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) 1999-2017 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
27 #include "assertion.h"
30 #include <cstdint> // for uintptr_t
35 /** Exception class thrown by functions to signal unimplemented functionality
36 * so the expression may just be .hold() */
39 // some compilers (e.g. cygwin) define a macro log2, causing confusion
44 unsigned log2(unsigned n);
46 /** Rotate bits of unsigned value by one bit to the left.
47 * This can be necessary if the user wants to define its own hashes. */
48 inline unsigned rotate_left(unsigned n)
50 return (n & 0x80000000U) ? (n << 1 | 0x00000001U) : (n << 1);
53 /** Compare two pointers (just to establish some sort of canonical order).
54 * @return -1, 0, or 1 */
56 inline int compare_pointers(const T * a, const T * b)
58 // '<' is not defined for pointers that don't point to the same array,
60 if (std::less<const T *>()(a, b))
62 else if (std::less<const T *>()(b, a))
67 /** Truncated multiplication with golden ratio, for computing hash values. */
68 inline unsigned golden_ratio_hash(uintptr_t n)
70 return n * UINT64_C(0x4f1bbcdd);
73 /* Compute the sign of a permutation of a container, with and without an
74 explicitly supplied comparison function. If the sign returned is 1 or -1,
75 the container is sorted after the operation. */
77 int permutation_sign(It first, It last)
89 It i = last, other = last;
98 } else if (!(*other < *i))
110 i = first; other = first;
119 } else if (!(*i < *other))
129 } while (first != last);
134 template <class It, class Cmp, class Swap>
135 int permutation_sign(It first, It last, Cmp comp, Swap swapit)
146 It i = last, other = last;
148 bool swapped = false;
150 if (comp(*i, *other)) {
155 } else if (!comp(*other, *i))
167 i = first; other = first;
171 if (comp(*other, *i)) {
176 } else if (!comp(*i, *other))
186 } while (first != last);
191 /* Implementation of shaker sort, only compares adjacent elements. */
192 template <class It, class Cmp, class Swap>
193 void shaker_sort(It first, It last, Cmp comp, Swap swapit)
203 It i = last, other = last;
205 bool swapped = false;
207 if (comp(*i, *other)) {
222 i = first; other = first;
226 if (comp(*other, *i)) {
239 } while (first != last);
242 /* In-place cyclic permutation of a container (no copying, only swapping). */
243 template <class It, class Swap>
244 void cyclic_permutation(It first, It last, It new_first, Swap swapit)
246 unsigned num = last - first;
248 if (first == new_first || num < 2)
251 unsigned num1 = new_first - first, num2 = last - new_first;
253 It a = first, b = new_first;
264 It a = new_first, b = last;
268 } while (a != first);
275 /** Generate all bounded combinatorial partitions of an integer n with exactly
276 * m parts (including zero parts) in non-decreasing order.
278 class partition_generator {
280 // Partitions n into m parts, not including zero parts.
281 // (Cf. OEIS sequence A008284; implementation adapted from Jörg Arndt's
285 // partition: x[1] + x[2] + ... + x[m] = n and sentinel x[0] == 0
289 mpartition2(unsigned n_, unsigned m_)
290 : x(m_+1), n(n_), m(m_)
292 for (int k=1; k<m; ++k)
296 bool next_partition()
298 int u = x[m]; // last element
307 return false; // current is last
318 int m; // number of parts 0<m<=n
319 mutable std::vector<int> partition; // current partition
321 partition_generator(unsigned n_, unsigned m_)
322 : mpgen(n_, 1), m(m_), partition(m_)
324 // returns current partition in non-decreasing order, padded with zeros
325 const std::vector<int>& current() const
327 for (int i = 0; i < m - mpgen.m; ++i)
328 partition[i] = 0; // pad with zeros
330 for (int i = m - mpgen.m; i < m; ++i)
331 partition[i] = mpgen.x[i - m + mpgen.m + 1];
337 if (!mpgen.next_partition()) {
338 if (mpgen.m == m || mpgen.m == mpgen.n)
339 return false; // current is last
340 // increment number of parts
341 mpgen = mpartition2(mpgen.n, mpgen.m + 1);
347 /** Generate all compositions of a partition of an integer n, starting with the
348 * compositions which has non-decreasing order.
350 class composition_generator {
352 // Generates all distinct permutations of a multiset.
353 // (Based on Aaron Williams' algorithm 1 from "Loopless Generation of
354 // Multiset Permutations using a Constant Number of Variables by Prefix
355 // Shifts." <http://webhome.csc.uvic.ca/~haron/CoolMulti.pdf>)
357 // element of singly linked list
361 element(int val, element* n)
362 : value(val), next(n) {}
364 { // recurses down to the end of the singly linked list
368 element *head, *i, *after_i;
369 // NB: Partition must be sorted in non-decreasing order.
370 explicit coolmulti(const std::vector<int>& partition)
371 : head(nullptr), i(nullptr), after_i(nullptr)
373 for (unsigned n = 0; n < partition.size(); ++n) {
374 head = new element(partition[n], head);
381 { // deletes singly linked list
384 void next_permutation()
387 if (after_i->next != nullptr && i->value >= after_i->next->value)
391 element *k = before_k->next;
392 before_k->next = k->next;
394 if (k->value < head->value)
399 bool finished() const
401 return after_i->next == nullptr && after_i->value >= head->value;
404 bool atend; // needed for simplifying iteration over permutations
405 bool trivial; // likewise, true if all elements are equal
406 mutable std::vector<int> composition; // current compositions
408 explicit composition_generator(const std::vector<int>& partition)
409 : cmgen(partition), atend(false), trivial(true), composition(partition.size())
411 for (unsigned i=1; i<partition.size(); ++i)
412 trivial = trivial && (partition[0] == partition[i]);
414 const std::vector<int>& current() const
416 coolmulti::element* it = cmgen.head;
418 while (it != nullptr) {
419 composition[i] = it->value;
427 // This ugly contortion is needed because the original coolmulti
428 // algorithm requires code duplication of the payload procedure,
429 // one before the loop and one inside it.
430 if (trivial || atend)
432 cmgen.next_permutation();
433 atend = cmgen.finished();
438 /** Compute the multinomial coefficient n!/(p1!*p2!*...*pk!) where
439 * n = p1+p2+...+pk, i.e. p is a partition of n.
442 multinomial_coefficient(const std::vector<int> & p);
445 // Collection of `construct on first use' wrappers for safely avoiding
446 // internal object replication without running into the `static
447 // initialization order fiasco'. This chest of numbers helps speed up
448 // the library but should not be used outside it since it is
449 // potentially confusing.
453 extern const numeric *_num_120_p;
454 extern const ex _ex_120;
455 extern const numeric *_num_60_p;
456 extern const ex _ex_60;
457 extern const numeric *_num_48_p;
458 extern const ex _ex_48;
459 extern const numeric *_num_30_p;
460 extern const ex _ex_30;
461 extern const numeric *_num_25_p;
462 extern const ex _ex_25;
463 extern const numeric *_num_24_p;
464 extern const ex _ex_24;
465 extern const numeric *_num_20_p;
466 extern const ex _ex_20;
467 extern const numeric *_num_18_p;
468 extern const ex _ex_18;
469 extern const numeric *_num_15_p;
470 extern const ex _ex_15;
471 extern const numeric *_num_12_p;
472 extern const ex _ex_12;
473 extern const numeric *_num_11_p;
474 extern const ex _ex_11;
475 extern const numeric *_num_10_p;
476 extern const ex _ex_10;
477 extern const numeric *_num_9_p;
478 extern const ex _ex_9;
479 extern const numeric *_num_8_p;
480 extern const ex _ex_8;
481 extern const numeric *_num_7_p;
482 extern const ex _ex_7;
483 extern const numeric *_num_6_p;
484 extern const ex _ex_6;
485 extern const numeric *_num_5_p;
486 extern const ex _ex_5;
487 extern const numeric *_num_4_p;
488 extern const ex _ex_4;
489 extern const numeric *_num_3_p;
490 extern const ex _ex_3;
491 extern const numeric *_num_2_p;
492 extern const ex _ex_2;
493 extern const numeric *_num_1_p;
494 extern const ex _ex_1;
495 extern const numeric *_num_1_2_p;
496 extern const ex _ex_1_2;
497 extern const numeric *_num_1_3_p;
498 extern const ex _ex_1_3;
499 extern const numeric *_num_1_4_p;
500 extern const ex _ex_1_4;
501 extern const numeric *_num0_p;
502 extern const basic *_num0_bp;
503 extern const ex _ex0;
504 extern const numeric *_num1_4_p;
505 extern const ex _ex1_4;
506 extern const numeric *_num1_3_p;
507 extern const ex _ex1_3;
508 extern const numeric *_num1_2_p;
509 extern const ex _ex1_2;
510 extern const numeric *_num1_p;
511 extern const ex _ex1;
512 extern const numeric *_num2_p;
513 extern const ex _ex2;
514 extern const numeric *_num3_p;
515 extern const ex _ex3;
516 extern const numeric *_num4_p;
517 extern const ex _ex4;
518 extern const numeric *_num5_p;
519 extern const ex _ex5;
520 extern const numeric *_num6_p;
521 extern const ex _ex6;
522 extern const numeric *_num7_p;
523 extern const ex _ex7;
524 extern const numeric *_num8_p;
525 extern const ex _ex8;
526 extern const numeric *_num9_p;
527 extern const ex _ex9;
528 extern const numeric *_num10_p;
529 extern const ex _ex10;
530 extern const numeric *_num11_p;
531 extern const ex _ex11;
532 extern const numeric *_num12_p;
533 extern const ex _ex12;
534 extern const numeric *_num15_p;
535 extern const ex _ex15;
536 extern const numeric *_num18_p;
537 extern const ex _ex18;
538 extern const numeric *_num20_p;
539 extern const ex _ex20;
540 extern const numeric *_num24_p;
541 extern const ex _ex24;
542 extern const numeric *_num25_p;
543 extern const ex _ex25;
544 extern const numeric *_num30_p;
545 extern const ex _ex30;
546 extern const numeric *_num48_p;
547 extern const ex _ex48;
548 extern const numeric *_num60_p;
549 extern const ex _ex60;
550 extern const numeric *_num120_p;
551 extern const ex _ex120;
554 // Helper macros for class implementations (mostly useful for trivial classes)
556 #define DEFAULT_CTOR(classname) \
557 classname::classname() { setflag(status_flags::evaluated | status_flags::expanded); }
559 #define DEFAULT_COMPARE(classname) \
560 int classname::compare_same_type(const basic & other) const \
562 /* by default, the objects are always identical */ \
566 #define DEFAULT_PRINT(classname, text) \
567 void classname::do_print(const print_context & c, unsigned level) const \
572 #define DEFAULT_PRINT_LATEX(classname, text, latex) \
573 DEFAULT_PRINT(classname, text) \
574 void classname::do_print_latex(const print_latex & c, unsigned level) const \
581 #endif // ndef GINAC_UTILS_H