/** @file utils.h
*
- * Interface to several small and furry utilities. */
+ * Interface to several small and furry utilities needed within GiNaC but not
+ * of any interest to the user of the library. */
/*
- * GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2002 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
#ifndef __GINAC_UTILS_H__
#define __GINAC_UTILS_H__
-#include <strstream>
-#include <string>
#include "config.h"
+
+#include <string>
+#include <stdexcept>
#include "assertion.h"
namespace GiNaC {
-template<class T>
-string ToString(T const & t)
-{
- char buf[256];
- ostrstream(buf,sizeof(buf)) << t << ends;
- return buf;
-}
+/** 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);
+#endif
-int compare_pointers(void const * a, void const * b);
+/** 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)
+{
+ if (a<b)
+ return -1;
+ else if (a>b)
+ return 1;
+ return 0;
+}
/** Rotate lower 31 bits of unsigned value by one bit to the left
- * (upper bits get cleared). */
+ * (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;
- }
- ASSERT(n<0x80000000U);
-
- return 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. */
+/** Golden ratio hash function for the 31 least significant bits. */
inline unsigned golden_ratio_hash(unsigned n)
{
// 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"
+#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-compliant:
- unsigned long long l = n * 0x4f1bbcddLL;
+ // 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
}
-// 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));
+/* 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;
}
-// 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);
- }
+/* 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;
+
+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 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_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 \
+{ \
+ if (is_a<print_tree>(c)) \
+ inherited::print(c, level); \
+ else \
+ c.s << text; \
+}
+
+#define DEFAULT_PRINT_LATEX(classname, text, latex) \
+void classname::print(const print_context & 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; \
+}
+
+// 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__
git://www.ginac.de / ginac.git / blobdiff