regexp: fix repeat of preferred empty match

In Perl mode, (|a)* should match an empty string at the start of the
input. Instead it matches as many a's as possible.
Because (|a)+ is handled correctly, matching only an empty string,
this leads to the paradox that e* can match more text than e+
(for e = (|a)) and that e+ is sometimes different from ee*.

This is a very old bug that ultimately derives from the picture I drew
for e* in https://swtch.com/~rsc/regexp/regexp1.html. The picture is
correct for longest-match (POSIX) regexps but subtly wrong for
preferred-match (Perl) regexps in the case where e has a preferred
empty match. Pointed out by Andrew Gallant in private mail.

The current code treats e* and e+ as the same structure, with
different entry points. In the case of e* the preference list ends up
not quite in the right order, in part because the “before e” and
“after e” states are the same state. Splitting them apart fixes the
preference list, and that can be done by compiling e* as if it were
(e+)?.

Like with any bug fix, there is a very low chance of breaking a
program that accidentally depends on the buggy behavior.

RE2, Go, and Rust all have this bug, and we've all agreed to fix it,
to keep the implementations in sync.

Fixes #46123.

Change-Id: I70e742e71e0a23b626593b16ddef3c1e73b413b0
Reviewed-on: https://go-review.googlesource.com/c/go/+/318750
Trust: Russ Cox <rsc@golang.org>
Run-TryBot: Russ Cox <rsc@golang.org>
Reviewed-by: Rob Pike <r@golang.org>
TryBot-Result: Go Bot <gobot@golang.org>

8 files changed, 176 insertions, 46 deletions

diff --git a/src/regexp/find_test.go b/src/regexp/find_test.go
index 87c49b074f..64c2239d90 100644
--- a/src/regexp/find_test.go
+++ b/src/regexp/find_test.go
@@ -97,6 +97,7 @@ var findTests = []FindTest{
 	{`\B`, "xx", build(1, 1, 1)},
 	{`\B`, "x y", nil},
 	{`\B`, "xx yy", build(2, 1, 1, 4, 4)},
+	{`(|a)*`, "aa", build(3, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2)},
 
 	// RE2 tests
 	{`[^\S\s]`, "abcd", nil},
diff --git a/src/regexp/onepass_test.go b/src/regexp/onepass_test.go
index 32264d5f1e..6a42eda391 100644
--- a/src/regexp/onepass_test.go
+++ b/src/regexp/onepass_test.go
@@ -142,7 +142,7 @@ var onePassTests = []struct {
 	{`^(?:(a)|(?:a*))$`, false},
 	{`^(?:(?:(?:.(?:$))?))$`, true},
 	{`^abcd$`, true},
-	{`^(?:(?:a{0,})*?)$`, true},
+	{`^(?:(?:a{0,})*?)$`, false},
 	{`^(?:(?:a+)*)$`, true},
 	{`^(?:(?:a|(?:aa)))$`, true},
 	{`^(?:[^\s\S])$`, true},
diff --git a/src/regexp/syntax/compile.go b/src/regexp/syntax/compile.go
index 7524d628fe..c9f9fa024b 100644
--- a/src/regexp/syntax/compile.go
+++ b/src/regexp/syntax/compile.go
@@ -57,8 +57,9 @@ func (l1 patchList) append(p *Prog, l2 patchList) patchList {
 
 // A frag represents a compiled program fragment.
 type frag struct {
-	i   uint32    // index of first instruction
-	out patchList // where to record end instruction
+	i        uint32    // index of first instruction
+	out      patchList // where to record end instruction
+	nullable bool      // whether fragment can match empty string
 }
 
 type compiler struct {
@@ -159,7 +160,7 @@ func (c *compiler) compile(re *Regexp) frag {
 
 func (c *compiler) inst(op InstOp) frag {
 	// TODO: impose length limit
-	f := frag{i: uint32(len(c.p.Inst))}
+	f := frag{i: uint32(len(c.p.Inst)), nullable: true}
 	c.p.Inst = append(c.p.Inst, Inst{Op: op})
 	return f
 }
@@ -194,7 +195,7 @@ func (c *compiler) cat(f1, f2 frag) frag {
 	// TODO: elide nop
 
 	f1.out.patch(c.p, f2.i)
-	return frag{f1.i, f2.out}
+	return frag{f1.i, f2.out, f1.nullable && f2.nullable}
 }
 
 func (c *compiler) alt(f1, f2 frag) frag {
@@ -211,6 +212,7 @@ func (c *compiler) alt(f1, f2 frag) frag {
 	i.Out = f1.i
 	i.Arg = f2.i
 	f.out = f1.out.append(c.p, f2.out)
+	f.nullable = f1.nullable || f2.nullable
 	return f
 }
 
@@ -228,7 +230,12 @@ func (c *compiler) quest(f1 frag, nongreedy bool) frag {
 	return f
 }
 
-func (c *compiler) star(f1 frag, nongreedy bool) frag {
+// loop returns the fragment for the main loop of a plus or star.
+// For plus, it can be used after changing the entry to f1.i.
+// For star, it can be used directly when f1 can't match an empty string.
+// (When f1 can match an empty string, f1* must be implemented as (f1+)?
+// to get the priority match order correct.)
+func (c *compiler) loop(f1 frag, nongreedy bool) frag {
 	f := c.inst(InstAlt)
 	i := &c.p.Inst[f.i]
 	if nongreedy {
@@ -242,8 +249,17 @@ func (c *compiler) star(f1 frag, nongreedy bool) frag {
 	return f
 }
 
+func (c *compiler) star(f1 frag, nongreedy bool) frag {
+	if f1.nullable {
+		// Use (f1+)? to get priority match order correct.
+		// See golang.org/issue/46123.
+		return c.quest(c.plus(f1, nongreedy), nongreedy)
+	}
+	return c.loop(f1, nongreedy)
+}
+
 func (c *compiler) plus(f1 frag, nongreedy bool) frag {
-	return frag{f1.i, c.star(f1, nongreedy).out}
+	return frag{f1.i, c.loop(f1, nongreedy).out, f1.nullable}
 }
 
 func (c *compiler) empty(op EmptyOp) frag {
@@ -255,6 +271,7 @@ func (c *compiler) empty(op EmptyOp) frag {
 
 func (c *compiler) rune(r []rune, flags Flags) frag {
 	f := c.inst(InstRune)
+	f.nullable = false
 	i := &c.p.Inst[f.i]
 	i.Rune = r
 	flags &= FoldCase // only relevant flag is FoldCase
diff --git a/src/regexp/syntax/prog_test.go b/src/regexp/syntax/prog_test.go
index 50bfa3d4be..5603aea228 100644
--- a/src/regexp/syntax/prog_test.go
+++ b/src/regexp/syntax/prog_test.go
@@ -89,6 +89,21 @@ var compileTests = []struct {
   2	anynotnl -> 3
   3	match
 `},
+	{"(?:|a)+", `  0	fail
+  1	nop -> 4
+  2	rune1 "a" -> 4
+  3*	alt -> 1, 2
+  4	alt -> 3, 5
+  5	match
+`},
+	{"(?:|a)*", `  0	fail
+  1	nop -> 4
+  2	rune1 "a" -> 4
+  3	alt -> 1, 2
+  4	alt -> 3, 6
+  5*	alt -> 3, 6
+  6	match
+`},
 }
 
 func TestCompile(t *testing.T) {
diff --git a/src/regexp/testdata/basic.dat b/src/regexp/testdata/basic.dat
index 7859290ba1..1776b1ff96 100644
--- a/src/regexp/testdata/basic.dat
+++ b/src/regexp/testdata/basic.dat
@@ -124,24 +124,20 @@ E	((a))			abc		(0,1)(0,1)(0,1)
 E	(a)b(c)			abc		(0,3)(0,1)(2,3)
 E	a+b+c			aabbabc		(4,7)
 E	a*			aaa		(0,3)
-#E	(a*)*			-		(0,0)(0,0)
-E	(a*)*			-		(0,0)(?,?)	RE2/Go
+E	(a*)*			-		(0,0)(0,0)
 E	(a*)+			-		(0,0)(0,0)
-#E	(a*|b)*			-		(0,0)(0,0)
-E	(a*|b)*			-		(0,0)(?,?)	RE2/Go
+E	(a*|b)*			-		(0,0)(0,0)
 E	(a+|b)*			ab		(0,2)(1,2)
 E	(a+|b)+			ab		(0,2)(1,2)
 E	(a+|b)?			ab		(0,1)(0,1)
 BE	[^ab]*			cde		(0,3)
-#E	(^)*			-		(0,0)(0,0)
-E	(^)*			-		(0,0)(?,?)	RE2/Go
+E	(^)*			-		(0,0)(0,0)
 BE	a*			NULL		(0,0)
 E	([abc])*d		abbbcd		(0,6)(4,5)
 E	([abc])*bcd		abcd		(0,4)(0,1)
 E	a|b|c|d|e		e		(0,1)
 E	(a|b|c|d|e)f		ef		(0,2)(0,1)
-#E	((a*|b))*		-		(0,0)(0,0)(0,0)
-E	((a*|b))*		-		(0,0)(?,?)(?,?)	RE2/Go
+E	((a*|b))*		-		(0,0)(0,0)(0,0)
 BE	abcd*efg		abcdefg		(0,7)
 BE	ab*			xabyabbbz	(1,3)
 BE	ab*			xayabbbz	(1,2)
diff --git a/src/regexp/testdata/nullsubexpr.dat b/src/regexp/testdata/nullsubexpr.dat
index 2e18fbb917..68d9c99996 100644
--- a/src/regexp/testdata/nullsubexpr.dat
+++ b/src/regexp/testdata/nullsubexpr.dat
@@ -1,8 +1,7 @@
 NOTE	null subexpression matches : 2002-06-06
 
 E	(a*)*		a		(0,1)(0,1)
-#E	SAME		x		(0,0)(0,0)
-E	SAME		x		(0,0)(?,?)	RE2/Go
+E	SAME		x		(0,0)(0,0)
 E	SAME		aaaaaa		(0,6)(0,6)
 E	SAME		aaaaaax		(0,6)(0,6)
 E	(a*)+		a		(0,1)(0,1)
@@ -19,8 +18,7 @@ E	SAME		aaaaaa		(0,6)(0,6)
 E	SAME		aaaaaax		(0,6)(0,6)
 
 E	([a]*)*		a		(0,1)(0,1)
-#E	SAME		x		(0,0)(0,0)
-E	SAME		x		(0,0)(?,?)	RE2/Go
+E	SAME		x		(0,0)(0,0)
 E	SAME		aaaaaa		(0,6)(0,6)
 E	SAME		aaaaaax		(0,6)(0,6)
 E	([a]*)+		a		(0,1)(0,1)
@@ -28,8 +26,7 @@ E	SAME		x		(0,0)(0,0)
 E	SAME		aaaaaa		(0,6)(0,6)
 E	SAME		aaaaaax		(0,6)(0,6)
 E	([^b]*)*	a		(0,1)(0,1)
-#E	SAME		b		(0,0)(0,0)
-E	SAME		b		(0,0)(?,?)	RE2/Go
+E	SAME		b		(0,0)(0,0)
 E	SAME		aaaaaa		(0,6)(0,6)
 E	SAME		aaaaaab		(0,6)(0,6)
 E	([ab]*)*	a		(0,1)(0,1)
@@ -41,11 +38,9 @@ E	SAME		bbbbbb		(0,6)(0,6)
 E	SAME		aaaabcde	(0,5)(0,5)
 E	([^a]*)*	b		(0,1)(0,1)
 E	SAME		bbbbbb		(0,6)(0,6)
-#E	SAME		aaaaaa		(0,0)(0,0)
-E	SAME		aaaaaa		(0,0)(?,?)	RE2/Go
+E	SAME		aaaaaa		(0,0)(0,0)
 E	([^ab]*)*	ccccxx		(0,6)(0,6)
-#E	SAME		ababab		(0,0)(0,0)
-E	SAME		ababab		(0,0)(?,?)	RE2/Go
+E	SAME		ababab		(0,0)(0,0)
 
 E	((z)+|a)*	zabcde		(0,2)(1,2)
 
@@ -65,8 +60,7 @@ B	\(a*\)*\(x\)\(\1\)	axa	(0,3)(0,1)(1,2)(2,3)
 B	\(a*\)*\(x\)\(\1\)\(x\)	axax	(0,4)(0,1)(1,2)(2,3)(3,4)
 B	\(a*\)*\(x\)\(\1\)\(x\)	axxa	(0,3)(1,1)(1,2)(2,2)(2,3)
 
-#E	(a*)*(x)		x	(0,1)(0,0)(0,1)
-E	(a*)*(x)		x	(0,1)(?,?)(0,1)	RE2/Go
+E	(a*)*(x)		x	(0,1)(0,0)(0,1)
 E	(a*)*(x)		ax	(0,2)(0,1)(1,2)
 E	(a*)*(x)		axa	(0,2)(0,1)(1,2)
 
diff --git a/src/regexp/testdata/re2-exhaustive.txt.bz2 b/src/regexp/testdata/re2-exhaustive.txt.bz2
index a357f28016..6638476dec 100644
--- a/src/regexp/testdata/re2-exhaustive.txt.bz2
+++ b/src/regexp/testdata/re2-exhaustive.txt.bz2
diff --git a/src/regexp/testdata/re2-search.txt b/src/regexp/testdata/re2-search.txt
index 4d02e9cebd..8c4098a4f1 100644
--- a/src/regexp/testdata/re2-search.txt
+++ b/src/regexp/testdata/re2-search.txt
@@ -1,5 +1,5 @@
 # RE2 basic search tests built by make log
-# Thu Sep 8 13:43:43 EDT 2011
+# Wed May 12 12:13:22 EDT 2021
 Regexp.SearchTests
 strings
 ""
@@ -227,22 +227,6 @@ regexps
 0-0;0-0;0-0;0-0
 strings
 ""
-""
-regexps
-"a*"
-0-0;0-0;0-0;0-0
-0-0;0-0;0-0;0-0
-"^(?:a*)$"
-0-0;0-0;0-0;0-0
-0-0;0-0;0-0;0-0
-"^(?:a*)"
-0-0;0-0;0-0;0-0
-0-0;0-0;0-0;0-0
-"(?:a*)$"
-0-0;0-0;0-0;0-0
-0-0;0-0;0-0;0-0
-strings
-""
 "xabcdx"
 regexps
 "ab|cd"
@@ -3651,6 +3635,86 @@ regexps
 0-1;0-1;0-1;0-1
 strings
 ""
+"a"
+regexps
+"a\\C+"
+-;-;-;-
+-;-;-;-
+"^(?:a\\C+)$"
+-;-;-;-
+-;-;-;-
+"^(?:a\\C+)"
+-;-;-;-
+-;-;-;-
+"(?:a\\C+)$"
+-;-;-;-
+-;-;-;-
+strings
+""
+"a"
+regexps
+"a\\C?"
+-;-;-;-
+0-1;0-1;0-1;0-1
+"^(?:a\\C?)$"
+-;-;-;-
+0-1;0-1;0-1;0-1
+"^(?:a\\C?)"
+-;-;-;-
+0-1;0-1;0-1;0-1
+"(?:a\\C?)$"
+-;-;-;-
+0-1;0-1;0-1;0-1
+strings
+""
+"a"
+regexps
+"a\\C*?"
+-;-;-;-
+0-1;0-1;0-1;0-1
+"^(?:a\\C*?)$"
+-;-;-;-
+0-1;0-1;0-1;0-1
+"^(?:a\\C*?)"
+-;-;-;-
+0-1;0-1;0-1;0-1
+"(?:a\\C*?)$"
+-;-;-;-
+0-1;0-1;0-1;0-1
+strings
+""
+"a"
+regexps
+"a\\C+?"
+-;-;-;-
+-;-;-;-
+"^(?:a\\C+?)$"
+-;-;-;-
+-;-;-;-
+"^(?:a\\C+?)"
+-;-;-;-
+-;-;-;-
+"(?:a\\C+?)$"
+-;-;-;-
+-;-;-;-
+strings
+""
+"a"
+regexps
+"a\\C??"
+-;-;-;-
+0-1;0-1;0-1;0-1
+"^(?:a\\C??)$"
+-;-;-;-
+0-1;0-1;0-1;0-1
+"^(?:a\\C??)"
+-;-;-;-
+0-1;0-1;0-1;0-1
+"(?:a\\C??)$"
+-;-;-;-
+0-1;0-1;0-1;0-1
+strings
+""
 "baba"
 regexps
 "a\\C*|ba\\C"
@@ -3666,7 +3730,50 @@ regexps
 -;-;-;-
 -;1-4;-;1-4
 strings
-"abc"
+""
+"Inc."
 regexps
-"a.*?c|a.*?b"
+"\\w*I\\w*"
+-;-;-;-
+-;0-3;-;0-3
+"^(?:\\w*I\\w*)$"
+-;-;-;-
+-;-;-;-
+"^(?:\\w*I\\w*)"
+-;-;-;-
+-;0-3;-;0-3
+"(?:\\w*I\\w*)$"
+-;-;-;-
+-;-;-;-
+strings
+""
+"aaa"
+regexps
+"(?:|a)*"
+0-0;0-0;0-0;0-0
+0-3;0-0;0-3;0-3
+"^(?:(?:|a)*)$"
+0-0;0-0;0-0;0-0
+0-3;0-3;0-3;0-3
+"^(?:(?:|a)*)"
+0-0;0-0;0-0;0-0
+0-3;0-0;0-3;0-3
+"(?:(?:|a)*)$"
+0-0;0-0;0-0;0-0
+0-3;0-3;0-3;0-3
+strings
+""
+"aaa"
+regexps
+"(?:|a)+"
+0-0;0-0;0-0;0-0
+0-3;0-0;0-3;0-3
+"^(?:(?:|a)+)$"
+0-0;0-0;0-0;0-0
+0-3;0-3;0-3;0-3
+"^(?:(?:|a)+)"
+0-0;0-0;0-0;0-0
+0-3;0-0;0-3;0-3
+"(?:(?:|a)+)$"
+0-0;0-0;0-0;0-0
 0-3;0-3;0-3;0-3