Fixed the problem with the double-probe hack by checking if the start

state is "default" (i.e., identity perms and zero orientations).  This
suffices for now.  Eventually we want to consider making this support
more general start states (either by inverting and conjugating by the
start state before the second probe, or by normalizing the start state
when we read the puzdef and pre/post-multiplying by the start state on
every input/output operation).  We can also consider reducing the pruning
table by inversions which would give a 2X improvement in memory efficiency
but we'd have to change the double-probe to an inversion reduction (so
one lookup instead of two) which likely would be faster anyway.

src/cpp/puzdef.cpp

@@ -283,3 +283,19 @@ void domove(const puzdef &pd, setval p, int mv) {
 void domove(const puzdef &pd, setval p, int mv, setval pt) {
   domove(pd, p, pd.moves[mv].pos, pt);
 }
+int puzdef::defaultstart() const {
+  const uchar *a = solved.dat;
+  for (int i = 0; i < (int)setdefs.size(); i++) {
+    const setdef &sd = setdefs[i];
+    int n = sd.size;
+    for (int i = 0; i < n; i++)
+      if (i != a[i])
+        return 0;
+    a += n;
+    for (int i = 0; i < n; i++)
+      if (a[i] != 0)
+        return 0;
+    a += n;
+  }
+  return 1;
+}

src/cpp/puzdef.h

@@ -127,12 +127,14 @@ struct puzdef {
   ull checksum;
   ull optionssum;
   vector<illegal_t> illegal;
-  char haveillegal, wildo, dense, uniq, caninvert;
+  char haveillegal, wildo, dense, uniq, caninvert, doubleprobe;
   int comparepos(const setval a, const setval b) const {
     return memcmp(a.dat, b.dat, totsize);
   }
   int canpackdense() const { return dense; }
   int invertible() const { return caninvert; }
+  int invertiblelookups() const { return doubleprobe; }
+  int defaultstart() const;
   void assignpos(setval a, const setval b) const {
     memcpy(a.dat, b.dat, totsize);
   }

src/cpp/readksolve.cpp

@@ -451,7 +451,7 @@ puzdef readdef(istream *f) {
   if (distinguishall) {
     pz.solved = pz.id;
   }
-  pz.caninvert = pz.uniq && !pz.wildo;
+  pz.doubleprobe = pz.uniq && !pz.wildo && pz.defaultstart();
   pz.checksum = checksum;
   curline.clear();
   return pz;

src/cpp/solve.cpp

@@ -175,7 +175,7 @@ int microthread::innerfetch(const puzdef &pd, prunetable &pt) {
      *   default (identity perm and zero orientations).  We need to fix this
      *   soon.
      */
-  } else if (0 && pd.invertible() && v < 2 + pt.baseval && invflag == 0) {
+  } else if (pd.invertiblelookups() && v < 2 + pt.baseval && invflag == 0) {
     invflag = 1;
     pd.inv(posns[sp], *invtmp);
     return 3;