b9ee78710d643a54b28914a1a9e7c36c108c350b
[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         bool has_derivative(void) const { return derivative_f != NULL; }
277
278 protected:
279         std::string name;
280         std::string TeX_name;
281
282         unsigned nparams;
283
284         eval_funcp eval_f;
285         evalf_funcp evalf_f;
286         derivative_funcp derivative_f;
287         series_funcp series_f;
288
289         bool evalf_params_first;
290
291         bool use_return_type;
292         unsigned return_type;
293         unsigned return_type_tinfo;
294
295         bool use_remember;
296         unsigned remember_size;
297         unsigned remember_assoc_size;
298         unsigned remember_strategy;
299
300         unsigned functions_with_same_name;
301
302         ex symtree;
303 };
304
305 /** The class function is used to implement builtin functions like sin, cos...
306         and user defined functions */
307 class function : public exprseq
308 {
309         GINAC_DECLARE_REGISTERED_CLASS(function, exprseq)
310
311         // CINT has a linking problem
312 #ifndef __MAKECINT__
313         friend void ginsh_get_ginac_functions(void);
314 #endif // def __MAKECINT__
315
316         friend class remember_table_entry;
317         // friend class remember_table_list;
318         // friend class remember_table;
319         friend ex Derivative_eval(const ex &, const ex &);
320
321 // member functions
322
323         // other ctors
324 public:
325         function(unsigned ser);
326         // the following lines have been generated for max. ${maxargs} parameters
327 $constructors_interface
328         // end of generated lines
329         function(unsigned ser, const exprseq & es);
330         function(unsigned ser, const exvector & v, bool discardable = false);
331         function(unsigned ser, exvector * vp); // vp will be deleted
332
333         // functions overriding virtual functions from bases classes
334 public:
335         void print(const print_context & c, unsigned level = 0) const;
336         unsigned precedence(void) const {return 70;}
337         int degree(const ex & s) const;
338         int ldegree(const ex & s) const;
339         ex coeff(const ex & s, int n = 1) const;
340         ex expand(unsigned options=0) const;
341         ex eval(int level=0) const;
342         ex evalf(int level=0) const;
343         unsigned calchash(void) const;
344         ex series(const relational & r, int order, unsigned options = 0) const;
345         ex thisexprseq(const exvector & v) const;
346         ex thisexprseq(exvector * vp) const;
347 protected:
348         ex derivative(const symbol & s) const;
349         bool is_equal_same_type(const basic & other) const;
350         bool match_same_type(const basic & other) const;
351         unsigned return_type(void) const;
352         unsigned return_type_tinfo(void) const;
353         
354         // new virtual functions which can be overridden by derived classes
355         // none
356         
357         // non-virtual functions in this class
358 protected:
359         ex pderivative(unsigned diff_param) const; // partial differentiation
360         static std::vector<function_options> & registered_functions(void);
361         bool lookup_remember_table(ex & result) const;
362         void store_remember_table(ex const & result) const;
363 public:
364         static unsigned register_new(function_options const & opt);
365         static unsigned find_function(const std::string &name, unsigned nparams);
366         unsigned get_serial(void) const {return serial;}
367         std::string get_name(void) const;
368         
369 // member variables
370
371 protected:
372         unsigned serial;
373 };
374
375 // utility functions/macros
376 /** Return the object of type function handled by an ex.
377  *  This is unsafe: you need to check the type first. */
378 inline const function &ex_to_function(const ex &e)
379 {
380         return static_cast<const function &>(*e.bp);
381 }
382
383 /** Specialization of is_exactly_a<function>(obj) for objects of type function. */
384 template<> inline bool is_exactly_a<function>(const basic & obj)
385 {
386         return obj.tinfo()==TINFO_function;
387 }
388
389 #define is_ex_the_function(OBJ, FUNCNAME) \\
390         (is_ex_exactly_of_type(OBJ, function) && static_cast<GiNaC::function *>(OBJ.bp)->get_serial() == function_index_##FUNCNAME)
391
392 } // namespace GiNaC
393
394 #endif // ndef __GINAC_FUNCTION_H__
395
396 END_OF_INTERFACE
397
398 $implementation=<<END_OF_IMPLEMENTATION;
399 /** \@file function.cpp
400  *
401  *  Implementation of class function. */
402
403 /*
404  *  This file was generated automatically by function.pl.
405  *  Please do not modify it directly, edit the perl script instead!
406  *  function.pl options: \$maxargs=${maxargs}
407  *
408  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
409  *
410  *  This program is free software; you can redistribute it and/or modify
411  *  it under the terms of the GNU General Public License as published by
412  *  the Free Software Foundation; either version 2 of the License, or
413  *  (at your option) any later version.
414  *
415  *  This program is distributed in the hope that it will be useful,
416  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
417  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
418  *  GNU General Public License for more details.
419  *
420  *  You should have received a copy of the GNU General Public License
421  *  along with this program; if not, write to the Free Software
422  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
423  */
424
425 #include <string>
426 #include <stdexcept>
427 #include <list>
428
429 #include "function.h"
430 #include "ex.h"
431 #include "lst.h"
432 #include "symmetry.h"
433 #include "print.h"
434 #include "archive.h"
435 #include "inifcns.h"
436 #include "utils.h"
437 #include "debugmsg.h"
438 #include "remember.h"
439
440 namespace GiNaC {
441
442 //////////
443 // helper class function_options
444 //////////
445
446 function_options::function_options()
447 {
448         initialize();
449 }
450
451 function_options::function_options(std::string const & n, std::string const & tn)
452 {
453         initialize();
454         set_name(n,tn);
455 }
456
457 function_options::~function_options()
458 {
459         // nothing to clean up at the moment
460 }
461
462 void function_options::initialize(void)
463 {
464         set_name("unnamed_function","\\\\mbox{unnamed}");
465         nparams = 0;
466         eval_f = evalf_f = derivative_f = series_f = 0;
467         evalf_params_first = true;
468         use_return_type = false;
469         use_remember = false;
470         functions_with_same_name = 1;
471         symtree = 0;
472 }
473
474 function_options & function_options::set_name(std::string const & n,
475                                               std::string const & tn)
476 {
477         name=n;
478         if (tn==std::string())
479                 TeX_name = "\\\\mbox{"+name+"}";
480         else
481                 TeX_name = tn;
482         return *this;
483 }
484
485 function_options & function_options::latex_name(std::string const & tn)
486 {
487         TeX_name=tn;
488         return *this;
489 }
490
491 // the following lines have been generated for max. ${maxargs} parameters
492 $eval_func_implementation
493 $evalf_func_implementation
494 $derivative_func_implementation
495 $series_func_implementation
496 // end of generated lines
497
498 function_options & function_options::set_return_type(unsigned rt, unsigned rtt)
499 {
500         use_return_type = true;
501         return_type = rt;
502         return_type_tinfo = rtt;
503         return *this;
504 }
505
506 function_options & function_options::do_not_evalf_params(void)
507 {
508         evalf_params_first = false;
509         return *this;
510 }
511
512 function_options & function_options::remember(unsigned size,
513                                               unsigned assoc_size,
514                                               unsigned strategy)
515 {
516         use_remember = true;
517         remember_size = size;
518         remember_assoc_size = assoc_size;
519         remember_strategy = strategy;
520         return *this;
521 }
522
523 function_options & function_options::overloaded(unsigned o)
524 {
525         functions_with_same_name = o;
526         return *this;
527 }
528
529 function_options & function_options::set_symmetry(const symmetry & s)
530 {
531         symtree = s;
532         return *this;
533 }
534         
535 void function_options::test_and_set_nparams(unsigned n)
536 {
537         if (nparams==0) {
538                 nparams = n;
539         } else if (nparams!=n) {
540                 // we do not throw an exception here because this code is
541                 // usually executed before main(), so the exception could not
542                 // caught anyhow
543                 std::cerr << "WARNING: number of parameters ("
544                           << n << ") differs from number set before (" 
545                           << nparams << ")" << std::endl;
546         }
547 }
548
549 GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
550
551 //////////
552 // default ctor, dtor, copy ctor assignment operator and helpers
553 //////////
554
555 // public
556
557 function::function() : serial(0)
558 {
559         debugmsg("function default ctor",LOGLEVEL_CONSTRUCT);
560         tinfo_key = TINFO_function;
561 }
562
563 // protected
564
565 void function::copy(const function & other)
566 {
567         inherited::copy(other);
568         serial = other.serial;
569 }
570
571 void function::destroy(bool call_parent)
572 {
573         if (call_parent)
574                 inherited::destroy(call_parent);
575 }
576
577 //////////
578 // other ctors
579 //////////
580
581 // public
582
583 function::function(unsigned ser) : serial(ser)
584 {
585         debugmsg("function ctor from unsigned",LOGLEVEL_CONSTRUCT);
586         tinfo_key = TINFO_function;
587 }
588
589 // the following lines have been generated for max. ${maxargs} parameters
590 $constructors_implementation
591 // end of generated lines
592
593 function::function(unsigned ser, const exprseq & es) : exprseq(es), serial(ser)
594 {
595         debugmsg("function ctor from unsigned,exprseq",LOGLEVEL_CONSTRUCT);
596         tinfo_key = TINFO_function;
597 }
598
599 function::function(unsigned ser, const exvector & v, bool discardable) 
600   : exprseq(v,discardable), serial(ser)
601 {
602         debugmsg("function ctor from string,exvector,bool",LOGLEVEL_CONSTRUCT);
603         tinfo_key = TINFO_function;
604 }
605
606 function::function(unsigned ser, exvector * vp) 
607   : exprseq(vp), serial(ser)
608 {
609         debugmsg("function ctor from unsigned,exvector *",LOGLEVEL_CONSTRUCT);
610         tinfo_key = TINFO_function;
611 }
612
613 //////////
614 // archiving
615 //////////
616
617 /** Construct object from archive_node. */
618 function::function(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
619 {
620         debugmsg("function ctor from archive_node", LOGLEVEL_CONSTRUCT);
621
622         // Find serial number by function name
623         std::string s;
624         if (n.find_string("name", s)) {
625                 unsigned int ser = 0;
626                 std::vector<function_options>::const_iterator i = registered_functions().begin(), iend = registered_functions().end();
627                 while (i != iend) {
628                         if (s == i->name) {
629                                 serial = ser;
630                                 return;
631                         }
632                         i++; ser++;
633                 }
634                 throw (std::runtime_error("unknown function '" + s + "' in archive"));
635         } else
636                 throw (std::runtime_error("unnamed function in archive"));
637 }
638
639 /** Unarchive the object. */
640 ex function::unarchive(const archive_node &n, const lst &sym_lst)
641 {
642         return (new function(n, sym_lst))->setflag(status_flags::dynallocated);
643 }
644
645 /** Archive the object. */
646 void function::archive(archive_node &n) const
647 {
648         inherited::archive(n);
649         GINAC_ASSERT(serial < registered_functions().size());
650         n.add_string("name", registered_functions()[serial].name);
651 }
652
653 //////////
654 // functions overriding virtual functions from bases classes
655 //////////
656
657 // public
658
659 void function::print(const print_context & c, unsigned level) const
660 {
661         debugmsg("function print", LOGLEVEL_PRINT);
662
663         GINAC_ASSERT(serial<registered_functions().size());
664
665         if (is_of_type(c, print_tree)) {
666
667                 c.s << std::string(level, ' ') << class_name() << " "
668                     << registered_functions()[serial].name
669                     << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
670                     << ", nops=" << nops()
671                     << std::endl;
672                 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
673                 for (unsigned i=0; i<seq.size(); ++i)
674                         seq[i].print(c, level + delta_indent);
675                 c.s << std::string(level + delta_indent, ' ') << "=====" << std::endl;
676
677         } else if (is_of_type(c, print_csrc)) {
678
679                 // Print function name in lowercase
680                 std::string lname = registered_functions()[serial].name;
681                 unsigned num = lname.size();
682                 for (unsigned i=0; i<num; i++)
683                         lname[i] = tolower(lname[i]);
684                 c.s << lname << "(";
685
686                 // Print arguments, separated by commas
687                 exvector::const_iterator it = seq.begin(), itend = seq.end();
688                 while (it != itend) {
689                         it->print(c);
690                         it++;
691                         if (it != itend)
692                                 c.s << ",";
693                 }
694                 c.s << ")";
695
696         } else if (is_of_type(c, print_latex)) {
697                 c.s << registered_functions()[serial].TeX_name;
698                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
699         } else {
700                 c.s << registered_functions()[serial].name;
701                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
702         }
703 }
704
705 ex function::expand(unsigned options) const
706 {
707         // Only expand arguments when asked to do so
708         if (options & expand_options::expand_function_args)
709                 return inherited::expand(options);
710         else
711                 return (options == 0) ? setflag(status_flags::expanded) : *this;
712 }
713
714 int function::degree(const ex & s) const
715 {
716         return is_equal(*s.bp) ? 1 : 0;
717 }
718
719 int function::ldegree(const ex & s) const
720 {
721         return is_equal(*s.bp) ? 1 : 0;
722 }
723
724 ex function::coeff(const ex & s, int n) const
725 {
726         if (is_equal(*s.bp))
727                 return n==1 ? _ex1() : _ex0();
728         else
729                 return n==0 ? ex(*this) : _ex0();
730 }
731
732 ex function::eval(int level) const
733 {
734         GINAC_ASSERT(serial<registered_functions().size());
735
736         if (level>1) {
737                 // first evaluate children, then we will end up here again
738                 return function(serial,evalchildren(level));
739         }
740
741         const function_options &opt = registered_functions()[serial];
742
743         // Canonicalize argument order according to the symmetry properties
744         if (seq.size() > 1 && !(opt.symtree.is_zero())) {
745                 exvector v = seq;
746                 GINAC_ASSERT(is_ex_exactly_of_type(opt.symtree, symmetry));
747                 int sig = canonicalize(v.begin(), ex_to<symmetry>(opt.symtree));
748                 if (sig != INT_MAX) {
749                         // Something has changed while sorting arguments, more evaluations later
750                         if (sig == 0)
751                                 return _ex0();
752                         return ex(sig) * thisexprseq(v);
753                 }
754         }
755
756         if (opt.eval_f==0) {
757                 return this->hold();
758         }
759
760         bool use_remember = opt.use_remember;
761         ex eval_result;
762         if (use_remember && lookup_remember_table(eval_result)) {
763                 return eval_result;
764         }
765
766         switch (opt.nparams) {
767                 // the following lines have been generated for max. ${maxargs} parameters
768 ${eval_switch_statement}
769                 // end of generated lines
770         default:
771                 throw(std::logic_error("function::eval(): invalid nparams"));
772         }
773         if (use_remember) {
774                 store_remember_table(eval_result);
775         }
776         return eval_result;
777 }
778
779 ex function::evalf(int level) const
780 {
781         GINAC_ASSERT(serial<registered_functions().size());
782
783         // Evaluate children first
784         exvector eseq;
785         if (level == 1)
786                 eseq = seq;
787         else if (level == -max_recursion_level)
788                 throw(std::runtime_error("max recursion level reached"));
789         else
790                 eseq.reserve(seq.size());
791         level--;
792         exvector::const_iterator it = seq.begin(), itend = seq.end();
793         while (it != itend) {
794                 eseq.push_back((*it).evalf(level));
795                 it++;
796         }
797         
798         if (registered_functions()[serial].evalf_f==0) {
799                 return function(serial,eseq).hold();
800         }
801         switch (registered_functions()[serial].nparams) {
802                 // the following lines have been generated for max. ${maxargs} parameters
803 ${evalf_switch_statement}
804                 // end of generated lines
805         }
806         throw(std::logic_error("function::evalf(): invalid nparams"));
807 }
808
809 unsigned function::calchash(void) const
810 {
811         unsigned v = golden_ratio_hash(golden_ratio_hash(tinfo()) ^ serial);
812         for (unsigned i=0; i<nops(); i++) {
813                 v = rotate_left_31(v);
814                 v ^= this->op(i).gethash();
815         }
816         v &= 0x7FFFFFFFU;
817         if (flags & status_flags::evaluated) {
818                 setflag(status_flags::hash_calculated);
819                 hashvalue = v;
820         }
821         return v;
822 }
823
824 ex function::thisexprseq(const exvector & v) const
825 {
826         return function(serial,v);
827 }
828
829 ex function::thisexprseq(exvector * vp) const
830 {
831         return function(serial,vp);
832 }
833
834 /** Implementation of ex::series for functions.
835  *  \@see ex::series */
836 ex function::series(const relational & r, int order, unsigned options) const
837 {
838         GINAC_ASSERT(serial<registered_functions().size());
839
840         if (registered_functions()[serial].series_f==0) {
841                 return basic::series(r, order);
842         }
843         ex res;
844         switch (registered_functions()[serial].nparams) {
845                 // the following lines have been generated for max. ${maxargs} parameters
846 ${series_switch_statement}
847                 // end of generated lines
848         }
849         throw(std::logic_error("function::series(): invalid nparams"));
850 }
851
852 // protected
853
854 /** Implementation of ex::diff() for functions. It applies the chain rule,
855  *  except for the Order term function.
856  *  \@see ex::diff */
857 ex function::derivative(const symbol & s) const
858 {
859         ex result;
860         
861         if (serial == function_index_Order) {
862                 // Order Term function only differentiates the argument
863                 return Order(seq[0].diff(s));
864         } else if (serial == function_index_Derivative) {
865                 // Inert derivative performs chain rule on the first argument only, and
866                 // adds differentiation parameter to list (second argument)
867                 GINAC_ASSERT(is_ex_exactly_of_type(seq[0], function));
868                 GINAC_ASSERT(is_ex_exactly_of_type(seq[1], function));
869                 ex fcn = seq[0];
870                 ex arg_diff;
871                 for (unsigned i=0; i!=fcn.nops(); i++) {
872                         arg_diff = fcn.op(i).diff(s);
873                         if (!arg_diff.is_zero()) {
874                                 lst new_lst = ex_to<lst>(seq[1]);
875                                 new_lst.append(i);
876                                 result += arg_diff * Derivative(fcn, new_lst);
877                         }
878                 }
879         } else {
880                 // Chain rule
881                 ex arg_diff;
882                 unsigned num = seq.size();
883                 for (unsigned i=0; i<num; i++) {
884                         arg_diff = seq[i].diff(s);
885                         // We apply the chain rule only when it makes sense.  This is not
886                         // just for performance reasons but also to allow functions to
887                         // throw when differentiated with respect to one of its arguments
888                         // without running into trouble with our automatic full
889                         // differentiation:
890                         if (!arg_diff.is_zero())
891                                 result += pderivative(i)*arg_diff;
892                 }
893         }
894         return result;
895 }
896
897 int function::compare_same_type(const basic & other) const
898 {
899         GINAC_ASSERT(is_of_type(other, function));
900         const function & o = static_cast<const function &>(other);
901
902         if (serial != o.serial)
903                 return serial < o.serial ? -1 : 1;
904         else
905                 return exprseq::compare_same_type(o);
906 }
907
908 bool function::is_equal_same_type(const basic & other) const
909 {
910         GINAC_ASSERT(is_of_type(other, function));
911         const function & o = static_cast<const function &>(other);
912
913         if (serial != o.serial)
914                 return false;
915         else
916                 return exprseq::is_equal_same_type(o);
917 }
918
919 bool function::match_same_type(const basic & other) const
920 {
921         GINAC_ASSERT(is_of_type(other, function));
922         const function & o = static_cast<const function &>(other);
923
924         return serial == o.serial;
925 }
926
927 unsigned function::return_type(void) const
928 {
929         if (seq.empty())
930                 return return_types::commutative;
931         else
932                 return seq.begin()->return_type();
933 }
934
935 unsigned function::return_type_tinfo(void) const
936 {
937         if (seq.empty())
938                 return tinfo_key;
939         else
940                 return seq.begin()->return_type_tinfo();
941 }
942
943 //////////
944 // new virtual functions which can be overridden by derived classes
945 //////////
946
947 // none
948
949 //////////
950 // non-virtual functions in this class
951 //////////
952
953 // protected
954
955 ex function::pderivative(unsigned diff_param) const // partial differentiation
956 {
957         GINAC_ASSERT(serial<registered_functions().size());
958         
959         if (registered_functions()[serial].derivative_f==0) {
960                 return Derivative(*this, lst(ex(diff_param)));
961         }
962         switch (registered_functions()[serial].nparams) {
963                 // the following lines have been generated for max. ${maxargs} parameters
964 ${diff_switch_statement}
965                 // end of generated lines
966         }
967         throw(std::logic_error("function::pderivative(): no diff function defined"));
968 }
969
970 std::vector<function_options> & function::registered_functions(void)
971 {
972         static std::vector<function_options> * rf = new std::vector<function_options>;
973         return *rf;
974 }
975
976 bool function::lookup_remember_table(ex & result) const
977 {
978         return remember_table::remember_tables()[serial].lookup_entry(*this,result);
979 }
980
981 void function::store_remember_table(ex const & result) const
982 {
983         remember_table::remember_tables()[serial].add_entry(*this,result);
984 }
985
986 // public
987
988 unsigned function::register_new(function_options const & opt)
989 {
990         unsigned same_name = 0;
991         for (unsigned i=0; i<registered_functions().size(); ++i) {
992                 if (registered_functions()[i].name==opt.name) {
993                         same_name++;
994                 }
995         }
996         if (same_name>=opt.functions_with_same_name) {
997                 // we do not throw an exception here because this code is
998                 // usually executed before main(), so the exception could not
999                 // caught anyhow
1000                 std::cerr << "WARNING: function name " << opt.name
1001                                   << " already in use!" << std::endl;
1002         }
1003         registered_functions().push_back(opt);
1004         if (opt.use_remember) {
1005                 remember_table::remember_tables().
1006                         push_back(remember_table(opt.remember_size,
1007                                                                          opt.remember_assoc_size,
1008                                                                          opt.remember_strategy));
1009         } else {
1010                 remember_table::remember_tables().push_back(remember_table());
1011         }
1012         return registered_functions().size()-1;
1013 }
1014
1015 /** Find serial number of function by name and number of parameters.
1016  *  Throws exception if function was not found. */
1017 unsigned function::find_function(const std::string &name, unsigned nparams)
1018 {
1019         std::vector<function_options>::const_iterator i = function::registered_functions().begin(), end = function::registered_functions().end();
1020         unsigned serial = 0;
1021         while (i != end) {
1022                 if (i->get_name() == name && i->get_nparams() == nparams)
1023                         return serial;
1024                 i++;
1025                 serial++;
1026         }
1027         throw (std::runtime_error("no function '" + name + "' with " + ToString(nparams) + " parameters defined"));
1028 }
1029
1030 /** Return the print name of the function. */
1031 std::string function::get_name(void) const
1032 {
1033         GINAC_ASSERT(serial<registered_functions().size());
1034         return registered_functions()[serial].name;
1035 }
1036
1037 } // namespace GiNaC
1038
1039 END_OF_IMPLEMENTATION
1040
1041 print "Creating interface file function.h...";
1042 open OUT,">function.h" or die "cannot open function.h";
1043 print OUT $interface;
1044 close OUT;
1045 print "ok.\n";
1046
1047 print "Creating implementation file function.cpp...";
1048 open OUT,">function.cpp" or die "cannot open function.cpp";
1049 print OUT $implementation;
1050 close OUT;
1051 print "ok.\n";
1052
1053 print "done.\n";