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__
32 #if defined(HAVE_SSTREAM)
34 #elif defined(HAVE_STRSTREAM)
37 #error Need either sstream or strstream
39 #include "assertion.h"
43 // This should be obsoleted once <sstream> is widely deployed.
45 std::string ToString(const T & t)
47 #if defined(HAVE_SSTREAM)
48 std::ostringstream buf;
49 buf << t << std::ends;
53 std::ostrstream(buf,sizeof(buf)) << t << std::ends;
58 /** Exception class thrown by classes which provide their own series expansion
59 * to signal that ordinary Taylor expansion is safe. */
62 /** Exception class thrown when a singularity is encountered. */
63 class pole_error : public std::domain_error {
65 explicit pole_error(const std::string& what_arg, int degree);
66 int degree(void) const;
71 // some compilers (e.g. cygwin) define a macro log2, causing confusion
73 unsigned log2(unsigned n);
76 /** Compare two pointers (just to establish some sort of canonical order).
77 * @return -1, 0, or 1 */
78 inline int compare_pointers(const void * a, const void * b)
87 /** Rotate lower 31 bits of unsigned value by one bit to the left
88 * (upper bit gets cleared). */
89 inline unsigned rotate_left_31(unsigned n)
91 // clear highest bit and shift 1 bit to the left
92 n = (n & 0x7FFFFFFFU) << 1;
94 // overflow? clear highest bit and set lowest bit
96 n = (n & 0x7FFFFFFFU) | 0x00000001U;
98 GINAC_ASSERT(n<0x80000000U);
103 /** Golden ratio hash function for the 31 least significant bits. */
104 inline unsigned golden_ratio_hash(unsigned n)
106 // This function requires arithmetic with at least 64 significant bits
108 // So 'long' has 64 bits. Excellent! We prefer it because it might be
109 // more efficient than 'long long'.
110 unsigned long l = n * 0x4f1bbcddL;
111 return (l & 0x7fffffffU) ^ (l >> 32);
112 #elif SIZEOF_LONG_LONG >= 8
113 // This requires 'long long' (or an equivalent 64 bit type)---which is,
114 // unfortunately, not ANSI-C++-compliant.
115 // (Yet C99 demands it, which is reason for hope.)
116 unsigned long long l = n * 0x4f1bbcddL;
117 return (l & 0x7fffffffU) ^ (l >> 32);
118 #elif SIZEOF_LONG_DOUBLE > 8
119 // If 'long double' is bigger than 64 bits, we assume that the mantissa
120 // has at least 64 bits. This is not guaranteed but it's a good guess.
121 // Unfortunately, it may lead to horribly slow code.
122 const static long double golden_ratio = .618033988749894848204586834370;
123 long double m = golden_ratio * n;
124 return unsigned((m - int(m)) * 0x80000000);
126 #error "No 64 bit data type. You lose."
130 /* Compute the sign of a permutation of a container, with and without an
131 explicitly supplied comparison function. If the sign returned is 1 or -1,
132 the container is sorted after the operation. */
134 int permutation_sign(It first, It last)
145 It i = last, other = last;
147 bool swapped = false;
150 std::iter_swap(other, i);
154 } else if (!(*other < *i))
164 i = first; other = first;
169 std::iter_swap(i, other);
173 } else if (!(*i < *other))
181 } while (first != last);
186 template <class It, class Cmp>
187 int permutation_sign(It first, It last, Cmp comp)
198 It i = last, other = last;
200 bool swapped = false;
202 if (comp(*i, *other)) {
203 std::iter_swap(other, i);
207 } else if (!comp(*other, *i))
217 i = first; other = first;
221 if (comp(*other, *i)) {
222 std::iter_swap(i, other);
226 } else if (!comp(*i, *other))
234 } while (first != last);
239 /* Implementation of shaker sort, only compares adjacent elements. */
240 template <class It, class Cmp>
241 void shaker_sort(It first, It last, Cmp comp)
251 It i = last, other = last;
253 bool swapped = false;
255 if (comp(*i, *other)) {
256 std::iter_swap(other, i);
268 i = first; other = first;
272 if (comp(*other, *i)) {
273 std::iter_swap(i, other);
283 } while (first != last);
286 /* In-place cyclic permutation of a container (no copying, only swapping). */
288 void cyclic_permutation(It first, It last, It new_first)
290 unsigned num = last - first;
292 if (first == new_first || num < 2)
295 unsigned num1 = new_first - first, num2 = last - new_first;
297 It a = first, b = new_first;
299 std::iter_swap(a, b);
308 It a = new_first, b = last;
311 std::iter_swap(a, b);
312 } while (a != first);
319 /* Function objects for STL sort() etc. */
320 struct ex_is_less : public std::binary_function<ex, ex, bool> {
321 bool operator() (const ex &lh, const ex &rh) const { return lh.compare(rh) < 0; }
324 struct ex_is_equal : public std::binary_function<ex, ex, bool> {
325 bool operator() (const ex &lh, const ex &rh) const { return lh.is_equal(rh); }
328 // Collection of `construct on first use' wrappers for safely avoiding
329 // internal object replication without running into the `static
330 // initialization order fiasco'. This chest of numbers helps speed up
331 // the library but should not be used outside it since it is
332 // potentially confusing.
337 const numeric & _num_120(void); // -120
338 const ex & _ex_120(void);
339 const numeric & _num_60(void); // -60
340 const ex & _ex_60(void);
341 const numeric & _num_48(void); // -48
342 const ex & _ex_48(void);
343 const numeric & _num_30(void); // -30
344 const ex & _ex_30(void);
345 const numeric & _num_25(void); // -25
346 const ex & _ex_25(void);
347 const numeric & _num_24(void); // -24
348 const ex & _ex_24(void);
349 const numeric & _num_20(void); // -20
350 const ex & _ex_20(void);
351 const numeric & _num_18(void); // -18
352 const ex & _ex_18(void);
353 const numeric & _num_15(void); // -15
354 const ex & _ex_15(void);
355 const numeric & _num_12(void); // -12
356 const ex & _ex_12(void);
357 const numeric & _num_11(void); // -11
358 const ex & _ex_11(void);
359 const numeric & _num_10(void); // -10
360 const ex & _ex_10(void);
361 const numeric & _num_9(void); // -9
362 const ex & _ex_9(void);
363 const numeric & _num_8(void); // -8
364 const ex & _ex_8(void);
365 const numeric & _num_7(void); // -7
366 const ex & _ex_7(void);
367 const numeric & _num_6(void); // -6
368 const ex & _ex_6(void);
369 const numeric & _num_5(void); // -5
370 const ex & _ex_5(void);
371 const numeric & _num_4(void); // -4
372 const ex & _ex_4(void);
373 const numeric & _num_3(void); // -3
374 const ex & _ex_3(void);
375 const numeric & _num_2(void); // -2
376 const ex & _ex_2(void);
377 const numeric & _num_1(void); // -1
378 const ex & _ex_1(void);
379 const numeric & _num_1_2(void); // -1/2
380 const ex & _ex_1_2(void);
381 const numeric & _num_1_3(void); // -1/3
382 const ex & _ex_1_3(void);
383 const numeric & _num_1_4(void); // -1/4
384 const ex & _ex_1_4(void);
385 const numeric & _num0(void); // 0
386 const ex & _ex0(void);
387 const numeric & _num1_4(void); // 1/4
388 const ex & _ex1_4(void);
389 const numeric & _num1_3(void); // 1/3
390 const ex & _ex1_3(void);
391 const numeric & _num1_2(void); // 1/2
392 const ex & _ex1_2(void);
393 const numeric & _num1(void); // 1
394 const ex & _ex1(void);
395 const numeric & _num2(void); // 2
396 const ex & _ex2(void);
397 const numeric & _num3(void); // 3
398 const ex & _ex3(void);
399 const numeric & _num4(void); // 4
400 const ex & _ex4(void);
401 const numeric & _num5(void); // 5
402 const ex & _ex5(void);
403 const numeric & _num6(void); // 6
404 const ex & _ex6(void);
405 const numeric & _num7(void); // 7
406 const ex & _ex7(void);
407 const numeric & _num8(void); // 8
408 const ex & _ex8(void);
409 const numeric & _num9(void); // 9
410 const ex & _ex9(void);
411 const numeric & _num10(void); // 10
412 const ex & _ex10(void);
413 const numeric & _num11(void); // 11
414 const ex & _ex11(void);
415 const numeric & _num12(void); // 12
416 const ex & _ex12(void);
417 const numeric & _num15(void); // 15
418 const ex & _ex15(void);
419 const numeric & _num18(void); // 18
420 const ex & _ex18(void);
421 const numeric & _num20(void); // 20
422 const ex & _ex20(void);
423 const numeric & _num24(void); // 24
424 const ex & _ex24(void);
425 const numeric & _num25(void); // 25
426 const ex & _ex25(void);
427 const numeric & _num30(void); // 30
428 const ex & _ex30(void);
429 const numeric & _num48(void); // 48
430 const ex & _ex48(void);
431 const numeric & _num60(void); // 60
432 const ex & _ex60(void);
433 const numeric & _num120(void); // 120
434 const ex & _ex120(void);
437 // Helper macros for class implementations (mostly useful for trivial classes)
439 #define DEFAULT_COPY(classname) \
440 void classname::copy(const classname & other) \
442 inherited::copy(other); \
445 #define DEFAULT_DESTROY(classname) \
446 void classname::destroy(bool call_parent) \
449 inherited::destroy(call_parent); \
452 #define DEFAULT_CTORS(classname) \
453 classname::classname() : inherited(TINFO_##classname) \
455 debugmsg(#classname " default constructor", LOGLEVEL_CONSTRUCT); \
457 DEFAULT_COPY(classname) \
458 DEFAULT_DESTROY(classname)
460 #define DEFAULT_UNARCHIVE(classname) \
461 ex classname::unarchive(const archive_node &n, const lst &sym_lst) \
463 return (new classname(n, sym_lst))->setflag(status_flags::dynallocated); \
466 #define DEFAULT_ARCHIVING(classname) \
467 classname::classname(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) \
469 debugmsg(#classname " constructor from archive_node", LOGLEVEL_CONSTRUCT); \
471 DEFAULT_UNARCHIVE(classname) \
472 void classname::archive(archive_node &n) const \
474 inherited::archive(n); \
477 #define DEFAULT_COMPARE(classname) \
478 int classname::compare_same_type(const basic & other) const \
480 /* by default, the objects are always identical */ \
484 #define DEFAULT_PRINT(classname, text) \
485 void classname::print(const print_context & c, unsigned level) const \
487 debugmsg(#classname " print", LOGLEVEL_PRINT); \
488 if (is_of_type(c, print_tree)) \
489 inherited::print(c, level); \
494 #define DEFAULT_PRINT_LATEX(classname, text, latex) \
495 void classname::print(const print_context & c, unsigned level) const \
497 debugmsg(#classname " print", LOGLEVEL_PRINT); \
498 if (is_of_type(c, print_tree)) \
499 inherited::print(c, level); \
500 else if (is_of_type(c, print_latex)) \
508 #endif // ndef __GINAC_UTILS_H__