* of any interest to the user of the library. */
/*
- * GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2017 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
-#ifndef __GINAC_UTILS_H__
-#define __GINAC_UTILS_H__
+#ifndef GINAC_UTILS_H
+#define GINAC_UTILS_H
-#include <strstream>
-#include <string>
-#include "config.h"
#include "assertion.h"
-#ifndef NO_GINAC_NAMESPACE
+#include <functional>
+#include <cstdint> // for uintptr_t
+#include <string>
+
namespace GiNaC {
-#endif // ndef NO_GINAC_NAMESPACE
-template<class T>
-string ToString(T const & t)
-{
- char buf[256];
- ostrstream(buf,sizeof(buf)) << t << ends;
- return buf;
-}
+/** Exception class thrown by functions to signal unimplemented functionality
+ * so the expression may just be .hold() */
+class dunno {};
-/** Exception thrown by classes which provide their own series expansion to
- * signal that ordinary Taylor expansion is safe. */
-class do_taylor {};
+// some compilers (e.g. cygwin) define a macro log2, causing confusion
+#ifdef log2
+#undef log2
+#endif
unsigned log2(unsigned n);
-int compare_pointers(void const * a, void const * b);
+/** Rotate bits of unsigned value by one bit to the left.
+ * This can be necessary if the user wants to define its own hashes. */
+inline unsigned rotate_left(unsigned n)
+{
+ return (n & 0x80000000U) ? (n << 1 | 0x00000001U) : (n << 1);
+}
-/** Rotate lower 31 bits of unsigned value by one bit to the left
- * (upper bits get cleared). */
-inline unsigned rotate_left_31(unsigned n)
+/** 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)
{
- // clear highest bit and shift 1 bit to the left
- n=(n & 0x7FFFFFFFU) << 1;
+ // '<' 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;
+}
- // overflow? clear highest bit and set lowest bit
- if (n & 0x80000000U) {
- n=(n & 0x7FFFFFFFU) | 0x00000001U;
- }
- GINAC_ASSERT(n<0x80000000U);
+/** Truncated multiplication with golden ratio, for computing hash values. */
+inline unsigned golden_ratio_hash(uintptr_t n)
+{
+ return n * UINT64_C(0x4f1bbcdd);
+}
- return n;
+/* 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;
}
-/** Golden ratio hash function. */
-inline unsigned golden_ratio_hash(unsigned n)
+template <class It, class Cmp, class Swap>
+int permutation_sign(It first, It last, Cmp comp, Swap swapit)
{
- // This function requires arithmetic with at least 64 significant bits
-#if SIZEOF_LONG_DOUBLE > 8
- // If "long double" is bigger than 64 bits, we assume that the mantissa
- // has at least 64 bits. This is not guaranteed but it's a good guess.
- const static long double golden_ratio = .618033988749894848204586834370;
- long double m = golden_ratio * n;
- return unsigned((m - int(m)) * 0x80000000);
-#elif SIZEOF_LONG >= 8
- // "long" has 64 bits, so we prefer it because it might be more efficient
- // than "long long"
- unsigned long l = n * 0x4f1bbcddL;
- return (l & 0x7fffffffU) ^ (l >> 32);
-#elif SIZEOF_LONG_LONG >= 8
- // This requires ´long long´ (or an equivalent 64 bit type)---which is,
- // unfortunately, not ANSI-compliant:
- unsigned long long l = n * 0x4f1bbcddLL;
- return (l & 0x7fffffffU) ^ (l >> 32);
-#else
-#error "No 64 bit data type. You lose."
-#endif
+ 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;
}
-// modified from stl_algo.h: always do com(*first1,*first2) instead of comp(*first2,*first1)
-template <class InputIterator1, class InputIterator2, class OutputIterator,
- class Compare>
-OutputIterator mymerge(InputIterator1 first1, InputIterator1 last1,
- InputIterator2 first2, InputIterator2 last2,
- OutputIterator result, Compare comp) {
- while (first1 != last1 && first2 != last2) {
- if (comp(*first1, *first2)) {
- *result = *first1;
- ++first1;
- }
- else {
- *result = *first2;
- ++first2;
- }
- ++result;
- }
- return copy(first2, last2, copy(first1, last1, result));
+/* 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);
}
-// like merge(), but three lists with *last2<*first3
-template <class InputIterator1, class InputIterator2, class InputIterator3,
- class OutputIterator, class Compare>
-OutputIterator mymerge3(InputIterator1 first1, InputIterator1 last1,
- InputIterator2 first2, InputIterator2 last2,
- InputIterator3 first3, InputIterator3 last3,
- OutputIterator result, Compare comp) {
- while (first1 != last1 && first2 != last2) {
- if (comp(*first1, *first2)) {
- *result = *first1;
- ++first1;
- }
- else {
- *result = *first2;
- ++first2;
- }
- ++result;
- }
-
- if (first1==last1) {
- // list1 empty, copy rest of list2, then list3
- return copy(first3, last3, copy(first2, last2, result));
- } else {
- // list2 empty, merge rest of list1 with list3
- return mymerge(first1,last1,first3,last3,result,comp);
- }
+/* 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;
+ }
}
+/** Generate all bounded combinatorial partitions of an integer n with exactly
+ * m parts (including zero parts) in non-decreasing order.
+ */
+class partition_generator {
+private:
+ // Partitions n into m parts, not including zero parts.
+ // (Cf. OEIS sequence A008284; implementation adapted from Jörg Arndt's
+ // FXT library)
+ struct mpartition2
+ {
+ // partition: x[1] + x[2] + ... + x[m] = n and sentinel x[0] == 0
+ std::vector<int> x;
+ int n; // n>0
+ int m; // 0<m<=n
+ mpartition2(unsigned n_, unsigned m_)
+ : x(m_+1), n(n_), m(m_)
+ {
+ for (int k=1; k<m; ++k)
+ x[k] = 1;
+ x[m] = n - m + 1;
+ }
+ bool next_partition()
+ {
+ int u = x[m]; // last element
+ int k = m;
+ int s = u;
+ while (--k) {
+ s += x[k];
+ if (x[k] + 2 <= u)
+ break;
+ }
+ if (k==0)
+ return false; // current is last
+ int f = x[k] + 1;
+ while (k < m) {
+ x[k] = f;
+ s -= f;
+ ++k;
+ }
+ x[m] = s;
+ return true;
+ }
+ } mpgen;
+ int m; // number of parts 0<m<=n
+ mutable std::vector<int> partition; // current partition
+public:
+ partition_generator(unsigned n_, unsigned m_)
+ : mpgen(n_, 1), m(m_), partition(m_)
+ { }
+ // returns current partition in non-decreasing order, padded with zeros
+ const std::vector<int>& current() const
+ {
+ for (int i = 0; i < m - mpgen.m; ++i)
+ partition[i] = 0; // pad with zeros
+
+ for (int i = m - mpgen.m; i < m; ++i)
+ partition[i] = mpgen.x[i - m + mpgen.m + 1];
+
+ return partition;
+ }
+ bool next()
+ {
+ if (!mpgen.next_partition()) {
+ if (mpgen.m == m || mpgen.m == mpgen.n)
+ return false; // current is last
+ // increment number of parts
+ mpgen = mpartition2(mpgen.n, mpgen.m + 1);
+ }
+ return true;
+ }
+};
+
+/** Generate all compositions of a partition of an integer n, starting with the
+ * compositions which has non-decreasing order.
+ */
+class composition_generator {
+private:
+ // Generates all distinct permutations of a multiset.
+ // (Based on Aaron Williams' algorithm 1 from "Loopless Generation of
+ // Multiset Permutations using a Constant Number of Variables by Prefix
+ // Shifts." <http://webhome.csc.uvic.ca/~haron/CoolMulti.pdf>)
+ struct coolmulti {
+ // element of singly linked list
+ struct element {
+ int value;
+ element* next;
+ element(int val, element* n)
+ : value(val), next(n) {}
+ ~element()
+ { // recurses down to the end of the singly linked list
+ delete next;
+ }
+ };
+ element *head, *i, *after_i;
+ // NB: Partition must be sorted in non-decreasing order.
+ explicit coolmulti(const std::vector<int>& partition)
+ : head(nullptr), i(nullptr), after_i(nullptr)
+ {
+ for (unsigned n = 0; n < partition.size(); ++n) {
+ head = new element(partition[n], head);
+ if (n <= 1)
+ i = head;
+ }
+ after_i = i->next;
+ }
+ ~coolmulti()
+ { // deletes singly linked list
+ delete head;
+ }
+ void next_permutation()
+ {
+ element *before_k;
+ if (after_i->next != nullptr && i->value >= after_i->next->value)
+ before_k = after_i;
+ else
+ before_k = i;
+ element *k = before_k->next;
+ before_k->next = k->next;
+ k->next = head;
+ if (k->value < head->value)
+ i = k;
+ after_i = i->next;
+ head = k;
+ }
+ bool finished() const
+ {
+ return after_i->next == nullptr && after_i->value >= head->value;
+ }
+ } cmgen;
+ bool atend; // needed for simplifying iteration over permutations
+ bool trivial; // likewise, true if all elements are equal
+ mutable std::vector<int> composition; // current compositions
+public:
+ explicit composition_generator(const std::vector<int>& partition)
+ : cmgen(partition), atend(false), trivial(true), composition(partition.size())
+ {
+ for (unsigned i=1; i<partition.size(); ++i)
+ trivial = trivial && (partition[0] == partition[i]);
+ }
+ const std::vector<int>& current() const
+ {
+ coolmulti::element* it = cmgen.head;
+ size_t i = 0;
+ while (it != nullptr) {
+ composition[i] = it->value;
+ it = it->next;
+ ++i;
+ }
+ return composition;
+ }
+ bool next()
+ {
+ // This ugly contortion is needed because the original coolmulti
+ // algorithm requires code duplication of the payload procedure,
+ // one before the loop and one inside it.
+ if (trivial || atend)
+ return false;
+ cmgen.next_permutation();
+ atend = cmgen.finished();
+ return true;
+ }
+};
+
+/** Compute the multinomial coefficient n!/(p1!*p2!*...*pk!) where
+ * n = p1+p2+...+pk, i.e. p is a partition of n.
+ */
+const numeric
+multinomial_coefficient(const std::vector<int> & p);
+
+
// 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;
-
-numeric const & _num_12(void); // -12
-numeric const & _num_11(void); // -11
-numeric const & _num_10(void); // -10
-numeric const & _num_9(void); // -9
-numeric const & _num_8(void); // -8
-numeric const & _num_7(void); // -7
-numeric const & _num_6(void); // -6
-numeric const & _num_5(void); // -5
-numeric const & _num_4(void); // -4
-numeric const & _num_3(void); // -3
-numeric const & _num_2(void); // -2
-numeric const & _num_1(void); // -1
-numeric const & _num_1_2(void); // -1/2
-numeric const & _num_1_3(void); // -1/3
-numeric const & _num0(void); // 0
-numeric const & _num1_3(void); // 1/3
-numeric const & _num1_2(void); // 1/2
-numeric const & _num1(void); // 1
-numeric const & _num2(void); // 2
-numeric const & _num3(void); // 3
-numeric const & _num4(void); // 4
-numeric const & _num5(void); // 5
-numeric const & _num6(void); // 6
-numeric const & _num7(void); // 7
-numeric const & _num8(void); // 8
-numeric const & _num9(void); // 9
-numeric const & _num10(void); // 10
-numeric const & _num11(void); // 11
-numeric const & _num12(void); // 12
-ex const & _ex_12(void); // -12
-ex const & _ex_11(void); // -11
-ex const & _ex_10(void); // -10
-ex const & _ex_9(void); // -9
-ex const & _ex_8(void); // -8
-ex const & _ex_7(void); // -7
-ex const & _ex_6(void); // -6
-ex const & _ex_5(void); // -5
-ex const & _ex_4(void); // -4
-ex const & _ex_3(void); // -3
-ex const & _ex_2(void); // -2
-ex const & _ex_1(void); // -1
-ex const & _ex_1_2(void); // -1/2
-ex const & _ex_1_3(void); // -1/3
-ex const & _ex0(void); // 0
-ex const & _ex1_3(void); // 1/3
-ex const & _ex1_2(void); // 1/2
-ex const & _ex1(void); // 1
-ex const & _ex2(void); // 2
-ex const & _ex3(void); // 3
-ex const & _ex4(void); // 4
-ex const & _ex5(void); // 5
-ex const & _ex6(void); // 6
-ex const & _ex7(void); // 7
-ex const & _ex8(void); // 8
-ex const & _ex9(void); // 9
-ex const & _ex10(void); // 10
-ex const & _ex11(void); // 11
-ex const & _ex12(void); // 12
-
-#ifndef NO_GINAC_NAMESPACE
+
+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;
+
+
+// Helper macros for class implementations (mostly useful for trivial classes)
+
+#define DEFAULT_CTOR(classname) \
+classname::classname() { setflag(status_flags::evaluated | status_flags::expanded); }
+
+#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::do_print(const print_context & c, unsigned level) const \
+{ \
+ c.s << text; \
+}
+
+#define DEFAULT_PRINT_LATEX(classname, text, latex) \
+DEFAULT_PRINT(classname, text) \
+void classname::do_print_latex(const print_latex & c, unsigned level) const \
+{ \
+ c.s << latex; \
+}
+
} // namespace GiNaC
-#endif // ndef NO_GINAC_NAMESPACE
-#endif // ndef __GINAC_UTILS_H__
+#endif // ndef GINAC_UTILS_H
git://www.ginac.de / ginac.git / blobdiff