+/** Compare two pointers (just to establish some sort of canonical order).
+ * @return -1, 0, or 1 */
+template <class T>
+inline int compare_pointers(const T * a, const T * b)
+{
+ // '<' is not defined for pointers that don't point to the same array,
+ // but std::less is.
+ if (std::less<const T *>()(a, b))
+ return -1;
+ else if (std::less<const T *>()(b, a))
+ return 1;
+ return 0;
+}
+
+/** Truncated multiplication with golden ratio, for computing hash values. */
+inline unsigned golden_ratio_hash(uintptr_t n)
+{
+ return n * UINT64_C(0x4f1bbcdd);
+}
+
+/* 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)
+{
+ using std::swap;
+ 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) {
+ swap(*other, *i);
+ flag = other;
+ swapped = true;
+ sign = -sign;
+ } else if (!(*other < *i))
+ return 0;
+ --i;
+ if (i != first)
+ --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) {
+ swap(*i, *other);
+ flag = other;
+ swapped = true;
+ sign = -sign;
+ } else if (!(*i < *other))
+ return 0;
+ ++i;
+ if (i != last)
+ ++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;
+ if (i != first)
+ --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;
+ if (i != last)
+ ++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;
+ if (i != first)
+ --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;
+ if (i != last)
+ ++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 ex;
+
+extern const numeric *_num_120_p;
+extern const ex _ex_120;
+extern const numeric *_num_60_p;
+extern const ex _ex_60;
+extern const numeric *_num_48_p;
+extern const ex _ex_48;
+extern const numeric *_num_30_p;
+extern const ex _ex_30;
+extern const numeric *_num_25_p;
+extern const ex _ex_25;
+extern const numeric *_num_24_p;
+extern const ex _ex_24;
+extern const numeric *_num_20_p;
+extern const ex _ex_20;
+extern const numeric *_num_18_p;
+extern const ex _ex_18;
+extern const numeric *_num_15_p;
+extern const ex _ex_15;
+extern const numeric *_num_12_p;
+extern const ex _ex_12;
+extern const numeric *_num_11_p;
+extern const ex _ex_11;
+extern const numeric *_num_10_p;
+extern const ex _ex_10;
+extern const numeric *_num_9_p;
+extern const ex _ex_9;
+extern const numeric *_num_8_p;
+extern const ex _ex_8;
+extern const numeric *_num_7_p;
+extern const ex _ex_7;
+extern const numeric *_num_6_p;
+extern const ex _ex_6;
+extern const numeric *_num_5_p;
+extern const ex _ex_5;
+extern const numeric *_num_4_p;
+extern const ex _ex_4;
+extern const numeric *_num_3_p;
+extern const ex _ex_3;
+extern const numeric *_num_2_p;
+extern const ex _ex_2;
+extern const numeric *_num_1_p;
+extern const ex _ex_1;
+extern const numeric *_num_1_2_p;
+extern const ex _ex_1_2;
+extern const numeric *_num_1_3_p;
+extern const ex _ex_1_3;
+extern const numeric *_num_1_4_p;
+extern const ex _ex_1_4;
+extern const numeric *_num0_p;
+extern const basic *_num0_bp;
+extern const ex _ex0;
+extern const numeric *_num1_4_p;
+extern const ex _ex1_4;
+extern const numeric *_num1_3_p;
+extern const ex _ex1_3;
+extern const numeric *_num1_2_p;
+extern const ex _ex1_2;
+extern const numeric *_num1_p;
+extern const ex _ex1;
+extern const numeric *_num2_p;
+extern const ex _ex2;
+extern const numeric *_num3_p;
+extern const ex _ex3;
+extern const numeric *_num4_p;
+extern const ex _ex4;
+extern const numeric *_num5_p;
+extern const ex _ex5;
+extern const numeric *_num6_p;
+extern const ex _ex6;
+extern const numeric *_num7_p;
+extern const ex _ex7;
+extern const numeric *_num8_p;
+extern const ex _ex8;
+extern const numeric *_num9_p;
+extern const ex _ex9;
+extern const numeric *_num10_p;
+extern const ex _ex10;
+extern const numeric *_num11_p;
+extern const ex _ex11;
+extern const numeric *_num12_p;
+extern const ex _ex12;
+extern const numeric *_num15_p;
+extern const ex _ex15;
+extern const numeric *_num18_p;
+extern const ex _ex18;
+extern const numeric *_num20_p;
+extern const ex _ex20;
+extern const numeric *_num24_p;
+extern const ex _ex24;
+extern const numeric *_num25_p;
+extern const ex _ex25;
+extern const numeric *_num30_p;
+extern const ex _ex30;
+extern const numeric *_num48_p;
+extern const ex _ex48;
+extern const numeric *_num60_p;
+extern const ex _ex60;
+extern const numeric *_num120_p;
+extern const ex _ex120;
+