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Edit distance match finder

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Bimba Shrestha 2020-03-13 09:39:33 -05:00
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42
contrib/match_finders/README.md Normal file
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## Edit Distance Match Finder
```
/* This match finder leverages techniques used in file comparison algorithms
* to find matches between a dictionary and a source file.
*
* The original motivation for studying this approach was to try and optimize
* Zstandard for the use case of patching: the most common scenario being
* updating an existing software package with the next version. When patching,
* the difference between the old version of the package and the new version
* is generally tiny (most of the new file will be identical to
* the old one). In more technical terms, the edit distance (the minimal number
* of changes required to take one sequence of bytes to another) between the
* files would be small relative to the size of the file.
*
* Various 'diffing' algorithms utilize this notion of edit distance and
* the corrensponding concept of a minimal edit script between two
* sequences to identify the regions within two files where they differ.
* The core algorithm used in this match finder is described in:
*
* "An O(ND) Difference Algorithm and its Variations", Eugene W. Myers,
* Algorithmica Vol. 1, 1986, pp. 251-266,
* <https://doi.org/10.1007/BF01840446>.
*
* Additional algorithmic heuristics for speed improvement have also been included.
* These we inspired from implementations of various regular and binary diffing
* algorithms such as GNU diff, bsdiff, and Xdelta.
*
* Note: after some experimentation, this approach proved to not provide enough
* utility to justify the additional CPU used in finding matches. The one area
* where this approach consistenly outperforms Zstandard even on level 19 is
* when compressing small files (<10 KB) using a equally small dictionary that
* is very similar to the source file. For the use case that this was intended,
* (large similar files) this approach by itself took 5-10X longer than zstd-19 and
* generally resulted in 2-3X larger files. The core advantage that zstd-19 has
* over this appraoch for match finding is the overlapping matches. This approach
* cannot find any.
*
* I'm leaving this in the contrib section in case this ever becomes interesting
* to explore again.
* */
```

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contrib/match_finders/zstd_edist.c Normal file
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/*
* Copyright (c) 2016-present, Yann Collet, Facebook, Inc.
* All rights reserved.
*
* This source code is licensed under both the BSD-style license (found in the
* LICENSE file in the root directory of this source tree) and the GPLv2 (found
* in the COPYING file in the root directory of this source tree).
* You may select, at your option, one of the above-listed licenses.
*/
/*-*************************************
* Dependencies
***************************************/
/* Currently relies on qsort when combining contiguous matches. This can probabily
* be avoided but would require changes to the algorithm. The qsort is far from
* the bottleneck in this algorithm even for medium sized files so it's probably
* not worth trying to address */
#include <stdlib.h>
#include <assert.h>
#include "zstd_edist.h"
#include "mem.h"
/*-*************************************
* Constants
***************************************/
/* Just a sential for the entires of the diagnomal matrix */
#define ZSTD_EDIST_DIAG_MAX (S32)(1 << 30)
/* How large should a snake be to be considered a 'big' snake.
* For an explanation of what a 'snake' is with respect to the
* edit distance matrix, see the linked paper in zstd_edist.h */
#define ZSTD_EDIST_SNAKE_THRESH 20
/* After how many iterations should we start to use the heuristic
* based on 'big' snakes */
#define ZSTD_EDIST_SNAKE_ITER_THRESH 200
/* After how many iterations should be just give up and take
* the best availabe edit script for this round */
#define ZSTD_EDIST_EXPENSIVE_THRESH 1024
/*-*************************************
* Structures
***************************************/
typedef struct {
U32 dictIdx;
U32 srcIdx;
U32 matchLength;
} ZSTD_eDist_match;
typedef struct {
const BYTE* dict;
const BYTE* src;
size_t dictSize;
size_t srcSize;
S32* forwardDiag; /* Entires of the forward diagonal stored here */
S32* backwardDiag; /* Entires of the backward diagonal stored here.
* Note: this buffer and the 'forwardDiag' buffer
* are contiguous. See the ZSTD_eDist_genSequences */
ZSTD_eDist_match* matches; /* Accumulate matches of length 1 in this buffer.
* In a subsequence post-processing step, we combine
* contiguous matches. */
U32 nbMatches;
} ZSTD_eDist_state;
typedef struct {
S32 dictMid; /* The mid diagonal for the dictionary */
S32 srcMid; /* The mid diagonal for the source */
int lowUseHeuristics; /* Should we use heuristics for the low part */
int highUseHeuristics; /* Should we use heuristics for the high part */
} ZSTD_eDist_partition;
/*-*************************************
* Internal
***************************************/
static void ZSTD_eDist_diag(ZSTD_eDist_state* state,
ZSTD_eDist_partition* partition,
S32 dictLow, S32 dictHigh, S32 srcLow,
S32 srcHigh, int useHeuristics)
{
S32* const forwardDiag = state->forwardDiag;
S32* const backwardDiag = state->backwardDiag;
const BYTE* const dict = state->dict;
const BYTE* const src = state->src;
S32 const diagMin = dictLow - srcHigh;
S32 const diagMax = dictHigh - srcLow;
S32 const forwardMid = dictLow - srcLow;
S32 const backwardMid = dictHigh - srcHigh;
S32 forwardMin = forwardMid;
S32 forwardMax = forwardMid;
S32 backwardMin = backwardMid;
S32 backwardMax = backwardMid;
int odd = (forwardMid - backwardMid) & 1;
U32 iterations;
forwardDiag[forwardMid] = dictLow;
backwardDiag[backwardMid] = dictHigh;
/* Main loop for updating diag entries. Unless useHeuristics is
* set to false, this loop will run until it finds the minimal
* edit script */
for (iterations = 1;;iterations++) {
S32 diag;
int bigSnake = 0;
if (forwardMin > diagMin) {
forwardMin--;
forwardDiag[forwardMin - 1] = -1;
} else {
forwardMin++;
}
if (forwardMax < diagMax) {
forwardMax++;
forwardDiag[forwardMax + 1] = -1;
} else {
forwardMax--;
}
for (diag = forwardMax; diag >= forwardMin; diag -= 2) {
S32 dictIdx;
S32 srcIdx;
S32 low = forwardDiag[diag - 1];
S32 high = forwardDiag[diag + 1];
S32 dictIdx0 = low < high ? high : low + 1;
for (dictIdx = dictIdx0, srcIdx = dictIdx0 - diag;
dictIdx < dictHigh && srcIdx < srcHigh && dict[dictIdx] == src[srcIdx];
dictIdx++, srcIdx++) continue;
if (dictIdx - dictIdx0 > ZSTD_EDIST_SNAKE_THRESH)
bigSnake = 1;
forwardDiag[diag] = dictIdx;
if (odd && backwardMin <= diag && diag <= backwardMax && backwardDiag[diag] <= dictIdx) {
partition->dictMid = dictIdx;
partition->srcMid = srcIdx;
partition->lowUseHeuristics = 0;
partition->highUseHeuristics = 0;
return;
}
}
if (backwardMin > diagMin) {
backwardMin--;
backwardDiag[backwardMin - 1] = ZSTD_EDIST_DIAG_MAX;
} else {
backwardMin++;
}
if (backwardMax < diagMax) {
backwardMax++;
backwardDiag[backwardMax + 1] = ZSTD_EDIST_DIAG_MAX;
} else {
backwardMax--;
}
for (diag = backwardMax; diag >= backwardMin; diag -= 2) {
S32 dictIdx;
S32 srcIdx;
S32 low = backwardDiag[diag - 1];
S32 high = backwardDiag[diag + 1];
S32 dictIdx0 = low < high ? low : high - 1;
for (dictIdx = dictIdx0, srcIdx = dictIdx0 - diag;
dictLow < dictIdx && srcLow < srcIdx && dict[dictIdx - 1] == src[srcIdx - 1];
dictIdx--, srcIdx--) continue;
if (dictIdx0 - dictIdx > ZSTD_EDIST_SNAKE_THRESH)
bigSnake = 1;
backwardDiag[diag] = dictIdx;
if (!odd && forwardMin <= diag && diag <= forwardMax && dictIdx <= forwardDiag[diag]) {
partition->dictMid = dictIdx;
partition->srcMid = srcIdx;
partition->lowUseHeuristics = 0;
partition->highUseHeuristics = 0;
return;
}
}
if (!useHeuristics)
continue;
/* Everything under this point is a heuritic. Using these will
* substantially speed up the match finding. In some cases, taking
* the total match finding time from several minutes to seconds.
* Of course, the caveat is that the edit script found may no longer
* be optimal */
/* Big snake heuristic */
if (iterations > ZSTD_EDIST_SNAKE_ITER_THRESH && bigSnake) {
{
S32 best = 0;
for (diag = forwardMax; diag >= forwardMin; diag -= 2) {
S32 diagDiag = diag - forwardMid;
S32 dictIdx = forwardDiag[diag];
S32 srcIdx = dictIdx - diag;
S32 v = (dictIdx - dictLow) * 2 - diagDiag;
if (v > 12 * (iterations + (diagDiag < 0 ? -diagDiag : diagDiag))) {
if (v > best
&& dictLow + ZSTD_EDIST_SNAKE_THRESH <= dictIdx && dictIdx <= dictHigh
&& srcLow + ZSTD_EDIST_SNAKE_THRESH <= srcIdx && srcIdx <= srcHigh) {
S32 k;
for (k = 1; dict[dictIdx - k] == src[srcIdx - k]; k++) {
if (k == ZSTD_EDIST_SNAKE_THRESH) {
best = v;
partition->dictMid = dictIdx;
partition->srcMid = srcIdx;
break;
}
}
}
}
}
if (best > 0) {
partition->lowUseHeuristics = 0;
partition->highUseHeuristics = 1;
return;
}
}
{
S32 best = 0;
for (diag = backwardMax; diag >= backwardMin; diag -= 2) {
S32 diagDiag = diag - backwardMid;
S32 dictIdx = backwardDiag[diag];
S32 srcIdx = dictIdx - diag;
S32 v = (dictHigh - dictIdx) * 2 + diagDiag;
if (v > 12 * (iterations + (diagDiag < 0 ? -diagDiag : diagDiag))) {
if (v > best
&& dictLow < dictIdx && dictIdx <= dictHigh - ZSTD_EDIST_SNAKE_THRESH
&& srcLow < srcIdx && srcIdx <= srcHigh - ZSTD_EDIST_SNAKE_THRESH) {
int k;
for (k = 0; dict[dictIdx + k] == src[srcIdx + k]; k++) {
if (k == ZSTD_EDIST_SNAKE_THRESH - 1) {
best = v;
partition->dictMid = dictIdx;
partition->srcMid = srcIdx;
break;
}
}
}
}
}
if (best > 0) {
partition->lowUseHeuristics = 1;
partition->highUseHeuristics = 0;
return;
}
}
}
/* More general 'too expensive' heuristic */
if (iterations >= ZSTD_EDIST_EXPENSIVE_THRESH) {
S32 forwardDictSrcBest;
S32 forwardDictBest = 0;
S32 backwardDictSrcBest;
S32 backwardDictBest = 0;
forwardDictSrcBest = -1;
for (diag = forwardMax; diag >= forwardMin; diag -= 2) {
S32 dictIdx = MIN(forwardDiag[diag], dictHigh);
S32 srcIdx = dictIdx - diag;
if (srcHigh < srcIdx) {
dictIdx = srcHigh + diag;
srcIdx = srcHigh;
}
if (forwardDictSrcBest < dictIdx + srcIdx) {
forwardDictSrcBest = dictIdx + srcIdx;
forwardDictBest = dictIdx;
}
}
backwardDictSrcBest = ZSTD_EDIST_DIAG_MAX;
for (diag = backwardMax; diag >= backwardMin; diag -= 2) {
S32 dictIdx = MAX(dictLow, backwardDiag[diag]);
S32 srcIdx = dictIdx - diag;
if (srcIdx < srcLow) {
dictIdx = srcLow + diag;
srcIdx = srcLow;
}
if (dictIdx + srcIdx < backwardDictSrcBest) {
backwardDictSrcBest = dictIdx + srcIdx;
backwardDictBest = dictIdx;
}
}
if ((dictHigh + srcHigh) - backwardDictSrcBest < forwardDictSrcBest - (dictLow + srcLow)) {
partition->dictMid = forwardDictBest;
partition->srcMid = forwardDictSrcBest - forwardDictBest;
partition->lowUseHeuristics = 0;
partition->highUseHeuristics = 1;
} else {
partition->dictMid = backwardDictBest;
partition->srcMid = backwardDictSrcBest - backwardDictBest;
partition->lowUseHeuristics = 1;
partition->highUseHeuristics = 0;
}
return;
}
}
}
static void ZSTD_eDist_insertMatch(ZSTD_eDist_state* state,
S32 const dictIdx, S32 const srcIdx)
{
state->matches[state->nbMatches].dictIdx = dictIdx;
state->matches[state->nbMatches].srcIdx = srcIdx;
state->matches[state->nbMatches].matchLength = 1;
state->nbMatches++;
}
static int ZSTD_eDist_compare(ZSTD_eDist_state* state,
S32 dictLow, S32 dictHigh, S32 srcLow,
S32 srcHigh, int useHeuristics)
{
const BYTE* const dict = state->dict;
const BYTE* const src = state->src;
/* Found matches while traversing from the low end */
while (dictLow < dictHigh && srcLow < srcHigh && dict[dictLow] == src[srcLow]) {
ZSTD_eDist_insertMatch(state, dictLow, srcLow);
dictLow++;
srcLow++;
}
/* Found matches while traversing from the high end */
while (dictLow < dictHigh && srcLow < srcHigh && dict[dictHigh - 1] == src[srcHigh - 1]) {
ZSTD_eDist_insertMatch(state, dictHigh - 1, srcHigh - 1);
dictHigh--;
srcHigh--;
}
/* If the low and high end end up touching. If we wanted to make
* note of the differences like most diffing algorithms do, we would
* do so here. In our case, we're only concerned with matches
* Note: if you wanted to find the edit distance of the algorithm,
* you could just accumulate the cost for an insertion/deletion
* below. */
if (dictLow == dictHigh) {
while (srcLow < srcHigh) {
/* Reaching this point means inserting src[srcLow] into
* the current position of dict */
srcLow++;
}
} else if (srcLow == srcHigh) {
while (dictLow < dictHigh) {
/* Reaching this point means deleteing dict[dictLow] from
* the current positino of dict */
dictLow++;
}
} else {
ZSTD_eDist_partition partition;
partition.dictMid = 0;
partition.srcMid = 0;
ZSTD_eDist_diag(state, &partition, dictLow, dictHigh,
srcLow, srcHigh, useHeuristics);
if (ZSTD_eDist_compare(state, dictLow, partition.dictMid,
srcLow, partition.srcMid, partition.lowUseHeuristics))
return 1;
if (ZSTD_eDist_compare(state, partition.dictMid, dictHigh,
partition.srcMid, srcHigh, partition.highUseHeuristics))
return 1;
}
return 0;
}
static int ZSTD_eDist_matchComp(const void* p, const void* q)
{
S32 const l = ((ZSTD_eDist_match*)p)->srcIdx;
S32 const r = ((ZSTD_eDist_match*)q)->srcIdx;
return (l - r);
}
/* The matches from the approach above will all be of the form
* (dictIdx, srcIdx, 1). this method combines contiguous matches
* of length MINMATCH or greater. Matches less than MINMATCH
* are discarded */
static void ZSTD_eDist_combineMatches(ZSTD_eDist_state* state)
{
/* Create a new buffer to put the combined matches into
* and memcpy to state->matches after */
ZSTD_eDist_match* combinedMatches =
ZSTD_malloc(state->nbMatches * sizeof(ZSTD_eDist_match),
ZSTD_defaultCMem);
U32 nbCombinedMatches = 1;
size_t i;
/* Make sure that the srcIdx and dictIdx are in sorted order.
* The combination step won't work otherwise */
qsort(state->matches, state->nbMatches, sizeof(ZSTD_eDist_match), ZSTD_eDist_matchComp);
memcpy(combinedMatches, state->matches, sizeof(ZSTD_eDist_match));
for (i = 1; i < state->nbMatches; i++) {
ZSTD_eDist_match const match = state->matches[i];
ZSTD_eDist_match const combinedMatch =
combinedMatches[nbCombinedMatches - 1];
if (combinedMatch.srcIdx + combinedMatch.matchLength == match.srcIdx &&
combinedMatch.dictIdx + combinedMatch.matchLength == match.dictIdx) {
combinedMatches[nbCombinedMatches - 1].matchLength++;
} else {
/* Discard matches that are less than MINMATCH */
if (combinedMatches[nbCombinedMatches - 1].matchLength < MINMATCH) {
nbCombinedMatches--;
}
memcpy(combinedMatches + nbCombinedMatches,
state->matches + i, sizeof(ZSTD_eDist_match));
nbCombinedMatches++;
}
}
memcpy(state->matches, combinedMatches, nbCombinedMatches * sizeof(ZSTD_eDist_match));
state->nbMatches = nbCombinedMatches;
ZSTD_free(combinedMatches, ZSTD_defaultCMem);
}
static size_t ZSTD_eDist_convertMatchesToSequences(ZSTD_Sequence* sequences,
ZSTD_eDist_state* state)
{
const ZSTD_eDist_match* matches = state->matches;
size_t const nbMatches = state->nbMatches;
size_t const dictSize = state->dictSize;
size_t nbSequences = 0;
size_t i;
for (i = 0; i < nbMatches; i++) {
ZSTD_eDist_match const match = matches[i];
U32 const litLength = !i ? match.srcIdx :
match.srcIdx - (matches[i - 1].srcIdx + matches[i - 1].matchLength);
U32 const offset = (match.srcIdx + dictSize) - match.dictIdx;
U32 const matchLength = match.matchLength;
sequences[nbSequences].offset = offset;
sequences[nbSequences].litLength = litLength;
sequences[nbSequences].matchLength = matchLength;
nbSequences++;
}
return nbSequences;
}
/*-*************************************
* Interal utils
***************************************/
static size_t ZSTD_eDist_hamingDist(const BYTE* const a,
const BYTE* const b, size_t n)
{
size_t i;
size_t dist = 0;
for (i = 0; i < n; i++)
dist += a[i] != b[i];
return dist;
}
/* This is a pretty naive recursive implementation that should only
* be used for quick tests obviously. Don't try and run this on a
* GB file or something. There are faster implementations. Use those
* if you need to run it for large files. */
static size_t ZSTD_eDist_levenshteinDist(const BYTE* const s,
size_t const sn, const BYTE* const t,
size_t const tn)
{
size_t a, b, c;
if (!sn)
return tn;
if (!tn)
return sn;
if (s[sn - 1] == t[tn - 1])
return ZSTD_eDist_levenshteinDist(
s, sn - 1, t, tn - 1);
a = ZSTD_eDist_levenshteinDist(s, sn - 1, t, tn - 1);
b = ZSTD_eDist_levenshteinDist(s, sn, t, tn - 1);
c = ZSTD_eDist_levenshteinDist(s, sn - 1, t, tn);
if (a > b)
a = b;
if (a > c)
a = c;
return a + 1;
}
static void ZSTD_eDist_validateMatches(ZSTD_eDist_match* matches,
size_t const nbMatches, const BYTE* const dict,
size_t const dictSize, const BYTE* const src,
size_t const srcSize)
{
size_t i;
for (i = 0; i < nbMatches; i++) {
ZSTD_eDist_match match = matches[i];
U32 const dictIdx = match.dictIdx;
U32 const srcIdx = match.srcIdx;
U32 const matchLength = match.matchLength;
assert(dictIdx + matchLength < dictSize);
assert(srcIdx + matchLength < srcSize);
assert(!memcmp(dict + dictIdx, src + srcIdx, matchLength));
}
}
/*-*************************************
* API
***************************************/
size_t ZSTD_eDist_genSequences(ZSTD_Sequence* sequences,
const void* dict, size_t dictSize,
const void* src, size_t srcSize,
int useHeuristics)
{
size_t const nbDiags = dictSize + srcSize + 3;
S32* buffer = ZSTD_malloc(nbDiags * 2 * sizeof(S32), ZSTD_defaultCMem);
ZSTD_eDist_state state;
size_t nbSequences = 0;
state.dict = (const BYTE*)dict;
state.src = (const BYTE*)src;
state.dictSize = dictSize;
state.srcSize = srcSize;
state.forwardDiag = buffer;
state.backwardDiag = buffer + nbDiags;
state.forwardDiag += srcSize + 1;
state.backwardDiag += srcSize + 1;
state.matches = ZSTD_malloc(srcSize * sizeof(ZSTD_eDist_match), ZSTD_defaultCMem);
state.nbMatches = 0;
ZSTD_eDist_compare(&state, 0, dictSize, 0, srcSize, 1);
ZSTD_eDist_combineMatches(&state);
nbSequences = ZSTD_eDist_convertMatchesToSequences(sequences, &state);
ZSTD_free(buffer, ZSTD_defaultCMem);
ZSTD_free(state.matches, ZSTD_defaultCMem);
return nbSequences;
}

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contrib/match_finders/zstd_edist.h Normal file
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/*
* Copyright (c) 2016-present, Yann Collet, Facebook, Inc.
* All rights reserved.
*
* This source code is licensed under both the BSD-style license (found in the
* LICENSE file in the root directory of this source tree) and the GPLv2 (found
* in the COPYING file in the root directory of this source tree).
* You may select, at your option, one of the above-listed licenses.
*/
/* This match finder leverages techniques used in file comparison algorithms
* to find matches between a dictionary and a source file.
*
* The original motivation for studying this approach was to try and optimize
* Zstandard for the use case of patching: the most common scenario being
* updating an existing software package with the next version. When patching,
* the difference between the old version of the package and the new version
* is generally tiny (most of the new file will be identical to
* the old one). In more technical terms, the edit distance (the minimal number
* of changes required to take one sequence of bytes to another) between the
* files would be small relative to the size of the file.
*
* Various 'diffing' algorithms utilize this notion of edit distance and
* the corrensponding concept of a minimal edit script between two
* sequences to identify the regions within two files where they differ.
* The core algorithm used in this match finder is described in:
*
* "An O(ND) Difference Algorithm and its Variations", Eugene W. Myers,
* Algorithmica Vol. 1, 1986, pp. 251-266,
* <https://doi.org/10.1007/BF01840446>.
*
* Additional algorithmic heuristics for speed improvement have also been included.
* These we inspired from implementations of various regular and binary diffing
* algorithms such as GNU diff, bsdiff, and Xdelta.
*
* Note: after some experimentation, this approach proved to not provide enough
* utility to justify the additional CPU used in finding matches. The one area
* where this approach consistenly outperforms Zstandard even on level 19 is
* when compressing small files (<10 KB) using a equally small dictionary that
* is very similar to the source file. For the use case that this was intended,
* (large similar files) this approach by itself took 5-10X longer than zstd-19 and
* generally resulted in 2-3X larger files. The core advantage that zstd-19 has
* over this appraoch for match finding is the overlapping matches. This approach
* cannot find any.
*
* I'm leaving this in the contrib section in case this ever becomes interesting
* to explore again.
* */
#ifndef ZSTD_EDIST_H
#define ZSTD_EDIST_H
/*-*************************************
* Dependencies
***************************************/
#include <stddef.h>
#include "zstd_internal.h" /* ZSTD_Sequence */
/*! ZSTD_eDist_genSequences() :
* Will populate the provided ZSTD_Sequence buffer with sequences
* based on the optimal or near-optimal (depending on 'useHeuristics')
* edit script between 'dict' and 'src.'
* @return : the number of sequences found */
size_t ZSTD_eDist_genSequences(ZSTD_Sequence* sequences,
const void* dict, size_t dictSize,
const void* src, size_t srcSize,
int useHeuristics);
#endif