c76fe75385a184323aec6d86d7e5ae187b45ac72
[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 extern const unsigned function_index_##NAME; \\
43 template<${SEQ1}> \\
44 inline const GiNaC::function NAME(${SEQ2}) { \\
45         return GiNaC::function(function_index_##NAME, ${SEQ3}); \\
46 }
47
48 END_OF_DECLARE_FUNCTION_MACRO
49
50 $typedef_eval_funcp=generate(
51 'typedef ex (* eval_funcp_${N})(${SEQ1});'."\n",
52 'const ex &','','');
53
54 $typedef_evalf_funcp=generate(
55 'typedef ex (* evalf_funcp_${N})(${SEQ1});'."\n",
56 'const ex &','','');
57
58 $typedef_derivative_funcp=generate(
59 'typedef ex (* derivative_funcp_${N})(${SEQ1}, unsigned);'."\n",
60 'const ex &','','');
61
62 $typedef_series_funcp=generate(
63 'typedef ex (* series_funcp_${N})(${SEQ1}, const relational &, int, unsigned);'."\n",
64 'const ex &','','');
65
66 $eval_func_interface=generate('    function_options & eval_func(eval_funcp_${N} e);'."\n",'','','');
67
68 $evalf_func_interface=generate('    function_options & evalf_func(evalf_funcp_${N} ef);'."\n",'','','');
69
70 $derivative_func_interface=generate('    function_options & derivative_func(derivative_funcp_${N} d);'."\n",'','','');
71
72 $series_func_interface=generate('    function_options & series_func(series_funcp_${N} s);'."\n",'','','');
73
74 $constructors_interface=generate(
75 '    function(unsigned ser, ${SEQ1});'."\n",
76 'const ex & param${N}','','');
77
78 $constructors_implementation=generate(
79         <<'END_OF_CONSTRUCTORS_IMPLEMENTATION','const ex & param${N}','param${N}','');
80 function::function(unsigned ser, ${SEQ1})
81         : exprseq(${SEQ2}), serial(ser)
82 {
83         tinfo_key = TINFO_function;
84 }
85 END_OF_CONSTRUCTORS_IMPLEMENTATION
86
87 $eval_switch_statement=generate(
88         <<'END_OF_EVAL_SWITCH_STATEMENT','seq[${N}-1]','','');
89         case ${N}:
90                 eval_result = ((eval_funcp_${N})(registered_functions()[serial].eval_f))(${SEQ1});
91                 break;
92 END_OF_EVAL_SWITCH_STATEMENT
93
94 $evalf_switch_statement=generate(
95         <<'END_OF_EVALF_SWITCH_STATEMENT','eseq[${N}-1]','','');
96         case ${N}:
97                 return ((evalf_funcp_${N})(registered_functions()[serial].evalf_f))(${SEQ1});
98 END_OF_EVALF_SWITCH_STATEMENT
99
100 $diff_switch_statement=generate(
101         <<'END_OF_DIFF_SWITCH_STATEMENT','seq[${N}-1]','','');
102         case ${N}:
103                 return ((derivative_funcp_${N})(registered_functions()[serial].derivative_f))(${SEQ1},diff_param);
104 END_OF_DIFF_SWITCH_STATEMENT
105
106 $series_switch_statement=generate(
107         <<'END_OF_SERIES_SWITCH_STATEMENT','seq[${N}-1]','','');
108         case ${N}:
109                 try {
110                         res = ((series_funcp_${N})(registered_functions()[serial].series_f))(${SEQ1},r,order,options);
111                 } catch (do_taylor) {
112                         res = basic::series(r, order, options);
113                 }
114                 return res;
115 END_OF_SERIES_SWITCH_STATEMENT
116
117 $eval_func_implementation=generate(
118         <<'END_OF_EVAL_FUNC_IMPLEMENTATION','','','');
119 function_options & function_options::eval_func(eval_funcp_${N} e)
120 {
121         test_and_set_nparams(${N});
122         eval_f = eval_funcp(e);
123         return *this;
124 }
125 END_OF_EVAL_FUNC_IMPLEMENTATION
126
127 $evalf_func_implementation=generate(
128         <<'END_OF_EVALF_FUNC_IMPLEMENTATION','','','');
129 function_options & function_options::evalf_func(evalf_funcp_${N} ef)
130 {
131         test_and_set_nparams(${N});
132         evalf_f = evalf_funcp(ef);
133         return *this;
134 }
135 END_OF_EVALF_FUNC_IMPLEMENTATION
136
137 $derivative_func_implementation=generate(
138         <<'END_OF_DERIVATIVE_FUNC_IMPLEMENTATION','','','');
139 function_options & function_options::derivative_func(derivative_funcp_${N} d)
140 {
141         test_and_set_nparams(${N});
142         derivative_f = derivative_funcp(d);
143         return *this;
144 }
145 END_OF_DERIVATIVE_FUNC_IMPLEMENTATION
146
147 $series_func_implementation=generate(
148         <<'END_OF_SERIES_FUNC_IMPLEMENTATION','','','');
149 function_options & function_options::series_func(series_funcp_${N} s)
150 {
151         test_and_set_nparams(${N});
152         series_f = series_funcp(s);
153         return *this;
154 }
155 END_OF_SERIES_FUNC_IMPLEMENTATION
156
157 $interface=<<END_OF_INTERFACE;
158 /** \@file function.h
159  *
160  *  Interface to class of symbolic functions. */
161
162 /*
163  *  This file was generated automatically by function.pl.
164  *  Please do not modify it directly, edit the perl script instead!
165  *  function.pl options: \$maxargs=${maxargs}
166  *
167  *  GiNaC Copyright (C) 1999-2002 Johannes Gutenberg University Mainz, Germany
168  *
169  *  This program is free software; you can redistribute it and/or modify
170  *  it under the terms of the GNU General Public License as published by
171  *  the Free Software Foundation; either version 2 of the License, or
172  *  (at your option) any later version.
173  *
174  *  This program is distributed in the hope that it will be useful,
175  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
176  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
177  *  GNU General Public License for more details.
178  *
179  *  You should have received a copy of the GNU General Public License
180  *  along with this program; if not, write to the Free Software
181  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
182  */
183
184 #ifndef __GINAC_FUNCTION_H__
185 #define __GINAC_FUNCTION_H__
186
187 #include <string>
188 #include <vector>
189
190 // CINT needs <algorithm> to work properly with <vector>
191 #include <algorithm>
192
193 #include "exprseq.h"
194
195 // the following lines have been generated for max. ${maxargs} parameters
196 $declare_function_macro
197 // end of generated lines
198
199 #define REGISTER_FUNCTION(NAME,OPT) \\
200 const unsigned function_index_##NAME= \\
201         GiNaC::function::register_new(GiNaC::function_options(#NAME).OPT);
202
203 namespace GiNaC {
204
205 class function;
206 class symmetry;
207
208 typedef ex (* eval_funcp)();
209 typedef ex (* evalf_funcp)();
210 typedef ex (* derivative_funcp)();
211 typedef ex (* series_funcp)();
212
213 // the following lines have been generated for max. ${maxargs} parameters
214 $typedef_eval_funcp
215 $typedef_evalf_funcp
216 $typedef_derivative_funcp
217 $typedef_series_funcp
218 // end of generated lines
219
220 // Alternatively, an exvector may be passed into the static function, instead
221 // of individual ex objects.  Then, the number of arguments is not limited.
222 typedef ex (* eval_funcp_exvector)(const exvector &);
223 typedef ex (* evalf_funcp_exvector)(const exvector &);
224 typedef ex (* derivative_funcp_exvector)(const exvector &, unsigned);
225 typedef ex (* series_funcp_exvector)(const exvector &, const relational &, int, unsigned);
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(void);
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(void);
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(void) const { return name; }
257         unsigned get_nparams(void) const { return nparams; }
258         bool has_derivative(void) 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 /** The class function is used to implement builtin functions like sin, cos...
293         and user defined functions */
294 class function : public exprseq
295 {
296         GINAC_DECLARE_REGISTERED_CLASS(function, exprseq)
297
298         // CINT has a linking problem
299 #ifndef __MAKECINT__
300         friend void ginsh_get_ginac_functions(void);
301 #endif // def __MAKECINT__
302
303         friend class remember_table_entry;
304         // friend class remember_table_list;
305         // friend class remember_table;
306
307 // member functions
308
309         // other ctors
310 public:
311         function(unsigned ser);
312         // the following lines have been generated for max. ${maxargs} parameters
313 $constructors_interface
314         // end of generated lines
315         function(unsigned ser, const exprseq & es);
316         function(unsigned ser, const exvector & v, bool discardable = false);
317         function(unsigned ser, exvector * vp); // vp will be deleted
318
319         // functions overriding virtual functions from base classes
320 public:
321         void print(const print_context & c, unsigned level = 0) const;
322         unsigned precedence(void) const {return 70;}
323         ex expand(unsigned options=0) const;
324         ex eval(int level=0) const;
325         ex evalf(int level=0) const;
326         unsigned calchash(void) const;
327         ex series(const relational & r, int order, unsigned options = 0) const;
328         ex thisexprseq(const exvector & v) const;
329         ex thisexprseq(exvector * vp) const;
330 protected:
331         ex derivative(const symbol & s) const;
332         bool is_equal_same_type(const basic & other) const;
333         bool match_same_type(const basic & other) const;
334         unsigned return_type(void) const;
335         unsigned return_type_tinfo(void) const;
336         
337         // new virtual functions which can be overridden by derived classes
338         // none
339         
340         // non-virtual functions in this class
341 protected:
342         ex pderivative(unsigned diff_param) const; // partial differentiation
343         static std::vector<function_options> & registered_functions(void);
344         bool lookup_remember_table(ex & result) const;
345         void store_remember_table(ex const & result) const;
346 public:
347         static unsigned register_new(function_options const & opt);
348         static unsigned current_serial;
349         static unsigned find_function(const std::string &name, unsigned nparams);
350         unsigned get_serial(void) const {return serial;}
351         std::string get_name(void) const;
352
353 // member variables
354
355 protected:
356         unsigned serial;
357 };
358
359 // utility functions/macros
360
361 /** Specialization of is_exactly_a<function>(obj) for objects of type function. */
362 template<> inline bool is_exactly_a<function>(const basic & obj)
363 {
364         return obj.tinfo()==TINFO_function;
365 }
366
367 #define is_ex_the_function(OBJ, FUNCNAME) \\
368         (GiNaC::is_exactly_a<GiNaC::function>(OBJ) && GiNaC::ex_to<GiNaC::function>(OBJ).get_serial() == GiNaC::function_index_##FUNCNAME)
369
370 } // namespace GiNaC
371
372 #endif // ndef __GINAC_FUNCTION_H__
373
374 END_OF_INTERFACE
375
376 $implementation=<<END_OF_IMPLEMENTATION;
377 /** \@file function.cpp
378  *
379  *  Implementation of class of symbolic functions. */
380
381 /*
382  *  This file was generated automatically by function.pl.
383  *  Please do not modify it directly, edit the perl script instead!
384  *  function.pl options: \$maxargs=${maxargs}
385  *
386  *  GiNaC Copyright (C) 1999-2002 Johannes Gutenberg University Mainz, Germany
387  *
388  *  This program is free software; you can redistribute it and/or modify
389  *  it under the terms of the GNU General Public License as published by
390  *  the Free Software Foundation; either version 2 of the License, or
391  *  (at your option) any later version.
392  *
393  *  This program is distributed in the hope that it will be useful,
394  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
395  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
396  *  GNU General Public License for more details.
397  *
398  *  You should have received a copy of the GNU General Public License
399  *  along with this program; if not, write to the Free Software
400  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
401  */
402
403 #include <iostream>
404 #include <string>
405 #include <stdexcept>
406 #include <list>
407
408 #include "function.h"
409 #include "fderivative.h"
410 #include "ex.h"
411 #include "lst.h"
412 #include "symmetry.h"
413 #include "print.h"
414 #include "archive.h"
415 #include "inifcns.h"
416 #include "tostring.h"
417 #include "utils.h"
418 #include "remember.h"
419
420 namespace GiNaC {
421
422 //////////
423 // helper class function_options
424 //////////
425
426 function_options::function_options()
427 {
428         initialize();
429 }
430
431 function_options::function_options(std::string const & n, std::string const & tn)
432 {
433         initialize();
434         set_name(n,tn);
435 }
436
437 function_options::~function_options()
438 {
439         // nothing to clean up at the moment
440 }
441
442 void function_options::initialize(void)
443 {
444         set_name("unnamed_function","\\\\mbox{unnamed}");
445         nparams = 0;
446         eval_f = evalf_f = derivative_f = series_f = 0;
447         evalf_params_first = true;
448         use_return_type = false;
449         eval_use_exvector_args = false;
450         evalf_use_exvector_args = false;
451         derivative_use_exvector_args = false;
452         series_use_exvector_args = false;
453         use_remember = false;
454         functions_with_same_name = 1;
455         symtree = 0;
456 }
457
458 function_options & function_options::set_name(std::string const & n,
459                                               std::string const & tn)
460 {
461         name = n;
462         if (tn==std::string())
463                 TeX_name = "\\\\mbox{"+name+"}";
464         else
465                 TeX_name = tn;
466         return *this;
467 }
468
469 function_options & function_options::latex_name(std::string const & tn)
470 {
471         TeX_name = tn;
472         return *this;
473 }
474
475 // the following lines have been generated for max. ${maxargs} parameters
476 $eval_func_implementation
477 $evalf_func_implementation
478 $derivative_func_implementation
479 $series_func_implementation
480 // end of generated lines
481
482 function_options& function_options::eval_func(eval_funcp_exvector e)
483 {
484         eval_use_exvector_args = true;
485         eval_f = eval_funcp(e);
486         return *this;
487 }
488 function_options& function_options::evalf_func(evalf_funcp_exvector ef)
489 {
490         evalf_use_exvector_args = true;
491         evalf_f = evalf_funcp(ef);
492         return *this;
493 }
494 function_options& function_options::derivative_func(derivative_funcp_exvector d)
495 {
496         derivative_use_exvector_args = true;
497         derivative_f = derivative_funcp(d);
498         return *this;
499 }
500 function_options& function_options::series_func(series_funcp_exvector s)
501 {
502         series_use_exvector_args = true;
503         series_f = series_funcp(s);
504         return *this;
505 }
506
507
508 function_options & function_options::set_return_type(unsigned rt, unsigned rtt)
509 {
510         use_return_type = true;
511         return_type = rt;
512         return_type_tinfo = rtt;
513         return *this;
514 }
515
516 function_options & function_options::do_not_evalf_params(void)
517 {
518         evalf_params_first = false;
519         return *this;
520 }
521
522 function_options & function_options::remember(unsigned size,
523                                               unsigned assoc_size,
524                                               unsigned strategy)
525 {
526         use_remember = true;
527         remember_size = size;
528         remember_assoc_size = assoc_size;
529         remember_strategy = strategy;
530         return *this;
531 }
532
533 function_options & function_options::overloaded(unsigned o)
534 {
535         functions_with_same_name = o;
536         return *this;
537 }
538
539 function_options & function_options::set_symmetry(const symmetry & s)
540 {
541         symtree = s;
542         return *this;
543 }
544         
545 void function_options::test_and_set_nparams(unsigned n)
546 {
547         if (nparams==0) {
548                 nparams = n;
549         } else if (nparams!=n) {
550                 // we do not throw an exception here because this code is
551                 // usually executed before main(), so the exception could not
552                 // caught anyhow
553                 std::cerr << "WARNING: number of parameters ("
554                           << n << ") differs from number set before (" 
555                           << nparams << ")" << std::endl;
556         }
557 }
558
559 /** This can be used as a hook for external applications. */
560 unsigned function::current_serial = 0;
561
562
563 GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
564
565 //////////
566 // default ctor, dtor, copy ctor, assignment operator and helpers
567 //////////
568
569 // public
570
571 function::function() : serial(0)
572 {
573         tinfo_key = TINFO_function;
574 }
575
576 // protected
577
578 void function::copy(const function & other)
579 {
580         inherited::copy(other);
581         serial = other.serial;
582 }
583
584 void function::destroy(bool call_parent)
585 {
586         if (call_parent)
587                 inherited::destroy(call_parent);
588 }
589
590 //////////
591 // other ctors
592 //////////
593
594 // public
595
596 function::function(unsigned ser) : serial(ser)
597 {
598         tinfo_key = TINFO_function;
599 }
600
601 // the following lines have been generated for max. ${maxargs} parameters
602 $constructors_implementation
603 // end of generated lines
604
605 function::function(unsigned ser, const exprseq & es) : exprseq(es), serial(ser)
606 {
607         tinfo_key = TINFO_function;
608 }
609
610 function::function(unsigned ser, const exvector & v, bool discardable) 
611   : exprseq(v,discardable), serial(ser)
612 {
613         tinfo_key = TINFO_function;
614 }
615
616 function::function(unsigned ser, exvector * vp) 
617   : exprseq(vp), serial(ser)
618 {
619         tinfo_key = TINFO_function;
620 }
621
622 //////////
623 // archiving
624 //////////
625
626 /** Construct object from archive_node. */
627 function::function(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
628 {
629         // Find serial number by function name
630         std::string s;
631         if (n.find_string("name", s)) {
632                 unsigned int ser = 0;
633                 std::vector<function_options>::const_iterator i = registered_functions().begin(), iend = registered_functions().end();
634                 while (i != iend) {
635                         if (s == i->name) {
636                                 serial = ser;
637                                 return;
638                         }
639                         ++i; ++ser;
640                 }
641                 throw (std::runtime_error("unknown function '" + s + "' in archive"));
642         } else
643                 throw (std::runtime_error("unnamed function in archive"));
644 }
645
646 /** Unarchive the object. */
647 ex function::unarchive(const archive_node &n, const lst &sym_lst)
648 {
649         return (new function(n, sym_lst))->setflag(status_flags::dynallocated);
650 }
651
652 /** Archive the object. */
653 void function::archive(archive_node &n) const
654 {
655         inherited::archive(n);
656         GINAC_ASSERT(serial < registered_functions().size());
657         n.add_string("name", registered_functions()[serial].name);
658 }
659
660 //////////
661 // functions overriding virtual functions from base classes
662 //////////
663
664 // public
665
666 void function::print(const print_context & c, unsigned level) const
667 {
668         GINAC_ASSERT(serial<registered_functions().size());
669
670         if (is_of_type(c, print_tree)) {
671
672                 c.s << std::string(level, ' ') << class_name() << " "
673                     << registered_functions()[serial].name
674                     << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
675                     << ", nops=" << nops()
676                     << std::endl;
677                 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
678                 for (unsigned i=0; i<seq.size(); ++i)
679                         seq[i].print(c, level + delta_indent);
680                 c.s << std::string(level + delta_indent, ' ') << "=====" << std::endl;
681
682         } else if (is_of_type(c, print_csrc)) {
683
684                 // Print function name in lowercase
685                 std::string lname = registered_functions()[serial].name;
686                 unsigned num = lname.size();
687                 for (unsigned i=0; i<num; i++)
688                         lname[i] = tolower(lname[i]);
689                 c.s << lname << "(";
690
691                 // Print arguments, separated by commas
692                 exvector::const_iterator it = seq.begin(), itend = seq.end();
693                 while (it != itend) {
694                         it->print(c);
695                         ++it;
696                         if (it != itend)
697                                 c.s << ",";
698                 }
699                 c.s << ")";
700
701         } else if (is_of_type(c, print_latex)) {
702                 c.s << registered_functions()[serial].TeX_name;
703                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
704         } else {
705                 c.s << registered_functions()[serial].name;
706                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
707         }
708 }
709
710 ex function::expand(unsigned options) const
711 {
712         // Only expand arguments when asked to do so
713         if (options & expand_options::expand_function_args)
714                 return inherited::expand(options);
715         else
716                 return (options == 0) ? setflag(status_flags::expanded) : *this;
717 }
718
719 ex function::eval(int level) const
720 {
721         GINAC_ASSERT(serial<registered_functions().size());
722
723         if (level>1) {
724                 // first evaluate children, then we will end up here again
725                 return function(serial,evalchildren(level));
726         }
727
728         const function_options &opt = registered_functions()[serial];
729
730         // Canonicalize argument order according to the symmetry properties
731         if (seq.size() > 1 && !(opt.symtree.is_zero())) {
732                 exvector v = seq;
733                 GINAC_ASSERT(is_a<symmetry>(opt.symtree));
734                 int sig = canonicalize(v.begin(), ex_to<symmetry>(opt.symtree));
735                 if (sig != INT_MAX) {
736                         // Something has changed while sorting arguments, more evaluations later
737                         if (sig == 0)
738                                 return _ex0;
739                         return ex(sig) * thisexprseq(v);
740                 }
741         }
742
743         if (opt.eval_f==0) {
744                 return this->hold();
745         }
746
747         bool use_remember = opt.use_remember;
748         ex eval_result;
749         if (use_remember && lookup_remember_table(eval_result)) {
750                 return eval_result;
751         }
752         current_serial = serial;
753         if (registered_functions()[serial].eval_use_exvector_args)
754                 eval_result = ((eval_funcp_exvector)(registered_functions()[serial].eval_f))(seq);
755         else
756         switch (opt.nparams) {
757                 // the following lines have been generated for max. ${maxargs} parameters
758 ${eval_switch_statement}
759                 // end of generated lines
760         default:
761                 throw(std::logic_error("function::eval(): invalid nparams"));
762         }
763         if (use_remember) {
764                 store_remember_table(eval_result);
765         }
766         return eval_result;
767 }
768
769 ex function::evalf(int level) const
770 {
771         GINAC_ASSERT(serial<registered_functions().size());
772
773         // Evaluate children first
774         exvector eseq;
775         if (level == 1)
776                 eseq = seq;
777         else if (level == -max_recursion_level)
778                 throw(std::runtime_error("max recursion level reached"));
779         else
780                 eseq.reserve(seq.size());
781         --level;
782         exvector::const_iterator it = seq.begin(), itend = seq.end();
783         while (it != itend) {
784                 eseq.push_back(it->evalf(level));
785                 ++it;
786         }
787         
788         if (registered_functions()[serial].evalf_f==0) {
789                 return function(serial,eseq).hold();
790         }
791         current_serial = serial;
792         if (registered_functions()[serial].evalf_use_exvector_args)
793                 return ((evalf_funcp_exvector)(registered_functions()[serial].evalf_f))(seq);
794         switch (registered_functions()[serial].nparams) {
795                 // the following lines have been generated for max. ${maxargs} parameters
796 ${evalf_switch_statement}
797                 // end of generated lines
798         }
799         throw(std::logic_error("function::evalf(): invalid nparams"));
800 }
801
802 unsigned function::calchash(void) const
803 {
804         unsigned v = golden_ratio_hash(golden_ratio_hash(tinfo()) ^ serial);
805         for (unsigned i=0; i<nops(); i++) {
806                 v = rotate_left_31(v);
807                 v ^= this->op(i).gethash();
808         }
809         v &= 0x7FFFFFFFU;
810         if (flags & status_flags::evaluated) {
811                 setflag(status_flags::hash_calculated);
812                 hashvalue = v;
813         }
814         return v;
815 }
816
817 ex function::thisexprseq(const exvector & v) const
818 {
819         return function(serial,v);
820 }
821
822 ex function::thisexprseq(exvector * vp) const
823 {
824         return function(serial,vp);
825 }
826
827 /** Implementation of ex::series for functions.
828  *  \@see ex::series */
829 ex function::series(const relational & r, int order, unsigned options) const
830 {
831         GINAC_ASSERT(serial<registered_functions().size());
832
833         if (registered_functions()[serial].series_f==0) {
834                 return basic::series(r, order);
835         }
836         ex res;
837         current_serial = serial;
838         if (registered_functions()[serial].series_use_exvector_args) {
839                 try {
840                         res = ((series_funcp_exvector)(registered_functions()[serial].series_f))(seq, r, order, options);
841                 } catch (do_taylor) {
842                         res = basic::series(r, order, options);
843                 }
844                 return res;
845         }
846         switch (registered_functions()[serial].nparams) {
847                 // the following lines have been generated for max. ${maxargs} parameters
848 ${series_switch_statement}
849                 // end of generated lines
850         }
851         throw(std::logic_error("function::series(): invalid nparams"));
852 }
853
854 // protected
855
856 /** Implementation of ex::diff() for functions. It applies the chain rule,
857  *  except for the Order term function.
858  *  \@see ex::diff */
859 ex function::derivative(const symbol & s) const
860 {
861         ex result;
862
863         if (serial == function_index_Order) {
864                 // Order Term function only differentiates the argument
865                 return Order(seq[0].diff(s));
866         } else {
867                 // Chain rule
868                 ex arg_diff;
869                 unsigned num = seq.size();
870                 for (unsigned i=0; i<num; i++) {
871                         arg_diff = seq[i].diff(s);
872                         // We apply the chain rule only when it makes sense.  This is not
873                         // just for performance reasons but also to allow functions to
874                         // throw when differentiated with respect to one of its arguments
875                         // without running into trouble with our automatic full
876                         // differentiation:
877                         if (!arg_diff.is_zero())
878                                 result += pderivative(i)*arg_diff;
879                 }
880         }
881         return result;
882 }
883
884 int function::compare_same_type(const basic & other) const
885 {
886         GINAC_ASSERT(is_of_type(other, function));
887         const function & o = static_cast<const function &>(other);
888
889         if (serial != o.serial)
890                 return serial < o.serial ? -1 : 1;
891         else
892                 return exprseq::compare_same_type(o);
893 }
894
895 bool function::is_equal_same_type(const basic & other) const
896 {
897         GINAC_ASSERT(is_of_type(other, function));
898         const function & o = static_cast<const function &>(other);
899
900         if (serial != o.serial)
901                 return false;
902         else
903                 return exprseq::is_equal_same_type(o);
904 }
905
906 bool function::match_same_type(const basic & other) const
907 {
908         GINAC_ASSERT(is_of_type(other, function));
909         const function & o = static_cast<const function &>(other);
910
911         return serial == o.serial;
912 }
913
914 unsigned function::return_type(void) const
915 {
916         if (seq.empty())
917                 return return_types::commutative;
918         else
919                 return seq.begin()->return_type();
920 }
921
922 unsigned function::return_type_tinfo(void) const
923 {
924         if (seq.empty())
925                 return tinfo_key;
926         else
927                 return seq.begin()->return_type_tinfo();
928 }
929
930 //////////
931 // new virtual functions which can be overridden by derived classes
932 //////////
933
934 // none
935
936 //////////
937 // non-virtual functions in this class
938 //////////
939
940 // protected
941
942 ex function::pderivative(unsigned diff_param) const // partial differentiation
943 {
944         GINAC_ASSERT(serial<registered_functions().size());
945         
946         // No derivative defined? Then return abstract derivative object
947         if (registered_functions()[serial].derivative_f == NULL)
948                 return fderivative(serial, diff_param, seq);
949
950         current_serial = serial;
951         if (registered_functions()[serial].derivative_use_exvector_args)
952                 return ((derivative_funcp_exvector)(registered_functions()[serial].derivative_f))(seq, diff_param);
953         switch (registered_functions()[serial].nparams) {
954                 // the following lines have been generated for max. ${maxargs} parameters
955 ${diff_switch_statement}
956                 // end of generated lines
957         }
958         throw(std::logic_error("function::pderivative(): no diff function defined"));
959 }
960
961 std::vector<function_options> & function::registered_functions(void)
962 {
963         static std::vector<function_options> * rf = new std::vector<function_options>;
964         return *rf;
965 }
966
967 bool function::lookup_remember_table(ex & result) const
968 {
969         return remember_table::remember_tables()[serial].lookup_entry(*this,result);
970 }
971
972 void function::store_remember_table(ex const & result) const
973 {
974         remember_table::remember_tables()[serial].add_entry(*this,result);
975 }
976
977 // public
978
979 unsigned function::register_new(function_options const & opt)
980 {
981         unsigned same_name = 0;
982         for (unsigned i=0; i<registered_functions().size(); ++i) {
983                 if (registered_functions()[i].name==opt.name) {
984                         ++same_name;
985                 }
986         }
987         if (same_name>=opt.functions_with_same_name) {
988                 // we do not throw an exception here because this code is
989                 // usually executed before main(), so the exception could not
990                 // caught anyhow
991                 std::cerr << "WARNING: function name " << opt.name
992                           << " already in use!" << std::endl;
993         }
994         registered_functions().push_back(opt);
995         if (opt.use_remember) {
996                 remember_table::remember_tables().
997                         push_back(remember_table(opt.remember_size,
998                                                  opt.remember_assoc_size,
999                                                  opt.remember_strategy));
1000         } else {
1001                 remember_table::remember_tables().push_back(remember_table());
1002         }
1003         return registered_functions().size()-1;
1004 }
1005
1006 /** Find serial number of function by name and number of parameters.
1007  *  Throws exception if function was not found. */
1008 unsigned function::find_function(const std::string &name, unsigned nparams)
1009 {
1010         std::vector<function_options>::const_iterator i = function::registered_functions().begin(), end = function::registered_functions().end();
1011         unsigned serial = 0;
1012         while (i != end) {
1013                 if (i->get_name() == name && i->get_nparams() == nparams)
1014                         return serial;
1015                 ++i;
1016                 ++serial;
1017         }
1018         throw (std::runtime_error("no function '" + name + "' with " + ToString(nparams) + " parameters defined"));
1019 }
1020
1021 /** Return the print name of the function. */
1022 std::string function::get_name(void) const
1023 {
1024         GINAC_ASSERT(serial<registered_functions().size());
1025         return registered_functions()[serial].name;
1026 }
1027
1028 } // namespace GiNaC
1029
1030 END_OF_IMPLEMENTATION
1031
1032 print "Creating interface file function.h...";
1033 open OUT,">function.h" or die "cannot open function.h";
1034 print OUT $interface;
1035 close OUT;
1036 print "ok.\n";
1037
1038 print "Creating implementation file function.cpp...";
1039 open OUT,">function.cpp" or die "cannot open function.cpp";
1040 print OUT $implementation;
1041 close OUT;
1042 print "ok.\n";
1043
1044 print "done.\n";