4d19e6295897a3ed19b7d70e103d39de13e9fe7a
[ginac.git] / ginac / function.pl
1 $maxargs=13;
2
3 sub generate_seq {
4         my ($seq_template,$n)=@_;
5         my ($res,$N);
6         
7         $res='';
8         for ($N=1; $N<=$n; $N++) {
9                 $res .= eval('"' . $seq_template . '"');
10                 if ($N!=$n) {
11                         $res .= ', ';
12                 }
13         }
14         return $res;
15 }
16
17 sub generate_from_to {
18         my ($template,$seq_template1,$seq_template2,$seq_template3,$from,$to)=@_;
19         my ($res,$N,$SEQ);
20
21         $res='';
22         for ($N=$from; $N<=$to; $N++) {
23                 $SEQ1=generate_seq($seq_template1,$N);
24                 $SEQ2=generate_seq($seq_template2,$N);
25                 $SEQ3=generate_seq($seq_template3,$N);
26                 $res .= eval('"' . $template . '"');
27                 $SEQ1=''; # to avoid main::SEQ1 used only once warning
28                 $SEQ2=''; # same as above
29                 $SEQ3=''; # same as above
30         }
31         return $res;
32 }
33
34 sub generate {
35         my ($template,$seq_template1,$seq_template2,$seq_template3)=@_;
36         return generate_from_to($template,$seq_template1,$seq_template2,$seq_template3,1,$maxargs);
37 }
38
39 $declare_function_macro = generate(
40         <<'END_OF_DECLARE_FUNCTION_MACRO','typename T${N}','const T${N} & p${N}','GiNaC::ex(p${N})');
41 #define DECLARE_FUNCTION_${N}P(NAME) \\
42 class NAME##_SERIAL { public: static unsigned serial; }; \\
43 template<${SEQ1}> const GiNaC::function NAME(${SEQ2}) { \\
44         return GiNaC::function(NAME##_SERIAL::serial, ${SEQ3}); \\
45 }
46
47 END_OF_DECLARE_FUNCTION_MACRO
48
49 $typedef_eval_funcp=generate(
50 'typedef ex (* eval_funcp_${N})(${SEQ1});'."\n",
51 'const ex &','','');
52
53 $typedef_evalf_funcp=generate(
54 'typedef ex (* evalf_funcp_${N})(${SEQ1});'."\n",
55 'const ex &','','');
56
57 $typedef_derivative_funcp=generate(
58 'typedef ex (* derivative_funcp_${N})(${SEQ1}, unsigned);'."\n",
59 'const ex &','','');
60
61 $typedef_series_funcp=generate(
62 'typedef ex (* series_funcp_${N})(${SEQ1}, const relational &, int, unsigned);'."\n",
63 'const ex &','','');
64
65 $eval_func_interface=generate('    function_options & eval_func(eval_funcp_${N} e);'."\n",'','','');
66
67 $evalf_func_interface=generate('    function_options & evalf_func(evalf_funcp_${N} ef);'."\n",'','','');
68
69 $derivative_func_interface=generate('    function_options & derivative_func(derivative_funcp_${N} d);'."\n",'','','');
70
71 $series_func_interface=generate('    function_options & series_func(series_funcp_${N} s);'."\n",'','','');
72
73 $constructors_interface=generate(
74 '    function(unsigned ser, ${SEQ1});'."\n",
75 'const ex & param${N}','','');
76
77 $constructors_implementation=generate(
78         <<'END_OF_CONSTRUCTORS_IMPLEMENTATION','const ex & param${N}','param${N}','');
79 function::function(unsigned ser, ${SEQ1})
80         : exprseq(${SEQ2}), serial(ser)
81 {
82         tinfo_key = TINFO_function;
83 }
84 END_OF_CONSTRUCTORS_IMPLEMENTATION
85
86 $eval_switch_statement=generate(
87         <<'END_OF_EVAL_SWITCH_STATEMENT','seq[${N}-1]','','');
88         case ${N}:
89                 eval_result = ((eval_funcp_${N})(registered_functions()[serial].eval_f))(${SEQ1});
90                 break;
91 END_OF_EVAL_SWITCH_STATEMENT
92
93 $evalf_switch_statement=generate(
94         <<'END_OF_EVALF_SWITCH_STATEMENT','eseq[${N}-1]','','');
95         case ${N}:
96                 return ((evalf_funcp_${N})(registered_functions()[serial].evalf_f))(${SEQ1});
97 END_OF_EVALF_SWITCH_STATEMENT
98
99 $diff_switch_statement=generate(
100         <<'END_OF_DIFF_SWITCH_STATEMENT','seq[${N}-1]','','');
101         case ${N}:
102                 return ((derivative_funcp_${N})(registered_functions()[serial].derivative_f))(${SEQ1},diff_param);
103 END_OF_DIFF_SWITCH_STATEMENT
104
105 $series_switch_statement=generate(
106         <<'END_OF_SERIES_SWITCH_STATEMENT','seq[${N}-1]','','');
107         case ${N}:
108                 try {
109                         res = ((series_funcp_${N})(registered_functions()[serial].series_f))(${SEQ1},r,order,options);
110                 } catch (do_taylor) {
111                         res = basic::series(r, order, options);
112                 }
113                 return res;
114 END_OF_SERIES_SWITCH_STATEMENT
115
116 $eval_func_implementation=generate(
117         <<'END_OF_EVAL_FUNC_IMPLEMENTATION','','','');
118 function_options & function_options::eval_func(eval_funcp_${N} e)
119 {
120         test_and_set_nparams(${N});
121         eval_f = eval_funcp(e);
122         return *this;
123 }
124 END_OF_EVAL_FUNC_IMPLEMENTATION
125
126 $evalf_func_implementation=generate(
127         <<'END_OF_EVALF_FUNC_IMPLEMENTATION','','','');
128 function_options & function_options::evalf_func(evalf_funcp_${N} ef)
129 {
130         test_and_set_nparams(${N});
131         evalf_f = evalf_funcp(ef);
132         return *this;
133 }
134 END_OF_EVALF_FUNC_IMPLEMENTATION
135
136 $derivative_func_implementation=generate(
137         <<'END_OF_DERIVATIVE_FUNC_IMPLEMENTATION','','','');
138 function_options & function_options::derivative_func(derivative_funcp_${N} d)
139 {
140         test_and_set_nparams(${N});
141         derivative_f = derivative_funcp(d);
142         return *this;
143 }
144 END_OF_DERIVATIVE_FUNC_IMPLEMENTATION
145
146 $series_func_implementation=generate(
147         <<'END_OF_SERIES_FUNC_IMPLEMENTATION','','','');
148 function_options & function_options::series_func(series_funcp_${N} s)
149 {
150         test_and_set_nparams(${N});
151         series_f = series_funcp(s);
152         return *this;
153 }
154 END_OF_SERIES_FUNC_IMPLEMENTATION
155
156 $interface=<<END_OF_INTERFACE;
157 /** \@file function.h
158  *
159  *  Interface to class of symbolic functions. */
160
161 /*
162  *  This file was generated automatically by function.pl.
163  *  Please do not modify it directly, edit the perl script instead!
164  *  function.pl options: \$maxargs=${maxargs}
165  *
166  *  GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
167  *
168  *  This program is free software; you can redistribute it and/or modify
169  *  it under the terms of the GNU General Public License as published by
170  *  the Free Software Foundation; either version 2 of the License, or
171  *  (at your option) any later version.
172  *
173  *  This program is distributed in the hope that it will be useful,
174  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
175  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
176  *  GNU General Public License for more details.
177  *
178  *  You should have received a copy of the GNU General Public License
179  *  along with this program; if not, write to the Free Software
180  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
181  */
182
183 #ifndef __GINAC_FUNCTION_H__
184 #define __GINAC_FUNCTION_H__
185
186 #include <string>
187 #include <vector>
188
189 // CINT needs <algorithm> to work properly with <vector>
190 #include <algorithm>
191
192 #include "exprseq.h"
193
194 // the following lines have been generated for max. ${maxargs} parameters
195 $declare_function_macro
196 // end of generated lines
197
198 #define REGISTER_FUNCTION(NAME,OPT) \\
199 unsigned NAME##_SERIAL::serial = \\
200         GiNaC::function::register_new(GiNaC::function_options(#NAME).OPT);
201
202 namespace GiNaC {
203
204 class function;
205 class symmetry;
206
207 typedef ex (* eval_funcp)();
208 typedef ex (* evalf_funcp)();
209 typedef ex (* derivative_funcp)();
210 typedef ex (* series_funcp)();
211
212 // the following lines have been generated for max. ${maxargs} parameters
213 $typedef_eval_funcp
214 $typedef_evalf_funcp
215 $typedef_derivative_funcp
216 $typedef_series_funcp
217 // end of generated lines
218
219 // Alternatively, an exvector may be passed into the static function, instead
220 // of individual ex objects.  Then, the number of arguments is not limited.
221 typedef ex (* eval_funcp_exvector)(const exvector &);
222 typedef ex (* evalf_funcp_exvector)(const exvector &);
223 typedef ex (* derivative_funcp_exvector)(const exvector &, unsigned);
224 typedef ex (* series_funcp_exvector)(const exvector &, const relational &, int, unsigned);
225
226
227 class function_options
228 {
229         friend class function;
230         friend class fderivative;
231 public:
232         function_options();
233         function_options(std::string const & n, std::string const & tn=std::string());
234         ~function_options();
235         void initialize();
236         function_options & set_name(std::string const & n, std::string const & tn=std::string());
237         function_options & latex_name(std::string const & tn);
238 // the following lines have been generated for max. ${maxargs} parameters
239 $eval_func_interface
240 $evalf_func_interface
241 $derivative_func_interface
242 $series_func_interface
243 // end of generated lines
244         function_options & eval_func(eval_funcp_exvector e);
245         function_options & evalf_func(evalf_funcp_exvector ef);
246         function_options & derivative_func(derivative_funcp_exvector d);
247         function_options & series_func(series_funcp_exvector s);
248
249         function_options & set_return_type(unsigned rt, unsigned rtt=0);
250         function_options & do_not_evalf_params();
251         function_options & remember(unsigned size, unsigned assoc_size=0,
252                                     unsigned strategy=remember_strategies::delete_never);
253         function_options & overloaded(unsigned o);
254         function_options & set_symmetry(const symmetry & s);
255         void test_and_set_nparams(unsigned n);
256         std::string get_name() const { return name; }
257         unsigned get_nparams() const { return nparams; }
258         bool has_derivative() const { return derivative_f != NULL; }
259
260 protected:
261         std::string name;
262         std::string TeX_name;
263
264         unsigned nparams;
265
266         eval_funcp eval_f;
267         evalf_funcp evalf_f;
268         derivative_funcp derivative_f;
269         series_funcp series_f;
270
271         bool evalf_params_first;
272
273         bool use_return_type;
274         unsigned return_type;
275         unsigned return_type_tinfo;
276
277         bool use_remember;
278         unsigned remember_size;
279         unsigned remember_assoc_size;
280         unsigned remember_strategy;
281
282         bool eval_use_exvector_args;
283         bool evalf_use_exvector_args;
284         bool derivative_use_exvector_args;
285         bool series_use_exvector_args;
286
287         unsigned functions_with_same_name;
288
289         ex symtree;
290 };
291
292
293 /** Exception class thrown by classes which provide their own series expansion
294  *  to signal that ordinary Taylor expansion is safe. */
295 class do_taylor {};
296
297
298 /** The class function is used to implement builtin functions like sin, cos...
299         and user defined functions */
300 class function : public exprseq
301 {
302         GINAC_DECLARE_REGISTERED_CLASS(function, exprseq)
303
304         // CINT has a linking problem
305 #ifndef __MAKECINT__
306         friend void ginsh_get_ginac_functions();
307 #endif // def __MAKECINT__
308
309         friend class remember_table_entry;
310         // friend class remember_table_list;
311         // friend class remember_table;
312
313 // member functions
314
315         // other constructors
316 public:
317         function(unsigned ser);
318         // the following lines have been generated for max. ${maxargs} parameters
319 $constructors_interface
320         // end of generated lines
321         function(unsigned ser, const exprseq & es);
322         function(unsigned ser, const exvector & v, bool discardable = false);
323         function(unsigned ser, exvector * vp); // vp will be deleted
324
325         // functions overriding virtual functions from base classes
326 public:
327         void print(const print_context & c, unsigned level = 0) const;
328         unsigned precedence() const {return 70;}
329         ex expand(unsigned options=0) const;
330         ex eval(int level=0) const;
331         ex evalf(int level=0) const;
332         unsigned calchash() const;
333         ex series(const relational & r, int order, unsigned options = 0) const;
334         ex thiscontainer(const exvector & v) const;
335         ex thiscontainer(exvector * vp) const;
336 protected:
337         ex derivative(const symbol & s) const;
338         bool is_equal_same_type(const basic & other) const;
339         bool match_same_type(const basic & other) const;
340         unsigned return_type() const;
341         unsigned return_type_tinfo() const;
342         
343         // new virtual functions which can be overridden by derived classes
344         // none
345         
346         // non-virtual functions in this class
347 protected:
348         ex pderivative(unsigned diff_param) const; // partial differentiation
349         static std::vector<function_options> & registered_functions();
350         bool lookup_remember_table(ex & result) const;
351         void store_remember_table(ex const & result) const;
352 public:
353         static unsigned register_new(function_options const & opt);
354         static unsigned current_serial;
355         static unsigned find_function(const std::string &name, unsigned nparams);
356         unsigned get_serial() const {return serial;}
357         std::string get_name() const;
358
359 // member variables
360
361 protected:
362         unsigned serial;
363 };
364
365 // utility functions/macros
366
367 /** Specialization of is_exactly_a<function>(obj) for objects of type function. */
368 template<> inline bool is_exactly_a<function>(const basic & obj)
369 {
370         return obj.tinfo()==TINFO_function;
371 }
372
373 template <typename T>
374 inline bool is_the_function(const ex & x)
375 {
376         return is_exactly_a<function>(x)
377             && ex_to<function>(x).get_serial() == T::serial;
378 }
379
380 // Check whether OBJ is the specified symbolic function.
381 #define is_ex_the_function(OBJ, FUNCNAME) (GiNaC::is_the_function<FUNCNAME##_SERIAL>(OBJ))
382
383 } // namespace GiNaC
384
385 #endif // ndef __GINAC_FUNCTION_H__
386
387 END_OF_INTERFACE
388
389 $implementation=<<END_OF_IMPLEMENTATION;
390 /** \@file function.cpp
391  *
392  *  Implementation of class of symbolic functions. */
393
394 /*
395  *  This file was generated automatically by function.pl.
396  *  Please do not modify it directly, edit the perl script instead!
397  *  function.pl options: \$maxargs=${maxargs}
398  *
399  *  GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
400  *
401  *  This program is free software; you can redistribute it and/or modify
402  *  it under the terms of the GNU General Public License as published by
403  *  the Free Software Foundation; either version 2 of the License, or
404  *  (at your option) any later version.
405  *
406  *  This program is distributed in the hope that it will be useful,
407  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
408  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
409  *  GNU General Public License for more details.
410  *
411  *  You should have received a copy of the GNU General Public License
412  *  along with this program; if not, write to the Free Software
413  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
414  */
415
416 #include <iostream>
417 #include <string>
418 #include <stdexcept>
419 #include <list>
420
421 #include "function.h"
422 #include "operators.h"
423 #include "fderivative.h"
424 #include "ex.h"
425 #include "lst.h"
426 #include "symmetry.h"
427 #include "print.h"
428 #include "archive.h"
429 #include "inifcns.h"
430 #include "tostring.h"
431 #include "utils.h"
432 #include "remember.h"
433
434 namespace GiNaC {
435
436 //////////
437 // helper class function_options
438 //////////
439
440 function_options::function_options()
441 {
442         initialize();
443 }
444
445 function_options::function_options(std::string const & n, std::string const & tn)
446 {
447         initialize();
448         set_name(n,tn);
449 }
450
451 function_options::~function_options()
452 {
453         // nothing to clean up at the moment
454 }
455
456 void function_options::initialize()
457 {
458         set_name("unnamed_function","\\\\mbox{unnamed}");
459         nparams = 0;
460         eval_f = evalf_f = derivative_f = series_f = 0;
461         evalf_params_first = true;
462         use_return_type = false;
463         eval_use_exvector_args = false;
464         evalf_use_exvector_args = false;
465         derivative_use_exvector_args = false;
466         series_use_exvector_args = false;
467         use_remember = false;
468         functions_with_same_name = 1;
469         symtree = 0;
470 }
471
472 function_options & function_options::set_name(std::string const & n,
473                                               std::string const & tn)
474 {
475         name = n;
476         if (tn==std::string())
477                 TeX_name = "\\\\mbox{"+name+"}";
478         else
479                 TeX_name = tn;
480         return *this;
481 }
482
483 function_options & function_options::latex_name(std::string const & tn)
484 {
485         TeX_name = tn;
486         return *this;
487 }
488
489 // the following lines have been generated for max. ${maxargs} parameters
490 $eval_func_implementation
491 $evalf_func_implementation
492 $derivative_func_implementation
493 $series_func_implementation
494 // end of generated lines
495
496 function_options& function_options::eval_func(eval_funcp_exvector e)
497 {
498         eval_use_exvector_args = true;
499         eval_f = eval_funcp(e);
500         return *this;
501 }
502 function_options& function_options::evalf_func(evalf_funcp_exvector ef)
503 {
504         evalf_use_exvector_args = true;
505         evalf_f = evalf_funcp(ef);
506         return *this;
507 }
508 function_options& function_options::derivative_func(derivative_funcp_exvector d)
509 {
510         derivative_use_exvector_args = true;
511         derivative_f = derivative_funcp(d);
512         return *this;
513 }
514 function_options& function_options::series_func(series_funcp_exvector s)
515 {
516         series_use_exvector_args = true;
517         series_f = series_funcp(s);
518         return *this;
519 }
520
521 function_options & function_options::set_return_type(unsigned rt, unsigned rtt)
522 {
523         use_return_type = true;
524         return_type = rt;
525         return_type_tinfo = rtt;
526         return *this;
527 }
528
529 function_options & function_options::do_not_evalf_params()
530 {
531         evalf_params_first = false;
532         return *this;
533 }
534
535 function_options & function_options::remember(unsigned size,
536                                               unsigned assoc_size,
537                                               unsigned strategy)
538 {
539         use_remember = true;
540         remember_size = size;
541         remember_assoc_size = assoc_size;
542         remember_strategy = strategy;
543         return *this;
544 }
545
546 function_options & function_options::overloaded(unsigned o)
547 {
548         functions_with_same_name = o;
549         return *this;
550 }
551
552 function_options & function_options::set_symmetry(const symmetry & s)
553 {
554         symtree = s;
555         return *this;
556 }
557         
558 void function_options::test_and_set_nparams(unsigned n)
559 {
560         if (nparams==0) {
561                 nparams = n;
562         } else if (nparams!=n) {
563                 // we do not throw an exception here because this code is
564                 // usually executed before main(), so the exception could not
565                 // caught anyhow
566                 std::cerr << "WARNING: " << name << "(): number of parameters ("
567                           << n << ") differs from number set before (" 
568                           << nparams << ")" << std::endl;
569         }
570 }
571
572 /** This can be used as a hook for external applications. */
573 unsigned function::current_serial = 0;
574
575
576 GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
577
578 //////////
579 // default constructor
580 //////////
581
582 // public
583
584 function::function() : serial(0)
585 {
586         tinfo_key = TINFO_function;
587 }
588
589 //////////
590 // other constructors
591 //////////
592
593 // public
594
595 function::function(unsigned ser) : serial(ser)
596 {
597         tinfo_key = TINFO_function;
598 }
599
600 // the following lines have been generated for max. ${maxargs} parameters
601 $constructors_implementation
602 // end of generated lines
603
604 function::function(unsigned ser, const exprseq & es) : exprseq(es), serial(ser)
605 {
606         tinfo_key = TINFO_function;
607
608         // Force re-evaluation even if the exprseq was already evaluated
609         // (the exprseq copy constructor copies the flags)
610         clearflag(status_flags::evaluated);
611 }
612
613 function::function(unsigned ser, const exvector & v, bool discardable) 
614   : exprseq(v,discardable), serial(ser)
615 {
616         tinfo_key = TINFO_function;
617 }
618
619 function::function(unsigned ser, exvector * vp) 
620   : exprseq(vp), serial(ser)
621 {
622         tinfo_key = TINFO_function;
623 }
624
625 //////////
626 // archiving
627 //////////
628
629 /** Construct object from archive_node. */
630 function::function(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
631 {
632         // Find serial number by function name
633         std::string s;
634         if (n.find_string("name", s)) {
635                 unsigned int ser = 0;
636                 std::vector<function_options>::const_iterator i = registered_functions().begin(), iend = registered_functions().end();
637                 while (i != iend) {
638                         if (s == i->name) {
639                                 serial = ser;
640                                 return;
641                         }
642                         ++i; ++ser;
643                 }
644                 throw (std::runtime_error("unknown function '" + s + "' in archive"));
645         } else
646                 throw (std::runtime_error("unnamed function in archive"));
647 }
648
649 /** Unarchive the object. */
650 ex function::unarchive(const archive_node &n, lst &sym_lst)
651 {
652         return (new function(n, sym_lst))->setflag(status_flags::dynallocated);
653 }
654
655 /** Archive the object. */
656 void function::archive(archive_node &n) const
657 {
658         inherited::archive(n);
659         GINAC_ASSERT(serial < registered_functions().size());
660         n.add_string("name", registered_functions()[serial].name);
661 }
662
663 //////////
664 // functions overriding virtual functions from base classes
665 //////////
666
667 // public
668
669 void function::print(const print_context & c, unsigned level) const
670 {
671         GINAC_ASSERT(serial<registered_functions().size());
672
673         if (is_a<print_tree>(c)) {
674
675                 c.s << std::string(level, ' ') << class_name() << " "
676                     << registered_functions()[serial].name
677                     << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
678                     << ", nops=" << nops()
679                     << std::endl;
680                 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
681                 for (size_t i=0; i<seq.size(); ++i)
682                         seq[i].print(c, level + delta_indent);
683                 c.s << std::string(level + delta_indent, ' ') << "=====" << std::endl;
684
685         } else if (is_a<print_csrc>(c)) {
686
687                 // Print function name in lowercase
688                 std::string lname = registered_functions()[serial].name;
689                 size_t num = lname.size();
690                 for (size_t i=0; i<num; i++)
691                         lname[i] = tolower(lname[i]);
692                 c.s << lname << "(";
693
694                 // Print arguments, separated by commas
695                 exvector::const_iterator it = seq.begin(), itend = seq.end();
696                 while (it != itend) {
697                         it->print(c);
698                         ++it;
699                         if (it != itend)
700                                 c.s << ",";
701                 }
702                 c.s << ")";
703
704         } else if (is_a<print_latex>(c)) {
705                 c.s << registered_functions()[serial].TeX_name;
706                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
707         } else {
708                 c.s << registered_functions()[serial].name;
709                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
710         }
711 }
712
713 ex function::expand(unsigned options) const
714 {
715         // Only expand arguments when asked to do so
716         if (options & expand_options::expand_function_args)
717                 return inherited::expand(options);
718         else
719                 return (options == 0) ? setflag(status_flags::expanded) : *this;
720 }
721
722 ex function::eval(int level) const
723 {
724         GINAC_ASSERT(serial<registered_functions().size());
725
726         if (level>1) {
727                 // first evaluate children, then we will end up here again
728                 return function(serial,evalchildren(level));
729         }
730
731         const function_options &opt = registered_functions()[serial];
732
733         // Canonicalize argument order according to the symmetry properties
734         if (seq.size() > 1 && !(opt.symtree.is_zero())) {
735                 exvector v = seq;
736                 GINAC_ASSERT(is_a<symmetry>(opt.symtree));
737                 int sig = canonicalize(v.begin(), ex_to<symmetry>(opt.symtree));
738                 if (sig != INT_MAX) {
739                         // Something has changed while sorting arguments, more evaluations later
740                         if (sig == 0)
741                                 return _ex0;
742                         return ex(sig) * thiscontainer(v);
743                 }
744         }
745
746         if (opt.eval_f==0) {
747                 return this->hold();
748         }
749
750         bool use_remember = opt.use_remember;
751         ex eval_result;
752         if (use_remember && lookup_remember_table(eval_result)) {
753                 return eval_result;
754         }
755         current_serial = serial;
756         if (registered_functions()[serial].eval_use_exvector_args)
757                 eval_result = ((eval_funcp_exvector)(registered_functions()[serial].eval_f))(seq);
758         else
759         switch (opt.nparams) {
760                 // the following lines have been generated for max. ${maxargs} parameters
761 ${eval_switch_statement}
762                 // end of generated lines
763         default:
764                 throw(std::logic_error("function::eval(): invalid nparams"));
765         }
766         if (use_remember) {
767                 store_remember_table(eval_result);
768         }
769         return eval_result;
770 }
771
772 ex function::evalf(int level) const
773 {
774         GINAC_ASSERT(serial<registered_functions().size());
775
776         const function_options &opt = registered_functions()[serial];
777
778         // Evaluate children first
779         exvector eseq;
780         if (level == 1 || !(opt.evalf_params_first))
781                 eseq = seq;
782         else if (level == -max_recursion_level)
783                 throw(std::runtime_error("max recursion level reached"));
784         else {
785                 eseq.reserve(seq.size());
786                 --level;
787                 exvector::const_iterator it = seq.begin(), itend = seq.end();
788                 while (it != itend) {
789                         eseq.push_back(it->evalf(level));
790                         ++it;
791                 }
792         }
793
794         if (opt.evalf_f==0) {
795                 return function(serial,eseq).hold();
796         }
797         current_serial = serial;
798         if (opt.evalf_use_exvector_args)
799                 return ((evalf_funcp_exvector)(opt.evalf_f))(seq);
800         switch (opt.nparams) {
801                 // the following lines have been generated for max. ${maxargs} parameters
802 ${evalf_switch_statement}
803                 // end of generated lines
804         }
805         throw(std::logic_error("function::evalf(): invalid nparams"));
806 }
807
808 unsigned function::calchash() const
809 {
810         unsigned v = golden_ratio_hash(golden_ratio_hash(tinfo()) ^ serial);
811         for (size_t i=0; i<nops(); i++) {
812                 v = rotate_left(v);
813                 v ^= this->op(i).gethash();
814         }
815
816         if (flags & status_flags::evaluated) {
817                 setflag(status_flags::hash_calculated);
818                 hashvalue = v;
819         }
820         return v;
821 }
822
823 ex function::thiscontainer(const exvector & v) const
824 {
825         return function(serial,v);
826 }
827
828 ex function::thiscontainer(exvector * vp) const
829 {
830         return function(serial,vp);
831 }
832
833 /** Implementation of ex::series for functions.
834  *  \@see ex::series */
835 ex function::series(const relational & r, int order, unsigned options) const
836 {
837         GINAC_ASSERT(serial<registered_functions().size());
838
839         if (registered_functions()[serial].series_f==0) {
840                 return basic::series(r, order);
841         }
842         ex res;
843         current_serial = serial;
844         if (registered_functions()[serial].series_use_exvector_args) {
845                 try {
846                         res = ((series_funcp_exvector)(registered_functions()[serial].series_f))(seq, r, order, options);
847                 } catch (do_taylor) {
848                         res = basic::series(r, order, options);
849                 }
850                 return res;
851         }
852         switch (registered_functions()[serial].nparams) {
853                 // the following lines have been generated for max. ${maxargs} parameters
854 ${series_switch_statement}
855                 // end of generated lines
856         }
857         throw(std::logic_error("function::series(): invalid nparams"));
858 }
859
860 // protected
861
862 /** Implementation of ex::diff() for functions. It applies the chain rule,
863  *  except for the Order term function.
864  *  \@see ex::diff */
865 ex function::derivative(const symbol & s) const
866 {
867         ex result;
868
869         if (serial == Order_SERIAL::serial) {
870                 // Order Term function only differentiates the argument
871                 return Order(seq[0].diff(s));
872         } else {
873                 // Chain rule
874                 ex arg_diff;
875                 size_t num = seq.size();
876                 for (size_t i=0; i<num; i++) {
877                         arg_diff = seq[i].diff(s);
878                         // We apply the chain rule only when it makes sense.  This is not
879                         // just for performance reasons but also to allow functions to
880                         // throw when differentiated with respect to one of its arguments
881                         // without running into trouble with our automatic full
882                         // differentiation:
883                         if (!arg_diff.is_zero())
884                                 result += pderivative(i)*arg_diff;
885                 }
886         }
887         return result;
888 }
889
890 int function::compare_same_type(const basic & other) const
891 {
892         GINAC_ASSERT(is_a<function>(other));
893         const function & o = static_cast<const function &>(other);
894
895         if (serial != o.serial)
896                 return serial < o.serial ? -1 : 1;
897         else
898                 return exprseq::compare_same_type(o);
899 }
900
901 bool function::is_equal_same_type(const basic & other) const
902 {
903         GINAC_ASSERT(is_a<function>(other));
904         const function & o = static_cast<const function &>(other);
905
906         if (serial != o.serial)
907                 return false;
908         else
909                 return exprseq::is_equal_same_type(o);
910 }
911
912 bool function::match_same_type(const basic & other) const
913 {
914         GINAC_ASSERT(is_a<function>(other));
915         const function & o = static_cast<const function &>(other);
916
917         return serial == o.serial;
918 }
919
920 unsigned function::return_type() const
921 {
922         const function_options &opt = registered_functions()[serial];
923
924         if (opt.use_return_type) {
925                 // Return type was explicitly specified
926                 return opt.return_type;
927         } else {
928                 // Default behavior is to use the return type of the first
929                 // argument. Thus, exp() of a matrix behaves like a matrix, etc.
930                 if (seq.empty())
931                         return return_types::commutative;
932                 else
933                         return seq.begin()->return_type();
934         }
935 }
936
937 unsigned function::return_type_tinfo() const
938 {
939         const function_options &opt = registered_functions()[serial];
940
941         if (opt.use_return_type) {
942                 // Return type was explicitly specified
943                 return opt.return_type_tinfo;
944         } else {
945                 // Default behavior is to use the return type of the first
946                 // argument. Thus, exp() of a matrix behaves like a matrix, etc.
947                 if (seq.empty())
948                         return tinfo_key;
949                 else
950                         return seq.begin()->return_type_tinfo();
951         }
952 }
953
954 //////////
955 // new virtual functions which can be overridden by derived classes
956 //////////
957
958 // none
959
960 //////////
961 // non-virtual functions in this class
962 //////////
963
964 // protected
965
966 ex function::pderivative(unsigned diff_param) const // partial differentiation
967 {
968         GINAC_ASSERT(serial<registered_functions().size());
969         
970         // No derivative defined? Then return abstract derivative object
971         if (registered_functions()[serial].derivative_f == NULL)
972                 return fderivative(serial, diff_param, seq);
973
974         current_serial = serial;
975         if (registered_functions()[serial].derivative_use_exvector_args)
976                 return ((derivative_funcp_exvector)(registered_functions()[serial].derivative_f))(seq, diff_param);
977         switch (registered_functions()[serial].nparams) {
978                 // the following lines have been generated for max. ${maxargs} parameters
979 ${diff_switch_statement}
980                 // end of generated lines
981         }
982         throw(std::logic_error("function::pderivative(): no diff function defined"));
983 }
984
985 std::vector<function_options> & function::registered_functions()
986 {
987         static std::vector<function_options> * rf = new std::vector<function_options>;
988         return *rf;
989 }
990
991 bool function::lookup_remember_table(ex & result) const
992 {
993         return remember_table::remember_tables()[serial].lookup_entry(*this,result);
994 }
995
996 void function::store_remember_table(ex const & result) const
997 {
998         remember_table::remember_tables()[serial].add_entry(*this,result);
999 }
1000
1001 // public
1002
1003 unsigned function::register_new(function_options const & opt)
1004 {
1005         size_t same_name = 0;
1006         for (size_t i=0; i<registered_functions().size(); ++i) {
1007                 if (registered_functions()[i].name==opt.name) {
1008                         ++same_name;
1009                 }
1010         }
1011         if (same_name>=opt.functions_with_same_name) {
1012                 // we do not throw an exception here because this code is
1013                 // usually executed before main(), so the exception could not
1014                 // caught anyhow
1015                 std::cerr << "WARNING: function name " << opt.name
1016                           << " already in use!" << std::endl;
1017         }
1018         registered_functions().push_back(opt);
1019         if (opt.use_remember) {
1020                 remember_table::remember_tables().
1021                         push_back(remember_table(opt.remember_size,
1022                                                  opt.remember_assoc_size,
1023                                                  opt.remember_strategy));
1024         } else {
1025                 remember_table::remember_tables().push_back(remember_table());
1026         }
1027         return registered_functions().size()-1;
1028 }
1029
1030 /** Find serial number of function by name and number of parameters.
1031  *  Throws exception if function was not found. */
1032 unsigned function::find_function(const std::string &name, unsigned nparams)
1033 {
1034         std::vector<function_options>::const_iterator i = function::registered_functions().begin(), end = function::registered_functions().end();
1035         unsigned serial = 0;
1036         while (i != end) {
1037                 if (i->get_name() == name && i->get_nparams() == nparams)
1038                         return serial;
1039                 ++i;
1040                 ++serial;
1041         }
1042         throw (std::runtime_error("no function '" + name + "' with " + ToString(nparams) + " parameters defined"));
1043 }
1044
1045 /** Return the print name of the function. */
1046 std::string function::get_name() const
1047 {
1048         GINAC_ASSERT(serial<registered_functions().size());
1049         return registered_functions()[serial].name;
1050 }
1051
1052 } // namespace GiNaC
1053
1054 END_OF_IMPLEMENTATION
1055
1056 print "Creating interface file function.h...";
1057 open OUT,">function.h" or die "cannot open function.h";
1058 print OUT $interface;
1059 close OUT;
1060 print "ok.\n";
1061
1062 print "Creating implementation file function.cpp...";
1063 open OUT,">function.cpp" or die "cannot open function.cpp";
1064 print OUT $implementation;
1065 close OUT;
1066 print "ok.\n";
1067
1068 print "done.\n";