GiNaC: utils.h Source File

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00001 
00006 /*
00007  *  GiNaC Copyright (C) 1999-2010 Johannes Gutenberg University Mainz, Germany
00008  *
00009  *  This program is free software; you can redistribute it and/or modify
00010  *  it under the terms of the GNU General Public License as published by
00011  *  the Free Software Foundation; either version 2 of the License, or
00012  *  (at your option) any later version.
00013  *
00014  *  This program is distributed in the hope that it will be useful,
00015  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
00016  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
00017  *  GNU General Public License for more details.
00018  *
00019  *  You should have received a copy of the GNU General Public License
00020  *  along with this program; if not, write to the Free Software
00021  *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
00022  */
00023 
00024 #ifndef GINAC_UTILS_H
00025 #define GINAC_UTILS_H
00026 
00027 #include "assertion.h"
00028 #ifdef HAVE_CONFIG_H
00029 #include "config.h"
00030 #endif
00031 
00032 #include <functional>
00033 #ifdef HAVE_STDINT_H
00034 #include <stdint.h> // for uintptr_t
00035 #endif
00036 #include <string>
00037 
00038 namespace GiNaC {
00039 
00042 class dunno {};
00043 
00044 // some compilers (e.g. cygwin) define a macro log2, causing confusion
00045 #ifdef log2
00046 #undef log2
00047 #endif
00048 
00049 unsigned log2(unsigned n);
00050 
00053 inline unsigned rotate_left(unsigned n)
00054 {
00055     return (n & 0x80000000U) ? (n << 1 | 0x00000001U) : (n << 1);
00056 }
00057 
00060 template <class T>
00061 inline int compare_pointers(const T * a, const T * b)
00062 {
00063     // '<' is not defined for pointers that don't point to the same array,
00064     // but std::less is.
00065     if (std::less<const T *>()(a, b))
00066         return -1;
00067     else if (std::less<const T *>()(b, a))
00068         return 1;
00069     return 0;
00070 }
00071 
00072 #ifdef HAVE_STDINT_H
00073 typedef uintptr_t p_int;
00074 #else
00075 typedef unsigned long p_int;
00076 #endif
00077 
00079 inline unsigned golden_ratio_hash(p_int n)
00080 {
00081     // This function works much better when fast arithmetic with at
00082     // least 64 significant bits is available.
00083     if (sizeof(long) >= 8) {
00084     // So 'long' has 64 bits.  Excellent!  We prefer it because it might be
00085     // more efficient than 'long long'.
00086     unsigned long l = n * 0x4f1bbcddUL;
00087     return (unsigned)l;
00088     }
00089 #ifdef HAVE_LONG_LONG
00090     else if (sizeof(long long) >= 8) {
00091     // This requires 'long long' (or an equivalent 64 bit type)---which is,
00092     // unfortunately, not ANSI-C++-compliant.
00093     // (Yet C99 demands it, which is reason for hope.)
00094     unsigned long long l = n * 0x4f1bbcddULL;
00095     return (unsigned)l;
00096     }
00097 #endif
00098     // Without a type with 64 significant bits do the multiplication manually
00099     // by splitting n up into the lower and upper two bytes.
00100     const unsigned n0 = (n & 0x0000ffffU);
00101     const unsigned n1 = (n & 0xffff0000U) >> 16;
00102     return (n0 * 0x0000bcddU) + ((n1 * 0x0000bcddU + n0 * 0x00004f1bU) << 16);
00103 }
00104 
00105 /* Compute the sign of a permutation of a container, with and without an
00106    explicitly supplied comparison function. If the sign returned is 1 or -1,
00107    the container is sorted after the operation. */
00108 template <class It>
00109 int permutation_sign(It first, It last)
00110 {
00111     if (first == last)
00112         return 0;
00113     --last;
00114     if (first == last)
00115         return 0;
00116     It flag = first;
00117     int sign = 1;
00118 
00119     do {
00120         It i = last, other = last;
00121         --other;
00122         bool swapped = false;
00123         while (i != first) {
00124             if (*i < *other) {
00125                 std::iter_swap(other, i);
00126                 flag = other;
00127                 swapped = true;
00128                 sign = -sign;
00129             } else if (!(*other < *i))
00130                 return 0;
00131             --i;
00132             if (i != first)
00133                 --other;
00134         }
00135         if (!swapped)
00136             return sign;
00137         ++flag;
00138         if (flag == last)
00139             return sign;
00140         first = flag;
00141         i = first; other = first;
00142         ++other;
00143         swapped = false;
00144         while (i != last) {
00145             if (*other < *i) {
00146                 std::iter_swap(i, other);
00147                 flag = other;
00148                 swapped = true;
00149                 sign = -sign;
00150             } else if (!(*i < *other))
00151                 return 0;
00152             ++i;
00153             if (i != last)
00154                 ++other;
00155         }
00156         if (!swapped)
00157             return sign;
00158         last = flag;
00159         --last;
00160     } while (first != last);
00161 
00162     return sign;
00163 }
00164 
00165 template <class It, class Cmp, class Swap>
00166 int permutation_sign(It first, It last, Cmp comp, Swap swapit)
00167 {
00168     if (first == last)
00169         return 0;
00170     --last;
00171     if (first == last)
00172         return 0;
00173     It flag = first;
00174     int sign = 1;
00175 
00176     do {
00177         It i = last, other = last;
00178         --other;
00179         bool swapped = false;
00180         while (i != first) {
00181             if (comp(*i, *other)) {
00182                 swapit(*other, *i);
00183                 flag = other;
00184                 swapped = true;
00185                 sign = -sign;
00186             } else if (!comp(*other, *i))
00187                 return 0;
00188             --i;
00189             if (i != first)
00190                 --other;
00191         }
00192         if (!swapped)
00193             return sign;
00194         ++flag;
00195         if (flag == last)
00196             return sign;
00197         first = flag;
00198         i = first; other = first;
00199         ++other;
00200         swapped = false;
00201         while (i != last) {
00202             if (comp(*other, *i)) {
00203                 swapit(*i, *other);
00204                 flag = other;
00205                 swapped = true;
00206                 sign = -sign;
00207             } else if (!comp(*i, *other))
00208                 return 0;
00209             ++i; 
00210             if (i != last)
00211                 ++other;
00212         }
00213         if (!swapped)
00214             return sign;
00215         last = flag;
00216         --last;
00217     } while (first != last);
00218 
00219     return sign;
00220 }
00221 
00222 /* Implementation of shaker sort, only compares adjacent elements. */
00223 template <class It, class Cmp, class Swap>
00224 void shaker_sort(It first, It last, Cmp comp, Swap swapit)
00225 {
00226     if (first == last)
00227         return;
00228     --last;
00229     if (first == last)
00230         return;
00231     It flag = first;
00232 
00233     do {
00234         It i = last, other = last;
00235         --other;
00236         bool swapped = false;
00237         while (i != first) {
00238             if (comp(*i, *other)) {
00239                 swapit(*other, *i);
00240                 flag = other;
00241                 swapped = true;
00242             }
00243             --i;
00244             if (i != first)
00245                 --other;
00246         }
00247         if (!swapped)
00248             return;
00249         ++flag;
00250         if (flag == last)
00251             return;
00252         first = flag;
00253         i = first; other = first;
00254         ++other;
00255         swapped = false;
00256         while (i != last) {
00257             if (comp(*other, *i)) {
00258                 swapit(*i, *other);
00259                 flag = other;
00260                 swapped = true;
00261             }
00262             ++i;
00263             if (i != last)
00264                 ++other;
00265         }
00266         if (!swapped)
00267             return;
00268         last = flag;
00269         --last;
00270     } while (first != last);
00271 }
00272 
00273 /* In-place cyclic permutation of a container (no copying, only swapping). */
00274 template <class It, class Swap>
00275 void cyclic_permutation(It first, It last, It new_first, Swap swapit)
00276 {
00277     unsigned num = last - first;
00278 again:
00279     if (first == new_first || num < 2)
00280         return;
00281 
00282     unsigned num1 = new_first - first, num2 = last - new_first;
00283     if (num1 >= num2) {
00284         It a = first, b = new_first;
00285         while (b != last) {
00286             swapit(*a, *b);
00287             ++a; ++b;
00288         }
00289         if (num1 > num2) {
00290             first += num2;
00291             num = num1;
00292             goto again;
00293         }
00294     } else {
00295         It a = new_first, b = last;
00296         do {
00297             --a; --b;
00298             swapit(*a, *b);
00299         } while (a != first);
00300         last -= num1;
00301         num = num2;
00302         goto again;
00303     }
00304 }
00305 
00306 
00307 // Collection of `construct on first use' wrappers for safely avoiding
00308 // internal object replication without running into the `static
00309 // initialization order fiasco'.  This chest of numbers helps speed up
00310 // the library but should not be used outside it since it is
00311 // potentially confusing.
00312 
00313 class ex;
00314 
00315 extern const numeric *_num_120_p;
00316 extern const ex _ex_120;
00317 extern const numeric *_num_60_p;
00318 extern const ex _ex_60;
00319 extern const numeric *_num_48_p;
00320 extern const ex _ex_48;
00321 extern const numeric *_num_30_p;
00322 extern const ex _ex_30;
00323 extern const numeric *_num_25_p;
00324 extern const ex _ex_25;
00325 extern const numeric *_num_24_p;
00326 extern const ex _ex_24;
00327 extern const numeric *_num_20_p;
00328 extern const ex _ex_20;
00329 extern const numeric *_num_18_p;
00330 extern const ex _ex_18;
00331 extern const numeric *_num_15_p;
00332 extern const ex _ex_15;
00333 extern const numeric *_num_12_p;
00334 extern const ex _ex_12;
00335 extern const numeric *_num_11_p;
00336 extern const ex _ex_11;
00337 extern const numeric *_num_10_p;
00338 extern const ex _ex_10;
00339 extern const numeric *_num_9_p;
00340 extern const ex _ex_9;
00341 extern const numeric *_num_8_p;
00342 extern const ex _ex_8;
00343 extern const numeric *_num_7_p;
00344 extern const ex _ex_7;
00345 extern const numeric *_num_6_p;
00346 extern const ex _ex_6;
00347 extern const numeric *_num_5_p;
00348 extern const ex _ex_5;
00349 extern const numeric *_num_4_p;
00350 extern const ex _ex_4;
00351 extern const numeric *_num_3_p;
00352 extern const ex _ex_3;
00353 extern const numeric *_num_2_p;
00354 extern const ex _ex_2;
00355 extern const numeric *_num_1_p;
00356 extern const ex _ex_1;
00357 extern const numeric *_num_1_2_p;
00358 extern const ex _ex_1_2;
00359 extern const numeric *_num_1_3_p;
00360 extern const ex _ex_1_3;
00361 extern const numeric *_num_1_4_p;
00362 extern const ex _ex_1_4;
00363 extern const numeric *_num0_p;
00364 extern const basic *_num0_bp;
00365 extern const ex _ex0;
00366 extern const numeric *_num1_4_p;
00367 extern const ex _ex1_4;
00368 extern const numeric *_num1_3_p;
00369 extern const ex _ex1_3;
00370 extern const numeric *_num1_2_p;
00371 extern const ex _ex1_2;
00372 extern const numeric *_num1_p;
00373 extern const ex _ex1;
00374 extern const numeric *_num2_p;
00375 extern const ex _ex2;
00376 extern const numeric *_num3_p;
00377 extern const ex _ex3;
00378 extern const numeric *_num4_p;
00379 extern const ex _ex4;
00380 extern const numeric *_num5_p;
00381 extern const ex _ex5;
00382 extern const numeric *_num6_p;
00383 extern const ex _ex6;
00384 extern const numeric *_num7_p;
00385 extern const ex _ex7;
00386 extern const numeric *_num8_p;
00387 extern const ex _ex8;
00388 extern const numeric *_num9_p;
00389 extern const ex _ex9;
00390 extern const numeric *_num10_p;
00391 extern const ex _ex10;
00392 extern const numeric *_num11_p;
00393 extern const ex _ex11;
00394 extern const numeric *_num12_p;
00395 extern const ex _ex12;
00396 extern const numeric *_num15_p;
00397 extern const ex _ex15;
00398 extern const numeric *_num18_p;
00399 extern const ex _ex18;
00400 extern const numeric *_num20_p;
00401 extern const ex _ex20;
00402 extern const numeric *_num24_p;
00403 extern const ex _ex24;
00404 extern const numeric *_num25_p;
00405 extern const ex _ex25;
00406 extern const numeric *_num30_p;
00407 extern const ex _ex30;
00408 extern const numeric *_num48_p;
00409 extern const ex _ex48;
00410 extern const numeric *_num60_p;
00411 extern const ex _ex60;
00412 extern const numeric *_num120_p;
00413 extern const ex _ex120;
00414 
00415 
00416 // Helper macros for class implementations (mostly useful for trivial classes)
00417 
00418 #define DEFAULT_CTOR(classname) \
00419 classname::classname() { setflag(status_flags::evaluated | status_flags::expanded); }
00420 
00421 #define DEFAULT_COMPARE(classname) \
00422 int classname::compare_same_type(const basic & other) const \
00423 { \
00424     /* by default, the objects are always identical */ \
00425     return 0; \
00426 }
00427 
00428 #define DEFAULT_PRINT(classname, text) \
00429 void classname::do_print(const print_context & c, unsigned level) const \
00430 { \
00431     c.s << text; \
00432 }
00433 
00434 #define DEFAULT_PRINT_LATEX(classname, text, latex) \
00435 DEFAULT_PRINT(classname, text) \
00436 void classname::do_print_latex(const print_latex & c, unsigned level) const \
00437 { \
00438     c.s << latex; \
00439 }
00440 
00441 } // namespace GiNaC
00442 
00443 #endif // ndef GINAC_UTILS_H