X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Futils.h;h=a6e28d74ef6026c83a1ab90a9502b39940b82c74;hp=7be44f73281ed2c8829176f41938a509b1932ec1;hb=8cffcdf13d817a47f217f1a1043317d95969e070;hpb=d8148ca72f0e9c5f39b7142a87f004a7a5840d69

diff --git a/ginac/utils.h b/ginac/utils.h
index 7be44f73..a6e28d74 100644
--- a/ginac/utils.h
+++ b/ginac/utils.h
@@ -1,10 +1,10 @@
 /** @file utils.h
  *
  *  Interface to several small and furry utilities needed within GiNaC but not
- *  of interest to the user of the library. */
+ *  of any interest to the user of the library. */
 
 /*
- *  GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2019 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
@@ -18,128 +18,614 @@
  *
  *  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)
+/** Exception class thrown by functions to signal unimplemented functionality
+ *  so the expression may just be .hold() */
+class dunno {};
+
+// some compilers (e.g. cygwin) define a macro log2, causing confusion
+#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)
 {
-    char buf[256];
-    ostrstream(buf,sizeof(buf)) << t << ends;
-    return buf;
+	return (n & 0x80000000U) ? (n << 1 | 0x00000001U) : (n << 1);
 }
 
-/** Exception thrown by classes which provide their own series expansion to
- *  signal that ordinary Taylor expansion is safe. */
-class do_taylor {};
+/** 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;
+}
 
-unsigned log2(unsigned n);
+/** 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;
 
-int compare_pointers(void const * a, void const * b);
+	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);
 
-/** Rotate lower 31 bits of unsigned value by one bit to the left
- *  (upper bits get cleared). */
-inline unsigned rotate_left_31(unsigned n)
+	return sign;
+}
+
+template <class It, class Cmp, class Swap>
+int permutation_sign(It first, It last, Cmp comp, Swap swapit)
 {
-    // clear highest bit and shift 1 bit to the left
-    n=(n & 0x7FFFFFFFU) << 1;
+	if (first == last)
+		return 0;
+	--last;
+	if (first == last)
+		return 0;
+	It flag = first;
+	int sign = 1;
 
-    // overflow? clear highest bit and set lowest bit
-    if (n & 0x80000000U) {
-        n=(n & 0x7FFFFFFFU) | 0x00000001U;
-    }
-    GINAC_ASSERT(n<0x80000000U);
+	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 n;
+	return sign;
 }
 
-/** Golden ratio hash function. */
-inline unsigned golden_ratio_hash(unsigned n)
+/* 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)
 {
-	// 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;
+	--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;
+	}
+}
+
+/** Base class for generating all bounded combinatorial partitions of an integer
+ *  n with exactly m parts in non-decreasing order.
+ */
+class basic_partition_generator {
+protected:
+	// 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<unsigned> x;
+		unsigned n;   // n>0
+		unsigned m;   // 0<m<=n
+		mpartition2(unsigned n_, unsigned m_)
+		  : x(m_+1), n(n_), m(m_)
+		{
+			for (unsigned k=1; k<m; ++k)
+				x[k] = 1;
+			x[m] = n - m + 1;
+		}
+		bool next_partition()
+		{
+			unsigned u = x[m];  // last element
+			unsigned k = m;
+			unsigned s = u;
+			while (--k) {
+				s += x[k];
+				if (x[k] + 2 <= u)
+					break;
+			}
+			if (k==0)
+				return false;  // current is last
+			unsigned f = x[k] + 1;
+			while (k < m) {
+				x[k] = f;
+				s -= f;
+				++k;
+			}
+			x[m] = s;
+			return true;
+		}
+	};
+	mpartition2 mpgen;
+	basic_partition_generator(unsigned n_, unsigned m_)
+	  : mpgen(n_, m_)
+	{ }
+};
+
+/** Generate all bounded combinatorial partitions of an integer n with exactly
+ *  m parts (including zero parts) in non-decreasing order.
+ */
+class partition_with_zero_parts_generator : public basic_partition_generator {
+private:
+	unsigned m;  // number of parts 0<m
+	mutable std::vector<unsigned> partition;  // current partition
+	mutable bool current_updated;  // whether partition vector has been updated
+public:
+	partition_with_zero_parts_generator(unsigned n_, unsigned m_)
+	  : basic_partition_generator(n_, 1), m(m_), partition(m_), current_updated(false)
+	{ }
+	// returns current partition in non-decreasing order, padded with zeros
+	const std::vector<unsigned>& get() const
+	{
+		if (!current_updated) {
+			for (unsigned i = 0; i < m - mpgen.m; ++i)
+				partition[i] = 0;  // pad with zeros
+
+			for (unsigned i = m - mpgen.m; i < m; ++i)
+				partition[i] = mpgen.x[i - m + mpgen.m + 1];
+
+			current_updated = true;
+		}
+		return partition;
+	}
+	bool next()
+	{
+		current_updated = false;
+		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 bounded combinatorial partitions of an integer n with exactly
+ *  m parts (not including zero parts) in non-decreasing order.
+ */
+class partition_generator : public basic_partition_generator {
+private:
+	mutable std::vector<unsigned> partition;  // current partition
+	mutable bool current_updated;  // whether partition vector has been updated
+public:
+	partition_generator(unsigned n_, unsigned m_)
+	  : basic_partition_generator(n_, m_), partition(m_), current_updated(false)
+	{ }
+	// returns current partition in non-decreasing order, padded with zeros
+	const std::vector<unsigned>& get() const
+	{
+		if (!current_updated) {
+			for (unsigned i = 0; i < mpgen.m; ++i)
+				partition[i] = mpgen.x[i + 1];
+
+			current_updated = true;
+		}
+		return partition;
+	}
+	bool next()
+	{
+		current_updated = false;
+		return mpgen.next_partition();
+	}
+};
+
+/** 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 {
+			unsigned value;
+			element* next;
+			element(unsigned 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<unsigned>& 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<unsigned> composition;  // current compositions
+	mutable bool current_updated;  // whether composition vector has been updated
+public:
+	explicit composition_generator(const std::vector<unsigned>& partition)
+	  : cmgen(partition), atend(false), trivial(true), composition(partition.size()), current_updated(false)
+	{
+		for (unsigned i=1; i<partition.size(); ++i)
+			trivial = trivial && (partition[0] == partition[i]);
+	}
+	const std::vector<unsigned>& get() const
+	{
+		if (!current_updated) {
+			coolmulti::element* it = cmgen.head;
+			size_t i = 0;
+			while (it != nullptr) {
+				composition[i] = it->value;
+				it = it->next;
+				++i;
+			}
+			current_updated = true;
+		}
+		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();
+		current_updated = false;
+		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<unsigned> & 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 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;
+
+
+// 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; \
 }
 
-// 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));
+#define DEFAULT_PRINT(classname, text) \
+void classname::do_print(const print_context & c, unsigned level) const \
+{ \
+	c.s << text; \
 }
 
-// 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);
-    }
+#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; \
 }
 
-#ifndef NO_GINAC_NAMESPACE
 } // namespace GiNaC
-#endif // ndef NO_GINAC_NAMESPACE
 
-#endif // ndef __GINAC_UTILS_H__
+#endif // ndef GINAC_UTILS_H