* of any interest to the user of the library. */
/*
- * GiNaC Copyright (C) 1999-2002 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 "config.h"
+#include "assertion.h"
+#include <functional>
+#include <cstdint> // for uintptr_t
#include <string>
-#include <stdexcept>
-#include "assertion.h"
namespace GiNaC {
-/** Exception class thrown by classes which provide their own series expansion
- * to signal that ordinary Taylor expansion is safe. */
-class do_taylor {};
-
/** Exception class thrown by functions to signal unimplemented functionality
* so the expression may just be .hold() */
class dunno {};
-/** Exception class thrown when a singularity is encountered. */
-class pole_error : public std::domain_error {
-public:
- explicit pole_error(const std::string& what_arg, int degree);
- int degree(void) const;
-private:
- int deg;
-};
-
// some compilers (e.g. cygwin) define a macro log2, causing confusion
-#ifndef log2
-unsigned log2(unsigned n);
+#ifdef log2
+#undef log2
#endif
+unsigned log2(unsigned n);
+
+/** 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);
+}
+
/** Compare two pointers (just to establish some sort of canonical order).
* @return -1, 0, or 1 */
-inline int compare_pointers(const void * a, const void * b)
+template <class T>
+inline int compare_pointers(const T * a, const T * b)
{
- if (a<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 (a>b)
+ else if (std::less<const T *>()(b, a))
return 1;
return 0;
}
-/** Rotate lower 31 bits of unsigned value by one bit to the left
- * (upper bit gets cleared). */
-inline unsigned rotate_left_31(unsigned n)
-{
- // clear highest bit and shift 1 bit to the left
- n = (n & 0x7FFFFFFFU) << 1;
-
- // overflow? clear highest bit and set lowest bit
- if (n & 0x80000000U)
- n = (n & 0x7FFFFFFFU) | 0x00000001U;
-
- GINAC_ASSERT(n<0x80000000U);
-
- return n;
-}
-
-/** Golden ratio hash function for the 31 least significant bits. */
-inline unsigned golden_ratio_hash(unsigned n)
+/** Truncated multiplication with golden ratio, for computing hash values. */
+inline unsigned golden_ratio_hash(uintptr_t n)
{
- // This function requires arithmetic with at least 64 significant bits
-#if SIZEOF_LONG >= 8
- // So 'long' has 64 bits. Excellent! 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-C++-compliant.
- // (Yet C99 demands it, which is reason for hope.)
- unsigned long long l = n * 0x4f1bbcddL;
- return (l & 0x7fffffffU) ^ (l >> 32);
-#elif 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.
- // Unfortunately, it may lead to horribly slow code.
- const static long double golden_ratio = .618033988749894848204586834370;
- long double m = golden_ratio * n;
- return unsigned((m - int(m)) * 0x80000000);
-#else
-#error "No 64 bit data type. You lose."
-#endif
+ return n * UINT64_C(0x4f1bbcdd);
}
/* Compute the sign of a permutation of a container, with and without an
template <class It>
int permutation_sign(It first, It last)
{
+ using std::swap;
if (first == last)
return 0;
--last;
bool swapped = false;
while (i != first) {
if (*i < *other) {
- std::iter_swap(other, i);
+ swap(*other, *i);
flag = other;
swapped = true;
sign = -sign;
} else if (!(*other < *i))
return 0;
- --i; --other;
+ --i;
+ if (i != first)
+ --other;
}
if (!swapped)
return sign;
swapped = false;
while (i != last) {
if (*other < *i) {
- std::iter_swap(i, other);
+ swap(*i, *other);
flag = other;
swapped = true;
sign = -sign;
} else if (!(*i < *other))
return 0;
- ++i; ++other;
+ ++i;
+ if (i != last)
+ ++other;
}
if (!swapped)
return sign;
sign = -sign;
} else if (!comp(*other, *i))
return 0;
- --i; --other;
+ --i;
+ if (i != first)
+ --other;
}
if (!swapped)
return sign;
sign = -sign;
} else if (!comp(*i, *other))
return 0;
- ++i; ++other;
+ ++i;
+ if (i != last)
+ ++other;
}
if (!swapped)
return sign;
flag = other;
swapped = true;
}
- --i; --other;
+ --i;
+ if (i != first)
+ --other;
}
if (!swapped)
return;
flag = other;
swapped = true;
}
- ++i; ++other;
+ ++i;
+ if (i != last)
+ ++other;
}
if (!swapped)
return;
}
}
+/** 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
// the library but should not be used outside it since it is
// potentially confusing.
-class numeric;
class ex;
extern const numeric *_num_120_p;
-extern const numeric &_num_120;
extern const ex _ex_120;
extern const numeric *_num_60_p;
-extern const numeric &_num_60;
extern const ex _ex_60;
extern const numeric *_num_48_p;
-extern const numeric &_num_48;
extern const ex _ex_48;
extern const numeric *_num_30_p;
-extern const numeric &_num_30;
extern const ex _ex_30;
extern const numeric *_num_25_p;
-extern const numeric &_num_25;
extern const ex _ex_25;
extern const numeric *_num_24_p;
-extern const numeric &_num_24;
extern const ex _ex_24;
extern const numeric *_num_20_p;
-extern const numeric &_num_20;
extern const ex _ex_20;
extern const numeric *_num_18_p;
-extern const numeric &_num_18;
extern const ex _ex_18;
extern const numeric *_num_15_p;
-extern const numeric &_num_15;
extern const ex _ex_15;
extern const numeric *_num_12_p;
-extern const numeric &_num_12;
extern const ex _ex_12;
extern const numeric *_num_11_p;
-extern const numeric &_num_11;
extern const ex _ex_11;
extern const numeric *_num_10_p;
-extern const numeric &_num_10;
extern const ex _ex_10;
extern const numeric *_num_9_p;
-extern const numeric &_num_9;
extern const ex _ex_9;
extern const numeric *_num_8_p;
-extern const numeric &_num_8;
extern const ex _ex_8;
extern const numeric *_num_7_p;
-extern const numeric &_num_7;
extern const ex _ex_7;
extern const numeric *_num_6_p;
-extern const numeric &_num_6;
extern const ex _ex_6;
extern const numeric *_num_5_p;
-extern const numeric &_num_5;
extern const ex _ex_5;
extern const numeric *_num_4_p;
-extern const numeric &_num_4;
extern const ex _ex_4;
extern const numeric *_num_3_p;
-extern const numeric &_num_3;
extern const ex _ex_3;
extern const numeric *_num_2_p;
-extern const numeric &_num_2;
extern const ex _ex_2;
extern const numeric *_num_1_p;
-extern const numeric &_num_1;
extern const ex _ex_1;
extern const numeric *_num_1_2_p;
-extern const numeric &_num_1_2;
extern const ex _ex_1_2;
extern const numeric *_num_1_3_p;
-extern const numeric &_num_1_3;
extern const ex _ex_1_3;
extern const numeric *_num_1_4_p;
-extern const numeric &_num_1_4;
extern const ex _ex_1_4;
extern const numeric *_num0_p;
-extern const numeric &_num0;
+extern const basic *_num0_bp;
extern const ex _ex0;
extern const numeric *_num1_4_p;
-extern const numeric &_num1_4;
extern const ex _ex1_4;
extern const numeric *_num1_3_p;
-extern const numeric &_num1_3;
extern const ex _ex1_3;
extern const numeric *_num1_2_p;
-extern const numeric &_num1_2;
extern const ex _ex1_2;
extern const numeric *_num1_p;
-extern const numeric &_num1;
extern const ex _ex1;
extern const numeric *_num2_p;
-extern const numeric &_num2;
extern const ex _ex2;
extern const numeric *_num3_p;
-extern const numeric &_num3;
extern const ex _ex3;
extern const numeric *_num4_p;
-extern const numeric &_num4;
extern const ex _ex4;
extern const numeric *_num5_p;
-extern const numeric &_num5;
extern const ex _ex5;
extern const numeric *_num6_p;
-extern const numeric &_num6;
extern const ex _ex6;
extern const numeric *_num7_p;
-extern const numeric &_num7;
extern const ex _ex7;
extern const numeric *_num8_p;
-extern const numeric &_num8;
extern const ex _ex8;
extern const numeric *_num9_p;
-extern const numeric &_num9;
extern const ex _ex9;
extern const numeric *_num10_p;
-extern const numeric &_num10;
extern const ex _ex10;
extern const numeric *_num11_p;
-extern const numeric &_num11;
extern const ex _ex11;
extern const numeric *_num12_p;
-extern const numeric &_num12;
extern const ex _ex12;
extern const numeric *_num15_p;
-extern const numeric &_num15;
extern const ex _ex15;
extern const numeric *_num18_p;
-extern const numeric &_num18;
extern const ex _ex18;
extern const numeric *_num20_p;
-extern const numeric &_num20;
extern const ex _ex20;
extern const numeric *_num24_p;
-extern const numeric &_num24;
extern const ex _ex24;
extern const numeric *_num25_p;
-extern const numeric &_num25;
extern const ex _ex25;
extern const numeric *_num30_p;
-extern const numeric &_num30;
extern const ex _ex30;
extern const numeric *_num48_p;
-extern const numeric &_num48;
extern const ex _ex48;
extern const numeric *_num60_p;
-extern const numeric &_num60;
extern const ex _ex60;
extern const numeric *_num120_p;
-extern const numeric &_num120;
extern const ex _ex120;
// 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) {} \
-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) {} \
-DEFAULT_UNARCHIVE(classname) \
-void classname::archive(archive_node &n) const \
-{ \
- inherited::archive(n); \
-}
+#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 \
}
#define DEFAULT_PRINT(classname, text) \
-void classname::print(const print_context & c, unsigned level) const \
+void classname::do_print(const print_context & c, unsigned level) const \
{ \
- if (is_a<print_tree>(c)) \
- inherited::print(c, level); \
- else \
- c.s << text; \
+ c.s << text; \
}
#define DEFAULT_PRINT_LATEX(classname, text, latex) \
-void classname::print(const print_context & c, unsigned level) const \
+DEFAULT_PRINT(classname, text) \
+void classname::do_print_latex(const print_latex & c, unsigned level) const \
{ \
- if (is_a<print_tree>(c)) \
- inherited::print(c, level); \
- else if (is_a<print_latex>(c)) \
- c.s << latex; \
- else \
- c.s << text; \
+ c.s << latex; \
}
-// Obsolete convenience macros. TO BE PHASED OUT SOON!
-// Use the inlined template functions in basic.h instead. (FIXME: remove them)
-
-#define is_of_type(OBJ,TYPE) \
- (dynamic_cast<const TYPE *>(&OBJ)!=0)
-
-#define is_exactly_of_type(OBJ,TYPE) \
- ((OBJ).tinfo()==GiNaC::TINFO_##TYPE)
-
-#define is_ex_of_type(OBJ,TYPE) \
- (dynamic_cast<const TYPE *>((OBJ).bp)!=0)
-
-#define is_ex_exactly_of_type(OBJ,TYPE) \
- ((*(OBJ).bp).tinfo()==GiNaC::TINFO_##TYPE)
-
} // namespace GiNaC
-
-#endif // ndef __GINAC_UTILS_H__
+#endif // ndef GINAC_UTILS_H
git://www.ginac.de / ginac.git / blobdiff