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 inline int permutation_sign(It first, It last)
145 It i = last, other = last;
147 bool swapped = false;
154 } else if (!(*other < *i))
164 i = first; other = first;
173 } else if (!(*i < *other))
181 } while (first != last);
186 template <class It, class Cmp>
187 inline int permutation_sign(It first, It last, Cmp comp)
198 It i = last, other = last;
200 bool swapped = false;
202 if (comp(*i, *other)) {
207 } else if (!comp(*other, *i))
217 i = first; other = first;
221 if (comp(*other, *i)) {
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 inline void shaker_sort(It first, It last, Cmp comp)
251 It i = last, other = last;
253 bool swapped = false;
255 if (comp(*i, *other)) {
268 i = first; other = first;
272 if (comp(*other, *i)) {
283 } while (first != last);
286 /* Function objects for STL sort() etc. */
287 struct ex_is_less : public binary_function<ex, ex, bool> {
288 bool operator() (const ex &lh, const ex &rh) const { return lh.compare(rh) < 0; }
291 struct ex_is_equal : public binary_function<ex, ex, bool> {
292 bool operator() (const ex &lh, const ex &rh) const { return lh.is_equal(rh); }
295 // Collection of `construct on first use' wrappers for safely avoiding
296 // internal object replication without running into the `static
297 // initialization order fiasco'. This chest of numbers helps speed up
298 // the library but should not be used outside it since it is
299 // potentially confusing.
304 const numeric & _num_120(void); // -120
305 const ex & _ex_120(void);
306 const numeric & _num_60(void); // -60
307 const ex & _ex_60(void);
308 const numeric & _num_48(void); // -48
309 const ex & _ex_48(void);
310 const numeric & _num_30(void); // -30
311 const ex & _ex_30(void);
312 const numeric & _num_25(void); // -25
313 const ex & _ex_25(void);
314 const numeric & _num_24(void); // -24
315 const ex & _ex_24(void);
316 const numeric & _num_20(void); // -20
317 const ex & _ex_20(void);
318 const numeric & _num_18(void); // -18
319 const ex & _ex_18(void);
320 const numeric & _num_15(void); // -15
321 const ex & _ex_15(void);
322 const numeric & _num_12(void); // -12
323 const ex & _ex_12(void);
324 const numeric & _num_11(void); // -11
325 const ex & _ex_11(void);
326 const numeric & _num_10(void); // -10
327 const ex & _ex_10(void);
328 const numeric & _num_9(void); // -9
329 const ex & _ex_9(void);
330 const numeric & _num_8(void); // -8
331 const ex & _ex_8(void);
332 const numeric & _num_7(void); // -7
333 const ex & _ex_7(void);
334 const numeric & _num_6(void); // -6
335 const ex & _ex_6(void);
336 const numeric & _num_5(void); // -5
337 const ex & _ex_5(void);
338 const numeric & _num_4(void); // -4
339 const ex & _ex_4(void);
340 const numeric & _num_3(void); // -3
341 const ex & _ex_3(void);
342 const numeric & _num_2(void); // -2
343 const ex & _ex_2(void);
344 const numeric & _num_1(void); // -1
345 const ex & _ex_1(void);
346 const numeric & _num_1_2(void); // -1/2
347 const ex & _ex_1_2(void);
348 const numeric & _num_1_3(void); // -1/3
349 const ex & _ex_1_3(void);
350 const numeric & _num_1_4(void); // -1/4
351 const ex & _ex_1_4(void);
352 const numeric & _num0(void); // 0
353 const ex & _ex0(void);
354 const numeric & _num1_4(void); // 1/4
355 const ex & _ex1_4(void);
356 const numeric & _num1_3(void); // 1/3
357 const ex & _ex1_3(void);
358 const numeric & _num1_2(void); // 1/2
359 const ex & _ex1_2(void);
360 const numeric & _num1(void); // 1
361 const ex & _ex1(void);
362 const numeric & _num2(void); // 2
363 const ex & _ex2(void);
364 const numeric & _num3(void); // 3
365 const ex & _ex3(void);
366 const numeric & _num4(void); // 4
367 const ex & _ex4(void);
368 const numeric & _num5(void); // 5
369 const ex & _ex5(void);
370 const numeric & _num6(void); // 6
371 const ex & _ex6(void);
372 const numeric & _num7(void); // 7
373 const ex & _ex7(void);
374 const numeric & _num8(void); // 8
375 const ex & _ex8(void);
376 const numeric & _num9(void); // 9
377 const ex & _ex9(void);
378 const numeric & _num10(void); // 10
379 const ex & _ex10(void);
380 const numeric & _num11(void); // 11
381 const ex & _ex11(void);
382 const numeric & _num12(void); // 12
383 const ex & _ex12(void);
384 const numeric & _num15(void); // 15
385 const ex & _ex15(void);
386 const numeric & _num18(void); // 18
387 const ex & _ex18(void);
388 const numeric & _num20(void); // 20
389 const ex & _ex20(void);
390 const numeric & _num24(void); // 24
391 const ex & _ex24(void);
392 const numeric & _num25(void); // 25
393 const ex & _ex25(void);
394 const numeric & _num30(void); // 30
395 const ex & _ex30(void);
396 const numeric & _num48(void); // 48
397 const ex & _ex48(void);
398 const numeric & _num60(void); // 60
399 const ex & _ex60(void);
400 const numeric & _num120(void); // 120
401 const ex & _ex120(void);
404 // Helper macros for class implementations (mostly useful for trivial classes)
406 #define DEFAULT_COPY(classname) \
407 void classname::copy(const classname & other) \
409 inherited::copy(other); \
412 #define DEFAULT_DESTROY(classname) \
413 void classname::destroy(bool call_parent) \
416 inherited::destroy(call_parent); \
419 #define DEFAULT_CTORS(classname) \
420 classname::classname() : inherited(TINFO_##classname) \
422 debugmsg(#classname " default constructor", LOGLEVEL_CONSTRUCT); \
424 DEFAULT_COPY(classname) \
425 DEFAULT_DESTROY(classname)
427 #define DEFAULT_UNARCHIVE(classname) \
428 ex classname::unarchive(const archive_node &n, const lst &sym_lst) \
430 return (new classname(n, sym_lst))->setflag(status_flags::dynallocated); \
433 #define DEFAULT_ARCHIVING(classname) \
434 classname::classname(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) \
436 debugmsg(#classname " constructor from archive_node", LOGLEVEL_CONSTRUCT); \
438 DEFAULT_UNARCHIVE(classname) \
439 void classname::archive(archive_node &n) const \
441 inherited::archive(n); \
444 #define DEFAULT_COMPARE(classname) \
445 int classname::compare_same_type(const basic & other) const \
447 /* by default, the objects are always identical */ \
451 #define DEFAULT_PRINT(classname, text) \
452 void classname::print(const print_context & c, unsigned level) const \
454 debugmsg(#classname " print", LOGLEVEL_PRINT); \
455 if (is_of_type(c, print_tree)) \
456 inherited::print(c, level); \
461 #define DEFAULT_PRINT_LATEX(classname, text, latex) \
462 void classname::print(const print_context & c, unsigned level) const \
464 debugmsg(#classname " print", LOGLEVEL_PRINT); \
465 if (is_of_type(c, print_tree)) \
466 inherited::print(c, level); \
467 else if (is_of_type(c, print_latex)) \
475 #endif // ndef __GINAC_UTILS_H__