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) 1999-2002 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 extern const numeric *_num_120_p;
311 extern const numeric &_num_120;
312 extern const ex _ex_120;
313 extern const numeric *_num_60_p;
314 extern const numeric &_num_60;
315 extern const ex _ex_60;
316 extern const numeric *_num_48_p;
317 extern const numeric &_num_48;
318 extern const ex _ex_48;
319 extern const numeric *_num_30_p;
320 extern const numeric &_num_30;
321 extern const ex _ex_30;
322 extern const numeric *_num_25_p;
323 extern const numeric &_num_25;
324 extern const ex _ex_25;
325 extern const numeric *_num_24_p;
326 extern const numeric &_num_24;
327 extern const ex _ex_24;
328 extern const numeric *_num_20_p;
329 extern const numeric &_num_20;
330 extern const ex _ex_20;
331 extern const numeric *_num_18_p;
332 extern const numeric &_num_18;
333 extern const ex _ex_18;
334 extern const numeric *_num_15_p;
335 extern const numeric &_num_15;
336 extern const ex _ex_15;
337 extern const numeric *_num_12_p;
338 extern const numeric &_num_12;
339 extern const ex _ex_12;
340 extern const numeric *_num_11_p;
341 extern const numeric &_num_11;
342 extern const ex _ex_11;
343 extern const numeric *_num_10_p;
344 extern const numeric &_num_10;
345 extern const ex _ex_10;
346 extern const numeric *_num_9_p;
347 extern const numeric &_num_9;
348 extern const ex _ex_9;
349 extern const numeric *_num_8_p;
350 extern const numeric &_num_8;
351 extern const ex _ex_8;
352 extern const numeric *_num_7_p;
353 extern const numeric &_num_7;
354 extern const ex _ex_7;
355 extern const numeric *_num_6_p;
356 extern const numeric &_num_6;
357 extern const ex _ex_6;
358 extern const numeric *_num_5_p;
359 extern const numeric &_num_5;
360 extern const ex _ex_5;
361 extern const numeric *_num_4_p;
362 extern const numeric &_num_4;
363 extern const ex _ex_4;
364 extern const numeric *_num_3_p;
365 extern const numeric &_num_3;
366 extern const ex _ex_3;
367 extern const numeric *_num_2_p;
368 extern const numeric &_num_2;
369 extern const ex _ex_2;
370 extern const numeric *_num_1_p;
371 extern const numeric &_num_1;
372 extern const ex _ex_1;
373 extern const numeric *_num_1_2_p;
374 extern const numeric &_num_1_2;
375 extern const ex _ex_1_2;
376 extern const numeric *_num_1_3_p;
377 extern const numeric &_num_1_3;
378 extern const ex _ex_1_3;
379 extern const numeric *_num_1_4_p;
380 extern const numeric &_num_1_4;
381 extern const ex _ex_1_4;
382 extern const numeric *_num0_p;
383 extern const numeric &_num0;
384 extern const ex _ex0;
385 extern const numeric *_num1_4_p;
386 extern const numeric &_num1_4;
387 extern const ex _ex1_4;
388 extern const numeric *_num1_3_p;
389 extern const numeric &_num1_3;
390 extern const ex _ex1_3;
391 extern const numeric *_num1_2_p;
392 extern const numeric &_num1_2;
393 extern const ex _ex1_2;
394 extern const numeric *_num1_p;
395 extern const numeric &_num1;
396 extern const ex _ex1;
397 extern const numeric *_num2_p;
398 extern const numeric &_num2;
399 extern const ex _ex2;
400 extern const numeric *_num3_p;
401 extern const numeric &_num3;
402 extern const ex _ex3;
403 extern const numeric *_num4_p;
404 extern const numeric &_num4;
405 extern const ex _ex4;
406 extern const numeric *_num5_p;
407 extern const numeric &_num5;
408 extern const ex _ex5;
409 extern const numeric *_num6_p;
410 extern const numeric &_num6;
411 extern const ex _ex6;
412 extern const numeric *_num7_p;
413 extern const numeric &_num7;
414 extern const ex _ex7;
415 extern const numeric *_num8_p;
416 extern const numeric &_num8;
417 extern const ex _ex8;
418 extern const numeric *_num9_p;
419 extern const numeric &_num9;
420 extern const ex _ex9;
421 extern const numeric *_num10_p;
422 extern const numeric &_num10;
423 extern const ex _ex10;
424 extern const numeric *_num11_p;
425 extern const numeric &_num11;
426 extern const ex _ex11;
427 extern const numeric *_num12_p;
428 extern const numeric &_num12;
429 extern const ex _ex12;
430 extern const numeric *_num15_p;
431 extern const numeric &_num15;
432 extern const ex _ex15;
433 extern const numeric *_num18_p;
434 extern const numeric &_num18;
435 extern const ex _ex18;
436 extern const numeric *_num20_p;
437 extern const numeric &_num20;
438 extern const ex _ex20;
439 extern const numeric *_num24_p;
440 extern const numeric &_num24;
441 extern const ex _ex24;
442 extern const numeric *_num25_p;
443 extern const numeric &_num25;
444 extern const ex _ex25;
445 extern const numeric *_num30_p;
446 extern const numeric &_num30;
447 extern const ex _ex30;
448 extern const numeric *_num48_p;
449 extern const numeric &_num48;
450 extern const ex _ex48;
451 extern const numeric *_num60_p;
452 extern const numeric &_num60;
453 extern const ex _ex60;
454 extern const numeric *_num120_p;
455 extern const numeric &_num120;
456 extern const ex _ex120;
459 // Helper macros for class implementations (mostly useful for trivial classes)
461 #define DEFAULT_COPY(classname) \
462 void classname::copy(const classname & other) \
464 inherited::copy(other); \
467 #define DEFAULT_DESTROY(classname) \
468 void classname::destroy(bool call_parent) \
471 inherited::destroy(call_parent); \
474 #define DEFAULT_CTORS(classname) \
475 classname::classname() : inherited(TINFO_##classname) {} \
476 DEFAULT_COPY(classname) \
477 DEFAULT_DESTROY(classname)
479 #define DEFAULT_UNARCHIVE(classname) \
480 ex classname::unarchive(const archive_node &n, const lst &sym_lst) \
482 return (new classname(n, sym_lst))->setflag(status_flags::dynallocated); \
485 #define DEFAULT_ARCHIVING(classname) \
486 classname::classname(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) {} \
487 DEFAULT_UNARCHIVE(classname) \
488 void classname::archive(archive_node &n) const \
490 inherited::archive(n); \
493 #define DEFAULT_COMPARE(classname) \
494 int classname::compare_same_type(const basic & other) const \
496 /* by default, the objects are always identical */ \
500 #define DEFAULT_PRINT(classname, text) \
501 void classname::print(const print_context & c, unsigned level) const \
503 if (is_a<print_tree>(c)) \
504 inherited::print(c, level); \
509 #define DEFAULT_PRINT_LATEX(classname, text, latex) \
510 void classname::print(const print_context & c, unsigned level) const \
512 if (is_a<print_tree>(c)) \
513 inherited::print(c, level); \
514 else if (is_a<print_latex>(c)) \
523 #endif // ndef __GINAC_UTILS_H__