258f4a07b82ea18fce25d639ea58317d68b1cbfe
[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         debugmsg(\"function ctor from unsigned,${N}*ex\",LOGLEVEL_CONSTRUCT);
84         tinfo_key = TINFO_function;
85 }
86 END_OF_CONSTRUCTORS_IMPLEMENTATION
87
88 $eval_switch_statement=generate(
89         <<'END_OF_EVAL_SWITCH_STATEMENT','seq[${N}-1]','','');
90         case ${N}:
91                 eval_result = ((eval_funcp_${N})(registered_functions()[serial].eval_f))(${SEQ1});
92                 break;
93 END_OF_EVAL_SWITCH_STATEMENT
94
95 $evalf_switch_statement=generate(
96         <<'END_OF_EVALF_SWITCH_STATEMENT','eseq[${N}-1]','','');
97         case ${N}:
98                 return ((evalf_funcp_${N})(registered_functions()[serial].evalf_f))(${SEQ1});
99 END_OF_EVALF_SWITCH_STATEMENT
100
101 $diff_switch_statement=generate(
102         <<'END_OF_DIFF_SWITCH_STATEMENT','seq[${N}-1]','','');
103         case ${N}:
104                 return ((derivative_funcp_${N})(registered_functions()[serial].derivative_f))(${SEQ1},diff_param);
105 END_OF_DIFF_SWITCH_STATEMENT
106
107 $series_switch_statement=generate(
108         <<'END_OF_SERIES_SWITCH_STATEMENT','seq[${N}-1]','','');
109         case ${N}:
110                 try {
111                         res = ((series_funcp_${N})(registered_functions()[serial].series_f))(${SEQ1},r,order,options);
112                 } catch (do_taylor) {
113                         res = basic::series(r, order, options);
114                 }
115                 return res;
116 END_OF_SERIES_SWITCH_STATEMENT
117
118 $eval_func_implementation=generate(
119         <<'END_OF_EVAL_FUNC_IMPLEMENTATION','','','');
120 function_options & function_options::eval_func(eval_funcp_${N} e)
121 {
122         test_and_set_nparams(${N});
123         eval_f = eval_funcp(e);
124         return *this;
125 }
126 END_OF_EVAL_FUNC_IMPLEMENTATION
127
128 $evalf_func_implementation=generate(
129         <<'END_OF_EVALF_FUNC_IMPLEMENTATION','','','');
130 function_options & function_options::evalf_func(evalf_funcp_${N} ef)
131 {
132         test_and_set_nparams(${N});
133         evalf_f = evalf_funcp(ef);
134         return *this;
135 }
136 END_OF_EVALF_FUNC_IMPLEMENTATION
137
138 $derivative_func_implementation=generate(
139         <<'END_OF_DERIVATIVE_FUNC_IMPLEMENTATION','','','');
140 function_options & function_options::derivative_func(derivative_funcp_${N} d)
141 {
142         test_and_set_nparams(${N});
143         derivative_f = derivative_funcp(d);
144         return *this;
145 }
146 END_OF_DERIVATIVE_FUNC_IMPLEMENTATION
147
148 $series_func_implementation=generate(
149         <<'END_OF_SERIES_FUNC_IMPLEMENTATION','','','');
150 function_options & function_options::series_func(series_funcp_${N} s)
151 {
152         test_and_set_nparams(${N});
153         series_f = series_funcp(s);
154         return *this;
155 }
156 END_OF_SERIES_FUNC_IMPLEMENTATION
157
158 $interface=<<END_OF_INTERFACE;
159 /** \@file function.h
160  *
161  *  Interface to class of symbolic functions. */
162
163 /*
164  *  This file was generated automatically by function.pl.
165  *  Please do not modify it directly, edit the perl script instead!
166  *  function.pl options: \$maxargs=${maxargs}
167  *
168  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
169  *
170  *  This program is free software; you can redistribute it and/or modify
171  *  it under the terms of the GNU General Public License as published by
172  *  the Free Software Foundation; either version 2 of the License, or
173  *  (at your option) any later version.
174  *
175  *  This program is distributed in the hope that it will be useful,
176  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
177  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
178  *  GNU General Public License for more details.
179  *
180  *  You should have received a copy of the GNU General Public License
181  *  along with this program; if not, write to the Free Software
182  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
183  */
184
185 #ifndef __GINAC_FUNCTION_H__
186 #define __GINAC_FUNCTION_H__
187
188 #include <string>
189 #include <vector>
190
191 // CINT needs <algorithm> to work properly with <vector>
192 #include <algorithm>
193
194 #include "exprseq.h"
195
196 // the following lines have been generated for max. ${maxargs} parameters
197 $declare_function_macro
198 // end of generated lines
199
200 #define REGISTER_FUNCTION(NAME,OPT) \\
201 const unsigned function_index_##NAME= \\
202         GiNaC::function::register_new(GiNaC::function_options(#NAME).OPT);
203
204 #define BEGIN_TYPECHECK \\
205 bool automatic_typecheck=true;
206
207 #define TYPECHECK(VAR,TYPE) \\
208 if (!is_exactly_a<TYPE>(VAR)) { \\
209         automatic_typecheck=false; \\
210 } else
211
212 #define TYPECHECK_INTEGER(VAR) \\
213 if (!(VAR).info(GiNaC::info_flags::integer)) { \\
214         automatic_typecheck=false; \\
215 } else
216
217 #define END_TYPECHECK(RV) \\
218 {} \\
219 if (!automatic_typecheck) { \\
220         return RV.hold(); \\
221 }
222
223 namespace GiNaC {
224
225 class function;
226 class symmetry;
227
228 typedef ex (* eval_funcp)();
229 typedef ex (* evalf_funcp)();
230 typedef ex (* derivative_funcp)();
231 typedef ex (* series_funcp)();
232
233 // the following lines have been generated for max. ${maxargs} parameters
234 $typedef_eval_funcp
235 $typedef_evalf_funcp
236 $typedef_derivative_funcp
237 $typedef_series_funcp
238 // end of generated lines
239
240 class function_options
241 {
242         friend class function;
243         friend class fderivative;
244 public:
245         function_options();
246         function_options(std::string const & n, std::string const & tn=std::string());
247         ~function_options();
248         void initialize(void);
249         function_options & set_name(std::string const & n, std::string const & tn=std::string());
250         function_options & latex_name(std::string const & tn);
251 // the following lines have been generated for max. ${maxargs} parameters
252 $eval_func_interface
253 $evalf_func_interface
254 $derivative_func_interface
255 $series_func_interface
256 // end of generated lines
257         function_options & set_return_type(unsigned rt, unsigned rtt=0);
258         function_options & do_not_evalf_params(void);
259         function_options & remember(unsigned size, unsigned assoc_size=0,
260                                     unsigned strategy=remember_strategies::delete_never);
261         function_options & overloaded(unsigned o);
262         function_options & set_symmetry(const symmetry & s);
263         void test_and_set_nparams(unsigned n);
264         std::string get_name(void) const { return name; }
265         unsigned get_nparams(void) const { return nparams; }
266         bool has_derivative(void) const { return derivative_f != NULL; }
267
268 protected:
269         std::string name;
270         std::string TeX_name;
271
272         unsigned nparams;
273
274         eval_funcp eval_f;
275         evalf_funcp evalf_f;
276         derivative_funcp derivative_f;
277         series_funcp series_f;
278
279         bool evalf_params_first;
280
281         bool use_return_type;
282         unsigned return_type;
283         unsigned return_type_tinfo;
284
285         bool use_remember;
286         unsigned remember_size;
287         unsigned remember_assoc_size;
288         unsigned remember_strategy;
289
290         unsigned functions_with_same_name;
291
292         ex symtree;
293 };
294
295 /** The class function is used to implement builtin functions like sin, cos...
296         and user defined functions */
297 class function : public exprseq
298 {
299         GINAC_DECLARE_REGISTERED_CLASS(function, exprseq)
300
301         // CINT has a linking problem
302 #ifndef __MAKECINT__
303         friend void ginsh_get_ginac_functions(void);
304 #endif // def __MAKECINT__
305
306         friend class remember_table_entry;
307         // friend class remember_table_list;
308         // friend class remember_table;
309
310 // member functions
311
312         // other ctors
313 public:
314         function(unsigned ser);
315         // the following lines have been generated for max. ${maxargs} parameters
316 $constructors_interface
317         // end of generated lines
318         function(unsigned ser, const exprseq & es);
319         function(unsigned ser, const exvector & v, bool discardable = false);
320         function(unsigned ser, exvector * vp); // vp will be deleted
321
322         // functions overriding virtual functions from base classes
323 public:
324         void print(const print_context & c, unsigned level = 0) const;
325         unsigned precedence(void) const {return 70;}
326         int degree(const ex & s) const;
327         int ldegree(const ex & s) const;
328         ex coeff(const ex & s, int n = 1) const;
329         ex expand(unsigned options=0) const;
330         ex eval(int level=0) const;
331         ex evalf(int level=0) const;
332         unsigned calchash(void) const;
333         ex series(const relational & r, int order, unsigned options = 0) const;
334         ex thisexprseq(const exvector & v) const;
335         ex thisexprseq(exvector * vp) const;
336 protected:
337         ex derivative(const symbol & s) const;
338         bool is_equal_same_type(const basic & other) const;
339         bool match_same_type(const basic & other) const;
340         unsigned return_type(void) const;
341         unsigned return_type_tinfo(void) const;
342         
343         // new virtual functions which can be overridden by derived classes
344         // none
345         
346         // non-virtual functions in this class
347 protected:
348         ex pderivative(unsigned diff_param) const; // partial differentiation
349         static std::vector<function_options> & registered_functions(void);
350         bool lookup_remember_table(ex & result) const;
351         void store_remember_table(ex const & result) const;
352 public:
353         static unsigned register_new(function_options const & opt);
354         static unsigned find_function(const std::string &name, unsigned nparams);
355         unsigned get_serial(void) const {return serial;}
356         std::string get_name(void) const;
357         
358 // member variables
359
360 protected:
361         unsigned serial;
362 };
363
364 // utility functions/macros
365 /** Return the object of type function handled by an ex.
366  *  This is unsafe: you need to check the type first. */
367 inline const function &ex_to_function(const ex &e)
368 {
369         return static_cast<const function &>(*e.bp);
370 }
371
372 /** Specialization of is_exactly_a<function>(obj) for objects of type function. */
373 template<> inline bool is_exactly_a<function>(const basic & obj)
374 {
375         return obj.tinfo()==TINFO_function;
376 }
377
378 #define is_ex_the_function(OBJ, FUNCNAME) \\
379         (is_ex_exactly_of_type(OBJ, function) && static_cast<GiNaC::function *>(OBJ.bp)->get_serial() == function_index_##FUNCNAME)
380
381 } // namespace GiNaC
382
383 #endif // ndef __GINAC_FUNCTION_H__
384
385 END_OF_INTERFACE
386
387 $implementation=<<END_OF_IMPLEMENTATION;
388 /** \@file function.cpp
389  *
390  *  Implementation of class of symbolic functions. */
391
392 /*
393  *  This file was generated automatically by function.pl.
394  *  Please do not modify it directly, edit the perl script instead!
395  *  function.pl options: \$maxargs=${maxargs}
396  *
397  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
398  *
399  *  This program is free software; you can redistribute it and/or modify
400  *  it under the terms of the GNU General Public License as published by
401  *  the Free Software Foundation; either version 2 of the License, or
402  *  (at your option) any later version.
403  *
404  *  This program is distributed in the hope that it will be useful,
405  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
406  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
407  *  GNU General Public License for more details.
408  *
409  *  You should have received a copy of the GNU General Public License
410  *  along with this program; if not, write to the Free Software
411  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
412  */
413
414 #include <string>
415 #include <stdexcept>
416 #include <list>
417
418 #include "function.h"
419 #include "fderivative.h"
420 #include "ex.h"
421 #include "lst.h"
422 #include "symmetry.h"
423 #include "print.h"
424 #include "archive.h"
425 #include "inifcns.h"
426 #include "tostring.h"
427 #include "utils.h"
428 #include "debugmsg.h"
429 #include "remember.h"
430
431 namespace GiNaC {
432
433 //////////
434 // helper class function_options
435 //////////
436
437 function_options::function_options()
438 {
439         initialize();
440 }
441
442 function_options::function_options(std::string const & n, std::string const & tn)
443 {
444         initialize();
445         set_name(n,tn);
446 }
447
448 function_options::~function_options()
449 {
450         // nothing to clean up at the moment
451 }
452
453 void function_options::initialize(void)
454 {
455         set_name("unnamed_function","\\\\mbox{unnamed}");
456         nparams = 0;
457         eval_f = evalf_f = derivative_f = series_f = 0;
458         evalf_params_first = true;
459         use_return_type = false;
460         use_remember = false;
461         functions_with_same_name = 1;
462         symtree = 0;
463 }
464
465 function_options & function_options::set_name(std::string const & n,
466                                               std::string const & tn)
467 {
468         name=n;
469         if (tn==std::string())
470                 TeX_name = "\\\\mbox{"+name+"}";
471         else
472                 TeX_name = tn;
473         return *this;
474 }
475
476 function_options & function_options::latex_name(std::string const & tn)
477 {
478         TeX_name=tn;
479         return *this;
480 }
481
482 // the following lines have been generated for max. ${maxargs} parameters
483 $eval_func_implementation
484 $evalf_func_implementation
485 $derivative_func_implementation
486 $series_func_implementation
487 // end of generated lines
488
489 function_options & function_options::set_return_type(unsigned rt, unsigned rtt)
490 {
491         use_return_type = true;
492         return_type = rt;
493         return_type_tinfo = rtt;
494         return *this;
495 }
496
497 function_options & function_options::do_not_evalf_params(void)
498 {
499         evalf_params_first = false;
500         return *this;
501 }
502
503 function_options & function_options::remember(unsigned size,
504                                               unsigned assoc_size,
505                                               unsigned strategy)
506 {
507         use_remember = true;
508         remember_size = size;
509         remember_assoc_size = assoc_size;
510         remember_strategy = strategy;
511         return *this;
512 }
513
514 function_options & function_options::overloaded(unsigned o)
515 {
516         functions_with_same_name = o;
517         return *this;
518 }
519
520 function_options & function_options::set_symmetry(const symmetry & s)
521 {
522         symtree = s;
523         return *this;
524 }
525         
526 void function_options::test_and_set_nparams(unsigned n)
527 {
528         if (nparams==0) {
529                 nparams = n;
530         } else if (nparams!=n) {
531                 // we do not throw an exception here because this code is
532                 // usually executed before main(), so the exception could not
533                 // caught anyhow
534                 std::cerr << "WARNING: number of parameters ("
535                           << n << ") differs from number set before (" 
536                           << nparams << ")" << std::endl;
537         }
538 }
539
540 GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
541
542 //////////
543 // default ctor, dtor, copy ctor assignment operator and helpers
544 //////////
545
546 // public
547
548 function::function() : serial(0)
549 {
550         debugmsg("function default ctor",LOGLEVEL_CONSTRUCT);
551         tinfo_key = TINFO_function;
552 }
553
554 // protected
555
556 void function::copy(const function & other)
557 {
558         inherited::copy(other);
559         serial = other.serial;
560 }
561
562 void function::destroy(bool call_parent)
563 {
564         if (call_parent)
565                 inherited::destroy(call_parent);
566 }
567
568 //////////
569 // other ctors
570 //////////
571
572 // public
573
574 function::function(unsigned ser) : serial(ser)
575 {
576         debugmsg("function ctor from unsigned",LOGLEVEL_CONSTRUCT);
577         tinfo_key = TINFO_function;
578 }
579
580 // the following lines have been generated for max. ${maxargs} parameters
581 $constructors_implementation
582 // end of generated lines
583
584 function::function(unsigned ser, const exprseq & es) : exprseq(es), serial(ser)
585 {
586         debugmsg("function ctor from unsigned,exprseq",LOGLEVEL_CONSTRUCT);
587         tinfo_key = TINFO_function;
588 }
589
590 function::function(unsigned ser, const exvector & v, bool discardable) 
591   : exprseq(v,discardable), serial(ser)
592 {
593         debugmsg("function ctor from string,exvector,bool",LOGLEVEL_CONSTRUCT);
594         tinfo_key = TINFO_function;
595 }
596
597 function::function(unsigned ser, exvector * vp) 
598   : exprseq(vp), serial(ser)
599 {
600         debugmsg("function ctor from unsigned,exvector *",LOGLEVEL_CONSTRUCT);
601         tinfo_key = TINFO_function;
602 }
603
604 //////////
605 // archiving
606 //////////
607
608 /** Construct object from archive_node. */
609 function::function(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
610 {
611         debugmsg("function ctor from archive_node", LOGLEVEL_CONSTRUCT);
612
613         // Find serial number by function name
614         std::string s;
615         if (n.find_string("name", s)) {
616                 unsigned int ser = 0;
617                 std::vector<function_options>::const_iterator i = registered_functions().begin(), iend = registered_functions().end();
618                 while (i != iend) {
619                         if (s == i->name) {
620                                 serial = ser;
621                                 return;
622                         }
623                         ++i; ++ser;
624                 }
625                 throw (std::runtime_error("unknown function '" + s + "' in archive"));
626         } else
627                 throw (std::runtime_error("unnamed function in archive"));
628 }
629
630 /** Unarchive the object. */
631 ex function::unarchive(const archive_node &n, const lst &sym_lst)
632 {
633         return (new function(n, sym_lst))->setflag(status_flags::dynallocated);
634 }
635
636 /** Archive the object. */
637 void function::archive(archive_node &n) const
638 {
639         inherited::archive(n);
640         GINAC_ASSERT(serial < registered_functions().size());
641         n.add_string("name", registered_functions()[serial].name);
642 }
643
644 //////////
645 // functions overriding virtual functions from base classes
646 //////////
647
648 // public
649
650 void function::print(const print_context & c, unsigned level) const
651 {
652         debugmsg("function print", LOGLEVEL_PRINT);
653
654         GINAC_ASSERT(serial<registered_functions().size());
655
656         if (is_of_type(c, print_tree)) {
657
658                 c.s << std::string(level, ' ') << class_name() << " "
659                     << registered_functions()[serial].name
660                     << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
661                     << ", nops=" << nops()
662                     << std::endl;
663                 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
664                 for (unsigned i=0; i<seq.size(); ++i)
665                         seq[i].print(c, level + delta_indent);
666                 c.s << std::string(level + delta_indent, ' ') << "=====" << std::endl;
667
668         } else if (is_of_type(c, print_csrc)) {
669
670                 // Print function name in lowercase
671                 std::string lname = registered_functions()[serial].name;
672                 unsigned num = lname.size();
673                 for (unsigned i=0; i<num; i++)
674                         lname[i] = tolower(lname[i]);
675                 c.s << lname << "(";
676
677                 // Print arguments, separated by commas
678                 exvector::const_iterator it = seq.begin(), itend = seq.end();
679                 while (it != itend) {
680                         it->print(c);
681                         ++it;
682                         if (it != itend)
683                                 c.s << ",";
684                 }
685                 c.s << ")";
686
687         } else if (is_of_type(c, print_latex)) {
688                 c.s << registered_functions()[serial].TeX_name;
689                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
690         } else {
691                 c.s << registered_functions()[serial].name;
692                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
693         }
694 }
695
696 ex function::expand(unsigned options) const
697 {
698         // Only expand arguments when asked to do so
699         if (options & expand_options::expand_function_args)
700                 return inherited::expand(options);
701         else
702                 return (options == 0) ? setflag(status_flags::expanded) : *this;
703 }
704
705 int function::degree(const ex & s) const
706 {
707         return is_equal(*s.bp) ? 1 : 0;
708 }
709
710 int function::ldegree(const ex & s) const
711 {
712         return is_equal(*s.bp) ? 1 : 0;
713 }
714
715 ex function::coeff(const ex & s, int n) const
716 {
717         if (is_equal(*s.bp))
718                 return n==1 ? _ex1() : _ex0();
719         else
720                 return n==0 ? ex(*this) : _ex0();
721 }
722
723 ex function::eval(int level) const
724 {
725         GINAC_ASSERT(serial<registered_functions().size());
726
727         if (level>1) {
728                 // first evaluate children, then we will end up here again
729                 return function(serial,evalchildren(level));
730         }
731
732         const function_options &opt = registered_functions()[serial];
733
734         // Canonicalize argument order according to the symmetry properties
735         if (seq.size() > 1 && !(opt.symtree.is_zero())) {
736                 exvector v = seq;
737                 GINAC_ASSERT(is_a<symmetry>(opt.symtree));
738                 int sig = canonicalize(v.begin(), ex_to<symmetry>(opt.symtree));
739                 if (sig != INT_MAX) {
740                         // Something has changed while sorting arguments, more evaluations later
741                         if (sig == 0)
742                                 return _ex0();
743                         return ex(sig) * thisexprseq(v);
744                 }
745         }
746
747         if (opt.eval_f==0) {
748                 return this->hold();
749         }
750
751         bool use_remember = opt.use_remember;
752         ex eval_result;
753         if (use_remember && lookup_remember_table(eval_result)) {
754                 return eval_result;
755         }
756
757         switch (opt.nparams) {
758                 // the following lines have been generated for max. ${maxargs} parameters
759 ${eval_switch_statement}
760                 // end of generated lines
761         default:
762                 throw(std::logic_error("function::eval(): invalid nparams"));
763         }
764         if (use_remember) {
765                 store_remember_table(eval_result);
766         }
767         return eval_result;
768 }
769
770 ex function::evalf(int level) const
771 {
772         GINAC_ASSERT(serial<registered_functions().size());
773
774         // Evaluate children first
775         exvector eseq;
776         if (level == 1)
777                 eseq = seq;
778         else if (level == -max_recursion_level)
779                 throw(std::runtime_error("max recursion level reached"));
780         else
781                 eseq.reserve(seq.size());
782         --level;
783         exvector::const_iterator it = seq.begin(), itend = seq.end();
784         while (it != itend) {
785                 eseq.push_back(it->evalf(level));
786                 ++it;
787         }
788         
789         if (registered_functions()[serial].evalf_f==0) {
790                 return function(serial,eseq).hold();
791         }
792         switch (registered_functions()[serial].nparams) {
793                 // the following lines have been generated for max. ${maxargs} parameters
794 ${evalf_switch_statement}
795                 // end of generated lines
796         }
797         throw(std::logic_error("function::evalf(): invalid nparams"));
798 }
799
800 unsigned function::calchash(void) const
801 {
802         unsigned v = golden_ratio_hash(golden_ratio_hash(tinfo()) ^ serial);
803         for (unsigned i=0; i<nops(); i++) {
804                 v = rotate_left_31(v);
805                 v ^= this->op(i).gethash();
806         }
807         v &= 0x7FFFFFFFU;
808         if (flags & status_flags::evaluated) {
809                 setflag(status_flags::hash_calculated);
810                 hashvalue = v;
811         }
812         return v;
813 }
814
815 ex function::thisexprseq(const exvector & v) const
816 {
817         return function(serial,v);
818 }
819
820 ex function::thisexprseq(exvector * vp) const
821 {
822         return function(serial,vp);
823 }
824
825 /** Implementation of ex::series for functions.
826  *  \@see ex::series */
827 ex function::series(const relational & r, int order, unsigned options) const
828 {
829         GINAC_ASSERT(serial<registered_functions().size());
830
831         if (registered_functions()[serial].series_f==0) {
832                 return basic::series(r, order);
833         }
834         ex res;
835         switch (registered_functions()[serial].nparams) {
836                 // the following lines have been generated for max. ${maxargs} parameters
837 ${series_switch_statement}
838                 // end of generated lines
839         }
840         throw(std::logic_error("function::series(): invalid nparams"));
841 }
842
843 // protected
844
845 /** Implementation of ex::diff() for functions. It applies the chain rule,
846  *  except for the Order term function.
847  *  \@see ex::diff */
848 ex function::derivative(const symbol & s) const
849 {
850         ex result;
851
852         if (serial == function_index_Order) {
853                 // Order Term function only differentiates the argument
854                 return Order(seq[0].diff(s));
855         } else {
856                 // Chain rule
857                 ex arg_diff;
858                 unsigned num = seq.size();
859                 for (unsigned i=0; i<num; i++) {
860                         arg_diff = seq[i].diff(s);
861                         // We apply the chain rule only when it makes sense.  This is not
862                         // just for performance reasons but also to allow functions to
863                         // throw when differentiated with respect to one of its arguments
864                         // without running into trouble with our automatic full
865                         // differentiation:
866                         if (!arg_diff.is_zero())
867                                 result += pderivative(i)*arg_diff;
868                 }
869         }
870         return result;
871 }
872
873 int function::compare_same_type(const basic & other) const
874 {
875         GINAC_ASSERT(is_of_type(other, function));
876         const function & o = static_cast<const function &>(other);
877
878         if (serial != o.serial)
879                 return serial < o.serial ? -1 : 1;
880         else
881                 return exprseq::compare_same_type(o);
882 }
883
884 bool function::is_equal_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 false;
891         else
892                 return exprseq::is_equal_same_type(o);
893 }
894
895 bool function::match_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         return serial == o.serial;
901 }
902
903 unsigned function::return_type(void) const
904 {
905         if (seq.empty())
906                 return return_types::commutative;
907         else
908                 return seq.begin()->return_type();
909 }
910
911 unsigned function::return_type_tinfo(void) const
912 {
913         if (seq.empty())
914                 return tinfo_key;
915         else
916                 return seq.begin()->return_type_tinfo();
917 }
918
919 //////////
920 // new virtual functions which can be overridden by derived classes
921 //////////
922
923 // none
924
925 //////////
926 // non-virtual functions in this class
927 //////////
928
929 // protected
930
931 ex function::pderivative(unsigned diff_param) const // partial differentiation
932 {
933         GINAC_ASSERT(serial<registered_functions().size());
934         
935         // No derivative defined? Then return abstract derivative object
936         if (registered_functions()[serial].derivative_f == NULL)
937                 return fderivative(serial, diff_param, seq);
938
939         switch (registered_functions()[serial].nparams) {
940                 // the following lines have been generated for max. ${maxargs} parameters
941 ${diff_switch_statement}
942                 // end of generated lines
943         }
944         throw(std::logic_error("function::pderivative(): no diff function defined"));
945 }
946
947 std::vector<function_options> & function::registered_functions(void)
948 {
949         static std::vector<function_options> * rf = new std::vector<function_options>;
950         return *rf;
951 }
952
953 bool function::lookup_remember_table(ex & result) const
954 {
955         return remember_table::remember_tables()[serial].lookup_entry(*this,result);
956 }
957
958 void function::store_remember_table(ex const & result) const
959 {
960         remember_table::remember_tables()[serial].add_entry(*this,result);
961 }
962
963 // public
964
965 unsigned function::register_new(function_options const & opt)
966 {
967         unsigned same_name = 0;
968         for (unsigned i=0; i<registered_functions().size(); ++i) {
969                 if (registered_functions()[i].name==opt.name) {
970                         ++same_name;
971                 }
972         }
973         if (same_name>=opt.functions_with_same_name) {
974                 // we do not throw an exception here because this code is
975                 // usually executed before main(), so the exception could not
976                 // caught anyhow
977                 std::cerr << "WARNING: function name " << opt.name
978                           << " already in use!" << std::endl;
979         }
980         registered_functions().push_back(opt);
981         if (opt.use_remember) {
982                 remember_table::remember_tables().
983                         push_back(remember_table(opt.remember_size,
984                                                  opt.remember_assoc_size,
985                                                  opt.remember_strategy));
986         } else {
987                 remember_table::remember_tables().push_back(remember_table());
988         }
989         return registered_functions().size()-1;
990 }
991
992 /** Find serial number of function by name and number of parameters.
993  *  Throws exception if function was not found. */
994 unsigned function::find_function(const std::string &name, unsigned nparams)
995 {
996         std::vector<function_options>::const_iterator i = function::registered_functions().begin(), end = function::registered_functions().end();
997         unsigned serial = 0;
998         while (i != end) {
999                 if (i->get_name() == name && i->get_nparams() == nparams)
1000                         return serial;
1001                 ++i;
1002                 ++serial;
1003         }
1004         throw (std::runtime_error("no function '" + name + "' with " + ToString(nparams) + " parameters defined"));
1005 }
1006
1007 /** Return the print name of the function. */
1008 std::string function::get_name(void) const
1009 {
1010         GINAC_ASSERT(serial<registered_functions().size());
1011         return registered_functions()[serial].name;
1012 }
1013
1014 } // namespace GiNaC
1015
1016 END_OF_IMPLEMENTATION
1017
1018 print "Creating interface file function.h...";
1019 open OUT,">function.h" or die "cannot open function.h";
1020 print OUT $interface;
1021 close OUT;
1022 print "ok.\n";
1023
1024 print "Creating implementation file function.cpp...";
1025 open OUT,">function.cpp" or die "cannot open function.cpp";
1026 print OUT $implementation;
1027 close OUT;
1028 print "ok.\n";
1029
1030 print "done.\n";