediately.
+                        * Otherwise, see if there's a better match at the next
+                        * position.
+                        */
 
-                       /* 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);
@@ -2117,53 +2654,56 @@ lzx_compress_lazy(struct lzx_compressor *c, struct lzx_output_bitstream *os,
                                              &next_offset);
 
                        if (next_len <= cur_len - 2) {
+                               /* No potentially better match was found. */
                                in_next++;
                                skip_len = cur_len - 2;
                                goto choose_cur_match;
                        }
 
-                       next_offset_data = next_offset + LZX_OFFSET_ADJUSTMENT;
-                       next_score = lzx_explicit_offset_match_score(next_len, next_offset_data);
+                       next_adjusted_offset = next_offset + LZX_OFFSET_ADJUSTMENT;
+                       next_score = lzx_explicit_offset_match_score(next_len, next_adjusted_offset);
 
-                       rep_max_len = lzx_find_longest_repeat_offset_match(in_next,
-                                                                          in_end - in_next,
-                                                                          recent_offsets,
-                                                                          &rep_max_idx);
+                       best_rep_len = lzx_find_longest_repeat_offset_match(in_next,
+                                                                           recent_offsets,
+                                                                           max_len,
+                                                                           &best_rep_idx);
                        in_next++;
 
-                       if (rep_max_len >= 3 &&
-                           (rep_score = lzx_repeat_offset_match_score(rep_max_len,
-                                                                      rep_max_idx)) >= next_score)
+                       if (best_rep_len != 0 &&
+                           (rep_score = lzx_repeat_offset_match_score(best_rep_len,
+                                                                      best_rep_idx)) >= next_score)
                        {
 
                                if (rep_score > cur_score) {
                                        /* The next match is better, and it's a
-                                        * repeat offset match.  */
-                                       lzx_record_literal(c, *(in_next - 2),
+                                        * repeat offset match. */
+                                       lzx_choose_literal(c, *(in_next - 2),
                                                           &litrunlen);
-                                       cur_len = rep_max_len;
-                                       cur_offset_data = rep_max_idx;
+                                       cur_len = best_rep_len;
+                                       cur_adjusted_offset = best_rep_idx;
                                        skip_len = cur_len - 1;
                                        goto choose_cur_match;
                                }
                        } else {
                                if (next_score > cur_score) {
                                        /* The next match is better, and it's an
-                                        * explicit offset match.  */
-                                       lzx_record_literal(c, *(in_next - 2),
+                                        * explicit offset match. */
+                                       lzx_choose_literal(c, *(in_next - 2),
                                                           &litrunlen);
                                        cur_len = next_len;
-                                       cur_offset_data = next_offset_data;
+                                       cur_adjusted_offset = next_adjusted_offset;
                                        cur_score = next_score;
                                        goto have_cur_match;
                                }
                        }
 
-                       /* The original match was better */
+                       /* The original match was better; choose it. */
                        skip_len = cur_len - 2;
 
                choose_cur_match:
-                       lzx_record_match(c, cur_len, cur_offset_data,
+                       /* Choose a match and have the matchfinder skip over its
+                        * remaining bytes. */
+                       lzx_choose_match(c, cur_len, cur_adjusted_offset,
                                         recent_offsets, is_16_bit,
                                         &litrunlen, &next_seq);
                        in_next = CALL_HC_MF(is_16_bit, c,
@@ -2173,35 +2713,52 @@ lzx_compress_lazy(struct lzx_compressor *c, struct lzx_output_bitstream *os,
                                             in_end - in_begin,
                                             skip_len,
                                             next_hashes);
-               } while (in_next < in_block_end);
 
-               lzx_finish_sequence(next_seq, litrunlen);
+                       /* Keep going until it's time to end the block. */
+               } while (in_next < in_max_block_end &&
+                        !(c->split_stats.num_new_observations >=
+                                       NUM_OBSERVATIONS_PER_BLOCK_CHECK &&
+                          in_next - in_block_begin >= MIN_BLOCK_SIZE &&
+                          in_end - in_next >= MIN_BLOCK_SIZE &&
+                          lzx_should_end_block(&c->split_stats)));
 
-               lzx_finish_block(c, os, in_block_begin, in_next - in_block_begin, 0);
+               /* Flush the block. */
+               lzx_finish_sequence(next_seq, litrunlen);
+               lzx_flush_block(c, os, in_block_begin, in_next - in_block_begin, 0);
 
+               /* Keep going until we've reached the end of the input buffer. */
        } while (in_next != in_end);
 }
 
 static void
-lzx_compress_lazy_16(struct lzx_compressor *c, struct lzx_output_bitstream *os)
+lzx_compress_lazy_16(struct lzx_compressor *c, const u8 *in, size_t in_nbytes,
+                    struct lzx_output_bitstream *os)
 {
-       lzx_compress_lazy(c, os, true);
+       lzx_compress_lazy(c, in, in_nbytes, os, true);
 }
 
 static void
-lzx_compress_lazy_32(struct lzx_compressor *c, struct lzx_output_bitstream *os)
+lzx_compress_lazy_32(struct lzx_compressor *c, const u8 *in, size_t in_nbytes,
+                    struct lzx_output_bitstream *os)
 {
-       lzx_compress_lazy(c, os, false);
+       lzx_compress_lazy(c, in, in_nbytes, os, false);
 }
 
-/* Generate the acceleration tables for offset slots.  */
+/******************************************************************************/
+/*                          Compressor operations                             */
+/*----------------------------------------------------------------------------*/
+
+/*
+ * Generate tables for mapping match offsets (actually, "adjusted" match
+ * offsets) to offset slots.
+ */
 static void
 lzx_init_offset_slot_tabs(struct lzx_compressor *c)
 {
        u32 adjusted_offset = 0;
        unsigned slot = 0;
 
-       /* slots [0, 29]  */
+       /* slots [0, 29] */
        for (; adjusted_offset < ARRAY_LEN(c->offset_slot_tab_1);
             adjusted_offset++)
        {
@@ -2210,7 +2767,7 @@ lzx_init_offset_slot_tabs(struct lzx_compressor *c)
                c->offset_slot_tab_1[adjusted_offset] = slot;
        }
 
-       /* slots [30, 49]  */
+       /* slots [30, 49] */
        for (; adjusted_offset < LZX_MAX_WINDOW_SIZE;
             adjusted_offset += (u32)1 << 14)
        {
@@ -2223,7 +2780,7 @@ lzx_init_offset_slot_tabs(struct lzx_compressor *c)
 static size_t
 lzx_get_compressor_size(size_t max_bufsize, unsigned compression_level)
 {
-       if (compression_level <= LZX_MAX_FAST_LEVEL) {
+       if (compression_level <= MAX_FAST_LEVEL) {
                if (lzx_is_16_bit(max_bufsize))
                        return offsetof(struct lzx_compressor, hc_mf_16) +
                               hc_matchfinder_size_16(max_bufsize);
@@ -2240,6 +2797,7 @@ lzx_get_compressor_size(size_t max_bufsize, unsigned compression_level)
        }
 }
 
+/* Compute the amount of memory needed to allocate an LZX compressor. */
 static u64
 lzx_get_needed_memory(size_t max_bufsize, unsigned compression_level,
                      bool destructive)
@@ -2251,10 +2809,11 @@ lzx_get_needed_memory(size_t max_bufsize, unsigned compression_level,
 
        size += lzx_get_compressor_size(max_bufsize, compression_level);
        if (!destructive)
-               size += max_bufsize; /* in_buffer */
+               size += max_bufsize; /* account for in_buffer */
        return size;
 }
 
+/* Allocate an LZX compressor. */
 static int
 lzx_create_compressor(size_t max_bufsize, unsigned compression_level,
                      bool destructive, void **c_ret)
@@ -2262,87 +2821,75 @@ lzx_create_compressor(size_t max_bufsize, unsigned compression_level,
        unsigned window_order;
        struct lzx_compressor *c;
 
+       /* Validate the maximum buffer size and get the window order from it. */
        window_order = lzx_get_window_order(max_bufsize);
        if (window_order == 0)
                return WIMLIB_ERR_INVALID_PARAM;
 
+       /* Allocate the compressor. */
        c = MALLOC(lzx_get_compressor_size(max_bufsize, compression_level));
        if (!c)
                goto oom0;
 
-       c->destructive = destructive;
-
-       c->num_main_syms = lzx_get_num_main_syms(window_order);
        c->window_order = window_order;
+       c->num_main_syms = lzx_get_num_main_syms(window_order);
+       c->destructive = destructive;
 
+       /* Allocate the buffer for preprocessed data if needed. */
        if (!c->destructive) {
                c->in_buffer = MALLOC(max_bufsize);
                if (!c->in_buffer)
                        goto oom1;
        }
 
-       if (compression_level <= LZX_MAX_FAST_LEVEL) {
-
-               /* Fast compression: Use lazy parsing.  */
+       if (compression_level <= MAX_FAST_LEVEL) {
 
+               /* Fast compression: Use lazy parsing. */
                if (lzx_is_16_bit(max_bufsize))
                        c->impl = lzx_compress_lazy_16;
                else
                        c->impl = lzx_compress_lazy_32;
+
+               /* Scale max_search_depth and nice_match_length with the
+                * compression level. */
                c->max_search_depth = (60 * compression_level) / 20;
                c->nice_match_length = (80 * compression_level) / 20;
 
                /* lzx_compress_lazy() needs max_search_depth >= 2 because it
                 * halves the max_search_depth when attempting a lazy match, and
-                * max_search_depth cannot be 0.  */
-               if (c->max_search_depth < 2)
-                       c->max_search_depth = 2;
+                * max_search_depth must be at least 1. */
+               c->max_search_depth = max(c->max_search_depth, 2);
        } else {
 
-               /* Normal / high compression: Use near-optimal parsing.  */
-
+               /* 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.  */
+               /* Scale max_search_depth and nice_match_length with the
+                * compression level. */
                c->max_search_depth = (24 * compression_level) / 50;
                c->nice_match_length = (48 * compression_level) / 50;
 
-               /* Set a number of optimization passes appropriate for the
-                * compression level.  */
-
+               /* Also scale num_optim_passes with the compression level.  But
+                * the more passes there are, the less they help --- so don't
+                * add them linearly.  */
                c->num_optim_passes = 1;
-
-               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++;
-               }
+               c->num_optim_passes += (compression_level >= 45);
+               c->num_optim_passes += (compression_level >= 70);
+               c->num_optim_passes += (compression_level >= 100);
+               c->num_optim_passes += (compression_level >= 150);
+               c->num_optim_passes += (compression_level >= 200);
+               c->num_optim_passes += (compression_level >= 300);
+
+               /* max_search_depth must be at least 1. */
+               c->max_search_depth = max(c->max_search_depth, 1);
        }
 
-       /* 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;
-
+       /* Prepare the offset => offset slot mapping. */
        lzx_init_offset_slot_tabs(c);
+
        *c_ret = c;
        return 0;
 
@@ -2352,6 +2899,7 @@ oom0:
        return WIMLIB_ERR_NOMEM;
 }
 
+/* Compress a buffer of data. */
 static size_t
 lzx_compress(const void *restrict in, size_t in_nbytes,
             void *restrict out, size_t out_nbytes_avail, void *restrict _c)
@@ -2360,35 +2908,46 @@ lzx_compress(const void *restrict in, size_t in_nbytes,
        struct lzx_output_bitstream os;
        size_t result;
 
-       /* Don't bother trying to compress very small inputs.  */
-       if (in_nbytes < 100)
+       /* Don't bother trying to compress very small inputs. */
+       if (in_nbytes < 64)
                return 0;
 
-       /* Copy the input data into the internal buffer and preprocess it.  */
-       if (c->destructive)
-               c->in_buffer = (void *)in;
-       else
+       /* If the compressor is in "destructive" mode, then we can directly
+        * preprocess the input data.  Otherwise, we need to copy it into an
+        * internal buffer first. */
+       if (!c->destructive) {
                memcpy(c->in_buffer, in, in_nbytes);
-       c->in_nbytes = in_nbytes;
-       lzx_preprocess(c->in_buffer, in_nbytes);
+               in = c->in_buffer;
+       }
+
+       /* Preprocess the input data. */
+       lzx_preprocess((void *)in, in_nbytes);
 
-       /* Initially, the previous Huffman codeword lengths are all zeroes.  */
+       /* 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.  */
+       /* Initialize the output bitstream. */
        lzx_init_output(&os, out, out_nbytes_avail);
 
-       /* Call the compression level-specific compress() function.  */
-       (*c->impl)(c, &os);
+       /* Call the compression level-specific compress() function. */
+       (*c->impl)(c, in, in_nbytes, &os);
 
-       /* Flush the output bitstream and return the compressed size or 0.  */
+       /* Flush the output bitstream. */
        result = lzx_flush_output(&os);
-       if (!result && c->destructive)
-               lzx_postprocess(c->in_buffer, c->in_nbytes);
+
+       /* If the data did not compress to less than its original size and we
+        * preprocessed the original buffer, then postprocess it to restore it
+        * to its original state. */
+       if (result == 0 && c->destructive)
+               lzx_postprocess((void *)in, in_nbytes);
+
+       /* Return the number of compressed bytes, or 0 if the input did not
+        * compress to less than its original size. */
        return result;
 }
 
+/* Free an LZX compressor. */
 static void
 lzx_free_compressor(void *_c)
 {
diff --git a/tools/log2_interpolation.r b/tools/log2_interpolation.r
new file mode 100644 (file)
index 0000000..9523ec1
--- /dev/null
@@ -0,0 +1,47 @@
+#
+# This R language script finds a degree 2 interpolating polynomial for f =
+# log2(x) over the interval [1, 2).
+#
+
+f = function(x) { log2(x) }
+
+get.chebyshev.points = function(a, b, n)
+{
+    (a+b)/2 + (b-a)/2 * cos(((2*(1:n)-1)*pi)/(2*n))
+}
+
+build.vandermonde.matrix = function(x)
+{
+    n = length(x)
+    V = matrix(nrow=n, ncol=n)
+    for (j in 1:n)
+        V[,j] = x^(j-1)
+    return(V)
+}
+
+evaluate.polynomial = function(coeffs, x)
+{
+    y = coeffs[length(coeffs)]
+    for (i in (length(coeffs)-1):1)
+        y = y*x + coeffs[i]
+    return(y)
+}
+
+x.plot = seq(1, 2, length=1000)
+x.chebychev = get.chebyshev.points(1, 2, 3)
+V = build.vandermonde.matrix(x.chebychev)
+coeffs.a = solve(V, f(x.chebychev))
+coeffs.a = c(coeffs.a)
+polynomial.interp = function(x) { evaluate.polynomial(coeffs.a, x) }
+cat("Coefficients of degree 2 interpolating polynomial:\n")
+options(digits=10)
+cat(coeffs.a, "\n")
+pdf("polynomial-interp.pdf")
+plot(x.plot, f(x.plot), col="black", type="l", xlab="x", ylab="y",
+        main="f(x) and interpolating polynomial approximation")
+points(x.chebychev, f(x.chebychev), pch=19, col="red")
+lines(x.plot, polynomial.interp(x.plot), col="blue")
+legend("topleft", pch=c(NA, NA, 19),
+          col=c("black", "blue", "red"), lty=c(1,1,0),
+       legend=c("f(x)", "Interpolating polynomial", "Chebychev points"),
+       inset=0.07)