- do something about the mad cast disease.
[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,$from,$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                 $res .= eval('"' . $template . '"');
26                 $SEQ1=''; # to avoid main::SEQ1 used only once warning
27                 $SEQ2=''; # same as above
28         }
29         return $res;
30 }
31
32 sub generate {
33         my ($template,$seq_template1,$seq_template2)=@_;
34         return generate_from_to($template,$seq_template1,$seq_template2,1,$maxargs);
35 }
36
37 $declare_function_macro = <<'END_OF_DECLARE_FUNCTION_1_AND_2P_MACRO';
38 #define DECLARE_FUNCTION_1P(NAME) \
39 extern const unsigned function_index_##NAME; \
40 inline GiNaC::function NAME(const GiNaC::ex & p1) { \
41         return GiNaC::function(function_index_##NAME, p1); \
42 }
43 #define DECLARE_FUNCTION_2P(NAME) \
44 extern const unsigned function_index_##NAME; \
45 inline GiNaC::function NAME(const GiNaC::ex & p1, const GiNaC::ex & p2) { \
46         return GiNaC::function(function_index_##NAME, p1, p2); \
47 }
48
49 END_OF_DECLARE_FUNCTION_1_AND_2P_MACRO
50
51 $declare_function_macro .= generate_from_to(
52         <<'END_OF_DECLARE_FUNCTION_MACRO','const GiNaC::ex & p${N}','p${N}',3,$maxargs);
53 #define DECLARE_FUNCTION_${N}P(NAME) \\
54 extern const unsigned function_index_##NAME; \\
55 inline GiNaC::function NAME(${SEQ1}) { \\
56         return GiNaC::function(function_index_##NAME, ${SEQ2}); \\
57 }
58
59 END_OF_DECLARE_FUNCTION_MACRO
60
61 $typedef_eval_funcp=generate(
62 'typedef ex (* eval_funcp_${N})(${SEQ1});'."\n",
63 'const ex &','');
64
65 $typedef_evalf_funcp=generate(
66 'typedef ex (* evalf_funcp_${N})(${SEQ1});'."\n",
67 'const ex &','');
68
69 $typedef_derivative_funcp=generate(
70 'typedef ex (* derivative_funcp_${N})(${SEQ1}, unsigned);'."\n",
71 'const ex &','');
72
73 $typedef_series_funcp=generate(
74 'typedef ex (* series_funcp_${N})(${SEQ1}, const relational &, int, unsigned);'."\n",
75 'const ex &','');
76
77 $eval_func_interface=generate('    function_options & eval_func(eval_funcp_${N} e);'."\n",'','');
78
79 $evalf_func_interface=generate('    function_options & evalf_func(evalf_funcp_${N} ef);'."\n",'','');
80
81 $derivative_func_interface=generate('    function_options & derivative_func(derivative_funcp_${N} d);'."\n",'','');
82
83 $series_func_interface=generate('    function_options & series_func(series_funcp_${N} s);'."\n",'','');
84
85 $constructors_interface=generate(
86 '    function(unsigned ser, ${SEQ1});'."\n",
87 'const ex & param${N}','');
88
89 $constructors_implementation=generate(
90         <<'END_OF_CONSTRUCTORS_IMPLEMENTATION','const ex & param${N}','param${N}');
91 function::function(unsigned ser, ${SEQ1})
92         : exprseq(${SEQ2}), serial(ser)
93 {
94         debugmsg(\"function ctor from unsigned,${N}*ex\",LOGLEVEL_CONSTRUCT);
95         tinfo_key = TINFO_function;
96 }
97 END_OF_CONSTRUCTORS_IMPLEMENTATION
98
99 $eval_switch_statement=generate(
100         <<'END_OF_EVAL_SWITCH_STATEMENT','seq[${N}-1]','');
101         case ${N}:
102                 eval_result=((eval_funcp_${N})(registered_functions()[serial].eval_f))(${SEQ1});
103                 break;
104 END_OF_EVAL_SWITCH_STATEMENT
105
106 $evalf_switch_statement=generate(
107         <<'END_OF_EVALF_SWITCH_STATEMENT','eseq[${N}-1]','');
108         case ${N}:
109                 return ((evalf_funcp_${N})(registered_functions()[serial].evalf_f))(${SEQ1});
110 END_OF_EVALF_SWITCH_STATEMENT
111
112 $diff_switch_statement=generate(
113         <<'END_OF_DIFF_SWITCH_STATEMENT','seq[${N}-1]','');
114         case ${N}:
115                 return ((derivative_funcp_${N})(registered_functions()[serial].derivative_f))(${SEQ1},diff_param);
116 END_OF_DIFF_SWITCH_STATEMENT
117
118 $series_switch_statement=generate(
119         <<'END_OF_SERIES_SWITCH_STATEMENT','seq[${N}-1]','');
120         case ${N}:
121                 try {
122                         res = ((series_funcp_${N})(registered_functions()[serial].series_f))(${SEQ1},r,order,options);
123                 } catch (do_taylor) {
124                         res = basic::series(r, order, options);
125                 }
126                 return res;
127 END_OF_SERIES_SWITCH_STATEMENT
128
129 $eval_func_implementation=generate(
130         <<'END_OF_EVAL_FUNC_IMPLEMENTATION','','');
131 function_options & function_options::eval_func(eval_funcp_${N} e)
132 {
133         test_and_set_nparams(${N});
134         eval_f=eval_funcp(e);
135         return *this;
136 }        
137 END_OF_EVAL_FUNC_IMPLEMENTATION
138
139 $evalf_func_implementation=generate(
140         <<'END_OF_EVALF_FUNC_IMPLEMENTATION','','');
141 function_options & function_options::evalf_func(evalf_funcp_${N} ef)
142 {
143         test_and_set_nparams(${N});
144         evalf_f=evalf_funcp(ef);
145         return *this;
146 }        
147 END_OF_EVALF_FUNC_IMPLEMENTATION
148
149 $derivative_func_implementation=generate(
150         <<'END_OF_DERIVATIVE_FUNC_IMPLEMENTATION','','');
151 function_options & function_options::derivative_func(derivative_funcp_${N} d)
152 {
153         test_and_set_nparams(${N});
154         derivative_f=derivative_funcp(d);
155         return *this;
156 }        
157 END_OF_DERIVATIVE_FUNC_IMPLEMENTATION
158
159 $series_func_implementation=generate(
160         <<'END_OF_SERIES_FUNC_IMPLEMENTATION','','');
161 function_options & function_options::series_func(series_funcp_${N} s)
162 {
163         test_and_set_nparams(${N});
164         series_f=series_funcp(s);
165         return *this;
166 }        
167 END_OF_SERIES_FUNC_IMPLEMENTATION
168
169 $interface=<<END_OF_INTERFACE;
170 /** \@file function.h
171  *
172  *  Interface to abstract class function (new function concept). */
173
174 /*
175  *  This file was generated automatically by function.pl.
176  *  Please do not modify it directly, edit the perl script instead!
177  *  function.pl options: \$maxargs=${maxargs}
178  *
179  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
180  *
181  *  This program is free software; you can redistribute it and/or modify
182  *  it under the terms of the GNU General Public License as published by
183  *  the Free Software Foundation; either version 2 of the License, or
184  *  (at your option) any later version.
185  *
186  *  This program is distributed in the hope that it will be useful,
187  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
188  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
189  *  GNU General Public License for more details.
190  *
191  *  You should have received a copy of the GNU General Public License
192  *  along with this program; if not, write to the Free Software
193  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
194  */
195
196 #ifndef __GINAC_FUNCTION_H__
197 #define __GINAC_FUNCTION_H__
198
199 #include <string>
200 #include <vector>
201
202 // CINT needs <algorithm> to work properly with <vector> 
203 #include <algorithm>
204
205 #include "exprseq.h"
206
207 // the following lines have been generated for max. ${maxargs} parameters
208 $declare_function_macro
209 // end of generated lines
210
211 #define REGISTER_FUNCTION(NAME,OPT) \\
212 const unsigned function_index_##NAME= \\
213         GiNaC::function::register_new(GiNaC::function_options(#NAME).OPT);
214
215 #define BEGIN_TYPECHECK \\
216 bool automatic_typecheck=true;
217
218 #define TYPECHECK(VAR,TYPE) \\
219 if (!is_exactly_a<TYPE>(VAR)) { \\
220         automatic_typecheck=false; \\
221 } else
222
223 #define TYPECHECK_INTEGER(VAR) \\
224 if (!(VAR).info(GiNaC::info_flags::integer)) { \\
225         automatic_typecheck=false; \\
226 } else
227
228 #define END_TYPECHECK(RV) \\
229 {} \\
230 if (!automatic_typecheck) { \\
231         return RV.hold(); \\
232 }
233
234 namespace GiNaC {
235
236 class function;
237 class symmetry;
238
239 typedef ex (* eval_funcp)();
240 typedef ex (* evalf_funcp)();
241 typedef ex (* derivative_funcp)();
242 typedef ex (* series_funcp)();
243
244 // the following lines have been generated for max. ${maxargs} parameters
245 $typedef_eval_funcp
246 $typedef_evalf_funcp
247 $typedef_derivative_funcp
248 $typedef_series_funcp
249 // end of generated lines
250
251 class function_options
252 {
253         friend class function;
254 public:
255         function_options();
256         function_options(std::string const & n, std::string const & tn=std::string());
257         ~function_options();
258         void initialize(void);
259         function_options & set_name(std::string const & n, std::string const & tn=std::string());
260         function_options & latex_name(std::string const & tn);
261 // the following lines have been generated for max. ${maxargs} parameters
262 $eval_func_interface
263 $evalf_func_interface
264 $derivative_func_interface
265 $series_func_interface
266 // end of generated lines
267         function_options & set_return_type(unsigned rt, unsigned rtt=0);
268         function_options & do_not_evalf_params(void);
269         function_options & remember(unsigned size, unsigned assoc_size=0,
270                                     unsigned strategy=remember_strategies::delete_never);
271         function_options & overloaded(unsigned o);
272         function_options & set_symmetry(const symmetry & s);
273         void test_and_set_nparams(unsigned n);
274         std::string get_name(void) const { return name; }
275         unsigned get_nparams(void) const { return nparams; }
276
277 protected:
278         std::string name;
279         std::string TeX_name;
280
281         unsigned nparams;
282
283         eval_funcp eval_f;
284         evalf_funcp evalf_f;
285         derivative_funcp derivative_f;
286         series_funcp series_f;
287
288         bool evalf_params_first;
289
290         bool use_return_type;
291         unsigned return_type;
292         unsigned return_type_tinfo;
293
294         bool use_remember;
295         unsigned remember_size;
296         unsigned remember_assoc_size;
297         unsigned remember_strategy;
298
299         unsigned functions_with_same_name;
300
301         ex symtree;
302 };
303
304 /** The class function is used to implement builtin functions like sin, cos...
305         and user defined functions */
306 class function : public exprseq
307 {
308         GINAC_DECLARE_REGISTERED_CLASS(function, exprseq)
309
310         // CINT has a linking problem
311 #ifndef __MAKECINT__
312         friend void ginsh_get_ginac_functions(void);
313 #endif // def __MAKECINT__
314
315         friend class remember_table_entry;
316         // friend class remember_table_list;
317         // friend class remember_table;
318
319 // member functions
320
321         // other ctors
322 public:
323         function(unsigned ser);
324         // the following lines have been generated for max. ${maxargs} parameters
325 $constructors_interface
326         // end of generated lines
327         function(unsigned ser, const exprseq & es);
328         function(unsigned ser, const exvector & v, bool discardable=0);
329         function(unsigned ser, exvector * vp); // vp will be deleted
330
331         // functions overriding virtual functions from bases classes
332 public:
333         void print(const print_context & c, unsigned level = 0) const;
334         unsigned precedence(void) const {return 70;}
335         int degree(const ex & s) const;
336         int ldegree(const ex & s) const;
337         ex coeff(const ex & s, int n = 1) const;
338         ex expand(unsigned options=0) const;
339         ex eval(int level=0) const;
340         ex evalf(int level=0) const;
341         unsigned calchash(void) const;
342         ex series(const relational & r, int order, unsigned options = 0) const;
343         bool match(const ex & pattern, lst & repl_lst) const;
344         ex thisexprseq(const exvector & v) const;
345         ex thisexprseq(exvector * vp) const;
346 protected:
347         ex derivative(const symbol & s) const;
348         bool is_equal_same_type(const basic & other) const;
349         unsigned return_type(void) const;
350         unsigned return_type_tinfo(void) const;
351         
352         // new virtual functions which can be overridden by derived classes
353         // none
354         
355         // non-virtual functions in this class
356 protected:
357         ex pderivative(unsigned diff_param) const; // partial differentiation
358         static std::vector<function_options> & registered_functions(void);
359         bool lookup_remember_table(ex & result) const;
360         void store_remember_table(ex const & result) const;
361 public:
362         static unsigned register_new(function_options const & opt);
363         static unsigned find_function(const std::string &name, unsigned nparams);
364         unsigned get_serial(void) const {return serial;}
365         std::string get_name(void) const;
366         
367 // member variables
368
369 protected:
370         unsigned serial;
371 };
372
373 // utility functions/macros
374 /** Return the object of type function handled by an ex.
375  *  This is unsafe: you need to check the type first. */
376 inline const function &ex_to_function(const ex &e)
377 {
378         return static_cast<const function &>(*e.bp);
379 }
380
381 /** Specialization of is_exactly_a<function>(obj) for objects of type function. */
382 template<> inline bool is_exactly_a<function>(const basic & obj)
383 {
384         return obj.tinfo()==TINFO_function;
385 }
386
387 #define is_ex_the_function(OBJ, FUNCNAME) \\
388         (is_ex_exactly_of_type(OBJ, function) && static_cast<GiNaC::function *>(OBJ.bp)->get_serial() == function_index_##FUNCNAME)
389
390 } // namespace GiNaC
391
392 #endif // ndef __GINAC_FUNCTION_H__
393
394 END_OF_INTERFACE
395
396 $implementation=<<END_OF_IMPLEMENTATION;
397 /** \@file function.cpp
398  *
399  *  Implementation of class function. */
400
401 /*
402  *  This file was generated automatically by function.pl.
403  *  Please do not modify it directly, edit the perl script instead!
404  *  function.pl options: \$maxargs=${maxargs}
405  *
406  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
407  *
408  *  This program is free software; you can redistribute it and/or modify
409  *  it under the terms of the GNU General Public License as published by
410  *  the Free Software Foundation; either version 2 of the License, or
411  *  (at your option) any later version.
412  *
413  *  This program is distributed in the hope that it will be useful,
414  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
415  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
416  *  GNU General Public License for more details.
417  *
418  *  You should have received a copy of the GNU General Public License
419  *  along with this program; if not, write to the Free Software
420  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
421  */
422
423 #include <string>
424 #include <stdexcept>
425 #include <list>
426
427 #include "function.h"
428 #include "ex.h"
429 #include "lst.h"
430 #include "symmetry.h"
431 #include "print.h"
432 #include "archive.h"
433 #include "inifcns.h"
434 #include "utils.h"
435 #include "debugmsg.h"
436 #include "remember.h"
437
438 namespace GiNaC {
439
440 //////////
441 // helper class function_options
442 //////////
443
444 function_options::function_options()
445 {
446         initialize();
447 }
448
449 function_options::function_options(std::string const & n, std::string const & tn)
450 {
451         initialize();
452         set_name(n,tn);
453 }
454
455 function_options::~function_options()
456 {
457         // nothing to clean up at the moment
458 }
459
460 void function_options::initialize(void)
461 {
462         set_name("unnamed_function","\\\\mbox{unnamed}");
463         nparams=0;
464         eval_f=evalf_f=derivative_f=series_f=0;
465         evalf_params_first=true;
466         use_return_type=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         }
481         return *this;
482 }
483
484 function_options & function_options::latex_name(std::string const & tn)
485 {
486         TeX_name=tn;
487         return *this;
488 }
489
490 // the following lines have been generated for max. ${maxargs} parameters
491 $eval_func_implementation
492 $evalf_func_implementation
493 $derivative_func_implementation
494 $series_func_implementation
495 // end of generated lines
496
497 function_options & function_options::set_return_type(unsigned rt, unsigned rtt)
498 {
499         use_return_type=true;
500         return_type=rt;
501         return_type_tinfo=rtt;
502         return *this;
503 }
504
505 function_options & function_options::do_not_evalf_params(void)
506 {
507         evalf_params_first=false;
508         return *this;
509 }
510
511 function_options & function_options::remember(unsigned size,
512                                               unsigned assoc_size,
513                                               unsigned strategy)
514 {
515         use_remember=true;
516         remember_size=size;
517         remember_assoc_size=assoc_size;
518         remember_strategy=strategy;
519         return *this;
520 }
521
522 function_options & function_options::overloaded(unsigned o)
523 {
524         functions_with_same_name=o;
525         return *this;
526 }
527
528 function_options & function_options::set_symmetry(const symmetry & s)
529 {
530         symtree = s;
531         return *this;
532 }
533         
534 void function_options::test_and_set_nparams(unsigned n)
535 {
536         if (nparams==0) {
537                 nparams=n;
538         } else if (nparams!=n) {
539                 // we do not throw an exception here because this code is
540                 // usually executed before main(), so the exception could not
541                 // caught anyhow
542                 std::cerr << "WARNING: number of parameters ("
543                           << n << ") differs from number set before (" 
544                           << nparams << ")" << std::endl;
545         }
546 }
547
548 GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
549
550 //////////
551 // default ctor, dtor, copy ctor assignment operator and helpers
552 //////////
553
554 // public
555
556 function::function() : serial(0)
557 {
558         debugmsg("function default ctor",LOGLEVEL_CONSTRUCT);
559         tinfo_key = TINFO_function;
560 }
561
562 // protected
563
564 void function::copy(const function & other)
565 {
566         exprseq::copy(other);
567         serial=other.serial;
568 }
569
570 void function::destroy(bool call_parent)
571 {
572         if (call_parent) exprseq::destroy(call_parent);
573 }
574
575 //////////
576 // other ctors
577 //////////
578
579 // public
580
581 function::function(unsigned ser) : serial(ser)
582 {
583         debugmsg("function ctor from unsigned",LOGLEVEL_CONSTRUCT);
584         tinfo_key = TINFO_function;
585 }
586
587 // the following lines have been generated for max. ${maxargs} parameters
588 $constructors_implementation
589 // end of generated lines
590
591 function::function(unsigned ser, const exprseq & es) : exprseq(es), serial(ser)
592 {
593         debugmsg("function ctor from unsigned,exprseq",LOGLEVEL_CONSTRUCT);
594         tinfo_key = TINFO_function;
595 }
596
597 function::function(unsigned ser, const exvector & v, bool discardable) 
598   : exprseq(v,discardable), serial(ser)
599 {
600         debugmsg("function ctor from string,exvector,bool",LOGLEVEL_CONSTRUCT);
601         tinfo_key = TINFO_function;
602 }
603
604 function::function(unsigned ser, exvector * vp) 
605   : exprseq(vp), serial(ser)
606 {
607         debugmsg("function ctor from unsigned,exvector *",LOGLEVEL_CONSTRUCT);
608         tinfo_key = TINFO_function;
609 }
610
611 //////////
612 // archiving
613 //////////
614
615 /** Construct object from archive_node. */
616 function::function(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
617 {
618         debugmsg("function ctor from archive_node", LOGLEVEL_CONSTRUCT);
619
620         // Find serial number by function name
621         std::string s;
622         if (n.find_string("name", s)) {
623                 unsigned int ser = 0;
624                 std::vector<function_options>::const_iterator i = registered_functions().begin(), iend = registered_functions().end();
625                 while (i != iend) {
626                         if (s == i->name) {
627                                 serial = ser;
628                                 return;
629                         }
630                         i++; ser++;
631                 }
632                 throw (std::runtime_error("unknown function '" + s + "' in archive"));
633         } else
634                 throw (std::runtime_error("unnamed function in archive"));
635 }
636
637 /** Unarchive the object. */
638 ex function::unarchive(const archive_node &n, const lst &sym_lst)
639 {
640         return (new function(n, sym_lst))->setflag(status_flags::dynallocated);
641 }
642
643 /** Archive the object. */
644 void function::archive(archive_node &n) const
645 {
646         inherited::archive(n);
647         GINAC_ASSERT(serial < registered_functions().size());
648         n.add_string("name", registered_functions()[serial].name);
649 }
650
651 //////////
652 // functions overriding virtual functions from bases classes
653 //////////
654
655 // public
656
657 void function::print(const print_context & c, unsigned level) const
658 {
659         debugmsg("function print", LOGLEVEL_PRINT);
660
661         GINAC_ASSERT(serial<registered_functions().size());
662
663         if (is_of_type(c, print_tree)) {
664
665                 c.s << std::string(level, ' ') << class_name() << " "
666                     << registered_functions()[serial].name
667                     << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
668                     << ", nops=" << nops()
669                     << std::endl;
670                 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
671                 for (unsigned i=0; i<nops(); ++i)
672                         seq[i].print(c, level + delta_indent);
673                 c.s << std::string(level + delta_indent, ' ') << "=====" << std::endl;
674
675         } else if (is_of_type(c, print_csrc)) {
676
677                 // Print function name in lowercase
678                 std::string lname = registered_functions()[serial].name;
679                 for (unsigned i=0; i<lname.size(); i++)
680                         lname[i] = tolower(lname[i]);
681                 c.s << lname << "(";
682
683                 // Print arguments, separated by commas
684                 exvector::const_iterator it = seq.begin(), itend = seq.end();
685                 while (it != itend) {
686                         it->print(c);
687                         it++;
688                         if (it != itend)
689                                 c.s << ",";
690                 }
691                 c.s << ")";
692
693         } else if (is_of_type(c, print_latex)) {
694                 c.s << registered_functions()[serial].TeX_name;
695                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
696         } else {
697                 c.s << registered_functions()[serial].name;
698                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
699         }
700 }
701
702 ex function::expand(unsigned options) const
703 {
704         return this->setflag(status_flags::expanded);
705 }
706
707 int function::degree(const ex & s) const
708 {
709         return is_equal(*s.bp) ? 1 : 0;
710 }
711
712 int function::ldegree(const ex & s) const
713 {
714         return is_equal(*s.bp) ? 1 : 0;
715 }
716
717 ex function::coeff(const ex & s, int n) const
718 {
719         if (is_equal(*s.bp))
720                 return n==1 ? _ex1() : _ex0();
721         else
722                 return n==0 ? ex(*this) : _ex0();
723 }
724
725 ex function::eval(int level) const
726 {
727         GINAC_ASSERT(serial<registered_functions().size());
728
729         if (level>1) {
730                 // first evaluate children, then we will end up here again
731                 return function(serial,evalchildren(level));
732         }
733
734         const function_options &opt = registered_functions()[serial];
735
736         // Canonicalize argument order according to the symmetry properties
737         if (seq.size() > 1 && !(opt.symtree.is_zero())) {
738                 exvector v = seq;
739                 GINAC_ASSERT(is_ex_exactly_of_type(opt.symtree, symmetry));
740                 int sig = canonicalize(v.begin(), ex_to<symmetry>(opt.symtree));
741                 if (sig != INT_MAX) {
742                         // Something has changed while sorting arguments, more evaluations later
743                         if (sig == 0)
744                                 return _ex0();
745                         return ex(sig) * thisexprseq(v);
746                 }
747         }
748
749         if (opt.eval_f==0) {
750                 return this->hold();
751         }
752
753         bool use_remember=opt.use_remember;
754         ex eval_result;
755         if (use_remember && lookup_remember_table(eval_result)) {
756                 return eval_result;
757         }
758
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         exvector eseq=evalfchildren(level);
777         
778         if (registered_functions()[serial].evalf_f==0) {
779                 return function(serial,eseq).hold();
780         }
781         switch (registered_functions()[serial].nparams) {
782                 // the following lines have been generated for max. ${maxargs} parameters
783 ${evalf_switch_statement}
784                 // end of generated lines
785         }
786         throw(std::logic_error("function::evalf(): invalid nparams"));
787 }
788
789 unsigned function::calchash(void) const
790 {
791         unsigned v = golden_ratio_hash(golden_ratio_hash(tinfo()) ^ serial);
792         for (unsigned i=0; i<nops(); i++) {
793                 v = rotate_left_31(v);
794                 v ^= this->op(i).gethash();
795         }
796         v &= 0x7FFFFFFFU;
797         if (flags & status_flags::evaluated) {
798                 setflag(status_flags::hash_calculated);
799                 hashvalue = v;
800         }
801         return v;
802 }
803
804 ex function::thisexprseq(const exvector & v) const
805 {
806         return function(serial,v);
807 }
808
809 ex function::thisexprseq(exvector * vp) const
810 {
811         return function(serial,vp);
812 }
813
814 /** Implementation of ex::series for functions.
815  *  \@see ex::series */
816 ex function::series(const relational & r, int order, unsigned options) const
817 {
818         GINAC_ASSERT(serial<registered_functions().size());
819
820         if (registered_functions()[serial].series_f==0) {
821                 return basic::series(r, order);
822         }
823         ex res;
824         switch (registered_functions()[serial].nparams) {
825                 // the following lines have been generated for max. ${maxargs} parameters
826 ${series_switch_statement}
827                 // end of generated lines
828         }
829         throw(std::logic_error("function::series(): invalid nparams"));
830 }
831
832 bool function::match(const ex & pattern, lst & repl_lst) const
833 {
834         // Serial number must match
835         if (is_ex_of_type(pattern, function) && serial != ex_to<function>(pattern).serial)
836                 return false;
837         return inherited::match(pattern, repl_lst);
838 }
839
840 // protected
841
842
843 /** Implementation of ex::diff() for functions. It applies the chain rule,
844  *  except for the Order term function.
845  *  \@see ex::diff */
846 ex function::derivative(const symbol & s) const
847 {
848         ex result;
849         
850         if (serial == function_index_Order) {
851                 // Order Term function only differentiates the argument
852                 return Order(seq[0].diff(s));
853         } else if (serial == function_index_Derivative) {
854                 // Inert derivative performs chain rule on the first argument only, and
855                 // adds differentiation parameter to list (second argument)
856                 GINAC_ASSERT(is_ex_exactly_of_type(seq[0], function));
857                 GINAC_ASSERT(is_ex_exactly_of_type(seq[1], function));
858                 ex fcn = seq[0];
859                 ex arg_diff;
860                 for (unsigned i=0; i!=fcn.nops(); i++) {
861                         arg_diff = fcn.op(i).diff(s);
862                         if (!arg_diff.is_zero()) {
863                                 lst new_lst = ex_to<lst>(seq[1]);
864                                 new_lst.append(i);
865                                 result += arg_diff * Derivative(fcn, new_lst);
866                         }
867                 }
868         } else {
869                 // Chain rule
870                 ex arg_diff;
871                 for (unsigned i=0; i!=seq.size(); i++) {
872                         arg_diff = seq[i].diff(s);
873                         // We apply the chain rule only when it makes sense.  This is not
874                         // just for performance reasons but also to allow functions to
875                         // throw when differentiated with respect to one of its arguments
876                         // without running into trouble with our automatic full
877                         // differentiation:
878                         if (!arg_diff.is_zero())
879                                 result += pderivative(i)*arg_diff;
880                 }
881         }
882         return result;
883 }
884
885 int function::compare_same_type(const basic & other) const
886 {
887         GINAC_ASSERT(is_of_type(other, function));
888         const function & o = static_cast<const function &>(other);
889
890         if (serial!=o.serial) {
891                 return serial < o.serial ? -1 : 1;
892         }
893         return exprseq::compare_same_type(o);
894 }
895
896 bool function::is_equal_same_type(const basic & other) const
897 {
898         GINAC_ASSERT(is_of_type(other, function));
899         const function & o = static_cast<const function &>(other);
900
901         if (serial!=o.serial) return false;
902         return exprseq::is_equal_same_type(o);
903 }
904
905 unsigned function::return_type(void) const
906 {
907         if (seq.size()==0) {
908                 return return_types::commutative;
909         }
910         return (*seq.begin()).return_type();
911 }
912    
913 unsigned function::return_type_tinfo(void) const
914 {
915         if (seq.size()==0) {
916                 return tinfo_key;
917         }
918         return (*seq.begin()).return_type_tinfo();
919 }
920
921 //////////
922 // new virtual functions which can be overridden by derived classes
923 //////////
924
925 // none
926
927 //////////
928 // non-virtual functions in this class
929 //////////
930
931 // protected
932
933 ex function::pderivative(unsigned diff_param) const // partial differentiation
934 {
935         GINAC_ASSERT(serial<registered_functions().size());
936         
937         if (registered_functions()[serial].derivative_f==0) {
938                 return Derivative(*this, lst(ex(diff_param)));
939         }
940         switch (registered_functions()[serial].nparams) {
941                 // the following lines have been generated for max. ${maxargs} parameters
942 ${diff_switch_statement}
943                 // end of generated lines
944         }        
945         throw(std::logic_error("function::pderivative(): no diff function defined"));
946 }
947
948 std::vector<function_options> & function::registered_functions(void)
949 {
950         static std::vector<function_options> * rf = new std::vector<function_options>;
951         return *rf;
952 }
953
954 bool function::lookup_remember_table(ex & result) const
955 {
956         return remember_table::remember_tables()[serial].lookup_entry(*this,result);
957 }
958
959 void function::store_remember_table(ex const & result) const
960 {
961         remember_table::remember_tables()[serial].add_entry(*this,result);
962 }
963
964 // public
965
966 unsigned function::register_new(function_options const & opt)
967 {
968         unsigned same_name=0;
969         for (unsigned i=0; i<registered_functions().size(); ++i) {
970                 if (registered_functions()[i].name==opt.name) {
971                         same_name++;
972                 }
973         }
974         if (same_name>=opt.functions_with_same_name) {
975                 // we do not throw an exception here because this code is
976                 // usually executed before main(), so the exception could not
977                 // caught anyhow
978                 std::cerr << "WARNING: function name " << opt.name
979                                   << " already in use!" << std::endl;
980         }
981         registered_functions().push_back(opt);
982         if (opt.use_remember) {
983                 remember_table::remember_tables().
984                         push_back(remember_table(opt.remember_size,
985                                                                          opt.remember_assoc_size,
986                                                                          opt.remember_strategy));
987         } else {
988                 remember_table::remember_tables().push_back(remember_table());
989         }
990         return registered_functions().size()-1;
991 }
992
993 /** Find serial number of function by name and number of parameters.
994  *  Throws exception if function was not found. */
995 unsigned function::find_function(const std::string &name, unsigned nparams)
996 {
997         std::vector<function_options>::const_iterator i = function::registered_functions().begin(), end = function::registered_functions().end();
998         unsigned serial = 0;
999         while (i != end) {
1000                 if (i->get_name() == name && i->get_nparams() == nparams)
1001                         return serial;
1002                 i++;
1003                 serial++;
1004         }
1005         throw (std::runtime_error("no function '" + name + "' with " + ToString(nparams) + " parameters defined"));
1006 }
1007
1008 /** Return the print name of the function. */
1009 std::string function::get_name(void) const
1010 {
1011         GINAC_ASSERT(serial<registered_functions().size());
1012         return registered_functions()[serial].name;
1013 }
1014
1015 } // namespace GiNaC
1016
1017 END_OF_IMPLEMENTATION
1018
1019 print "Creating interface file function.h...";
1020 open OUT,">function.h" or die "cannot open function.h";
1021 print OUT $interface;
1022 close OUT;
1023 print "ok.\n";
1024
1025 print "Creating implementation file function.cpp...";
1026 open OUT,">function.cpp" or die "cannot open function.cpp";
1027 print OUT $implementation;
1028 close OUT;
1029 print "ok.\n";
1030
1031 print "done.\n";