Speed up printing of large permutations

lib/permutat.g

@@ -735,31 +735,33 @@ end );
 #m  String( <perm> )  . . . . . . . . . . . . . . . . . . . for a permutation
 ##
 BIND_GLOBAL("DoStringPerm",function( perm,hint )
-local   str,  i,  j;
+local   str,  i,  j, maxpnt, blist;
 
   if IsOne( perm ) then
       str := "()";
   else
       str := "";
+      maxpnt := LargestMovedPoint( perm );
+      blist := BlistList([1..maxpnt], []);
       for i  in [ 1 .. LargestMovedPoint( perm ) ]  do
-	  j := i ^ perm;
-	  while j > i  do j := j ^ perm;  od;
-	  if j = i and i ^ perm <> i  then
-	      Append( str, "(" );
-	      Append( str, String( i ) );
-	      j := i ^ perm;
-	      while j > i do
-		  Append( str, "," );
-		  if hint then Append(str,"\<\>"); fi;
-		  Append( str, String( j ) );
-		  j := j ^ perm;
-	      od;
-	      Append( str, ")" );
-	      if hint then Append(str,"\<\<\>\>"); fi;
-	  fi;
+      if not blist[i] and i ^ perm <> i  then
+          blist[i] := true;
+          Append( str, "(" );
+          Append( str, String( i ) );
+          j := i ^ perm;
+          while j > i do
+          blist[j] := true;
+          Append( str, "," );
+          if hint then Append(str,"\<\>"); fi;
+          Append( str, String( j ) );
+          j := j ^ perm;
+          od;
+          Append( str, ")" );
+          if hint then Append(str,"\<\<\>\>"); fi;
+      fi;
       od;
       if Length(str)>4 and str{[Length(str)-3..Length(str)]}="\<\<\>\>" then
-	str:=str{[1..Length(str)-4]}; # remove tailing line breaker
+          str:=str{[1..Length(str)-4]}; # remove tailing line breaker
       fi;
       ConvertToStringRep( str );
   fi;

src/permutat.cc

@@ -163,10 +163,8 @@ static Obj InvPerm(Obj perm);
 **  uses the degree to print all points with same width, which  looks  nicer.
 **  Linebreaks are prefered most after cycles and  next  most  after  commas.
 **
-**  It does not remember which points have already  been  printed.  To  avoid
-**  printing a cycle twice each is printed with the smallest  element  first.
-**  This may in the worst case, for (1,2,..,n), take n^2/2 steps, but is fast
-**  enough to keep a terminal at 9600 baud busy for all but the extrem cases.
+**  It remembers which points have already  been  printed, to avoid O(n^2)
+**  behaviour.
 */
 template <typename T>
 static void PrintPerm(Obj perm)
@@ -187,29 +185,34 @@ static void PrintPerm(Obj perm)
     else if ( degPerm < 10000 ) { fmt1 = "%>(%>%4d%<"; fmt2 = ",%>%4d%<"; }
     else                        { fmt1 = "%>(%>%5d%<"; fmt2 = ",%>%5d%<"; }
 
+    UseTmpPerm(SIZE_OBJ(perm));
+    T * ptSeen = ADDR_TMP_PERM<T>();
+
+    // clear the buffer bag
+    for (p = 0; p < DEG_PERM<T>(perm); p++)
+        ptSeen[p] = 0;
+
     /* run through all points                                              */
     isId = 1;
     ptPerm = CONST_ADDR_PERM<T>(perm);
     for ( p = 0; p < degPerm; p++ ) {
-
-        /* find the smallest element in this cycle                         */
-        q = ptPerm[p];
-        while ( p < q )  q = ptPerm[q];
-
         /* if the smallest is the one we started with lets print the cycle */
-        if ( p == q && ptPerm[p] != p ) {
+        if (!ptSeen[p] && ptPerm[p] != p) {
+            ptSeen[p] = 1;
             isId = 0;
             Pr(fmt1,(Int)(p+1),0L);
             ptPerm = CONST_ADDR_PERM<T>(perm);
             for ( q = ptPerm[p]; q != p; q = ptPerm[q] ) {
+                ptSeen[q] = 1;
                 Pr(fmt2,(Int)(q+1),0L);
                 ptPerm = CONST_ADDR_PERM<T>(perm);
+                ptSeen = ADDR_TMP_PERM<T>();
             }
             Pr("%<)",0L,0L);
             /* restore pointer, in case Pr caused a garbage collection */
             ptPerm = CONST_ADDR_PERM<T>(perm);
+            ptSeen = ADDR_TMP_PERM<T>();
         }
-
     }
 
     /* special case for the identity                                       */

tst/testinstall/perm.tst

@@ -1,4 +1,4 @@
-#@local checklens,n,permAll,permBig,permSml,x,y, moved
+#@local checklens,n,permAll,permBig,permSml,x,y,moved,p
 gap> START_TEST("perm.tst");
 
 # Permutations come in two flavors in GAP, with two TNUMs: T_PERM2 for
@@ -87,6 +87,17 @@ gap> Print(permBig * (5,999999), "\n");
   (    1,    2,    3)(    5,999999), (    1,    3,    2)(    5,999999), 
   (    1,    3)(    5,999999) ]
 
+# Check String of large permutation
+# Check length, beginning and end, as the string is too long to include in
+# a test file
+gap> p := String(PermList(Concatenation([2..2^20], [1])));;
+gap> Length(p) = 7277505;
+true
+gap> p{[1..40]};
+"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,"
+gap> p{[Length(p)-40..Length(p)]};
+",1048572,1048573,1048574,1048575,1048576)"
+
 #
 # EqPerm
 #