lz_optimal.h: Cleanup, better comments

[wimlib] / include / wimlib / lz_optimal.h

/*
 * lz_optimal.h
 *
 * Near-optimal LZ (Lempel-Ziv) parsing, or "match choosing".
 * See lz_get_near_optimal_match() for details of the algorithm.
 *
 * This code is not concerned with actually *finding* LZ matches, as it relies
 * on an underlying match-finder implementation that can do so.
 */

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

/* Define the following structures before including this header:
 *
 * LZ_COMPRESSOR
 * LZ_ADAPTIVE_STATE
 *
 * Also, the type lz_mc_cost_t can be optionally overridden by providing an
 * appropriate typedef and defining LZ_MC_COST_T_DEFINED.  */

#ifndef _LZ_OPTIMAL_H
#define _LZ_OPTIMAL_H

#include "wimlib/lz.h"

#ifndef LZ_MC_COST_T_DEFINED
   typedef input_idx_t lz_mc_cost_t;
#endif

#define LZ_MC_INFINITE_COST (~(lz_mc_cost_t)0)

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

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

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

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

        /* Format-dependent adaptive state that exists after an approximate
         * minimum-cost path to reach this position is taken.  For example, for
         * LZX this is the list of recently used match offsets.  If the format
         * does not have any adaptive state that affects match costs,
         * LZ_ADAPTIVE_STATE could be set to a dummy structure of size 0.  */
        LZ_ADAPTIVE_STATE state;
};

struct lz_match_chooser {
        /* Temporary space used for the match-choosing algorithm.  The size of
         * this array must be at least one more than @nice_len but otherwise is
         * arbitrary.  More space decreases the frequency at which the algorithm
         * is forced to terminate early.  4096 spaces seems sufficient for most
         * real data.  */
        struct lz_mc_pos_data *optimum;
        input_idx_t array_space;

        /* When a match with length greater than or equal to this length is
         * found, choose it immediately without further consideration.  */
        input_idx_t nice_len;

        /* When matches have been chosen, optimum_cur_idx is set to the position
         * in the window of the next match/literal to return and optimum_end_idx
         * is set to the position in the window at the end of the last
         * match/literal to return.  */
        input_idx_t optimum_cur_idx;
        input_idx_t optimum_end_idx;
};

/* Initialize the match-chooser.
 *
 * After calling this, multiple data buffers can be scanned with it if each is
 * preceded with a call to lz_match_chooser_begin().  */
static bool
lz_match_chooser_init(struct lz_match_chooser *mc,
                      input_idx_t array_space,
                      input_idx_t nice_len, input_idx_t max_match_len)
{
        input_idx_t extra_len = min(nice_len, max_match_len);

        LZ_ASSERT(array_space > 0);
        mc->optimum = MALLOC((array_space + extra_len) * sizeof(mc->optimum[0]));
        if (mc->optimum == NULL)
                return false;
        mc->array_space = array_space;
        mc->nice_len = nice_len;
        return true;
}

/* Free memory allocated in lz_match_chooser_init().  */
static void
lz_match_chooser_destroy(struct lz_match_chooser *mc)
{
        FREE(mc->optimum);
}

/* Call this before starting to parse each new input string.  */
static void
lz_match_chooser_begin(struct lz_match_chooser *mc)
{
        mc->optimum_cur_idx = 0;
        mc->optimum_end_idx = 0;
}

/*
 * Reverse the linked list of near-optimal matches so that they can be returned
 * in forwards order.
 *
 * Returns the first match in the list.
 */
static _always_inline_attribute struct raw_match
lz_match_chooser_reverse_list(struct lz_match_chooser *mc, input_idx_t cur_pos)
{
        unsigned prev_link, saved_prev_link;
        unsigned prev_match_offset, saved_prev_match_offset;

        mc->optimum_end_idx = cur_pos;

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

        do {
                prev_link = saved_prev_link;
                prev_match_offset = saved_prev_match_offset;

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

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

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

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

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

/* Format-specific functions inlined into lz_get_near_optimal_match().  */

/* Get the list of possible matches at the next position.  The return value must
 * be the number of matches found (which may be 0) and a pointer to the returned
 * matches must be written into @matches_ret.  Matches must be of distinct
 * lengths and sorted in decreasing order by length.  Furthermore, match lengths
 * may not exceed the @max_match_len passed to lz_match_chooser_init().  */
typedef u32 (*lz_get_matches_t)(LZ_COMPRESSOR *ctx,
                                const LZ_ADAPTIVE_STATE *state,
                                struct raw_match **matches_ret);

/* Skip the specified number of bytes (don't search for matches at them).  This
 * is expected to be faster than simply getting the matches at each position,
 * but the exact performance difference will be dependent on the match-finder
 * implementation.  */
typedef void (*lz_skip_bytes_t)(LZ_COMPRESSOR *ctx, input_idx_t n);

/* Get the cost of the literal located at the position at which matches have
 * most recently been searched.  This can optionally update the @state to take
 * into account format-dependent state that affects match costs, such as repeat
 * offsets.  */
typedef lz_mc_cost_t (lz_get_prev_literal_cost_t)(LZ_COMPRESSOR *ctx,
                                                  LZ_ADAPTIVE_STATE *state);

/* Get the cost of a match.  This can optionally update the @state to take into
 * account format-dependent state that affects match costs, such as repeat
 * offsets.  */
typedef lz_mc_cost_t (lz_get_match_cost_t)(LZ_COMPRESSOR *ctx,
                                           LZ_ADAPTIVE_STATE *state,
                                           input_idx_t length,
                                           input_idx_t offset);

/*
 * lz_get_near_optimal_match() -
 *
 * Choose an approximately optimal match or literal to use at the next position
 * in the string, or "window", being LZ-encoded.
 *
 * This is based on the algorithm used in 7-Zip's DEFLATE encoder, written by
 * Igor Pavlov.  However it also attempts to account for adaptive state, such as
 * a LRU queue of recent match offsets.
 *
 * Unlike a greedy parser that always takes the longest match, or even a "lazy"
 * parser with one match/literal look-ahead like zlib, the algorithm used here
 * may look ahead many matches/literals to determine the approximately optimal
 * match/literal to code next.  The motivation is that the compression ratio is
 * improved if the compressor can do things like use a shorter-than-possible
 * match in order to allow a longer match later, and also take into account the
 * estimated real cost of coding each match/literal based on the underlying
 * entropy encoding.
 *
 * Still, this is not a true optimal parser for several reasons:
 *
 * - Very long matches (at least @nice_len) are taken immediately.  This is
 *   because locations with long matches are likely to have many possible
 *   alternatives that would cause slow optimal parsing, but also such locations
 *   are already highly compressible so it is not too harmful to just grab the
 *   longest match.
 *
 * - Not all possible matches at each location are considered.  Users of this
 *   code are expected to provide a @get_matches() function that returns a list
 *   of potentially good matches at the current position, but no more than one
 *   per length.  It therefore must use some sort of heuristic (e.g. smallest or
 *   repeat offset) to choose a good match to consider for a given length, if
 *   multiple exist.  Furthermore, the @get_matches() implementation may limit
 *   the total number of matches returned and/or the number of computational
 *   steps spent searching for matches at each position.
 *
 * - This function relies on the user-provided @get_match_cost() and
 *   @get_prev_literal_cost() functions to evaluate match and literal costs,
 *   respectively, but real compression formats use entropy encoding of the
 *   literal/match sequence, so the real cost of coding each match or literal is
 *   unknown until the parse is fully determined.  It can be approximated based
 *   on iterative parses, but the end result is not guaranteed to be globally
 *   optimal.
 *
 * - Although this function allows @get_match_cost() and
 *   @get_prev_literal_cost() to take into account adaptive state, coding
 *   decisions made with respect to the adaptive state will be locally optimal
 *   but will not necessarily be globally optimal.  This is because the
 *   algorithm only keeps the least-costly path to get to a given location and
 *   does not take into account that a slightly more costly path could result in
 *   a different adaptive state that ultimately results in a lower global cost.
 *
 * - The array space used by this function is bounded, so in degenerate cases it
 *   is forced to start returning matches/literals before the algorithm has
 *   really finished.
 *
 * Each call to this function does one of two things:
 *
 * 1. Build a sequence of near-optimal matches/literals, up to some point, that
 *    will be returned by subsequent calls to this function, then return the
 *    first one.
 *
 * OR
 *
 * 2. Return the next match/literal previously computed by a call to this
 *    function.
 *
 * The return value is a (length, offset) pair specifying the match or literal
 * chosen.  For literals, the length is 0 or 1 and the offset is meaningless.
 *
 * NOTE: this code has been factored out of the LZX compressor so that it can be
 * shared by other formats such as LZMS.  It is inlined so there is no loss of
 * performance, especially with the different implementations of match-finding,
 * cost evaluation, and adaptive state.
 */
static _always_inline_attribute struct raw_match
lz_get_near_optimal_match(struct lz_match_chooser *mc,
                          lz_get_matches_t get_matches,
                          lz_skip_bytes_t skip_bytes,
                          lz_get_prev_literal_cost_t get_prev_literal_cost,
                          lz_get_match_cost_t get_match_cost,
                          LZ_COMPRESSOR *ctx,
                          const LZ_ADAPTIVE_STATE *initial_state)
{
        u32 num_possible_matches;
        struct raw_match *possible_matches;
        struct raw_match match;
        input_idx_t longest_match_len;

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

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

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

        mc->optimum_cur_idx = 0;
        mc->optimum_end_idx = 0;

        /* Get matches at this position.  */
        num_possible_matches = (*get_matches)(ctx,
                                              initial_state,
                                              &possible_matches);

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

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

        /* Greedy heuristic:  if the longest match that was found is greater
         * than nice_len, return it immediately; don't both doing more work.  */
        if (longest_match_len >= mc->nice_len) {
                (*skip_bytes)(ctx, longest_match_len - 1);
                return possible_matches[0];
        }

        /* Calculate the cost to reach the next position by coding a literal.
         */
        mc->optimum[1].state = *initial_state;
        mc->optimum[1].cost = (*get_prev_literal_cost)(ctx, &mc->optimum[1].state);
        mc->optimum[1].prev.link = 0;

        /* Calculate the cost to reach any position up to and including that
         * reached by the longest match.  Use the shortest available match that
         * reaches each position, assuming that @get_matches() only returned
         * shorter matches because their estimated costs were less than that of
         * the longest match.  */
        for (input_idx_t len = 2, match_idx = num_possible_matches - 1;
             len <= longest_match_len; len++)
        {

                LZ_ASSERT(match_idx < num_possible_matches);
                LZ_ASSERT(len <= possible_matches[match_idx].len);

                mc->optimum[len].state = *initial_state;
                mc->optimum[len].prev.link = 0;
                mc->optimum[len].prev.match_offset = possible_matches[match_idx].offset;
                mc->optimum[len].cost = (*get_match_cost)(ctx,
                                                          &mc->optimum[len].state,
                                                          len,
                                                          possible_matches[match_idx].offset);
                if (len == possible_matches[match_idx].len)
                        match_idx--;
        }

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

                /* Check termination conditions (2) and (3) noted above.  */
                if (cur_pos == len_end || cur_pos == mc->array_space)
                        return lz_match_chooser_reverse_list(mc, cur_pos);

                /* Retrieve a (possibly empty) list of potentially useful
                 * matches available at this position.  */
                num_possible_matches = (*get_matches)(ctx,
                                                      &mc->optimum[cur_pos].state,
                                                      &possible_matches);

                if (num_possible_matches == 0)
                        longest_match_len = 0;
                else
                        longest_match_len = possible_matches[0].len;

                /* Greedy heuristic and termination condition (1) noted above:
                 * if we found a match greater than @nice_len, choose it
                 * unconditionally and begin returning matches/literals.  */
                if (longest_match_len >= mc->nice_len) {
                        /* Build the list of matches to return and get
                         * the first one.  */
                        match = lz_match_chooser_reverse_list(mc, cur_pos);

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

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

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

                /* Load minimum cost to reach the current position.  */
                input_idx_t cur_cost = mc->optimum[cur_pos].cost;

                /* Consider proceeding with a literal byte.  */
                {
                        LZ_ADAPTIVE_STATE state;
                        lz_mc_cost_t cost;

                        state = mc->optimum[cur_pos].state;
                        cost = cur_cost + (*get_prev_literal_cost)(ctx, &state);

                        if (cost < mc->optimum[cur_pos + 1].cost) {
                                mc->optimum[cur_pos + 1].cost = cost;
                                mc->optimum[cur_pos + 1].prev.link = cur_pos;
                                mc->optimum[cur_pos + 1].state = state;
                        }
                }

                /* If no matches were found, continue to the next position.
                 * Otherwise, consider proceeding with a match.  */

                if (num_possible_matches == 0)
                        continue;

                /* Initialize any uninitialized costs up to the length of the
                 * longest match found.  */
                while (len_end < cur_pos + longest_match_len)
                        mc->optimum[++len_end].cost = LZ_MC_INFINITE_COST;

                /* Calculate the minimum cost to reach any position up to and
                 * including that reached by the longest match.  Use the
                 * shortest available match that reaches each position, assuming
                 * that @get_matches() only returned shorter matches because
                 * their estimated costs were less than that of the longest
                 * match.  */
                for (input_idx_t len = 2, match_idx = num_possible_matches - 1;
                     len <= longest_match_len; len++)
                {
                        LZ_ASSERT(match_idx < num_possible_matches);
                        LZ_ASSERT(len <= possible_matches[match_idx].len);

                        LZ_ADAPTIVE_STATE state;
                        lz_mc_cost_t cost;

                        state = mc->optimum[cur_pos].state;
                        cost = cur_cost + (*get_match_cost)(ctx,
                                                            &state,
                                                            len,
                                                            possible_matches[match_idx].offset);

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

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

#endif /* _LZ_OPTIMAL_H  */