3 * Interface to several small and furry utilities needed within GiNaC but not
4 * of any interest to the user of the library. */
7 * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
9 * This program is free software; you can redistribute it and/or modify
10 * it under the terms of the GNU General Public License as published by
11 * the Free Software Foundation; either version 2 of the License, or
12 * (at your option) any later version.
14 * This program is distributed in the hope that it will be useful,
15 * but WITHOUT ANY WARRANTY; without even the implied warranty of
16 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
17 * GNU General Public License for more details.
19 * You should have received a copy of the GNU General Public License
20 * along with this program; if not, write to the Free Software
21 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
24 #ifndef __GINAC_UTILS_H__
25 #define __GINAC_UTILS_H__
31 #include "assertion.h"
35 /** Exception class thrown by classes which provide their own series expansion
36 * to signal that ordinary Taylor expansion is safe. */
39 /** Exception class thrown by functions to signal unimplemented functionality
40 * so the expression may just be .hold() */
43 /** Exception class thrown when a singularity is encountered. */
44 class pole_error : public std::domain_error {
46 explicit pole_error(const std::string& what_arg, int degree);
47 int degree(void) const;
52 // some compilers (e.g. cygwin) define a macro log2, causing confusion
54 unsigned log2(unsigned n);
57 /** Compare two pointers (just to establish some sort of canonical order).
58 * @return -1, 0, or 1 */
59 inline int compare_pointers(const void * a, const void * b)
68 /** Rotate lower 31 bits of unsigned value by one bit to the left
69 * (upper bit gets cleared). */
70 inline unsigned rotate_left_31(unsigned n)
72 // clear highest bit and shift 1 bit to the left
73 n = (n & 0x7FFFFFFFU) << 1;
75 // overflow? clear highest bit and set lowest bit
77 n = (n & 0x7FFFFFFFU) | 0x00000001U;
79 GINAC_ASSERT(n<0x80000000U);
84 /** Golden ratio hash function for the 31 least significant bits. */
85 inline unsigned golden_ratio_hash(unsigned n)
87 // This function requires arithmetic with at least 64 significant bits
89 // So 'long' has 64 bits. Excellent! We prefer it because it might be
90 // more efficient than 'long long'.
91 unsigned long l = n * 0x4f1bbcddL;
92 return (l & 0x7fffffffU) ^ (l >> 32);
93 #elif SIZEOF_LONG_LONG >= 8
94 // This requires 'long long' (or an equivalent 64 bit type)---which is,
95 // unfortunately, not ANSI-C++-compliant.
96 // (Yet C99 demands it, which is reason for hope.)
97 unsigned long long l = n * 0x4f1bbcddL;
98 return (l & 0x7fffffffU) ^ (l >> 32);
99 #elif SIZEOF_LONG_DOUBLE > 8
100 // If 'long double' is bigger than 64 bits, we assume that the mantissa
101 // has at least 64 bits. This is not guaranteed but it's a good guess.
102 // Unfortunately, it may lead to horribly slow code.
103 const static long double golden_ratio = .618033988749894848204586834370;
104 long double m = golden_ratio * n;
105 return unsigned((m - int(m)) * 0x80000000);
107 #error "No 64 bit data type. You lose."
111 /* Compute the sign of a permutation of a container, with and without an
112 explicitly supplied comparison function. If the sign returned is 1 or -1,
113 the container is sorted after the operation. */
115 int permutation_sign(It first, It last)
126 It i = last, other = last;
128 bool swapped = false;
131 std::iter_swap(other, i);
135 } else if (!(*other < *i))
145 i = first; other = first;
150 std::iter_swap(i, other);
154 } else if (!(*i < *other))
162 } while (first != last);
167 template <class It, class Cmp, class Swap>
168 int permutation_sign(It first, It last, Cmp comp, Swap swapit)
179 It i = last, other = last;
181 bool swapped = false;
183 if (comp(*i, *other)) {
188 } else if (!comp(*other, *i))
198 i = first; other = first;
202 if (comp(*other, *i)) {
207 } else if (!comp(*i, *other))
215 } while (first != last);
220 /* Implementation of shaker sort, only compares adjacent elements. */
221 template <class It, class Cmp, class Swap>
222 void shaker_sort(It first, It last, Cmp comp, Swap swapit)
232 It i = last, other = last;
234 bool swapped = false;
236 if (comp(*i, *other)) {
249 i = first; other = first;
253 if (comp(*other, *i)) {
264 } while (first != last);
267 /* In-place cyclic permutation of a container (no copying, only swapping). */
268 template <class It, class Swap>
269 void cyclic_permutation(It first, It last, It new_first, Swap swapit)
271 unsigned num = last - first;
273 if (first == new_first || num < 2)
276 unsigned num1 = new_first - first, num2 = last - new_first;
278 It a = first, b = new_first;
289 It a = new_first, b = last;
293 } while (a != first);
301 // Collection of `construct on first use' wrappers for safely avoiding
302 // internal object replication without running into the `static
303 // initialization order fiasco'. This chest of numbers helps speed up
304 // the library but should not be used outside it since it is
305 // potentially confusing.
310 const numeric & _num_120(void); // -120
311 const ex & _ex_120(void);
312 const numeric & _num_60(void); // -60
313 const ex & _ex_60(void);
314 const numeric & _num_48(void); // -48
315 const ex & _ex_48(void);
316 const numeric & _num_30(void); // -30
317 const ex & _ex_30(void);
318 const numeric & _num_25(void); // -25
319 const ex & _ex_25(void);
320 const numeric & _num_24(void); // -24
321 const ex & _ex_24(void);
322 const numeric & _num_20(void); // -20
323 const ex & _ex_20(void);
324 const numeric & _num_18(void); // -18
325 const ex & _ex_18(void);
326 const numeric & _num_15(void); // -15
327 const ex & _ex_15(void);
328 const numeric & _num_12(void); // -12
329 const ex & _ex_12(void);
330 const numeric & _num_11(void); // -11
331 const ex & _ex_11(void);
332 const numeric & _num_10(void); // -10
333 const ex & _ex_10(void);
334 const numeric & _num_9(void); // -9
335 const ex & _ex_9(void);
336 const numeric & _num_8(void); // -8
337 const ex & _ex_8(void);
338 const numeric & _num_7(void); // -7
339 const ex & _ex_7(void);
340 const numeric & _num_6(void); // -6
341 const ex & _ex_6(void);
342 const numeric & _num_5(void); // -5
343 const ex & _ex_5(void);
344 const numeric & _num_4(void); // -4
345 const ex & _ex_4(void);
346 const numeric & _num_3(void); // -3
347 const ex & _ex_3(void);
348 const numeric & _num_2(void); // -2
349 const ex & _ex_2(void);
350 const numeric & _num_1(void); // -1
351 const ex & _ex_1(void);
352 const numeric & _num_1_2(void); // -1/2
353 const ex & _ex_1_2(void);
354 const numeric & _num_1_3(void); // -1/3
355 const ex & _ex_1_3(void);
356 const numeric & _num_1_4(void); // -1/4
357 const ex & _ex_1_4(void);
358 const numeric & _num0(void); // 0
359 const ex & _ex0(void);
360 const numeric & _num1_4(void); // 1/4
361 const ex & _ex1_4(void);
362 const numeric & _num1_3(void); // 1/3
363 const ex & _ex1_3(void);
364 const numeric & _num1_2(void); // 1/2
365 const ex & _ex1_2(void);
366 const numeric & _num1(void); // 1
367 const ex & _ex1(void);
368 const numeric & _num2(void); // 2
369 const ex & _ex2(void);
370 const numeric & _num3(void); // 3
371 const ex & _ex3(void);
372 const numeric & _num4(void); // 4
373 const ex & _ex4(void);
374 const numeric & _num5(void); // 5
375 const ex & _ex5(void);
376 const numeric & _num6(void); // 6
377 const ex & _ex6(void);
378 const numeric & _num7(void); // 7
379 const ex & _ex7(void);
380 const numeric & _num8(void); // 8
381 const ex & _ex8(void);
382 const numeric & _num9(void); // 9
383 const ex & _ex9(void);
384 const numeric & _num10(void); // 10
385 const ex & _ex10(void);
386 const numeric & _num11(void); // 11
387 const ex & _ex11(void);
388 const numeric & _num12(void); // 12
389 const ex & _ex12(void);
390 const numeric & _num15(void); // 15
391 const ex & _ex15(void);
392 const numeric & _num18(void); // 18
393 const ex & _ex18(void);
394 const numeric & _num20(void); // 20
395 const ex & _ex20(void);
396 const numeric & _num24(void); // 24
397 const ex & _ex24(void);
398 const numeric & _num25(void); // 25
399 const ex & _ex25(void);
400 const numeric & _num30(void); // 30
401 const ex & _ex30(void);
402 const numeric & _num48(void); // 48
403 const ex & _ex48(void);
404 const numeric & _num60(void); // 60
405 const ex & _ex60(void);
406 const numeric & _num120(void); // 120
407 const ex & _ex120(void);
410 // Helper macros for class implementations (mostly useful for trivial classes)
412 #define DEFAULT_COPY(classname) \
413 void classname::copy(const classname & other) \
415 inherited::copy(other); \
418 #define DEFAULT_DESTROY(classname) \
419 void classname::destroy(bool call_parent) \
422 inherited::destroy(call_parent); \
425 #define DEFAULT_CTORS(classname) \
426 classname::classname() : inherited(TINFO_##classname) \
428 debugmsg(#classname " default constructor", LOGLEVEL_CONSTRUCT); \
430 DEFAULT_COPY(classname) \
431 DEFAULT_DESTROY(classname)
433 #define DEFAULT_UNARCHIVE(classname) \
434 ex classname::unarchive(const archive_node &n, const lst &sym_lst) \
436 return (new classname(n, sym_lst))->setflag(status_flags::dynallocated); \
439 #define DEFAULT_ARCHIVING(classname) \
440 classname::classname(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) \
442 debugmsg(#classname " constructor from archive_node", LOGLEVEL_CONSTRUCT); \
444 DEFAULT_UNARCHIVE(classname) \
445 void classname::archive(archive_node &n) const \
447 inherited::archive(n); \
450 #define DEFAULT_COMPARE(classname) \
451 int classname::compare_same_type(const basic & other) const \
453 /* by default, the objects are always identical */ \
457 #define DEFAULT_PRINT(classname, text) \
458 void classname::print(const print_context & c, unsigned level) const \
460 debugmsg(#classname " print", LOGLEVEL_PRINT); \
461 if (is_a<print_tree>(c)) \
462 inherited::print(c, level); \
467 #define DEFAULT_PRINT_LATEX(classname, text, latex) \
468 void classname::print(const print_context & c, unsigned level) const \
470 debugmsg(#classname " print", LOGLEVEL_PRINT); \
471 if (is_a<print_tree>(c)) \
472 inherited::print(c, level); \
473 else if (is_a<print_latex>(c)) \
479 // Obsolete convenience macros. TO BE PHASED OUT SOON!
480 // Use the inlined template functions in basic.h instead. (FIXME: remove them)
482 #define is_of_type(OBJ,TYPE) \
483 (dynamic_cast<const TYPE *>(&OBJ)!=0)
485 #define is_exactly_of_type(OBJ,TYPE) \
486 ((OBJ).tinfo()==GiNaC::TINFO_##TYPE)
488 #define is_ex_of_type(OBJ,TYPE) \
489 (dynamic_cast<const TYPE *>((OBJ).bp)!=0)
491 #define is_ex_exactly_of_type(OBJ,TYPE) \
492 ((*(OBJ).bp).tinfo()==GiNaC::TINFO_##TYPE)
497 #endif // ndef __GINAC_UTILS_H__