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 class NAME##_SERIAL { public: static unsigned serial; }; \\
  43 template<${SEQ1}> const GiNaC::function NAME(${SEQ2}) { \\
  44         return GiNaC::function(NAME##_SERIAL::serial, ${SEQ3}); \\
  45 }
  46
  47 END_OF_DECLARE_FUNCTION_MACRO
  48
  49 $typedef_eval_funcp=generate(
  50 'typedef ex (* eval_funcp_${N})(${SEQ1});'."\n",
  51 'const ex &','','');
  52
  53 $typedef_evalf_funcp=generate(
  54 'typedef ex (* evalf_funcp_${N})(${SEQ1});'."\n",
  55 'const ex &','','');
  56
  57 $typedef_derivative_funcp=generate(
  58 'typedef ex (* derivative_funcp_${N})(${SEQ1}, unsigned);'."\n",
  59 'const ex &','','');
  60
  61 $typedef_series_funcp=generate(
  62 'typedef ex (* series_funcp_${N})(${SEQ1}, const relational &, int, unsigned);'."\n",
  63 'const ex &','','');
  64
  65 $typedef_print_funcp=generate(
  66 'typedef void (* print_funcp_${N})(${SEQ1}, const print_context &);'."\n",
  67 'const ex &','','');
  68
  69 $eval_func_interface=generate('    function_options & eval_func(eval_funcp_${N} e);'."\n",'','','');
  70
  71 $evalf_func_interface=generate('    function_options & evalf_func(evalf_funcp_${N} ef);'."\n",'','','');
  72
  73 $derivative_func_interface=generate('    function_options & derivative_func(derivative_funcp_${N} d);'."\n",'','','');
  74
  75 $series_func_interface=generate('    function_options & series_func(series_funcp_${N} s);'."\n",'','','');
  76
  77 $print_func_interface=generate(
  78         <<'END_OF_PRINT_FUNC_INTERFACE','','','');
  79     template <class Ctx> function_options & print_func(print_funcp_${N} p)
  80     {
  81         test_and_set_nparams(${N});
  82         set_print_func(Ctx::get_class_info_static().options.get_id(), print_funcp(p));
  83         return *this;
  84     }
  85 END_OF_PRINT_FUNC_INTERFACE
  86
  87 $constructors_interface=generate(
  88 '    function(unsigned ser, ${SEQ1});'."\n",
  89 'const ex & param${N}','','');
  90
  91 $constructors_implementation=generate(
  92         <<'END_OF_CONSTRUCTORS_IMPLEMENTATION','const ex & param${N}','param${N}','');
  93 function::function(unsigned ser, ${SEQ1})
  94         : exprseq(${SEQ2}), serial(ser)
  95 {
  96         tinfo_key = TINFO_function;
  97 }
  98 END_OF_CONSTRUCTORS_IMPLEMENTATION
  99
 100 $eval_switch_statement=generate(
 101         <<'END_OF_EVAL_SWITCH_STATEMENT','seq[${N}-1]','','');
 102         case ${N}:
 103                 eval_result = ((eval_funcp_${N})(opt.eval_f))(${SEQ1});
 104                 break;
 105 END_OF_EVAL_SWITCH_STATEMENT
 106
 107 $evalf_switch_statement=generate(
 108         <<'END_OF_EVALF_SWITCH_STATEMENT','eseq[${N}-1]','','');
 109         case ${N}:
 110                 return ((evalf_funcp_${N})(opt.evalf_f))(${SEQ1});
 111 END_OF_EVALF_SWITCH_STATEMENT
 112
 113 $diff_switch_statement=generate(
 114         <<'END_OF_DIFF_SWITCH_STATEMENT','seq[${N}-1]','','');
 115         case ${N}:
 116                 return ((derivative_funcp_${N})(opt.derivative_f))(${SEQ1},diff_param);
 117 END_OF_DIFF_SWITCH_STATEMENT
 118
 119 $series_switch_statement=generate(
 120         <<'END_OF_SERIES_SWITCH_STATEMENT','seq[${N}-1]','','');
 121         case ${N}:
 122                 try {
 123                         res = ((series_funcp_${N})(opt.series_f))(${SEQ1},r,order,options);
 124                 } catch (do_taylor) {
 125                         res = basic::series(r, order, options);
 126                 }
 127                 return res;
 128 END_OF_SERIES_SWITCH_STATEMENT
 129
 130 $print_switch_statement=generate(
 131         <<'END_OF_PRINT_SWITCH_STATEMENT','seq[${N}-1]','','');
 132                 case ${N}:
 133                         ((print_funcp_${N})(pdt[id]))(${SEQ1}, c);
 134                         break;
 135 END_OF_PRINT_SWITCH_STATEMENT
 136
 137 $eval_func_implementation=generate(
 138         <<'END_OF_EVAL_FUNC_IMPLEMENTATION','','','');
 139 function_options & function_options::eval_func(eval_funcp_${N} e)
 140 {
 141         test_and_set_nparams(${N});
 142         eval_f = eval_funcp(e);
 143         return *this;
 144 }
 145 END_OF_EVAL_FUNC_IMPLEMENTATION
 146
 147 $evalf_func_implementation=generate(
 148         <<'END_OF_EVALF_FUNC_IMPLEMENTATION','','','');
 149 function_options & function_options::evalf_func(evalf_funcp_${N} ef)
 150 {
 151         test_and_set_nparams(${N});
 152         evalf_f = evalf_funcp(ef);
 153         return *this;
 154 }
 155 END_OF_EVALF_FUNC_IMPLEMENTATION
 156
 157 $derivative_func_implementation=generate(
 158         <<'END_OF_DERIVATIVE_FUNC_IMPLEMENTATION','','','');
 159 function_options & function_options::derivative_func(derivative_funcp_${N} d)
 160 {
 161         test_and_set_nparams(${N});
 162         derivative_f = derivative_funcp(d);
 163         return *this;
 164 }
 165 END_OF_DERIVATIVE_FUNC_IMPLEMENTATION
 166
 167 $series_func_implementation=generate(
 168         <<'END_OF_SERIES_FUNC_IMPLEMENTATION','','','');
 169 function_options & function_options::series_func(series_funcp_${N} s)
 170 {
 171         test_and_set_nparams(${N});
 172         series_f = series_funcp(s);
 173         return *this;
 174 }
 175 END_OF_SERIES_FUNC_IMPLEMENTATION
 176
 177 $interface=<<END_OF_INTERFACE;
 178 /** \@file function.h
 179  *
 180  *  Interface to class of symbolic functions. */
 181
 182 /*
 183  *  This file was generated automatically by function.pl.
 184  *  Please do not modify it directly, edit the perl script instead!
 185  *  function.pl options: \$maxargs=${maxargs}
 186  *
 187  *  GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
 188  *
 189  *  This program is free software; you can redistribute it and/or modify
 190  *  it under the terms of the GNU General Public License as published by
 191  *  the Free Software Foundation; either version 2 of the License, or
 192  *  (at your option) any later version.
 193  *
 194  *  This program is distributed in the hope that it will be useful,
 195  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 196  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 197  *  GNU General Public License for more details.
 198  *
 199  *  You should have received a copy of the GNU General Public License
 200  *  along with this program; if not, write to the Free Software
 201  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 202  */
 203
 204 #ifndef __GINAC_FUNCTION_H__
 205 #define __GINAC_FUNCTION_H__
 206
 207 #include <string>
 208 #include <vector>
 209
 210 // CINT needs <algorithm> to work properly with <vector>
 211 #include <algorithm>
 212
 213 #include "exprseq.h"
 214
 215 // the following lines have been generated for max. ${maxargs} parameters
 216 $declare_function_macro
 217 // end of generated lines
 218
 219 #define REGISTER_FUNCTION(NAME,OPT) \\
 220 unsigned NAME##_SERIAL::serial = \\
 221         GiNaC::function::register_new(GiNaC::function_options(#NAME).OPT);
 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 typedef void (* print_funcp)();
 233
 234 // the following lines have been generated for max. ${maxargs} parameters
 235 $typedef_eval_funcp
 236 $typedef_evalf_funcp
 237 $typedef_derivative_funcp
 238 $typedef_series_funcp
 239 $typedef_print_funcp
 240 // end of generated lines
 241
 242 // Alternatively, an exvector may be passed into the static function, instead
 243 // of individual ex objects.  Then, the number of arguments is not limited.
 244 typedef ex (* eval_funcp_exvector)(const exvector &);
 245 typedef ex (* evalf_funcp_exvector)(const exvector &);
 246 typedef ex (* derivative_funcp_exvector)(const exvector &, unsigned);
 247 typedef ex (* series_funcp_exvector)(const exvector &, const relational &, int, unsigned);
 248 typedef void (* print_funcp_exvector)(const exvector &, const print_context &);
 249
 250
 251 class function_options
 252 {
 253         friend class function;
 254         friend class fderivative;
 255 public:
 256         function_options();
 257         function_options(std::string const & n, std::string const & tn=std::string());
 258         ~function_options();
 259         void initialize();
 260
 261         function_options & dummy() { return *this; }
 262         function_options & set_name(std::string const & n, std::string const & tn=std::string());
 263         function_options & latex_name(std::string const & tn);
 264 // the following lines have been generated for max. ${maxargs} parameters
 265 $eval_func_interface
 266 $evalf_func_interface
 267 $derivative_func_interface
 268 $series_func_interface
 269 $print_func_interface
 270 // end of generated lines
 271         function_options & eval_func(eval_funcp_exvector e);
 272         function_options & evalf_func(evalf_funcp_exvector ef);
 273         function_options & derivative_func(derivative_funcp_exvector d);
 274         function_options & series_func(series_funcp_exvector s);
 275
 276         template <class Ctx> function_options & print_func(print_funcp_exvector p)
 277         {
 278                 print_use_exvector_args = true;
 279                 set_print_func(Ctx::get_class_info_static().options.get_id(), print_funcp(p));
 280                 return *this;
 281         }
 282
 283         function_options & set_return_type(unsigned rt, unsigned rtt=0);
 284         function_options & do_not_evalf_params();
 285         function_options & remember(unsigned size, unsigned assoc_size=0,
 286                                     unsigned strategy=remember_strategies::delete_never);
 287         function_options & overloaded(unsigned o);
 288         function_options & set_symmetry(const symmetry & s);
 289
 290         std::string get_name() const { return name; }
 291         unsigned get_nparams() const { return nparams; }
 292
 293 protected:
 294         bool has_derivative() const { return derivative_f != NULL; }
 295         void test_and_set_nparams(unsigned n);
 296         void set_print_func(unsigned id, print_funcp f);
 297
 298         std::string name;
 299         std::string TeX_name;
 300
 301         unsigned nparams;
 302
 303         eval_funcp eval_f;
 304         evalf_funcp evalf_f;
 305         derivative_funcp derivative_f;
 306         series_funcp series_f;
 307         std::vector<print_funcp> print_dispatch_table;
 308
 309         bool evalf_params_first;
 310
 311         bool use_return_type;
 312         unsigned return_type;
 313         unsigned return_type_tinfo;
 314
 315         bool use_remember;
 316         unsigned remember_size;
 317         unsigned remember_assoc_size;
 318         unsigned remember_strategy;
 319
 320         bool eval_use_exvector_args;
 321         bool evalf_use_exvector_args;
 322         bool derivative_use_exvector_args;
 323         bool series_use_exvector_args;
 324         bool print_use_exvector_args;
 325
 326         unsigned functions_with_same_name;
 327
 328         ex symtree;
 329 };
 330
 331
 332 /** Exception class thrown by classes which provide their own series expansion
 333  *  to signal that ordinary Taylor expansion is safe. */
 334 class do_taylor {};
 335
 336
 337 /** The class function is used to implement builtin functions like sin, cos...
 338         and user defined functions */
 339 class function : public exprseq
 340 {
 341         GINAC_DECLARE_REGISTERED_CLASS(function, exprseq)
 342
 343         // CINT has a linking problem
 344 #ifndef __MAKECINT__
 345         friend void ginsh_get_ginac_functions();
 346 #endif // def __MAKECINT__
 347
 348         friend class remember_table_entry;
 349         // friend class remember_table_list;
 350         // friend class remember_table;
 351
 352 // member functions
 353
 354         // other constructors
 355 public:
 356         function(unsigned ser);
 357         // the following lines have been generated for max. ${maxargs} parameters
 358 $constructors_interface
 359         // end of generated lines
 360         function(unsigned ser, const exprseq & es);
 361         function(unsigned ser, const exvector & v, bool discardable = false);
 362         function(unsigned ser, std::auto_ptr<exvector> vp);
 363
 364         // functions overriding virtual functions from base classes
 365 public:
 366         void print(const print_context & c, unsigned level = 0) const;
 367         unsigned precedence() const {return 70;}
 368         ex expand(unsigned options=0) const;
 369         ex eval(int level=0) const;
 370         ex evalf(int level=0) const;
 371         unsigned calchash() const;
 372         ex series(const relational & r, int order, unsigned options = 0) const;
 373         ex thiscontainer(const exvector & v) const;
 374         ex thiscontainer(std::auto_ptr<exvector> vp) const;
 375 protected:
 376         ex derivative(const symbol & s) const;
 377         bool is_equal_same_type(const basic & other) const;
 378         bool match_same_type(const basic & other) const;
 379         unsigned return_type() const;
 380         unsigned return_type_tinfo() const;
 381
 382         // new virtual functions which can be overridden by derived classes
 383         // none
 384
 385         // non-virtual functions in this class
 386 protected:
 387         ex pderivative(unsigned diff_param) const; // partial differentiation
 388         static std::vector<function_options> & registered_functions();
 389         bool lookup_remember_table(ex & result) const;
 390         void store_remember_table(ex const & result) const;
 391 public:
 392         static unsigned register_new(function_options const & opt);
 393         static unsigned current_serial;
 394         static unsigned find_function(const std::string &name, unsigned nparams);
 395         unsigned get_serial() const {return serial;}
 396         std::string get_name() const;
 397
 398 // member variables
 399
 400 protected:
 401         unsigned serial;
 402 };
 403
 404 // utility functions/macros
 405
 406 /** Specialization of is_exactly_a<function>(obj) for objects of type function. */
 407 template<> inline bool is_exactly_a<function>(const basic & obj)
 408 {
 409         return obj.tinfo()==TINFO_function;
 410 }
 411
 412 template <typename T>
 413 inline bool is_the_function(const ex & x)
 414 {
 415         return is_exactly_a<function>(x)
 416             && ex_to<function>(x).get_serial() == T::serial;
 417 }
 418
 419 // Check whether OBJ is the specified symbolic function.
 420 #define is_ex_the_function(OBJ, FUNCNAME) (GiNaC::is_the_function<FUNCNAME##_SERIAL>(OBJ))
 421
 422 } // namespace GiNaC
 423
 424 #endif // ndef __GINAC_FUNCTION_H__
 425
 426 END_OF_INTERFACE
 427
 428 $implementation=<<END_OF_IMPLEMENTATION;
 429 /** \@file function.cpp
 430  *
 431  *  Implementation of class of symbolic functions. */
 432
 433 /*
 434  *  This file was generated automatically by function.pl.
 435  *  Please do not modify it directly, edit the perl script instead!
 436  *  function.pl options: \$maxargs=${maxargs}
 437  *
 438  *  GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
 439  *
 440  *  This program is free software; you can redistribute it and/or modify
 441  *  it under the terms of the GNU General Public License as published by
 442  *  the Free Software Foundation; either version 2 of the License, or
 443  *  (at your option) any later version.
 444  *
 445  *  This program is distributed in the hope that it will be useful,
 446  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 447  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 448  *  GNU General Public License for more details.
 449  *
 450  *  You should have received a copy of the GNU General Public License
 451  *  along with this program; if not, write to the Free Software
 452  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 453  */
 454
 455 #include <iostream>
 456 #include <string>
 457 #include <stdexcept>
 458 #include <list>
 459
 460 #include "function.h"
 461 #include "operators.h"
 462 #include "fderivative.h"
 463 #include "ex.h"
 464 #include "lst.h"
 465 #include "symmetry.h"
 466 #include "print.h"
 467 #include "archive.h"
 468 #include "inifcns.h"
 469 #include "tostring.h"
 470 #include "utils.h"
 471 #include "remember.h"
 472
 473 namespace GiNaC {
 474
 475 //////////
 476 // helper class function_options
 477 //////////
 478
 479 function_options::function_options()
 480 {
 481         initialize();
 482 }
 483
 484 function_options::function_options(std::string const & n, std::string const & tn)
 485 {
 486         initialize();
 487         set_name(n, tn);
 488 }
 489
 490 function_options::~function_options()
 491 {
 492         // nothing to clean up at the moment
 493 }
 494
 495 void function_options::initialize()
 496 {
 497         set_name("unnamed_function", "\\\\mbox{unnamed}");
 498         nparams = 0;
 499         eval_f = evalf_f = derivative_f = series_f = 0;
 500         evalf_params_first = true;
 501         use_return_type = false;
 502         eval_use_exvector_args = false;
 503         evalf_use_exvector_args = false;
 504         derivative_use_exvector_args = false;
 505         series_use_exvector_args = false;
 506         print_use_exvector_args = false;
 507         use_remember = false;
 508         functions_with_same_name = 1;
 509         symtree = 0;
 510 }
 511
 512 function_options & function_options::set_name(std::string const & n,
 513                                               std::string const & tn)
 514 {
 515         name = n;
 516         if (tn==std::string())
 517                 TeX_name = "\\\\mbox{"+name+"}";
 518         else
 519                 TeX_name = tn;
 520         return *this;
 521 }
 522
 523 function_options & function_options::latex_name(std::string const & tn)
 524 {
 525         TeX_name = tn;
 526         return *this;
 527 }
 528
 529 // the following lines have been generated for max. ${maxargs} parameters
 530 $eval_func_implementation
 531 $evalf_func_implementation
 532 $derivative_func_implementation
 533 $series_func_implementation
 534 // end of generated lines
 535
 536 function_options& function_options::eval_func(eval_funcp_exvector e)
 537 {
 538         eval_use_exvector_args = true;
 539         eval_f = eval_funcp(e);
 540         return *this;
 541 }
 542 function_options& function_options::evalf_func(evalf_funcp_exvector ef)
 543 {
 544         evalf_use_exvector_args = true;
 545         evalf_f = evalf_funcp(ef);
 546         return *this;
 547 }
 548 function_options& function_options::derivative_func(derivative_funcp_exvector d)
 549 {
 550         derivative_use_exvector_args = true;
 551         derivative_f = derivative_funcp(d);
 552         return *this;
 553 }
 554 function_options& function_options::series_func(series_funcp_exvector s)
 555 {
 556         series_use_exvector_args = true;
 557         series_f = series_funcp(s);
 558         return *this;
 559 }
 560
 561 function_options & function_options::set_return_type(unsigned rt, unsigned rtt)
 562 {
 563         use_return_type = true;
 564         return_type = rt;
 565         return_type_tinfo = rtt;
 566         return *this;
 567 }
 568
 569 function_options & function_options::do_not_evalf_params()
 570 {
 571         evalf_params_first = false;
 572         return *this;
 573 }
 574
 575 function_options & function_options::remember(unsigned size,
 576                                               unsigned assoc_size,
 577                                               unsigned strategy)
 578 {
 579         use_remember = true;
 580         remember_size = size;
 581         remember_assoc_size = assoc_size;
 582         remember_strategy = strategy;
 583         return *this;
 584 }
 585
 586 function_options & function_options::overloaded(unsigned o)
 587 {
 588         functions_with_same_name = o;
 589         return *this;
 590 }
 591
 592 function_options & function_options::set_symmetry(const symmetry & s)
 593 {
 594         symtree = s;
 595         return *this;
 596 }
 597
 598 void function_options::test_and_set_nparams(unsigned n)
 599 {
 600         if (nparams==0) {
 601                 nparams = n;
 602         } else if (nparams!=n) {
 603                 // we do not throw an exception here because this code is
 604                 // usually executed before main(), so the exception could not
 605                 // be caught anyhow
 606                 std::cerr << "WARNING: " << name << "(): number of parameters ("
 607                           << n << ") differs from number set before ("
 608                           << nparams << ")" << std::endl;
 609         }
 610 }
 611
 612 void function_options::set_print_func(unsigned id, print_funcp f)
 613 {
 614         if (id >= print_dispatch_table.size())
 615                 print_dispatch_table.resize(id + 1);
 616         print_dispatch_table[id] = f;
 617 }
 618
 619 /** This can be used as a hook for external applications. */
 620 unsigned function::current_serial = 0;
 621
 622
 623 GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
 624
 625 //////////
 626 // default constructor
 627 //////////
 628
 629 // public
 630
 631 function::function() : serial(0)
 632 {
 633         tinfo_key = TINFO_function;
 634 }
 635
 636 //////////
 637 // other constructors
 638 //////////
 639
 640 // public
 641
 642 function::function(unsigned ser) : serial(ser)
 643 {
 644         tinfo_key = TINFO_function;
 645 }
 646
 647 // the following lines have been generated for max. ${maxargs} parameters
 648 $constructors_implementation
 649 // end of generated lines
 650
 651 function::function(unsigned ser, const exprseq & es) : exprseq(es), serial(ser)
 652 {
 653         tinfo_key = TINFO_function;
 654
 655         // Force re-evaluation even if the exprseq was already evaluated
 656         // (the exprseq copy constructor copies the flags)
 657         clearflag(status_flags::evaluated);
 658 }
 659
 660 function::function(unsigned ser, const exvector & v, bool discardable)
 661   : exprseq(v,discardable), serial(ser)
 662 {
 663         tinfo_key = TINFO_function;
 664 }
 665
 666 function::function(unsigned ser, std::auto_ptr<exvector> vp)
 667   : exprseq(vp), serial(ser)
 668 {
 669         tinfo_key = TINFO_function;
 670 }
 671
 672 //////////
 673 // archiving
 674 //////////
 675
 676 /** Construct object from archive_node. */
 677 function::function(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
 678 {
 679         // Find serial number by function name
 680         std::string s;
 681         if (n.find_string("name", s)) {
 682                 unsigned int ser = 0;
 683                 std::vector<function_options>::const_iterator i = registered_functions().begin(), iend = registered_functions().end();
 684                 while (i != iend) {
 685                         if (s == i->name) {
 686                                 serial = ser;
 687                                 return;
 688                         }
 689                         ++i; ++ser;
 690                 }
 691                 throw (std::runtime_error("unknown function '" + s + "' in archive"));
 692         } else
 693                 throw (std::runtime_error("unnamed function in archive"));
 694 }
 695
 696 /** Unarchive the object. */
 697 ex function::unarchive(const archive_node &n, lst &sym_lst)
 698 {
 699         return (new function(n, sym_lst))->setflag(status_flags::dynallocated);
 700 }
 701
 702 /** Archive the object. */
 703 void function::archive(archive_node &n) const
 704 {
 705         inherited::archive(n);
 706         GINAC_ASSERT(serial < registered_functions().size());
 707         n.add_string("name", registered_functions()[serial].name);
 708 }
 709
 710 //////////
 711 // functions overriding virtual functions from base classes
 712 //////////
 713
 714 // public
 715
 716 void function::print(const print_context & c, unsigned level) const
 717 {
 718         GINAC_ASSERT(serial<registered_functions().size());
 719         const function_options &opt = registered_functions()[serial];
 720         const std::vector<print_funcp> &pdt = opt.print_dispatch_table;
 721
 722         // Dynamically dispatch on print_context type
 723         const print_context_class_info *pc_info = &c.get_class_info();
 724
 725 next_context:
 726         unsigned id = pc_info->options.get_id();
 727         if (id >= pdt.size() || pdt[id] == NULL) {
 728
 729                 // Method not found, try parent print_context class
 730                 const print_context_class_info *parent_pc_info = pc_info->get_parent();
 731                 if (parent_pc_info) {
 732                         pc_info = parent_pc_info;
 733                         goto next_context;
 734                 }
 735
 736                 // Method still not found, use default output
 737                 if (is_a<print_tree>(c)) {
 738
 739                         c.s << std::string(level, ' ') << class_name() << " "
 740                             << opt.name << " @" << this
 741                             << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 742                             << ", nops=" << nops()
 743                             << std::endl;
 744                         unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
 745                         for (size_t i=0; i<seq.size(); ++i)
 746                                 seq[i].print(c, level + delta_indent);
 747                         c.s << std::string(level + delta_indent, ' ') << "=====" << std::endl;
 748
 749                 } else if (is_a<print_csrc>(c)) {
 750
 751                         // Print function name in lowercase
 752                         std::string lname = opt.name;
 753                         size_t num = lname.size();
 754                         for (size_t i=0; i<num; i++)
 755                                 lname[i] = tolower(lname[i]);
 756                         c.s << lname;
 757                         printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 758
 759                 } else if (is_a<print_latex>(c)) {
 760                         c.s << opt.TeX_name;
 761                         printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 762                 } else {
 763                         c.s << opt.name;
 764                         printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 765                 }
 766
 767         } else {
 768
 769                 // Method found, call it
 770                 current_serial = serial;
 771                 if (opt.print_use_exvector_args)
 772                         ((print_funcp_exvector)pdt[id])(seq, c);
 773                 else switch (opt.nparams) {
 774                         // the following lines have been generated for max. ${maxargs} parameters
 775 ${print_switch_statement}
 776                         // end of generated lines
 777                 default:
 778                         throw(std::logic_error("function::print(): invalid nparams"));
 779                 }
 780         }
 781 }
 782
 783 ex function::expand(unsigned options) const
 784 {
 785         // Only expand arguments when asked to do so
 786         if (options & expand_options::expand_function_args)
 787                 return inherited::expand(options);
 788         else
 789                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 790 }
 791
 792 ex function::eval(int level) const
 793 {
 794         if (level>1) {
 795                 // first evaluate children, then we will end up here again
 796                 return function(serial,evalchildren(level));
 797         }
 798
 799         GINAC_ASSERT(serial<registered_functions().size());
 800         const function_options &opt = registered_functions()[serial];
 801
 802         // Canonicalize argument order according to the symmetry properties
 803         if (seq.size() > 1 && !(opt.symtree.is_zero())) {
 804                 exvector v = seq;
 805                 GINAC_ASSERT(is_a<symmetry>(opt.symtree));
 806                 int sig = canonicalize(v.begin(), ex_to<symmetry>(opt.symtree));
 807                 if (sig != INT_MAX) {
 808                         // Something has changed while sorting arguments, more evaluations later
 809                         if (sig == 0)
 810                                 return _ex0;
 811                         return ex(sig) * thiscontainer(v);
 812                 }
 813         }
 814
 815         if (opt.eval_f==0) {
 816                 return this->hold();
 817         }
 818
 819         bool use_remember = opt.use_remember;
 820         ex eval_result;
 821         if (use_remember && lookup_remember_table(eval_result)) {
 822                 return eval_result;
 823         }
 824         current_serial = serial;
 825         if (opt.eval_use_exvector_args)
 826                 eval_result = ((eval_funcp_exvector)(opt.eval_f))(seq);
 827         else
 828         switch (opt.nparams) {
 829                 // the following lines have been generated for max. ${maxargs} parameters
 830 ${eval_switch_statement}
 831                 // end of generated lines
 832         default:
 833                 throw(std::logic_error("function::eval(): invalid nparams"));
 834         }
 835         if (use_remember) {
 836                 store_remember_table(eval_result);
 837         }
 838         return eval_result;
 839 }
 840
 841 ex function::evalf(int level) const
 842 {
 843         GINAC_ASSERT(serial<registered_functions().size());
 844         const function_options &opt = registered_functions()[serial];
 845
 846         // Evaluate children first
 847         exvector eseq;
 848         if (level == 1 || !(opt.evalf_params_first))
 849                 eseq = seq;
 850         else if (level == -max_recursion_level)
 851                 throw(std::runtime_error("max recursion level reached"));
 852         else {
 853                 eseq.reserve(seq.size());
 854                 --level;
 855                 exvector::const_iterator it = seq.begin(), itend = seq.end();
 856                 while (it != itend) {
 857                         eseq.push_back(it->evalf(level));
 858                         ++it;
 859                 }
 860         }
 861
 862         if (opt.evalf_f==0) {
 863                 return function(serial,eseq).hold();
 864         }
 865         current_serial = serial;
 866         if (opt.evalf_use_exvector_args)
 867                 return ((evalf_funcp_exvector)(opt.evalf_f))(seq);
 868         switch (opt.nparams) {
 869                 // the following lines have been generated for max. ${maxargs} parameters
 870 ${evalf_switch_statement}
 871                 // end of generated lines
 872         }
 873         throw(std::logic_error("function::evalf(): invalid nparams"));
 874 }
 875
 876 unsigned function::calchash() const
 877 {
 878         unsigned v = golden_ratio_hash(golden_ratio_hash(tinfo()) ^ serial);
 879         for (size_t i=0; i<nops(); i++) {
 880                 v = rotate_left(v);
 881                 v ^= this->op(i).gethash();
 882         }
 883
 884         if (flags & status_flags::evaluated) {
 885                 setflag(status_flags::hash_calculated);
 886                 hashvalue = v;
 887         }
 888         return v;
 889 }
 890
 891 ex function::thiscontainer(const exvector & v) const
 892 {
 893         return function(serial, v);
 894 }
 895
 896 ex function::thiscontainer(std::auto_ptr<exvector> vp) const
 897 {
 898         return function(serial, vp);
 899 }
 900
 901 /** Implementation of ex::series for functions.
 902  *  \@see ex::series */
 903 ex function::series(const relational & r, int order, unsigned options) const
 904 {
 905         GINAC_ASSERT(serial<registered_functions().size());
 906         const function_options &opt = registered_functions()[serial];
 907
 908         if (opt.series_f==0) {
 909                 return basic::series(r, order);
 910         }
 911         ex res;
 912         current_serial = serial;
 913         if (opt.series_use_exvector_args) {
 914                 try {
 915                         res = ((series_funcp_exvector)(opt.series_f))(seq, r, order, options);
 916                 } catch (do_taylor) {
 917                         res = basic::series(r, order, options);
 918                 }
 919                 return res;
 920         }
 921         switch (opt.nparams) {
 922                 // the following lines have been generated for max. ${maxargs} parameters
 923 ${series_switch_statement}
 924                 // end of generated lines
 925         }
 926         throw(std::logic_error("function::series(): invalid nparams"));
 927 }
 928
 929 // protected
 930
 931 /** Implementation of ex::diff() for functions. It applies the chain rule,
 932  *  except for the Order term function.
 933  *  \@see ex::diff */
 934 ex function::derivative(const symbol & s) const
 935 {
 936         ex result;
 937
 938         if (serial == Order_SERIAL::serial) {
 939                 // Order Term function only differentiates the argument
 940                 return Order(seq[0].diff(s));
 941         } else {
 942                 // Chain rule
 943                 ex arg_diff;
 944                 size_t num = seq.size();
 945                 for (size_t i=0; i<num; i++) {
 946                         arg_diff = seq[i].diff(s);
 947                         // We apply the chain rule only when it makes sense.  This is not
 948                         // just for performance reasons but also to allow functions to
 949                         // throw when differentiated with respect to one of its arguments
 950                         // without running into trouble with our automatic full
 951                         // differentiation:
 952                         if (!arg_diff.is_zero())
 953                                 result += pderivative(i)*arg_diff;
 954                 }
 955         }
 956         return result;
 957 }
 958
 959 int function::compare_same_type(const basic & other) const
 960 {
 961         GINAC_ASSERT(is_a<function>(other));
 962         const function & o = static_cast<const function &>(other);
 963
 964         if (serial != o.serial)
 965                 return serial < o.serial ? -1 : 1;
 966         else
 967                 return exprseq::compare_same_type(o);
 968 }
 969
 970 bool function::is_equal_same_type(const basic & other) const
 971 {
 972         GINAC_ASSERT(is_a<function>(other));
 973         const function & o = static_cast<const function &>(other);
 974
 975         if (serial != o.serial)
 976                 return false;
 977         else
 978                 return exprseq::is_equal_same_type(o);
 979 }
 980
 981 bool function::match_same_type(const basic & other) const
 982 {
 983         GINAC_ASSERT(is_a<function>(other));
 984         const function & o = static_cast<const function &>(other);
 985
 986         return serial == o.serial;
 987 }
 988
 989 unsigned function::return_type() const
 990 {
 991         GINAC_ASSERT(serial<registered_functions().size());
 992         const function_options &opt = registered_functions()[serial];
 993
 994         if (opt.use_return_type) {
 995                 // Return type was explicitly specified
 996                 return opt.return_type;
 997         } else {
 998                 // Default behavior is to use the return type of the first
 999                 // argument. Thus, exp() of a matrix behaves like a matrix, etc.
1000                 if (seq.empty())
1001                         return return_types::commutative;
1002                 else
1003                         return seq.begin()->return_type();
1004         }
1005 }
1006
1007 unsigned function::return_type_tinfo() const
1008 {
1009         GINAC_ASSERT(serial<registered_functions().size());
1010         const function_options &opt = registered_functions()[serial];
1011
1012         if (opt.use_return_type) {
1013                 // Return type was explicitly specified
1014                 return opt.return_type_tinfo;
1015         } else {
1016                 // Default behavior is to use the return type of the first
1017                 // argument. Thus, exp() of a matrix behaves like a matrix, etc.
1018                 if (seq.empty())
1019                         return tinfo_key;
1020                 else
1021                         return seq.begin()->return_type_tinfo();
1022         }
1023 }
1024
1025 //////////
1026 // new virtual functions which can be overridden by derived classes
1027 //////////
1028
1029 // none
1030
1031 //////////
1032 // non-virtual functions in this class
1033 //////////
1034
1035 // protected
1036
1037 ex function::pderivative(unsigned diff_param) const // partial differentiation
1038 {
1039         GINAC_ASSERT(serial<registered_functions().size());
1040         const function_options &opt = registered_functions()[serial];
1041
1042         // No derivative defined? Then return abstract derivative object
1043         if (opt.derivative_f == NULL)
1044                 return fderivative(serial, diff_param, seq);
1045
1046         current_serial = serial;
1047         if (opt.derivative_use_exvector_args)
1048                 return ((derivative_funcp_exvector)(opt.derivative_f))(seq, diff_param);
1049         switch (opt.nparams) {
1050                 // the following lines have been generated for max. ${maxargs} parameters
1051 ${diff_switch_statement}
1052                 // end of generated lines
1053         }
1054         throw(std::logic_error("function::pderivative(): no diff function defined"));
1055 }
1056
1057 std::vector<function_options> & function::registered_functions()
1058 {
1059         static std::vector<function_options> * rf = new std::vector<function_options>;
1060         return *rf;
1061 }
1062
1063 bool function::lookup_remember_table(ex & result) const
1064 {
1065         return remember_table::remember_tables()[this->serial].lookup_entry(*this,result);
1066 }
1067
1068 void function::store_remember_table(ex const & result) const
1069 {
1070         remember_table::remember_tables()[this->serial].add_entry(*this,result);
1071 }
1072
1073 // public
1074
1075 unsigned function::register_new(function_options const & opt)
1076 {
1077         size_t same_name = 0;
1078         for (size_t i=0; i<registered_functions().size(); ++i) {
1079                 if (registered_functions()[i].name==opt.name) {
1080                         ++same_name;
1081                 }
1082         }
1083         if (same_name>=opt.functions_with_same_name) {
1084                 // we do not throw an exception here because this code is
1085                 // usually executed before main(), so the exception could not
1086                 // caught anyhow
1087                 std::cerr << "WARNING: function name " << opt.name
1088                           << " already in use!" << std::endl;
1089         }
1090         registered_functions().push_back(opt);
1091         if (opt.use_remember) {
1092                 remember_table::remember_tables().
1093                         push_back(remember_table(opt.remember_size,
1094                                                  opt.remember_assoc_size,
1095                                                  opt.remember_strategy));
1096         } else {
1097                 remember_table::remember_tables().push_back(remember_table());
1098         }
1099         return registered_functions().size()-1;
1100 }
1101
1102 /** Find serial number of function by name and number of parameters.
1103  *  Throws exception if function was not found. */
1104 unsigned function::find_function(const std::string &name, unsigned nparams)
1105 {
1106         std::vector<function_options>::const_iterator i = function::registered_functions().begin(), end = function::registered_functions().end();
1107         unsigned serial = 0;
1108         while (i != end) {
1109                 if (i->get_name() == name && i->get_nparams() == nparams)
1110                         return serial;
1111                 ++i;
1112                 ++serial;
1113         }
1114         throw (std::runtime_error("no function '" + name + "' with " + ToString(nparams) + " parameters defined"));
1115 }
1116
1117 /** Return the print name of the function. */
1118 std::string function::get_name() const
1119 {
1120         GINAC_ASSERT(serial<registered_functions().size());
1121         return registered_functions()[serial].name;
1122 }
1123
1124 } // namespace GiNaC
1125
1126 END_OF_IMPLEMENTATION
1127
1128 print "Creating interface file function.h...";
1129 open OUT,">function.h" or die "cannot open function.h";
1130 print OUT $interface;
1131 close OUT;
1132 print "ok.\n";
1133
1134 print "Creating implementation file function.cpp...";
1135 open OUT,">function.cpp" or die "cannot open function.cpp";
1136 print OUT $implementation;
1137 close OUT;
1138 print "ok.\n";
1139
1140 print "done.\n";