X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Futils.h;h=816679d7e0338201995ff0e2aca1e7dc9bb84c85;hp=4af88ebada3e0258ea7939a39dfcfd5f6ce5e9e6;hb=3a7031219dabf8e5d15dc63ca4975c88e20abaec;hpb=2565309dd7c38635c191eacf2a4af9b23fc0d310 diff --git a/ginac/utils.h b/ginac/utils.h index 4af88eba..816679d7 100644 --- a/ginac/utils.h +++ b/ginac/utils.h @@ -4,7 +4,7 @@ * of any interest to the user of the library. */ /* - * GiNaC Copyright (C) 1999-2000 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 @@ -18,232 +18,564 @@ * * 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 -#include -#include "config.h" #include "assertion.h" -#ifndef NO_GINAC_NAMESPACE +#include +#include // for uintptr_t +#include + namespace GiNaC { -#endif // ndef NO_GINAC_NAMESPACE -template -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(const void * a, const void * 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); +} + +/** Compare two pointers (just to establish some sort of canonical order). + * @return -1, 0, or 1 */ +template +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()(a, b)) + return -1; + else if (std::less()(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); +} -/** Rotate lower 31 bits of unsigned value by one bit to the left - * (upper bits get cleared). */ -inline unsigned rotate_left_31(unsigned 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 +int permutation_sign(It first, It last) { - // clear highest bit and shift 1 bit to the left - n=(n & 0x7FFFFFFFU) << 1; + using std::swap; + 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 (*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 n; + return sign; } -/** Golden ratio hash function. */ -inline unsigned golden_ratio_hash(unsigned n) +template +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 -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 +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 -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 +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 x; + int n; // n>0 + int m; // 0 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& 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." ) + 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& 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 composition; // current compositions +public: + explicit composition_generator(const std::vector& partition) + : cmgen(partition), atend(false), trivial(true), composition(partition.size()) + { + for (unsigned i=1; i& 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 & 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; -const numeric & _num_120(void); // -120 -const ex & _ex_120(void); -const numeric & _num_60(void); // -60 -const ex & _ex_60(void); -const numeric & _num_30(void); // -30 -const ex & _ex_30(void); -const numeric & _num_25(void); // -25 -const ex & _ex_25(void); -const numeric & _num_24(void); // -24 -const ex & _ex_24(void); -const numeric & _num_20(void); // -20 -const ex & _ex_20(void); -const numeric & _num_18(void); // -18 -const ex & _ex_18(void); -const numeric & _num_15(void); // -15 -const ex & _ex_15(void); -const numeric & _num_12(void); // -12 -const ex & _ex_12(void); -const numeric & _num_11(void); // -11 -const ex & _ex_11(void); -const numeric & _num_10(void); // -10 -const ex & _ex_10(void); -const numeric & _num_9(void); // -9 -const ex & _ex_9(void); -const numeric & _num_8(void); // -8 -const ex & _ex_8(void); -const numeric & _num_7(void); // -7 -const ex & _ex_7(void); -const numeric & _num_6(void); // -6 -const ex & _ex_6(void); -const numeric & _num_5(void); // -5 -const ex & _ex_5(void); -const numeric & _num_4(void); // -4 -const ex & _ex_4(void); -const numeric & _num_3(void); // -3 -const ex & _ex_3(void); -const numeric & _num_2(void); // -2 -const ex & _ex_2(void); -const numeric & _num_1(void); // -1 -const ex & _ex_1(void); -const numeric & _num_1_2(void); // -1/2 -const ex & _ex_1_2(void); -const numeric & _num_1_3(void); // -1/3 -const ex & _ex_1_3(void); -const numeric & _num_1_4(void); // -1/4 -const ex & _ex_1_4(void); -const numeric & _num0(void); // 0 -const ex & _ex0(void); -const numeric & _num1_4(void); // 1/4 -const ex & _ex1_4(void); -const numeric & _num1_3(void); // 1/3 -const ex & _ex1_3(void); -const numeric & _num1_2(void); // 1/2 -const ex & _ex1_2(void); -const numeric & _num1(void); // 1 -const ex & _ex1(void); -const numeric & _num2(void); // 2 -const ex & _ex2(void); -const numeric & _num3(void); // 3 -const ex & _ex3(void); -const numeric & _num4(void); // 4 -const ex & _ex4(void); -const numeric & _num5(void); // 5 -const ex & _ex5(void); -const numeric & _num6(void); // 6 -const ex & _ex6(void); -const numeric & _num7(void); // 7 -const ex & _ex7(void); -const numeric & _num8(void); // 8 -const ex & _ex8(void); -const numeric & _num9(void); // 9 -const ex & _ex9(void); -const numeric & _num10(void); // 10 -const ex & _ex10(void); -const numeric & _num11(void); // 11 -const ex & _ex11(void); -const numeric & _num12(void); // 12 -const ex & _ex12(void); -const numeric & _num15(void); // 15 -const ex & _ex15(void); -const numeric & _num18(void); // 18 -const ex & _ex18(void); -const numeric & _num20(void); // 20 -const ex & _ex20(void); -const numeric & _num24(void); // 24 -const ex & _ex24(void); -const numeric & _num25(void); // 25 -const ex & _ex25(void); -const numeric & _num30(void); // 30 -const ex & _ex30(void); -const numeric & _num60(void); // 60 -const ex & _ex60(void); -const numeric & _num120(void); // 120 -const ex & _ex120(void); - -#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