* Remove obsolete macros.
[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) 1999-2001 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         int degree(const ex & s) const;
324         int ldegree(const ex & s) const;
325         ex coeff(const ex & s, int n = 1) const;
326         ex expand(unsigned options=0) const;
327         ex eval(int level=0) const;
328         ex evalf(int level=0) const;
329         unsigned calchash(void) const;
330         ex series(const relational & r, int order, unsigned options = 0) const;
331         ex thisexprseq(const exvector & v) const;
332         ex thisexprseq(exvector * vp) const;
333 protected:
334         ex derivative(const symbol & s) const;
335         bool is_equal_same_type(const basic & other) const;
336         bool match_same_type(const basic & other) const;
337         unsigned return_type(void) const;
338         unsigned return_type_tinfo(void) const;
339         
340         // new virtual functions which can be overridden by derived classes
341         // none
342         
343         // non-virtual functions in this class
344 protected:
345         ex pderivative(unsigned diff_param) const; // partial differentiation
346         static std::vector<function_options> & registered_functions(void);
347         bool lookup_remember_table(ex & result) const;
348         void store_remember_table(ex const & result) const;
349 public:
350         static unsigned register_new(function_options const & opt);
351         static unsigned current_serial;
352         static unsigned find_function(const std::string &name, unsigned nparams);
353         unsigned get_serial(void) const {return serial;}
354         std::string get_name(void) const;
355
356 // member variables
357
358 protected:
359         unsigned serial;
360 };
361
362 // utility functions/macros
363
364 /** Specialization of is_exactly_a<function>(obj) for objects of type function. */
365 template<> inline bool is_exactly_a<function>(const basic & obj)
366 {
367         return obj.tinfo()==TINFO_function;
368 }
369
370 #define is_ex_the_function(OBJ, FUNCNAME) \\
371         (is_exactly_a<GiNaC::function>(OBJ) && ex_to<GiNaC::function>(OBJ).get_serial() == function_index_##FUNCNAME)
372
373 } // namespace GiNaC
374
375 #endif // ndef __GINAC_FUNCTION_H__
376
377 END_OF_INTERFACE
378
379 $implementation=<<END_OF_IMPLEMENTATION;
380 /** \@file function.cpp
381  *
382  *  Implementation of class of symbolic functions. */
383
384 /*
385  *  This file was generated automatically by function.pl.
386  *  Please do not modify it directly, edit the perl script instead!
387  *  function.pl options: \$maxargs=${maxargs}
388  *
389  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
390  *
391  *  This program is free software; you can redistribute it and/or modify
392  *  it under the terms of the GNU General Public License as published by
393  *  the Free Software Foundation; either version 2 of the License, or
394  *  (at your option) any later version.
395  *
396  *  This program is distributed in the hope that it will be useful,
397  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
398  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
399  *  GNU General Public License for more details.
400  *
401  *  You should have received a copy of the GNU General Public License
402  *  along with this program; if not, write to the Free Software
403  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
404  */
405
406 #include <iostream>
407 #include <string>
408 #include <stdexcept>
409 #include <list>
410
411 #include "function.h"
412 #include "fderivative.h"
413 #include "ex.h"
414 #include "lst.h"
415 #include "symmetry.h"
416 #include "print.h"
417 #include "archive.h"
418 #include "inifcns.h"
419 #include "tostring.h"
420 #include "utils.h"
421 #include "remember.h"
422
423 namespace GiNaC {
424
425 //////////
426 // helper class function_options
427 //////////
428
429 function_options::function_options()
430 {
431         initialize();
432 }
433
434 function_options::function_options(std::string const & n, std::string const & tn)
435 {
436         initialize();
437         set_name(n,tn);
438 }
439
440 function_options::~function_options()
441 {
442         // nothing to clean up at the moment
443 }
444
445 void function_options::initialize(void)
446 {
447         set_name("unnamed_function","\\\\mbox{unnamed}");
448         nparams = 0;
449         eval_f = evalf_f = derivative_f = series_f = 0;
450         evalf_params_first = true;
451         use_return_type = false;
452         eval_use_exvector_args = false;
453         evalf_use_exvector_args = false;
454         derivative_use_exvector_args = false;
455         series_use_exvector_args = false;
456         use_remember = false;
457         functions_with_same_name = 1;
458         symtree = 0;
459 }
460
461 function_options & function_options::set_name(std::string const & n,
462                                               std::string const & tn)
463 {
464         name = n;
465         if (tn==std::string())
466                 TeX_name = "\\\\mbox{"+name+"}";
467         else
468                 TeX_name = tn;
469         return *this;
470 }
471
472 function_options & function_options::latex_name(std::string const & tn)
473 {
474         TeX_name = tn;
475         return *this;
476 }
477
478 // the following lines have been generated for max. ${maxargs} parameters
479 $eval_func_implementation
480 $evalf_func_implementation
481 $derivative_func_implementation
482 $series_func_implementation
483 // end of generated lines
484
485 function_options& function_options::eval_func(eval_funcp_exvector e)
486 {
487         eval_use_exvector_args = true;
488         eval_f = eval_funcp(e);
489         return *this;
490 }
491 function_options& function_options::evalf_func(evalf_funcp_exvector ef)
492 {
493         evalf_use_exvector_args = true;
494         evalf_f = evalf_funcp(ef);
495         return *this;
496 }
497 function_options& function_options::derivative_func(derivative_funcp_exvector d)
498 {
499         derivative_use_exvector_args = true;
500         derivative_f = derivative_funcp(d);
501         return *this;
502 }
503 function_options& function_options::series_func(series_funcp_exvector s)
504 {
505         series_use_exvector_args = true;
506         series_f = series_funcp(s);
507         return *this;
508 }
509
510
511 function_options & function_options::set_return_type(unsigned rt, unsigned rtt)
512 {
513         use_return_type = true;
514         return_type = rt;
515         return_type_tinfo = rtt;
516         return *this;
517 }
518
519 function_options & function_options::do_not_evalf_params(void)
520 {
521         evalf_params_first = false;
522         return *this;
523 }
524
525 function_options & function_options::remember(unsigned size,
526                                               unsigned assoc_size,
527                                               unsigned strategy)
528 {
529         use_remember = true;
530         remember_size = size;
531         remember_assoc_size = assoc_size;
532         remember_strategy = strategy;
533         return *this;
534 }
535
536 function_options & function_options::overloaded(unsigned o)
537 {
538         functions_with_same_name = o;
539         return *this;
540 }
541
542 function_options & function_options::set_symmetry(const symmetry & s)
543 {
544         symtree = s;
545         return *this;
546 }
547         
548 void function_options::test_and_set_nparams(unsigned n)
549 {
550         if (nparams==0) {
551                 nparams = n;
552         } else if (nparams!=n) {
553                 // we do not throw an exception here because this code is
554                 // usually executed before main(), so the exception could not
555                 // caught anyhow
556                 std::cerr << "WARNING: number of parameters ("
557                           << n << ") differs from number set before (" 
558                           << nparams << ")" << std::endl;
559         }
560 }
561
562 /** This can be used as a hook for external applications. */
563 unsigned function::current_serial = 0;
564
565
566 GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
567
568 //////////
569 // default ctor, dtor, copy ctor, assignment operator and helpers
570 //////////
571
572 // public
573
574 function::function() : serial(0)
575 {
576         tinfo_key = TINFO_function;
577 }
578
579 // protected
580
581 void function::copy(const function & other)
582 {
583         inherited::copy(other);
584         serial = other.serial;
585 }
586
587 void function::destroy(bool call_parent)
588 {
589         if (call_parent)
590                 inherited::destroy(call_parent);
591 }
592
593 //////////
594 // other ctors
595 //////////
596
597 // public
598
599 function::function(unsigned ser) : serial(ser)
600 {
601         tinfo_key = TINFO_function;
602 }
603
604 // the following lines have been generated for max. ${maxargs} parameters
605 $constructors_implementation
606 // end of generated lines
607
608 function::function(unsigned ser, const exprseq & es) : exprseq(es), serial(ser)
609 {
610         tinfo_key = TINFO_function;
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, const 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, const 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_of_type(c, print_tree)) {
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 (unsigned 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_of_type(c, print_csrc)) {
686
687                 // Print function name in lowercase
688                 std::string lname = registered_functions()[serial].name;
689                 unsigned num = lname.size();
690                 for (unsigned 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_of_type(c, print_latex)) {
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 int function::degree(const ex & s) const
723 {
724         return is_equal(ex_to<basic>(s)) ? 1 : 0;
725 }
726
727 int function::ldegree(const ex & s) const
728 {
729         return is_equal(ex_to<basic>(s)) ? 1 : 0;
730 }
731
732 ex function::coeff(const ex & s, int n) const
733 {
734         if (is_equal(ex_to<basic>(s)))
735                 return n==1 ? _ex1 : _ex0;
736         else
737                 return n==0 ? ex(*this) : _ex0;
738 }
739
740 ex function::eval(int level) const
741 {
742         GINAC_ASSERT(serial<registered_functions().size());
743
744         if (level>1) {
745                 // first evaluate children, then we will end up here again
746                 return function(serial,evalchildren(level));
747         }
748
749         const function_options &opt = registered_functions()[serial];
750
751         // Canonicalize argument order according to the symmetry properties
752         if (seq.size() > 1 && !(opt.symtree.is_zero())) {
753                 exvector v = seq;
754                 GINAC_ASSERT(is_a<symmetry>(opt.symtree));
755                 int sig = canonicalize(v.begin(), ex_to<symmetry>(opt.symtree));
756                 if (sig != INT_MAX) {
757                         // Something has changed while sorting arguments, more evaluations later
758                         if (sig == 0)
759                                 return _ex0;
760                         return ex(sig) * thisexprseq(v);
761                 }
762         }
763
764         if (opt.eval_f==0) {
765                 return this->hold();
766         }
767
768         bool use_remember = opt.use_remember;
769         ex eval_result;
770         if (use_remember && lookup_remember_table(eval_result)) {
771                 return eval_result;
772         }
773         current_serial = serial;
774         if (registered_functions()[serial].eval_use_exvector_args)
775                 eval_result = ((eval_funcp_exvector)(registered_functions()[serial].eval_f))(seq);
776         else
777         switch (opt.nparams) {
778                 // the following lines have been generated for max. ${maxargs} parameters
779 ${eval_switch_statement}
780                 // end of generated lines
781         default:
782                 throw(std::logic_error("function::eval(): invalid nparams"));
783         }
784         if (use_remember) {
785                 store_remember_table(eval_result);
786         }
787         return eval_result;
788 }
789
790 ex function::evalf(int level) const
791 {
792         GINAC_ASSERT(serial<registered_functions().size());
793
794         // Evaluate children first
795         exvector eseq;
796         if (level == 1)
797                 eseq = seq;
798         else if (level == -max_recursion_level)
799                 throw(std::runtime_error("max recursion level reached"));
800         else
801                 eseq.reserve(seq.size());
802         --level;
803         exvector::const_iterator it = seq.begin(), itend = seq.end();
804         while (it != itend) {
805                 eseq.push_back(it->evalf(level));
806                 ++it;
807         }
808         
809         if (registered_functions()[serial].evalf_f==0) {
810                 return function(serial,eseq).hold();
811         }
812         current_serial = serial;
813         if (registered_functions()[serial].evalf_use_exvector_args)
814                 return ((evalf_funcp_exvector)(registered_functions()[serial].evalf_f))(seq);
815         switch (registered_functions()[serial].nparams) {
816                 // the following lines have been generated for max. ${maxargs} parameters
817 ${evalf_switch_statement}
818                 // end of generated lines
819         }
820         throw(std::logic_error("function::evalf(): invalid nparams"));
821 }
822
823 unsigned function::calchash(void) const
824 {
825         unsigned v = golden_ratio_hash(golden_ratio_hash(tinfo()) ^ serial);
826         for (unsigned i=0; i<nops(); i++) {
827                 v = rotate_left_31(v);
828                 v ^= this->op(i).gethash();
829         }
830         v &= 0x7FFFFFFFU;
831         if (flags & status_flags::evaluated) {
832                 setflag(status_flags::hash_calculated);
833                 hashvalue = v;
834         }
835         return v;
836 }
837
838 ex function::thisexprseq(const exvector & v) const
839 {
840         return function(serial,v);
841 }
842
843 ex function::thisexprseq(exvector * vp) const
844 {
845         return function(serial,vp);
846 }
847
848 /** Implementation of ex::series for functions.
849  *  \@see ex::series */
850 ex function::series(const relational & r, int order, unsigned options) const
851 {
852         GINAC_ASSERT(serial<registered_functions().size());
853
854         if (registered_functions()[serial].series_f==0) {
855                 return basic::series(r, order);
856         }
857         ex res;
858         current_serial = serial;
859         if (registered_functions()[serial].series_use_exvector_args) {
860                 try {
861                         res = ((series_funcp_exvector)(registered_functions()[serial].series_f))(seq, r, order, options);
862                 } catch (do_taylor) {
863                         res = basic::series(r, order, options);
864                 }
865                 return res;
866         }
867         switch (registered_functions()[serial].nparams) {
868                 // the following lines have been generated for max. ${maxargs} parameters
869 ${series_switch_statement}
870                 // end of generated lines
871         }
872         throw(std::logic_error("function::series(): invalid nparams"));
873 }
874
875 // protected
876
877 /** Implementation of ex::diff() for functions. It applies the chain rule,
878  *  except for the Order term function.
879  *  \@see ex::diff */
880 ex function::derivative(const symbol & s) const
881 {
882         ex result;
883
884         if (serial == function_index_Order) {
885                 // Order Term function only differentiates the argument
886                 return Order(seq[0].diff(s));
887         } else {
888                 // Chain rule
889                 ex arg_diff;
890                 unsigned num = seq.size();
891                 for (unsigned i=0; i<num; i++) {
892                         arg_diff = seq[i].diff(s);
893                         // We apply the chain rule only when it makes sense.  This is not
894                         // just for performance reasons but also to allow functions to
895                         // throw when differentiated with respect to one of its arguments
896                         // without running into trouble with our automatic full
897                         // differentiation:
898                         if (!arg_diff.is_zero())
899                                 result += pderivative(i)*arg_diff;
900                 }
901         }
902         return result;
903 }
904
905 int function::compare_same_type(const basic & other) const
906 {
907         GINAC_ASSERT(is_of_type(other, function));
908         const function & o = static_cast<const function &>(other);
909
910         if (serial != o.serial)
911                 return serial < o.serial ? -1 : 1;
912         else
913                 return exprseq::compare_same_type(o);
914 }
915
916 bool function::is_equal_same_type(const basic & other) const
917 {
918         GINAC_ASSERT(is_of_type(other, function));
919         const function & o = static_cast<const function &>(other);
920
921         if (serial != o.serial)
922                 return false;
923         else
924                 return exprseq::is_equal_same_type(o);
925 }
926
927 bool function::match_same_type(const basic & other) const
928 {
929         GINAC_ASSERT(is_of_type(other, function));
930         const function & o = static_cast<const function &>(other);
931
932         return serial == o.serial;
933 }
934
935 unsigned function::return_type(void) const
936 {
937         if (seq.empty())
938                 return return_types::commutative;
939         else
940                 return seq.begin()->return_type();
941 }
942
943 unsigned function::return_type_tinfo(void) const
944 {
945         if (seq.empty())
946                 return tinfo_key;
947         else
948                 return seq.begin()->return_type_tinfo();
949 }
950
951 //////////
952 // new virtual functions which can be overridden by derived classes
953 //////////
954
955 // none
956
957 //////////
958 // non-virtual functions in this class
959 //////////
960
961 // protected
962
963 ex function::pderivative(unsigned diff_param) const // partial differentiation
964 {
965         GINAC_ASSERT(serial<registered_functions().size());
966         
967         // No derivative defined? Then return abstract derivative object
968         if (registered_functions()[serial].derivative_f == NULL)
969                 return fderivative(serial, diff_param, seq);
970
971         current_serial = serial;
972         if (registered_functions()[serial].derivative_use_exvector_args)
973                 return ((derivative_funcp_exvector)(registered_functions()[serial].derivative_f))(seq, diff_param);
974         switch (registered_functions()[serial].nparams) {
975                 // the following lines have been generated for max. ${maxargs} parameters
976 ${diff_switch_statement}
977                 // end of generated lines
978         }
979         throw(std::logic_error("function::pderivative(): no diff function defined"));
980 }
981
982 std::vector<function_options> & function::registered_functions(void)
983 {
984         static std::vector<function_options> * rf = new std::vector<function_options>;
985         return *rf;
986 }
987
988 bool function::lookup_remember_table(ex & result) const
989 {
990         return remember_table::remember_tables()[serial].lookup_entry(*this,result);
991 }
992
993 void function::store_remember_table(ex const & result) const
994 {
995         remember_table::remember_tables()[serial].add_entry(*this,result);
996 }
997
998 // public
999
1000 unsigned function::register_new(function_options const & opt)
1001 {
1002         unsigned same_name = 0;
1003         for (unsigned i=0; i<registered_functions().size(); ++i) {
1004                 if (registered_functions()[i].name==opt.name) {
1005                         ++same_name;
1006                 }
1007         }
1008         if (same_name>=opt.functions_with_same_name) {
1009                 // we do not throw an exception here because this code is
1010                 // usually executed before main(), so the exception could not
1011                 // caught anyhow
1012                 std::cerr << "WARNING: function name " << opt.name
1013                           << " already in use!" << std::endl;
1014         }
1015         registered_functions().push_back(opt);
1016         if (opt.use_remember) {
1017                 remember_table::remember_tables().
1018                         push_back(remember_table(opt.remember_size,
1019                                                  opt.remember_assoc_size,
1020                                                  opt.remember_strategy));
1021         } else {
1022                 remember_table::remember_tables().push_back(remember_table());
1023         }
1024         return registered_functions().size()-1;
1025 }
1026
1027 /** Find serial number of function by name and number of parameters.
1028  *  Throws exception if function was not found. */
1029 unsigned function::find_function(const std::string &name, unsigned nparams)
1030 {
1031         std::vector<function_options>::const_iterator i = function::registered_functions().begin(), end = function::registered_functions().end();
1032         unsigned serial = 0;
1033         while (i != end) {
1034                 if (i->get_name() == name && i->get_nparams() == nparams)
1035                         return serial;
1036                 ++i;
1037                 ++serial;
1038         }
1039         throw (std::runtime_error("no function '" + name + "' with " + ToString(nparams) + " parameters defined"));
1040 }
1041
1042 /** Return the print name of the function. */
1043 std::string function::get_name(void) const
1044 {
1045         GINAC_ASSERT(serial<registered_functions().size());
1046         return registered_functions()[serial].name;
1047 }
1048
1049 } // namespace GiNaC
1050
1051 END_OF_IMPLEMENTATION
1052
1053 print "Creating interface file function.h...";
1054 open OUT,">function.h" or die "cannot open function.h";
1055 print OUT $interface;
1056 close OUT;
1057 print "ok.\n";
1058
1059 print "Creating implementation file function.cpp...";
1060 open OUT,">function.cpp" or die "cannot open function.cpp";
1061 print OUT $implementation;
1062 close OUT;
1063 print "ok.\n";
1064
1065 print "done.\n";