X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Futils.h;h=791cfb5d81eb71094807b96725cffdcd98032a46;hp=814654c65563b65c8a0b81009fee94c330526429;hb=e14a5df66cc2b30e31e58418079704f4dcd52616;hpb=8bcccf834ad41e94a1a4f3a0304c2945b228b4f4 diff --git a/ginac/utils.h b/ginac/utils.h index 814654c6..791cfb5d 100644 --- a/ginac/utils.h +++ b/ginac/utils.h @@ -1,9 +1,10 @@ /** @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 @@ -23,114 +24,515 @@ #ifndef __GINAC_UTILS_H__ #define __GINAC_UTILS_H__ -#include -#include #include "config.h" + +#include +#include #include "assertion.h" namespace GiNaC { -template -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 (ab) + 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 -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 +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 +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 -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 +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 +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(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(c)) \ + inherited::print(c, level); \ + else if (is_a(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(&OBJ)!=0) + +#define is_exactly_of_type(OBJ,TYPE) \ + ((OBJ).tinfo()==GiNaC::TINFO_##TYPE) + +#define is_ex_of_type(OBJ,TYPE) \ + (dynamic_cast((OBJ).bp)!=0) + +#define is_ex_exactly_of_type(OBJ,TYPE) \ + ((*(OBJ).bp).tinfo()==GiNaC::TINFO_##TYPE) + } // namespace GiNaC + #endif // ndef __GINAC_UTILS_H__