+/* Compute the sign of a permutation of a container, with and without an
+ explicitly supplied comparison function. If the sign returned is 1 or -1,
+ the container is sorted after the operation. */
+template <class It>
+int permutation_sign(It first, It last)
+{
+ if (first == last)
+ return 0;
+ --last;
+ if (first == last)
+ return 0;
+ It flag = first;
+ int sign = 1;
+
+ do {
+ It i = last, other = last;
+ --other;
+ bool swapped = false;
+ while (i != first) {
+ if (*i < *other) {
+ std::iter_swap(other, i);
+ flag = other;
+ swapped = true;
+ sign = -sign;
+ } else if (!(*other < *i))
+ return 0;
+ --i; --other;
+ }
+ if (!swapped)
+ return sign;
+ ++flag;
+ if (flag == last)
+ return sign;
+ first = flag;
+ i = first; other = first;
+ ++other;
+ swapped = false;
+ while (i != last) {
+ if (*other < *i) {
+ std::iter_swap(i, other);
+ flag = other;
+ swapped = true;
+ sign = -sign;
+ } else if (!(*i < *other))
+ return 0;
+ ++i; ++other;
+ }
+ if (!swapped)
+ return sign;
+ last = flag;
+ --last;
+ } while (first != last);
+
+ return sign;
+}
+
+template <class It, class Cmp, class Swap>
+int permutation_sign(It first, It last, Cmp comp, Swap swapit)
+{
+ if (first == last)
+ return 0;
+ --last;
+ if (first == last)
+ return 0;
+ It flag = first;
+ int sign = 1;
+
+ do {
+ It i = last, other = last;
+ --other;
+ bool swapped = false;
+ while (i != first) {
+ if (comp(*i, *other)) {
+ swapit(*other, *i);
+ flag = other;
+ swapped = true;
+ sign = -sign;
+ } else if (!comp(*other, *i))
+ return 0;
+ --i; --other;
+ }
+ if (!swapped)
+ return sign;
+ ++flag;
+ if (flag == last)
+ return sign;
+ first = flag;
+ i = first; other = first;
+ ++other;
+ swapped = false;
+ while (i != last) {
+ if (comp(*other, *i)) {
+ swapit(*i, *other);
+ flag = other;
+ swapped = true;
+ sign = -sign;
+ } else if (!comp(*i, *other))
+ return 0;
+ ++i; ++other;
+ }
+ if (!swapped)
+ return sign;
+ last = flag;
+ --last;
+ } while (first != last);
+
+ return sign;
+}
+
+/* Implementation of shaker sort, only compares adjacent elements. */
+template <class It, class Cmp, class Swap>
+void shaker_sort(It first, It last, Cmp comp, Swap swapit)
+{
+ if (first == last)
+ return;
+ --last;
+ if (first == last)
+ return;
+ It flag = first;
+
+ do {
+ It i = last, other = last;
+ --other;
+ bool swapped = false;
+ while (i != first) {
+ if (comp(*i, *other)) {
+ swapit(*other, *i);
+ flag = other;
+ swapped = true;
+ }
+ --i; --other;
+ }
+ if (!swapped)
+ return;
+ ++flag;
+ if (flag == last)
+ return;
+ first = flag;
+ i = first; other = first;
+ ++other;
+ swapped = false;
+ while (i != last) {
+ if (comp(*other, *i)) {
+ swapit(*i, *other);
+ flag = other;
+ swapped = true;
+ }
+ ++i; ++other;
+ }
+ if (!swapped)
+ return;
+ last = flag;
+ --last;
+ } while (first != last);
+}
+
+/* In-place cyclic permutation of a container (no copying, only swapping). */
+template <class It, class Swap>
+void cyclic_permutation(It first, It last, It new_first, Swap swapit)
+{
+ unsigned num = last - first;
+again:
+ if (first == new_first || num < 2)
+ return;
+
+ unsigned num1 = new_first - first, num2 = last - new_first;
+ if (num1 >= num2) {
+ It a = first, b = new_first;
+ while (b != last) {
+ swapit(*a, *b);
+ ++a; ++b;
+ }
+ if (num1 > num2) {
+ first += num2;
+ num = num1;
+ goto again;
+ }
+ } else {
+ It a = new_first, b = last;
+ do {
+ --a; --b;
+ swapit(*a, *b);
+ } while (a != first);
+ last -= num1;
+ num = num2;
+ goto again;
+ }
+}
+
+
+// Collection of `construct on first use' wrappers for safely avoiding
+// internal object replication without running into the `static
+// initialization order fiasco'. This chest of numbers helps speed up
+// the library but should not be used outside it since it is
+// potentially confusing.
+
+class numeric;
+class ex;
+
+const numeric & _num_120(void); // -120
+const ex & _ex_120(void);
+const numeric & _num_60(void); // -60
+const ex & _ex_60(void);
+const numeric & _num_48(void); // -48
+const ex & _ex_48(void);
+const numeric & _num_30(void); // -30
+const ex & _ex_30(void);
+const numeric & _num_25(void); // -25
+const ex & _ex_25(void);
+const numeric & _num_24(void); // -24
+const ex & _ex_24(void);
+const numeric & _num_20(void); // -20
+const ex & _ex_20(void);
+const numeric & _num_18(void); // -18
+const ex & _ex_18(void);
+const numeric & _num_15(void); // -15
+const ex & _ex_15(void);
+const numeric & _num_12(void); // -12
+const ex & _ex_12(void);
+const numeric & _num_11(void); // -11
+const ex & _ex_11(void);
+const numeric & _num_10(void); // -10
+const ex & _ex_10(void);
+const numeric & _num_9(void); // -9
+const ex & _ex_9(void);
+const numeric & _num_8(void); // -8
+const ex & _ex_8(void);
+const numeric & _num_7(void); // -7
+const ex & _ex_7(void);
+const numeric & _num_6(void); // -6
+const ex & _ex_6(void);
+const numeric & _num_5(void); // -5
+const ex & _ex_5(void);
+const numeric & _num_4(void); // -4
+const ex & _ex_4(void);
+const numeric & _num_3(void); // -3
+const ex & _ex_3(void);
+const numeric & _num_2(void); // -2
+const ex & _ex_2(void);
+const numeric & _num_1(void); // -1
+const ex & _ex_1(void);
+const numeric & _num_1_2(void); // -1/2
+const ex & _ex_1_2(void);
+const numeric & _num_1_3(void); // -1/3
+const ex & _ex_1_3(void);
+const numeric & _num_1_4(void); // -1/4
+const ex & _ex_1_4(void);
+const numeric & _num0(void); // 0
+const ex & _ex0(void);
+const numeric & _num1_4(void); // 1/4
+const ex & _ex1_4(void);
+const numeric & _num1_3(void); // 1/3
+const ex & _ex1_3(void);
+const numeric & _num1_2(void); // 1/2
+const ex & _ex1_2(void);
+const numeric & _num1(void); // 1
+const ex & _ex1(void);
+const numeric & _num2(void); // 2
+const ex & _ex2(void);
+const numeric & _num3(void); // 3
+const ex & _ex3(void);
+const numeric & _num4(void); // 4
+const ex & _ex4(void);
+const numeric & _num5(void); // 5
+const ex & _ex5(void);
+const numeric & _num6(void); // 6
+const ex & _ex6(void);
+const numeric & _num7(void); // 7
+const ex & _ex7(void);
+const numeric & _num8(void); // 8
+const ex & _ex8(void);
+const numeric & _num9(void); // 9
+const ex & _ex9(void);
+const numeric & _num10(void); // 10
+const ex & _ex10(void);
+const numeric & _num11(void); // 11
+const ex & _ex11(void);
+const numeric & _num12(void); // 12
+const ex & _ex12(void);
+const numeric & _num15(void); // 15
+const ex & _ex15(void);
+const numeric & _num18(void); // 18
+const ex & _ex18(void);
+const numeric & _num20(void); // 20
+const ex & _ex20(void);
+const numeric & _num24(void); // 24
+const ex & _ex24(void);
+const numeric & _num25(void); // 25
+const ex & _ex25(void);
+const numeric & _num30(void); // 30
+const ex & _ex30(void);
+const numeric & _num48(void); // 48
+const ex & _ex48(void);
+const numeric & _num60(void); // 60
+const ex & _ex60(void);
+const numeric & _num120(void); // 120
+const ex & _ex120(void);
+
+
+// Helper macros for class implementations (mostly useful for trivial classes)
+
+#define DEFAULT_COPY(classname) \
+void classname::copy(const classname & other) \
+{ \
+ inherited::copy(other); \
+}
+
+#define DEFAULT_DESTROY(classname) \
+void classname::destroy(bool call_parent) \
+{ \
+ if (call_parent) \
+ inherited::destroy(call_parent); \
+}
+
+#define DEFAULT_CTORS(classname) \
+classname::classname() : inherited(TINFO_##classname) \
+{ \
+ debugmsg(#classname " default constructor", LOGLEVEL_CONSTRUCT); \
+} \
+DEFAULT_COPY(classname) \
+DEFAULT_DESTROY(classname)
+
+#define DEFAULT_UNARCHIVE(classname) \
+ex classname::unarchive(const archive_node &n, const lst &sym_lst) \
+{ \
+ return (new classname(n, sym_lst))->setflag(status_flags::dynallocated); \
+}
+
+#define DEFAULT_ARCHIVING(classname) \
+classname::classname(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) \
+{ \
+ debugmsg(#classname " constructor from archive_node", LOGLEVEL_CONSTRUCT); \
+} \
+DEFAULT_UNARCHIVE(classname) \
+void classname::archive(archive_node &n) const \
+{ \
+ inherited::archive(n); \
+}
+
+#define DEFAULT_COMPARE(classname) \
+int classname::compare_same_type(const basic & other) const \
+{ \
+ /* by default, the objects are always identical */ \
+ return 0; \
+}
+
+#define DEFAULT_PRINT(classname, text) \
+void classname::print(const print_context & c, unsigned level) const \
+{ \
+ debugmsg(#classname " print", LOGLEVEL_PRINT); \
+ if (is_a<print_tree>(c)) \
+ inherited::print(c, level); \
+ else \
+ c.s << text; \