Improve performance of regular expression back-references.

In some cases, at the time that we're doing an NFA-based precheck
of whether a backref subexpression can match at a particular place
in the string, we already know which substring the referenced
subexpression matched.  If so, we might as well forget about the NFA
and just compare the substring; this is faster and it gives an exact
rather than approximate answer.

In general, this optimization can help while we are prechecking within
the second child expression of a concat node, while the capture was
within the first child expression; then the substring was saved during
cdissect() of the first child and will be available to NFA checks done
while cdissect() recurses into the second child.  It can help quite a
lot if the tree looks like

              concat
             /      \
      capture        concat
                    /      \
     expensive stuff        backref

as we will be able to avoid recursively dissecting the "expensive
stuff" before discovering that the backref isn't satisfied with a
particular midpoint that the lower concat node is testing.  This
doesn't help if the concat tree is left-deep, as the capture node
won't get set soon enough (and it's hard to fix that without changing
the engine's match behavior).  Fortunately, right-deep concat trees
are the common case.

Patch by me, reviewed by Joel Jacobson

Discussion: https://postgr.es/m/661609.1614560029@sss.pgh.pa.us

src/backend/regex/rege_dfa.c

@@ -58,6 +58,19 @@ longest(struct vars *v,
 	if (hitstopp != NULL)
 		*hitstopp = 0;
 
+	/* if this is a backref to a known string, just match against that */
+	if (d->backno >= 0)
+	{
+		assert((size_t) d->backno < v->nmatch);
+		if (v->pmatch[d->backno].rm_so >= 0)
+		{
+			cp = dfa_backref(v, d, start, start, stop, false);
+			if (cp == v->stop && stop == v->stop && hitstopp != NULL)
+				*hitstopp = 1;
+			return cp;
+		}
+	}
+
 	/* fast path for matchall NFAs */
 	if (d->cnfa->flags & MATCHALL)
 	{
@@ -210,6 +223,20 @@ shortest(struct vars *v,
 	if (hitstopp != NULL)
 		*hitstopp = 0;
 
+	/* if this is a backref to a known string, just match against that */
+	if (d->backno >= 0)
+	{
+		assert((size_t) d->backno < v->nmatch);
+		if (v->pmatch[d->backno].rm_so >= 0)
+		{
+			cp = dfa_backref(v, d, start, min, max, true);
+			if (cp != NULL && coldp != NULL)
+				*coldp = start;
+			/* there is no case where we should set *hitstopp */
+			return cp;
+		}
+	}
+
 	/* fast path for matchall NFAs */
 	if (d->cnfa->flags & MATCHALL)
 	{
@@ -467,6 +494,94 @@ matchuntil(struct vars *v,
 	return 1;
 }
 
+/*
+ * dfa_backref - find best match length for a known backref string
+ *
+ * When the backref's referent is already available, we can deliver an exact
+ * answer with considerably less work than running the backref node's NFA.
+ *
+ * Return match endpoint for longest or shortest valid repeated match,
+ * or NULL if there is no valid match.
+ *
+ * Should be in sync with cbrdissect(), although that has the different task
+ * of checking a match to a predetermined section of the string.
+ */
+static chr *
+dfa_backref(struct vars *v,
+			struct dfa *d,
+			chr *start,			/* where the match should start */
+			chr *min,			/* match must end at or after here */
+			chr *max,			/* match must end at or before here */
+			bool shortest)
+{
+	int			n = d->backno;
+	int			backmin = d->backmin;
+	int			backmax = d->backmax;
+	size_t		numreps;
+	size_t		minreps;
+	size_t		maxreps;
+	size_t		brlen;
+	chr		   *brstring;
+	chr		   *p;
+
+	/* get the backreferenced string (caller should have checked this) */
+	if (v->pmatch[n].rm_so == -1)
+		return NULL;
+	brstring = v->start + v->pmatch[n].rm_so;
+	brlen = v->pmatch[n].rm_eo - v->pmatch[n].rm_so;
+
+	/* special-case zero-length backreference to avoid divide by zero */
+	if (brlen == 0)
+	{
+		/*
+		 * matches only a zero-length string, but any number of repetitions
+		 * can be considered to be present
+		 */
+		if (min == start && backmin <= backmax)
+			return start;
+		return NULL;
+	}
+
+	/*
+	 * convert min and max into numbers of possible repetitions of the backref
+	 * string, rounding appropriately
+	 */
+	if (min <= start)
+		minreps = 0;
+	else
+		minreps = (min - start - 1) / brlen + 1;
+	maxreps = (max - start) / brlen;
+
+	/* apply bounds, then see if there is any allowed match length */
+	if (minreps < backmin)
+		minreps = backmin;
+	if (backmax != DUPINF && maxreps > backmax)
+		maxreps = backmax;
+	if (maxreps < minreps)
+		return NULL;
+
+	/* quick exit if zero-repetitions match is valid and preferred */
+	if (shortest && minreps == 0)
+		return start;
+
+	/* okay, compare the actual string contents */
+	p = start;
+	numreps = 0;
+	while (numreps < maxreps)
+	{
+		if ((*v->g->compare) (brstring, p, brlen) != 0)
+			break;
+		p += brlen;
+		numreps++;
+		if (shortest && numreps >= minreps)
+			break;
+	}
+
+	if (numreps >= minreps)
+		return p;
+	return NULL;
+}
+
 /*
  * lastcold - determine last point at which no progress had been made
  */
@@ -563,6 +678,8 @@ newdfa(struct vars *v,
 	d->lastpost = NULL;
 	d->lastnopr = NULL;
 	d->search = d->ssets;
+	d->backno = -1;				/* may be set by caller */
+	d->backmin = d->backmax = 0;
 
 	/* initialization of sset fields is done as needed */
 

src/backend/regex/regexec.c

@@ -77,6 +77,9 @@ struct dfa
 	chr		   *lastpost;		/* location of last cache-flushed success */
 	chr		   *lastnopr;		/* location of last cache-flushed NOPROGRESS */
 	struct sset *search;		/* replacement-search-pointer memory */
+	int			backno;			/* if DFA for a backref, subno it refers to */
+	short		backmin;		/* min repetitions for backref */
+	short		backmax;		/* max repetitions for backref */
 	bool		ismalloced;		/* should this struct dfa be freed? */
 	bool		arraysmalloced; /* should its subsidiary arrays be freed? */
 };
@@ -154,6 +157,7 @@ static int	creviterdissect(struct vars *, struct subre *, chr *, chr *);
 static chr *longest(struct vars *, struct dfa *, chr *, chr *, int *);
 static chr *shortest(struct vars *, struct dfa *, chr *, chr *, chr *, chr **, int *);
 static int	matchuntil(struct vars *, struct dfa *, chr *, struct sset **, chr **);
+static chr *dfa_backref(struct vars *, struct dfa *, chr *, chr *, chr *, bool);
 static chr *lastcold(struct vars *, struct dfa *);
 static struct dfa *newdfa(struct vars *, struct cnfa *, struct colormap *, struct smalldfa *);
 static void freedfa(struct dfa *);
@@ -342,13 +346,23 @@ static struct dfa *
 getsubdfa(struct vars *v,
 		  struct subre *t)
 {
-	if (v->subdfas[t->id] == NULL)
+	struct dfa *d = v->subdfas[t->id];
+
+	if (d == NULL)
 	{
-		v->subdfas[t->id] = newdfa(v, &t->cnfa, &v->g->cmap, DOMALLOC);
+		d = newdfa(v, &t->cnfa, &v->g->cmap, DOMALLOC);
 		if (ISERR())
 			return NULL;
+		/* set up additional info if this is a backref node */
+		if (t->op == 'b')
+		{
+			d->backno = t->backno;
+			d->backmin = t->min;
+			d->backmax = t->max;
 		}
-	return v->subdfas[t->id];
+		v->subdfas[t->id] = d;
+	}
+	return d;
 }
 
 /*
@@ -369,6 +383,7 @@ getladfa(struct vars *v,
 		v->ladfas[n] = newdfa(v, &sub->cnfa, &v->g->cmap, DOMALLOC);
 		if (ISERR())
 			return NULL;
+		/* a LACON can't contain a backref, so nothing else to do */
 	}
 	return v->ladfas[n];
 }
@@ -927,6 +942,9 @@ crevcondissect(struct vars *v,
 
 /*
  * cbrdissect - dissect match for backref node
+ *
+ * The backref match might already have been verified by dfa_backref(),
+ * but we don't know that for sure so must check it here.
  */
 static int						/* regexec return code */
 cbrdissect(struct vars *v,