fix repeat of preferred empty match

Ports fix of golang/go#46123 to RE2/J.

Original go fix:

golang/go@2a61b3c

Change description from that commit:

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*.

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+)?.

Fixes google#136.

java/com/google/re2j/Compiler.java

@@ -24,6 +24,7 @@ class Compiler {
   private static class Frag {
     final int i; // an instruction address (pc).
     int out; // a patch list; see explanation in Prog.java
+    boolean nullable; // whether the fragment can match the empty string
 
     Frag() {
       this(0, 0);
@@ -34,8 +35,13 @@ private static class Frag {
     }
 
     Frag(int i, int out) {
+      this(i, out, false);
+    }
+
+    Frag(int i, int out, boolean nullable) {
       this.i = i;
       this.out = out;
+      this.nullable = nullable;
     }
   }
 
@@ -56,7 +62,7 @@ static Prog compileRegexp(Regexp re) {
   private Frag newInst(int op) {
     // TODO(rsc): impose length limit.
     prog.addInst(op);
-    return new Frag(prog.numInst() - 1);
+    return new Frag(prog.numInst() - 1, 0, true);
   }
 
   // Returns a no-op fragment.  Sometimes unavoidable.
@@ -90,7 +96,7 @@ private Frag cat(Frag f1, Frag f2) {
     }
     // TODO(rsc): elide nop
     prog.patch(f1.out, f2.i);
-    return new Frag(f1.i, f2.out);
+    return new Frag(f1.i, f2.out, f1.nullable && f2.nullable);
   }
 
   // Given fragments for a and b, returns fragment for a|b.
@@ -107,11 +113,16 @@ private Frag alt(Frag f1, Frag f2) {
     i.out = f1.i;
     i.arg = f2.i;
     f.out = prog.append(f1.out, f2.out);
+    f.nullable = f1.nullable || f2.nullable;
     return f;
   }
 
-  // Given a fragment for a, returns a fragment for a? or a?? (if nongreedy)
-  private Frag quest(Frag f1, boolean nongreedy) {
+  // loop returns the fragment for the main loop of a plus or star.
+  // For plus, it can be used directly. with f1.i as the entry.
+  // 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.)
+  private Frag loop(Frag f1, boolean nongreedy) {
     Frag f = newInst(Inst.ALT);
     Inst i = prog.getInst(f.i);
     if (nongreedy) {
@@ -121,12 +132,12 @@ private Frag quest(Frag f1, boolean nongreedy) {
       i.out = f1.i;
       f.out = f.i << 1 | 1;
     }
-    f.out = prog.append(f.out, f1.out);
+    prog.patch(f1.out, f.i);
     return f;
   }
 
-  // Given a fragment a, returns a fragment for a* or a*? (if nongreedy)
-  private Frag star(Frag f1, boolean nongreedy) {
+  // Given a fragment for a, returns a fragment for a? or a?? (if nongreedy)
+  private Frag quest(Frag f1, boolean nongreedy) {
     Frag f = newInst(Inst.ALT);
     Inst i = prog.getInst(f.i);
     if (nongreedy) {
@@ -136,13 +147,21 @@ private Frag star(Frag f1, boolean nongreedy) {
       i.out = f1.i;
       f.out = f.i << 1 | 1;
     }
-    prog.patch(f1.out, f.i);
+    f.out = prog.append(f.out, f1.out);
     return f;
   }
 
+  // Given a fragment a, returns a fragment for a* or a*? (if nongreedy)
+  private Frag star(Frag f1, boolean nongreedy) {
+    if (f1.nullable) {
+      return quest(plus(f1, nongreedy), nongreedy);
+    }
+    return loop(f1, nongreedy);
+  }
+
   // Given a fragment for a, returns a fragment for a+ or a+? (if nongreedy)
   private Frag plus(Frag f1, boolean nongreedy) {
-    return new Frag(f1.i, star(f1, nongreedy).out);
+    return new Frag(f1.i, loop(f1, nongreedy).out, f1.nullable);
   }
 
   // op is a bitmask of EMPTY_* flags.
@@ -160,6 +179,7 @@ private Frag rune(int rune, int flags) {
   // flags : parser flags
   private Frag rune(int[] runes, int flags) {
     Frag f = newInst(Inst.RUNE);
+    f.nullable = false;
     Inst i = prog.getInst(f.i);
     i.runes = runes;
     flags &= RE2.FOLD_CASE; // only relevant flag is FoldCase

javatests/com/google/re2j/FindTest.java

@@ -249,6 +249,7 @@ public String toString() {
         35,
         35,
         36),
+    new Test("(|a)*", "aa", 3, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2),
   };
 
   @Parameters
@@ -538,7 +539,14 @@ private void testSubmatch(String testName, Test test, int n, String[] result) {
       System.err.println(testName + "  " + test + " " + n + " " + k + " ");
       String expect = test.submatchString(n, k / 2);
       if (!expect.equals(result[k / 2])) {
-        fail(String.format("%s %d: expected %s got %s: %s", testName, n, expect, result, test));
+        fail(
+            String.format(
+                "%s %d: expected %s got %s: %s",
+                testName,
+                n,
+                expect,
+                Arrays.toString(result),
+                test));
       }
     }
   }

javatests/com/google/re2j/ProgTest.java

@@ -94,6 +94,25 @@ public class ProgTest {
       "(?:(?:^).)",
       "0       fail\n" + "1*      empty 4 -> 2\n" + "2       anynotnl -> 3\n" + "3       match\n"
     },
+    {
+      "(?:|a)+",
+      "0       fail\n"
+          + "1       nop -> 4\n"
+          + "2       rune1 \"a\" -> 4\n"
+          + "3*      alt -> 1, 2\n"
+          + "4       alt -> 3, 5\n"
+          + "5       match\n"
+    },
+    {
+      "(?:|a)*",
+      "0       fail\n"
+          + "1       nop -> 4\n"
+          + "2       rune1 \"a\" -> 4\n"
+          + "3       alt -> 1, 2\n"
+          + "4       alt -> 3, 6\n"
+          + "5*      alt -> 3, 6\n"
+          + "6       match\n"
+    },
   };
 
   private final String input;

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)

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)
@@ -19,17 +18,15 @@ 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)
 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)